February 3, 2017 | Author: Ronny Roy | Category: N/A
Download Solution Set- Costing & O.R.-4th Edition...
Solutions Set for 4th Edition of CA. Parag Gupta Cost Accounting & Management: 1. CVP Analysis 2. Activity-based costing management 3. Target Costing, Value Chain analysis & Life Cycle Costing 4. Service Sector 5. Standard Costing & Variance Analysis 6. Budget & Budgetary Control 7. Transfer Pricing 8. Decision Making 9. Miscellaneous Theory Chapters
43 – 59 60 – 133 134 – 175 176 – 218 219 – 298 299 – 308
Operations Research: 10. Linear Programming Problems 11. The Transportation Problem 12. The Assignment Problem 13. Network Analysis-PERT/CPM 14. Simulation 15. Learning Curve Theory
309 – 330 331 – 359 360 – 373 374 – 397 398 – 410 411 – 416
1 – 12 13 – 33 34 – 42
1
CVP Ans. 13 (Pg. 11): Margin of Safety(%) = MoS Units/Actual Sales Units = 7500/(7500+2500) = 75% Total Sales Profit
= 187500/0.75 = Rs.2,50,000/= Total sales – Total Cost = 250000 – 193750
P/V Ratio
= Rs.56250
= Profit/MoS (Rs.) x 100 = 56250/187500 x 100 = 30% BEP Sales =
Total Sales / (100 – MS) = 2,50,000 x 0.25 Fixed Cost
= Rs.62,500
= Sales x P/V Ratio = 250000 x 0.30-56250 = 18750
Alternate Answer 1 Margin of Safety
=
Selling Price per unit x ( 7500 units) Rs. 187500 =
Selling Price per unit x ( 7500 units) Therefore , Selling Price per unit =
187500/7500
=Rs. 25
Profit
Rs. 10000 x 25
Sales
2,50,000
Less: Total Cost
1,93,75
Profit
56,250
P/V Ratio
Profit/Margin of Safety 56250/187500
30%
BEP Sales
2500 x25
Rs. 62,500
Fixed Cost Alternative Answer 2
62500 x 30%=
Rs.
Selling price = Rs 187500/ 7500 = Rs.25 Total Cost at Break Even point=Rs.25 x 2500 = 62500 = Break Even Sales (Total Cost – Total Cost of BE)/(Total Units – Break Even Units) = Variable Cost per Unit (93,750 – 62,500)/(10,000 – 2,500) = 1,31,250/7,500 = Rs.17.50 per unit Selling Price
= 25.00
Variable Cost
= 17.50
Contribution
= 7.50
P/V Ratio
= 7.50/25
Fixed Cost
= 7.50 x 2500 units =
Rs.18750.
Profit
= 7.50 x 7500
Rs. 56,250
Ans. 12 (Pg. 11) (1) P/V Ratio
= =
30%
2
In year 2, additional NP which means additional contribution
8,000
Additional sales
40,000
P/V Ratio
20%
Fixed cost = Contribution – NP = (2,40,000 * 20%) – 18,000 BEP = FC/PV Ratio
48,000 – 18000 30,000/0.20
30,000 1,50,000
2,40,000 – 1,50,000 2,80,000 – 1,50,000
90,000 1,30,000
(3) Margin of Safety Year 1 Year 2
( ) fi (Contribution*PV Ratio) – Fixed Cost
(2,00,000 * 20%) – 30,000
10,000
OR Cap Sales
2,00,000
(-) BEP
1,50,000
Margin of Safety
50,000
(-) PV Ratio
20%
NP
5) Sales Required
10,000
100/20 ( 30,000(FC) + 40,000(NP))
3,50,000
OR
BEP
1,50,000
Margin of Safety Req (100/20*40,000) Sales Required
2,00,000 3,50,000
3
(6) a) 20% decrease in sale Qty Reduction in Contribution & in net profit
20% *(2,80,000*20%)
Reduction in Contribution & in net profit (b) Revenue Sales (-) Revenue Cost
20% (56,000) Rs.11,200
( 2,80,000*80%) *110%
2,46,400
(2,80,000*80%) * 80%
1,79,200
Revenue contribution
67,200
(-) Revenue Fixed Cost
(26,500)
Revenue NP
40,700
(-) Given NP
(26,000)
Increase in NP
14,700 OR
4
(b) Revenue Sales
(2,80,000*80%) *110%
P/V Ratio (now)
100-80 = 20
(new)
110–80 =30
2,46,400
3/11
(Reconciliation of NP change) Change
Effection NP
1) Reduction in Sales Qty (as per (a))
(11,200)
2) Increase in Sales Price (2,80,000*80%*10%)
22,400
3) Reduction in Fixed Cost
3500
Increase in NP
14,700
Ans. 3 (Pg. 14) (1) Evaluation of proposal to replace product Z with product S. a: net profit if we continue with product Z. X
(5,00,000*40%/20)*(20-10)
1,00,000
Y
(5,00,000*35%/25)*(25-25)
70,000
Z
(5,00,000*25%/30)*(30-18)
50,000
Total contribution
2,20,000
(-) Fixed Cost
1,50,000
Net Profit
70,000
b) Net profit if we replace with S X Y
(4,50,000*50%/20)*10 (4,50,000*30%)/25*10
1,12,500 54,000
Z
(4,50,000*20%)/28*14
45,000
Total contribution
2,11,500
(-) Fixed Cost
1,60,000
Net Profit
51,500
The company should continue with product Z because the replacement of ‘Z’ with ‘S’ would result in reduction net profit.
2) Statement showing the overall breakeven point of the 2 alternatives. XYZ
XYZ
5
Contribution
2,20,000
2,11,500
Sales
5,00,000
4,50,000
Fixed cost
1,50,000
1,60,000
BEP 50/22*1,50,000
3,40,909
3,40,426
The above calculation are based on the presumption, in addition to the usual presumptions that the sales of products X, Y & Z would always be in the ratio of Rs.40:35:25 and that of X, Y & Z would be in the ratio of 50:30:20 Ans. 6 (Pg. 15) a) Statement showing the budgeted net income for 2003 2,00,000
Fees collected (4,000 *50) Less: Budgeted cost Evaluation 4000*20
80,000
G.B 4000* 10
40,000
Hall rev.
8,000
Hon. To Chief Adm.
6,000
Super changer (50*4 * 4000/100)
8,000 1,48,000
Total Budgeted N.I
52,000
b) (i) Calculation of supervision cost Fees per student
50
Less: Variable cost + semi variable cost Evaluation
20
QB
10 30
Semi- variable
2
(supervision)
32
Gross contribution
18
Gross Fixed Cost
20,000
Gross BEP
20,000/18
12
Therefore, no. of Supervisory required. Therefore, Supervision Cost Net fixed cost
1111.11
12*200
2,400
20,000+2,400
22,400
6
(ii) BEP Fixed Cost
22,400
Net CTR per student Fees
50
(-) Variable Cost (30)
20
BEP
1,120
(C) (i) Calculation of total contribution required Gross contribution per student
18
Gross Fixed Cost
20,000
Net Profit Required
20,000
Gross Total Contribution Required
40,000
Gross no. of students (40,000/18)
2,222.22
No. of Supervision required
23
Supervision cost (23*200)
4,600
Net Fixed Cost (20,000+4,600)
24,600
Net Contribution Required (20,000+24,600)
44,600
Net Total Contribution required
44,600
Net Contribution per Student Fees
50 (30)
20
No. of Students required
2230
(-) Variable Cost
Ans. 7 (Pg.15): (i)
Statement of profitability of Special Health Care
Department (for the years 2001 and 2002) Year 2001 Rs.
Total contribution : (A) 8,225 bed days × Rs. 260
21,38,500
Year 2002 Rs.
7
8,225 bed days × Rs. 243.50 (Refer to working notes 1, 2, & 3) Fixed costs : Department fixed costs Apportioned fixed costs (Refer to working note 4) Nursing staff 6 Total fixed costs : (B)
20,02,788
6,22,500 10,00,000
6,84,750 12,50,000
2,88,000 (6 Nurse × Rs. 48,000 19,10,500
3,24,000 (6 Nurse × Rs. 54,000) 22,58,750
2,28,000
(2,55,962)
Profit (Loss) : { (A) – (B)}
Working
notes :
1. Total number of bed days of occupancy = Total fees collected ÷ Fee per bed days = Rs. 34,95,625 ÷ Rs. 425 = 8,225 2. Variable cost per bed day Variable cost per bed das (Rs.) (Rs. 13,57,125 / 8,225) Variable cost per bed day (Rs.) in the year 2002 (Rs. 165 + 10% × Rs. 165) 3. Contribution per bed day Contribution per bed days in the year 2001 (Rs.) (Rs. 425 -- Rs. 165) Contribution per bed days In the year 2002 (Rs.) (Rs. 425 -- Rs. 181.50) 4. Departmental fixed costs Departmental fixed costs (Rs.) for the year 2001 Department fixed cost (Rs.) for the year 2002 (Rs. 6,22,500 + 10% × Rs. 6,22,500)
165.00 181.50
260.00 243.50
6,22,500 6,84,750
(ii) Break even bed capacity for the year 2002 = Total fixed costs ÷ Contribution per bed day = Rs. 22,58,750 ÷ Rs. 243.50 = 9,276 bed days (approx.) (this is not a valid answer because for 9,276 bed days 8 nurses service will be required)
8
Nursing staff required; Remuneration of 8 nursing staff (Rs.) 8 nurses × Rs. 54,000 Department fixed costs (Rs.) Apportioned fixed costs (Rs.) Total fixed costs
8 4,32,000 6,84,750 12,50,000 23,66,750
Break even point = Rs. 23,66,750 ÷ Rs. 243.50 = 9,720 bed days Increase in fee per day required to justify continuance of the Special Health Care department Desired contribution (Rs.) Bed days of occupancy
22,58,750 8,225
Contribution per bed days (Rs. ) ; (a) (Rs. 22,58,750 / 8,225) Variable costs (Rs.) ; (B) Required fee per bed day; {(A) + (B) } Increase in fee per bed day (Rs.) (Rs. 456.12 – 425) Ans. 9 (Pg. 16): (i) yearly basis.
274.62 181.50 456.12 31.12
Profit Statement of M/s Satish Enterprises for first and second year on monthly and First year
Sales revenue: (A)
Second Year
Monthly Rs.
Yearly Rs.
Monthly Rs.
Yearly Rs.
600
7,200
600
7,200
2,160
180
2,160
900
75
900
720
60
720
540
45
540
288
24
288
1,296
110
1,320
(3,000 units × Rs.200) Material cost
180 (3,000 units × Rs.60)
Labour cost
75 (3,000 units × Rs.25)
Variable overheads
60 (3,000 units × Rs.20)
Primary packing cost
45 (3,000 units × Rs.15
Boxes cost
24
Rs.3,000 units ×400 12 months Total fixed overhead
108
9
(Refer to note 1)
working
Rs.1,296 12 months
Rs.1,320 12 month
Total cost : (B)
492
5,904
494
5,928
Profit : C = [(A)-(B)]
108
1,296
106
1,272
Working Note : 1. (i) Fixed overhead
First year : (Rs.)
Second year (Rs.)
Depreciation
8,96,000
8,96,000
Other fixed overheads
4,00,000
4,24,000
Total Fixed overheads
12,96,000
13,20,000
Rs, 24,00,000 + Rs.2,88,000 duty 3 years
(ii) Statement of monthly break – even units of the first year. Levels – No. of units (Refer to working note)
1351 1400
–
1401 1450
–
1451 1500
–
1501 1500
–
Rs.
Rs.
Rs.
Rs.
Total fixed overheads per month (Refer to working note)
1,08,000
1,08,000
1,08,000
1,08,000
Semi – variable costs (Special boxes cost) – (B)
11,200
11,600
12,000
12,400
(28 boxes × Rs.400)
(29 boxes × Rs.400)
(30 boxes × Rs.400)
(31boxes × Rs.400
Total fixed and semi variable costs : (A+B)
1,19,200
1,19,600
1,20,000
1,20,000
Break-even level of units:
1490
1495
1500
1505
Fixed costs (A)
(Rs. (Rs. (Rs. (Rs. 1,19,200 / 1,19,600 / 1,20,000 / 1,20,000 Rs.80) Rs.80) Rs.80) / Rs.80) The first and second break-even level of unit viz. 1490 and 1495 units falls outside the range of 1351 – 1400 and 1401 – 1450 units respectively. Here a monthly break-even level of units is 1,500 units which lies in the range of 1451 – 1500 units.
Total fised and semi - variable costs Contribution per unit
Statement of yearly break-even points of the first year Levels No. of units Fixed Costs (A) Semi-variable costs (Special boxes costs): (B)
17851-17900
17901-17950
17951-18000
18001-18050
Rs.
Rs.
Rs.
Rs.
12,96,000
12,96,000
12,96,000
12,96,000
1,43,200
1,43,600
1,44,000
1,44,000
10
(358 boxes × Rs.400)
(359 boxes × Rs.400)
(360 boxes × Rs.400)
(361 boxes × Rs.400)
14,39,200
14,39,600
14,40,000
14,40,400
17,990
17,995
18,000
18,005
Total fixed and semivariable costs (A + B) Break-even level units
(Rs.14,39,200 (Rs.14,32,600 (Rs.14,40,000 (Rs.14,40,400 / Rs.80) / Rs.80) / Rs.80) / Rs.80) Have a break-even level of units (on yearly basis) is 18,000 units which lies in the range of 17,951 – 18,000 units as well. The other first two figures do not lie in the respective ranges, so they are rejected. Working note: Rs. 1.
Fixed overhead in the first year
12,06,000
Fixed overhead per month
1,08,000
Contribution per unit (S.P. per unit – VC per unit)
80
Hence the break-even number of units will be above 1,350 units
Rs.1,08,000 Rs.80 (iii) If the number of toys goes beyond the level of 1,500 numbers, one more box will be required to accommodate each 50 additional units of toys. In that case the additional cost of a box will be Rs.400/- this amount can be recovered by the additional contribution of 5 toys. Hence, the second break-even point in such a contingency is 1,505 toys. (Refer to 1(b) (ii) last column of first statement). (iv) Comments: Yearly break-even point of 18,000 units of toys in the first instance is equal to 12 times the monthly break-even point of 1,500 units, because the monthly and yearly figures of break-even point fell on the upper limit of the respective range. In the second instance, it is not so because the monthly and early break-even point fell within the range of 50 toys. Ans. 10 (Pg. 16): (a)
Statement showing total costs indicating each item of cost
No. of students
60
120
180
240
300
Rs.
Rs.
Rs.
Rs.
Rs.
420
840
1,260
1,680
2,100
1,800
3,600
5,400
7,200
9,000
180
360
540
720
900
300
600
900
1,200
1,500
Variable costs: Break fast Lunch Tea Entrance fee Aquarium
for
Zoo
&
11
Total (A)
2,700
5,400
8,100
10,800
13,500
Rent of buses
1,400
2,100
2,800
3,500
4,200
100
150
200
250
300
Daily allowance paid to teacher (Refer to working table)
400
600
800
1,000
1,200
Block entrance fee
200
300
300
450
450
1,050
1,050
1,300
1,400
1,500
Total (B)
3,150
4,200
5,400
6,600
7,650
Grand Total (A) + (B)
5,850
9,600
13,500
17,400
21,150
(Refer to working note 1) Special permit fee (Refer to working note 2)
(Refer to given table) Cost of prizes (Refer to given table)
(b) Average cost per student at each of the above levels No. of students: (A)
60
120
180
240
300
Total Costs (Rs.) : (B)
5,850
9,600
13,500
17,400
21,150
97.50
80
75
72.50
70.50
[Refer to (a) Part] Average cost (Rs.): (B)/(A) (c)
Statement showing number of students to break-even
No. of students in the trip
51-100
101-125
126-150
151-200
201-250
251-300
2
3
3
4
5
6
1,400
2,100
2,100
2,800
3,500
4,200
Permit fee (Rs.)
100
150
150
200
250
300
Block entrance fee (Rs.)
200
300
300
300
450
450
Daily allowance paid to teachers (Rs.)
400
600
600
800
1,000
1,200
Cost of prizes
1,050
1,050
1,200
1,300
1,400
1,500
Total cost (Rs.)
3,150
4,200
4,350
5,400
6,600
7,650
105
140
145
180
220
255
(Rs.3,150
Rs.4,200/
Rs.4,350/
Rs.5,400/
Rs.6,600/
Rs.7,650
No. of buses Semi costs
variable
Bus Rent (Rs.)
No. of students to break even: (Total
semi
12
variable cost/contribution per student)
/ Rs.30
Rs.30
Rs.30
Rs.30
Rs.30
/ Rs.30
As the figure of 105 and 140 student fall outside the limits (No. of students in the trip), therefore there are four break-even points in this case viz., 145,180, 220 and 255 students. The college authorities should keep these figures in mind while hiring 3, 4, 5 and 6 buses respectively to avoid losses. The college incurred loss during the previous year s they hired 5 buses and 72% of total students (216 out of 300 students) joined the trip. The break-even in case college authorities hire 5 buses for the trip comes to 220 students. Working Notes: 1. No. of buses required and Rent of buses @ Rs.700/- per bus No. of students
60
120
180
240
300
Bo. of buses
2
3
4
5
6
Rent of buses (Rs.)
1,400
2,100
2,800
3,500
4,200
100
150
200
250
300
600
800
1,000
1,200
(No. of buses × Rs.700) 2. Special permit fee: No. of buses × Rs.50)
3. Allowance paid to Teachers (Rs.) No. of buses × Rs.200)
400
4. Contribution per student towards semi-variable costs Rs. Collection from each student
65
Subsidy provided by the college
10 75
Less: Variable cost per student
45
Contribution per student
30
13
Activity Based Costing Ans. 9 The total production overheads are `26,00,000: Product A: 10,000 × `30 = `3,00,000 Product B: 20,000 × `40 = `8,00,000 Product C: 30,000 × ` 50 = `15,00,000 On the basis of ABC analysis this amount will be apportioned as follows: Statement of Activity Based Production Cost Activity Pool Stores Receiving
Purchase requisition
6:9:10
Total Amount (`) 2,96,000
Inspection
Production Runs
5:7:8
8,94,000
2,23,500
3,12,900
3,57,600
Dispatch
Orders Executed
6:9:10
2,10,000
50,400
75,600
84,000
Machine Setups
Set ups
12:13:15
12,00,000
3,60,000
3,90,000
4,50,000
7,04,940
8,85,060
10,10,000
Quantity Sold
10,000
20,000
30,000
Unit Cost
70.49
44.25
33.67
Add: Conversion Cost
80
80
90
Total
150.49
124.25
123.67
Total Cost
Cost
Cost Driver
Ratio
Activity
A
B
(`)
(`)
C
71,040
1,06,560
1,18,400
Ans 10: (i)
Traditional Method
`, Cost per Unit P Direct Method Direct Labour Overhead @ `6/Hr on Machine Hour
Workings under ABC Product No. of Units P 3000 Q
5000
R
20000
(ii) Activities
M Hrs/Unit 10
90 80 60 (10 x6) 230
Q 80 240 108 (18 x 6) 428
R 120 160 84 (14 x 6) 364
Batches Inspection Purchase Order 20 100 60 (3000/150) (20 x 5) (20 x 3) 18 90000 10 40 100 (5000/500) (10 x 4) (10 x 10) 14 280000 20 60 160 (20000/1000) (20 x 3) (20 x 8) 400000 50 200 320 Overhead @ `6/Hr =4L x 6`24L
%
M Hrs 30000
[`In ooo’s] Cost Pool
C Driver
CDQ
CDQ Rate(`)
14
MC Setup Mc Operation Inspection Mat
20 30 40 10 100
Product
Set up cost
P
192000 (20 x 9600) 96000 [10x9600] 192000 [20x9600]
Q R
480 720 960 240 2400
Batches M Hrs Inspection Purchase Order
50 Batches 4L 200 320
(iii) Link of overheads Machine Inspection Cost Operation Cost 54000 480000 [30000x1.8] [100x4800] 162000 192000 [90000x1.8] [40x4800] 504000 288000 [280000x1.8] [60x4800]
Purchase Order Cost 45000 [60x750] 75000 [100x750] 120000 [160x750]
9600 1.80 4800 750
Total
Rate
771000
257
525000
105
1104000
55.2
Cost sheet under ABC
Direct Material Direct Labour Overhead
P 90 80 257 427
Q 80 240 105 425
R 120.00 160.00 55.20 335.20
Ans. 11: (i) Computation of the activity based overheads Step 1: Compute cost per unit of cost driver = Cost pool / cost driver volume Activity
Cost Driver
Cost Pool (a)
Purchasing
Purchase orders
Setting
Batches produced
Materials handling
Material movements
Inspection
Batches produced
Machining
Machine hours
Cost driver volume/yr (b)
Cost/Unit of cost driver (a)/(b)
`75,000
1,500
`50/pruchse order
`112,000
2,800
`40/batch
`96,000
8,000
`12/movement
`70,000 `150 000
2,800 50,000
`25/batch `3/machine hour
Step 2: Compute the volume of cost drivers consumed by Product Nova Shaft Purchase orders (given) = 25 Batches = 15,000/100 = 150 Materials movement = 150 batches × 6 = 900 Machine hours = 15,000 units × 0.1 = 1,500 Step 3: Compute the Activity Based Overheads Cost for Product Nova Shaft Activity
Cost Driver
Costing Rate / Cost Driver Unit `
15
Purchasing
Purchase orders
50 25 order × `50
`1,250
Setting
Batches produced
40 150 batches × `40
`6,000
Material handling
Material movements
12 900 movement × `12
Inspection
Batches produced
Machining
Machine hours
25 150 batches × `25 3 1,500 hours × `3
`10,800 `3,750 `4,500
`26,300 (ii) Computation of budgeted overheads costs for Product Nova Shaft using absorption costing Budgeted overheads
= (`75,000 + `96,000 + `112,000 + `70,000 + `150,000) = `503,000
Budgeted absorption cost/machine hour = `503,000 / 50,000 = `10.06 Budgeted machining hours for Product Nova Shaft = 1,500 Budgeted absorbed overhead = 1,500 × `10.06 = `15,090 (iii) Ways in which the company can reduce the ABC for product Nova Shaft:
Reduce the number of batches by increasing the batch size which will then reduce the setting up overhead, materials handling and inspection costs.
Reduce the number of purchase orders
Innovate ways of speeding up production so that the machining hours are reduced.
Ans. 12: (a)
Sales (i)
Units ` Selling price/unit
A
B
C
Total
25,000
56,000
27,000
1,08,000
18
14
12
4,50,000
7,84,000
3,24,000
12
9
8
2,520
2,810
3,010
(ii)
Sales Value (`)
(iii)
Prime Cost Overhead
(iv)
No. of units/run
(v)
Prime Cost `
3,02,400
5,05,800
2,16,720
(vi)
Gross Margin (ii − v)
1,47,600
2,78,200
1,07,280
15,58,000
5,33,080
16
Workings: A
B
C
2,520
2,810
3,010
20
10
10
2,500
2,800
3,000
25,000
56,000
27,000
10
20
9
25,200
56,200
27,090
12
9
8
3,02,400
5,05,800
2,16,720
3
4
4
Inspection hours (10) = (9) × (5)
30
80
36
M/c hours / run (11)
20
12
30
M/c hours (12) = (1) × (5)
200
240
270
Dye Cost/run (13)
200
300
250
2,000 6,000 Conventional Accounting System Total
2,250
Gross Production/unit /run (1) Defectives/run (2) Good units / run (3) Sales (Goods units)(4) No. of runs (5) Gross Production (6) = (1) × (5) Prime Cost / unit (7) Prime Cost (8) ` Inspection hours/run (9)
Dye cost (14) (13) × (5)
A
Total
10,24,920 146 710 10,250 B
C
Sales – units / Production (good units)
1,08,000
25,000
56,000
27,000
Gross Margin (`)
5,33,080
1,47,600
2,78,200
1,07,280
Production overheads (`)
2,25,250
52,141
1,16,797
56,313
Selling Overhead (`)
1,62,000
37,500
84,000
40,500
Sub-Total Overhead (`)
3,87,250
89,641
2,00,797
96,813
Net profit (`)
1,45,830
57,959
77,403
10,467
17
Ranking
II
I
III
Activity Based System
Sub-Total Overhead (`)
62,787
2,16,963
1,07,500
Net profit (`)
84,813
61,237
(220)
I
II
III
Ranking
= `37424 Total Machine hours = Volume × Machine hour required for each period = (500 × ¼) + (5000 × ¼) + (600×1) + (7000 ×3/2) = 12475 hours Machine overhead charges = `37424/12475 hours = `3 per hour Setup Costs = `4355/17 i.e., total number of setups = `256.18 Material ordering cost = `1920/10 operations = `192 Material handling cost = `7580/27 operations = `280.74 Spare parts = `8600/12 parts = `716.67
Ans. 13: (i) Factory overhead applicable to machine oriented activity
Overheads Items Machine Overhead Setup cost Material ordering cost Material handling cost Spare parts cost
Products A 1/4×`3 = 0.75
B 1/4×`3 = 0.75
C 1× `3 = 3.00
D 3/2×`3 = 4.50
1×256.18/500 = .51 1×192/500=.38
6×256.18/5000=.31 4×192/5000=.15
2×256.18/600=.85 1×192/600=.32
8×256.18/7000=.29 4×192/7000=.29
2×280.74/500=1.12
10×280.74/5000=.56
3×280.74/600=1.40
12×280.74/7000=.48
2×716.67/500=2.87
5×716.67/5000=.72
12×716.67/600=1/19
4×716.67/7000=.41
(ii) Competition of overhead per unit based on two system and their difference Products Machine Setup Material Material Spare Total Old Difference overhead ordering handling parts (ABC system ` system) ` ` ` ` ` A 0.75 0.51 0.38 1.12 2.87 5.63 1.20 +4.43 B 0.75 0.31 0.15 0.56 0.72 2.49 1.20 +1.29 C 3.00 0.85 0.32 1.40 1.19 6.76 4.80 +1.96 D 4.50 0.29 0.11 0.48 0.41 5.79 7.20 -1.41 The traditional system does not make correct assumptions that all overheads are related to volume and machine time. Under traditional system products A and C are under costed because it misallocates costs for small volume products. The activity based costing system recognizes the amount of input to each cost unit. Product B previously avoided its full share of overheads because of its low machine time and may still do so if part of `37425 of machine oriented overhead should be apportioned on some other basis. Product D is overcosted because the additional system loaded it with overhead attributable to activities concerned with products A, B & C as a result of using a volume-based and machine oriented rate which failed to pay proper attention to activity costing.
Ans.: 14 (i)
Statement of Operating income and Operating income as a percentage of revenues for each product line
18
(When support costs are allocated to product lines on the basis of cost of goods sold of each product) Soft Fresh Packaged Total Rs. Drinks Produce Foods Rs. Rs. Rs. Revenues: (A) 7,93,500 21,00,600 12,09,900 41,04,000 Cost of Goods sold (COGS): 6,00,000 15,00,000 9,00,000 30,00,000 (B) Support cost (30% of COGS): 1,80,000 4,50,000 2,70,000 9,00,000 (C) Total cost: (D) = {(B) + (C)} 7,80,000 19,50,000 11,70,000 39,00,000 Operating income: E= {(A)13,500 1,50,600 39,900 2,04,000 (D)} Operating income as a 1.70% 7.17% 3.30% 4.97% percentage of revenues: (E/A) x 100) Working notes: 1. Total support cost: Rs. 12,000 1,56,000 2,52,000 1,72,800 3,07,200 9,00,000
Bottles returns Ordering Delivery Shelf stocking Customer support Total support cost 2.
Percentage of support cost to cost of goods sold (COGS):
=
Total support cost × 100 Total cost of goods sold
=
Rs.9,00,000 × 100 = 30% Rs.30,00,000
3. Cost for each activity cost driver: Cost allocation Activity Total cost Rs. base (1) (2) (3) 1,560 purchase Ordering 1,56,000 orders Delivery 2,52,000 3,150 deliveries Shelf-stocking 1,72,800 8,640 hours Customer support
3,07,200
15,36,000 sold
Cost driver rate (4)=[(2)÷(3)]
100 per purchase order 80 per delivery 20 per stocking hour items 0.20 per item sold
(ii) Statement of Operating income and Operating income as a percentage of revenues for each product line
19
(When support costs are allocated to product lines using an activity-based costing system) Fresh Soft drinks Packaged Total Produce Food Rs. Rs. Rs. Rs. Revenues: (A) 7,93,500 21,00,600 12,09,900 41,04,000 Cost & Goods sold 6,00,000 15,00,000 9,00,000 30,00,000 Bottle return costs 12,000 0 0 12,000 Ordering cost* 36,000 84,000 36,000 1,56,000 (360:840:360) Delivery cost* 24,000 1,75,200 52,800 2,52,000 (300:2,190:660) Shelf stocking cost* 10,800 1,08,000 54,000 1,72,800 (540:5,400:2,700) Customer Support cost* 25,200 2,20,800 61,200 3,07,200 (1,26,000:11,04,000:3,06,000) Total cost: (B) 7,08,000 20,88,000 11,04,000 39,00,000 Operating income C:{(A)85,500 12,600 1,05,900 2,04,000 (B)} Operating income as a % of 10.78% 0.60% 8.75% 4.97% revenues * Refer to working note 3 (iii) Comment: Managers believe that activity based costing (ABC) system is more credible than the traditional costing system. The ABC system distinguishes with different type of activities at family store more precisely. It also tracks more precisely how individual product lines use resources. Soft drinks consume less resources than either fresh produce or packaged food. Soft drinks have fewer deliveries and require less shelf stocking time. Family store managers can use ABC information to guide their decisions, such as how to allocate a planned increase in floor space. Pricing decision can also be made in a more informed way with ABC information. Ans. 15 (a) Statement showing total cost of different products, assuming absorption of overhead on a machine hour basis Product A Product B Product C Product D Direct material 40 50 30 60 Direct labour* 28 21 14 21 Overhead 80 60 40 60 Cost of production 148 131 84 141 per unit Output in units 120 100 80 120 17760 13100 6720 16920 Total Costs (`) * Rate per machine hour = `26000/1300 hours = `20 Machine Hours = 480 + 300 + 160 + 360 = 1300 hours (b) Drivers No. Cost/unit of driver Cost ` Setups 5250 Production runs 21* `250 Stores/receiving 3600 Requisitions 80@ 45 Inspection/quality 2100 Production runs 21 100
20
Handling/dispatch 4620 Orders 42 110 * Production runs = (120/20) + (100/20) + (80/20) + (120/20) @ Requisitions = 20 for each product or 80 in total. It may be pointed out that machine department cost of `10430 will continue to be absorbed on a machine hour basis as before. The relevant absorption rate will be = `10430/1300 = `8.02 per machine hour. Total cost (`) A B C S Direct material 4800 5000 2400 7200 Direct labour 3360 2100 1120 2520 Set-ups 1500 1250 1000 1500 Stores/receiving 900 900 900 900 Inspection/quality 600 500 400 600 Handling/dispatch 1320 1100 880 1320 Machine dept. 3851 2407 1284 2888 costs 16331 13257 7984 16928 Cost per unit 136.09 132.57 99.80 141.07 (c) A B C D Cost per unit (a) 148 131 84 141 Cost per unit (b) 136.09 132.57 99.80 141.07 Difference (11.91) 1.57 15.80 0.07 The total overheads which are spread over the four products have been apportioned on different bases, causing the product cost to differ substantially in respect of products A and C. A change from traditional machine hour rate to an activity based system may have effect on: (a) pricing and profits tot the extent that pricing is based on a ‘cost plus’ approach. (b) Reported profits to the extent that stock levels fluctuate between reporting periods.
Ans. 16
(a) Total cost of different products (overhead absorption on Machine hour basis) A
B
C
D
`
`
`
`
Direct material
42
45
40
48
Direct labour
10
09
07
08
Overhead
72
54
36
18
Cost of production per unit
124
108
83
74
Out put in unit
720
600
480
504
89,280
64,800
39,840
37,296
Total cost
Machine hours (720 × 4 + 600 × 3 + 480 × 2 + 504 × 1) = 6,144 hours. Rate per hour =
Rs 1,10,592 = `18 per hour. 6,144 hours
(b) Activity based costing system
Machine operation and maintenance cost of ` 63,000 to be distributed in the ratio of 4: 3: 2.
Set up
Store receiving
Inspection
28,000
21,000
14,000
21
` Drivers
Cost
No
Cost per unit of driver (`)
96
500
200
180 250
Set up
48,000 Production runs
Store receiving
36,000 Requisitions raised
Inspection
24,000 Production runs
96
Orders
192
Material handling and disp
2,592
13.50
Production Run for A (720/24) = 30 ; B (600/24) = 25 ; C (480/24) = 20 ; D (504/24) = 21. A (`)
B(`)
C(`)
D(`)
30,240
27,000
19,200
24,192
7,200
5,400
3,360
4,032
15,000
12,500
10,000
10,500
Store receiving
9,000
9,000
9,000
9,000
Inspection
7,500
6,250
5,000
5,250
810
675
540
567
Total cost
69,750
60,825
47,100
53,541
Per unit cost
96.875
101.375
98.125
106.23
Direct material Direct labour Setup
Material handling and dispatch
(c) A
B
C
D
Cost per unit (a)
124
108
83
74
Cost per unit (b)
96.88
101.38
98.13
106.23
(27.12)
(6.62)
15.13
32.23
Difference
The total overheads which are spread over the four products have been apportioned on different bases, causing the product cost to differ substantially: in respect of product A and D a change from traditional machine hour rate to an activity system may have effect on price and profits to the extent that pricing is based on cost plus approach.
Ans. 17: (a)
Budget Cost Statement Activity
1.ATM Services
Activity Cost Activity Driver (`) (Budgeted) 8,00,000 ATM Transaction
No. of Units of Activity Driver (Budget)
Deposits
Activity Rate (`)
2,00,000
4 0.50
6,00,000
Loans
Credit Cards - 2,00,000
2. Computer Processing
10,00,000 Computer Transaction
20,00,000
3. Issuing Statements
20,00,000 No. of Statements
5,00,000
4.00 14,00,000 2,00,000 4,00,000
4. Customer Inquiries
3,60,000 Telephone Minutes
7,20,000
0.50
Budgeted Cost
41,60,000
7,50,000 1,00,000 1,50,000
1,80,000
90,000
90,000
29,30,000 3,90,000
8,40,000
22
Units of product as estimated in the budget period
58,600
13,000
14,000
50
30
60
Budgeted Cost per unit of the product
Working Notes: (i)
ATM
4,00,000 + 2,00,000 + 2 × 1,00,000
(ii)
Computer
(iii)
Issuing Statements
= 8,00,000
5,00,000 (Fixed = 2,50,000) Variable= 10,00,000 2,50,000 increase to 3 times = 7,50,000 2,00,000 + 80% × 2,00,000 = 2 + 1.6
= 3,60,000
Ans. 18:
(a) Working: Calculation of Direct Labour hours:
Total Indirect Costs (`)* Total Direct labour hours (30,000 + 9,750) Overhead absorption rate (i)
` 23,85,000 39,750 Rs. 23,85,000 = Rs. 60 per hour 39,750 hours
Statement showing total manufacturing costs and profits Product A
Direct materials Direct labour Prime cost Indirect costs (absorbed on the basis of direct labour hours) Total cost Sales Profit (Sales – Total cost)
(60,000 units) Per unit Amount (`) 18.75 11,25,000 10.00 6,00,000 28.75 17,25,000 30.00 18,00,000 (18,00,000/ (30,000 hours 60,000 @ `60 per units) hour)
Product B (15,000 units) Per unit 45.00 13.00 58.00 39.00 (5,85,000/ 15,000 units)
Amount (`) 6,75,000 1,95,000 8,70,000 5,85,000 (9,750 hours @ `60 per hour)
Total (`)
18,00,000 7,95,000 25,95,000 23,85,000
58.75 63.00
35,25,000 37,80,000
97.00 137.00
14,55,000 20,55,000
49,80,000 58,35,000
4.25
2,55,000
40.00
6,00,000
8,55,000
* Calculation of total Indirect Cost:
`
Cleaning and maintenance wages Designing costs Set-up costs Manufacturing operations cost Shipment costs Distribution costs Factory Administration Costs Indirect cost allocation to products A and B:
2,70,000 4,50,000 3,00,000 6,37,500 81,000 3,91,500 2,55,000 23,85,000
23
Product B
Product A 30,000
Direct labour hours Direct labour hour rate:
9,750
`
60 60
5,85,000
`18,00,000
Indirect costs Output (units) Cost per unit of output
15,000
60,000
39
`
30 Statement showing the total manufacturing costs and profits using direct labour hour basis of absorption and treating cleaning and maintenance cost as indirect cost:
Output (units)
Product A `/unit Amount 60,000
Product B `/unit Amount 15,000
`
Sales Direct Materials Direct Labour Prime Cost Indirect costs Total costs Profit
Total
`
`
63.00 37,80,000 18.75 11,25,000
137.00 20,55,000 45.00 6,75,000
58,35,000 18,00,000
10.00 6,00,000 28.75 17,25,000 30.00 18,00,000 58.75 35,25,000 4.25 2,55,000
13.00 1,95,000 58.00 8,70,000 39.00 5,85,000 97.00 14,55,000 40.00 6,00,000
7,95,000 25,95,000 23,85,000 49,80,000 8,55,000
(ii)
Calculation of Setup hours
Total Output (in units) No. of quantity produced per batch Setup time per batch Setup hours (Total) (No. of batches × set up time per batch)
Product A 60,000 240
Product B 15,000 50
2 hours
5 hours
60,000 × 2 = 500 240
15,000 × 5 = 1,500 50
Calculation of Cost Driver, Rates and summary of indirect cost relating to Product A & B: Activity and Cost Drivers
Amount
Cost Drivers for Product
Activity Cost Rates
B
(Amount / total of cost driver)
Indirect Costs
(`) A
Product A
Product B
Cleaning & Maintenance (Direct Labour hours)
2,70,000
30,000
9,750
39,750
6.7925 per Direct labour hour
2,03,775
66,227
Designing costs (square feet)
4,50,000
30 sq. feet
70 sq. feet
100
4,500 per sq. feet
1,35,000
3,15,000
24
Setup costs (setup hours)
3,00,000
500 hours
1,500 hours
2,000
150 per setup hour
75,000
2,25,000
Manufacturing operations costs (molding machine hours)
6,37,500
9,000
3,750
12,750
50 per molding hours
4,50,000
1,87,500
81,000
100
100
200
405 per shipment
40,500
40,500
22, 500 cubic feet
67,500
5.80 per cubic feet
2,61,000
1,30,500
9,750
39,750
6.4151 per labour hour
1,92,453
62,547
13,57,728
10,27,274
60,000
15,000
22.63
68.48
Shipment costs (No. of shipments) Distribution costs (area in cubic feet)
3,91,500
Factory administration costs (direct labour hours)
2,55,000
45,000 cubic feet 30,000
Production (units)
Cost Sheet based on activity based costing system: Product A
Description
Sales Direct Cost Direct Materials Direct Labour Total Indirect costs Total costs Profit
Product B Total cost Per unit
Total cost
Per unit
`
`
`
`
37,80,000
63.00
20,55,000
137.00
11,25,000
18.75
6,75,000
45.00
6,00,000
10.00
1,95,000
13.00
17,25,000 13,57,728 30,82,728 6,97,272
28.75 22.63 51.38 11.62
8,70,000 10,27,274 18,97,274 1,57,726
58.00 68.48 126.48 10.52
(iii) Comparison of results:
Description
Selling Price Direct costs Indirect costs Total cost per unit Profit per unit
Product A
Product B Traditional Activity Traditional Activity Costing Based Costing Based System System System System ` ` ` ` 63.00 28.75 30.00 58.75
63.00 28.75 22.63 51.38
137.00 58.00 39.00 97.00
137.00 58.00 68.48 126.48
4.25
11.62
40.00
10.52
Opinion: In the traditional costing system, Product B appears to be more profitable than Product A whereas under the activity based costing system, Product A appears to be more profitable than product B. The activities
25
like designing, set up, manufacturing operation cost, shipment and distribution are support service activities and the consumption of resources relating to these activities are not dependent on direct labour hours. The quantum of consumption of resource of each support service activity is different in respect of the two products manufactured and hence activity based costing presents a true view of cost of production. Moreover, the suggestion to treat cleaning and maintenance activity as a direct cost pool is commendable because costs should be charged direct wherever possible. The results reveal that the company should concentrate upon product B.
Alternative Solution: Cleaning and maintenance activity will not find a place in the statement of calculation of cost driver rates. However, other cost driver rates will be unchanged. Statement showing total cost and profits on the basis of Activity Based Costing Product A
Direct materials Direct labour Cleaning & maintenance expenses Prime cost
Indirect costs: Designing Setup Manufacturing operation Shipments Distribution Factory administration Total indirect costs Total costs
Sales Profits (Sales – total costs) *
Per unit 18.75 10.00 2.00
Amount (`)
30.75
18,45,000
68.00
10,20,000
28,65,000
2.25 1.25 7.50
1,35,000 75,000 4,50,000
21.00 15.00 12.50
3,15,000 2,25,000 1,87,500
4,50,000 3,00,000 6,37,500
0.67 4.35 3.21
40,500 2,61,000 1,92,453
2.70 8.70 4.17
40,500 1,30,500 62,547
81,000 3,91,500 2,55,000
19.23 49.98 63.00
11,53,953 29,98,953 37,80,000
64.07 132.07 137.00
9,61,047 19,81,047 20,55,000
21,15,000 49,80,000 58,35,000
13.23
7,81,047
4.93
74,953
8,55,000
11,25,000 6,00,000 1,20,000*
The Cost Accountant identified `1,20,000 for `1,50,000 of cleaning and maintenance wages for Product B.
Product
(iii) Comparison of results: Product A
Allocation basis
Total (`)
Product B Per unit Amount (`) 45.00 6,75,000 13.00 1,95,000 10.00 1,50,000*
Direct Labour
Activity Based
Product B Direct Activity Labour Based
18,00,000 7,95,000 2,70,000
A
and
balance
26
Selling Price Prime cost Total Indirect costs Total costs (Prime cost + Total indirect costs) Profit per unit
Hour 63 28.75 30.00
Costing 63 30.75 19.23
Hour 137.00 58.00 39.00
Costing 137.00 68.00 64.07
58.75
49.98
97.00
132.07
4.25
13.02
40.00
4.93
Comments:
It is evident from the comparison of results that under single cost pool system the product A is overcost and product B is undercost. This is due to allocation of indirect cost on the basis of blanket rate based on direct labour hour and considering one of the significant cost as an indirect one. Cost Accountant’s decision for allocation of indirect costs on the basis of ABC methods and identifying be cleaning and maintenance cost as direct element of cost appears to be a good decision. Result show that the firm enjoys competitive advantage with regards to product A. Ans. 19 (1) Single factory direct labour hour overhead rate =
Rs 3,10,000 = ` 155 per direct labour hour 2,000
Computation of unit cost ( existing system) R (`) 300 1,200 3,875 5,375 560 9.60
Direct labour cost @ ` 12 per hour Direct material Overheads(direct labour hours × ` 155 per hour Quantity Produced (No) Cost per unit
S(`) 5,760 2,900 74,400 83,060 12,800 6.49
T(`) 600 1,800 7,750 10,150 2,400 4.23
(2) ABC system involves the following stages, 1.
Identifying the major activities that take place in an organisation.
2.
Creating a cost pool /cost centre for each activity
3.
Determining the cost driver for each activity
4.
Assigning the cost of activities to cost objects (e.g. products, components, customers etc) The most significant activities have been identified e.g. receiving components consignments from suppliers, setting up equipment for production runs, quality inspections, and despatching orders to customers. The following shows the assignment of the costs to these activities, (` ,000)
Receiving supplies
Set ups
Quality Despatch inspection
Total
18.75
87.50
18.75
125.00
Maintenance
3.75
17.50
3.75
25.00
Technicians wages initially
3.83
17.85
3.82
25.50
Equipment operation expenses
27
allocated to Maintenance(30% of ` 85,000= ` 25,500 and then reallocated on same basis on maintenance) Balance of technicians wages allocated to set ups and quality inspections Stores wages - Receiving
34.00
25.50
59.50
35.00
35.00
Despatch wages - Despatch 61.33
156.85
25.50
40.00
40.00
66.32
310.00
Note : Equipment operation expenses and Maintenance allocated on the basis 15%,70% and 15% as specified in the question. The next stage is to identify the cost drivers for each activity and establish cost driver rates by dividing the activity costs by a measure of cost driver usage for the period. The calculations are as follows :Receiving supplies (
Rs 61,330 ) = ` 62.58 per component. 980
Performing set ups (
1,56,850 ) = ` 153.77 per set up 1,020
Despatching goods ( Quality inspection (
66,320 ) = ` 157.93 per despatch 420
25,500 ) = ` 39.84 per quality inspection 640
Finally, costs are assigned to components based on their cost driver usage. The assignments are as follows, R (` )
S(`)
T(`)
300
5,760
600
1,200
2,900
1,800
Receiving supplies
2,628.36
1,501.92
1,752.24
Performing set ups
2,460.32
2,767.86
1,845.24
Quality inspections
398.40
318.72
717.12
Despatching goods
3,474.46
13,424.05
7,264.78
10,461.54
26,672.55
13,979.38
560
12,800
2,400
18.682
2.08
5.82
Direct labour Direct materials
Total costs No of units produced Cost per unit
For components, the overhead costs have been assigned as follows, (Component R) Receiving supplies (42 receipts at ` 62.58) Performing set ups (16 production runs at ` 153.77) Quality inspections (10 at ` 39.84)
28
Despatching goods ( 22 at ` 157.93). Ans 20: Overhead rate per labour hour =
Overhead incurred in first half year Direct labour hours worked
= `21,00,000 = `52.50 per labour hour 40,000 hours
Apportionment of technical staff salaries Machine maintenance = 6,37,500 X 31/100 Set up = 6,37,500 X 40/100 Quality Inspection = 6,37,500 X 30/100
= ` 1,91,250 = ` 2,55,000 = ` 1,91,250
Statement showing apportionment of ‘Machine operation’ and ‘Machine maintenance’ between stares and production activity (set up) in ratio 20:80 Particulars Total Stores / Set up/ Expenses Receiving Production run Machine operation 10,12,500 2,02,500 8,10,000 Machine maintenance 3,78,750 75,750 3,03,000 (`1,87,500 + `1,91,250) Particulars
Total Expenses
Stores / Receiving
Set up / Production run
Wages and salaries of stores staff Component of set- up cost
2,62,500 2,55,000
2,62,500 -
2,55,000
Total
19,08,750
5,40,750
13,68,000
Rate per activity cost driver Particulars Total overheads Units of activities carries out Rate per activity cost driver (`)
(`)
Stores / Receiving 5,40,750 1,960 275.89
Set up/ Production run 13,68,000 2,040 670.59
Quality inspection 1,91,250 1,280 149.41
Statement showing computation of cost of products P and Q (Based on the existing system of single overhead recovery rate) Particulars Product P Q Direct Labour hours 960 100 Unit made 15,000 5,000 Direct materials cost 6,000 4,000 Direct labour cost (@ `6 per D.L.H.) 5,760 600 Overheads ( @ `52.50 per D.L.H.) 50,400 5,250 Total cost of products 62,160 9,850 Cost per unit
4.144
Statement showing computation af cost of products P and Q (Using activity based costing system)
1.97
29
Particulars
Product
Units Direct materials cost Receiving/ Stores cost Receiving Stores cost
P 15,000 6,000 5,760 13,243
Q 5,000 4,000 600 14,346
24,141
16,094
4,482
1,494
53,626 3.58
36,534 7.31
Production runs / Set ups cost Inspection cost
(48 X 275.89) (52 X 275.89) (36 X 670.59) (24 X 670.59) (30 X 149.41) (10 X 149.41)
Total Cost products Coat per unit
Computation of sales value per quarter of component K (Using activity based costing system) Units of component K To be delivered per quarter
3,000
`
7,500 12,000 1,800 5,518 4,024 3,586 34,428 8,607
Component of initial design cost per quarter ( `60,0000/8 quarters) Direct material costs Direct labour cost (600 hours X `6) Receiving cost (50 X `275.89) Production runs cost (6 X `670.59) Inspection cost (24 X `149.41) Total cost Add: Mark up (25% of cost) Sales value Selling price per unit of K (`43,035/3,000 units)
43,035 16.34
Ans 21 (i)
Job cost sheet for Host Restaurant and Pizza Hut (using a simplified costing system) Host Restaurant (`)
Pizza Hut (` )
Professional labour cost: 25 hours @ `60 per hour 40 hours @ `60 per hour (Refer to working note 1) Professional Support staff
1,500
25 hours @ `120per hour 40 hours @ `120 per hour (Refer to working note 2)
3,000
Total (ii) Job cost sheet using an Activity based costing
2,400
4,800 4,500 Host Restaurant
Professional labour cost
(` ) 500
7,200 Pizza Hut (` )
30
3,000
5 hours @ `100 per hour 30 hours @ `100 per hour (Refer to working note 3) Associate labour cost
800 400
20 hours @ `40 10 hours @ `40 (Refer to working note 4) Design support
1,690 4,420
`1.30 × `1,300 `1.30 × `3,400 (Refer to working note 5) Staff support
1,056 1,689
25 hours @ `42.22 40 hours @ `42.22 (Refer to working note 6) 4,046
9,509
(iii) Determining the amount by which each job was under or overcosted using a simplified costing system. Host Restaurant
Pizza Hut
Cost using simplified system
(` ) 4,500
(`) 7,200
Cost using Activity Based system
4,046
9,509
454
(2,309)
Difference
The simplified costing system overcosted Host Restaurant job by `454 and undercosted Pizza Hut job by `2,309.
31
32
Ans. 22:
(i) Comparison of manufacturing cost per unit. Audio Player Model ‘AB 100’
‘AB 200’
`
`
1,000.00
800.00
Direct manufacturing labour cost
200.00
180.00
Machining costs
200.00
160.00
Testing costs
250.00
200.00
Rework costs
150.00
75.00
2.00
1.25
198.00
198.00
2,000.00
1,614.25
Direct material cost
Ordering costs Engineering costs Total manufacturing cost per unit Working notes for audio player model ‘AB 200’ (i) Machining hours and cost:
Machining hours = (1 hour–0.20 hours) or 0.80 hours) Machining cost is 0.80 hours × `200 or `160
(ii) Testing hours and cost:
Testing hours = 2 hours × (1 hour – 0.20) or 1.60 hours. Testing cost is 1.60 hours × `125 or `200
(iii) Rework cost per unit: Rework units = 5% × 10,000 units or 500 units. Rework cost = 500 units × `1,500 or `7,50,000. Rework cost per unit `7,50,000 / 10,000 units or `75 per unit. (iv) Ordering cost: No. of orders per month 50 components × 2 orders = 100 Ordering cost per month 100 orders × `125 per order = `12,500 Ordering cost per unit = `12,500 / 10,000 units = `1.25 per unit. (v) It is assumed that total available engineering hours will be used for manufacturing ‘AB 200’ model of audio player. (ii) Effect of design change and pricing decision on operating income of ABC. (`Lakhs) Revenue loss on 10,000 units
(40)
(`10,000 units × `400) Saving in cost: Direct material costs
20.00
(`200 × 10,000 units) Direct manufacturing labour costs
2.00
(`20 × 10,000 units) Rework costs
7.50
29.50
33
(5% × 10,000 units × `1,500) Net effect on operating income
(10.50)
Conclusion: Operating income per month will be reduced by `10.50 Lakhs. Effects of reduction in components, machining time, and testing time will not have any immediate effect, because it is difficult to adjust the available facilities in ordering department, machining department and testing department.
34
Target Costing, Value Chain Analysis Ans. 7: Maximum capacity 80,000 units Presented sales 20,000 units @ `100 p.u. Selling price/unit
Demand
100
20,000
90
40,000
80 ∴Target cost/unit
80,000 = Full capacity
= 80 –25% of sales = 80- 20 = 60 p.u.
(b) At present Variable cost/unit = 40% of cost i.e. 75 = `30 ∴Fixed cost/unit = 100 –25% = 75 COS
75
Less: Variable cost/unit Fixed cost
30 45 p.u. Total fixed
cost 45×80,000 = 36 lakhs ∴Add full capacity target cost
= `60/unit ×80,000 units = `48 lakhs
Total estimate cost Fixed cost Variable cost (80,000 ×40)
36 lakhs 24 lakhs 60 lakhs
∴Required. Cost reduction following value engineering is `12 lakhs. (e) Rate of return 15%
Profit p.u. 25% of 80 = 20/unit
Profit before tax = 20×80,000 = 16 lakhs ROCE = (PBI/Investment) ∴Investment = (PBI/ROCE) = 16 lakhs/15% = `10666667. Ans. 8: Target profit Add: Fixed cost Add: Additional Advertisement (a) Total contribution (b) Required. Sales volume contribution/unit (a¸b) Target Selling price/unit Less: Contribution/unit Target variable cost p.u. Less: material cost p.u. Labour + Variable overhead
25,000 1,40,000 28,500 1,93,500 12,000 16.125 32 16.125 15.875 8.000 7.875
35
Labour: x hr. @ 4 Variable overhead x hr. @ 0.5 ∴4.5x = x (hr.) Time/unit Present Time reduced
7.875 1.75 1.75 _ 2.00 0.25 hr.
Ans. 9
(i) Cost of product as per Target Costing
Coco 23.00 4.60
Stawberry 18.00 3.60
Vanilla 13.00 2.60
18.40
14.40
10.40
Coco 60,500
Stawberry 24,200
Vanilla 72,600
8.00 5.00 13.00 3.90 16.90 10,22,450
6.00 4.00 10.00 3.00 13.00 3,14,600
5.00 3.00 8.00 2.40 10.40 7,55,040
(iii) Cost of product as per Activity Based Costing Coco Maximum Volume (units) 60,500
Stawberry 24,200
Vanilla 72,600
Material Labour Prime Cost Overheads (Working Note-2) Total Cost per unit Total Cost
6.00 4.00 10.00 5.23 15.23 3,68,670
5.00 3.00 8.00 2.17 10.17 7,38,100
Selling Price per unit Less: Markup (25% of cost or 20% of selling Price) Target Cost per unit (`) (ii) Cost of product as per Traditional Costing Maximum Volume (units) Material Labour Prime Cost Store Support (30% of Prime Cost) Total Cost per unit Total Cost
`
`
`
`
8.00 5.00 13.00 3.29 16.29 9,85,320
(iv) Comparision in Cost of each product under each method Coco Stawberry As per Target Costing 18.40 14.40 As per Traditional Costing 16.90 13.00 As per Activity based Costing 16.29 15.23
`
`
Vanilla 10.40 10.40 10.17
Comment: Since cost of Strawberry is high in ABC costing in comparison to target costing and traditional methods, it is indicating that actual profit under target costing is less than targeted. Working Note-1 : Current Selling Price per unit (`) Current Sales (units) Selling Price (`) Revised Sales (units) Selling Price (`) Revised Sales (units) (upto production capacity)
Coco 25.00 50,000 24.00 55,000 23.00 60,500
Stawberry 20.00 20,000 19.00 22,000 18.00 24,200
Vanilla 15.00 60,000 14.00 66,000 13.00 72,600
36
Working Note-2 : Ordering Cost (35/30/15 @ 800) Delivery Cost (112/66/48 @ 700) Shelf Stocking (130/150/160 @ 199) Customer Support (60,500/24,200/72,600 @ 1.1) TOTAL COST No. of units Cost per unit
Coco 28,000 78,400 25,870 66,550
Stawberry 24,000 46,200 29,850 26,620
Vanilla 12,000 33,600 31,840 79,860
1,98,820 60,500 3.29
1,26,670 24,200 5.23
1,57,300 72,600 2.17
Note: On calculation of total overhead costs under traditional & ABC system, costs are same i.e. `4,82,790, hence we will ignore the line “In ABC these costs are coming under customer support and assistance.” written in question.
Ans. 10: (a) (i)
The target cost of each product after reduction is computed as follows: Product
Present Price (`)
Proposed Price (`)
Target Cost (`) (with 25% Margin)
A
180
175
140
B
175
170
136
C
130
125
100
D
180
175
140
(ii) Statement showing cost/unit of Driver as per ABC Cost
Amount
Driver
No.
Cost/unit of Driver
Set-ups Stores receiving
26,250 18,000
Production runs Requisition
105* 400**
`250.00 `45.00
Inspection/Quality
10,500
Production runs
105
`100.00
Handling/Dispatch
23,100
Orders
210
`110.00
Machine Department
52,130
Machine Hrs.
6,500
`8.02
* Production runs = (600/20) + (500/20) + (400/20) + (600/20) = 105 ** Requisitions = 100 for each product or 400 total Machine hours = 2,400 + 1,500 + 800 + 1,800 = 6,500 hours. Statement showing Total Cost and Cost Per Unit as per ABC Item
A `
B `
C `
D `
Direct Material Direct Labour
24,000 16,800
25,000 10,500
12,000 5,600
36,000 12,600
Set-up
7,500
6,250
5,000
7,500
Stores receiving
4,500
4,500
4,500
4,500
Inspection/Quality
3,000
2,500
2,000
3,000
Handling/Dispatch
6,600
5,500
4,400
6,600
37
Machine Dept. Cost
19,248
12,030
6,416
14,436
Total Cost
81,648
66,280
39,916
84,636
600
500
400
600
99.79
141.06
Output (Units)
Cost per unit 136.08 132.56 (iii) Comparison of Actual Cost and Target Cost Cost
A `
B `
C `
D `
Actual Target
136.08 140.00
132.56 136.00
99.79 100.00
141.06 140.00
Difference
(-) 3.92
(-) 3.44
(-) 0.21
(+) 1.06
Comment: The total actual cost of A, B and C product is less than the target cost so there is no problem in reducing the cost of these product by `5 from the present price. It will increase the profitability of the company but the cost of D is slightly more than the target cost, it is therefore, suggested that the company should either control it or redesign it. Ans. 11: Working Notes: Particulars
P
Q
1,00,000
50,000
(a)
Production/Sales Quantity (units)
(b)
Batch Size (units)
1000
500
(c)
No. of batches
100
100
(d)
Set up time per batch (hours)
(e)
Total set up hours (c d) (hours)
(f)
Machine set up cost (`) Cost driver per machine set up hour
(g)
30
36
3,000
3,600 4,62,000
4,62,000 = ` 70 6,600 (h)
Testing time per unit
(i)
Total testing time (a h) (hours)
(j)
Testing cost
5 hours
9 hours
5,00,000
4,50,000
`23,75,000 (k)
Cost driver per testing hour 23,75,000 = `2.50 9,50,000
(a) Computation of full cost per unit using Activity Based Costing: Particulars
Basis
P
Q
Direct material
Direct
42,00,000
30,00,000
Direct labour
Direct
15,00,000
10,00,000
Direct machine cost
Direct
7,00,000
5,50,000
Machine set up cost
3,000 hours @ `70 3,600 hours @ `70
2,10,000 2,52,000
38
Testing cost
5,00,000 hours @ `2.50
Engineering cost
4,50,000 hours @ `2.50 Allocated
Total cost (`)
12,50,000 11,25,000 8,40,000
14,10,000
87,00,000
73,37,000
87.00
146.74
Cost per unit (`) (b) Mark up on full cost basis for Product P: Particulars
Per unit
Selling price
100.05
Less: Full cost
87.00
Mark up
13.05
Percentage of mark up on full cost = 13.05 /87 = 15 % (c) Target cost of Product P after new design is implemented Target price (given)
86.25
86.25 ×15
11.25
Mark-up
115
Target cost per unit (` )
75.00
(d) Statement of cost for new design of P Particulars
Basis
Cost P.U.
Total Cost
Direct Material
Decreased by `5 p.u.
37.00
37,00,000
Direct Labour
Decreased by `2 p.u. No change as machine is dedicated
13.00
13,00,000
Direct Machining cost
7.00
7,00,000
Machine set up cost Testing cost
100 set up 28 hours 1,00,000 units `2.5
1.96 10.00
1,96,000 10,00,000
Engineering cost
No change
8.40
8,40,000
77.36
77,36,000
Total cost
`70
4 hours
The target cost is `75 p.u. and estimated cost of new design is `77.36 p.u. The new design does not achieve the target cost set by Computo Ltd. Hence the target mark up shall not be achieved. (e) Possible Management Action: Value engineering and value analysis to reduce the direct material costs. Time and motion study in order to redefine the direct labour time and related costs. Exploring possibility of cost reduction in direct machining cost by using appropriate techniques. Identification of non-value added activities and eliminating them in order to reduce overheads. The expected selling price based on estimated cost of `77.36 per unit is (`77.36 + 15%) `88.96. Introduce sensitivity analysis after implementation of new design to study the sales quantity changes in the price range of ` 86.25 to `88.96.
Ans. 12:
39
P1
P2
`/unit Material
`/unit
407.5
292.1
Overhead-Material handling
85×1.2 = 102
46×1.2 = 55.2
Assembly Management
40×3.2 = 128
40×1.9 = 76
Machine insertion
48×0.7 = 33.6
31×0.7 = 21.7
Manual insertion
36×2.1 = 75.6
25×2.1= 31.5
1.4×25 = 35
1.1×25 = 27.5
Present cost
781.70
504.00
Target cost
680.00
390.00
Revised P1 `/unit
Revised P2 `/unit
381.20
263.10
Material handling
(71×1.2) = 85.2
(39×1.2) = 46.8
Assembly hour
(21×40) = 84.0
(1.6×40) = 64.0
Machine inspection
(59×0.7) = 41.3
(29×0.7) = 20.30
Manual inspection
(12×2.10) = 25.2
(10×2.10) = 21.00
Electronics
(1.2×25) = 30.00
(0.9×25) = 22.50
Estimated cost
646.90
437.70
Target cost
680.00
390.00
Achieved
not achieved
Quality testing
Direct material Overhead:
Ans. 24: Machine X-Life 12 years Purchase price Overhead cost Trade-in-value Annual repair cost
Year
Cost
0 8 12 1-12
19,000 4,000 (3,000) 2,000
Purchase price Overhead cost Trade-in –value Annual repair cost
Discounted Cost ` 19,000 1,880 (960) 13,620 33,540
=`33,540 / 6.81=`4,925
Annualized equivalent Machine W-Life 6 years
Discount Factor 1.00 0.47 0.32 6.81
`
Year
Cost
0 4 6 1-6
13,000 2,000 (3,000) 2,600
`
Annualized equivalent `24,601 / 4.36=`5,508 Recommendation : Purchase machine ‘X’ Assumptions: a. Same performance, capacity and speed. b. No. inflation. c. 12 year-estimates are as accurate as 6 – year estimates.
Discount Factor 1.00 0.68 0.56 4.36
Discounted Cost ` 13,000 1,360 (1,680) 11,336 24,016
40
d. Cash flow at the year end. Ans. 25: The cost driver rates are as follows: Product design = `250 per design hour (`2m/8000 hours) Purchasing = `50 per purchase order (`200000/4000 orders) Production (excluding depreciation) = `100 per machine hour ((`1 500000-`300000)/ 12000 hours) Packing =`20 per cubic meter (`400000/ 20000) Distribution =`5 per kg (`600000/ 120000) The activity –based overhead cost per unit is as follows: Product design Purchasing Production Depreciation Packing Distribution Total costs
(400 design hours at `250 per hour=`100000 Divided by life –cycle output of 5000 units) (5 purchase orders at 50 units per order costing A total of `250 per output of 250 units) (0.75 machine hours at `100 per machine hour) (Asset cost over life cycle of 4 years= 16 quarters Depreciation at `8000 per quarter divided by life cycle Output of 5000 units) (0.4 cubic meters at `20) (3 kg at `5)
(`)
20.00 1.00 75.00 25.60 8.00 15.00 144.60
Ans. 26: The total cost consists of the installation cost plus electrical charges for 5 years. (i) So total cost for Electric immersion heater =`160 + 200X5 =`1160 (ii) Total cost for a gas boiler =`760 + `80X5 =`1160 Hence, on the total cost basis, both the equipments have equal preference, and the housewife can choose any one. Let us now calculate the present value of money for each of the two possibilities. Year PV factor @ Electric Immersion heater Gas Boiler 9% p.a Operating Cost Discounted Operating Cost ` Discounted Cost ` ` Cost ` 0 1.0000 160 160.00 760 760.00 1 0.9174 200 183.48 80 73.39 2 0.8417 200 168.34 80 67.33 3 0.7722 200 154.44 80 61.78 4 0.7084 200 141.68 80 56.67 5 0.6499 200 129.98 80 51.99 Total Cost Total Cost=937.92 =1071.16 (`938,say) (`1071 say) On the basis of present value @ 9% p.a over a period of five years, the total cost of Electric immersion heater is `938 and that of a Gas boiler is `1071. Hence, the housewife is advised to purchase an electric immersion heater. If the equipment are to be considered for a period of 8 years, then =`1760 Total cost for electrical immersion heater =`160+200X8 Total cost for gas boiler =`760+`80X8 =`1400 Hence, the housewife will be advised to purchase a gas boiler. Year PV factor @ Electric Immersion heater Gas Boiler 9% p.a Operating Cost Discounted Operating Cost ` Discounted Cost ` ` Cost ` 6 0.5963 200 119.26 80 47.70 7 0.5470 200 109.40 80 43.76 8 0.5019 200 100.38 80 40.15 329.04 (329,say) 131.61 (`132 say)
41
Present value in case of electric immersion heater =`1267 = P.V. over five years + P.V. over next three years =`938+`329 Present value in case of gas boiler =`1071+`132 =`1203 Hence, over a 8 years period, the present value of a gas boiler is less. On the basis of total cost as well as present value of money, gas boiler is cheaper over 8 years period, hence the housewife is advised to purchase a gas boiler. Ans. 27: Relevant Operating Cash outflow p.a. if part X 248 is outsourced Purchase Cost (Cash outflow) (a) 50000 Relevant Cash inflow from outsourcing: Direct materials 22000 Direct Labour 11000 Variable Overhead 7000 Product and Process engineering 4000 Rent 1000 Total Cash Savings (b) 45000 Net Cash Outflow (a) - (b) (5000) Net Present Value of cash inflow if part is outsourced Particulars Year P.V. factor @ 12% Amount ` P.V ` Disposal value of machine 0 15000 1000 15000 Cash Outflow due to outsourcing 1 5000 0.893 (4465) 2 5000 0.797 (3985) 3 5000 0.712 (3560) 4 5000 0.636 (3180) 5 5000 0.567 (2835) NPV (3025) Analysis : Since the NPV is negative , it is desirable to manufacture the part internally. Notes: (1) Equipment depreciation is a non- cash cost item. Therefore, it is not relevant. (2) Product and process engineering cost being avoidable hence relevant for the entire period of outsourcing i.e. for 5 years. (3) Allocated rent is irrelevant but rent saved (i.e, `1000) is relevant. (4) Allocated general plant overhead is irrelevant. (ii) Sensitivity analysis with respect to quantity is desirable: If demand for the part decreases vendor is willing to supply a lower quantity at the same price (` 50/-). If the part is continued to be made internally, the costs would not decrease quite fast with lower quantities because of fixed costs. Net cash outflows of outsourcing will be smaller if lower quantities of the part are demanded. But if the demand increase, it would be preferable to make the part – in – house. Non – financial factors: Will the units of part required be delivered on schedule? Will quality be maintained? Can suggested modifications be really accommodated? Will the subcontractor remain in business for next five years? (iii) As the outsourcing of part X – 248 will start from July ‘1998, the bonus of Gemini enterprises based on the accounting income, which Mr. Sen wishes to maximise will remain unchanged for the year 1997 - 98 Ans. 28: Evaluation of Alternative proposals Alternative I :Repairs to existing machine: Cost of Repairs Equivalent annual cost for 5 years Add: Running and Maintenance cost p.a net of tax Present value of cash outflows p.a
19000 X 50 / 100 (9500 / 3.791) (20000 X 50 / 100)
=`9500
(` ) 2506 10000 12506
42
Alternative II : Replace the old machine Purchase cost of new machine Less: sale proceeds of old machine Net: Cash Outflow Equivalent annual cost for 10 years Add: Running and maintenance cost p.a. net of tax
49000 5000 44000 (44000 / 6.145) 7160 (14000 X 50 / 100) 7000 14160 Less : Tax Saving on depreciation (49000 / 10 ) X 50 / 100 2450 Present value of cash outflow p.a. 11710 Analysis : From the above analysis it is observed that alternative II i.e., replacement of old machine with a new machine is more profitable, since the cash outflow p.a. will decrease by `796 (i.e. `12506 – `11710 ) if old machine is replaced with new machine.
43
Costing in Service Sector Ans. 8. Total Room days =No of rooms x Days in a year = 300 rooms x 365 days = 10,95,000 Rooms days = Rs. 50-Rs.10 = Rs.40 Dally contribution required per room Desired profit after tax Add Income Tax (Rs.6,00,000X40/60) Desired profit before tax Add: Fixed cost Total Revenue to be earned No. of room days to be rented No. of rooms to be rented to attain break- even
(Rs.)
600000 400000 10,00,000 7,50,000 17,50,000 = Rs.17,50,000 / Rs.40 = 43.750 Room days = Rs.7,50,000 / Rs.40 = 18.750 Room days
Ans 9: Room Occupancy days per annum Single rooms (180 rooms X 365days X85/100) Double rooms (60 rooms X 365 days X 85/100) Variable and Fixed cost p.a. Particulars Room occupancy days Variable cost per day Total Variable cost Fixed cost per room day Total Fixed cost
Single rooms 55845 300 16753500 500 27922500
55845 18615
Double rooms 18615 500 9307500 780 14519700
Total 26061000 42442200
Margin of Safety desired at 20% of total revenue. Therefore, Break even should be at 80% of total revenue. Revenue at break even level = Variable cost + Fixed cost = 26061000+42442200 = Rs. 68503200 Desired total revenue to be = Rs. 68503200 X 100/80 = Rs. 85629000 (i) Computation of tariff per room day Single room days occupancy Double room days occupancy equivalent to single room day (18615X160/100) Total single room days Rent per single room day = Rs. 85620000/85629 room days = Rs. 1000 Rent per double room day = Rs. 1000 X 160/100 = Rs. 1600 Tariff per room for single room = Rs. 1000 X 100/80 = Rs. 1250 Tariff per room for double room = Rs. 1600 X 100/80 = Rs. 2000 (ii) Computation of increase in occupancy of the remaining single rooms days loss arising from the discount. Number of single rooms intends to reserve for corporate customers = 12 Occupancy days for reserved rooms = 12 rooms X 365 days X 85/100 Discount given on room rent per day = Rs. 1000 X 10/100 Amount of revenue lost due to discounting = 3723 room days X 100 Contribution per day on a single room = Rs. 1000- Rs. 300 Increase in occupancy days required in single rooms = Rs. 372300/Rs. 700 Ans. 10 Working Name: Calculation of occupancy (a) Single room occupancy p. a.
( 100 rooms X 365 days X 75/100)
55845 29784 85629
required to compensate the = 3723 = Rs. 100 = Rs.372300 = Rs. 700 = 532 days
27,375
44
(b) Double room occupancy p. a. ( 20 rooms X 365 X 75/1000) = 5475 Conversion of double room to single room occupancy ( 5,475 X 1.20) Total
6,570 33,945
Statement of Rent chargeable to single room and double room per day Particulars Single Room No. of occupancy days (a) 27,375 Costs per day Rs. Variable cost 400 Fixed cost 200 (b) 600 Total (Rs.) (a) X (b) 1,64,25,000 Total Cost Add: 20% Margin safety on hire of room Total rental charges to be received
(a) Single Room (b) Double Room Profitability statement of restaurant Sales Revenue Contribution Less: Fixed cost p. a. Profit
(Rs.)
(Rs.1,64,25,000 + Rs.41,06,250) (Rs.25% 0n cost)
Room rent per day to be collected
Double room 5,475 Rs. 500 250 750 41,06,250
(Rs.)
(Rs.2,56,64,062 / 33,945) (Rs.756 X 1.20)
756 907 (Rs.)
(Rs.1,00,000 X 365 days) (30% of Rs.365 Lakhs)
2,05,31,250 51,32,812 2,56,64,062
3,65,00,000 1,09,50,000 10,00,000 99,50,000
Profitability statement of sports centre Contribution p. a. Less: Fixed Cost p. a. Profit
(Rs.)
(50 persons X Rs.50X 365 days)
9,12,500 5,00,000 4,12,500
Profitability statement of shopping arcade Contribution p. a. Less: Fixed Cost p. a. Profit
(Rs.)
(Rs.50,000 X 12 months)
Ans. 11 (i) Income Statement of Kangan Resort for the next year Rs. Sales Revenue Lodging house room receipts (40 Rooms × 200 days Rs. 200 × 85%)
13,60,000
Shopping Arcade (40 Rooms × 2 persons × 200 days × Rs. 50 ×85%)
6,80,000
Restaurant (40 Rooms × 2 persons × 200 days) × Rs. 80 × 85%)
10,88,000
6,00,000 6,00,000 Nil
45
Total Sales Revenue
31,28,000
Less: Variable Cost Lodging house rooms (40 Rooms × 200 days × Rs. 30 × 85%)
2,04,000
Shopping Arcade (50% of Rs. 6,80,000)
3,40,000
Restaurant (60% of Rs. 10,88 ,000)
6,52,800
Total Variable Cost
11,96,800
Contribution (Total Sales Revenue – Total Variable Cost)
19,31,200
Less: Fixed Cost
10,00,000
Profit (Estimated)
9,31,200
(ii) Income Statement on the basis of reduced room rent Rs. Sales Revenue Lodging house room receipts (40 Rooms × 200 days Rs. 150 × 95%)
11,40,000
Shopping Arcade (40 Rooms × 2 persons × 200 days × Rs. 50 ×95%)
7,60,000
Restaurant (40 Rooms × 2 persons × 200 days) × Rs. 80 × 95%)
12,16,000
Total Sales Revenue
31,16,000
Less: Variable Cost Lodging house rooms (40 Rooms × 200 days × Rs. 30 × 85%)
2,28,000
Shopping Arcade (50% of Rs. 7,60,000)
3,80,000
Restaurant (60% of Rs. 12,16 ,000)
7,29,600
Total Variable Cost
13,37,600
Contribution (Total Sales Revenue – Total Variable Cost)
17,78,400
Less: Fixed Cost
10,00,000
Profit 7,78,400 The profitability decreases by 9,31,200 – 7,78,400 = Rs. 1,52,800. Hence reducing room rent proposal may not be accepted. Ans. 12 Estimated Income Statement for the coming year Revenue Hotel Room Rent (100 rooms X 250 days X Rs.150 X 75/100) Receipts from shop (100 rooms X 2 persons X 250 days X Rs.30 X 75/100) Receipts from Restaurant (100 rooms X 2 persons X 250 days X Rs.60 X 75/100) (a) Variable Cost Hotel Rooms (100 rooms X 250 days X Rs.25 X 75/100) Shops (Rs.11,25,000 X 50/100) Restaurant (Rs.22,50,000 X 55/100) (b)
(Rs.) 28,12,500 11,25,000 22,50,000 61,87,500 4,68,750 5,62,500 12,37,500 22,68,750
46
Contribution Less: Fixed Costs Estimated Profit
(a) - (b)
39,18,750 19,50,000 19,68,750
(a) Revised estimated income statement or the coming year ( if room rent reduced to Rs.125 per day to enhance occupancy to 90%) (Rs.) Revenue 28,12,500 Hotel Room Rent (100 rooms X 250 days X Rs.125 X 90/100) 13,50,000 Receipts from shop (100 rooms X 2 persons X 250 days X Rs.30 X 90/100) Receipts from Restaurant (100 rooms X 2 persons X 250 days X Rs.60 X 90/100) 27,00,000 (a) 68,62,500 Variable Cost Hotel Rooms (100 rooms X 250 days X Rs.25 X 90/100) 5,62,500 Shops (Rs.13,50,000 X 50/100) 6,75,000 Restaurant (Rs.27,00,000 X 55/100) 14,85,000 (b) 27,22,500 Contribution (a) - (b) 41,40,000 Less: Fixed Costs 19,50,000 Estimated Profit 21,90,000 (b) Analysis: With the reduction in room rent from Rs.150 per day to Rs.125 the occupancy will increase to 90% which will result in increase of profit by Rs.2,21,250 (i.e, Rs.21,90,000- Rs.19,68,750). Ans. 13 (i) Occupancy: Single rooms 100 X 365 X 80/100=29,200 Double rooms 20 X 365 X 80/100 = 5,840 Variable costs: Single rooms (29,200 X 220) Double rooms (5,840 X 350) Fixed Costs: Single rooms (29,200 X 120) Double rooms (5,840 X 250) Total costs: Margin of safety 20%, Break- even point 80% Sales at BEP = Total Costs Total revenue = 1,34,32,000 X 100 80
64,24,000 20,44,000 35,04,000 14,60,000
Rent per day per Double room
= 1,67,90,000 36,500 =Rs.460 X 1.25
(ii) Restaurant (a) Sales /day Rs.25,000 Contribution 30% Total contribution 25,000 X 30/100 = Rs.7,500 per day Contribution p. a. Fixed cost p. a.
49,64,000 1,34,32,000
=Rs.1,34,32,000 =Rs.1,67,90,000
Single rooms (29,200 X 1) Double rooms (5,840 X 1.25) National single rooms/days Rent per day per Single room
84,68,000
(7,500 X 365)
(Rs.)
29,200 7,300 36,500
= Rs.460 = Rs.575
(Rs.) 27,37,500 8,00,000
47
Profit
19,37,500
(b) Sports centre No. of persons /days Average contribution per person / day Total contribution/day
(Rs.) (50X 15)
Total contribution/p. a. (750X 365) Fixed Overheads Loss (c) Shopping arcade Average contribution p.m. Rs.35,000 Average contribution p. a. (Rs.35,000 X 12) Fixed expenses Profit Profit Statement Hotel accommodation Rentals Less: Costs Restaurant Sports centre Shopping arcade Total (III) Reservation = 10 rooms X 365 X 80 /100 Rent = 2,920 X 460 Discount 10%
(Rs.) 2,73,750 4,00,000 1,26,250
1,67,90,000 1,34,32,00
= 2,920 =Rs.13,43,200 =Rs. 1,34,320
Total contribution of remaining rooms Single 90 X 365 X 80/100 X (460-220) Double 20 X 365 X 80/100 X (575-350) Total Increase in contribution required 76,21,200 + 1,34,320 = Rs.77,55,520 % occupancy Alternatively,
(Rs.) 4,20,000 4,00,000 20,000 (Rs.) 33,58,000 19,37,500 (1,26,250) 20,000 51,89,250
(Rs.) 63,07,200 13,14,000 76,21,200
7755520 × 80 (i.e. Current Occupancy level) = 81.41 7621200 = Say 81.5%
=
% Increase in contribution required =
134320 × 100 = 1.76% 7621200
Current occupancy level = 80 Revised occupancy level = 101.76% of 80 = 81.41% = Say 81.5% (IV) Total profit per annum = Rs.51, 89,250 Capital recovery factor Discounted income for 5 years Lease rent Hence lease not acceptable
50 15 750
3.79 Rs.1, 96, 67,257 Rs.1, 75, 00,000
Ans 14: Calculation of variable cost
Distance X
Distance Y
48
One side distance Round trip Variable cost @ 0.80 per km
24 km 48 km Rs. 38.40
16 km 32 km Rs. 25.60
Distance X
Distance Y
120 Min 40 Min 40 Min 200 Min
80 Min 30 Min 40 Min 150 Min
Rs. 25
Rs. 18.75
8 tones 24 km 192
8 tones 16 km 128
Calculation of fixed cost
Actual running time for round trip distance at the Speed of 24 km per hour Filling time Empty time Total time Fixed cost @ Rs. 7.50 per hour Calculation of ton km Capacity Full load Tons km Cost per ton km
38.40 + 25 = Rs. 0.33 192
25.60 + 18.75 = Rs. 0.347 128
Ans.15 Working notes: (1) Total distance travelled (in 25 days) = 60 km.(two sides ) X 6 trips per day X 25 days = 9,000 km. (2) Total passenger km. = 9,000 km. X 20 seats = 1,80,000 passenger km. (3) Depreciation p.a. = Purchase price – Scrap value = (Rs.4,00,000-Rs.10,000) =Rs.78,000 5 Years 5 Years Statement suggesting fare per passenger – km (Rs.) Fixed Expenses Cost per annum Cost per annum Insurance 15,000 Garage rent 9,000 Road Tax 3,000 Administrative charges 5,000 Depreciation 78,000 10,000 Interest on Loan 1,20,000 10,000 Running Expenses Repair and maintenance 1,250 Replacement of tyre-tube 300 Diesel and oil cost (9,000 km. X Rs.5 45,000 5,000 Driver and conductor’s salary 61,550.00 Total cost (per month) 15,387.50 Add: Profit (20% of total revenue or 25% of total cost Total Revenue Rate per passenger – km
=Rs.76,937.50/1,80,000 passenger km.=0.4274305 or 0.43 Paise
76,937.50
49
Ans.16 (i) Comparative cost sheet Particulars Total trips per day No. of days per month Total trips per month Tonnes carried per truck Capacity to be handed p.m. tones No .of trucks required No. of drivers (including relievers) Total km. run per truck per month (120 X 12) Total km. run by all trucks per month Km. per litre of diesel Diesel required ( Litres) Monthly Sheet No. of Trucks
10 Tonne Capacity Trucks
8 Tonne Capacity Trucks
10 Tonne Capacity 20
10 Tonne Capacity 25
5 24 120 1,200 24,000 20 22 1,440 28,800 3 9,600
(a) Variable with km run Diesel @ Rs.10 per litre Oil and sundries Rs.10 per 100 km. Total (b) Variable with No. of trucks run Repairs & Maintenance Road Tax Drivers Salary Depreciation Total © Fixed Supervisor Mechanic Fitter Miscellaneous Expenses Total Grand Total Tonnage hauled Cost / Tonne Cost/Tonne:
10 Tonne Trucks 8 Tonne Trucks Hire charges
Rs.14.27 Rs.15.90 Rs.18.00
5 24 120 960 24,000 25 27 1,440 36,000 4 9,000
96,000 2,880 98,880
90,000 3,600 93,600
78,500 4,000 35,200 1,16,000 2,33,700
80,000 5,000 43,200 1,50,000 2,78,200
3,200 2,000 1,600 3,000 9,800 3,42,380 24,000 14.27
3,200 2,000 1,600 3,000 9,800 3,81,600 24,000 15.90
Hence buy 10 tonne trucks. (iii) Before taking final decision on purchase of trucks, on factor that may have to be given weight age is that we have assumed consistent operation of all the 20 trucks for 24 days in a month, transporting 24,000 tonnes without default for a period of five years. This aspect must be considered on the basis of past recorded of hiring trucks on day to day basis over a three y3ear period so that optimum calculations on saving get properly weighed down. Second issue that an immediate investment of Rs.86 lakhs in purchase of 20 tracks has to be made. This could be totally from own resources or totally out to borrowings or could be partly either way. For own investment technique of discounted cash flow is to be applied while is case of borrowings, recurrent interest cost as also initial cost of procuring the same has to be provided out of saving from year to year apart from meeting normal schedule of loan repayment. Net
50
saving works out to Rs.10.74 lakhs per annum on hauling of 24,000 tonnes for 12 months in comparison to hiring of trucks. Third issue is to compare return on investment of own funds made for procurement of trucks either fully or in part vis-à-vis return in alternate outlets. This is opportunity cost of capital will have to be given consideration. Decision will be made after considering all the above factors. Ans. 17:
Costs specific to booking operations: Direct person’s salary
20,000
Mobile expenses
3,000
Conveyance
4,000
27,000
Share of other overheads: Office space
4,000
General Telephone
2,400
Security/Maintenance
1,600
Miscellaneous Expenses
1,000
Total Cost allocated to the service Average demand per month= Total cost per booking=
Revenue per ticket
9,000 36,000
2500×3+1000×2+700×7 =1200 12
Total cost per month 36000 = =`30 average booking per month 1200
= Rs. 30
Total revenue less total cost = 30 - 30 = 0 Assuming that other overheads will anyway exist even of the service is not provided, the manager can hope to achieve a profit of Rs. 30x 1,200 - 27,000 is Rs. 9,000 for the full year. Minimum average volume to set up the service will be the amount needed to recover the specific costs of this service, is 27,000 per month. Minimum average bookings
=
27,000
= 900 bookings 30
Ans.18 Working Notes: (1) Calculation of requirement of trucks: No. of Trips X No. of working days in a month X No. of tones 10 tonne = 5 X 24 X 10 = 1,200 tonnes 8 tonne = 5 X 24 x 8 = 960 tonnes No. of trucks required to handle 24,000 tonnes 10 tonne trucks 8 tonne trucks
=24,000 tonnes/1200 tonnes =24,000 tonnes/960 tonnes
(2) No. of drivers required: 10 tonne =20 trucks X 2 drivers
= 20 trucks =25 trucks =40 Drivers
51
8 tonne
=25 trucks X 2drivers
=50 Drivers
(3) Total monthly depreciation: 10 tonne
= 20 trucks X Rs.10,00,000 5 years
8 tonne
= 25 trucks X Rs.8,50,000 5 years
X 1 =Rs.3,33,333 12 X
1 =Rs.3,54,167 12
(4) Diesel Required: (No. of km. X No. of trips X No. of days in month X No. of trucks) Diesel required =(6 km. X 10 trips X 24 days x 20 trucks )/No. km. per litre of diesel 10 tonne =(6 km. X 10 trips X 24 days x 20 trucks )/3. km. per litre 8 tonne =(6 km. X 10 trips X 24 days x 25 trucks )/4. km. per litre Comparative Cost Sheet Particulars Fixed charges (p.m.) Drivers salary(@ Rs.3,000 p.m) Staff Expenses Other fixed expenses Operating and Maintenance charges Depreciation Diesel Cost Lubricants & Sundries Repairs & Maintenance
=9,600 litres =9,000 litres
10 tonne
(i)
8 tonne 1,20,000 9,000 5,000 1,34,000
(Rs.) 1,50,000 9,000 3,000 1,62,000
3,33,333 3,54,167 1,44,000 1,35,000 5,760 7,200 1,00,000 1,00,000 (ii) Total 5,83,093 5,96,367 Operating Cost (i) + (ii) 7,17,093 7,58,367 Tonnage carried (tonnes) 24,000 24,000 Cost per tonne Rs.29.88 Rs.31.60 Analysis : From the above analysis it is observed that cost per tonne is lowest if 10 tonne trucks are used, and the cost of Rs.50 per tonne presently incurring is highest and it can be reduced to Rs.29.88 by using 10 tonne trucks. Ans.19 (a)
Statement of operating income of Modern Airways operating between EXETOWN and WYETOWN (on each one way flight) Rs. Fare received (per flight): (A) 10,00,000 200 passenger × Rs. 5,000 Variable costs (per flight) Commission paid Rs. 10,00,000 × 8% Food services 200 passengers × Rs. 200 Fuel costs Total variable costs: (B) Contribution (per flight): (C): {(A) – (B)} Fixed costs (per flight): Fixed annual lease costs Baggage handling (Fixed ground services) costs Fixed salaries of flight crew
80,000 40,000 1,40,000 2,60,000 7,40,000 5,30,000 70,000 ___40,000
52
Total fixed costs: (D) Operating income (per flight): {(C) – (D)} (b)
Fare received (per flight): (X) 212 passenger × Rs. 4,800
6,40,000 1,00,000 Rs. 10,17,600
Variable costs: Commission paid Rs. 10,17,600 × 8% Food services 212 passenger × Rs. 200 Fuel costs Total variable cost: (Y) Contribution per flight: (Z): {(X) – (Y)} Excess contribution due to lowering of fare: {(Z) – (C)} [Refer to (a) part] (Rs. 7,53,792 – Rs. 7,40,000)
81,408 42,400 1,40,000 2,63,808 7,53,792 13,792
Modern Airways should lower its fare as it would increase it contribution towards profit by Rs. 13,792 per flight. (C)
Financial consideration of Modern Airways to Charter its plane to Zed Tours and Travel should use option (b) and not (a). Rs. Under option (b) Modern Airways Receives contribution (per flight): 7,53,792 Modern Airways would get (per flight) 7,50,000 If it charters the plane A comparison of the above data clearly shows that the Modern Airways would be financially better off by not chartering the plane. Other consideration with regard to chartering a plane to Zed Tours and Travels 1.
The loss of contribution involved in chartering a plane is Rs. 3,792 (per flight). This loss is on a lower side as compared with uncertainties about the number of passengers on scheduled fights.
2.
modern Airways passengers may be inconvenienced when a plane is chartered to zed Tour and Travel. They may go other airlines.
3.
The relationship between the two parties is important. If it is not a long term arrangement. Modern Airways may lose.
Ans.20 Working Notes: Calculation operating capacity of a single aircraft =160 seats X 60/100 (i) Calculation of net operating income per flight Fare collection (96 X 7000) Variable costs: Fuel Food (96 X 130) Commission @ 5% Total Variable costs Contribution per flight Fixed Costs: Lease 3,50,000
=96 passengers per flight (Rs.)
6,72,000 95,000 12,480 33,600 1,41,080 5,30,920
53
Crew
Net Income per flight
72,000
4,22,000 1,08,920
(ii) Evaluation of proposal if Occupancy increases to 108 passengers per flight and the fare reduced to Rs.6,720 (Rs.) Fare collection Variable costs: Fuel Food Commission @ 5%
(108 X 6720)
7,25,760
95,000 14,040 36,288 1,45,328 Contribution 5,80,432 Analysis: The contribution will increase by Rs.49,512 (i.e Rs.5,80,432-Rs.5,30,920). Hence, it is suggested to accept the proposal (iii) Evaluation of proposal to charter the aircraft Current contribution 5,30,920 Less: Fixed charge 5,00,000 Loss: 30,920 (108 X 130)
Analysis: if the aircraft is given on charter, it will cause loss of contribution by Rs.30,920. Hence the proposal is not suggested. Ans. 21:
(i)
With respect to the passenger,
the only variable costs are :
10% Commission on fare
Rs. 500
Food
Rs. 300
Total variable cost/passenger
Rs. 800
Revenue per passenger = gross fare = 5000 Contribution = 5000 – 800 = Rs. 4200 Total Contribution
4200 x 240
10,08,000
Less: Costs/flight Fuel
90,000
Lease
(ii)
2,00,000
Baggage
40,000
Flight Crew
48,000
Profit per flight Cost per flight Rs. 3,78,000 are fixed in relation to the number of passengers. B.E.=
Effect of Mid Air’s offer A to D
378000 =90 passengers 4200
Rs Fare
2000
Less: Comm.
200 1800
3,78,000 6,30,000
54
Less:Snacks Contribution per passenger
300
1500 Additional Cost ( Rs)
50 seats x 2500 ( D to B )
Additional Revenue (Rs) 1,25,000
Fuel
45,000
Baggage
19,000
Snacks @ Rs 200 for passenger ( 240 -25+ 50): 200 x [ 240 – 25 + 50 ]
53,000
Additional Contribution (A to D) 60 x 1500 Contribution lost (A to B) : 25 x 4200 ( opportunity cost)
90,000 1,05,000
Aero will loose Rs. 7,000 per flight if it accepts Mid Air’s offer.
2,22,000
2,15,000
Decision : Reject Mid Air’s offer. Ans.22 Calculation of variable cost per student of last year Revenue 1. Students tuition-75% (Rs.3,600 X 12,000 students) 2. Endowment & contribution-25% (Rs.432 lakhs X 25/75) Total revenue Less: Fixed cost Variable cost
(Rs.lakhs) 432 144 576 300 276
Variable cost per student
=Rs.2,76,00,000 12,000 students =Rs.2,300 per student (i) Calculation of amount available in the first year for capital improvements and building (Rs.lalhs) Revenue 1. Tuition Fee (Rs.4,200 X 11,200 students) 2. Endowment & contribution 3. Grant Total revenue Less: Variable cost (2,300 X 1.10 X 11200 students) Contribution Less: Fixed cost (Rs.300 lakhs + Rs.30 lakhs) Balance available for capital improvements and building
470.40 144.00 50.00 664.40 283.36 381.04 330.00 51.04
Calculation of break-even if the grant is received and costs increases as predicted for the coming year (Rs.lakhs) Variable cost (Rs.2,300 X 1.10 X 12,000 students) 303.60 Fixed Cost (Rs.300 lakhs + Rs. 30 lakhs) 330.00 Capital improvement 40.40 Total cost 674.00 Less: Endowment and contribution 144.00
55
Grant 50.00 Balance amount to be collected as tuition fee Tuition fee to be collected per student = Rs.4,80,00,000 12,000 students Ans.23 Working Notes: (i) Expected Variable cost this year Variable cost last year Add: Expected increase this year (25% of Re.0.80) Expected variable cost this year
194.00 480.00 =Rs.4,000 per student
(Re.per ride)
(ii) Expected fixed costs this year Fixed cost last year Add: Expected increase this year (10% of Rs.32,00,000) Expected variable cost this year
0.80 0.20 1.00
(Rs.) 32,00,000 3,20,000 35,20,000
(1) Rides which DD Amusement park sell last year (No. of rides DD sell last year) = Total Sales of rides last year Charges per ride last year
=Rs.48,00,000 =12,00,000 rides Rs.4
(2) Expected net income for the year if price increase if not implemented Charges per ride Less: Expected Variable cost per ride Contribution per ride No. of rides Total expected contribution Less: Expected fixed costs Expected net income
(Rs.)
4 1 3 12,00,000 36,00,000 35,20,000 80,000
(3)Price indifference point for the new ride Price indifference point is a point at which the expected profits remains the same irrespective of sales price and costs. (Rs.) New ride price Less: Variable cost Contribution per ride Fixed Costs of this year Net Income of last year Contribution require
5.00 1.00 4.00 35,20,000 6,40,000 41,60,000
Price- Indifference point = Rs.41,60,000 =10,40,000 rides Rs.4 (4) Break –even point for this year using the old price and the new price Break-even point = Fixed costs Contribution per ride At old price
= Rs.35,20,000 Rs.4-Re.1
=11,73,334 rides
At New price
= Rs.35,20,000
=8,80,000 rides
56
Rs.5-Re.1 (5) Expected net income if the price increase will reduce ride volume by 10% from the last year’s levels (Rs.) Charges per ride 5.00 Less: Variable cost 1.00 Contribution per ride: (a) 4.00 No. of rides (12,00,000-1,20,000): (b) 10,80,000 Total contribution for all rides: (a) X (b) 43,20,000 Less: fixed costs 35,20,000 Expected net income 80,000 Justification: Since the increase in price of a ride will increase the net income by Rs.1,60,000(Rs.8,00,000Rs.6,40,000) the management should raise the price of a ride. Ans 24: (1) Total number of patients attended
Number of patients attended per day by a physician: 20 Number of physicians employed 6 Number of days in week 6 Number of weeks in a year 52 Total number of patients attended = 20×6 ×6×52 = 37,440.
(2)
Patient Mix: Adults (50%) Children (40%) Senior Citizens (10%)
(3)
Patient Appointments: No treatment required (70%) 37,440 ×70/100 = Minor treatment (20%) 37,440×20/100 = Major treatment (10%) 37,440 ×10/100 =
(4)
Income from Insurance Companies: Number of patients (A) No treatment patients 26,208 Minor treatment patients 7,488 Major treatment patients 3,744
(5) (Rs.)
37,440 ×50/100 = 37,440 ×40/100 = 37,440 ×10/100 =
Co-payment from adult patients:
Total number of adult patients No treatment patients (70%) Minor treatment (20%) Major treatment (10%) Total
18,720 14,976 __3,744 37,440 26,208 7,488 ___3,744 37,440 Rs.
Total Number of Patients 18,720 13,104 3,744 1,872
Rs.
(B) 60 250 500
(A×B) 15,72,480 18,72,000 18,72,000 53,16,480
Payment Rs. 60 250 500
Total Payment 7,86,240 9,36,000 9,36,000 26,58,240
57
(6)
Net income:
Payment from Insurance companies Co-payment from adult patients Total Other Income (fixed) Total Income (A) Less: Expenditure Variable expenses: Material and consumables Fixed expenses: Physician’s salary (6 ×4,50,000) Assistants salary (7 ×1,50,000) Administrative staff’s salary (2 ×90,000) Establishment and other operating costs Total Expenditure (B) Net Income (A – B) (ii)
1.
Rs. 53,16,480 26,58,240 79,74,720 2,25,280
27,00,000 10,50,000 1,80,000 16,00,000
Contribution Analysis:
Break-even patients:
55,30,000 77,62,000 __4,38,000 (Rs.) 79,74,720 22,32,000 57,42,720 153.38 (Rs.) 55,30,000 2,25,280 53,04,720
Fixed costs Less: Fixed income Net Fixed costs Break-even patients = (Net fixed costs÷ Contribution per patient) = (53,04,720÷ 34,585) 3.
82,00,000
22,32,000
Total Fees from Insurance Companies and adult patients Less: Variable costs Contribution Average contribution per patient (57,42,720÷37,440) 2.
Rs.
153.38
Percentage of maximum capacity required to be utilized in order to break-even Present utilization =
20 patients = 83.33% = 37,440 24 patients
100% patient capacity is 37,440 ÷0.8333 =44,930 patients Percentage of maximum capacity required to be utilized in order to break-even Break Even patients ÷100% patients capacity ×100 = {(34,585÷ 44,930)×100 } = 76.98% say 77%. Assumption: Patient mix and mix of patient appointments will be same in the next year.
58
Ans 25 (a) Statement of Total Cost Total cost
Amount (Rs)
Salary of Supervisor , Nurses, Ward boys
4,25,000
Repairs and Maintenance
90,000
Salary of doctors
13,50,000
Food supplied to patients
40,000
Laundry charges for their bed linens
80,500
Medicines supplied
74,000
Cost of oxygen, X ray etc, other than directly borne for treatment of patients
49,500
General administration charges
63,000
Rs 21,72,000
(10 × 12,000)
Rs 1,20,000
Building rent Additional building rent on takings
5% on Total Taking
Hire charges extra beds
Rs 12,000
Fees to heart specialists
(3 × 15,000)
Rs 45,000
Total cost
Rs 23,49,000 + 5% on Total Taking
Profit
20% on Total Taking
Total takings
Rs 23,49,000 + 25% of Total Taking
Total taking(assuming X to be the rent per day)
1,05,000 × X
Rent to be charged 1,05,000 × X = 23,49,000 +25% (1,05,000 × X) = 78750 X = 23,49,000 or X = 29.83(Rounded Off) No of beds with Equivalent Rent Occupancy
Weight of rent
Ward Days
100 × 360 × 100%
36,000 × 1
36,000
12,000 20
600 × 1
600
Cottage ward
50 × 360 × 80%
14,400 × 2.5
36,000
Deluxe ward
50 × 360 × 60%
6,480 × 5
Nature of wards General ward Additional general ward
Total
32,400 1,05,000
Rent to be charged Particulars
Basic
Service tax
Total
General ward
29.83
2.39
32.22
59
Cottage ward
74.58
5.97
80.55
Deluxe ward
149.15
11.93
161.08
Note : You may assume Total Taking to include Service Tax also. Rent = 23,49,000 + 25% × (1,05,000 X × 1.08) + 0.08 × (1,05,000X ) = 1,05,000X × 1.08 = 23,49,000 + 28350X + 8400X = 1,13,400X Therefore X = Rs 30.65 Rent to be charged Particulars
Basic
Service tax
Total
General ward
30.65
2.45
33.10
Cottage ward
76.63
6.13
82.76
Deluxe ward
153.25
12.26
165.51
60
Standard Costing Ans.2 Working Notes (1) For actual (standard) output of 85 kgs. Std. Input is 100 kgs.
100kgs ×1700kgs 85kgs
For actual output of 1,700 kgs. the Std. input =
=2,000 kgs.
(2) 2,000 kgs of standard input for an actual output of 1,700 kgs. Contains the Materials A and B in the proportion of (40:60) i.e., 800 kgs. of A and 1,200 kgs. of Material B. (3) Actual Material consumption for 1,700 kgs. of actual output Particulars
(Kgs.) Materials B 35 800 835 5 830
A Stock on 1-9-2004 Add: Purchase during Sept. 2004 Less: Stock on 30-09-2004 Material consumed during Sept.2004
40 1,200 1,240 50 1,190
(4) Calculation actual purchase price per kg. of material A
=
Rs.3400 = Rs.4.25 800kgs
B
=
Rs.3000 = Rs.2.50 1200kgs
Statement shoeing Standard and Actual Cost of Actual output Material Standard Quantity Rate Amount Kg. Rs. Rs. A 800 4 3,200 B
Loss Output
1,200
3
2,000 300 1,700
3,600
6,800
Calculation of Material Variances (a) Material price variance Actual quantity (Std. price – Actual Price) A = [35 (4 – 4)] + [ 795 ( 4 – 4.25)] B = [40 ( 3 – 3)] +[1,150 ( 3 – 2.50 )]
=Rs.198.75 =Rs. 575
(b) Material Usage variance Std. rate (Std. quantity – Actual Quantity) A = 4 (800 – 830) B = 3 (1,200 – 1,190)
=Rs.120 =Rs. 30
(c) Material Yield Variance Std. rate of output (Actual yield – Std. Yield) =[Rs.6,800 x ( 1,700 kg. – 1,717 kg.)] 1,700 * Std. Yield
=
Actual std Output × Actual input Std. Input
Quantity Kg. 35 830 795
Actual Rate Rs. 4.00 4.25
Amount Rs. 140.00 3,378.75
40 1190 1150
3.00 2.50
120.00 2,875.00
2,020 320 1,700
6,513.75
(A) (F)
=Rs.376.25 (F)
(A) (F)
=Rs.90 (A)
=Rs.68 (A)
=
85kgs × 2020kgs = 1717 kgs 100kgs
(d) Material Mix Variance Actual Quantity ( Std. cost of Std. mix per kg. – Std. cost of actual mix per kg. )
61
Rs. 6800 Rs. 6890* = 2020 kgs − 2000 kgs 2020 kgs *[(830 kgs. x Rs.4)] + [(1,190 kgs x Rs.3 )]
=Rs.22(A) =Rs.6,890
(e) Total Materials Cost Variance Std. Cost – Actual Cost =Rs.6,800 – Rs.6,513.75
=Rs.286.25 (F)
Summary of Material variance Price variance Usage variance 1. Yield variance 2. Mix variance Total Material cost variance
(Rs.) 376.25 (F) 68 (A) 22 (A)
90 (A) 286.25 (A)
Ans. 3: Working Note:
Standard cost Component
Actual cost
Revised std.quantity
Qty.
Rate
Amount
Qty.
Rate Amount
Oty.
Kg.
Rs.
Rs.
Kg.
Rs.
Rs.
Kg.
A
48
10
480
72 (B.F.)
12
864
54
B
112
30
224
108
8
864
126
Total Input
160
704
180
1728
180
(-) Loss
16(10%)
36
Total output
144
144
5,360
—
Solution
(i)
Mix variance
(ii)
Yield variance
= Std. price (Revised Std. quantity – Actual quantity) A: 10 × (54-72) = 180 (A) B: 2 × (126-108) = 36 (F) 144 (A) = Std. price of yield (Actual yield – Std. yield for actual mix) = Rs.
880 × (144 –180×90%) = Rs. 88 (A) 180
(iii)
Price variance
=Actual qty. (Std. price – Actual price.) A: 72 × (10-12) = 144 (A) B: 108 × (2-8) = 648 (A) 792 (A)
(iv)
Total usage variance = Std. price (Std. qty. – Actual qty.) A: 10 × (48-72) = 240 (A) 8 (F) B: 2 × (112-108) = 232 (A)
Ans. 4: Take the good output of 182 kgs. The standard quantity of material required for 182 kg. of output
62
is
182 ×100 = 202.22 90 Statement showing the standard and actual costs and standard cost of actual mix Standard cost Component
Actual cost
Revised std.quantity
Qty.
Rate
Amount
Qty.
Rate Amount
Oty.
Kg.
Rs.
Rs.
Kg.
Rs.
Rs.
Kg.
80.89
60
4,853.40
90
18
1,620
80
B (60% of 202.22 kg.)
121.33
30
3,639.90
110
34
3,740
120
Total Input
202.22
8,493.30
200
5,360
200
(-) Loss
20.22
18
Total output
182.00
182
5,360
—
A (40% of 202.22 kg.)
Standard yield in actual input is 90 % of 200 kg. i.e. 180 kg. Variances : (i)
Price variance
(ii)
Total usage variance = Std. price (Std. qty. – Actual qty.)
(iii)
Mix variance
(iv) Yield variance
=Actual qty. (Std. price – Actual price.) A: 90 × (60-18) = 3780 (F) B: 110 × (30-34) = 440 (A) 3340 (F)
A: 60 × (80.89-90) = 546.60 (A) B: 30 × (121.33-110) = 339.90 (A) 206.70 (A) = Std. price (Revised Std. quantity – Actual quantity) A: 60 × (80-90) = 600 (A) B: 30 × (120-110) = 300 (F) 300 (A) = Std. price of yield (Actual yield – Std. yield for actual mix) = Rs.
(v)
Total variance
8493.30 182 × 200 ) = Rs. 93.30 (F) × (182 – 202.22 182
= Std. cost – Actual cost = Rs. 8,493.30 – Rs. 5,360 = Rs. 3133.30 (F)
Note : (iii) and (iv) above are subparts of total usage variance Proof : Price variance + Mix variance + Yield variance = Total variance Rs. 3340 (F) + Rs.300 (A) + Rs. 93.30 (F) = Rs. 3133.30 (F)
Ans. 5: Working Notes : (i)
Since the actual output is 1,000 units, the standard quantity of materials required for the actual output is 1,000 units × 4 kgs. = 4,000 kgs.
(ii) Statement showing computation of standard cost, standard cost of actual quantity and actual cost.
63
Material Std. cost per Kg.
A B C D
Actual cost per Kg.
Std. qty in Kgs.
Actual qty in Kgs.
Std. cost (Std. qty × Std. price) Rs.
Std. cost of actual qty. (Actual qty. × Std. price) Rs.
Actual cost (Actual qty. × Actual price) Rs.
f = a×d
g = b×d
Rs.
Rs.
a
b
c
d
e = a×c
1.25 1.50 3.50 3.00
1.30 1.80 3.40 3.00
1,200 1,600 800 400 4,000
1,180 1,580 830 440 4,030
1,500 2,400 2,800 1,200 7,900
1,475 2,370 2,905 1,320 8,070
1,534 2,844 2,822 1,320 8,520
(iii) Standard cost per unit of the standard mix = (iv)
Rs. 7,900 4,000 Kgs. = Rs.1.975
Standard cost per unit of the actual mix =
Rs.8070 = Rs.2.002 4030kgs
Variances: (i) Price variance
= Actual qty. (Std. price – Actual price) = Rs.8,070 – Rs. 8,520 = Rs. 450 (A) = Total actual qty. (Std. cost per unit of (ii) Mix variance std.mix – Std. cost per unit of actual mix) = 4,030 Kgs. (Rs. 1.975 – Rs. 2.002) = Rs. 110 (A) = Std. price per unit of std. mix (Total std. qty – (iii) Sub usage variance Total actual qty.) = Rs. 1.975 (4,000 – 4,030) = Rs. 60.00 (A) (iv) Total material cost variance = Std. cost – Actual cost = Rs. 7,900 – Rs.8,520 = Rs. 620 (A)
Proof :
Price variance + Mix variance + Sub-usage variance
= Total variance
Rs. 450 (A) + Rs. 110 (A) + Rs. 60 (A) = Rs. 620 (A) Note : ‘Mix variance’ and sub usage variance are sub-part of total usage variance which may be calculated as below: Usage variance
= Std. price (Std. qty. – Actual qty.) = Standard cost – Standard cost of actual quantity
= Rs. 7,900 – Rs. 8,070 = Rs. 170 (A) Ans.6 Basic data for calculation of Labour variances Category of Workmen Standard Weeks Rate Amount Rs. Rs. Skilled 3,000 60 1,80,000 Semi – Skilled 1,200 36 43,200 Unskilled 1,800 24 43,200 Total 6,000 2,66,400
Actual Rate Rs.
Weeks 2,560 1,600 2,240 6,400
65 40 20
Amount Rs. 1,66,400 64,000 44,800 2,75,200
64
Calculation of Labour variances (1) Direct Labour Cost Variance Std. cost for actual output – Actual Cost =2,75,200 – 2,66,400
(2)
(3)
(a)
Direct Labour Rate Variance Actual time (Std. rate – Actual rate) Skilled = 2,560 (60 – 65) Semi – Skilled =1,600 (36 – 40) Unskilled =2,240 (24 – 20)
=Rs.8,800 (A)
=Rs.12,800 (A) =Rs. 6,400 (A) =Rs. 8,960 (F)
=Rs.10,240(A)
Direct Labour Efficiency Variance Std. rate ( Std. time for actual output – Actual time) Skilled =60(3,000 -2,560 ) =Rs.26,400 (F) Semi – Skilled =36 (1,200 -1,600) =Rs.14,400 (A) Unskilled =24 (1,800 – 2,240) =Rs.10,560(A) Direct Material efficiency Variance can be further analysed into: Direct Labour Mix Variance Std. rate ( Revised Std. time – Actual time) Skilled =60(3,200 -2,560 ) Semi – Skilled =36 (1,280 -1,600) Unskilled =24 (1,920 – 2,240) * Revised Std. time
=Rs.1,440(F)
=Rs.38,400 (F) =Rs.11,520 (A) =Rs. 7,680 (A)
Skilled
=6,400 x 3,000 6,000
=3,200
Semi- skilled
=6,400 x 1,200 6,000
=1,280
=Rs.19,200 (F)
=1,920 =6,400 x 1,800 6,000 (b) Direct Labour Revised Efficiency variance Std. rate ( Std. time for actual output –Revised Std. time) Skilled =60(3,000 -3,200 ) =Rs.12,000 (A) Semi – Skilled =36 (1,200 -1,280) =Rs. 2,880 (A) Unskilled =24 (1,800 – 1,920) =Rs. 2,880 (A) Summary of Labour variances Rate variance Efficiency variance (a) Mix variance 19,200 (F) (b) Revised efficiency variance 17,760 (A) Direct Material cost variance Unskilled
=Rs.17,760(A) (Rs.) 10,240 (A)
1,440 (F) 8,800 (A)
Ans. 7: In a 40 hour week, the standard gang should have produced 1,000 std. hours as shown below: Gang: Skilled
16 No. of workers × 40 hrs.
640
Semi - skilled
6 No. of workers × 40 hrs.
240
Unskilled
3 No. of workers × 40 hrs.
120
65
1,000 hours However, the actual output is 900 standard hours. Hence to find out the total labour cost variance, the standard cost (or cost charged to production) is to be computed with reference to 900 standard hours. This is done in the following statement: Statement showing the Standard cost, Actual cost and Standard cost of Actual time for Actual output, i.e. 900 Standard hours. Gang
Standard cost Hours Rate Rs.
Actual cost Amount Rs.
Hours
Standard cost of Actual time Rate Amount Hours Rate Amount Rs Rs. Rs. Rs.
Skilled 600 × 900 1000 576
3
1,728 14×40 = 560
Semi-skilled 240 × 900 1000 216 2 Unskilled 120 × 900 1000 108 1 900 2.52
432
108 2,268
4
2,240
560
3
1,680
9 × 40 = 360
3
1,080
360
2
720
2 × 40 = 80
2
160
80
1
80
1,000
3.48
3,480
1,000
2.48
2,480
Variances: (i)
= Actual time (Std. rate – Actual rate) = (Standard cost of actual time – Actual cost) = Rs. 2,480 – Rs.3,480 = Rs. 1,000 (A)
Rate variance
(ii) Gang variance
= Total actual time ( Std. rate of std. gang– Std. rate of actual gang) = 1,000 (Rs. 2.52 – Rs. 2.48) = Rs. 40(F)
(iii) Sub-efficiency variance
= Std. rate (Total std. time – Total actual time) = Rs. 2.52 (900 hours – 1,000) = Rs. 252 (A)
(iv) Total labour cost variance
= Std. labour cost – Actual labour cost = Rs. 2,268 – Rs. 3,480 = Rs. 1,212 (A)
The gang composition variance may also be known as labour mix variance and is part of efficiency variance which may be computed as under: Efficiency variance
= Std. rate (Std. time – Actual time) = Standard cost – Std. cost of actual time = Rs. 2,268 – Rs. 2,480 = Rs.212 (A)
Ans. 8: Standard cost charged to production
(1,000 units× 2.5 hours × Rs.2) Actual wages paid Actual wage rate per hour (Rs. 4500÷2000) Std. wage rate per hour Abnormal idle time (25% of 2,000 hours) Variances : (i) Wage rate variance
Rs. 5,000 Rs. 4,500 Rs. 2.25 Rs. 2.00 500 hrs.
= Actual time (Std.rate – Actual rate)
66
= 2,000 hours (Rs.2 – Rs.2.25) = Rs.500 (A) (ii) Efficiency variance
= Std. rate (Std.time – Actual time*) Rs.2 (2,500 hrs. –1500 hrs.) = Rs. 2,000 (F)
(iii) Idle time variance
= Idle time × Std.rate = 500 hrs. × Rs. 2 = Rs. 1,000 (A)
(iv) Total variance
= Std.labour cost – Actual labour cost Rs. 5,000 – Rs. 4,500 = Rs. 500 (F)
*Actual time less idle time.
Ans.9 Basic data for Standard and actual labour cost of producing 1,000 articles of ‘A’ and standard cost of actual labour hours Standard Cost Actual Cost Labour Hours Rate Amount Hours Rate Amount Std. cost of Rs. Rs. Rs. Rs. actual labour hours ( Actual hours x Std. rate)Rs Skilled 10,000 3.00 30,000 9,000 4.00 36,000 27,000 Semi – Skilled 8,000 1.50 12,000 8,400 1.50 12,600 12,600 Unskilled 16,000 1.00 16,000 20,000 0.90 18,000 20,000 Total 34,000 58,000 37,400 66,600 59,600 Calculation of Labour variances (1) Labour Cost Variance Std. cost – Actual Cost =Rs.58,000 – Rs.66,600
(2)
Labour Rate Variance Actual Hours (Standard rate – Actual rate) OR Std. cost of actual hours – Actual Cost =Rs.59,600 – Rs.66,600
(3)
=Rs.7,000 (A)
Labour Efficiency Variance Std. rate of Std. mix (Total Std. hours for actual output – Total Actual hours) =
(4)
=Rs.8,600 (A)
Rs. 58000 ( 34000 − 37400 ) 34000
=Rs.5,800(A)
Labour Mix Variance Total actual hours ( Std. rate of standard mix – Std. rate of actual mix)
58000 59600 = 34000 − 34000 37400 Summary of Labour variances Rate variance Efficiency variance Mix variance Labour Cost variance
=Rs.4,200(F) (Rs.) 7,000 (A) 5,800 (A) 4,200 (F) 8,600 (A)
67
Ans. 10: (i) Variable overhead variance:
= (Standard variable overhead – Actual variable overhead) = (Rs. 2,40,000 – Rs. 2,00,000) = Rs. 40,000 (Favourable) (Refer to Working note 1) (ii) Variable overhead budget variance: = (Budgeted variable overhead for actual hours – Actual variable overhead) = Rs. 2,24,000 – Rs. 2,00,000 = Rs. 24,000 (Favourable) (Refer to Working note 2) (iii) Variable overhead efficiency variance: = Standard variable overhead rate per hour [Std. hours for actual output – Actual hours] = Rs. 2 [1,20,000 hours – 1,12,000 hours] = Rs.2 × 8,000 hours = Rs. 16,000 (Favourable) Working notes: (1) Standard variable overhead = Standard cost of actual output
= 20,000 units × 6 hours × Rs. 2 = Rs. 2,40,000
(2) Budgeted variable overhead (for actual hours) = 1,12,000 hours × Rs.2 = Rs.2,24,000 Ans. 11: Actual output = 9,000 units Idle time = 5,000 hours Production time (Actual) = 1,05,000 hours Standard hours for actual production = 10 hours / unit × 9,000 units = 90,000 hours. Labour efficiency variance = 3,75,000 (A) i.e. Standard rate × (Standard Production time – Actual production time) = 3,75,000(A). SR (90,000 – 1,05,000) = – 3,75,000 SR =
− 3,75,000 = Rs. 25 − 15,000
(i)
Idle time variance = 5,000 hours × 25 Rs. / hour = 1,25,000. (A)
(ii)
Standard Variable Overhead = Rs. 150 / unit Standard hours = 10 hours / unit Standard Variable Overhead rate / hour = 150 / 10 = Rs. 15 / hour Total Variable Overhead variance = Standard Variable Overhead – Actual Variable Overhead = Standard Rate × Standard hours – Actual rate × Actual hours =
(15) × (10 × 9,000) – 16,00,000
=
13,50,000 – 16,00,000
Total Variable Overhead Variance = 2,50,000 (A) (iii) Variable Overhead Expenditure Variance = (Standard Rate × Actual Hours) – (Actual Rate × Actual Hours) =
(15 × 1,05,000) – 16,00,000
=
15,75,000 – 16,00,000
68
=
25,000 (A)
(iv) Variable Overhead Efficiency Variance = Standard Rate × (Standard Hours for actual output – Actual hours for Actual output) =
15 (90,000 – 1,05,000)
=
15 (–15,000)
=
2,25,000 (A)
(b) Alternative Solution Actual Output = 9,000 Units Idle time = 5,000 hrs Direct Wages Paid = 1,10,000 hours @ Rs. 22 out of which 5,000 hours being idle, were not recorded in production. Standard hours
=
10 per unit.
Labour efficiency variance = Rs. 3,75,000 (A) or Standard Rate (Standard Time – Actual Time) = – 3,75,000 Or Standard Rate = Rs 25/(i)
Idle time variance = Standard Rate × Idle time
25 × 5,000 = Rs 1,25,000 (A) (ii) Standard Variable Overhead / unit = 150 Standard Rate =
150 = Rs.15/hour 10
Standard Quantity = 10 hours Actual Variable Overhead
= 16,00,000
Standard Variable Overhead = 150 × 9,000 = 13,50,000 Actual Variable Overhead
= 16,00,000
Total Variable Overhead Variance (iii) Variable Overhead expenditure
= 2,50,000 (A) = Standard Variable Overhead for actual hours – Actual Variable Overhead =
(iv) Variable overhead efficiency variance
(150 × 1,05,000) – 16,00,000
=
15,75,000 – 16,00,000
=
25,000 (A) =
Standard Variable Overhead for actual output Standard Variable Overhead for Actual hours)
=
15 (10 hours × 90,000 units – 1,05,000)
=
15 (90,000 – 1,05,000)
= =
15 (–15,000) 2,25,000 (A)
Ans.12: Computation of standard cost and actual cost Standard Cost Direct Materials Direct Labour Variable Overheads Total standard Costs Actual Costs Direct Materials
(6,000 x Rs.12) (6,000 x Rs.4.40) (6,000 x Rs.3) (a) (12,670meters x Rs.5.70)
72,000 26,400 18,000 1,16,400
–
69
Direct Wages Variable Overheads Total Actual Costs Total Variance
72,219 27,950 20,475 1,20,644 4,244,(A)
(b) (a)-(b)
Computation of Missing figures (1) Actual Labour hours Standard variable overhead rate hour (Standard hours – Actual hours) = Rs.1,500 (A) Rs.1,500 A =Rs.3 (6,000 x 1 hour – Actual hours) Rs.1,500 A =Rs.18,000 –(Rs.3 x actual hours) (Rs.3 x Actual hours) =Rs.18,000 + Rs.1,500 Actual hours =Rs.19,500 / 3 = 6,500 hours =Rs.4.3
=Rs.27,950 = Actual wages paid Total Actual hours 6,500 hours Computation of Material Labour and Variable Overhead Variances 1. Material variances (1) Material Cost Variance Standard Cost- Actual Cost =(Rs.72,000 – Rs.72,219) (2) Material Price Variance Actual Quantity of Material consumed (Std, price- Actual Price) =12,670 meters (Rs.6- Rs.5.70) (3) Material Usage Variance Standard price (Standard Quantity –Actual Quantity) =Rs.6 (12,000 metres -12,670 metres) 2. Labour Variances (2) Actual Wage rate hour
3.
=Rs.219 (A)
=Rs.3,801 (F)
=Rs.4,020 (A)
(1) Labour Cost Variance Standard Cost- Actual Cost =(Rs.26,400 – Rs.27,950) (3) Labour Rate Variance Actual hours (Std. wage rate per hour- Actual wage rate per hour) =6,500 hours (Rs.4.40- Rs.4.30) (3) Labour Efficiency Variance Standard rate per hour (Standard hours –Actual hours) =Rs.4.40 (6,000 hours- 6,500 hours) Variable Overhead Variances
=Rs.1,550 (A)
=Rs.650 (F)
=Rs.2,200 (A)
(1) Total Variable overhead Variance Standard Variable Overhead- Actual Variable Overhead =Rs.18,000 – Rs.20,475 =Rs.2,475 (A) (4) Variable overhead Efficiency Variance Standard Variable overhead rate per hour (Std. hours for actual output-Actual hours) =Rs.3 ( 6,000 – 6,500) =Rs.1,500 (A) (3) Variable overhead Budget Variance Budgeted variable overhead –Actual variable overhead) =(Actual hours worked x Std. variable overhead per hour) – Actual variable overhead =(6,500 x Rs.3 ) – Rs.20,475 =Rs.975 (A) Note: (F) denoted Favourable Variance; (A) denoted Adverse Variance
Ans 13: Working Notes : 1. Standard cost of raw-material consumed :
Rs.
Total standard cost of ZED (1,000 units × Rs.21) Less: Standard cost : Labour
Rs. 21,000
8,000
70
Overheads
1,600
Standard cost of raw materials used 2. Standard cost of raw–material per finished unit.
9,600 11,400
3. Standard quantity of raw - material per finished unit and total quantity of raw material required:
Total quantity – 3.8 kg. × 1,000 units = 3,800 kgs. 4. Total material cost variance : Actual cost of raw material Rs.10,000 Standard cost of raw material Rs.11,400 Total material cost variance Rs. 1,400 (F) 5. Actual quantity (A Q) of raw–material (in kgs): Material usage variance = Standard rate (Standard quantity – Actual quantity). or, Rs. 600 (A) = Rs. 3 (3,800 Kgs. – AQ) or, 3AQ = 12,000 kgs. or, AQ = 4,000 kgs. (Material usage variance is as given in the question and standard quantity is as per (3) above ) 6. Actual rate of raw material per kg
7. Standard direct labour rate Standard direct labour hours = 1,600 (given) Standard direct labour cost
= Rs. 8,000 (given)
8. Actual labour cost and actual labour rate per hour: Actual total cost of 1,000 units Rs. 21,070 1,000 units (Rs. 21 + Re. 0.07) Less : Actual cost of material Rs. 10,000 Actual variable overheads Rs. 1,62 Rs. 11,620 Actual direct labour cost Rs. 9,450
9. Standard labour hours to produce one unit:
10.
Standard labour cost per unit: Standard labour cost per unit = 1.6 hours × Rs. 5 = Rs.8
11.
Actual hourly rate of variable overheads
(a)
: Standard qu antity of raw material per unit of ZED : 3.8 kg. (Refer to working note 3).
(b)
Standard direct labour rate per hour Rs. 5 (Refer to working note 7).
71
(c)
Standard direct material cost per unit of ZED : Rs. 11.40 (Refer to working note 2 ) .
(d)
Standard direct labour cost per unit of ZED: Rs. 8 (Refer to working note 10).
(e)
Standard total material cost for the output: Rs. 11,400 (Refer to working note 1). (f) Actual
total direct labour cost for the output: Rs. 9,450 (Refer to working note 8). (g)
Material price
variance = Total material cost variance – Material usage variance. = Rs. 1,400 (favourable)* – Rs. 600 (Adverse) (*Refer to working note 4) = Rs. 2000 (Favourable) Alternatively, = Actual quantity (Standard rate – Actual rate) = 4,000 units (Rs. 3 – Rs. 2.50)*
(* Refer to working note 6)
= Rs. 2,000 (Favourable) (h)
Labour rate variance: = Actual hours (Standard rate – Actual rate) = 1,800 hours (Rs. 5 – Rs. 5.25) = Rs. 450 (Adverse)
(i)
Labour efficiency variance:
(j)
Standard rate (Standard hours – Actual hours) = Rs. 5 per hour (1,600 hours – 1,800 hours) = Rs. 1,000 (Adverse) Variable overhead expenditure variance : = Actual hours (Standard rate – Actual rate) = 1,800 hours (Re. 1 – Re. 0.90)* = Rs. 180 (Favourable) (*Refer to working note)
(k) Variable overhead efficiency variance = Standard rate (Standard hours – Actual hours) = Re. 1 per hour (1,600 hours – 1,800 hours) = Rs. 200 (Adverse)
Ans. 14: Budgeted daily hours per day of June = Actual available hours for June Calendar Variance
12000hrs = 500hrs / day 24days
= 500 hours × 25 days = 12,500 hours
= Std. fixed overhead rate per hr (No. of hrs. in actualperiod– No. of hrs. in budgeted period) = Re.0.50 (12,500 hours – 12,000 hours) = Rs. 250 (F)
Alternatively, this variance can be calculated by using number of days instead of hours. In that case, overhead rate will be on per day basis.
Ans. 15:Actual output : 8,400 hours × 22days × 1.2 units per hour = 2,21,760 units. Standard output per man hour: 1 Standard hours produced or std. hrs. for actual production :2,21,760 units×1 hr. = 2,21,760 hrs. Budgeted hrs. in budgeted days: 8,000 hours × 20 days = 1,60,000 hours Budgeted hours (capacity) in actual working days: 8,000 hrs. × 22 days = 1,76,000 hours Actual hours worked: 8,400 hours × 22 days = 1,84,800 hours Overheads as per budget: 8,000 hours × 20 days × Rs. 2 per hour = Rs.3,20,000
72
Rs. (a) Standard cost charged to production : 2,21,760 hours × Rs.2 4,43,520 (b) Actual hours worked × Standard rate : 1,84,800 hours × Rs.2 3,69,600 (c) Budgeted hours in actual days × Std. rate: 1,76,000 × Rs.2 3,52,000 3,20,000 (d) Overheads as per budget 3,25,000 (e) Actual overheads = Std.fixed overhead rate per hour (Std. hrs. for Efficiency variance production – Actual hrs.) = Rs.2 (2,21,760 hours – 1,84,800 hours) = Rs.73,920 (F) = Standard fixed overhead rate per hour (Actual capacity – Capacity variance Budgeted capacity) = Rs.2 (1,84,800 hours – 1,76,000 hours) = Rs.17,600 (F) = Standard fixed overhead rate per hour (Budgeted hrs. in Calendar variance actual days – Budgeted hrs. in budgeted days) = Rs.2 (1,76,000 hours – 1,60,000 hours) = Rs.32,000 (F) = Standard fixed overhead rate per hour Volume variance (Actual volume in hrs. – Budgeted volume in hrs.) = Rs.2 (2,21,760 hours – 1,60,000 hours) = Rs. 1,23,520(F) = Budgeted expenses – Actual expenses Expenses variance = Rs.3,20,000 – Rs.3,25,000 = Rs.5,000 (A) = Overheads charged to production – Actual overheads Total variance = Rs. 4,43,520 – Rs.3,25,000 = Rs. 1,18,520 (F) OR Rs. Efficiency variance : (a – b) 73,920 (F) Capacity variance : (b – c) 17,600 (F) Calendar variance : (c – d) 32,000 (F) Volume variance : (a – d) 1,23,520 (F) Expense variance : (d – e) 5,000 (A) Total variance : (a – e) 1,18,520 (F)
Ans. 16: (a)Total fixed overhead variance = Absorbed fixed overheads – Actual fixed overheads = (5,200units× Rs. 2) – Rs. 10,200 = Rs.200 (F) (b) Expenditure variance
= Budgeted overheads–Actual overheads = Rs. 10,000 – Rs. 10,200 = Rs. 200(A)
(c) Volume variance
= Standard rate of absorption per unit × (Actual production – Budgeted production = Rs.2 (5,200 units —5,000 units)=Rs. 400 (F)
This can be divided into capacity variance and efficiency variance as shown below : Capacity variance
Efficiency variance
= Standard rate of absorption per hour (Actual hours capacity – Budgeted hours capacity) = Re. 0.50 (20,100 hours – 20,000 hours) = Rs 50(F) = Standard rate of absorption per hour (Standard hours required – Actual hours) = Re.0.50 (20,800 hours – 20,100 hours) = Rs.350 (F)
73
Working Notes :
Rs.10000 = Rs.2 5000units
Std. fixed overhead rate of absorption per unit = Std. fixed overhead rate of absorption per hour:
Rs.10000 = Re.0.50 5000units × 4hrs.
Std. hours required for actual production: 5,200 units × 4 hours = 20,800 hours Ans. 17: Working Notes: 1) Budgeted output in units 40,000 man hours X 3.2 units per man hours
= 1,28,000 units.
2) Standards variable overhead rate per unit Rs, 1,02,400/1,28,000 units
= Rs. 0.80 per unit
3) Standard variable overhead rate per man hour Rs. 1,02,400/40,000 man hours
= Rs. 2.56 per man hour
4) Standard fixed overhead rate per unit Rs 32,000/1,28,000 units
= Rs. 0.25 per unit
5) Actual Production units 43,000 man hours X 3 units per man hour
= 1,29,000 units
Computation of variable Overhead variances: i)
Total Variable Overhead Variances = Variable overhead recovered on actual output – Actual variable overhead = (1,29,000 units X 0.80 P – Rs. 1,14,000) = Rs. 11,200 (A)
ii) Variable Overhead Expenditure Variance = Budgeted variable overhead for actual hours – Actual Variable overhead = (43,000 X 2.56 – Rs. 1,14,400) = Rs. 4,320 (A) iii) Variable Overhead Efficiency Variance = Standard variable overhead rate per hour (Standard hours for actual output- Actual hours) = Rs. 2.56 (40,312.5 hours – 43,000 Hours) = Rs. 6,880 (A)
Computation on Fixed Overhead Variances: i) Total Fixed Overhead Cost Variance = Fixed overhead recovered on actual output – Actual fixed overhead = (1,29,000 units – 0.25 P – Rs. 31,500) = Rs. 750 (F) ii) Fixed Overhead Expenditure Variance = Budgeted fixed overhead – Actual fixed overhead = (Rs. 32,000 – Rs. 31,500)
= Rs. 500 (F)
iii) Fixed Overhead Volume Variance = Standard fixed overhead per unit (Actual output units – Budgeted output units) = 0.25 P (1,29,000 – 1,28,000) = Rs. 250 (F) iv) Fixed Overhead Efficiency Variance = Standard fixed overhead rate per unit (Actual Quantity – Standard Quantity)
74
= 0.25 P (43,000 hours X 3.2 units – 1,29,000 units)
= Rs. 2,150 (A)
v) Fixed Overhead Capacity Variance = Standard fixed overhead rate per hour (Actual capacity hours – Budgeted capacity hours in = (Rs. 32,000/40,000 hours) (43,000 – 21 days X 2,000 hours) = Rs. 800 (F) vi) Calendar Variance = (Budgeted Days – Actual Days) Standard fixed overhead per day = (20 days – 21 days) (Rs. 32,000/20 days) = Rs. 1,600 (F) Computation of Total Overhead Variances = Total variable overhead variances + Total fixed overhead variances = Rs. 11,200 (A) + Rs. 750 (F) = Rs. 10,450
Ans. 18: Basic calculation: Product
Budgeted price
A B C D
a Rs. 2.50 5.00 7.50 10.00
Actual Budgeted Actual Budgeted Actual Actual price quantity quantity sales quantity at sales budgeted sales Price b c d (e)=a × c f=(a × d) g=(b × d) Rs. Rs. Rs. Rs. 3.00 2,000 2,400 5,000 6,000 7,200 1,500 1,400 7,500 7,000 6,300 4.50 1,000 1,200 7,500 9,000 8,400 7.00 500 400 5,000 4,200 10.50 4,000 5,000 5,400 25,000 26,000 26,100
Computation of Variances : Sales price variance
= Actual quantity (Actual price – Budgeted price) = Actual sales – Standard sales = Rs.26,100 – Rs. 26,000 = Rs.100(F)
Sales volume variance = Budgeted price (Actual quantity – Budgeted quantity) = Std. sales – Budgeted sales = Rs.26,000 – Rs.25,000 = Rs.1,000 (F) Total variance
= Actual sales – Budgeted sales = Rs.26,100 – Rs.25,000 = Rs.1,100 (F)
Average budgeted price per unit of budgeted mix: Average budgeted price per unit of actual mix: Hence, Sales mix variance = Actual total qty. (Budgeted price per unit of actual mix – Budgeted price per unit of budgeted mix)
actual days)
75
= 5,400 units (Rs.4.815—Rs.5.00) = Rs. 1,000 (A) Sales quantity variance
= Budgeted price per unit of budgeted mix = (Actual total qty. – Budgeted total qty.) = Rs.5 (5,400 – 5,000) = Rs. 2,000 (F)
Note: Instead of computing average price, one may use total figures to do away with the effect of rounding off. For example, in case of sales mix variance figures may be as under:
= Rs. 26,000 – Rs 27,000 = Rs.1,000 (A)
Ans. 19: A. (a) Analysis of variances to show the effects on turnover : B. Working Notes : ( 1 ) Budgeted sales : Budgeted sales units at budgeted (or standard) prices. Units Bravo Champion Super
5,000 4,000 6,000
Price Rs. 100 200 180
Amount Rs. 5,00,000 8,00,000 10,80,000
15,000
23,80,000
(2) Actual sales : Actual sales units at actual prices Units Price Bravo Champion Super
(3)
5,750 4,850 5,000 15,600
Rs. 120 180 165
Amount Rs. 6,90,000 8,73,000 8,25,000 23,88,000
Standard sales: Actual sales units at Budgeted (or Standard) prices. Units Price Amount Rs. Rs. Bravo 5,750 100 5,75,000 Champion 4,850 200 9,70,000 Super 5,000 180 9,00,000 15,600 24,45,000 Computation of Variances : (i) Sales price variance = Actual quantity (Actual price – Budgeted price) or Actual sales – Standard sales
76
= Rs.23,88,000 – Rs.24,45,000 = Rs.57,000 (A) (ii) Sales mix variance
= Total actual quantity (Budgeted price of actual mix – Budgeted price of budgeted mix
Rs.2445000 Rs.2380000 = 15600units − 15000 15600 =Rs. 2475200 – Rs. 2380000 = Rs. 95200F (iii) Sales quantity variance
= Rs. 24,45,000 – Rs. 24,75,200 = Rs. 30,200 (A) = Budgeted price of budgeted mix × (Total actual quantity – Total budgeted quantity) Rs. 23,80,000 = 15,000 units ( 15,600 units – 15,000 units)
= Rs. 24,75,200 – Rs. 23,80,000 = Rs. 95,200 (F) (iv) Total sales value variance = Actual sales – Budgeted sales = Rs.23,88,000 – Rs.23,80,000 = Rs. 8,000 (F) (b) Analysis of variances to show the effects on profit : Working Notes : (1) Budgeted margin per unit
Bravo Champion Super (2) Actual margin per unit
Sales price Rs. 100 200 180
Cost Rs. 90 170 130
Margin Rs. 10 30 50
77
Computation of variances: (i) Sale margin price variance Actual quantity (Actual margin – Budgeted margin) or Actual profit – Standard profit Rs. 3,96,000 – Rs. 4,53,000 = Rs. 57,000 (A)
(ii) Sales margin mix variance = Total actual quantity (Budgeted margin on actual mix – Budgeted Margin on budgeted mix
= Rs. 4,53,000 – Rs. 4,88,800 = Rs. 35,800 (A) (iii) Sales quantity variance = Budgeted margin on budgeted mix (Total actual qty. – Total budgeted qty.)
= Rs. 4,88,800 – Rs. 4,70,000 = Rs. 18,800 (F) (iv) Total sales margin variance = Actual profit – Budgeted profit = Rs. 3,96,000 – Rs. 4,70,000 = Rs. 74,000 (A) Ans. 20:Working Notes: 1. Statement of budgeted average contribution margin per unit for the year 1995: Product different PC models
PC Portable PC Super PC
Budgeted contribution margin per unit of each product
Budgeted sales volume
Total budgeted contribution margin
(Rs.)
(Units)
(Rs.)
10,000
7,000
7,00,00,000
6,000
1,000
60,00,000
40,000
2,000
8,00,00,000
Budgeted average contribution margin per unit
=
10,000 15,60,00,000 Rs.15,60,00,000
10,000 units
= Rs.15,600
78
2.
Actual market share percentage
= =
Actual sales of - 3 PC models Actual industry sales 11,000 units 68,750 units
× 100
× 100
= 16 3.
Actual sales mix percentage of product =
Actual sales of Product Total Actual sale of 3 PC models
Actual sales mix percentage of product PC
=
Actual sales mix %age of product Portable PC = Actual sales mix %age of product Super PC (i)
=
8,250 units 11,000 units 1,650 units 11,000 units
1,100 units 11,000 units
× 100
× 100 = 75 × 100 = 15 × 100 = 10
Computation of individual product and total sales volume variance
Actual Budgeted Budgeted contribution Sales Sales × Sales = − Volume Volume margin per in units in units unit
Individual product sales volume variance: PC = (8,250 units – 7,000 units) × Rs.10,000 = Rs.1,25,00,000 (Fav.) Portable PC = (1,650 units – 1,000 units) × Rs.6,000 = Rs.39,00,000 (Fav.) Super PC = (1,100 units – 2,000 units) × Rs.40,000 = Rs.2,60,00,000 (Adv.) Total Sales Volume Variance = Rs.1,96,00,000 (Adv.) (ii) Computation of total sales quantity variance: Total sales quantity variance =
Total actual sales Unit
Budgeted average Total Budgeted − × contribution margin Sales units per unit
= (11,000 units – 10,000 units) × Rs.15,600 = Rs.1,56,00,000 (Fav.) (iii) Computation of the market size and market share variance 1.
Market size variance:
Budgeted average
Budgeted market Share %age =
Actual Industry Budgeted Industry Sales in units − Sales in units × contribution margin per unit
= 0.20 (68,750 units – 50,000 units) × Rs.15,600 = Rs.5,85,00,000 (Fav.) 2.
Market share variance:
79
=
Actual Total Budgeted average Actual market Budgeted market − Sales Volume × Contribution margin share percentage share percentage in units per unit
= (0.16 – 0.20) × 68,750 units × Rs.15,600 = Rs.4,29,00,000 (Adv.) (iv) Computation of individual product and total sales mix variances 1.
Individual product and total sales mix variance: Sales mix variance: Budgeted Actual sales Budgeted sales Actual Total Individual mix %age of − mix %age of × Sales Volume × Contribution product product margin in units
PC***
Budgeted average − contribution margin
= (0.75 – 0.70) × 11,000 units × (Rs.10,000 – Rs.15,600) = Rs.30,80,000 (Adv.)
Super PC****= (0.10 – 0.20) × 11,000 units × (Rs.40,000 – Rs.15,600) = Rs.2,68,40,000 (Adv.) 2.
Total sales mix variance
= rs.3,52,00,000 (Adv.)
* Refer to working note 1. **Refer to working note 2. ***Refer to working note 3. Note: Sales variances can also be calculated by using sales value approach. (v) Comment on above results: 1.
Favourable sales quantity variance of Rs.1.56 crores was because of growth in industry as a whole. However the firm could not retain the budgeted market share of 20%. As a result the benefit of increased market size i.e. Rs.5.85 crores is partly offset by loss due to fall in market share i.e. Rs.4.29 crores.
2.
Increase in the percentage sale of computers below-average budgeted margins and a decrease in the percentage sale of computers above-average budgeted margins had resulted in the reduction of operating profit by Rs.3.52 crores.
3.
As a result of above, the operating profit of ‘Super Computers’ had been adversely affected by Rs.1.96 crores due to sales variances.
Ans 21:Working Notes 1. Material data
Quantity Kgs. 36,000
Actual output 6,400 units Actual data for actual output Price Amount Per Kg. Rs. 7.50 2,70,000
Labour
Actual output 6,400 units Actual data for actual output Rate/hour Amount
Standard data for actual output Quantity Kgs. 32,000 2.
Price Per Kg. 8
Amount Rs. 2,56,000
Labour data Standard data for actual output Labour
Rate/hour
Amount
80
hours 32,000 3.
Rs. 8
Standard variable overhead Rate/hour Standard variable overhead rate/ unit
Rs. 7.50
6,000
6,50,000
Actual data Actual variable overheads (Rs.) Actual Units Actual Hours
3.
6,48,000 6,400 65,000
Rs. 10 Rs. 100
Budgeted data Budgeted Margin p.u. Rs. 50 (Rs. 250 – Rs. 200)
Amount Rs.
Sales Units
3,00,000
6,400
Actual data Actual Margin p.u. Rs. 65 (Rs. 265 – Rs. 200)
Amount Rs. 4,16,000
Market Size Variance = Budgeted market share percentage [Actual industry sales in units – Budgeted industry sales in units] Budgeted contribution margin per unit = 0.12 [60,000 units – 6,000 units/12%] Rs. 50 = 0.12 [60,000 units – 50,000 units] Rs. 50
2.
Rs. 2,70,000
Sales data
Sales Units
1.
hours 36,000
Variable overheads data
Standard/Budgeted data Budgeted variable overheads for actual hours
4.
Rs. 2,56,000
= Rs. 60,000 (F)
Market Share Variance =[ =[0.106666 – 0.12] 60,000 units X 50 = (6,400 units – 7,200 units) Rs. 50
= Rs. 40,000 (A)
Gross Margin Sales Volume Variance = (Actual quantity – Budgeted quantity) Budgeted margin per unit = (6,400 units – 6,000 units) Rs. 50
= Rs. 20,000 (F)
4.
Gross Margin Sales Price Variance = (Actual margin per unit – Budgeted margin per unit) Actual quantity of units sold = [(Rs. 65 – Rs. 50) 6,400] 6,400 units = Rs. 96,000 (F)
5.
Direct Material Usage Variance = (Standard quantity – Actual Quantity) Standard Price per kg. = (32,000 kgs – 36,000 kgs.) Rs. 8
= Rs. 32,000 (A)
Direct Material Price Variance = (Standard price/kg. – Actual price/kg.) Actual quantity of material used = (Rs. 8 – Rs. 7.50) 3,600 kgs. = Rs. 18,000 (F) 6.
Direct Labour Efficiency Variance = (Standard labour hours – Actual labour hours) Standard rate per hour = (64,000 hours – 65,000 hours) Rs. 6 = Rs. 6,000 (A) Direct Labour Rate Variance = (Standard labour rate per hour – Actual labour rate per hour) Actual time taken in hours
81
= (Rs. 6 – Rs. 6.40) 65,000 hours 7.
= Rs. 26,000 (A)
Variable Overhead Efficiency Variance = (Standard hours for actual output – Actual Hours) Standard variable overhead per hour = (64,000 hours – 65,000 hours) Rs. 10 = Rs. 10,000 (A) Variable Overhead Expense Variance = Budgeted Variable Overhead – Actual Variable Overhead = Rs. 6,50,000 – Rs. 6,48,000 = Rs. 2,000 (F) Operating Statement (Reconciling the budgeted contribution with actual contribution
Budgeted Contribution Gross margin sales volume variance Gross margin sales price variance Cost Variances Material usage Material price Labour efficiency Labour rate Variable overhead efficiency Variable overhead expense
Rs.
Rs.
20,000 96,000
-
18,000 2,000 20,000
32,000 6,000 26,000 10,000 74,000
Total Actual Contribution
Rs. 3,00,000 1,16,000 4,16,000
54,000 3,62,000
Verification: Actual Contribution = Actual sales revenue – Actual variable costs = Rs. 16,96,000 – [ RS. 2,70,000 (actual material cost) + Rs. 4,16,000 (actual labour cost) + Rs. 6,48,000 (actual variable overheads)] = Rs. 16,96,000 – Rs. 13,34,000 = Rs. 3,62,000
Ans.22:Working (i) Normal / Budgeted hours (ii) Budgeted output (iii) Budgeted fixed overhead rate (iv) standard cost and profit per unit Direct materials Direct labour Variable overheads Fixed Overheads Total Selling price Standard profit
(v) Actual profit Sales Less: cost of sales; Direct Material Direct wages Overheads Actual profit Direct Material variances
=60,000 Direct Labour hours. =60,000/ 12 =5,000 units =9,00,000 / 60,000 =Rs.15 per hour or 9,00,000 / 5,000 =Rs.180 per unit (Rs.) (20kg X 10) (12 hrs. X 5.50) (12 hrs. X 10) (12 hrs. X 15)
200 66 120 180 566 600 34
(Rs.) 28,32,000 10,50,000 3,10,000 15,26,000
28,86,000 (54,000)
82
DMCV DMPV DMUV
= Standard Cost for actual output – Actual cost =(4,800 X 200 )-10,50,000 =9,60,000-10,50,000 =Rs.90,000 (A) = Actual qty. X ( standard rate – Actual rate) =1,00,000 X (10-10.5) =Rs.50,000 (A) = Std. rate X (std. qty. for actual output- actual qty.) =10 x ( 4,800 X 20)-1,00,000 ) =10 X (96,000-1,00,000) =Rs.40,000 (A)
Direct Labour variances DLCV = Standard Cost of actual output – Actual cost =(4,800 X 12 X 5.50 )-3,10,000 =3,16,800-3,10,000 =Rs.6,800 (F) DLRV = Actual Time X ( Standard rate – Actual rate) =62,000 X (5.50-5) =Rs.31,000 (F) DLEV = Std. Rate X (Std. Time. for actual output- actual Time) =5.50 x ( 4,800 X 12)-62,000 ) =5.50 x (57,600-62,000) =Rs.24,200 (A) Overhead variances VOCV = Recovered variable Overheads – Actual variable Overheads =(4,800 X 120 ) – 5,86,000 = 5,76,000 – 5,86,000 =Rs.10,000 (A) FOCV = Recovered fixed overheads – Actual fixed overheads =(4,800 X 180 ) – 9,40,000 =8,64,000 – 9,40,000 =Rs.76,000 (A) FOEXPV = Budgeted fixed overheads – Actual fixed overheads =9,00,000 – 9,40,000 =Rs.40,000 (A) FOVV = Recovered fixed overheads – Budgeted fixed overheads =8,64,000 – 9,00,000 =Rs.36,000 (A) FOCAPV = Std. rate per hour (Actual time – budgeted time) =15 X (62,000 – 60,000 ) =Rs.30,000 (F) FOEFEV =Std. Rate per hour X (Std. time for actual output – Actual time) =15 X (4,800 X 12) – 62,0000 =15 X (57,600 – 62,0000=15 X 4400 =Rs.66,000(A) Sales Variances Sales Value = Budgeted Sales – Actual Sales Variance =( 5,000 X 600 ) -28,32,000 = Rs.30,00,000 – Rs.28,32,000 =1,68,000(A) Sales Price = Actual qty. (Std. Price – Actual price) Variance = 4,800 X ( 600 – 590) =Rs.48,000 (A) Sales Volume = Std. Price X (Budgeted qty. – Actual qty.) Variance =600 X ( 5,000 – 4,800) =Rs.1,20,000(A) Loss of profit due to loss of sales volume = 200 X 34 =Rs.6,800 (A)
Ans. 23:Working Notes : ( a ) Actual sales Less : Price variance (Favourable) Standard sales Units sold
Rs. 2,22,750 6,750 2,16,000 4,800
83
( d ) Standard direct wage rate is Rs.4.50 per hour. Hence standard time per unit: Rs. 9 ÷ 4.50 hour = 2 hours (e) Variable overheads : Standard rate Rs.7.50 per hour Variable overhead per unit: 2 hrs. × Rs.7.50 = Rs. 15 (Note : Alternatively, this may be calculated by adjusting variances as in other cases). (f) Fixed overhead spent
Rs.39,000
Less : Fixed overhead expense variance (Adverse) Budgeted overheads
Rs.1,500 Rs. 37,500
(g) Fixed overhead recovered: 4,800 units × Rs.7.50 = Rs.36,000 (h) Fixed overhead volume variance Rs.36,000 – Rs.37,500
= Rs.1,500 (Adverse)
(i) Budgeted sales: 5,000 units × Rs.45
= Rs.2,25,000
(j) Standard sales: 4,800 units × Rs.45
= Rs.2,16,000
(k) Actual sales
= Rs.2,22,750
(1) Sales volume variance: Rs. 2,16,000 – Rs.2,25,000
= Rs.9,000 (Adverse)
(m) Sales price variance: Rs.2,22,750 – Rs.2,16,000 (i) Original budget: Budgeted sales : (A)
= Rs. 6,750 (Favourable) (5,000 units × Rs.45)
Rs. 2,25,000
84
Budgeted costs Direct material Direct wages Variable overheads Fixed overheads
(5,000 units × Rs.6) (5,000 units × Rs.9) (5,000 units × Rs.15) (5,000 units × Rs.7.50)
30,000 45,000 75,000 37,500 1,87,500 37,500
Total budgeted costs : (B) Profit : (A) – (B) (ii) Standard product cost sheet per unit
Rs. 6.00 9.00 15.00 15.00 7.50 37.50 7.50 45.00
Direct materials Direct wages Prime cost Variable overheads Fixed overheads Total cost Profit Selling price
(iii) Statement showing Reconciliation of the original Budgeted Profit and the Actual Profit. Rs. Rs. Budgeted profit 37,500 Less: Sales margin volume variance (Adverse)* or loss of profit on sales volume variance = Rs. 9000 × 16
2 % ** 3
1500
Standard profit *Sales margin volume variance (Adverse) (200 units × Rs.7.50 = Rs.1,500) **Profit as % of selling price : Rs. 7.50 ×
36,000
%
Add: Sales price variance (Favourable) Add: Favourable cost variances: Wage rate Variable overhead expenses Less : Adverse cost variances Material price Material usage Labour efficiency Variable overhead efficiency Fixed overhead expense Less: Fixed overhead volume variance (Adverse) [See working note (h)]
6,750 42,750 750 3,000 300 600 2,250 3,750 1,500
3,750 46,500
8,400 38,100 1,500 36,600
85
Ans. 24:Details of original and revised standards and actual achieved Original standards
Revised standards
× Rs16 700 Kgs × Rs10 99 Kgs × Rs 33.2 1 Kg × Rs 200 400 Kgs
Fruit Glucose Pectin Citric acid
1,200 kgs Labour
Rs 200
× Rs 19 700 Kgs × Rs12 99 Kgs × Rs 33.2 1 Kg × Rs 200
Rs16,886.8
1,200 kgs
Rs6,400 Rs7,000 Rs 3286.8
Rs7,600
428 Kgs × Rs 18
Rs7,704
Rs 8,400
742 Kgs
Rs 8,904 Rs 4,100
Rs 200
× Rs 12 125Kgs × Rs 32.8 1 Kg × Rs 95
Rs19,486.8
1,296 kgs
Rs20,803
400 Kgs
Rs 3286.8
Rs 585.0 1,200 kgs
Loss
Rs 585.0
17,471.8
1,200 kgs
36 kgs 1,164kgs
(i)
Actual
Rs 600
20,071.8
1,296 kgs
36kgs Rs 17,471.8
1,164kgs
Rs 20,071.8
1,164 Kgs
Fruit extract (6,400 less 7,600)
Rs 1,200(Adverse)
Glucose syrup (7,000 less 8,400)
Rs1,400(Adverse)
Total
Rs 2,600(Adverse)
* (Std qty × Std price less Std qty × Revised Std price) (ii) Ingredients operating variances Total (19,486.8 less 20,803)
= Rs 1,316.2(Adverse)
Ingredients Price variance (Revised Material Price – Actual Material Price) × ( Actual Qty Consumed) Variance in Rs (19 – 18) × 428
Fruit extract
428(F)
Glucose syrup Pectin Citric acid
Nil (33.2 – 32.8) × 125
50(F)
(200 – 95) × 1
105(F) 583(F)
Usage variance (Std Qty on Actual Production less Actual Qty on Actual Production)
× Revised Std Price/Unit
Rs
Variance in Rs
Fruit extract
(400 – 428) × 19
532(A)
Glucose syrup
(700 – 742) × 12
504(A)
Pectin
(99 – 125) × 33.2
863.2(A)
Citric acid
Nil 1,899.2(A)
(iii) Mix Variance
(Actual usage in std mix less Actual usage in actual mix ) × std price Variance in Rs Fruit extract
(432 – 428) × 19
21,403
132
Planning variances *
Rs 95
76(F)
Rs 21,403
86
Glucose syrup
(756 – 742) × 12
168 (F)
Pectin
(106.92 – 125) × 33.2
600.3(A)
Citric acid
(1.08 – 1) × 200
16(F) 340.3 (A)
Yield variance (Actual yield – Std yield from actual output) × Std cost per unit of output = (1,164 – 1,296 × 0.97) ×
19486.8 = 1,558.9(A) 1164 Labour operating variance
585 – 600 = 15(A) (iv) Total variance = Planning variance + Usage Variance + Price Variance + labour operating Variance.
Or Total Variance = (2,600) + ( 1,899.2 ) + 583 + (15) = 3931.2 (A). Ans.26: Standard hours produced Product X 1,200 8 9,600
Out put (units) Hours per unit Standard hours
Product Y 800 12 9,600
Total
19,200
Actual hours worked 100 workers × 8 hours × 22 days =
17,600
Budgeted hours per month 1,86,000/12 =
15,500
actual hours 17,600 = × 100 = Budgeted hours 15,500
Capacity Ratio =
Efficiency Ratio =
Activity Ratio =
113.55 %
Standard Hours Produced 19,200 × 100 = × 100 Actual hours 17,600
Standard Hours Produced 19,200 × 100 = × 100 Budget hours 15,500
Relationship : Activity Ratio = Efficiency Ratio × Capacity Ratio
or
123.87 =
109.09 × 113.55 100
Ans: 27: (1) Capacity Ratio = Actual working Hours Budgeted working hours
x 100
109.09%
123.87%
87
= 25 days x 8 hours x 50 workers 8,500 hours (i.e.,1,02,000/12)
x 100
=117.65%
(2) Activity Ratio =Actual production in standard hours x 100 Budgeted hours =(1,000 units x 5 hours) + (600 units x 10 hours) 8,5000 hours (3) Efficiency Ratio =Standard hours for actual production Actual hours
x 100
=129.41%
x 100
=110% =(1,000 units x 5 hours ) + (600 units x 10 hours) x 100 10,000 hours Inter – relationship Capacity Ratio x Efficiency Ratio =Activity Ratio 117.65% x 110% =129.41%
Ans. 28: Report to the Departmental Manager showing the cost ratios: Standard hours produced 2112 = × 100 = 110% Actual hours worked 1920 Standard hours produced 2112 Activity Ratio = = × 100= 82.50% Budgeted Std. Hours 2560
(a) Efficiency Ratio = (b)
Budgeted Std. Hours 2560 = × 100= 80% Maximum Possible Hours 3200 Actual hours worked 1920 (d) Actual Capacity utilisation Ratio = = × 100= 75% Budgeted hours 2560
(c) Standard Capacity usage Ratio =
(e) Calendar Ratio =
24 × 100 = 96% 25
(ii) Report to the Departmental Manager Setting out the analysis of variances Standard fixed overhead rate per hour =
15360 = Rs.6 2560
A. Fixed Overheads (a) Charged to production (2112 × 6)
Rs. 12672
(b) Actual hours × Std. rate (1920 × 6) (c) Revised budgeted hours × Std. rate (24×8×16×
11520 80 100
×6)
14746
(d) Original budgeted overheads
15360
(e) Actual overheads
16500
Variances: Efficiency variance (a-b) Capacity variance (b-c)
1152(F) 3226(A)
88
Calendar variance (c-d)
614(A)
Volume variance (a-d)
2688(A)
Expenditure variance (d-e)
1140(A)
Total variance
3828(A)
B. Variable overheads: Standard variable overhead rate per hour =
20840 2560
=Rs.8
(a) Charged to production (2112 × 8) (b) Actual hours × Std. rate (1920 × 8)
16896 15360
(c) Actual overheads
14500
Variances: Efficiency variance (a-b) Expenditure variance (b-c)
1536(F) 860(F)
Total variance (a-c)
2396(F)
Working note: Maximum possible hours (25×8×16)
3200
Budgeted hours: 3200 less 20% downtime
2560
Actual hours
1920
Budgeted standard hours
2560
Standard hours produced
5112
Budgeted working days
25
Actual working days
24
Ans. 29: Maximum capacity in a budget period = 50 employees × 8 hrs.×5 days×4 weeks = 8,000 hrs. Budgeted hours 40 employees ×8 hrs.×5 days×4 weeks = 6,400 hrs. Actual hrs. = 6,000 hrs. (from the sum) Standard hrs. for actual output = 7,000 hrs. Budget no. of days = 20 days = 20 days (4 weeks ´5 days) Actual no. of days = 20-1 = 19 days 1. Efficiency ratio =
Standard Hrs × 100 = {(7000 ÷ 6000) × 100} = 116.67% Actual Hrs
2.
Activity ratio = {(7,000÷6,400)×100} = 109.375%
3.
Calendar Ratio = (Available working days ÷ budgeted working days) × 100
89
4.
5.
6.
= {(19÷20)×100} = 95% Standard Capacity Usage Ratio = (Budgeted hours ÷ Max. possible hours in the budgeted period) × 100 = {(6,400÷8,000)×100} = 80% Actual Capacity Usage Ratio = (Actual hours worked ÷ Maximum possible working hours in a period) × 100 = {(6,000÷8,000)×100} = 75% Actual Usage of Budgeted Capacity Ratio = (Actual working hours ÷ Budgeted hours) × 100 = {(6,000÷6,400)×100} = 93.75%
Ans.30: (i)
(ii)
(iii)
Dr. Material Control A/c Dr. or Cr. Material Price Variance A/c Cr. Creditors A/c (Being price variance during purchase of materials) Dr. WIP Control A/c Dr. or Cr. Material Usage Variance A/c Cr. Material Control A/c (Being recording of usage variance at Standard cost of excess/under utilized quantity) Dr. Wages Control A/c Dr. or Cr. Labour Rate Variance A/c Cr. Cash (Being entry to record wages at standard rate)
Ans. 31:(A) The cost sheet for 900 units will appear as under : Cost
Std. qty.
Std. rate
Std.cost Rs.
Direct material
9,000
1.00
9,000
Direct labour
2,250
3.00
6,750
Overheads
2,250
6.00
13,500 29,250
(B) Calculation of variances: Material price variance
= 9,500 Pcs. (Re. 1.00 – Rs.1.10) = Rs. 950 (A)
Material usage variance
= Re. 1.00 (9,000 pcs. – 9,500 pcs.) = Rs. 500 (A)
Labour rate variance
= 2,475 hrs. (Rs. 3.00 – Rs. 3.50) = Rs. 1,237.50 (A)
Labour efficiency variance
= Rs. 3.00 (2,250 hrs. – 2,475 hrs.) = Rs. 675(A)
Overhead variances : (a) Charged to production as per cost sheet
Rs. 13,500 (b) Actual
90
hours × Std. rate: 2,475 hrs. × Rs. 6
Rs.
Overheads as per budget
Rs. 16,500
(d) Actual overheads
Rs. 17,000
Efficiency variance :
(a – b) Rs. 1,350 (A)
Capacity variance :
(b – c) Rs.1,650 (A) (idle time)
Expense variance :
(c – d) Rs. 500 (A)
14,850
(c)
(a – d) Rs. 3,500 (A) Total variance : (C) The. journal entries for recording these transactions are as under
(i)
Material Control A/c
Dr.
Dr.
Cr.
Rs.
Rs.
11,000 11,000
To General Ledger Adjustment A/c (Being the purchase value of 10,000 pieces of materials at Rs. 1.10 each) (ii) Work-in-Progress A/c
Dr.
10,450
To Material Control A/c
10,450
(Being the cost of 9,500 pieces of materials actually issued to production at the actual price of Rs. 1.10 each) (iii) Work-in-Progress A/c
Dr. 8,662.50
To Wages Control A/c
8,662.50
(Being the actual amount of direct wages paid for 2,475 hours at Rs. 3.50 per hour (iv) Work-in-Progress A/c
Dr. 17,000
To Overhead Expense Control A/c
17,000
(Being the actual overhead expenses incurred) (v) Finished Stock Control A/c
Dr. 29,250
To Work-in-Progess A/c
29,250
(Being the standard cost of production transferred to finished goods account) (vi) Cost of Sales A/c To Finished Stock Control A/c
Dr. 29,250 29,250
(Being the standard cost of goods sold transferred to Cost of Sales A/c) After the basic transactions are posted, the materials control account will show the actual value of stock of material in hand and the work-in-progress account will show a balance representing the cumulative variances on all the accounts and closing balance of work-in- progress at standard cost. The variances have already been analysed in Para (B) above and they will be carried to the respective accounts pending investigation before being finally disposed off. In this problem we have assumed that there is no closing balance of work-in- progress. (D) The journal entries for transferring the variances to their respective
91
accounts are as under price variance A/c Material usage variance A/c Labour rate variance A/c Labour efficiency variance A/c
Dr. Dr. Dr. Dr.
Rs. 950.00 500.00 1,237.50 675.00
Overhead efficiency variance A/c
Dr.
1,350.00
Overhead capacity variance A/c
Dr.
1,650.00
Overhead expense variance A/c
Dr.
500.00
To work-in-progress A/c (E) The ledger accounts will appear as under: Dr.
Rs. Material
6,862.5
Material Control A/c
Cr.
Rs. To Opening balance
-
To General Ledger
Rs. By Work-in-Progress A/c
10,450
By Balance c/d
Adjustment A/c
550
11,000 11,000
11,000
Work-in-Progress Control A/c To To To To
Rs. Opening balance – Material control A/c 10,450.00 Wages control A/c 8,662.50 Overheads control A/c 17,000.00
36,112.50
Rs. By Finished stock control A/c 29,250.00 By material price variance A/c 950.00 By material usage variance A/c 500.00 By labour rate variance A/c 1,237.50 By labour efficiency variance A/c 675.00 By overhead efficiency A/c Variance A/c 1,350.00 By overhead capacity Variance A/c . 1,650.00 By overhead expense Variance A/c 500.00 36,112.50
Ans. 32:(A)Computation of variance: (i) Material price variance: 8,600 pcs. (Rs. 2.15 – Rs. 2.50) = Rs. 3,010 (A) (ii) Material usage variance: Rs. 2.15 (8,400 Pcs. – 8,600 Pcs.) = Rs. 430 (A) [Standard requirement of materials = 2,800 units produced × 3 pcs. per unit = 8,400 pcs.] (iii) Labour efficiency variance: Dept. A: Standard time required = 2,800 pcs. × 2 hrs. = 5,600 hours. Dept. B: Standard time required = 2,800 pcs. × 4 hrs. = 11,200 hours. Variances : Dept. A: 1.75 (5,600 – 5,200) = Rs. 700 (F) Dept. B: 1.50 (11,200 – 12,000) = Rs. 1,200 (A) (iv) Overheads variances:
92
(i)
Material Control A/c Material price variance A/c To Creditors A/c (ii) Work-in-Progress Dept. A. A/c Material usage variance A/c To Material Control A/c (iii) Work-in-progress Dept. A. A/c To wages control A/c (iv) Wages Control A/c To Labour Efficiency Variance Dept A A/c (v) Work-in-Progress Dept. B A/c. Labour Efficiency Variance Dept. B A/c To Wages Control A/c (vi) Work-in-Progress Dept. A A/c Overhead Capacity Variance Dept. A. A/c To Overhead Efficiency Variance Dept. A. A/c To Overhead Expense Control Dept. A A/c (vii) Work-in-Progress Dept. B A/c Overhead Efficiency Variance A/c Overhead Expenses Variance A/c To Overhead Control Dept. B A/c (viii) Work-in-Progress Dept. B A/c To Work-in-Progress Dept. A A/c (Being the transfer at standard cost of finished Production of Department A to Department B for processing in Department B) (ix) Finished Stock control A/c
Dr. Dr.
18,490 3,010 21,500
Dr. Dr.
18,060 430 18,490
Dr.
9,800 9,800
Dr.
700 700
Dr. Dr.
16,800 1,200 18,000
Dr. Dr.
2,800 400 200 3,000
Dr. Dr. Dr.
11,200 800 500 12,500
Dr.
30,660 30,660
Dr.
58,660
93
To Work-in-Progress Dept. B A/c
58,660
94
95
Ans.33:All figures of Ans. 31are 5 times of Ans. 32 Ans. 34: Material – 1 Rate Variance = Standard cost of material purchased – Actual cost = Rs24, 000 – Rs21, 600 = Rs2, 400 (F) Material – 2 Quantity Variance
= SR × SQ – SR × AQ = Rs900 × 80 units – Rs75, 600 = Rs3, 600 (A)
Labour Spending Variance
= SR × AH – AR × AH = Rs24/per hour × 2300 hours – Rs51, 750 = Rs3, 450 (A)
Labour Efficiency Variance
= SR × (SH – AH) – 7200
= 24 (SH – 2300)
SH
= 2000 Hrs. Rs
Total Cost of material purchased
1,27,200
Less Purchase Value of Material – 2
1,05,600
Cost of material –1 Working Notes:
21,600
(1) Standard Cost of Material – 2 actually consumed in production = Rs72, 000 (Given) Standard cost of Material – 2 per unit: 5 litres × Rs180 ∴No of units produced Total material – 1 used in production Add Closing Inventory Less Opening Inventory Hence Standard Cost of Material – 1 purchased
= Rs900 = Rs72, 000 / Rs900 = 80 units = Rs18, 000 (Given) = Rs6, 000 (Given) =0 = Rs24, 000
96
(2) Standard Rate of Material -1
= Rs24, 000 / 1,000kg = Rs24 per kg
Standard Cost of Material – 1
= Rs18, 000
Add favourable Quantity Variance
= Rs1, 200
Material – 1 allowed
= Rs19, 200
Standard quantity of Material – 1 allowed
= Rs19, 200/Rs24= 800 Kg.
Standard quantity per unit
= 800kg/80units = 10 kg
Standard purchase price for Material – 2
= (550liters × Rs180)= Rs99, 000
Add unfavourable Rate Variance
= Rs6, 600
Actual cost Price of Material – 2
= Rs1, 05, 600
(3) Opening balance of Material – 2
= Rs18, 000
Add Standard Cost of Purchase (550 litres × Rs180)
= Rs99, 000
Less Closing Balance
= Rs41, 400
Material-2 Consumed at Standard cost
= Rs75, 600
Ans. 35: (i) Budgeted Machine Hours: We know that: Volume variance =
Std. fixed overhead Std. machine hours rate per hour
for actual output
−
Budgeted machined hours for actual output
or Rs.80,000 (Fav.) = Rs.100 (11,300 – Y) or 800
= 11,300 – Y
or Y = (11,300 – 800) hours or Y = 10,500 hours Hence budgeted machine hours for actual output are 10,500 hours. (ii)
Actual machine Hours: We know that: Efficiency variance =
Std. variable overhead Std. hours for rate per hour
or Rs.36,000 (Fav.)
Actual hours − actual output for actual output
= Rs.60 (11,300 hours – X)
or 600
= 11,300 hours – X
or X
= 10,700 hours.
Hence Actual machine hours are 10,700 hours. (iii) Applied Manufacturing Overhead: Applied Manufacturing overhead Actual overhead incurred + Total Variance = Rs.16,50,000 + Rs.30,000 (Refer to working note) = Rs.16,80,000 Hence total applied manufacturing overhead are Rs.16,80,000.
97
(iv) Total Amount of Fixed Overhead Cost: We know that: Spending variance = (Flexible budget for actual hours – Actual factory overhead incurred) Rs.86,000 (Adv.) = 10,700 hours × Rs.60 + total amount of fixed overhead) – Rs.16,50,000) Rs.86,000 (Adv.) = (Rs.6,42,000 + Total amount of fixed overhead cost (budgeted) – Rs.16,50,000) Total amount of fixed overhead cost = Rs.10,08,000 – Rs.86,000 = Rs.9,22,000 Total amount of fixed overhead cost = Rs.9,22,000 Working note: Given that: Spending variance (Rs.)
86,000 (Adv.)
Efficiency variance (Rs.)
36,000 (Fav.)
Volume variance (Rs.)
80,000 (Fav.)
Therefore, Total variance = Spending variance + Efficiency variance + Volume variance = Rs.86,000 (Adv.) + Rs.36,000 (Fav.) + Rs.80,000 (Fav.) = Rs.30,000 (Fav.) Alternative approach: Total factory overhead variance = {factory overhead applied - actual factory overhead incurred} = (Std. hours for actual output × Budget rate per hour – Actual cost incurred) = (11,300 hours × Rs.160 – Rs.16,50,000) = Rs.1,58,000 (Fav.) Under alternative approach, Applied Manufacturing Overhead and Total Amount of Fixed Overhead Cost would come to Rs.18,08,000 and Rs.10,50,000. Budgeted and actual machine hours would come to 10,500 and 10,700. Spending, Efficiency and Volume Variances would come to Rs.42,000 (Fav.), Rs.36,000 (Fav.) and Rs.80,000 (Fav.) respectively.
Ans. 36: (1)
Actual material cost incurred
Material cost variance = Standard cost of material of actual output – Actual material cost incurred Standard variable of material Material cost − variance of actual output
Or Actual material cost incurred =
= (10,000 units × 2 units× Rs.15 + Rs.50,000) = Rs.3,00,000 + Rs.50,000 (2) Standard cost of materials actually consumed Material price variance = (Standard cost – Actual cost) Actual quantity consumed Actual material Material price + variance cost incurred
Or Standard cost of materials actually consumed = = Rs.3,50,000 – Rs.70,000 = Rs.2,80,000 (3) Labour efficiency variance (Refer to working note 1)
98
Standard hours for Actual hours Standard rate = − per hour worked actual output
= (10,000 units × 3 hours – 35,000 hours) Rs.20 = (Rs.6,00,000 – Rs.7,00,000) = Rs.1,00,000 (Adv.) (4) Variable OH efficiency variance (Refer to working note 2) =
Standard variable overhead Standard rate per hour
hours
−
Actual
hours
= Rs.5 (30,000 hours – 35,000 hours) – Rs.25,000 (Adv.) (5) Variable OH expenditure variance (Refer to working note 1)
Budgeted variable overhead Actual variable − overhead for actual hours
=
= (Rs.5 × 35,000 hours – Rs.2,00,000) – Rs.25,000 (Adv.) (6) Fixed OH efficiency variance (Refer to working notes 1 & 2)
Standard fixed overhead Standard hour for Actual = − − actual ouput hours rate per hour = Rs.5 (30,000 hours – 35,000 hours) = Rs.25,000 (Adv.) Fixed OH capacity variance (Refer to working notes 1 & 2)
Standard variable overhead Actual capacity Budgeted = − − capacity hours rate per hour hours = Rs.5 (35,000 hours – 50,000 hours) = Rs.75,000 (Adv.) (7) Fixed OH volume variance (Refer to working note 3) =
Standard variable overhead Actual
Budgeted
− output output
rate per hour
= Rs.15 10,000 units −
50,000 hours 3 hours
= Rs.1,50,000 – Rs.2,50,000 = Rs.1,00,000 (Adv.) Working notes: 1.
Labour rate variance: = (Standard rate per hour – Actual rate per hour) Actual hours (x) Or Rs.50,000 = 20x – Rs.6,50,000 Or x = 35,000 hours
2.
Standard hours = 10,000 units × 2 hours = 30,000 hours
30,000 hours × 100 = 50,000 hours 60
Budgeted hours =
Budgeted fixed overhead
= Actual fixed overhead + Expenditure variance = Rs.3,00,000 – Rs.50,000 = Rs.2,50,000
99
Standard fixed overhead recovery rate per hour
=
Total overhead rate per hour
= Rs.10
Rs.2,50,000 50,000 hours
= Rs.5 per hour
Variable overhead rate per hour = Rs.5 (Rs.10 – Rs.5) 3.
Standard fixed overhead per unit = Rs.15 (3 hours × Rs.5/-)
Ans. 37: Working notes: 1.
(a) Budgeted fixed overhead per unit: = (Budgeted fixed overheads p.a / Budgeted output for the year) = Rs.4,80,000 p.a. / 1,20,000 units = Rs.4 per unit. (b) Budgeted fixed overhead hour: = Budgeted fixed overhead per unit / Standard labour hours per unit = Rs.4 / 2 hours = Rs.2 per hour
2.
(a) Standard cost per unit: Rs. Direct material
20
(5 kg × Rs.4/- per kg) Direct labour
6
(2 hours × Rs.3/- per hour) Fixed overhead
4
(2 hours × Rs.2) Total standard cost (per unit)
30
(b) Budgeted selling price per unit Standard cost per unit
30
Standard profit per unit
10
(25% on slaes or 33 – 1/3% of standard cost) Budgeted selling price per unit 3
40
(a) Actual output units for April, 2001: Fixed overhead volume Variance = Efficiency variance + Capacity variance or (Budgeted output units – Actual output units) Budgeted fixed overhead p.u. Rs.2,400 (Favourable) + Rs.4,000 (Adverse) = Rs.1,600 (Adverse) or (10,000 units – x units) Rs.4 – Rs.1,600 (Adverse) or (10,000 units – 400 units) = x (Actual output units) or Actual output units = 9,600 units (b) Actual fixed overhead expenses: (budgeted fixed overhead – Actual fixed overhead) = Fixed overhead expenses variance or (Rs.40,000 – x) = Rs.1,400 (Favourable)
100
or x = Rs.40,000 – Rs.1,400 = Rs.38,600 4.
(a) Actual sales quantity units: Sales volume variance
Actual sales
Budgeted
quantity units quantity units
= Budgeted margin per unit
−
= Rs.4,000 (Adverse) = Rs.10 (x – 10,000 units) or 400 units = x – 10,000 units or x (Actual sales quantity) = 9,600 units (b) Actual selling price per units
Actual Selling Budgeted selling Actual − Sales units price per unit price per unit
Sales price variance =
or Rs.9,600 (Fav.) = (x – Rs.40) × 9,600 units or Actual selling price per unit = Rs.41/5.
(a) Actual quantity of material consumed:
Standard Actual Standard price − quantity quantity per unit
Material usage variance =
or 6,400 (Adv.) = (9,600 units × 5 kgs.) Rs.4 or x kgs. = 49,600 kgs. (actual quantity of material consumed) (b) Actual price per kg: Actual price per kg.: Material price variance = (Standard price per kg – Actual price per kg) Actual quantity of material consumed
6.
-Rs.4,960
=
(Rs.4 –Rs. y per kg.) 49,600 kg.
-0.1
=
(Rs.4 – Rs. y per kg)
or y
=
Rs.4.10 per kg.
(a) Actual direct labour hour used: Labour efficiency variance = (Standard hours – Actual hours) Standard rate per hour Rs.3,600 (Favourable)
= (9,600 units × 2 hours – p hours) Rs.3
Rs.3,600 (Favourable)
= (19,200 hours – p hours) Rs.3
P hours
= (19,200 hours – 1,200 hours) – 18,000 hours (Actual direct labour hours)
(b) Actual direct labour hour rate:
Standard
Labour rate variance =
−
Actual rate Actual Direct
rate per hour per hour
labour hours
Rs.3,600 (Adverse) = (Rs.3 per hour – t per hour) 18,000 hours or t
= Rs.3 + Rs.0.20 – Rs.3.20 per hour
101
(actual direct labour hour rate) 7.
Actual fixed overheads: Fixed overhead expense variance
= Budgeted fixed overhead – Actual fixed overhead
or Rs.1,400 (Favourable)
= 10,000 units × Rs.4 p.u. – Actual fixed overhead
or Actual fixed overhead
= Rs.40,000 – Rs.1,400
or Actual fixed overhead
= Rs.38,600 Annual financial Profit /Loss Statement (for April, 2001)
Account (a) Sales: (A)
Qty./ Hours
Rate/Price
Actual/ Value
(b)
(c)
(d)=(b)×(c)
9,600 units
41
3,93,600
49,600 kgs.
4.10 per kg.
2,03,360
18,000 hours
3,20 per hour
57,600
18,000 hours
2.14444 per hour
38,600
(Refer to working note 4) Direct Materials (Refer to working note 5) Direct labour (Refer to working note 6) Fixed Overheads (Refer to working note 6 (a) and 7) (Rs.38,600/18,000 hours) (absorbed on direct labour hour basis) Total costs: (B)
2,99,560
Profit : [(A) – (B)]
94,040
Ans: 38. Working notes: 1. Direct material units in actual output Output of units produced Add: Closing WIP units (200 units x 50% complete) Less: Opening WIP units (300 units x 100% complete) Total direct material units in actual output (work done)(i.e. units introduced) 2.
(Units) 7,620 100 (300) 7,420
Basic data of direct materials
Standard Data Standard quantity of material 11.130 (7,420 units x 1.5 kgs.)
S.P./ KG. Rs.
Amount Rs.
Actual output units Actual Data Actual qty. of material kgs.
24
2,67,120
11,224
7,420 A.P./KG. Rs.
Amount Rs.
23.75
2,66,570
3. Direct wages and overhead units in actual output Output of units produced Add: Closing WIP units (200 units x 40% complete) Less: Opening WIP units (300 units x 60% complete) Total direct wages and overhead units in actual output (work done)(i.e. units introduced) 4. Basic data of direct wages Actual output units Standard Data Actual Data
(Units) 7,620 80 (180) 7,520 7,520
102
Standard Labour hours
S.W./ hour Rs.
Amount Rs.
Actual Labour hours
A.W./ hour Rs.
Amount Rs.
22,560 (7,520 units x 3 hours)
400
90,240
22,400
4.30
96,320
5.
Budgeted variable overhead per unit
= Difference in factory overhead Difference in output = Rs.92,400 – Rs.81,600 (7,500 units – 6,000 units) =Rs.7.20 per unit
6 Budgeted fixed overheads Total overhead on 8,000 units Less: Variable overhead of Budgeted fixed overheads
(8,000 units x 12 0 8,000 units @ Rs.7.20 per unit
7. Basic data for variable overhead Budgeted data Budgeted variable overhead For actual hours (22,400 hours x Rs.2.40 Standard hours required per unit Standard variable overhead rate p.u
Rs.53,760 3 Rs.7.20
Standard variable overhead rate p.u.
Rs.38,400
Budgeted output Budgeted hours Standard fixed overhead rate per hour Standard fixed overhead p.u Standard hours required p.u.
2. Material price variance
3. Material cost variance
Labour variances 1. Labour efficiency variance
2. Labour rate variance
3. Labour cost variance
Variable Overhead variances
Rs.58,240 7,520 22,400 Rs.2.60
Rs.240
8. Basic data for fixed overhead Standard / Budgeted data Budgeted fixed overhead
Computation of Variances: Material variances 1. Material usage variance
Actual data Actual variable overhead Actual output units Actual hours Actual variable overhead Recovery rate per hour
(Rs.) 96,000 (57,600) 38,400
8,000 units 24,000 Rs.1.60 Rs.4.80 3
Actual data Actual fixed overhead (Rs.96,440 – Rs.58,240) Actual output Actual hours
Rs.38,200 7,520 units 22,400
= =
(S.Q.-A.Q.) S.P. (11,130 kgs.-11,224 kgs.) Rs.24
=Rs.2,256 (A)
= =
(S.P.-A.P.) A.Q (Rs.24-Rs.23.75) 11,224 kgs.
=Rs.2,806 (F)
= =
(S.C.-A.C.) (Rs.2,67,120-Rs.2,66,570)
=Rs.550 (F)
= =
(S.H.-A.H.) S.R. (22,500 hours- 22,400 hours) Rs.4
=Rs.640 (F)
= =
(S.R.-A.R.) A.H (Rs.4-Rs.4.3) 22,400 hours
=Rs.6,720 (A)
= =
(S.C.-A.C.) (Rs.90,240 - Rs.96,320)
=Rs.6,080 (A)
103
1. Variable overhead Expenditure variance
={ Budgeted variable overhead – Actual variable overhead} = (Rs.53,760 – Rs.58,240) =Rs.4,480 (A) =Standard variable {Standard hrs. – Actual hrs} overhead rate per hour =Rs.2,40 (22,560 hrs – 22,400 hrs) =Rs.384 (F)
2. Variable overhead Efficiency variance
3. Total variable overhead cost variance = { Standard variable overhead –Actual variable overhead} = (7,520 units x Rs.7.20 – Rs.58,240) Fixed Overhead variances 1. Expenditure variance
=Rs.4,096 (A)
={ Budgeted fixed overhead – Actual fixed overhead} = (Rs.38,400 – Rs.38,200) =Rs.200 (F) = { Budgeted volume – Actual volume} Standard fixed overhead rare per unit
2. Volume variance
=(8,000 units – 7,520 units) Rs.4.80 3. Efficiency variance
=Rs.2,304 (A)
= { Standard hours for actual production –Actual hours} Standard fixed overhead rate per hour = 22,560 hours – 22,400 hours) Rs.1.60 =Rs.256 (F) ={Budgeted hours – Actual Hours } standard fixed overhead rate per hour = (24,000 hours – 22,400 hours ) Rs.1.60 =Rs.2,560 (A)
4.Capacity variance
5.Total fixed overhead cost variance ={Fixed overhead recovered – Actual overhead} ={7,520 units x Rs.4.80 – Rs.38,200} =Rs.2,104 (A) Ans. 39:
Statement of Equivalent Production in Units Particulars
Wages & Overhead
Materials
Units Completed Closing W.I.P.
% age
Units %age
Units
100% 100%
9000 100% 900 50%
9000 900
9900
9900
Equivalent Units
Material Variances Standard qty for actual output ** x std price Material A
19,800 @ 3
Material B
9,900 @ 4 29,700
= 59,400
Actual qty X actual price 22,
[email protected]*
= 39,600 10,889 @4.1* 99,000
33,165
= 62,370 = 44,649 1,07,019
*Actual Cost / Actual Quantity ** Standard Quantity for actual output = ( std qty/ budgeted prod) x actual output MCV = TSC – TAC = 99,000 – 1,07,019 = 8,019 (A) MPV = AQ (SP – AP) A
= 22,275 (3 – 2.80) =
4,455 (F)
B
= 10,890 (4 – 4.10) =
1,089 (A)
104
3,366 (F) MUV = SP (SQ – AQ) A
= 3 (19,800 – 22,275) =
7,425 (A)
B
= 4 (9,900 – 10,890) =
3,960 (A) 11,385 (A)
MMV = SP (RSQ – AQ) A
= 3 {19,800 ÷ 29,700 × 33,165 – 22,275} =
495 (A)
B
= 4 {9,900 ÷ 29,700 × 3,165 – 10,890}
660 (F)
=
165 (F) MYV
= S. C Per Unit (S. O. For Actual Mix – A. O.) = 99,000 ÷ 9,900 {9,900 ÷ 29,700 × 33,165 – 9,900} = 10 (11.055 – 9,900) = 11,550 (A)
Labour Variances: LCV
= TSC – TAC = 2,40,000 ÷ 12,000 × 9,450 – 1,91,250 = 2,250 (A)
LRV
= AH (SR – AR) = 48,000 {4 – (1,91,250 ÷ 48,000)} = 750 (F)
LITV
= No. of Idle hours × SR = 48,000 – (47,500 ÷ 4) = 1,200 (A)
LEV
= SR (SH – AH) = 4 {(60,000 ÷ 12,000) × 9,450 – 47,700} = 1,800 (A)
(ii)
Variable Overhead Variances
VOC
= Recovered Overheads – Actual Overheads = 9,450 × 5 – 45,000 = 2,250 (F)
V.O (Exp.) V
= Standard V.O. – Actual V.O. = 47,700 × 1 – 45,000 = 2,700 (F)
V.O. (Eff.) V
= Recovered Overheads – Standard Overheads = 9,450 × 5 – 47,700 = 450 (A)
Fixed Overheads Variances FOCV
= Recovered Overheads – Actual Overheads = (1,20,000 ÷ 12,000) × 9,450 – 1,20,900 = 94,500 – 1,20,900 = 26,400 (A)
F.O.(Exp.) V
= Budgeted Overheads – Actual Overheads = 1,20,000 – 1,20,900 = 900 (A)
FOVV
= Recovered Overheads – Budgeted Overheads = 95,500 – 1,20,000 = 25,500 (A)
Sales Variances Sales Price Variance
= Actual Unit Sold (SP – AP)
105
= 9,000 {50 – (4,57,500 ÷ 9,000)} = 7,500 (F) Sales Volume Variance (Contribution Loss) = S. R. of Profit (Budgeted Qty. – Actual Qty.) = (60,000 ÷ 12,000) (12,000 – 9,000) = 15,000 (A) Ans 40:. (a) sales Variance Present Market size
=60,000 units. 16 100
At 16% the share should have been = 60,000 x
=9,600 units.
Standard Gross Margin : SP Rs.53 – ( DM Rs.9 + DL Rs.24 + VO Rs.4 + FO Rs.12) = Rs.4 Budgeted Qty. Revised Budgeted Actual Qty. Booked Actual Qty. Std. Gross Margin Qty Supplied (Rs.) 8,000 9,600 8,200 7,500 4
Budgeted Qty. x Std. G.M. 32,000
Revised Budgeted Qty x Std. G.M. 38,400
Actual Qty. Booked x Std. G.M. 32,800
Actual Qty. Supplied x Std.G.M. 30,000
Actual G.M.
5
Market size variance 32,000 - 38,400 Market share variance 38,400 – 32,800 Sales volume variance 32,800 – 30,000 Sales price variance 30,000 – 37,500 Sales Margin Production Quantity Variance = (7500-8200)X4
(Rs.) Actual Qty. supplied x Actual G.M. 37,500
=6,400 F =5,600 A =2,800 A =7,500 F = 2800 A
[Note: Since actual order received ≠ actual sales quantity, Market share variance will be on the basis of actual order received and we will also calculate one further variance regarding inefficiency of production department about fulfilling order quantity, Sales Margin Production Quantity Variance = (Actual sales quantity – Sales order quantity) × Std. margin p.u. While calculating all other variance sales order quantity shall be ignored.] (b) Direct Material Variances (Units) Production 7,500 - Op. Stock 600 + Cl. Stock 300 Introduced 7200 Std. Qty.
Actual Qty.
S.P.
10,800
12,000
Rs. 6
Usage Variance Price Variance Total Variance
Std. requirement 7,200 units @ 1.5 kg.
Std. Qty. x SP Rs. 64,800
Actual Qty. x SP Rs. 72,000
Rs.64,800 – Rs.72,000 Rs.72,000 – Rs.78,000 Rs.64,800 – Rs.78,000
(c ) Direct Labour Variance Production Less: Op. Stock
75 600 x 100
Add: Cl. Stock
60 300 x 100
7,500 450
180 7,230
=10,800 kg.
AP
Actual Qty. x AP Rs. 78,000
Rs. 6/50
=Rs.7,200 A =Rs.6,000 A =Rs.13,200 A
Std. hours produced 7,230 x 4
= 28,920
106
Std. Hours
Actual Hours
S.R.
28,920
29,000
Rs. 6
Efficiency Variance Rate Variance Total variance
Std. Hrs. x SR Rs. 1,73,520
Actual Hrs. x SR Rs. 1,74,000
AR
Actual Hrs. x AR Rs. 1,81,250
Rs. 6 / 25
(1,73,520 – 1,74,000) (1,74,000 – 1,81,250)
=480 A =7,250 A =7,730 A
(d) Variable Overheads Variance Rs. 28,920
Efficiency variance
=Rs.80A
=Std. Cost of Actual Hours 29,000 x 1
29,000
Expenditure variance
=Rs.7,000 A
=Actual Overheads
36,000
A
=Charged to Production 28,920 x 1
B
C
A – C Total V
=Rs.7,080 A
(e) Fixed Overhead Variance (Rs.) A = Charged to Production 28,920 x 3 B = Std. Cost of Act. Hrs. 29,000 x 3 C = Budget D = Actual Efficiency Variance (86,760 – 87,000) Volume Variance (86,760 – 94,000)
86,760 87,000 96,000 94,000 =Rs.240 (A) =Rs.9,240 (A)
Ans. 41:
(1)
(2) (3)
(4)
Budgeted contribution = Budgeted Profit + Budgeted Fixed Cost Plus Contribution quantity variance Total Standard contribution Standard Contribution per unit Actual Sales Volume Actual Sales Volume 10,600 × 17 Actual quantity of Raw Materials used Standard consumption 10,600 × 5 400 Add: Material Usage Variance .2 Actual consumption Labour Efficiency variance Standard labour cost for Standard hours (63,000 + 600) Standard labour cost for actual hours
Rs. 15,000 + 15,000 = 30,000 1,800 31,800 3 10,600 units 1,80,200 2,000 Kgs. 2,000 kgs. 55,000 Kgs. 63,600 61,950
107
(5)
Labour efficiency variance Actual variable overhead Selling Overhead variance – Variable overhead
(6)
Variable Overhead efficiency variance Actual hours (AH) Standard hours (SH) Standard rate per hour (SR)
(7) (8)
1,650 F Rs. 84,800 − Rs. 1,800 = Rs. 83,000
61,950 1.5
41,300 hours
60,600 × 4
42,400 hours Rs. 1.5
63,600 10,600 × 4
Efficiency variance SR (SH – AH) = 2 (42,400 – 41,300) = 2,200F Actual fixed overheads: Budgeted Overhead + Fixed Overhead variance = 15,000 + 600 = Rs. 15,600. Operating profit variance If budgeted profit is considered (15,000 – 7,000) = Rs. 8,000 adverse If standard profit is considered (16,800 – 7,000) = Rs. 9,800 adverse
Ans. 42:
Where RSQ B = Revised Standard Quantity of ‘B’ = (Actual total qty of all DM used) × Standard Mix %age of ‘B’ and SQ B = Standard quantity of DM ‘B’ for Actual Production = Standard quantity of all DM allowed for actual output × Standard Mix %age of ‘B’ Since Standard Mix %age is the same for both ‘A’ and ‘B’ (1: 1) we have, Total Yield variance for ‘A’ and ‘B’= T × (Std price of ‘A’ + Std price of ‘B’) Where T = (Std qty of all DM allowed for actual output - Actual total qty of all DM used)× 0.5 As Total Yield variance for ‘A’ and ‘B’ is given as – Rs 270, we have - Rs 270 = T × Rs 24 + T × Rs 30 Or T = - 5 Hence Yield Variance for ‘A’ = - 5 × 24 = - Rs 120 and
108
Yield variance for ‘B’ = - 5 × 30 = - Rs 150. Also Similarly (SQ B - RSQ B ) × 30 = - 150 or SQ B - RSQ B = - 5 Alternative 1 Let total actual quantity consumed; X kg. Then, Quantity of A = X – 70 X X RSQ = of A & of B. (Since the Mix ratio is 1:1) 2 2 The Standard input for both ‘A’ and ‘B’ will be 0.5X – 5 Since Cost Variance for ‘A’ is given to be nil, we have, (SP A × SQ A) − (AQ A × AP A) = 0 i.e. 24 × (0.5 X – 5) – (X − 70) × 30 = 0 or X = 110 Kgs Therefore Actual Input for ‘A’ = 110 – 70 = 40 Kgs
Alternative 2 Let the standard input of ‘A’ = X kg. Therefore, the total standard input for ‘A’ + ‘B’= 2X Actual input = (2X + 10) Kgs. ∴ Actual input for ‘A’ = (2X +10 – 70)= (2X – 60)Kgs Forming the equation for nil cost variance of ‘A’. Rs. 24 × X – Rs. 30 × (2X – 60) = 0 Or X = 50 Kgs. Using this quantity in the Cost Variance of ‘B’, the actual price per kg. of ‘B’ (AP B) will be , 50 × 30 – 70 × AP B = −1,300 Or AP B = Rs. 40. Alternative 3 Let the actual input of ‘A’ =X Then the total actual input = (X + 70). Therefore, RSQ of ‘A’ and ‘B’ each = 0.5X + 35 and Standard Input of ‘A’ and ‘B’ each = 0.5X +30. Forming the equation for nil cost variance of ‘A’, we have, 24 × (0.5X + 30) – 30 × X = 0 Or X = 40 Kgs. ∴Standard Input will be 50 Kgs. Using this, quantity in the Cost Variance of ‘B’, the actual price per kg. of ‘B’ (AP B) will be, 50 × 30 – 70 × AP B = −1,300 Or AP B = Rs. 40. Substituting various values for quantity and price, we get the following table. (1)
(2)
(3)
(4)
109
Std. Price × SQ
Std. Price × RSQ
Std. Price × Actual Qty.
Actual Price × Actual Qty.
A
24 × 50 = 1200
24 × 55 = 1320
24 × 40 = 960
30 × 40 = 1200
B
30 × 50 = 1500
30 × 55 = 1650
30 × 70 = 2100
40 × 70 = 2800
2700
2970
3060
4000
(1) – (2)
(2) – (3)
(1) – (3)
(3) – (4)
(1) – (4)
Yld variance
Mix variance
Usage variance
Price variance
Cost variance
A
1200 − 1320 = 120(A)
1320 − 960 = 360(F)
1200 − 960 = 240(F)
960 − 1200 = 240(A)
1200 − 1200 = 0
B
1500 − 1650 = 150(A)
1650 − 2100 = 450(A)
1500 − 2100 = 600(A)
2100 − 2800 = 700(A)
1500 − 2800 = 1300(A)
270A)
90A)
360A)
940A)
1300A)
Actual Output = 90 Kgs. (Actual output and standard o utput are always equal numerically in any material variance analysis) Standard output = Standard input – Standard loss or 100 – 10 = 90 Kgs. Ans. 43: Working Notes a)
Computation of Standard Price per kg of Material Let ‘x’ be the standard price per kg Direct material price variance = Rs. 15,750 (A) (given) A.Q. (S.P. – A.P.) = DMVP 63,000 kgs (x – 3.25) = -15,750 63,000 x – 2,04,750 = -15,750 63,000x = 1,89,000 x = 1,89,000 / 63,000 = 3 ∴ Standard price per kg of material is Rs. 3
b) Computation of Standard Quantity of material for actual output Let ‘x’ be the standard quantity Direct material usage variance = Rs. 27,000 (A) (given) S.P. (S.Q. – A.Q.) = DMUV 3(x – 63,000) = -27,000 3x – 1,89,000 = -27,000 3x = 1,62,000 x = 1,62,000/ 3 = 54,000 ∴ Standard Quantity for actual output is 54,000 kgs. c)
Computation of Standard Labours hours per unit Let ‘x’ be the Standard labour hours per unit D.L. rate variance + D.L. efficiency variance =D.L. Cost Variance Rs. 6,840 (A) + Rs. 10,800 (F) = Rs. 3,960 (F) Direct labour cost variance = Rs. 3,960 (F) (given) Standard cost of Standard hours – Actual cost of actual hours = Rs. 3,960 (F) (x X Rs.6) – (Rs. 2,12,040 = Rs. 3,960 (F) 6x = Rs. 2,16,000 x = 2,16,000 / 6 = 36,000
110
∴ Standard hours for actual output is 36,000 hours Standard hours per unit = 36,000 hours/ 18,000 units d) Computation of Actual Hours per unit Let ‘x’ be actual hours Direct labour efficiency variance (Standard hours – Actual hours) Std. rate [(18,000 units X 2) – x] Rs. 6 2,16,000 – 6x 6x x
= 2 hrs.
= Rs. 10,800 (F) (given) = DLEV = Rs. 10,800 (F) = 10,800 = 2,16,000 – 10,800 = 34,200
∴ Actual labour hours are 34,200 for actual output Actual labour hours per unit = 34,200 hrs / 18,000 units = 1.9 hrs. e)
Computation of Standard variable overhead per hour Budgeted fixed overheads – Actual fixed overheads = Fixed overhead expense variance Let Budgeted fixed overheads be ‘x’ FOEV = Rs. 25,000 (A) (given) x – Rs. 3,25,000 = Rs. 25,000 (A) x = 3,25,000 – 25,000 = 3,00,000
∴ Budgeted fixed overheads is Rs. 3,00,000 Standard fixed overhead rate per unit = Rs. 3,00,000/ 20,000 units = Rs. 15 per unit fixed overhead rate per hour = Rs. 15 / 2 hours = Rs. 7.50 per hour f)
Computation of Budgeted selling price per unit Let ‘x’ be the budgeted selling price per unit Sales price variance = Rs. 45,000 (F) (given) Actual quantity (Actual selling price – Budgeted selling price) = Sales price variance 18,000 units (Rs. 67.50 – y) = Rs. 45,000 (F) 12,15,000 – 18,000y = 45,000 18,000y = 12,15,000 – 45,000 y = 11,70,000 / 18,000 = 65 ∴ Budgeted selling price is Rs. 65 per unit. Budgeted Sales Quantity Price Amount (Units) (Rs. p.u.) Rs. 20,000 65 13,00,000
Quantity (Units) 18,000
Actual Sales Price (Rs. p.u.) 67.50
Statement showing Standard Cost per unit and Budgeted Profit for 20,000 units. Particulars Per Unit Sales (a) 65 Costs: Direct Material 9 Direct Labour 12 Variable Overhead 16 Fixed Overhead 15 Total Cost (b) 52 Standard Gross Margin 13
Amount Rs. 12,15,000
For 20,000 Units 13,00,000 1,80,000 2,40,000 3,20,000 3,00,000 10,40,000 2,60,000
(ii) Computation of sales gross margin volume and fixed overheads volume variances Sales Gross Margin Volume Variance = Standard Margin per unit (Actual Quantity – Budgeted Quantity) = Rs. 13 (18,000 units – 20,000 units) = Rs. 26,000 (A) Fixed Overhead Volume Variance = Standard fixed overhead rate per unit (Actual output – Budgeted output)
Standard
111
= Rs. 15 (18,000 units – 20,000 units)
= Rs. 30,000 (A)
Operating Statement Reconciling the Budgeted Profit with Actual Profit Budgeted Profit (20,000 units X Rs. 13 p.u.) Sales Margin Volume Variance Standard Profit Sales Price Variance Cost Variances: Direct Material Price Variance Direct Material Usage Variance Direct Labour Rate Variance Direct Labour Efficiency Variance Variable Overheads Expense Variance Variable Overheads Efficiency Variance Fixed Overheads Expense Variance Fixed Overheads Volume Variance
Favourable 10,800 14,400 25,200
(Rs.) 2,60,000 26,000 (A) 2,34,000 45,000 (F) 2,79,000 Adverse 15,750 27,000 6,840 3,420 25,000 30,000 1,08,010
Actual Profit
82,810 (A) 1,96,190
Ans: 44: Reconciliation Statement of Actual profit and Standard profit. Budgeted Profit Less: Sales volume variance (Adverse) Standard profit
(Rs)
(10,000 @ Rs.32) (Rs.32 (8,000-10,000) (8,000 units @ Rs.32)
Cost Variances: 1. Direct Materials (i) Price variance 16,500(Rs.20-Rs.24) (ii) Usage Variance Rs.20 (16,000-16,500) 2. Direct labour (i) Labour rate variance 1,70,000(Rs.2.00-Rs.2.04) (ii) Labour efficiency variance Rs.2 (1,60,000-1,66,000) (iii) Idle time variance (Rs.2.00 x 4,0000 3. Variable Overheads (Rs.8 x 8,000) – Rs.60,000 4. Fixed Overheads (i) Expenses variance (Rs.20 x 10,000) –Rs.1,84,000 (ii) Efficiency variance Rs.20 (8,000 – 8,300) (iii) Capacity variance Rs.20 (8,300 – 10,000) Total Less: Net Adverse variance Actual profit for the period
3,20,000 64,000 2,56,000
Adverse
Favourable
66,000 10,000 6,800 12,000 8,000 4,000 16,000 6,000 34,000 1,42,800
20,000 1,22,800 1,33,200
Ans. 45: (b) Working notes: (i) (ii) (iii) (iv)
Ravi 1,875
Richard 2,250
Standard selling expenses per unit (Rs.) 120 (Std. selling expenses/Std. sales units) Actual sales units : 2,000 Actual sales÷Rs. 400 Rs. Actual selling costs Daily allowance 16,000
110
100
150
2,500
2,625
1,300
Rs. 14,000
Rs. 18,000
Rs. 20,000
Standard sales units : Sales quota ÷ Rs. 400
Rahim Roop Singh 2,875 1,500
112
Conveyance allowances 30,000 27,000 27,000 45,000 Salaries 80,000 80,000 80,000 80,000 Free samples 9,000 7,500 5,375 8,000 Postage & stationery 8,000 9,000 10,000 6,000 Other expenses 9,000 5,000 4,000 10,000 Commission on sales 48,000 50,000 52,500 26,000 Corporate sales office expenses 60,000 75,000 1,05,000 52,000 2,60,000 2,67,500 3,01,875 2,47,000 Total actual selling cost (v) Standard selling cost 2,40,000 2,75,000 2,62,500 1,95,000 (Actual units sold × Std. selling expenses per unit) Since all the selling expenses have been related to sales units, only one variance can be calculated by comparing the standard and actual selling costs as is shown in the schedule below: Schedule showing the selling cost variances by salesman Rs. Standard Selling expenses (Refer to Working Note (v))
Rs.
2,40,000 2,75,000
Actual selling expenses (Refer to Working Note (iv)) 2,60,000 2,67,500 Selling cost variance (20,000) 7,500 (F) (A) A = Adverse F = Favourable
Rs.
Rs.
Total (Rs.)
2,62,500
1,95,000
9,72,500
3,01,875 (39,375) (A)
2,47,000 10,76,375 (52,000) (1,03,875) (A) (A)
Ans 46: Statement showing the computation of standard cost of production of shirts Lot no.
Units (Dozen) 1,700 1,200 1,000
45(UK) 46(US) 47(CAN) Total
Cost per Dozen 531.00 477.60 531.00
Total standard cost( Rs.) 9,02,700 5,73,120 5,31,000 20,06,820
Cost per Dozen of 46 (US) lot.
(Rs.)
Material cost 100% Conversion cost 80%(80%of Rs.267)
Total
264.00 213.60 477.60
Statement of material used and its variance Lot no.
Output Dozen
45(UK) 46(US) 47(CAN) Total
1,700 1,200 1,000
Std. Qty per Dozen ( Mtrs.) 24 24 24
Total Total Std. qty. ( Mtrs.) 40,800 28,800 24,000 93,600
Actual Qty. ( Mtrs.) 40,440 28,825 24,100 93,365
Total labour hours
Total actual labour hours
Variation 360(F) 25(A) 100(A) 235(F)
Statement of labour hour worked and its variance Lot no.
Output Dozen
Std.labour hour per Dozen
Variation (Hours)
113
45(UK) 46(US) 47(CAN) Total
1,700 960 (1200×0.8) 1,000
3 3
5,100 2,880
5,130 2,980
30(A) 10(A)
3
3,000 10,980
2,890 11,000
20(F) 20(A)
Calculation of variances (1) Material price variance actual quantity (standard rate –actual rate) = (95,000 metres *Rs. 11)-Rs.10,64,000 = Rs.10,45,000-Rs. 10,64,000 (2) Labour rate variance actual hour (Std. rate per hour – actual rate per hour ) = 11,000 (Rs. 49-Rs.50) (3) Variable overhead efficiency variance Std. variable overhead rate per hour (Std.hour –actual hour) = Rs. 24(10980-11,000) (4) Fixed overhead volume variance Std. fixed overhead rate per hour (Std.hour for actual output–Budgeted hour) = Rs. 16(10980-48000×3/12)
=Rs. 19,000(A) = Rs.11,000(A) = Rs. 480 (A) = Rs. 16,320(A)
Working Notes : (1) standard variance overhead rate per hour = 40*60/100 = Rs.24 (2) standard fixed overhead rate per hour = Rs. 40*40/100= Rs. 16 Ans: 47. 1. Sales variances (5) Sales Volume Margin Variance (Std. Margin on actual Sales – Budgeted Margin) =(Rs.25,000 units x Rs.6) – (36,000 units x Rs.6) =(Rs.1,50,000 – Rs.2,16,000) (6) Sales Price Variance (Actual Sales at actual price – Actual Sales at Std. Price) =(25,000 Units x Rs.51.50)-(25,000 units x Rs.50) =(Rs.12,87,500 – Rs.12,50,000) 2.
Material variances (1) Material Price Variance (Std Cost of Material Used- Actual Material Cost =(96,000 kgs x Rs.2) – (96,000 kg. x Rs.2.25) =(Rs.1,92,000 – Rs.2,16,000) (3) Material Usage Variance Std Material cost of Actual production- Std. Cost of Material used) =(1,00,000 kgs. x Rs.2) – (96,000 Kgs. x Rs.2) =(Rs.2,00,000 – Rs.1,92,000)
3.
Labour Variances (1) Labour Wages Rate Variance (Actual Labour hrs. at Std. rate- Actual Labour Wages) =(1,60,000 hrs x Rs.4) – (1,60,000 hrs. x Rs.4.10) =(Rs.6,40,00 – Rs.6,56,000)
=Rs.66,000 (A)
=Rs.37,500 (F)
=Rs.24,000(A)
=Rs.8,000 (F)
=Rs.16,000 (A)
114
(2) Labour Efficiency Variance Std. Labour Wages for actual production –Actual Labour hours worked at Std. rate) =(1,50,000 hrs. x Rs.4) –(1,54,000 hrs. xRs.4) =(Rs.6,00,000 – Rs.6,16,000) =Rs.16,000 (A) (3) Idle Time variance (6,000 hrs. x Rs.4 variance)
=Rs.24,000 (A)
4.
Variable Overhead Variances (1) Total Variable overhead Variance (Allowed Expenditure for actual hours-Actual variable overheads) =Rs.(1,84,000 – Rs.1,82,000) =Rs.2,800 (F) (2) Variable overhead Efficiency Variance ( Allowed Expenditure for Std. hours- Allowed Expenditure for actual hours) =(Rs.1,50,000 hrs. x Rs.1.20)- 1,54,000 hrs. x Rs.1.20) =(Rs.1,80,000 – Rs.1,84,800) =Rs.4,800 (A) 5. Fixed Overhead Variances (1) Fixed Overhead Expenditure variance (Budgeted Expenditure – Actual Expenditure) =(Rs.1,44,000 – Rs.1,50,000) =Rs.6,000 (A) (2) Fixed Overheads Efficiency variance (Std. hours of production x Std. fixed overhead recovery rate per hour)-(Actual hours worked x Fixed overhead recovery rate per hour) =(Rs.1,50,000 hrs. x Re.0.80)-(1,54,000 hrs. x Re.0.80) =(Rs.1,20,000 – Rs.1,23,200) =Rs.3,200(A) (3) Fixed Overhead Capacity variance (Actual hours worked x Fixed overhead recovery rate per hour)-(Std. Fixed overhead recovery r rate per hour x Budgeted capacity hours) =(1,54,000 hrs. x 0.80)-(Re.0.80 x 1,80,000 hrs.) =(Rs.1,23,200 – Rs.1,44,000) =Rs.20,800(A) A. Std. Variable Overhead Rate per hour. = Std. Variable Overheads Total Std. hours =(30,000 units x Rs.12)-Rs.1,44,000 1,80,000 units B. Std Fixed Overheads rate per hour =Budgeted Overheads Budgeted hours =Rs.1,44,000 / 1,80,000 hrs.
=Rs.1.20
=Rs.0.80
Statement of actual profit / loss for the second quarter of the year Direct Material (96,000
[email protected]) Direct Wages (1,60,000 hrs. ‘ Rs.4.10) Overhead Total Cost Sales Revenue (25,000 units @ 51.50) Actual Profit
Operating Statement reconciling the budgeted profit with actual profit Particulars Reference to working note Budgeted profit (36,000 units x Rs.6) 1. Sales – Volume Margin Variance Price Variance Profit before adjustment of Cost Variances
(1) (2)
(Rs.) 2,16,000 6,56,000 3,32,000 12,04,000 12,87,500 83,500 (Rs.) Actual
Variance Favourable 37,500
Adverse 66,000 -
2,16,000 1,87,500
115
II Material
- Price - Usage III. Labour - Rate -Efficiency -Idle time IV. V. Overheads -Expenditure -Efficiency V. F. Overheads -Expenditure - Efficiency -Capacity Actual Profit
(1) (2) (1) (2) (3) (1) (2) (1) (2) (3)
8,000 2,800 10,800
24,000 16,000 16,000 24,000 4,800 6,000 3,200 20,800 1,14,800
1,04,000 83,500
Ans. 48:
Expenses
Indirect material Indirect labour Maintenance Power Sundries Total variable overheads Fixed overheads Total overheads
Overhead Expenses Schedule Budget: 120 Std. Hours Actual: 156 Hours Rate per hour Expenses Rate per hour Expenses Rs. Rs. Rs. Rs. 0.40 48 0.50 78 0.60 72 0.60 94 0.40 48 0.45 70 0.30 36 0.32 50 0.30 36 0.29 45 2.00
240
2.00
240 480
2.16
337 250 587
Actual output = 12,160 units. Hence standard hours produced or std. hours for actual production =
Computation of variances: A. Fixed expenses (a) Charged to production (152 hours × Rs. 2 per hours) (b) Fixed expenses as per budget (c) Actual fixed overheads
Rs. 304 Rs. 240 Rs. 250
Volume variance = Fixed overhead recovery rate (Actual volume in std. hrs. – Budgeted volume in standard hrs.) = Rs.2 (152 – 120) = Rs.64 (F) Expenses variance = Total variance Volume variance: (a – b) Expenses variance: (b – c) Total variance : (a – c)
(Budgeted expenses – Actual expenses) = Rs.240 – Rs.250 = Rs. 10 (A)
= (Fixed overheads absorbed – Actual fixed overheads) = Rs.304 – Rs.250 = Rs.54 (F) Or Rs.64 (F) Rs. 10 (A) Rs.54 (F)
B. Variable expenses (a) Charged to production: (152 hours × Rs.2)
Rs.304
116
(b) Actual expenses Variable overhead cost variance (a – b)
Rs.337 Rs.33 (A)
Ans. 49: Basic Data: (1) Statement showing standard and actual costs of material for 1,000 units of output and standard cost of actual input Standard Cost
Ma
Actual cost
Standard cost of actual input = (Actual quantity × Standard price)
Qty.
Price
Amount
Qty.
Price
Amount
Actual Qty.
Standard Price/kg
Amount
Kg.
Rs.
Rs.
Kg.
Rs.
Rs.
Kg.
Rs.
Rs.
A
12,000
10
1,20,000
11,000
11
1,21,000
11,000
10
1,10,000
B
5,000
6
30,000
5,200
5.50
28,600
5,200
6
31,200
1,50,000
1,000 units
Standard yield (units) =
17,000 Kg.
1,49,600
1,41,200
× 16,200 kg. = 952.941764 units approx.
(2) Statement showing standard and actual labour cost of 1,000 units produced and standard cost of actual labour hrs. Hours
5,000
(3) Overheads
Rate p.h.
Amount
Rs.
Rs.
3
15,000
Hours
5,500
Rate p.h.
Amount
Rs.
Rs.
3.1818
17,500
Fixed overheads (Rs.)
Hours
5,500
Rate p.h.
Amount
Rs.
Rs.
3
17,500
Budgeted
Actual
Hours
38,500
39,000
Output
5,500
5,500
Standard time p.u. (hrs.)
1,100
1,000
Standard fixed overheads p.u. (Rs.)
5
Standard fixed overhead rate p.h. (Rs.)
35
Computation of material variances (Refer to Basic data 1): Computation of material variances (Refer to Basic data (1): Material cost variance
7
= Standard cost – Actual cost = Rs.1,50,000 – Rs.1,59,500 = Rs.9,500 (Adv.)
Material price variance
= Actual quantity (Std. price – Actual price) = 12,000 kg (Rs.10 – Rs.11) + 5,000 kg (Rs.6 – Rs.5.50) = Rs.12,000 (Adv.) + Rs.2,500 (Fav.) = Rs.9,500 (Adv.)
Material usage variance
= Standard price (Standard quantity – Actual quantity)
117
= Rs.10 (12,000 kg – 11,000 kg) + Rs.6(5,000 kg–5,200 kg) = Rs.10,000 (Fav.) + Rs.1,200 (Adv.) = Rs.8,800 (Fav.) Material mix variance
Std. price of Std. price of = Total actual quantity − Std. mix per kg 16,200 kg
Rs.1,50,000 Rs.1,41,200 − 16,200 kg 17,000 kg
= 16,200 kg
= Rs.1,741.18 (Fav.) Material yield variance
= Std. Rate (Actual yield – Std. Yield = Rs.150 (1,000 units – 952.9411764 units) = Rs.7058.82
Material purchase price variance: = Actual quantity of material purchased (Std. Price per kg. – Actual price per kg) = 12,000 kg (Rs.10 – Rs.11) + 5,000 kg (Rs.6 – Rs.5.50) = Rs.12,000 (Adv.) + Rs.2,500 (Fav.) = Rs.9,500 (Adv.) Computation of labour variances (Refer to basic data 2): Labour cost variance
= (Standard cost – Actual cost) = Rs.15,000 – Rs.17,500 = Rs.2,500 (Adv.)
Labour rate variance
= Actual hrs. (Std. Rate – Actual rate) = 5,500 (Rs.3 – Rs.3.1818) = Rs.1,000 (Adv.)
Labour efficiency variance
= Std. rate p.h. (Std. Hours – Actual hours) = Rs.3 (5,000 hrs. – 5,500 hrs.) = Rs.1,500 (Adv.)
Computation of fixed overhead variance: Total fixed overhead variance: = Fixed overhead absorbed – Actual fixed overhead = 1,000 units × Rs.35 – Rs.39,000 = Rs.35,000 – Rs.39,000 = Rs.4,000 (Adv.) Fixed overhead expenditure variance: = Budgeted fixed overhead – Actual fixed overhead = Rs.38,500 – Rs.39,000 = Rs.500 (Adv.) Fixed overhead volume variance: = Std. Fixed overhead rate per unit (Actual output – Budgeted output) = Rs.35 (1,000 units – 1,000 units) = Rs.3,500 (Adv.) Efficiency variance: = Std. fixed overhead rate per unit (Actual output – Budgeted output)
118
= Rs.35 (1,000 units – 1,000 units) = Rs.3,500 (Adv.) Ans. 50: (i) Working Notes: 1.
Standard quantity and cost of raw material required for actual output Actual output of EXE (units) Standard output per kg. of raw material (units) Standard quantity of raw material required for actual output (kgs.) (4,680 units / 12 units) Standard cost of 390 kgs. of raw material at Rs.60 per kg. (Rs.)
2.
Basic data for the computation of labour variances: Standard labour data for actual output
Std. Time hours
2,340
Actual data
Rate p.h.
Amount
Standard cost of actual hours
Actual cost hours
Rate p.h.
Amount
5
11,700
12,000
240
4.80
1,152
320
5.20
1,664
1,840
5.00
9,200
(4,680 units ×½ hr.)
2,340 11,700 12,000 2,400 3. Basic data for the computation of fixed overhead variances: Budgeted / Std. data Budgeted fixed overhead (Rs.) (for 1 week)
Actual data 24,400
Budgeted hours
2,400
(60 workers×40 hrs. per week) Budgeted output (units)
Actual fixed overhead (Rs.)
8.50
Std. rate p.u. (Rs.)
4.25
2,400
Actual output (units)
4,680
Computation of labour and overhead (variances): Labour cost variance: (Refer to working Note 2) = (Std. cost of labour – Actual cost of labour) = Rs.11,700 – Rs.12,016 = Rs.316 (Adverse) Labour rate variance: = Actual hours (Std. rate – Actual rate) = Rs.12,000 – Rs.12,016 = Rs.16 (Adv.) Labour efficiency variance:
19,800
Actual labour hours
4,800
Std. rate p.h. (Rs.)
(i)
12,016
119
= Standard rate per hr. (Std. hours – Actual hours paid) = (Rs.11,700 – Rs.12,000) = Rs.300 (Adv.) = Total fixed overhead cost variance: = (Fixed overhead absorbed – Actual fixed overhead) = [(4,680 units × Rs.4.25) – Rs.19,800] = Rs.19,890 – Rs.19,800 = Rs.90 (Fav.) Fixed overhead volume variance: = Std. fixed overhead rate per unit [Actual output – Budgeted output] = Rs.4.25 (4,680 units – 4,800units) = Rs.510 (Adv.) Fixed overhead expenditure variance: = [Budgeted fixed overhead – Actual fixed overhead] = [Rs.20,400 – Rs.19,800] – Rs.600 (Fav.) (ii) Statement showing total standard cost, standard profit and actual profit for the week. Sales
Rs.
4,680 units × Rs.15
Rs. 70,200
Less: Standard cost of : Direct material
23,400
Direct labour
11,700
Overheads
19,890
54,990
(4,680 × Rs.4.25) (Refer to working notes 1 to 3) Standard Profit
15,210
Less: Adjustment for variance: Raw Material: Price variance : 800 (A) Usage variance : 600 (A)
1,400 (A)
Labour: Rate Variance : 16 (A) Efficiency variance : 300 (A)
316 (A)
Overhead: Expenditure variance: 600 (F) Volume variance: 510 (F)
90 (F)
Actual Profit Ans.51: Sales variances (Sales Value Method) Budgeted Calculations: Budgeted Sales Actual Sales
1,626 13,584
120
Product
Qty.
Rate
Amount
Qty.
Rate
Amount
Units
Rs.
Rs.
Units
Rs.
Rs.
Actual quantity× Budgeted price
Rs. 10,000 12 1,20,000 11,000 11.50 1,26,500 1,32,000 6,000 15 90,000 5,000 15.10 75,500 75,000 8,000 9 72,000 9,000 8.55 76,950 81,000 24,000 2,82,000 25,000 2,78,950 2,88,000 Computation of sales variances : (1) Sales value variance = Actual sales – Budgeted sales = Rs. 2,78,950 – Rs. 2,82,000 = Rs. 3,050 (A) (2) Sales price variance = Actual quantity (Actual price – Budgeted price) = Rs. 2,78,950 – Rs. 2,88,000
A B C
= Rs. 9,050 (A) = Budgeted price (Actual Qty. –Budgeted Qty.)
(3) Sales volume variance
= Rs. 2,88,000 – Rs. 2,82,000 = Rs. 6,000 (F) (4) Sales mix variance
= Total actual qty. (Budgeted price of actual mix – Budgeted price of budgeted mix)
= = 25,000 units (Rs. 11.52 – Rs. 11.75) Rs. 5,750 (A) (5) Sales quantity variance
= Budgeted price of budgeted mix (Total actual quantity – Total budgeted qty.) = Rs. 11.75 (25,000 – 24,000) = Rs. 11,750 (F)
Check Sales value variance
= Sales price variance + Sales volume variance
Rs. 3,050 (A)
= Rs. 9,050 (A) + Rs. 6,000 (F)
Sales volume variance
= Sales mix variance + Sales quantity variance
Rs. 6,000 (F)
= Rs. 5,750 (A) + Rs. 11,750 (F)
Alternative solution (sales margin method) Basic calculations : Budgeted margin
Actual margin
Actual quantity × Budgeted margin
Product
Qty.
Rate Amount
Units
Rs.
A
10,000
B
6,000
Qty.
Rate
Amount
Rs.
Units
Rs.
Rs.
Rs.
5
50,000
11,000
4.50
49,500
55,000
6
36,000
5,000
6.10
30,500
30,000
121
C
8,000
3
24,000
24,000
9,000
1,10,000
25,000
Computation of variances: Sales margin variance
2.55
22,950
27,000
1,02,950
1,12,000
= Actual margin – Budgeted margin = Rs. 1,02,950 – Rs. 1,10,000 = Rs. 7,050 (A)
Sales price margin variance
= Actual quantity (Actual margin – Budgeted margin)
Sales margin mix variance
= Rs. 1,02,950 – Rs. 1,12,000 = Rs. 9,050 (A) = Total actual quantity (Budgeted margin of actual mix –Budgeted margin of budgeted mix
Material Variances: Basic Calculations Standard and actual costs of material for actual output i.e. 11,000 units of A, 5,000 units of B and 9,000 units of C and standard cost of actual input material. Material
X Y
Standard cost
Actual cost
Qty Units
Rate Rs.
Amount Rs.
Qty. Units
Rs.
51,000* 74,000** 1,25,000
2 1
1,02,000 74,000 1,76,000
54,000 72,000 1,26,000
1,09,620 73,000 1,82,620
Actual quantity × standard price Rate Amount Rs. 1,08,000 72,000 1,80,000
* 11,000 × 2 + 5,000 × 4 + 9,000 × 1 = 51,000 **11,000 × 3 + 5,000 × 1 + 9,000 × 4 = 74,000.
Computation of variances : Material cost variance = Standard cost – Actual cost = Rs. 1,76,000 – 1,82,620 = Rs. 6,620 (A) Material price variance = Actual quantity (Standard price – Actual price) = Rs. 1,80,000 – Rs. 1,82,620 = Rs. 2,620 (A) Material mix variance = Total quantity (Standard price of standard mix – Standard price of actual mix
122
Check: Material cost variance Rs. 6,620(A)
= Material price variance + Material mix variance + Material yield variance = Rs. 2,620(A) + Rs. 2,592(A) + Rs. 1,408(A)
Ans. 52 (i) Reconciliation statement showing which factor has contributed change in profit (Rs. in lacs) Increase in contribution due to increase in volume (Rs.280 lacs – Rs.240 lacs) (Refer to working note 3)
Favourable
Adverse
40
—
Sales price variance (Refer to working note 3)
140
Material usage variance (Refer to working note 4)
52
Material price variance (Refer to working note 4)
—
0
Direct labour rate variance (Refer to working note 4)
—
28
Direct labour efficiency variance (Refer to working note 4)
36
—
—
140
268
168
Fixed overhead expenditure variance (Refer to working note 3) Total change in profit
100
=
Break-even sales (Year 2)
160 lakhs = Rs. 800 lakhs Rs. 240 lakhs 100 × Rs. 1200 lakhs
123
(Refer to working note 3)
=
300 lakhs = Rs. 962.50 lakhs Rs. 480 lakhs × 100 Rs. 1540 lakhs
(iii) Percentage increase in selling price needed over the sales value of year 2 to earn a margin of safety of 45% in year 2 P/V ratio = (Rs. 480 lacs/Rs. 1,540 lacs) × 100 = 31.169%
If Margin of safety to be earned is 45% then Break-even point should be 55% Revised contribution = 1,540 lacs × 35.4193% = 545.45 lacs Present contribution
= Rs. 480 lacs
Increase in selling price required
= Rs. 65.45 lacs (Rs. 545.45 lacs – Rs. 480 lacs)
Working notes: 1. Budgeted sales in year 2 If actual sales in year 2 is Rs. 110 then budgeted sales is Rs. 100.
3.
Statement of figures extracted from working results of a company (Figure in lacs of Rs.)
Sales : (A)
Year 1 Actual
Year 2 (Budgeted)
Year 2 Actual
Total Variance
(a)
(b)
(c)
d = (c) – (b)
1,200
1,400
1,540
140 (Fav.)
124
(Refer to working note 1) Variable costs : Direct material (Refer to working note 2) Direct wages and variable overhead (Refer to working note 2)
600
700
648
52 (Fav.)
360
420
412
8 (Fav.)
Total variable costs : (B)
960
1,120
1,060
60(Fav.)
Contribution (C) = {(A) – (B)}
240
280
480
200 (Fav.)
Less : Fixed cost
160
160
300
140 (Adv.)
80
120
180
60(Fav)
Total variable costs : (B)
960
1,120
1,060
60(Fav.)
Contribution (C) = {(A) – (B)}
240
280
480
200 (Fav.)
Less : Fixed cost
160
160
300
140 (Adv.)
Profit
Total variable costs : (B)
960
1,120
1,060
60(Fav.)
Contribution (C) = {(A) – (B)}
240
280
480
200 (Fav.)
Less : Fixed cost
160
160
300
140 (Adv.)
Profit
80
120
180
60(Fav)
(4) (i) Data for Material variances : Standard data for actual output Quantity
Rate per
of material
m/t
Actual data Amount
Quantity
Rate per
of material
m/t
m/t
5,83,333
Amount
m/t Rs.
Rs.
120
700 lacs
5,40,000
Rs.
Rs.
120
648 lacs
Material price variance = (Standard rate – Actual rate ) Actual quantity = Nil Material usage variance = (Standard quantity - Actual quantity) Standard rate per m/t = (5,83,333 – 5,40,000) Rs.120 = Rs. 52 lacs (Fav.) (ii) Data for labour variances overhead variances Standard data for actual output Labour hours 87,50,000
Actual data
Rate per hour Rs.
Amount
4.80
4.20 lacs
Labour hours
Rs. 80,00,000
Rate per hour Rs.
Amount
5.15
412 lacs
Labour rate variance = (Standard rate – Actual rate) Actual labour hours = (Rs.4.80 – Rs.5.15) 80,00,000 = Rs. 28 lacs (Adv.) Labour and variable overhead efficiency variance : = {Standard labour hours – Actual labour hours} × Standard rate per hour = {87,50,000 – 80,00,000} Rs. 4.80 = Rs. 36 lacs (Adv.)
Rs.
125
Ans. 53: Basic Calculations Equivalent Production in Units Particulars Direct Material Units completed 100 % Work-in-progress 100 % Total Equivalent Units
6,000 600 6,600
Labour & Overhead 100 % 50 %
6,000 300 6,300
(a) Direct Material Variances
Standard output 6,600 units
Material Qty. 13,200 6,600 19,800
A B
Rate (Rs.) 3 4
Amount (Rs.) 39,600 26,400 66,000
Qty. (kg) 14,850 7,260 22,110
Actual output 6,600 units Rate (Rs.) 2.90* 4.098*
Amount (Rs.) 43,065 29,750 72,815
*(Actual Cost/ Actual Quantity) DMCV
A B
= = = = =
A B
= = =
DMPV
DMUV
DMMV A B
DMYV
= = = = =
= = =
Standard Cost for actual output – Actual Cost 66,000 – 72, 815 = Rs. 6,815 (A) Actual Qty. (Std, Rate – Actual Rate) 14,850 (3 – 2.90) = 1,485 (F) 7,260 (4 - 4.098) = 710 (A) 775 (F) Std. Rate (Std. Qty. for actual output – Actual Qty.) 3 (13,200 – 14,850) = 4,950 (A) 4 (6,600 – 7,260) = 2,640 (A) 7,590 (A) Std. Rate (Revised Std. Qty. – Actual Qty.) 3 3 (14,740 – 14,850) = 330 (A) 4 4 (7,370 – 7,260) = 440 (F) 110 (F) Std. Cost per Unit (Std. output for actual mix – Actual output) 66,000 10 (7,370 -6,600) = Rs. 7,700 (A)
(b) Direct Labour Variances DLCV
= =
Std. Cost for Actual Output – Actual Cost (6,300 X 20) – 1,27,500
= Rs. 1,500 (A)
= =
Actual Time (Std. Rate – Actual Rate) 32,000 [
= Rs. 500 (F)
ITV
= =
Std. Rate X Idle Hours 4 X 200 = Rs. 800 (A)
DLEV
= = =
Std. Rate (Std. Time for actual production – Actual time worked) 4 [(6,300 X5) – 31,800] 4 (31,500 – 31,800) = Rs. 1,200 (A)
DLRV
(c) Variable Overhead Variances VOC
=
Recovered Overheads – Actual Overheads
126
VOEXPV
VOEEFV
= =
6,300 X 5 – 30,000 31,500 – 30,000
= = = = =
Std. Variable Overheads – Actual Variable Overheads. (31,800 X 1) – 30,000 31,800 – 30,000 = Rs. 1,800 (F) Recovered Overheads – Standard Overheads 1 X (31,500 -31,800) = Rs. 300 (A)
= Rs. 1,500 (A)
(d) Fixed Overhead Variances FOCV
= = =
Recovered Fixed Overheads – Actual Fixed Overheads (6,300 X 10) – 80,600 63,000 – 80,600 = Rs. 17,600 (A)
FOEXPV
= =
Budgeted Fixed Overheads – Actual Fixed Overheads (8,000 X 10) – 80,600 = Rs. 600 (A)
FOVV
= =
Recovered Fixed Overhead – Budgeted Fixed Overhead 63,000 – 80,000 = Rs. 17,000 (A)
Fixed Overhead Volume Variances may be segregated into the following: FOEFFV
= =
Std. Rate (Std. time for actual production – Actual time booked) 2 (31,500 – 31,800) = Rs. 600 (A)
FOITV
= = = =
Std. Rate per hour X Idle hours 2 X 200 = Rs. 400 (A) Std. Rate per hour (Actual time – Budgeted time) 2 (32,000 – 40,000) = Rs. 16,000 (A)
FOCAPV
(e) Sales Variances SPV
= =
Actual Qty. (Std. Price – Actual Price) 6,000
= Rs. 5,000 (F)
Sales Volume Variance (Contribution loss) : = Std. Rate of profit (Budgeted Qty. – Actual Qty.) = 5 (8,000 – 6,000) = Rs. 10,000 (A)
Operating Statement showing the Reconciliation between Budgeted and Actual Profit for the Month (Rs.) Budgeted Profit (8,000 X Rs. 5) Sales Variances Volume Total Cost Variances: Direct Materials Price Yield Mix Direct Wages Rate Efficiency Idle Time
Rs. Price 5,000 (F) 10,000 (A) 5,000 (A)
775 (F) 7,700 (A) 110 (F) 500 (F) 1,200 (A) 800 (A)
40,000
5,000 (A)
127
Variable Overheads Expense Efficiency Fixed Overheads Expense Efficiency Idle Time Capacity Total Cost Variances Actual Profit
1,800 (F) 300 (A) 600 (A) 600 (A) 400 (A) 16,000 (A) 24,415 (A)
Ans:54:Computation of Variances (a) Material Price variance Material Qty. Purchase Std. Price Rs. (1) Kg. (2) (3) A 9,000 10.00 B 5,000 3.00
(b) Material Usage Variance Material Std. Qty. for Actual Qty. (1) actual output (3) (2) A 8,000 7,800 B 4,000 4,300
(C ) Labour Rate Variance Actual Hours Std. Rate (1) (2) Rs. 4200
3
(d) Labour Efficiency Variance Std. Hours Actual Hours for actual (2) output (1) 4,000 4,200
24,415 (A) 10,585
Actual Price Rs.(4) 10.25 2.75
Std. cost Rs. (2x3)=5 90,000 15,000 1,05,000
Actual Cost Rs. (2x4)=(6) 92,250 13,750 1,06,000
Price Variance Rs. (5-6)=(7) 2,250 (A) 1,250 (F) 1,000 (A)
Std. Price (4)
Std. Cost of Std. Qty. (2x4)=5 80,000 12,000 92,000
Std. Cost of Actual (4x5)=6 78,000 12,900 90,900
Usage Variance (5-6)=(7)
10 3
2,000 (F) 900 (A) 1,100 (F)
Actual Rate (3) Rs.
Std. Wage (4)=(1x2) Rs.
Actual Wages (5)=(1x3) Rs.
Rate Variance (6)=(4-5) Rs.
2,875
12,600
12,075
525 (F)
Std. Rate (3) Rs. 3
Std. Cost of Std. Hours (4)=(1x3) Rs. 12,000
Std. Cost. Of Actual Hours (5)=(2x3) Rs. 12,600
Overhead Variances Basic calculations (a)
Budgeted overheads for November
(b) (c ) (d) (e) (f)
Std. hours produced for November Fixed production overheads per hour Recovered overhead Actual overheads Standard overheads
= 10,800 X 25 =Rs.22,500 12 = 800 units X 5 hrs per unit=4,000 = 25/5=5 = 4,000 X 5 =Rs.20,000 = Rs.23,500 = 4,200 X 5 =Rs.21,000
Variances Overhead Cost variance =Recovered Overheads- Actual Overheads =20,000-23,5000 =Rs.3,500 (A) Overhead Expenditure Variance =Budgeted Overheads-Actual overheads =22,500-23,500 =Rs.1,000 (A)
Efficiency Variance (6)=(5-6) Rs. 600 (A)
128
Overheads Volume variance =Recovered Overheads-Budgeted Overheads =20,000-22,500 =Rs.2,500 (A) Overhead Volume Variance may be segregated into: (a) Overhead Capacity Variance =( Std. Overhead rate per hour) X (Actual hours-Budgeted hours) = Standard Overheads-Budgeted Overheads =21,000-22,500 =Rs.1,500 (A) (b) Overhead Revised Capacity variance = ( Std. rate per hour ) X (Std. hrs. produced – Actual hours) Or = Recovered overheads- Std. overheads =20,000-21,000 (ii) Operating Statement (a) Sales Less: std. Cost of Sales Standard profit (b) Variances Materials Price Usage Direct Labour Rate Efficiency Fixed Overheads Expenditure Capacity 1,500 (A) Efficiency 1,000 (A) ( c)
=Rs.1,000 (A) (Rs.)
(800 X Rs.200) (800 X Rs.155)
1,60,000 1,24,000 36,000
Favourable
Adverse
1,100
1,000 -
525 -
600
-
1,000
1,625
2,500 5,100
Actual Profit
3,475 (A) 32,525
(iii) In the solution given the price variance has been calculated at the point of purchase. In case it is calculated at the point of issue the variance will be as follows: (Rs.) A 7,800 X (10-10.25) 1,950 (A) B 4,300 X ( 3-2.75) 1,075 (F) 875 (A) Present variance 1,000 (A) Hence difference 125 Actual profit as in (ii) above 32,525 Price variance difference 125 Actual profit as per question 32,650
Ans: 55: Statement showing the computation of standard cost per unit Particulars Direct Material Direct Wages Variable overhead Fixed overhead Total Cost Profit Balancing figure
Actual 960 units 792 1,192 1,940 1,040 4,964 976 5,940
Variance (-) Adv. (+) Fav. (-)24 (-) 40 (-) 20 (-) 40 (-)124 (+)56 (+)180
(Rs.) Standard 960 units 768 1,152 1,920 1,000 4,840 920 5,760
Standard cost per unit 0.80 1.20 2.00 1.04 5.04 0.96 6.00
129
Original Budget and Flexible budget for sales achieved Particulars
Standard Cost (per unit) 0.80 1.20 2.00 1.04 5.04 0.96 6.00
Direct Material Direct Wages Variable overhead Fixed overhead Cost of Sales Profit Sales
Ans: 56: (i)
Original Budget 20,000
1 Sales Variable costs Direct Materials Direct Labour Factory Overheads Selling overheads Total Contribution (A) Fixed Cost Factory overheads Selling overheads Total (B) Profit (A-B) Volume variance Net Loss
(ii)
Variance Analysis
(1)
Sales Std. Price Std. profit Actual quantity Turnover on Std. Price Actual turnover is given at Rs.22 lakhs. : Price Variance Std. Qty X Std. Profit Actual Qty .X Std. Profit Quantity Variance Direct Materials Std. Cost Actual Qty.=18,000 AQ X SC Total Actual Cost Material Price Variance Direct Wages Std. Time per unit Std. hourly rate Std. Hours produced Std. Hours=90,000 (a) Std. Hrs. X Std. rate (b) Actual Hrs. X Actual Rate © Actual Hrs. X Std. Rate Efficiency variance
(3)
Flexible budget (960 units) 768 1,152 1,920 1,040 4,880 880 5,760
Flexible budget for May 2004
Units
(2)
(Rs.) Original budget (1,000 units) 800 1,200 2,000 1,040 5,040 960 6,000
2 24,00,000 6,00,000 8,00,000 2,00,000 3,00,000 19,00,000 5,00,000
Flexible Budget for May 2004 18,000 3 21,60,000 5,40,000 7,20,000 1,80,000 2,70,000 17,10,000 4,50,000
Actuals may 2004 18,000 4 22,00,000 5,20,000 7,56,000 1,84,000 2,88,000 17,48,000 4,52,000
1,00,000 2,00,000 3,00,000 1,50,000 -
1,16,000 1,84,000 3,00,000 1,52,000
1,00,000 2,00,000 3,00,000 2,00,000 2,00,000 -1,50,000
Variance
5 40,000 F 20,000 F 36,000 A 4,000 A 18,000 A 38,000 A 2,000 F 16,000 A 16,000 F 2,000 F 50,000 A (48,000)
=Rs.24 lakhs /20,000 =Rs.2 lakhs / 20,000 =18,000 and standard price =18,000 X 120
=Rs.120 =Rs.10 =Rs.120 =Rs.21,60,000
=40,000 (F) =20,000 X 10 =18000 X 10 =Rs.20,000 A
=Rs.2 lakhs =Rs.180 lakhs
=Rs.6,00,000/20,000 =18,000 X 30
=Rs.30 =Rs.5,40,000 =Rs.5,20,000 =Rs.20,000 (F)
=1,00,000/20,000 =8,00,000/1,00,000 =18,000 units X 5 hrs. Actual Hours=95,000 =90,000 X 8. =Rs.7,56,000 =95,000 X 8 =(a)-( c)=Rs.40,000 (A)
=5 hours =Rs.8/hr. =90,000 hrs. Std. Rate Rs.8 =Rs.7,20,000 =Rs.7,60,000
130
(4)
(5)
(6)
(7)
Rate Variance =( c) –(b)=Rs.4,000 (F) Factory Variable overheads: Std. Rate =Rs.2,00,000/1,00,000 (a) Charged to production =90,000 X2 (b) Std. cost of actual hours =95,000 X 2 (c ) Actual overheads (a) – (b) =Rs.10,000 (A) (b) – (c ) =Rs.6,000 (F) Selling variable overheads: Std. Rate =Rs.3,00,000/20,000 (a) Std. cost of output =18,000 X 15 (b) Actual overheads Adverse Variance Factory overheads- Fixed: Std. Rate = Rs.1,00,000/1,00,000 (a) Std. cost of output of 90,000 (b) Std. cost of actual hours. (95,000) (c ) Budgeted (d) actual Efficiency variance : (a) – ( b) =Rs.5,000 (A) Capacity variance : (b) – ( c) =Rs.5,000 (A) Expenses variance : (c )- (d) =Rs.16,000 (A) Selling overheads : Fixed: Standard =Rs.2 lakhs / 20,000 (a) Std. cost of output =18,000 x 10 (b) Budget (c )Actual Volume variance = (a) – (b) Expense variance = (b)-( c)
=Rs.2/hr. =Rs.1,80,000 =Rs.1,90,000 =Rs.1,84,000 Being efficiency variance Being expense variance
Ans: 57:Working Notes: 1. Sales Variances (1) Sales Volume Margin Variance (Actual Sales Volume – Budgeted Volume ) x Standard Margin =(22,000 units – 20,000 units) x Re.1 (2) Sales Margin Price Variance Actual Sales Volume x (Actual Selling Price – Budgeted Selling Price) =(14,000 units (Rs.5 – Rs.5) + ( 8,000 units x (Rs.4.75 – Rs.5) 2. Material Variances (1) Material Price Variance (Std. Price – Actual Price) x Actual Quantity A : (0.30 – 0.20) x 16,000 kg. B : (0.70 – 0.80) x 10,000 kg.
=Rs.1,600 (F) =Rs.1,000 (A)
=Rs.15 / unit =Rs.2,70,00 =2,88,000 =18,000 =Re.1/hr. =Rs.90,000 =Rs.95,000 =Rs.1,00,000
=Rs.10 per unit =Rs.1,80,000 =Rs.2,00,000 =Rs.1,84,000 =Rs.20,000 (A) =Rs.16,000 (F)
=Rs.2,000 (F)
=Rs.2,000 (A)
=Rs.600 (F)
(2) Material Mix Variance Total Actual Quantity (S.C. of Std. mix per kg. – S.C. of actual mix per kg.)
Rs.10000 Rs.11800 − 20000kg 26000kg
= 26000kg
=Rs.1,200 (F) (3) Material Yield Variance Std. rate per kg. of output (Actual Yield – Std. Yield ) = 0.50 ( 24,000 kg. – 26,000 kg.) (3) Labour Variance (1) Labour Rate Variance (Std. rate p.h. – Actual rate p.h. ) x Actual hours Skilled Labour : (Rs.3 – Rs.2.95 ) x 13,000 hrs.
=Rs.1,000 (A)
=Rs.650(F)
131
Unskilled Labour : (Rs.2.50 – Rs.2.60 ) x 6,300 hrs. =Rs.630(A) (2) Labour Efficiency Variance (Std. hrs. for Actual output – Actual hours ) x Std. rate p.h. Skilled Labour : (Rs.10,800 hrs-12,000 hrs.) x Rs.3 =Rs.3,600 (A) Unskilled Labour : (6,240 hrs. – 6,300 hrs.) x Rs.2.50 =Rs.150 (A) (3) Idle Time Variance (Idle hours x Standard Wage rate p.h) Skilled Labour : 1,000 hours x Rs.3 (4) Variable Overhead Variance (1) Variable Overhead Expenditure Variance (Variable Overhead recovered on actual output – Actual Variable Overhead) = (24,000 units x Re.0.50) – Rs.15,000 (5) Fixed Overhead Variances (1) Fixed Overhead Expenditure Variance (Budgeted Expenditure – Actual Expenditure) = (Rs.20,000 – Rs.18,020) (2) Fixed Overhead Volume Variance (Budgeted Volume – Actual Volume ) x Std. rate per unit = (20,000 units – 24,000 units ) x Re.1 Statement reconciling Actual Profit and Budgeted Profit Particulars Reference to working note
=Rs.3,000 (A)
=Rs.3,000 (A)
=Rs.1,980 (F)
=Rs.4,000 (F)
Actual Adverse
-
Profit before adjustment of Cost Variances II Material - Price - Mix - Yield III. Labour Variance - Rate -Efficiency -Idle time IV. V. Overheads -Expenditure V. F. Overheads
=Rs.3,750 (A)
Variance Favourable
Budgeted profit (as per Budgeted income statement) 1.Sales Variances Sales Volume Margin Variance Sales Volume Margin Variance
=Rs.20(F)
20,000
(1) (2)
2,000 -
2,000
(1) (2) (3)
600 1,200 -
1,000
(1) (2) (3) (1)
20 -
3,750 3,000 3,000
(1) (2)
1,980 4,000 7,800
10,750
20,000
-Expenditure -Volume
Actual Profit
Ans. 58: (1)
2,950 17,050
Statement showing the amount of sales target fixed and the actual amount of contribution earned.
(Rs.’000) Zonal Sales Officers
A
B
C
D
Commission earned
29.9
23.5
24.5
25.8
(Commission earned / 5%)
598
470
490
516
Sales price variance
4 (F)
6 (A)
5 (A)
2 (A)
Sales volume variance
6 (A)
26 (F)
15 (F)
8 (F)
Actual sales:
132
Sales target / Budgeted sales
600
450
480
510
Standard cost of sales target
500
375
400
425
Standard margin/ Budgeted margin
100
75
80
85
Sales margin mix variance
14 (A)
8 (F)
17 (F)
3 (A)
Sales price variance
4 (F)
6 (A)
5 (A)
2 (A)
90
77
92
80
Actual margin
Note: As there is no information about sales margin quantity variances, therefore for calculating actual contribution the same has been assumed to be zero. (2) Statement to evaluate the performance of zonal sales officers Zonal Sales Officers S. No.
Base factor to evaluate performance
A
B
C
D
(a) Whether target achieved
No
Yes
Yes
Yes
(b) Actual sales to Target sales ratio (Actual / target) (%)
99.67 598 × 100
104.44 470 × 100
102.98 490 × 100
101.18 516 × 100
600
450
480
510
Efficiency towards the target sales: 1.
2.
3..
(c) Ranking
IV
I
II
III
(a) Contribution earned (in Rs.’000)
90
77
92
80
(b) Ranking
II
IV
I
III
(a) Standard margin/ sales target ratio
16.67
16.67
16.67
16.67
(b) Actual margin / Actual sales ratio (%)
15.05
16.38
18.78
15.50
IV
II
I
III
(c) Ranking
Recommendation: A review of performance of four officers based on three based factors, shows that the performance of officer C is the best. Ans. 69:Kitchen King’s Score card should describe its product differentiation strategy. The key points that should be included in its balance score card are Financial Prospective – Increase in operating income by charging higher margins on Maharaja. Customer Prospective – Market share in high-end kitchen range market and customer satisfaction. Internal business perspectives: Manufacturing quality, order delivery time, on time delivery and new product feature added. Learning and Growth prospective: Development time for designing new end product and improvement in manufacturing process. Operative Income: (Amount in 000 Rs.) 2003 2004 Revenue (40000×1000: 42000×1100) 40000 46200
133
Direct Material 12000 13530 Conversion cost 10000 11000 Selling and Customer service 7200 7250 Total cost 29200 31780 Operative Income 10800 14420 Change in operating Income 36, 20,000 (F) A. Growth Component (a) Revenue effect = Output Price in 2003{Actual units sold in 04 – Actual units sold in 03} = Rs.1, 000 (42,000 units – 40,000 units) = Rs.20, 00,000 (F) (b) The cost effect = Input price in 2003{Actual units of input to produce 2003 output less Actual units of input which would have been used to produce year 2004 output on the basis of 2003} (i) Direct Material = Rs.100 [1, 20,000sqft – 1, 20,000sqft × 42000 units]
40000 units = Rs.6, 00,000 (A) (ii) Conversion cost and selling and customer service will not change since adequate capacity exists in 2003 to support 2004 output and customers. Hence variance Conversion cost = 200(50000 – 50000) = 0 S & Customer Service = 25000(300 – 300) = 0 Increase in operating effect of Growth component is Rs14, 00,000 (F) B. Price recovery Component: (i) Revenue effect = Actual output in 2004 [Selling price per unit in 2004 less Selling price per unit in 2003] = 42,000units (Rs.1, 100 – Rs1, 000) = Rs.42, 00,000 (F) (ii) Cost effect = Unit of input based on 2003 actual that would have been used to produce 2004 output {Input prices per unit in 2003 less Input prices per unit in 2004} (a) Direct material = 1, 26,000sqft (Rs.100/sqft – Rs.110/sqft) = Rs.12, 60,000 (A) (b) Conversion Cost = 50,000 units (Rs.200/unit –Rs.220/unit) = Rs.10, 00,000 (A) (c) S & Custr Service = 300 customers (Rs.24, 000 –Rs.25,000) = Rs.3,00,000 (A) = Rs.25, 60,000 (A) Increase in Operating income due to Price Recovery is Rs.16, 40,000 (F) {Rs.42, 00,000 – Rs.25, 60,000} (C) Productivity Component Productivity component = Input Prices in 04 {Actual units of input which would have been used to produce year 2004 output on the basis of 2003 actual less Actual Input} (i) Direct Material: Rs.110/sqft (1, 26,000 units – 1, 23,000 units) = Rs.3, 30,000(F) (ii) Conversion Cost: Rs.200/unit (50,000 units – 50,000 units) = 0 (iii) Selling & Customer = Rs.25, 000 (300 customers – 290 customers) = Rs.2,50,000 (F) = Rs. 5,80,000 (F) The change in operating income from 2003 to 2004 is analyzed as follows: (Amount in 000 Rs.) 2003 Growth component Price recovery Cost effect of productivity component 2004 Revenue 40000 2000 (F) 4200 (F) -----------46200 Cost 29200 600 (A) 2560 (A) 580 (F) 31780 Operating Income 10800 1400(F) 1640 (F) 580 (F) 14420
134
Key Factor, Throughput Accounting & Budgeting Ans.1: Statement showing ranking Products Particulars P Q Selling Price/unit (Rs.) 25.00 30.00 Variable cost/unit (Rs.) Direct material 11.00 16.25 Direct labour 2.50 2.50 Other variable costs 1.50 2.25 Contribution per unit (Rs.) 10.00 9.00 Machine hours/unit 0.67 0.33 Contribution/machine hour 15 27 Ranking III I
R 35.00 21.00 2.50 3.50 8.00 0.4167 19.2 II
Ans: 2 Working Note The limiting factor in the company is the No. of labour hours in department II. Hence, contribution per labour hour of department II has to be found and products ranked on that basis. A B C Selling price / unit 100 130 175 Less: Variable cost: Direct materials 40 50 64 Direct Labour: Department I 10 12 15 Department II 6 12 12 Department III 12 15 18 Variable overhead 12 80 11 100 16 125 50 20 30 Contribution per unit 1 hr. 0.5 hr. 1 hr. Time taken in department II Contribution per labour hour of Department II 20/0.5 = 40 30 50 Ranking for allotment of department II labour hour II III I Solution Product
A B C
(a) Current mix profit and total labour hour in dept. IIs No. of units Contribution Total Labour time Total labour / unit contribution in time in department department II per unit II 30,000 Rs.20 Rs.6 lakhs 0.5 hr. 15,000 hr. 40,000 Rs.30 12 lakhs 1.0 hr. 40,000 hr. 25,000 Rs.50 12.50 lakhs 1.0 hr. 25,000 hr. Total 30.50 80,000 hr. FOH 25.00
135
Profit
5.50
The suggested product mix is the optimum one because the first ranked product C is proposed to be produced & sold to the maximum of 30,000 units. Similarly, the second ranked product A can be produced and sold up to 50,000 units. The balance hours can be utilized to produce B to the extent of 25,000 units only. This will be optimum mix as indicated below: Product C A B
Product C A B Less: FOH Profit Profit under proposed plan in question Increase in profit
Ranking I II III
No. of Units 30,000 (Maximum) 50,000 (Maximum) 25,000 (Balance) Total (b) Statement of increase in profit No. of Units Contribution per unit 30,000 50 50,000 20 25,000 30 Total
No. of hours in Dept. II 30,000 25,000 25,000 (Balance) 80,000 Amounts (Rs.lakhs) 15.00 10.00 7.50 32.50 25.00 7.50 5.50 2.00
If the suggestion for optimum product mix is implemented, the increase in profit would be Rs.2.00 lakhs. Ans: 3 Working Notes Statement of contribution per machine hour (Limiting factor ) and ranking Particulars PIE SIGMA Selling price 20 30 Less: Variable cost 16 11 Contribution per unit 9 14 Contribution per machine hour = 9/1 14/2 =Rs.9.00 Rs.7.00 Ranking I II Solution (a) Best combination: Pie should be produced fully one lakh units. Then , sigma should be produced within the balance machine hours. This combination will give optimum contribution as follows: Product Ranking No. of Units No. of CPU Total Machine contribution(Rs.) Hours
136
Pie Sigma
I II
1,00,000 1,50,000 (300000 /2 )
Total
1,00,000 3,00,000 (Balance) 4,00,000
9.00 14.00
9,00,000 21,00,000 30,00,000 (Optimum) 26,00,000 4,00,000
Less: Fixed Profit
(b) There is market for Sigma for one lakh units (i.e., 2,50,000 – 1,50,000 units). Two machine hours are required per unit of production of Sigma. That is 1,00,000 units at 2 hours = 2,00,000 machine hours required. For this purpose, 7 machines are to be taken on rental basis. Then, the profit will improve as follows: (Rs.lakhs) Pie 1 lakh units at Rs.9 9.00 Sigma 2.5 lakh units at Rs.14 35.00 Total contribution 44.00 Less: Fixed cost 26.00 Rent 7 X 1.5 = 10.50 36.50 Profit 7.50 (c) There is no change in number of machines required on rental basis. Total rental charges will come down and profit will improve further as follows: (Rs.lakhs) Total contribution (as calculated above) 44.00 Less: Fixed cost 26.00 Rent 7 X 1.25 = 8.75 34.75 Profit 9.25 Ans. 4: Working Notes Particulars Selling Price/unit (Rs.) Variable cost/unit (Rs.) Contribution per unit Machine hours/unit Contribution/machine hour Ranking
X 1900 700 1200 3 400 III
Products Y 2400 1200 1200 2 600 II
(b) Machine hours available will be only 20000 hours Product Ranking No. of units DLH Z I 1000 1000 Y II 2000 4000 X III 5000 (15000/3) 15000 (B.F.) Total 20000 Ans. 5: Statement of Ranking Working Notes
Products
Z 4000 2800 1200 1 1200 I
CPU 1200 1200 1200
Total contribution 1200000 2400000 6000000 Rs. 9600000
137
Particulars Selling Price/unit (Rs.) Variable cost/unit (Rs.) Direct material(@Rs. 8 p.kg) Direct labour(@Rs. 8 p.h.) Variable overheads(@Rs. 5.6 p.h.) Sellling commission (10% of SP)
X 30
Y 40
Z 50
Contribution/unit
5.6 8 5.6 3 22.2 7.8
3.2 16 11.2 4 34.4 5.6
12 12 8.4 5 37.4 12.6
Raw material per unit (kg) Contribution per kg (Rs.) Ranking
0.7 11.14 II
0.4 14 I
1.5 8.4 III
Statement of Ranking (if additional 4500kg are made of RM is available) Products Particulars X Y Selling Price/unit (Rs.) 30 40 Variable cost/unit (Rs.) Direct material(@Rs. 8 p.kg) 5.6 3.2 Direct labour(@Rs. 10 p.h.) 10 20 Variable overheads(@Rs. 7 p.h.) 7 14 Sellling commission (10% of SP) 3 4 25.6 41.2 Contribution/unit 4.4 (1.2)
12 15 10.5 5 42.5 7.5
Raw material per unit (kg) Contribution per kg (Rs.) Ranking
1.5 5 II
0.7 6.28 I
(a) Raw material available will be only 10400 kg Product Ranking No. of units Y I 6000 X II 8000 Z III 1600 (2400/1.5) Total Less: Fixed overheads Profit
0.4 (3) -
RM (kgs) 2400 5600 2400 (B.F.) 10400
(b) Raw material available will be only 14900(10400+4500) kg Product Ranking No. of units RM (kgs) X I 8000 5600 Z II 5000 7500 Balance 1800 Total 14900 Less: Fixed overheads
Z 50
CPU 5.6 7.8 12.6
Total contribution 33600 62400 20160 Rs. 116160 50000 66160
CPU 4.4 7.5
Total contribution 35200 37500 Rs. 72700 75000
138
Profit Hence firm should not go into further production Ans. 6: Statement of Ranking Working Notes Particulars Selling Price/unit (Rs.) Variable cost/unit (Rs.) Direct material Direct labour Variable overheads Contribution/unit Units Total contribution Ranking Raw material per unit (kg) Contribution per kg (Rs.) Ranking DLH required per unit Contribution per DLH Ranking
A 20
(2300)
Products B 16
C 10
6 3 2 11 9 10000 90000 III
4 3 1 8 8 12000 96000 II
2.00 1.50 1.00 4.50 5.50 20000 110000 I
0.6 15 III
0.4 20 II
0.10 27.50 I
0.20 Rs. 45 II
0.20 Rs. 40 III
0.10 Rs. 55 I
Solution (a) Raw material available will be only 12100 kg Product Ranking No. of units C I 20000 B II 12000 A III 5500 (3300/0.6) Total Less: Fixed overheads Profit
RM (kgs) 4000 4800 3300 (B.F.) 12100
(b) Direct labour hours available will be only 5000 hours Product Ranking No. of units DLH C I 20000 2000 A II 10000 2000 B III 5000 (1000/0.2) 1000 (B.F.) Total 5500 Less: Fixed overheads Profit
CPU 5.50 8 9
Total contribution 110000 96000 49500 Rs. 255500 138000 117500
CPU 5.50 9 8
Total contribution 110000 90000 40000 Rs. 240000 138000 102000
(c) No shortage of materials and labour: Ranking as per total contribution is to be considered. Product Ranking No. of units CPU Total contribution
139
C B A
I II III
25000 (20000 + 25%) 12000 10000
5.50 9 8
Total Less: Advertisement cost Net contribution Less: Fixed overheads Profit
137500 96000 90000 Rs. 323500 20000 303500 138000 165500
Ans 7: Working Notes Statement of comparative contribution and Ranking (Direct labour Hour (DLH) is key factor) Particulars A B C Selling 28 60 125 Less: Variable cost 23 45 95 Contribution per unit (CPU) 5 15 30 DLH per unit 10/10 = 1 2 5 Contribution per DLH 5/1 15/2 30/5 =CPU/DLH =5.00 =7.50 =6.00 Ranking III I II Solution (a) Profit according to current plan Product
No. of Units
A B C D
500 (Minimum) 500 (Minimum) 500 (Minimum) 1,400(from surplus DLH) Total
DLH
CPU
500 1,000 2,500 7,000 (Balance) 11,000
5 15 30 30
Total amount(Rs.) 2,500 7,500 15,000 42,000 67,000 25,000 42,000
Less :Fixed overheads Profit (b) Alternative plan for maximum profit
Product B is a Rank No. 1. Hence, instead of C Product. B should be manufactured by using surplus labour hours. This will maximize the profit as follows: Product
No. of Units
A
500 (Minimum)
DLH
CPU 500
5
Total amount(Rs.) 2,500
140
B C D
500 (Minimum) 500 (Minimum) 3,500(from surplus DLH) Total
1,000 2,500 7,000 (Balance) 11,000
15 30 15
Less :Fixed overheads Profit Note: This profit of Rs.52,500 is higher than current plan.
7,500 15,000 52,500 77,500 25,000 52,500
( C ) BEP (units and value) At BEP, contribution is equal to fixed overheads, i.e., and C=F. In such case, the company has to earn the contribution of Rs.25,000 in order to get BEP as follows: Rank I II II
Product
No. of Units
B C A
500 (Minimum) 500 (Minimum) 500 (Minimum)
CPU 15 30 5
Total contribution Less: Fixed overheads Profit BEP (Units and Value) Product No. of Units
Total amount(Rs.) 7,500 15,000 2,500 25,000
25,000 Nil
Selling Price Per unit 60 125 28
B 500 C 500 A 500 Total 1500 BEP in terms of units: 1,500 units BEP in terms of Sales Value : Rs.1,06,500 (d) Profit after tax (PAT) 24% on 1,00,0000 Tax Rate 50% Hence, Profit Before tax 24,000 x 100 50 Less: Tax at 50% PAT
Sales Value at BEP (Rs.) 30,000 62,500 14,000 1,06,500
Rs.24,000 Rs.48,000 Rs.24,000 24,000
Note: By production and selling minimum quantities of A,B and C, BEP is achieved. Hence, in order to earn profit before tax of 48,000, Rank No.1, Product B should be sold to the extent of 3,2000 units (48,000 / CUP rs.15). Then, the position will be as follows: Product No. of Units DLH
CPU
Total
141
A B C
500 500 500
500 1,000 2,500
5 15 30
B
3,200 Total
6,400 10,400
15
Less: Fixed overheads Profit
amount(Rs.) 2,500 7,500 15,000 25,000 48,000 73,000 25,000 48,000
No. of Units and Sales value: Product
No. of Units
A B C Total
500 3,700 500 4,700
Selling Price Per unit 28 60 125
Sales Value (Rs.) 14,000 2,22,000 62,500 2,98,500
The sales value of Rs.2,98,500 will earn the profit of Rs.48,000 (Profit Before Tax) as worked out in the previous statement. PBT 48,000 Less: Tax at 50% 24,000 PAT 24,000 (24% on capital employed of Rs.1,00,000) Ans: 8 Working Notes Statement of contributions per unit of raw material (Key factor) A B C Contribution per 2,00,000/20,000=Rs.10 4,00,000/40,000=Rs.10 3,00,000/20,000=Rs.15 unit= Contribution per 10/4 = Rs.2.50 10/5 = Rs.2.00 15/6 = Rs.2.50 unit of Materials Ranking I II I Solution (i) Production / Sales mix. Product Units A C B Total Less: Fixed Cost Loss
20,000 20,000 20,000 60,000
Materials (Units)
CPU
20,000 X 4 = 80,000 20,000 X 6 = 1,20,000 Balance 1,00,000 3,00,000
10 15 10
(-)
Total Amount(Rs.) 2,00,000 3,00,000 2,00,000 7,00,000 7,50,000
142
50,000 (ii) Product No. of Units CPU Total Amount(Rs.) A 20,000 10 2,00,000 C 20,000 15 3,00,000 B 20,000 10 2,00,000 B 40,000 6.25(Notes) 2,50,000 Total 1,00,000 9,50,000 Less: fixed Cost 7,50,000 + 50,000 = 8,00,000 Profit 1,50,000 Yes, The company can optimize production of 1,00,000 units with local substitute materials. Note 1. Imported Raw material cost Rs.3.00 per unit x 5 units = Rs.15.00 Local substitute materials 3.75 per unit x 5 unit = 18.75 0.75 per unit 3.75 Extra cost of materials Contribution = 10.00-3.75= Rs.6.25 per unit (iii) Product A C B
No. of Units 20,000 20,000 10,000
Total Add: Lease amount
50,000
CPU 10 15 10
Total Amount(Rs.) 2,00,000 3,00,000 1,00,000
Less: Fixed cost Profit 60,000-50,000 = 10,000 The company cannot enhance profits by leasing out a part of the plant. Conclusion – The proposal at (ii) will maximize the profit at Rs.1,50,000. Ans:9 Working Notes Sales Less: Variable cost Contribution
Product A (Rs.per unit) 2,500 1,500 1,000 1,000 2,500 =40%
6,00,000 2,75,000 8,75,000 7,50,000 1,25,000
Product B (Rs. per unit) 5,000 3,250 1,750 1,750 x 100 5,000 =35%
P/V ratio = C x 100 = S Solution (i) When total sales in value is limited: Product A is more profitable as its P/v ratio is 40% which is higher than that of B. (ii) When raw material is in short supply: Product A B Raw material required per unit 10 kg. 25 kg. Rs.500/50= (Rs.1,250/50)
143
Contribution per kg of material =Contribution per unit /kg
1,000/10 kg. =Rs.100
1,750/25 Rs.70
In this case also, product A is more profitable as its contribution per kg of raw material is Rs.100 which is higher than that of B. (iii) When Production capacity is the limiting factor: Product A B Direct Labour hours (DLH) Required per unit = Rs.750/30 25 hours 1,500 / 30 = 50 hours Contribution per DLH =Contribution per unit/No. of DLH 1,000 / 25 hours =Rs.40 1,750 /50 hours =Rs.35 In this case also, Product A is more profitable as its contribution per DLH is Rs.40 which is higher than that of B (iv) Statement of Product Mix and Maximum profit: Product Raw No. of Units. Contribution per Unit Amount (Rs.) Material (kg) (Rs.) A 10,000 1,000 1,000 10,00,000 B 10,000 400 1,750 7,00,000 (Balance) (10,000/25) Total 20,000 17,00,000 Less: Fixed 10,00,000 Overheads 7,00,000 Profit (Maximum) Ans:10 To maximize Profit. (a) Statement of current profit Products A Direct Materials : 10,000 x 20 2.00 Direct labour : 10,000 x 12 1.20 Variable overheads : 10,000 x 8 0.80 Marginal cost 4.00 Sales 10,000 x 64 6.40 Contribution 2.40 Less: Fixed overheads 10,000 x 6 0.60 Profit 10,000 x 18 1.80 Ranking according to I profitability P/v Ratio = C x 100 2.40 x 100 S 6.40 =37.5%
0.80 0.70 0.50 2.00 3.00 1.00
(Rs.lakhs) C 1.44 0.96 0.48 2.88 4.16 1.28
0.30 0.70 III
0.32 0.96 II
1.00 x 100 3.00 1 33 -- % 3
1.28 x 100 4.16
B
30.77%
Total 4.24 2.86 1.78 8.88 13.56 4.68 1.22 3.46
144
( b) Though the contribution per unit of C is lowest, it should not be discontinued. Instead, B should be discontinued. Total contribution from C is more than that of B. Analysis: Product A Selling price 64 Less: Variable cost 40 CPU 24 If C is discontinued, Sales of A and B will increase by 50%.
B 60 40 20
C 52 36 16 Rs.lakhs
Contribution A 10,000 + 50% = 15,000 units at 24= 3.60 B 5,000 + 50% = 7,500 units at 20= 1.50 5.10 1.22 3.88
Less: Fixed overheads Profit If B is discontinued, sales of A and C will increase by 50% Contribution A C
3.60 1.92 5.52 1.22 4.30
8,000 + 50% = 12,000 units at 16 =
Less: Fixed overheads Profit
Hence, C should not be discontinued. Product B should be discontinued. Then , the profit will improve to Rs. 4,30,000. Present profit 3,46,000 Proposed profit 4,30,000 Increase in profit 84,000 C.
Product D: Selling Price Less: Marginal cost Contribution per unit
Rs.
48 25 23
Total contribution Rs.5,52,000 less contribution from a & C 3,68,000 = 1,84,000 Minimum sales = Rs.1,84,000/23 = 8,000 units are to be sold in order to ensure maximum profit as per (b) above, i.e., Rs.4,30,000. Statement of Profitability Rs.lakhs Contribution from A (original level) 2.40 Contribution from C (original level) 1.28 Contribution from D ( proposed ) 8,000 x 23 1.84 Total 5.52
145
Less: Fixed overheads Profit
1.22 4.30
Ans:12 Working Note Statement of contribution per labour hour (limiting Factor) P Q Selling price / unit (Rs.) 80 60 Variable cost / unit (Rs.) 62 49 Contribution (Rs.) 18 11 Labour hrs/unit 20/10= 2 1.5 9 7.33 Contribution /labour hr(Rs.) 18/2= 15,000 20,000 Current sales (Units) Solution (a) Current Profit Contribution: P : 15,000 x Rs.18 Q : 20,000 x Rs.11 R : 10,000 x Rs.14 Total contribution Less: Fixed overheads Profit as per estimate
= = =
R 50 36 14 1 14 10,000
Rs.2,70,000 Rs.2,20,000 Rs.1,40,000 Rs.6,30,000 Rs.5,50,000 Rs. 80,000
(b) Labour is the limiting factor Total Labour Hours utilized for the above production units : (Production and sales same). P = 30,000 hrs.(15,000 x 2) Q = 30,000 hrs.(20,000 x 1.5) R = 10,000 hrs.(10,000 x 1) 70,000 hrs Available hrs. 75,000 hrs. Since contribution per labour hour is Maximum for R, and since labour hour is the limiting Factor, normally this excess 5,000 hrs have to be allocated to R. But, increase in production / sales is limited to 25% of current sales of any one of the products: Product Labour hours Production/sal 25% of Lower of Contributio Total available es possible current sales the (iii) & n per unit contrib (i) (ii) (iii) (iv) (iv) (Rs.) ution Rs. P 5,000 2,500 3,750 2,500 18 45,000 Q 5,000 3,333 5,000 3,333 11 36,663 R 5,000 5,000 2,500 2,500 14 35,000 Contribution is highest for P.P should be chosen and after deduction of Rs. 30,000 for advertisement, profit is Rs.15,000. © If selling price is reduced by 5% the position will be as follows:
146
Product
Reduced Selling price Rs.
Variable cost Rs.
P Q R
80-5%=76 60-5%=57 50-5% 47.50
62 49 36
Contribution Labour hrs per unit Rs. reqd per unit 14 8 11.50
2 1.5 1
Contribution Ranking per labour for hour production Rs. 7 II 5.33 III 11.50 I
Since labour hours are limited to 75000 hours only,product mix will be as follows: Product No of units with Labour hrs. reqd. Total contribution increase R 15,000 15,000 @ Rs.11.5=1,72,500 P 22,500 45,000 @ Rs.14 =3,15,000 Q 10,000 (15,000/1.5) @ Rs. 8 = 80,000 15,000 (Bal.Fig) 75,000 5,67,500 Less: Fixed overheads Profit This proposal is not recommended because of lower profit. Ans. 13:
5,50,000 17,500
147
148
149
Contribution per unit
120
125
121
-
Option 1: Units
-
115
100
215
Contribution (Rs.)
-
14,375 12,100
26,475
Option 2: Units Contribution (Rs.) Option 3: Units Contribution (Rs.)
100
115
-
215
12,000 14,375
-
26,375
80
-
135
215
9,600
-
16,335
25,935
26,780
(305)
22,000
4,375
24,780
1,155
Best strategy is to produce 100 units of product A and 115 units of product B during off - season. Maximum profit = Rs. 4,375. (i)
Best strategy for peak-season is to produce 202 units of A. (ii) Maximum profit for off-season Rs. 4,375.
Ans:14 Products Sale Value Per acre 10 x 1000= Variable cost per acre Contribution per acre Area occupied (acres) Total contribution 25 x 5,300= Less: Fixed overheads Profit
(a) Profit for the current year (Rs.) A B C 10,000 10,000 13,500
D 16,200
4,700 5,300 25
5,100 4,900 20
5,950 7,550 30
6,600 9,600 25
1,32,500
98,000
2,26,500
2,40,000
Total
100 6,97,000 5,40,000 1,57,000
(b) profit for the product mix The land which is being used for A and B can be used for either items. A gives higher contribution per acre. Hence, b should be produced to the minimum of 40 tonnes and in balance land A should be produced. Similarly, the land which is being used for C and D can be used for either items. D gives higher contribution per acre. Hence, C should be produced to the minimum of 36 tonnes and in balance land , D should be produced. Then, the position will be as follows: A + B Area occupied = 25 + 20 = 45 acres. B : Minimum production : 40 tonnes i.e., 40 = 5 8 Acres required.
150
A : Balance 40 acres : A should be produced C + D : Area occupied = 30 + 25 = 55 acres C : Minimum production = 36 tonnes, i.e., 36 = 4 acres required. D : Balance 51 acres : D should be produced. Then, the profitability will improve as follows: Products A B C No of acres 40 5 4 Contribution per 5,300 4,900 7,550 acre 2,12,000 24,500 30,200 Total Contribution Less: Fixed Overheads Profit
D 51 9,600 4,89,600
Total 100 Rs. 7,56,300 5,40,000 2,16,300
The profit will improve from Rs.1,57,000 to Rs.2,16,300 Ans. 15: Calculation of area to be cultivated in respect of each crop to achieve the largest total profit Available information: Land available for all four vegetables
340 hectares
Land available for peas and carrots
140
Total land available
480
Min. requirement of each variety
500 boxes
Max. requirement of each variety
113750 boxes Potato
Peas
Carrots
Tomatoes
Boxes per hectare
350
100
70
180
(a) Market price
Rs. 30.76
Rs. 31.74
Rs. 36.80
Rs. 44.55
Direct material
2.72*
4.32
5.49
3.47
Labour – Growing
5.12*
12.16
10.63
5.87
7.20
6.56
8.80
10.40
Transport per box
10.40
10.40
8.00
19.20
Total variable costs
25.44
33.44
32.92
38.94
(c) Contribution per box (a)-(b)
5.32
(1.70)
3.88
5.61
Contribution per hectare ×
1862
(170)
271.60
1009.80
(b) Variable costs:
- Harvesting & Packing
Boxes per hectare (c)
151
Ranking
I
IV
III
II
*Cost per hectare ÷Boxes per hectare Best cultivation plan: From 140 hectares for peas and carrots: Peas: Minimum 5000 boxes = 5000÷100 = 50 hectares Carrots: Balance land 140 hectares – 50 hectares = 90 hectares From 340 hectares all four vegetables: Tomatoes: Minimum 5000 boxes = 5000÷180 = 28 hectares (in terms of complete hectares) Potatoes: Balance of land i.e. 340 -28 = 312 hectares Area to be cultivated for each variety and total contribution Potatoes
Peas
Carrots
Tomatoes
312
50
90
28
Rs. 1862
(170)
271.60
1009.80
Rs. 580944
(8500)
24444
28274.40
Hectares Contribution per hectares Contribution Total contribution
Rs. 625162.40
Less: Fixed expenses
424000.00
Profit
201162.40
(ii) Analysis to show whether land development should be undertaken Carrot yield a lower contribution per hectare than Potatoes and Tomatoes, but it is grown in excess of the requirement of 5000 boxes or 72 hectares i.e. 5000 boxes ÷700. Therefore, 18 hectares i.e., 90 hectares – 72 hectares can be made available for Potatoes and Tomatoes by land improvement. After land improvement the contribution per hectare of Tomatoes will be foloows: Present contribution per hectare
Rs. 1009.80
Saving per hectare after land improvement Rs. 2.60 ×180 boxes
460.00 1477.80
Allocation of 18 hectares available Crop
Maximum Sales (Boxes)
Present Production
Potatoes
113750
Tomatoes
113750
* 312 hectares X 350 boxes = 109200
(Boxes)
Yield hectare
109200*
4550
350
13
5000
900
180
5(B.F.)
(Boxes)
Addl. Reqt.
(Boxes)
per Additional hectares to be allotted
152
Profit by revised Cultivation plan Potatoes
Peas
Carrots
Tomatoes
Total
Hectares
325
50
72
33
480
Contribution per hectare
Rs. 1862
(170)
271.60
1477.80
Total contribution
Rs. 605150
(8500) 19555.20
48767.40
664972.60
Less: Fixed cost (revised)*
440200.00
Profit
2224772.60
*Capital expenditure
= 18 hectares X 6000 = 108000
Interest ( 108000 X 0.15)
= Rs. 16200
Existing fixed expenses
424000 440200
Conclusion: Since the profit after land development is greater, the company should implement the proposal to develop 18 hectares of land. Question 16: (i) Statement of Cost break-up Sambalpur
Bilaspur
Total cost (Rs. Lacs)
Cost per M.T. of output (Rs.)
Total cost (Rs. Lacs)
Cost per M.T. output (Rs.)
198
1,650
240
1,600
(Refer to working note)
(6,000 M. T. × Rs.1,800 + 3,600 M. T. × Rs.2,500)
(Rs.198 lacs/ 12,000 M. T.)
(12,000 M. T. × Rs.12,000)
(Rs. 240 lacs/ 15,000 M. T.)
Other variables
156
1,300
192
1,280
Material cost
(156 lacs/ 12,000 M. T.) Fixed Cost
108
900
(192 lacs/ 15,000 M. T.) 120
(108 lacs/ 12,000 M. T.) Total Cost Working Note:
462
3,850
800 (120 lacs/ 15,000 M. T.)
552
3,680
Sambalpur
Bilaspur
Annual output (M. T.)
12,000
15,000
Maximum possible output (M. T.)
15,000
25,000
(12,000/80%)
(15,000/60%)
9,600
12,000
(12,000 × 80%)
(15,000 × 80%)
Basic raw material requirement (M. T.)
153
Material available locally (M. T.)
6,000
16,000
Possible output from local material (M. T.)
7,500
20,000
(6,000 / 80%)
(16,000 / 80%)
(ii) Quantity of production at each unit from the availability of local supplies of basic raw material: Sambalpur
Bilaspur
15,000
25,000
1,440 (6,000 × Rs.1,800) / 7,500 M T.
1,600
1,300
1,280
Total variable cost / M. T. of output
2,740
2,880
Possible output (M. T.) from local supplies of basic raw material
7,500
19,500
Maximum output/ possible (M. T.) (Refer to above working note) Material cost/ M. T. of output from locals (Rs.)
Other variables / M. T. of output from locals (Rs.) [Refer to part (i)]
(Balancing Figure) (iii) Cost saving as per revised schedule of production : Sambalpur
Bilaspur
Total
(Rs. lacs)
(Rs. lacs)
(Rs. lacs)
205.5
561.6
767.1
(7,500 M. T. × Rs.2,740)
(19,500 M. T. × Rs.2,880)
Fixed Cost
108.0
120.0
228.0
Total cost: (A)
313.5
681.6
995.1
Previous total cost: (B)
462.0
552.0
1014.0
148.5
(129.6)
18.9
Total variable cost of output (Refer to part ii)
[as per (i) above] Cost savings: {(B) – (A)} Ans. 17
Statement of cost per tonne and net profit earned in respect of each factory
Present production tonnes: (A) Cost of raw material (Rs. in lacs) (Refer to working note 1) Other variable costs (Rs. in lacs) Fixed cost (Rs. in lacs) Total cost (Rs. in lacs): (B) Cost per tonne (Rs) : (C) = [(B) / (A)]
Lucknow 7,200 Rs. 59.04
Pune 10,800 Rs. 87.48
22.32 18.00 99.36 1,380
32.94 24.84 145.26 1,345
154
Selling price (Rs. Per tonne: (D) Net profit per tonne (Rs.) : [(D) – (C)] Total net profit (Rs. in lacs)
1,450 70 5.04 (Rs.70 ×7,200 tonnes)
Total profit of the company = Rs.15.46 lacs
1,460 115 12.42 (Rs.115×10,800 tonnes)
(Rs.5.04 lacs + Rs.12.42 lacs) Alternative production plan to earn optimum Lucknow
Pune
Maximum production capacity (tonnes)
9,000
11,880
Present production (tonnes)
7,200
10,800
Rs.
Rs.
800
810
880
880
310
305
Rs.22.32 Lacs 7,200 tonnes
Rs.32.94 Lacs 10,800 tonnes
1,450
1,460
Contribution per tonne of Output : [(D)–{(A)+(C)}]
340
345
Contribution per tonne of Output : [(D) – {(B)+(C)}]
260
275
Cost per tonne of output: Cost per tonne of output manufactured from locally purchased raw material: (A) (Refer to working note 2) Cost per tonne of output manufactured from material purchased from Bhopal : (B) (Return to working note 3) Other variable cost (Rs.) : (C)
Selling price per tonne (Rs.) : (D)
(When material was purchased from Bhopal) The priority to produce 18,000 tonnes of total output is as below as apparent from the above data: Priority Pune factory (Local purchase of raw material)
1st
Lucknow factory (local) purchase of raw material)
2nd
Pune factory (raw material purchased from Bhopal)
3rd
Lucknow factory (raw material purchased from Bhopal)
4th
Suggested alternative production plan : Production priority
Raw Material
Output (in tonnes)
Input(in tonnes)
Lucknow
Pune
Total
I
11,700 tonnes
13,000
--
11,700
11,700
II
5,400 tonnes
6,000
5,400
--
5,400
III
(11,880 – 11,700) = 180 tonnes
200
--
180
180
IV
720 tonnes balancing figure
800
720
--
720
155
(18,000 – 17,280 tonnes) 20,000
6,120
11,880
18,000
Working Notes: 1.
Lucknow
Pune
Present production output (tonnes)
7,200
10,800
Total raw material required for present production (tonnes)
8,000
12,000
100 7,200 × 90
100 10,800 × 90
Raw material produced locally (tonnes)
6,000
12,000
Raw material product from Bhopal
2,000
--
Cost of raw material purchased locally
59.04
87.48
(Rs.720×6,000+ Rs.792 × 2,000)
(12,000 × Rs.729)
800
810
100 720 × 90
100 729 × 90
880
880
and from Bhopal (Rs. in lacs) 2.
Cost per tone of output manufactured from locally purchased raw material (in Rs.)
3.
Cost per tonne of output manufactured from material purchased from Bhopal (in Rs.)
100 792 × 90
Ans.: 20:Throughout Accounting ratio is highest for ‘Machine 2’. ∴ ‘Machine 2’ is the bottleneck Contribution per unit of bottleneck machine hour :
A
B
C
Total ‘Machine 2’ hours available = 6,000
Ans. 21:
A.
Contribution per unit (Rs.)
30
25
15
B.
‘Machine 2’ hours
15
3
6
C.
Contribution per ‘Machine 2’ hours (A / B)
2
8.33
2.50
D.
Ranking
3
1
2
E.
Maximum Demand
500
500
500
‘Machine 2’ hours required (B × E)
7,500
1,500
3,000
‘Machine 2’ hours available
1,500
1,500
3,000
Units
100
500
500
156
Production B C
A
Total
Mach Capacity
Demand (units) 200 200 200 Hrs. required in Dept. Machine 1 2,400 800 400 3,600 2 3,600 1,200 600 5,400 3 1,200 400 200 1,800 ∴Machine 2 is the bottleneck Note-2: Through put contribution & rank A 24 18 1.33 III
(a) Throughput Contribution (b) MR/unit in Machine 2 (c) Contribution/hr. Machine –2 Rank Identification of product mix.
3,200 112.5% 3,200 168.75% 3,200 56.25%
B 20 6 3.33 II
Hrs. in machine 2 3,200 _600
Available Less: Rank I C
TA ratio
Less: Rank II B Less: Rank III A
C 12 3 4 I units 200 2,600 200 77.77 i.e. 77 units
1,200 18
Ans. 22:
(a)
Machine
Time required for products A
B
C
D
Total Time
Time Machine Available utilization
1
2000
1200
400
200
3800
3000
126.67%
2
2000
1800
600
300
4700
3000
156.67%
3 2000 600 200 100 2900 3000 96.67% Since Machine 2 has the highest machine Utilization it represents the bottleneck activity hence product, ranking & resource allocation should be based on contribution/machine hour of Machine 2. Allocation of Resources A
B
C
D
Machine Utilization
Spare Capacity
157
Contribution unit (Rs.)
per
Time required Machine 2
in
1500
1200
1000
600
10
9
3
1.5
150
133.33
333.33
400
3r d
4th
2n d
1st
Contribution per Machine – hour (Rs.) Rank as per contribution / mach. Hour
200×10 = 2000
Allocation of Machine 2 time
200
Production Quantity
2000
Allocation Machine 1 time
2000
100 (balan cing figure)
200×3 = 600
200×1.5 = 300
200
100/9=11.1 1
400
11.11×6 = 66.66
200 200 100
3000
2666.66
333.34
2333.33
666.67
200
11.11×3 = 33.33
Allocation of Machine 3 time
Ans. 23: W. Note 1 Rs. p. u
Rs. p. u.
A
B
2
40
Variable production overhead cost
28
4
TVC
30
44
Selling price
60
70
(a)
Contribution
30
26
(b)
Limiting factor (hr./u)
0.25
0.15
(c)
Contribution/hr. (a/b) Rs.
120
173.33
(d)
Rank
II
II
(e)
Budgeted production & sales
1,20,000
45,000
(f)
Maximum demand
1,44,000
54,000
Total Fixed cost Rs
14,70,000
Material
W. Note-2: Fixed overhead recovery rate =(Amount÷Budgeted hours) = 14,70,000 ÷36,750 = Rs. 40/hr.
Budgeted hours
A
1,20,000 units @ Rs. 0.25 = 30,000 hrs.
B
45,000 units @ Rs. 0.15
= 6,750 hrs. 36,750 hrs.
(a) Contribution per unit Rs.
A
B
30
26
158
Less: Fixed overhead per unit Rs.
10
6
(a)
Profit per unit Rs.
20
20
(b)
Units
1,20,000
Total (a×b)
45,000
24 lakhs + 9 lakhs = 33 lakhs
Management is indifferent on the basis of profit per unit however this is wrong concept on selecting the product mix. (b)
A
B
(a) Contribution per unit Rs.
30
26
(b)
Limiting time/unit
0.02
0.015
Contribution /hr. (a/b)
Rs. 1,500
Rank
Rs. 1,733
II
II
Statement of product mix & profit Hrs. Available
3,075
Less: for Rank I
810
For Rank II
2,265/0.02
units
Contribution/u
Total
54,000
26
14,04,000
1,13,250
30
33,97,500
Product A
48,01,500 Less: Fixed cost
14,70,000
Profit
33,31,500
(c) Return per bottleneck hour = (selling price – material cost)/ (Time on bottleneck resource) Product A
= Rs. 2,900 [(Rs. 60 – Rs. 2)/ Rs. 0.02 hours]
Product B
= Rs. 2,000 [(Rs. 70 – Rs. 40)/ 0.015 hours]
Product A should be sold up to its maximum capacity of utilizing 2,880 bottleneck hours (1,44,000 units × 0.02 hours). This will leave 195 hours for product B thus enabling 13,000 units (195/0.015) to be produced. The maximum profit is calculated as follows: Rs. Throughput return from product A (1,44,000 × Rs. 58)
83,52,000
Contribution from product B (13,000 × Rs. 30)
3,90,000 87,42,000
Less: Variable overheads
35,40,000
Fixed overhead cost
14,70,000
Net profit
37,32,000
Note: It is assumed that the variable overheads (e.g. direct labour) are fixed in the short term. They are derived from part (a) – [(120,000 × Rs. 28) + (45,000 × Rs. 4)]
Ans. 30: Installed Capacity for the machine =
365 * 8 *3 * 500 = 43.8 lakh units
159
Practical Capacity = ( 365 – 52 - 13 ) * ( 8 - 1) * 3 * 500 = 31.5 lakh units Out of the past five years, normal capacity is average of 3 normal years. Normal Capacity = ( 30.1 + 29.7 + 30.2 ) / 3 = 30.0 lakh units Actual Capacity Utilization = 30.1 lakh units = 68.7 % Idle Capacity = ( 43.8 – 30.1) = 13.7 lakh unit = 31.3 % Abnormal idle capacity = 31.5 – 30.1 = 1.4 lakh units Ans. 31: Details of Computation
Machine hours
1. Maximum capacity ( 365 days × 8 hours per day) 2. Practical capacity Maximum capacity (in hours) 2,920 Less: Idle capacity Sundays: (52 days × 8 hours) 416 Holidays (10 days × 8 hours) 80 Plant maintenance 200 3. Normal capacity 4. Expected capacity
2,920
Capacity Production units @ 10 units per hour 29,200
2,224 2,000 1,900
22,240 20,000 19,000
Determination of Factory overhead application rate (a) Total Budgeted overheads Fixed overhead costs Variable overhead costs (2,000 hours × Rs. 100)
Rs. 6,00,000 2,00,000 8,00,000 2000 400 40
(b) Normal Capacity (machine-hours) (c) (i) Factory overhead application rate (Rs. 8,00,000÷2,000) per hour (ii) Factory overhead application rate (Rs. 8,00,000÷2,0000) per unit Ans. 32 Working Notes:
(Amount in Rupees) X
Y
Z
135.00
140.00
200.00
32.00
76.00
58.50
Department 1
45.00
25.00
50.00
Department 2
15.00
12.00
21.00
Department 3
20.00
10.00
40.00
8.00
4.50
10.50
120.00
127.50
180.00
15.00
12.50
20.00
Selling price per unit (A) Variable costs per unit Direct material Direct labour
Variable overheads Total variable costs (B) Contribution per unit (A−B)
160
(i)
Statement of budgeted profitability X
Y
Z
Budgeted quantity (units)
19,500
15,600
15,600
Contribution per unit (Rs.)
15.00
12.50
20.00
2,92,500
1,95,000
3,12,000
Total contribution (Rs.) Contribution fund (Rs.) Fixed overheads (Rs.) Profit (Rs.) (ii)
3,99,500 Contribution per direct labour hour for Department 2 X
Y
Z
15.00
12.50
20
5
4
7
3.00
3.125
2.857
Rank
II I Total hours available in department 2
III
X
19,500 units × 5 = 97,500 hours
Y
15,600 units × 4 = 62,400 hours
Z
15,600 units × 7 = 1,09,200 hours
Contribution per unit (Rs.) Direct labour hours per unit Contribution per labour hour (iii)
Total
= 2,69,100 hours
Y
19,500
2,69,100
4
19,500
78,000
1,91,100
X
23,400
1,91,100
5
23,400
1,17,000
74,100
Z
19,500
74,100
7
10,585
74,095
5
Optimal profit (Rs.) Contribution (Rs.) Y
19,500 × Rs. 12.50 = Rs. 2,43,750
X
23,400 × Rs. 15
= Rs. 3,51,000
Z
10,585 × Rs. 20
= Rs. 2,11,700
Total Contribution Less fixed cost
= Rs. 8,06,450 = Rs. 4,00,000
161
Profit
= Rs. 4,06,450
Ans 33: (a)
Flexible Budget
Output level (units)
50,000
Sales Direct Material 12.5 per unit (reduction for 1,00,000 units by Rs.0.50) Direct wages (5.00 per unit) Semi variable cost (variable) Factory overhead (V) Rs.5 per unit) Selling and Adm. (25% variable) Total variable cost Contribution Fixed factory overheads (5×60,000) Selling and adm. (6 × 60,000) Semi variable fixed part Increase due to expansion Interest Depreciation Special Advertisement exp. Total fixed costs
80,000
1,00,000
(Rs. in lakhs)
(Rs. in lakhs)
(Rs. in lakhs)
20.00 6.25
32.00 10.00
36.00 12.00
2.50 0.25 2.50 1.00 12.50 7.50 3.00 3.60 .30
4.00 0.40 4.00 1.60 20.00 12.00 3.00 3.60 .30 2.00 .60 .50 . .50 6.90 10.50 0.60 1.50 Therefore activity level 80,000 units is most profitable level. Calculation of
5.00 0.50 5.00 2.08 24.58 11.42 3.00 3.60 .30 2.80 .60 .50 . 10.80 0.62
Break even point P/V ratio 7.5/20.00 × 100 = 37.5%, 12.00/32.00 × 100 = 37.5%, 11.42/36.00 × 100 = 31.72%BEP (value) = 6.90/37.5% = Rs.18,40,000, 10.50/37.5% = Rs.28,00,000, 10.80/31.72% = 34,04,792 BEP (Units)
6.90lakhs Rs.15
10.50lakhs Rs.15
10.80lakhs Rs.15
= 46,000 units = 70,000 units = 94,571 units Alternative Solution (BEP in Sales) Break Even Point in value of sales:
(F x S) / (S – V)
At 50000 units’ level :
(6,90,000 x 20,00,000)/7,50,000
= Rs. 18,40,000
At 80000 units’ level :
(10,50,000 x 32,00,000)/12,00,000
= Rs. 28,00,000
At 100000 units’ level :
(10,80,000 x 36,00,000)/11,42,000
= Rs. 34,04,553
162
Ans. 34: Overheads
Budget statement for April Budget Fixed Variable Total Management Rs.30,000 30,000 Shift premium 3,600 3,600 ESI 6,000 7,920 13,920 Inspection 20,000 9,000 29,000 Supplies 6,000 6,480 12,480 Power 7,200 7,200 Lighting and heating 4,000 4,000 Rates 9,000 9,000 Repairs 8,000 5,400 13,400 Materials handling 10,000 10,800 20,800 Depreciation 15,000 15,000 Administration 12,000 12,000 Idle time 1,20,000 50,400 1,70,400
Actual 30,000 4,000 15,000 28,000 12,700 7,800 4,200 9,000 15,100 21,400 15,000 11,500 1,600 1,75,300
Variance Adverse Favourable 400 1,080 1,000 220 600 200 1,700 600 500 1,600 6,400 1,500 Rs.4,900 (A)
(b) E.S.I. This variance may be due to increase of E.S.I. rates. If this assumption is correct, then the variance will be beyond the control of management. It should be noted that actual activity is less than budgeted activity. It is , therefore, unlikely that increase is due to increase in the number of labour hours worked. Another possibility is that E.S.I. Payment might have got increased due to increase in E.S.I. rates. Inspection: There is a possibility that standard inspection has been lowered, thus resulting in a saving in costs. If this is not due to management policy, then the variance requires immediate investigation. Another possibility is that a number of staff members have resigned and consequently actual inspection is less than the budget. Repairs and Maintenance: This increase may be due to unexpected repair, which might not have been envisaged. The variance for this item over a period of several months should be studied to form an opinion. Idle Time: No Idle time has been included in the budget. Consequently this idle time must be of an abnormal nature. Possible uncontrollable causes include a power failure or machine breakdown. Controllable causes may include poor scheduling or lack of material. (c ) (i) Calling for comments on variances in excess of a specific figure may not be satisfactory for control purpose. For decision on whether to investigate or not, Cost of investigation should be compared with benefits of investigation. Statistical tests may also be applied. (ii) The statement could be improved by analyzing the expense items into their controllable and non- controllable elements. Variances should be analysed according to whether they are due to price and quantity changes. Analysis should include non- financial measures such as a comparison of actual hours worked with standard hours produced. (d) (i) Overhead absorbed = Rs.1,58,400, i.e.,36,000 hrs x Rs.4.40 (ii) Over spending = Rs.4,900 (iii) Actual production was 4,000 standard hours less than budgeted production and this decline in output has resulted in a failure to recover Rs.12,000 fixed overheads. This under recovery of Rs.12,000 is also known as the volume variance.
163
Ans. 35:
A.Z. Limited Analysis of the information required for preparation of cash budget (Rs.’000) April May June July August Sales receipts 401.70 450.28 425.88 Variable cost of sales (60%) 240.00 270.00 312.00 252.00 288.00 Variable production costs: In the month of sales (60%) 144.00 162.00 187.20 151.20 In prior month (40%) 108.00 124.80 100.80 115.20 252.00 286.80 288.00 266.40 Material costs 60% of production cost 151.20 172.08 172.80 159.84 Purchases: In the month of production (50%) 75.60 86.04 86.40 79.92 In prior month (50%) 86.04 86.40 79.92 Payment to supplier 161.64 172.44 166.32 Labour costs (Variable production cost x 0.3) 75.60 86.04 86.40 79.92 Variable overhead 25.20 28.68 28.80 26.64 (Variable production cost x 0.1) Variable cost was paid as follows: Paid in the month of incurrence (40%) 10.08 11.47 11.52 10.66 Paid in the following month (60%) 15.12 17.21 17.28 Variable overhead expenditure 26.59 28.73 27.94 Cash budget for the month of May to July 1997 May June 401.70 450.28
Receipts from sales Payments: Materials Labour Variable overhead Fixed costs (12,00,000-3,00,000)/12 Capital expenditure Total expenditure Net inflow (outflow) Balance b/f Balance c/f
July 425.88
161.64 86.04 26.59 75.00
172.44 86.40 28.73 75.00
166.32 79.92 27.94 75.00
349.27 52.43 40.00 92.43
552.57 (102.29) 92.43 (9.86)
349.18 76.70 (9.86) 66.84
Note. In this question language should be given particular attention: (a) Variable production cost 60% in the same month 40% in the prior month. Production cost relevant for cash budget for each month should be found. (b) 60% of production cost is material 50% in the same month and 50% in the prior month. 30% of production cost is labour which is paid the same month. 10% of production cost is variable overhead, 40% is paid the same month. 60% is paid in the following months. (c) This question illustrates the interaction of sales, purchase and manufacturing process and requires the reader to think clearly about these relationships Ans. 36
Note: Since question has not clearly specified that whether labour efficiency is lower by
164
ANOTHER 1% or by 1%, also it is unclear that efficiency is to reduced based on BUDGETED EFFICIENCY OR ACTUAL EFFICIENCY, hence this question can be solved in following 3 ways (after giving prompt assumption) Solution – Way 1 Production Cost Budget (for 6 months ending 30th September, 2009) 30,000 units Cost per unit Total Rs. Rs. Material cost 180 54,00,000 Labour cost 115.47 34,64,208 Variable overhead 23.65 7,09,500 23.2 6,96,000 Fixed overhead 342.34 1,02,69,708 Assumption : Here, difference in actual and standard time is also considered for calculating the lower efficiency i.e. 3.74% + 1% = 4.74% based on budgeted efficiency Working Notes: I. Material cost Material consumption per unit = 1,600MT ÷16,000 = 0.10 MT Consumption for 30,000 units = 3,000 MT. Cost of 3,000 MT @ Rs. 1,800 per MT = Rs. 54,00,000. II.
Labour cost can be calculated as follows: 2008 – Total Budgeted Hour = 16,00,000 ÷40 Labour hour budget for each unit = 40,000÷ 16,000 Actual time paid = 15,99,840÷ 44
= 40,000 hours = 2.5 = 36,360 hours
Less: Standard labour hours for 14,000 units (i.e. 14,000×2.5)= 35,000 hours Difference in actual and standard hours = 1,360 3.74% = Difference in actual and standard hours ÷ Actual hours ×100 = 1,360 hours÷ 36,360 hours Budget unit (2008) for each labour hour = 16,000÷40000 Less: (3.74% + 1%) = 4.74% for lower efficiency Budget unit (2009) for each labour hour
= 0.4 units = 0.01896 units = 0.38104 units
Time required for 30,000 units (30,000 ÷ 0.38104)
= 78,732 hours
Labour cost = 78,732 hours× 44 per hour = Rs. 34,64,208. III.
Variable overhead Actual rate = Rs.2,76,000 ÷14,000 units Add: 20 % New rate
= 19.71 per unit = 3.94 23.65
165
Total variable overhead = 30,000 ×23.65 = Rs. 7,09,500 IV. Fixed overhead Actual = Rs. 5,80,000 = Rs. 1,16,000 Add: 20% = Rs. 6,96,000 According to above the production cost budget will be as follows: Solution – Way 2 Production Cost Budget (for 6 months ending 30th September, 2009) 30,000 units Cost per unit Rs. Material cost 180 Labour cost 111.11 Variable overhead 23.65 Fixed overhead 23.2 337.96
Total Rs. 54,00,000 33,33,352 7,09,500 6,96,000 1,01,38,652
Assumption : Here, lower efficiency of 1% is based on budgeted efficiency Working Notes: I. Material cost Material consumption per unit = 1,600MT ÷ 16,000 = 0.10 MT Consumption for 30,000 units = 3,000 MT. Cost of 3,000 MT @ Rs. 1,800 per MT = Rs. 54,00,000. II. Labour Cost: 2008 – Total Budgeted Hour = 16,00,000 ÷40 Budget unit (2008) for each labour hour = 16,000÷40000 Less: 1% for lower efficiency Budget unit (2009) for each labour hour Time required for 30,000 units (30,000 ÷ 0.396)
= 40,000 hours = 0.4 units = 0.004units = 0.396 units = 75,758 hours
Labour cost = 75,758 hours × 44 per hour = Rs. 33,33,352 III. Variable overhead Actual rate = Rs.2,76,000÷14,000 units Add: 20 % New rate Total variable overhead = 30,000 ×23.65 IV. Fixed overhead Actual Add: 20%
= 19.71 per unit = 3.94 23.65 = Rs. 7,09,500 = Rs. 5,80,000 = Rs. 1,16,000 = Rs. 6,96,000
166
Solution – Way 3 Production Cost Budget (for 6 months ending 30th September, 2009) 30,000 units Cost per unit Rs. Material cost 180 Labour cost 115.44 Variable overhead 23.65 Fixed overhead 23.2 342.29
Total Rs. 54,00,000 34,63,196 7,09,500 6,96,000 1,02,68,696
Assumption : Here, lower efficiency of 1% is based on actual efficiency Working Notes: I. Material cost Material consumption per unit = 1,600MT ÷ 16,000 = 0.10 MT Consumption for 30,000 units = 3,000 MT. Cost of 3,000 MT @ Rs. 1,800 per MT = Rs. 54,00,000. II. Labour Cost: 2008 – Total Actual Hour = 15,99,840 ÷44 Actual unit (2008) for each labour hour = 14000÷36360 Less: 1% for lower efficiency Budget unit (2009) for each labour hour Time required for 30,000 units (30,000 ÷ 0.38115)
= 36,360 hours = 0.385 units = 0.00385units = 0.38115 units = 78,709 hours
Labour cost = 78,709 hours × 44 per hour = Rs. 34,63,196 III. Variable overhead Actual rate = Rs.2,76,000÷14,000 units Add: 20 % New rate Total variable overhead = 30,000 ×23.65 IV. Fixed overhead Actual Add: 20%
Ans. 37: (a)
= 19.71 per unit = 3.94 23.65 = Rs. 7,09,500 = Rs. 5,80,000 = Rs. 1,16,000 = Rs. 6,96,000
Cash Budget for October, November and December 1990 October November Opening balance of bank (overdraft) Rs.35,000 Rs.(9,100) Cash inflows – Sales: From cash sales of current month 5,000 6,000 From credit sales of previous month 15,000 18,000 Total Receipts (A) 55,000 14,900 Cash outflows:
December Rs.(12,600) 8,000 20,000 15,400
167
Creditors for purchases of the preceding month Equipment Wages Administration Rent Dividend Total payment (B) Closing balance (Overdraft) (A-B)
40,000 16,000 3,000 1,500 3,600 64,100 (9,100)
23,000 3,000 1,500 27,500 (12,600)
(b) Budgeted Income Statement for three months ending 31st December 1990 Sales Less: Cost of Goods Sold: Rs.20,000 Material- Opening Stock Add: Purchases (23,000 + 27,000 + 26,000) 76,000 96,000 Less: Closing stock 43,500 Cost of material consumed 52,500 Wages (3,000 x 3) 9,000 Gross profit Less: Rent [ 3,600 x (3 / 12 ) ] 900 Administration (1,500 x 3) 4,500 Depreciation [3,000 x (3 / 12)] 750 Loss on sale of asset ( Rs.15,000 – Rs.14,000) 1,000 Net profit
Working Notes: (i) Total Sales October 1990 November 1990 December 1990
Credit Sales Rs.18,000 20,000 25,000 63,000
For Cost of Sales: (ii) Sales for the quarter Less: Gross Profit 25% of Sales Cost of sales (iii) For Material consumed: Cash of sales for three months Less: Wages (3,000 x 3) Cost of material consumed (iv) For closing stock of material Opening stock of material Add: Purchases (23,000 + 27,000 + 26,000) Less: Material consumed Closing stock of material
Cash Sales Rs.5,000 6,000 8,000 19,000 Rs.82,000 20,500 61,500 Rs.61,500 9,000 52,500 Rs.20,000 76,000 96,000 52,500 43,500
27,000 3,000 1,500 15,000 46,500 (31,100) Rs.82,000
61,500 20,500
7,150 13,350
Total Rs.23,000 26,000 33,000 82,000
168
Ans. 38:
Nov 6120
Shirt Dec 6242
Jan 6367
Feb -
15000
15300
15606
15919
21120
21542
Op. Stock
6000
Production
15120
Cl. Stock( 40% Of next month) Sales Total
Nov 8160
Short Dec 8320
Jan 8490
Feb -
20000
20400
20800
21224
21973
28160
28720
29290
6120
6242
8000
8160
8320
15422
15731
20160
20560
20970
Shirts Opening stock
Shorts
6000
8000
Sales November
6000 40%
8000 = 20,000 40%
= 15,000
December
1.02 x 15,000 = 15,300
1.02 X 20,000 = 20400
January
1.02 x 15,300 = 15,606
1.02 X 20,400 = 20,808
February
1.02 X 15, 606 = 15, 919
1.02 X 20,808 = 21,224
Alternative: Opening Stock Shirts = 6000 = 40% of November Sales November sales
6000 40%
= l5,000
Opening Stock of Shorts = 8000 =40% of November Sales 8000 = 20,000 40%
Dec. Sales
l.02 x l5,000 = l5,300
l.02 x 20,000 = 20400
Closing Stock November
40% x l5, 300 = 6,l20
40% x 20,400 = 8l60
November Production = l5, l20 Closing Stock + sales – Opening stock
20,l60
December Production
l.02 X l5, l20 = l5422
l.02 X 20,l60 = 20, 560
January Production
l.02 Xl5422 = l5, 73l
l.02 X 20,560 = 20, 970
Ans39:
(a) Production Budget for product A and B A units
B units
Inventory at the end of the year
1,000
2,000
Sales forecast
8,000
15,000
169
Total requirements
9,000
17,000
Less: Beginning inventory
3,000
5,000
Production
6,000
12,000
Budgeted requirements of components P, Q and R Components
P
Q
R
For Product A: Production 6,000 units P: 6,000 × 1 per unit
6,000
Q: 6,000 × 2 per unit
12,000
For Product B: Production 12,000 units P: 12,000 × 2 per unit
24,000
Q: 12,000 × 1 per unit
12,000
R: 12,000 × 2 per unit
24,000
For comp R: Production 24,000 comp Q: 24,000 × 1 per component R
24,000
Total requirements (b) The company is advised to adopt EOQ system. P
EOQ
48,000
24,000
Q
2 × 30,000 × 15 2 × 20%
= 1,500 components
30,000
2 × 48,000 × 15 0.8 × 20%
= 3,000 components
(c) Calculation of savings arising from switching over to the new ordering system. Existing situation: P Present order quantity (units)
Q
30,000 × ¼
7,500
48,000 × ¼
12,000
7,500 × ½
3,750
12,000 × ½
6,000
3,750 × Rs. 2
7,500
6,000 × Re. 0.80
4,800
(equivalent to 3 months consumption) Average stock (units) Investment in inventory of P & Q Total investment
Rs. 7,500 +
Carrying cost @ 20% p.a. of average inventory investment
Rs. 12,300 × 20%
Ordering cost:
P = 4×Rs. 15
Rs. 4, 800
=Rs. 12,300 Rs. 2,460
= Rs. 60
Total cost
Rs. 120 Rs. 2,580
After switching over: Economic order quantity (units)
P
Q
1,500
3,000
170
Average stock (units) Investment in inventory of P & Q
1,500 × ½
750
3,000 × ½
1,500
750 × Rs. 2
1,500
1,500 × Re. 0.80
1,200
Total investment
Rs. 1,500 +
Carrying cost @ 20% p.a. of average inventory investment Ordering cost:
Rs. 1,200
=Rs. 2,700
Rs. 2,700 × 20%
Rs. 540
P = 20×Rs. 15
= Rs. 300
Q = 16×Rs. 15
= Rs. 240
Rs. 540
Total cost
Rs. 1,080
Saving in costs: Rs. 2,580 – Rs. 1,080 = Rs. 1,500 Reduction in working capital: Rs. 12,300 – Rs.2,700 = Rs. 9600 Ans. 42:
Production Budget (showing quantities to be manufactured) Chairs Units to be sold (Note 1) 4,200 Add: Closing inventory as per budget 200 4,400 Less: Opening inventory as per budget 400 4,000 (b) Material Purchase Budget (in quantities)
Material required for production (Note 1) Add: Closing stock as per budget Less: Opening stock as per budget Raw materials to b purchased
Timber (cu. ft.) 4,450 650 5,100 600 4,500
Tables 800 300 1,100 100 1,000
Benches 500 50 550 50 500
Upholstery (Sq. yards) 1,000 260 1,260 400 800
Materials Purchase (in rupees) Quantities to be purchased Timber (c.ft.) 4,500 Upholstery (sq. yds.) 860 (c)
Rate 50 20
Amount Rs.2,25,000 17,200 2,42,200
Direct wage Cost Budget
Carpenter’s time and wages Fixer’s and finisher’s time and wages
Total hrs. 4,625 1,500
Rate p.h. 6.00 4.80
Amount Rs.27,750 7,200 34,950
(d) Statement showing the variable cost of manufacture per unit of all three products. Chairs Tables Benches
171
Raw materials – Timer Upholstery Fixing and finishing materials cost (Note 2) Wages Carpenters Fixer’s and finisher’s
(e)
Rs.25.00 (0.5 x Rs.50) 5.00 (0.25 x 20) 1.50
60.00 (1.2 x Rs.50) -
125.00 (2.5 x Rs.50) -
3.00
6.25
4.50 (45/60) x Rs.6 1.20 (15/60) x 4.80 37.20
6.00 (60/60) x Rs.6 1.20 (15/60) x 4.80 70.20
7.50 (75/60) x Rs.6 2.40 (30/60) x 4.80 141.15
Budgeted Net Income Statement (For the quarter)
Selling price (per unit) Less: Variable cost Contribution per unit (A) Units to be sold (B) Total contribution Fixed cost for the quarter (Rs.8,000 x 30 Budgeted net income
Chairs Rs.50.00 37.20 12.80 4,200 53,760
Tables Rs.85.00 70.20 14.80 800 11,840
Benches Rs.158.00 141.15 16.85 500 8,425
2. Per unit cost of materials of fixing and finishing
Ans. 43:Necessary Calculations
74,025 24,000 50,025
Working Notes: 1. Raw Materials, Carpenter’s Time and Fixer’s and finisher’s Time Chairs Tables Benches Units to be manufactured 4,000 1,000 500 Timber (c. ft.) 2,000 1,200 1,250 (4,000 x 0.5) (1,000 x 1.2) (500 x 2.5) Upholstery (sq. yards) 1,000 (4,000 x 0.25) Carpenter’s time (hrs.) 3,000 1,000 625 (4,000 x(45 /60) 1,000 x (60/60) 500 x (75/60) Fixer’s and Finisher’s 1,000 250 250 time(hrs.) 4,000 x(15/60) 1,000 x (15/60) 500 x (30/60)
Total cost of Timber and Upholstery Fixing and Finishing Material will cost 5% Of total cost of timber and upholstery
Total Rs.
Chairs Rs.30 1.5 (5% of 30)
Tables Rs.60
Benches Rs.125
3 6.25 (5% of Rs.60) (5% of Rs.125)
Total 4,450 1,000 4,625 1,500
172
Statement showing total cost and selling price and sales in units for each product (Working Note 1) Working A Working B Working C Materials Rs. Rs. Rs. (Rs.2x5 units) 10 2x12 24 M1 M2
-
(4x10)
40
M3
(Rs.1x5 units)
5 15
(1x5)
5 45
Labour Department I Department II Department 1II Variable overhead
(Rs.2.5x4) (Rs.2.0x6) (Rs.1.5x2)
10 12 3 10
(2.5x2) (2x2) (1.5x4)
5 4 6 20
Fixed Cost(Working Note 2) Department I (Rs.5x4 hrs.) 20 Department II (Rs.3x6 hrs) 18 Department 1II (Rs.6x2 hrs.) 12 Total production cost 100 Adm.(Based on 20% of production cost) 20 Selling and Distb. Cost (40% of prod. Cost) 40 Total cost 160 Profit (25% of total cost) 40 Selling price per unit 200 Sales in rupees 15,00,000 Sales in units 7,500 Sales in rupees / Selling price (per unit) (a) Production Budget for July 1986 Sales Less: Closing stock (given) Add: Closing stock : 20% reduction (working Note 3) Production (b) Material Usage budget for July 1986 Product Units of Qty. per product unit of product A B C Total usage in unit
6,900 4,600 5,500
5 12
(5x2) (3x2) (6x4)
(12 ½ % of total cost)
(4x9)
36 60
10 6 24 120 24 48 192 24
216 10,80,000 5,000
(2.5x2) (2x3) (1.5x6)
5 6 9 15
(5x2) (3x3) (6x6)
10 9 36 150 30 60 240 40
(16 2/3% of total cost
280 16,80,000 6,000
A (Units) 7,500 3,000 4,500
B (units) 5,000 2,000 3,000
C (Units) 6,000 2,500 3,500
2,400 6,900
1,600 4,600
2,000 5,500
M 1 total Qty reqd. 34,500 66,000 1,00,500
Qty. per unit of product 10 9
M2 Total Qty reqd.
M 3 Qty Total per units Qty. of reqd. product 5 34,500 46,000 5 23,000 49,500 95,500 57,500
173
(c ) Material Purchase Budget
M1 Rs. 2,01,000
Units 95,500
M2 Rs. 3,82,000
Units 57,500
M3 Rs. 57,500
24,500 76,000
49,000 1,52,000
20,500 75,000
82,000 3,00,000
17,500 40,000
17,500 40,000
22,050 98,050
44,100 1,96,100
18,450 93,450
73,800 3,73,800
15,750 55,750
15,750 55,750
Units 1,00,000
Usage (price is given Less: O/stock (Add: C/stock) (10% reduction)
(d) Budgeted profit and loss account for each product and in total A B C Sales Rs.15,00,000 Rs.10,80,000 Rs.16,80,000 Less: cost (Working Notes) 12,00,000 9,60,000 14,40,000 Profit 3,00,000 1,20,000 2,40,000
Total Rs.42,60,000 36,00,000 6,60,000
Working Notes Note: 1. Price per unit of material and material units required for each product should be multiplied. Note:2. Fixed overhead rate Deptt. I = Rs.2,39,000 or Rs.5 per hour 47,800
Deptt. II
= Rs.2,01,300 or Rs.3 per hour 67,100
Deptt. II
= Rs.3,91,200 or Rs.6 per hour 65,200
Note:3. A = 3,000 x 80 100
or 2,400 , B = 2,000 x 80 100
A -7,500 x 160 C – 6,000 x 240
Note:4.
or 1,600, C = 2,500 x 80 or 2,000 100
=Rs. 12,00,000; =Rs.14,40,000
B - 5,000 x 192
Rs.9,60,000;
Ans. 44: Responsibility Accounting Reports For the production manager Cutting Department Cloth Cutting Labour
Budgeted Rs. 31,000 6,000
Actual Rs. Variance Rs. 36,000 6,600
5,000 (A) 600 (A)
174
Cutting utilises Total cutting Deptt. (A)
800 37,800
700 43,300
100 (A) 5,700 (A)
500 17,000 900 18,400 56,200
450 18,400 950 19,800 63,100
50 (F) 1,400 (A) 50 (F) 1,400 (A) 6,900 (A)
Sewing Department: Thread Sewing Labour Sewing utilities Total Sewing Dept. (B) Total (A + B)
For the director-Manufacturing Production Department * Production engineering expenses Production manager-office expenses
56,200 13,000 18,000
63,100 12,200 17,000
6,900 (A) 800 (F) 1,000 (F)
Total
87,200
92,300
5,100 (A)
(* As per responsibility accounting report for the production manager) For the Direct-Marketing Sales representative: Travelling expenses Sales commission Total (A)
9,000 7,000 16,000
10,200 7,000 17,200
1,200 (A) -1,200 (A)
16,000 4,000 20,000
15,700 4,000 19,700
300 (F) — 300 (F)
8,000 1,200 5,000 14,200 50,200
8,000 1,050 3,000 12,050 48,950
150 (F) 2,000 (F) 2,150 (F) 1,250 (F)
Sales Management: Office expenses Advertising Total (B) Credit Department: Salaries Credit reports Bad debt Losses Total Total (A + B + C)
Note: ‘F’ denotes favourable variance while ‘A’ denotes adverse variance. Ans. 45:
Performance Budget
Revenue (5,000×10) (4,000×10) (4,000×11) Variable (5,000×4) Costs (4,000×4) (4,000×4.5)
Original Plan Rs. 50,000 40,000
Revised Budgeted Rs.
Actual Variance Result Rs. Rs.
44,000
4,000 (F)
18,000
2,000 (A)
20,000 16,000
175
Contribution (5,000×4) (4,000×6) (4,000×6.5) Fixed costs Net Profit
30,000 24,000 20,000 10,000
26,000 20,000 4,000
2,000 (F) 21,000 5,000
Summary Report on Profit Plan Planned Income (from Project plan) Rs. 10,000 Activity variance (lost contribution margin due to shortage of materials) (6,000) Selling price variance (increased Selling price of Re. 1/- per unit) 4,000 Variance cost variance (increased production Costs at 0.50 per unit) (2,000) Fixed cost variance (new research programme to Develop raw materials and processes) (1,000) Actual income (from income statement)
5,000
1,000 (A) 1,000 (F)
176
TRANSFER PRICING Ans 9 (i)
In this case there are two options available – (a)
(b)
Sell at the sub assembly stage (after completion of Div. A) @ Rs. 2000/Incremental cost in Div. A
Rs 1,200/-
Contribution
Rs
Sell at the final product stage
Rs. 3,000
Cost at Div. A and Div. B Rs(1200+1500)
Rs 2,700
800/-
Contribution Rs 300 Therefore it is profitable to sell at the subassembly stage because of higher contribution, provided there is a market. Hence, if there is market at intermediate stage, first priority is to sell assembly).Therefore, 800 units should be sold as sale of intermediary.
intermediary (sub
The balance capacity available of (1000 – 800) = 200 units should be transferred to B and B should complete the assembly and sell as final product, since the company can earn Rs. 300 per unit for each unit of such sale. (ii) If B Div. receives the subassembly at market price of Rs. 2,000, plus its own incremental cost of Rs. 1,500 will give total cost of Rs. 3,500, thereby yielding a loss of Rs. 3500 – Rs. 3000 = Rs. 500 per unit, whereas the company makes a profit of Rs. 300 per unit. In order to keep the manager of Div. B motivated, the profit earned of Rs. 300 per unit should be shared between A and B. Hence transfer price will be variable cost of Div. A + 50% of profit earned in the final product = 1200 + 150 = Rs. 1,350 (iii) Both Div. A and the Company make higher contribution by selling to intermediate market. If the market demand increases to 1,000 units, the full quantity should be sold outside as intermediary and nothing should be transferred to Div. B Ans.10: Transfer Price is Rs. 4,500 for each consulting day. Profit mark-up = 150% Let cost = x Profit = x ×
150 = 1.5x 100
Cost + profit = Transfer price x + 1.5x = 4,500 2.5x = 4,500 x = 1,800 ∴Cost = Rs. 1,800 and profit = 1.5x = 1.5×1,800 = Rs. 2,700 Variable cost (80%) = Rs. 1,800× 80% = Rs. 1,440 Fixed cost (20%) = Rs. 1,800 ×20% = Rs. 360. Scenario (i): Every consultancy team is fully engaged. There is no idle time or spare capacity. Hence, transfer price = Marginal cost plus opportunity cost Marginal cost = Rs. 1,440 Saving for internal work = Rs. 200 Net Marginal Cost = Rs. 1,240
177
Opportunity cost is the lost contribution. Lost contribution = Contribution from external client = Fee charged from external client – Variable cost = Rs. (4,500 – 1,440) = Rs. 3,060. ∴Transfer price = Rs. 1,240 + 3,060 = Rs. 4,300 per consulting day per team. Scenario (ii): One team is idle. Idle time has no opportunity cost. Variable cost for internal work is Rs. 1,240 per consulting day. Second team is busy. Hence opportunity cost is relevant in case of second team. Hence charge of second team is Rs. 4,300 per consulting day per team. Average of charge of two teams = Rs. (1,240 + 4,300) / 2 = Rs. 2,770 per consulting day per team. Scenario (iii): New client offers a fee of Rs. 15,84,000 Duration: 5 days of 48 weeks ×2 teams Fee per day 15,84,000 / 480 Variable cost = Rs. 1,440 Contribution Rs. (3,300 – 1,440) Fee for consulting day for internal work: Variable cost Contribution lost Fee to be charged
= 480 days = Rs. 3,300 = Rs. 1,860 = Rs. 1,240 = Rs. 1,860 = Rs. 3,100 per consulting day per team.
Ans.11: 100% capacity 4,000 tones (Maximum) Distribution market Processing unit
2,000 Tones 2,000 Tones
80% capacity 3,200 tones Market Processing unit
2,000 Tones 12,00 Tones
(a) 80% capacity – price Rs. 400 per ton (Rs.) Particulars Basic unit Particulars Processing unit Sales (3,200 * 400) 12,80,000 (24,000 * 40) 9,60,000 Raw materials (3,200 * 70) 2,24,000 Tr. Price (1,200 * 4,80,000 Variable cost (3,200 * 140) 4,48,000 400) 2,04,000 (1,200 * 170) Fixed overhead 3,00,000 1,20,000 9,72,000 8,04,000 Profit 3,08000 1,56,000 Total profit of the company = Rs. 4, 64,000 (b) 100% capacity – price Rs. 400 per ton Particulars Basic unit Sales (4,000 X 400) Raw materials (4,000 X 70) Variable cost (4,000 X 140) Fixed overheads Profit
Particulars
16,00,000 (4000 X 320) 2,80,000 Tr. Price (2,000 X 400) 5,60,000 (2,000 X 170) 3,00,000 14,00,000 4,60,000 Total Profit of the Company = Rs. 4,80,000
(Rs.) Processing unit 12,80,000 8,00,000 3,40,000 1,20,000 12,60,000 20,000
178
(c ) 80% capacity- Market price @ Rs.360 & Transfer price to processing @ Rs. 400 per tonne Particulars Sales (2,000 X 360) + (1,200 X 400) Raw materials (3,200 X 70) Variable Cost (3,200 X 140) Fixed overheads
Basic unit
(Rs) Processing unit
Particulars
12,00,000 (24,000 X 40) 2,24,000 Tr. Price (1,200 X 400) 4,48,000 (1,200 X 170) 3,00,000 9,72,000 2,28,000 Total Profit of the Company = Rs. 3,84,000
Profit
9,60,000 4,80,000 2,04,000 1,20,000 8,04,000 1,56,000
(d) 100% capacity- Price Rs. 360 per tonne Particulars Basic unit Particulars Sales (4,000 X 360) 14,40,000 Raw material (4,0000 X 70) 2,80,000 Tr Price (2,000 X 360) 5,60,000 (2,000 X 170) Variable overheads (4,000 X 140) 3,00,000 Fixed overheads 11,40,000 Profit 3,00,000 Total profit o the Company = 4,00,000
(Rs.) Processing units 12,80,000 7,20,000 3,40,000 1,20,000 11,80,000 1,00,000
Comments : At Rs. 400 per tonne, the processing unit will not be interested in buying more than 1,200 tonnes because the profitability of the processing unit will be reduce from Rs. 1,56,000 to Rs. 2,000. When the market price reduce to Rs. 360 per tonne the processing unit will not be interested in purchasing more than 1,200 tonnes because at this level it can maintain the same level of profit. Even if the price is reduced to Rs.360 for the processing unit, it may not be interested in buying more than 1,200 tonnes as its profitability will be reduced from Rs.1,56,000 to Rs.1,00,000. When the market price reduced to Rs.360 per tonne and the transfer price is maintained at Rs.400, the processing unit may get its suppliers of 1,200 tonnes via open market at the price less than Rs.400 per tonne. This will increase the profitability of the processing unit but reduced the profitability of the basic unit. Thus the present policy market price for transfer pricing does not offer incentive to the processing unit. Hence cost plus method should be restored to. Ans. 12 (i)
(a)
At 80% level (in Rs)
-Textile unit Sales (4,00,000 × 6) Less Raw material (4,00,000 Variable cost (4,00,000 Fixed cost Profit
24,00,000
× 3) × 1.2)
12,00,000 4,80,000 4,12,000 3,08,000
-Process house Sales(1,50,000/100) × 825 Less Transfer Price (1,50,000 × 6) Variable cost (1,500 Fixed cost Profit
×
80)
12,37,500 9,00,000 1,20,000 1,00,000 1,17,500
Overall profit = 3,08,000 + 1,17,500 = Rs 4,25,500 At 100% level Sales (5,00,000
×
30,00,000
6)
Less Raw material (5,00,000
×
Sales (2,50,000/100)
× 725
18,12,500
Less 3)
×
15,00,000
Transfer × 6)
Price
(2,50,000
15,00,000
6,00,000
Variable cost
2,00,000
Fixed cost
4,12,000
Fixed cost
1,00,000
Profit
4,88,000
Profit
Variable 1.2)
cost
(5,00,000
12,500
Overall profit = 4,88,000+12,500 = Rs 5,00,500 (b)
At 80% level (market price 5.60 and transfer price 6/-) Textile unit Sale (2,50,000
× 5.6)
(in Rs) Process house
1400000
179
(1,50,000
× 6.0)
900000 23,00,000
Less Raw material (4,00,000 Variable cost (4,00,000
× 3) × 1.2)
12,00,000 4,80,000
Fixed cost
4,12,000
Profit
2,08,000
Profit
1,17,500
Overall profit = 2,08,000+1,17,500 =Rs 3,25,500 (c)
Sales 100% level at (5.60) (in Rs)
Sale (5,00,000
×
5.6)
Less Raw material (5,00,000
× 3)
Variable cost (5,00,000
× 1.20)
× 725)
28,00,000
Sales(2,50,000
15,00,000
Transfer Profit (2,50,000 × 5.6)
18,12,500
Less
×
14,00,000
6,00,000
Variable cost (2,500 80)
2,00,000
Fixed cost
4,12,000
Fixed cost
1,00,000
Profit
2,88,000
Profit
1,12,500
Overall profit = 2,88,000 + 1,12,500 =4,00,500 (ii)
Comments on the profitability of processing units:(a)
Transfer price (Rs)
Profit (Rs) 1,17,500
80% capacity
6.00
100% capacity
6.00
12,500
(b)
80% capacity
6.00
1,17,500
(c)
100% capacity
5.60
1,12,500
Processing house will not be interested to buy more than 1,50,000 meters from textile units.
Ans.: 13 Particulars Selling Price Variable costs Contribution Alternative I Division AD
(Rs.) BRITE 300 150 150
LITE 60 40 20
TITE 700 590 110
(Rs) Contribution (15,000 units of BRITE X Rs.150) (40,000 units of LITE X Rs.20) Total Contribution Fixed Expenses Profit
22,50,000 8,00,000 30,50,000 20,00,000 10,50,000
(a)
Division CD (Rs) Contribution (5,000 units of TITE X Rs.110) Fixed Expenses Profit Overall profit of the company
(b) (a + b)
5,50,000 4,00,000 1,50,000 Rs.12,00,000
Alternative II Division AD (Rs)
180
Contribution (15,000 units BRITE outside customer @ Rs.150) (5,000 units of BRITE Division CD @ 150) (20,000 units of LITE (limited capacity) @ Rs.20) Total contribution Fixed expenses Profit
22,50,000 7,50,000 4,00,000 34,00,000 20,00,000 14,00,000
(a)
Division CD Extra cost of labour Rs.50 and variable cost Rs.640 Hence contribution Rs.700 - Rs.640 = Rs.60 (Rs) Contribution (5,000 units @ Rs.60) Fixed Expenses Loss Overall profit of the company
300,000 400,000 100,000 13,00,000
(b) (a-b)
Alternative III Division AD Price of BRITE to CD reduced by Rs.50 Hence Contribution/unit Rs.250 – Rs.150 = Rs.100 (Rs) Contribution (15,000 units of BRITE outside party @ Rs150) (5,000 units of BRITE to CD @ Rs100) (20,000 units of LITE to capacity @ Rs20) Total contribution Fixed expenses Profit Division CD BRITE from AD Rs.250 contribution Rs.700-Rs.590 = Rs.110 per unit Lobour and overhead Rs.340, Variable costs Rs.590 Contribution (5,000 units @ Rs.110) Fixed expenses Loss Overall profit of the company
(a)
22,50,000 5,00,000 4,00,000 31,50,000 20,00,000 11,50,000
(Rs.) 5,50,000 4,00,000 1,50,000 Rs.13,00,000
(b) (a+b)
Alternative 1V Division AD Contribution (15,000 units BRITE outside customer @ Rs.150) (10,000 units of BRITE to CD @ Rs.250 i.e., contribution @ Rs.100) Total contribution Fixed expenses Profit (a)
(Rs.) 22,50,000 10,00,000 32,50,000 20,00,000 12,50,000
Division CD (Rs.) Contribution (10,000 units with BRITE of AD @ Rs.110) 11,00,000 (2,000 units with imported component @ Rs.110) 2,20,000 Total contribution 13,20,000 Fixed expenses 11,70,000 Profit (b) 1,50,000 Overall profit of the company (a+b) Rs.14,00,000 Recommendation on best alternative Alternative (iv) seems to be the best because it leads to the maximum profit of Rs. 1400000 for the company. But management should consider whether stopping the production of Lite altogether will, in any way, be detrimental to company’s interests. Negotiated price of Rs. 240 per unit. The price of Rs. 240 per unit will be acceptable to AD because it will lead to a contribution of Rs. 22.50 per hour i.e. (Rs. 240-Rs.150)÷4 hours. If this proposal is not accepted AD will have to produce Lite which will yield a contribution of only Rs. 20 per hour, i.e. (Rs. 60-Rs.40)÷1 hour.
181
Ans.: 14: Alternative I AJ Sales : outside (18,000x15) DJ (2,000x10) Total Less V. Costs( 20,000x8.50) Net Contribution Alternative II Sales : (20,000x15) Variable costs(20,000x8.50) Contribution
Alternative III Sales : (20,000x15) Variable costs(20,000x8.50) Contribution
Alternative IV Sales : (22,000x15) Variable costs 1,87,000 Over time 4,000 Contribution
Rs. DJ 2,70,000 Sales (2,000 x 105) 20,000 Variable Costs (2,000 x 99) 2,90,000 Contribution 1,70,000 Interest 1,20,000 Net Contribution Total Group contribution =Rs.1,31,000
Rs. 2,10,000 1,98,000 12,000 1,000 11,000
3,00,000 Sales (2,000 x 105) 1,70,000 Variable Costs (2,000 x104) 1,30,000 Contribution Interest Net Contribution Total Group contribution = Rs.1,31,000
2,10,000 2,08,000 2,000 1,000 1,000
3,00,000 Sales (2,000 x 105) 1,70,000 Variable Costs (2,000x 104) 1,30,000 Contribution Interest Net Contribution Total Group contribution = Rs.1,31,000
2,10,000 2,08,000 2,000 1,000 1,000
3,30,000 Sales (2,000 x 105) Variable Costs(2,000 x 104) 1,91,000 Contribution 1,39,000 Interest Net Contribution Total Group contribution = Rs.1,40,000
2,10,000 2,08,000 2,000 1,000 1,000
Comments: Alternative 1: AJ can supply part 35 to DJ at Rs.10 because the variable cost is Rs.8.50 only and by this transaction a contribution of Rs.1.50 is available. But the overall contribution which would have been Rs.13,000 if the part has been sold to outside buyers, would come down to Rs.1,20,000. DJ however, will earn a net contribution of Rs.11,000. Thus the divisional performance of AJ will go down and that of DJ will boost up at the cost of AJ. Alternative 2: AJ will maintain its performance but DJ’s performance will be reduced to a contribution of Rs.1,000 only. Alternative 3: AJ will maintain its performance but DJ’s performance will be reduced to a contribution of Rs.1,000 only. In these three cases the group income will not change but the performance of the individual divisions will vary. Alternative 4: AJ’s performance will boost up but DJ’s performance will remain at the low level .DJ cannot show better performance except at the cost of AJ. Hence AJ should not reduce the price particularly when it has an assured market for part 35 at Rs.15 each. Ans.: 15: Statement showing profitability of two divisions at two different levels of output using different transfer prices
182
No. of bottles
8,00,000 Rs. 91,20,000
12,00,000 Rs. 1,27,80,000
Sales value (Packed Product) : (A) Less : Costs Product Manufacturing Division 64,80,000 96,80,000 Bottle Manufacturing Division 10,40,000 14,40,000 75,20,000 1,11,20,000 Total costs : (B) Profit :{(A) – (B)} 16,00,000 16,60,000 Profit pro-rated to Bottle Mfg. Division and Product Mfg. Division. Share of Bottle Manufacturing Division: 16,00,000 × 10,40,000/75,20,000 2,21,276 16,60,000 × 14,40,000/1,11,20,000 2,14,964 Balance profit relates to Product Mfg. Division 13,78,724 14,45,036 16,00,000 16,60,000 Rs. Rs. Transfer prices of bottles Costs 10,40,000 14,40,000 Profit as computed above 2,21,276 2,14,964 12,61,276 16,54,964 Total price Rs. 1.577 Rs. 1.379 Transfer price per bottle From the above computations, it is observed that shared profit relative to the cost involved is Rs. 2,21,276 (Re. 0.2766 per bottle) at 8,00,000 production level and Rs. 2,14,964 (Re. 0.179 per bottle) at 12,00,000 production level. The profit of Product Mfg. Division is Rs.13,78,724 (Rs.1.723 per bottle) at 8,00,000 production level and Rs. 14,45,036 (Rs. 1.2042 per bottle) at 12,00,000 production level. Profitability based on market price No. of bottles Bottle Mfg. Division Market price Less: Cost Profit (i) Product Mfg. Division Sales Less: Bottle cost Product cost Profit (ii) Total profit : (i) + (ii)
Production level 8,00,000 bottles 12,00,000 bottles Observations: 1. 2.
Profit based on cost (Rs.Lakhs) Product Bottle Mfg. Div. Mfg. Div. 2.21 13.79 2.15 14.45
8,00,000
12,00,000
Rs. 14,00,000 10,40,000 3,60,000
Rs. 20,00,000 14,40,000 5,60,000
91,20,000 14,00,000 64,80,000 12,40,000 16,00,000
1,27,80,000 20,00,000 96,80,000 11,00,000 16,60,000
Profit based on Market price (Rs.Lakhs) Product Bottle Mfg. Div. Mfg. Div. 3.60 12.40 5.60 11.00
Market price methods gives a better profitability to Bottle Mfg. Division at both the production levels. Market price method gives a lower profitability to Product Mfg. Division as compared to Bottle
183
3.
Mfg. Division. Under Cost-based method, there is a better profit at lower level of production in Bottle Mfg. Division. However in Product Mfg. Division 12,00,000 production level gives a higher profit. But in Market price method, the position is quite reverse.
Ans. 16 (i) Statement of contribution (a) When component is purchased by Division B from outside Division A Division B Sales (2000x 400) Less: Cost of Purchase (2000x 200) 400000 Variable costs (200x 150) 300000 Company’s total contribution
(Rs.) Nil 8,00,000 3,80,000
(b) When component is purchased from Division A by Division B Division A Sales (2000x 220) 4,40,000 Less: Variable costs (2000x 190) 7,00,000 Division B Sales (2000x 400) 8,00,000 Less: Variable Costs: Purchase cost in Division A (2000x 220) 440000 Variable cost in Division B (2000x 150) 300000 7,40,000 Company’s total contribution
1,00,000 1,00,000 (Rs.)
60,000
60,000 1,20,000
Thus, it will be beneficial for the company as a whole to ask Division B to buy the component from Division A. (ii) Statement of total contribution if Division A could be put to alternative use: Division A: Contribution from alternative use of facilities Division B: 30,000 Sales (2000x 400) 8,00,000 Less: Variable costs: Cost of purchase (2000x 400) 400000 Division B (2000x 150) 300000 7,00,000 1,00,000 Company’s total contribution 1,30,000 Since, the company’s contribution when component is purchased from outside, shows as increase of Rs.30,000 as compared to when there is inter departmental transfer. Hence, it will be beneficial to purchase the component from outside.
(iii) Statement of total contribution when component is available from outside at Rs. 185 Division A: Nil Division B: Sales (2000x 400) 8,00,000 Less: Variable costs: Cost of purchase (2000x 185) 370000 Division B (2000x 150) 300000 6,70,000 1,30,000 Company’s total contribution 1,30,000 If the component is purchased by Division B from Division A, the contribution is only Rs.1,20,000 as calculated under above. Hence it will be beneficial to buy the component from outside.
184
(iv)
Fixations of transfer price (a) When there are no alternative uses of production facilities of Dept. A: In such a case the variable cost i.e. Rs.190 per component will be charged. (b) If facilities of Division A can be put to alternative uses: (Rs.) Variable cost Opportunity cost Transfer price
(c) If market price gets reduced to Rs.185 and there is no alternative use of facilities of A. the variable cost of Rs.190 per component should be charged.
190 15 205
Division
Ans.17 For the budgeted level of activities and expenses of LD the various costs and prices can be worked out as follows: (Rs.) Total overheads 7,56,000 Less: Variable overheads 4,20,000 Fixed overheads per year 3,36,000
Variable overheads
Fixed overheads per year At the budgeted level of activities
LX 4,20,000 x 90,000 2,10,000 1,80,000
LY 4,20,000 x 1,20,000 2,10,000 2,40,000
3,36,000 x 90,000 2,10,000 1,44,000
3,36,000 x 1,20,000 2,10,000 1,92,000
The costs and selling prices of the products of LD for normal sale to outside parties will be as under: (Rs.per kg.) Particulars LX LY Direct material 36 28 Direct wages 30 20 Variable overheads 60 40 Total Variable cost: 126 88 Fixed costs 48 32 Total costs 174 120 Add: Mark-up 50% 87 60 Selling price 261 180 Labour hours calculated as under: Particulars Direct wages Wages rate (Rs./hr.) Direct labour hr.
LX
LY 30 5 6
Committed production of LY of 6,000 kg. would involve labour of 6000 x 4 = 24,000 Balance labour available for: Production of LX Production of LY
= 42,000-24,000 = 18,000 hrs. / 6 DLH
= 18,000 Hrs. = 3,000 Kg.
20 5 4
185
Cost estimate of KX it KD purchase Lx from LD at normal prices (Rs.) Cost of LX Processing materials & Wage costs Variable Overheads Total Variable Cost
261 30 4 295
Profit Statement of LD & KD (1) Transfer price based on total cost LD Rs. KD Sales LX (3000 x 261) 7,83,000 Sales KX (2000 x 300) LY (6000 x 180) 10,80,000 Total Sales 18,63,000 Variable cost Variable cost (2000 x 295) LX (2000 x 122) 2,44,000 (1000 x 126) 1,26,000 LY (6000 x 88) 5,28,000 Total variable cost 8,98,000 Fixed costs Fixed cost 3,36,000 Total costs Total cost 12,34,000 Profit Loss 6,29,000 Total profit for the company
= 6,29,000 – 90,000
5,90,000
1,00,000 6,90,000 (-)90,000
=Rs.5,39,000
(ii) Transfer price based on total Cost after adjustment for selling expenses LD Rs. KD Sales LX (2000 x 257) 5,14,000 Sales (2000 x 300) (1000 x 261) 2,61,000 LY (6000 x 180) 10,80,000 Total Sales 18,55,000 Less: Costs as above 12,34,000 Total costs (690000-4 x 2000) Profit 6,21,000 Less
(iii) Total profit to the company =6,21,000-82,000 =Rs.5,39,000 LD Rs. KD Sales LX (2000 x 122) 2,44,000 Sales KX (2000 x 300) (1000 x 261) 2,61,000 LY (6000 x 180) 10,80,000 Variable cost (2000 x 156) Fixed costs Total Sales 15,85,000 Total costs Less: Total Costs as above 12,34,000 Profit 3,51,000 Profit
(iv)
Rs. 6,00,000
Rs. 6,00,000
6,82,000 (-)82,000
Rs. 6,00,000 3,12,000 1,00,000 4,12,000 1,88,000
Total profit for the Company =3,51,000 + 1,88,000 =Rs.5,39,000 LD Rs. KD Rs. Sales LX (3000 x 152) (a) 3,04,000 Sales KX (2000 x 300)(a) 6,00,000 (Including Rs.30 oT) (3000 x261) 7,83,000 LY (6000 x 180) 3,72,000 10,80,000 Variable cost (2000 x 186) Total Sales 1,00,000
186
Variable cost LX (2000 x 152) (3000 x 126) LY (6000 x 88)
21,67,000
3,04,000 3,78,000 5,28,000 Total variable cost 12,10,000 Fixed costs 3,36,000 Total costs (b) Total costs 15,46,000 Profit (a-b) Profit 6,21,000 Total profit for the company =6,21,000 + 1,28,000
Ans.18 (i) Department ‘A’ By product BYEA Sales Income
(iii) Department ‘C’ Production of POTS 5% wastage
200 300 Total
%
4,72,000 1,28,000 Rs.7,49,000
Production 3000 Tonnes (30% of 3000 Tonnes @ Rs.200) (70% of 3000 Tonnes @ Rs.1200) Total
(ii) Department ‘B’ Production of RESP (3000 x 200,i.e.,600000 litres) Sales (600000 litres @ Rs.15) Costs: Opportunity Cost of BYEA Variable Costs (600000 @ Rs.4) Fixed Costs Total Profit
(a) Sales Pack (ML)
(b) (a-b)
(Rs.) 1,80,000 25,20,000 27,00,000
(a)
(b) (a-b)
(Rs.) 90,00,000 27,00,000 24,00,000 12,00,000 63,00,000 27,00,000 (ltrs.)
(600000 x 1.6)
Litres
75 25
9,60,000 48,000 9,12,000
No.of packs
Price/Pack Rs. 34,20,000 2.50 7,60,000 3.50
6,84,000 2,28,000 9,12,000
Sales Value Rs 85,50,000 26,60,000 1,12,10,000
(b) Costs (Rs.) RESP Mfg. Cost Total
(600000 x 15) (912000 x 1.50)
Profit (a-b) (iv) Total Profit under the existing arrangement A-27,00,000 + B-27,00,000 + C-8,42,000 Under the new proposal Total quantity of RESP purchased Production of POTs
90,00,000 13,68,000 1,03,68,000 8,42,000 =Rs.62,42,000
(3000 x 120) (360000 x 1.60)
(Ltrs.) 3,60,000 5,76,000
187
Amount of Saleable POTs
(a) Sales Pack (ML) 200 300 Total
% 75 25
(b) Costs RESP Mfg. Cost Fixed Overhead of Dept. B
(576000 x 95/100)
Litres 4,10,400 1,36,800 5,47,200
No.of packs
Price/Pack Rs. 2,05,200 2.50 4,56,000 3.50
5,47,200
Sales Value Rs 51,30,000 15,96,000 67,26,000 (Rs.)
(360000 x 6.25) (547200 x 1.50)
22,50,000 8,20,000 12,00,000
42,70,800
Profit (a)- (b) 24,55,200 Analysis : Since under the new proposal profit gets lowered from Rs.62,42,000 to Rs.24,55,200 the proposal is not acceptable.
Ans.19. The transfer price will be notional revenue to S and notional cost to T. (a) S will continue to produce more output until the costs of further production exceed the transfer price revenue. (b) T will continue to want to receive more output from S until its net revenue from further processing is not sufficient to cover the incremental transfer price costs. Output Units 600 700 800 900 1000 1100 1200
Division S Incremental Cost Rs. 100 140 160 200 250 350
Division T Incremental Costs Rs. 300 280 250 220 200 150
Since S will continue to produce more output if the transfer price exceeds the incremental costs of production, a price of at least Rs.200 per 100 units (Rs. 2 per unit ) is required to ‘persuade’ the manager of S of produce as many as 1,000 units, but a price in excess of Rs.250 per 100 units would motivate the manager of S to produce 1,100 units (or more). By a similar argument, T will continue to want more output from S if the incremental revenue exceed the transfer costs from S. If T wants 1,000 units the transfer price must be less than Rs.220 per 100 units. How ever, if the transfer price is lower than Rs.200 per 100 units, T will ask for 1100 units from S in order to improve its divisional profit further. In summary (a) The total company profit I maximised at 1,000 units of output. (b) Division S will, want to produce 1,000 units, no more and no less, if the transfer price is between Rs.2 and Rs.2.50(Rs.200 to Rs.250 per 100 units). (c) Division T will want to receive and process 1,000 units, no more and no less, if the transfer price is between Rs.2 and Rs.2.20 (d) A transfer price must therefore be selected in the range Rs.2.00 to Rs.2.20 per unit(exclusive).
188
Thus, if a price of Rs.2.10 per unit is selected, profits at 1,000 units of output would be; (Rs.) Particulars Division S Division T Total Sales/Net revenue 2,100 4,000 4,000 Costs 1,200 2,100 1,200 Profit 900 1,900 2,800 At a transfer price of Rs.2.10 any increase in output above 1,000 units, or shortfall in output below this amount, would reduce the profits of company as a whole, but also the divisional profits of S and T. Ans.20. (a)The problem The overall company interest is obviously to produce 1,400 units which will given the maximum profit. The problem is to fix the transfer price (TP) with which both X and Y will find 1,400 units to be the optimum output for them severally. Let us analyse and examine the incremental costs at X and the incremental revenue at Y Level of output Incremental Cost for Incremental Net Company profit X revenue for Y Rs. 1,000 3,100 1,100 100 300 3,300 1,200 120 240 3,420 1,300 130 190 3,480 1,400 150 170 3,500 1,500 180 130 3,450 1,600 220 80 3,310 A price of at least Rs. 150 per 100 units (Rs.1.50 per unit) is required to induce the manager of X to produce as many as 1,400 units; but the price must not exceed Rs.180 per 100 units, for in that event X would like to produce 1,500 units (or more) Similarly, Y will keep producing so long as the incremental revenues exceed the transfer cost from X. in order that Y wants 1,400 units, the TP must be lower than Rs.170 per 100units; but it shall not be lower than Rs.130,for Y will then ask for 1,500 units from X to increase his (Y’s) divisional profit further. If the TP is selected at Rs.1.60 per unit, profits at 1,400 units of output would be (Rs.) Particulars X Y Company Sales / Net revenue 2,240 4,900 4,900 Costs 1,400 2,240 1,400 Profit 840 2,660 3,500 At a TP of Rs.1.60 any increase in output above 1,400 units or shortfall in output below this level would reduce the profits of the company as a whole and also the divisional profits of X and y. With Rs.1.60 as TP, neither X or Y will like to deviate from 1,400 units, which incidentally is also wanted y the corporate Management. Ans. 21. (i) Calculation of transfer price to be quoted by Alfa to Beta based on residual income (Rs.) Fixed Costs 80 Return on capital employed (Rs.750 lakhs x 12/100) 90 Residual income desired 100 Total 270
189
Desired contribution per unit =Selling price p.u.-Variable cost p.u. =Rs.180- Rs.60 =Rs.20 p.u. Total desired contribution =12,00,000 units x Rs.20 p.u =Rs.240 lakhs Minimum contribution to be earned from sale of additional 3 lakh units. Rs.270 lakhs-Rs.240 lakhs
=Rs30 lakhs.
Contribution p.u. on additional 3,00,000 units =Rs.30,00,000/3,00,000 units = 10 p.u. Variable cost of modification per unit
=Rs.5
Hence, the minimum transfer price per unit to be quoted will be =Rs.160 + 10 + 5 =Rs.175 (ii) If Beta can buy from outside at less than the variable cost of manufacture, Rs.165, than only the decision to transfer at the price of Rs.175 will become sub-optimal for the group as a whole. Ans.22. Working Notes: (i) Computation of Sales revenue from Foam Division (Rs.) Sales of Foam Division to outside customers Less: Variable Mfg. Costs
(Rs.1,600-Rs.200) (Rs.1,200-Rs.200)
1,400 1,000 400
Mark-up on outside Sale (Rs.400/Rs.1000)x 100=40% Transfer Price of Foam to Upholstery Division Sales of Foam Division to outside Customers Total (ii) Variable Mfg. Cost of Upholstery Division =(Rs.680-Rs.200 + Rs.280)
(Rs.’000) =Rs.760
(iii) Computation of Traceable Administration Expenses Divisions Foam Carpets Given Administration expenses 134 116 Less: Common expenses (10% of Gross Profit) 40 40 Traceable Administration Expenses 94 76 (iv) Computation of Traceable Selling Expenses Divisions Foam Given Selling expenses 202 Less: Common expenses (2.5% of Sales) 40 Traceable Selling Expenses 162
280 1,400 1,680
Carpets
( Rs.’000) Upholstery Total 172 422 50
130
122
292
210
Upholstery 232
30 180
30 202
(a) Revised operating statement (using Contribution approach) Divisions Sales Revenue Less: Variable Mfg. Costs Contribution (i) Traceable Costs: Fixed Mfg. Costs Admn. Expenses
( Rs.’000) Total 644 100 544 (Rs.000)
Foam 1,680 1,200 480
Carpets 1,200 700 500
Upholstery 1,200 760 440
Total 4,080 2,660 1,420
-
100 76
20 122
120 292
190
Selling Expenses Total (ii) Operating Income (i)-(ii) Less: Common expenses Net Income of the Company
94 162 256 224
180 356 144
202 344 96
544 956 464 230 234
(b) (i) Computation of contribution Margin (Rs.’000) Contribution X 100 Contribution Margin Ratio % = Sales
Foam Carpets Upholstery
(Rs.480/Rs.1680) x100 (Rs.500/Rs.1200) x 100 (Rs.440/Rs.1200) x 100
(Ranks) 28.57% 41.67% 36.67%
III I II
(ii) Computation of Net Contribution Ratio (Rs.’000) Net Contribution Ratio (%)
Foam Carpets Upholstery
= Net Contribution X 100 Sales
(Rs.224/Rs.1680) x100 (Rs.144/Rs.1200) x 100 (Rs.96/Rs.1200) x 100
13.33% 12% 8%
III I II
It is observed from the above analysis that foam Division’s Manager argument I correct when we look at the calculation given above which shows that even though contribution margin ratio of Foam Division is lower, the divisions ranking is higher based on the Net Contribution Ration. The use of contribution approach for reporting is more realistic for assessing the performance of various divisions as it considers variable and traceable costs only and avoids common costs while finding out profitability. This approach enables the management to rightly interpret the information. Further, pricing of internal transfers at market price will give due credit to specific profits centre i.e. transferor. Ans. 23 The desired rate of return is 28% on investments. Investments include: (i) Fixed assets after depreciation (ii) Net working capital. In the question, current assets and debtors are given but current liabilities and creditors are not indicated. Therefore, these are assumed to have nil value. Investments Fixed assets 5,00,000 Net working capital Rs. Current assets 3,00,000 Debtors 2,00,000 5,00,000 Total investments The desired rate of return is 28% The profit margin will be Budgeted volume Profit margin per unit (Rs. 280000 ÷ 400000 units) Fixed cost per unit Variable cost per unit
10,00,000 Rs. 280000 400000unit Rs. 0.70 2.00 10.00
191
Transfer price per unit
Ans.24 (i) Profit Average assets Sundry Debtors Inventories Plant & equipment
12.70
=20% return on average assets employed (Rs.Lakhs) 2 5 5 12
Total Profit =Rs.12,00,000 x 20 /100 =Rs.2,40,000 (2) Budgeted sales revenue (2,00,000 units of component X) Fixed cost Variable cost (2,00,000 units @ Rs.1) Profit Total Sales
(Rs.Lakhs) 5.00 2.00 2.40 9.40
Selling price per unit of component X =Rs.9,40,000/2,00,000 units =Rs.4.70 per unit Options in hand with Division A Option 1 -Sell 1,50,000 units in market and transfer 50,000 units to Division B Option 11 -Sell only 1,50,000 units in market. Statement of profitability of Division A under two options (Rs.) Particulars Option-I Option-II Sales (1,50,000 units @ Rs.4.70) 7,05,000 7,05,000 Transfer to Division-B (50,000 units @ Rs.2) 1,00,000 Total Sales revenue 8,05,000 7,05,000 Less: variable overhead 2,00,000 1,50,000 Contribution 6,05,000 5,55,000 Less: Fixed Cost 5,00,000 4,75,000 Profit (a) 1,05,000 80,000 Capital employed (b) 12,00,000 10,00,000 Return on capital employed (a)/(b)X100 8.75% 8% Analysis : From the analysis of the above it is observed that under Option-I, Division A’s, Profit and ROCE is increased by Rs.25,000 and 0.75% respectively. Hence Option-I is suggested for Division-A. Ans. 25 (i) The company as a whole will not benefit if Division C bought the component from an outside supplier at Rs.135/- per unit. Rs. Purchase cost from outside supplier
1,35,000
(1,000 units × Rs.135 per unit) Less: Saving in variable cost of division A by reducing Division’s output
1,20,000
(1,000 units × Rs.120 per unit) Net cost (benefit) to the company as a whole
15,000
The company as a while will not benefit, as it will be required to incur an additional cost of Rs.15,000 if Division C bought the component from outside supplier.
192
(ii) The company will be benefited if C purchased the component from an outside supplier and Division A uses the facilities for other activities. Rs.
Rs.
Purchase cost from outside supplier
1,35,000
(1,000 units × Rs.135) Less: Saving in variable cost of Division A for the units purchased by Division C from outside
1,20,000
(1,000 units × Rs.120 per unit) Cash operating saving of Division A for the use of facilities for other activities
18,000
1,38,000
Net cost (benefit) to the company as a whole
(3,000)
It is advisable that Division C should purchase the component from outside sources as this decision will benefit the company by Rs.3,000. (iii) The company will be benefited if C purchase the component from an outside supplier and there is no alternative use of Division A’s facilities. Rs. Purchase cost from outside supplier
1,15,000
(1,000 units × Rs.115) Less: Saving in variable cost of Division A by reducing division’s output
1,20,000
(1,000 units × Rs.120)
.
Net cost (benefit) to the company
(5,000)
It is advisable that the Division C should buy the component from outside as this decision will benefit the company by Rs.5,000. Ans 26
(i) 1.
Working notes: Contribution per hour of Super-chips and Okay-chips: Super-chips
Okay-chips
Selling price per unit (Rs.)
600
120
Less: Variable cost per unit (Rs.)
300
80
Contribution per unit (Rs.)
300
40
2
0.5
150
80
(Rs.300/2 hrs)
(Rs.40/0.5 hrs)
Hours required per unit Contribution per hour 2.
Details of hours utilized in meting the demand of 15,000 units of Super-chips and utilizing the remaining hours for Okay-chips out of available hours of 50,000 per annum: Rs. Hours utilized for manufacturing 15,000 units of Super-chips
30,000
(15,000 units × 2 hours) Hours utilized for manufacturing 40,000 units of Okay-chips
20,000
(40,000 units × 0.5 hours) 50,000 3.
Contribution of a process control unit (using an imported complex circuit board): Rs.
193
Selling price per unit: (A)
1,400
Variable costs Circuit board (Imported)
600
Other parts
80
Labour cost (5 hours × Rs.100)
500
Total variable costs: (B) 4.
1,180
Contribution per unit (Rs.) : [(A) – (B)] Contribution of process control unit (using a Super-chips):
220 Rs.
Selling price per unit: (A)
1,400
Variable costs Super-chip
300
(Material + Labour costs) Other parts
5.
80
Labour (6 hours × Rs.100)
600
Total variable costs: (B)
980
Contribution per unit (Rs.) : [(A) – (B)]
420
Incremental contribution per unit of a process control unit, when instead of using imported complex circuit board Super-chip is used: Rs. Incremental contribution per unit (Rs.420 – Rs.220) (Refer to W. N. 3&4) 200
(ii)
Super-chips to be transferred to Mini Computer Division to replace Circuit Boards: Out of 50,000 available hours 30,000 hours are utilized for meeting the demand of 15,000 unit of Super-chips, the rest 20,000 hours may be used for manufacturing 40,000 Okay-chips, which yields a contribution of Rs.40 per unit or Rs.80/- per hour (Refer to working note 1) or a contribution of Rs.160 per two equivalent hours. In case the company decides to forego the manufacturing of 20,000 units of Okay-chips in favour of 5,000 additional units of Super-chips to be used by Mini-Computer division (instead of complex imported Circuit Board) for manufacturing process control units. This decision would increase the existing contribution of Mini-computer Division by Rs.200/- per two-equivalent hours (Refer to working note 5). Hence the entire requirement of 5,000 units of Super-chips be produced and transferred to MiniComputer Division.
(ii)
Minimum transfer price of Super-chip to Mini Computer Division: Variable cost of a Super-chip
=
Rs.300 + 2 hours × Rs.80
=
Rs.460
+
Opportunity cost of foregoing the production of an Okay-chip and using craftsmen time for Super-chip
(iii) Super –chips to be produced for the production of 12,000 units of process control units: After meeting out the order of 15,000 Super-chips per year, the concern is left out with 20,000 hours. Use of Super-chips for control units production would increase the existing contribution of MiniComputer Division by Rs.200/- per unit. Out of the remaining 20,000 craftsmen hours, 10,000 units of Super-chips can be made, which may be used for the production of 10,000 process control units. Ans 27
194
(i)
Statement of the overall profit of the company (By harvesting 2,000 kgs of oil seeds, processing it into edible oil & selling the same in 2 kg cans)
Output of department
each
Harvesting Division
Oil Mill Division
Marketing Division
2,000 kgs of oil seed
1,000 kgs. of oil produced
500 cans of 2 kg each
5,000
10,000
1,875
(2,000 kgs × Rs.2.50)
(1,000 kgs × Rs.10)
(500 × Rs.3.75)
10,000
7,500
4,375
(2,000 kgs × Rs.5)
(1,000 kgs × Rs.7.50)
(500 × Rs.8.75)
15,000
17,500
6,250
Total Rs.
Total costs Variable cost (Rs.) : (A)
Fixed cost (Rs.): (B)
Total cost (Rs.): (C) = [(A)+(B)] Sales revenue (Rs.): (D)
16,875
21,875
38,750 75,000
(500 cans × Rs.150) Profit (Rs.) [(D) – (C)]
36,250
(ii) Working note: (a) Total Contribution
=
(Sales revenue – total variable cost)
=
Rs.75,000 – Rs.16,875 = Rs.58,125
(b) Amount of shared contribution in relation to variable costs: Harvesting Division
=
Rs.58,125 ×
Oil Mill Division
=
Rs.58,125 ×
Marketing Division
=
Rs.58,125 ×
Rs.5,000 Rs.16,875
Rs.10,000 Rs.16,875 Rs.1,875 Rs.16,875
= Rs.17,222 = Rs.34,445 = Rs.6,458
Computation of Transfer Price (for internal transfers) under the following pricing methods: (1) Shared contribution in relation to variable costs: Transfer price from harvesting Division to Oil Mill Division =
Variable cost of Harvesting Division + Shared contribution of Harvesting Division in relation to variable costs
=
Rs.5,000 + Rs.17,222 (Refer to working note 2) = Rs.22,222 Transfer price from Oil Mill Division to Marketing Division
=
Transfer price from Harvesting Division to Oil Mill Division + Variable cost of Oil Mill Division + Shared contribution of Oil Mill Division in relation to variable costs (Refer to working note 2)
=
Rs.22,222 + Rs.10,000 + 34,445
=
Rs.66,667
(2) Market price: Transfer price from Harvesting Division to Oil Mill Division =
Market price of 2,000 kgs of Oil seeds transferred to Oil Mill Division
195
=
2,000 kgs. × Rs.12.50 = Rs.25,000
Transfer price from Oil Mill Division to Marketing Division =
Market price of 1,000 kgs of edible oil
=
1,000 of kgs × Rs.62.50 – Rs.62,500
(iii) Statement of profitability (under different transfer prices method) From Harvesting Division to Oil Mill Division
From Oil Mil to Marketing Division
From Marketing Division to market (500 cans of 2 Kgs.)
Rs.
Rs.
Rs.
22,222
66,667
75,000
__
22,222
66,667
5,000
10,000
1,875
10,000
7,500
4,375
7.222
26,945
2,083
25,000
62,500
75,000
__
25,000
62,500
5,000
10,000
1,875
10,000
7,500
4,375
Shared contribution method Transfer price: (Refer to (1) above) Less: Transfer price (Refer to (ii) above) Less: Variable cost Less: Fixed cost (Refer to (i) above) Profit Market price method Transfer price (Refer to (2) above) Less: Transfer in price (Refer to (ii) above) Less: Variable cost (Refer to (ii) above) Less: Fixed cost (Refer to (i) above) Profit 10,000 20,000 6,250 Decision: Divisional Manager of Harvesting Division would prefer the use of market price method for transferring 2,000 kgs of oil seeds to Oil Mill Division because its usage increases the profit by Rs.2,778 (Rs.7,222) over the shared contribution method. Whereas Oil Mill Division manager would prefer the use of shared contribution method over the market price method because its use would increase its profit by Rs.6,945 (Rs.26,945 – Rs.20,000). Similarly Marketing Divisional Manager would be benefited to the extent of Rs.4,167 (Rs.6,250 – Rs.2,083) by using market price method. Ans 28 (i) Statement of profitability of Division X No. of components
(a) 5,000 10,000
Transfer price for the component to Department Y@ Rs.90 per unit
Total cost of components (Rs.)
Profit / (Loss) (Rs.)
(b)
(c)
(d) = {(b) – (c)}
4,50,000
5,62,500
(1,12,500)
9,000
9,00,000
__
196
15,000
13,50,000
12,37,500
1,12,500
20,000
18,00,000
15,75,000
1,25,000
25,000
22,50,000
19,12,500
3,37,500
30,000
27,00,000
22,50,000
4,50,000
Statement of profitability of Division Y No. of Components
Sale revenue on average price basis
Component cost (Transfer price) to Dept. Y
Manufacturing cost in division Y
Total cost
Profit/(Loss)
Rs.
Rs.
Rs.
Rs.
Rs.
(b)
(c)
(d)
(e)={(c)+(d)}
(f)={(b)-(e)}
5,000
19,68,750
4,50,000
14,06,250
18,56,250
1,12,500
10,000
29,85,000
9,00,000
16,87,500
25,87,500
3,97,500
15,000
37,12,500
13,50,000
19,68,750
33,18,750
3,93,750
20,000
41,70,000
18,00,000
22,50,000
40,50,000
1,20,000
25,000
45,00,000
22,50,000
25,31,250
47,81,250
(2,81,250)
30,000
45,00,000
27,00,000
28,12,500
55,12,500
(9,90,000)
(a)
(ii) Profitability of the company as a whole (a) At 30,000 units level, at which Division X’s net profit is maximum
Rs.
Profit of Division X
4,50,000
Profit of division Y
(9,00,000)
Operating profitability / (Loss) of the company
(5,40,000)
(b) At 10,000 units level, at which Division Y’s net profit is maximum
Rs.
Profit of division X
NIL
Profit of division Y
3,97,500
Operating profitability of the company
3,97,500
(iii) Profitability of the company, if it is not organised on profit centre basis No. of components
Sales revenue on average basis
Cost of component to division X
Manufacturing cost in division Y
Total cost
Profit/ (Loss)
(Rs.)
(Rs.)
(Rs.)
(Rs.)
(Rs.)
(a)
(b)
(c)
(d)
(e)={(c) + (d)}
(f)={(b)–(e)}
5,000
19,68,750
5,62,500
14,06,250
19,68,750
-
10,000
29,85,000
9,00,000
16,87,500
25,87,500
3,97,500
15,000
37,12,500
12,37,500
19,68,750
32,06,250
5,06,250
20,000
4170,000
15,75,000
22,50,000
38,25,000
3,45,000
25,000
45,00,000
19,12,500
25,31,250
44,43,750
56,250
30,000
45,22,500
22,50,000
28,12,500
50,62,500
(5,40,000)
The level of output, the company will earn maximum profit, if the company is not organized on profit centre basis is 15,000 components.
197
Ans.29. Statement showing contribution P.U. of ranking Particulars A Market Price P.U. 150 Less: Variable Production Cost P.U 130 Contribution P.U. 20 Labour hours P.U. 3 Contribution per labour hour (i)/(ii) 6.67 Ranking IV (i) Allocation of 20,000 labour hours C D B A (Balance)
(Rs.) Product B 146 100 46 4 11.5 III
(2,300 units x 2 L.H.) (1,600 units x 3 L.H.) (2,500 units x 4 L.H.) (200 units x 3 L.H.0
C 140 90 50 2 25 I
D 130 85 45 3 15 II
4,600 4,800 10,000 600 20,000
Product D can be transferred to Division Y, but the maximum Quantity that might be required for transfer is 2,500 units of D. Time required for 2,500 units of D =2,500 units x 3 L.H =7,500 L.H 2,500 units of Product D for Division Y can be met by sacrificing as follows: (Labour hours) Product A (200 units x 3 L.H.) 600 Product B (Balance) (1,725 units x 4 L.H.) 6,900 7,500 Transfer price to be charged by Division Z to Division y on supply of 2,500 units of product D. (Rs.) Variable cost (2,500 units x Rs.85) 2,12,500 Add: opportunity cost of contribution foregone Product A (200 units x Rs.20) 4,000 Product B (1,725 units x Rs.46) 79,350 Transfer Price 2,95,850 Transfer Price P.U. (Rs.2,95,850 / 2,500 units) 118.34 (ii) Allocation of 30,000 Labour Hours C D B A Idle Labour (Balance) Total
(2,300 units x 2 L.H.) (1,600 units x 3 L.H.) (2,500 units x 4 L.H.) (2,800 units x 3 L.H.)
2,500 units of Product D for Division Y can be met by sacrificing as follows: Idle labour hour Product A (1,725 units x 3 L.H.) Total Calculation of transfer price
4,600 4,800 10,000 8,400 2,200 30,000
2,200 5,300 7,500 (Rs.)
198
Variable cost (2,500 units x Rs.85) Opportunity cost of Contribution foregone of Product A (1,767 units x Rs.20) Transfer price P.U.
2,12,500 35,340 2,47,840 99.14
(Rs.2,47,840 / 2,500 units)
Ans. 30 Working Notes: (i)
Hours required to meet maximum demand: External sales (i)
Hours reqd.
Total Hrs. per unit
(ii)
(iii) = (i) × (ii)
X 800 units
3
2,400
Y 500 units
4
2,000
Z 300 units
2 Total
600 5,000
(ii)
Contribution per unit: X Rs.
Y Rs.
Z Rs.
Selling price
48
46
40
Less : Variable cost
33
24
28
Contribution per unit : (A)
15
22
12
Labour hours required per unit : (B)
3
4
2
Contribution per hour (Rs) : (A) / (B)
5
5.5
6
III
II
I
Product
Ranking (a)
If only 3,800 hours are available in Division A.
300 units of Z (maximum), which will take*
600 hrs.
500 units of Y (maximum), which will take
2,000 hrs.
400 units of X to use remaining hrs.
1,200 hrs. 3,800 hrs.
*Note:
Labour hours required per unit are given in the question. If 300 units of Y are to be transferred to ‘B’ division, then 1,200 hours will have to be used for production of Y instead of X. It means Division A will sacrifice production of 400 units of X, which are yielding Rs. 5 per hr. Given above is the optimum mix for Division A for 3,800 hrs. If 300 units of Y are to be transferred to ‘B’ division with time constraint of 3,800 hours, then additional 300 units of Y will have to be produced sacrificing the production of 400 units of X which is yielding contribution.
Transfer price (i) Variable cost of Y Opportunity cost (ii) Contribution relating to ‘X’ forgone for producing additional units of Y (4 hrs × Rs. 5*)
Rs. 24.00
*Y takes 4 hours and in each hour production of X would have generated contribution of
20.00 44.00
199
Rs. 5. (b) If 5,600 hours are available Maximum time required to meet external sales (Refer to Working note 1) 5,000 hrs. Hours now available 5,600 hrs. (i) It means 600 hrs can be easily used for the production of Y and transfer price will be variable cost only i.e. (600 hrs. 4 hrs) × Rs. 24 Rs. 3,600 Note: Y takes 4 hours per unit (ii) For producing additional 150 units, production of X will be disturbed. Variable costs (i) 150 units of X @ Rs. 24 Rs. 3,600 Opportunity cost (ii) Contribution of ‘X’ units forgone (600 hrs. × Rs. 5) Rs. 3,000* 6,600 10,200 Total price for 300 units Average transfer price should be Rs. 34 per unit *Contribution per hr. of X forgone.
Ans.31. (1) Maximum hours required to meet the present outside market requirement Maximum sales units Hours required per Total hours unit Vx 900 3 X1 300 2 Xt 600 4 Maximum total hours required to meet the outside market requirement 5,700 (2) Contribution per unit, per hour and ranking Product Selling price per units Less: Variable cost per unit Contribution per unit Labour hours required per unit Contribution per hour Ranking
2,700 600 2,400
(Rs.) V 24 17 7 3 2.33 II
(3) Utilisation of 4,800 available hours according to ranking 300 units of products X1 (300 units x 2 hours) 900 units of products Vx (300 units x 3 hours) 375 units of products Xt (300 units x 4 hours) Total hours
X 23 12 11 2 5.5 I
X 20 14 6 4 1.5 III (hours) 600 2,700 1,500 4,800
(a) computation of transfer price for each unit of Vx if total labour hours available in Department x are 4,800 According to the ranking 4,800 available hours are utilized to produce 300 units of X 900 units of Vx and 375 units of X. The aforesaid product mix would give rise to optimum mix for optimum profit.
200
In case 400 units of Vx are to be supplied to Department y in addition to existing outside sale then the production of product X is to be curtailed partially and the hours thus obtained will be utilized for the production of 400 additional units of Vx. The new product mix will be as follows: (Hours) 300 units of products X1 (300 units x 2 hours) 600 1,300 units of products Vx (1,300 units x 3 hours) 3,900 75 units of products Xt (75 units x 4 hours) 300 Total hours 4,800 Computation of transfer price per unit Variable cost of one unit of Vx Contribution foregone (opportunity cost) per unit due to the curtailment of Xt(3 hours x Rs.1.5) Transfer price per unit
(Rs.) 17.00 4.50 21.50
(b) Computation of transfer price for each unit of Vx, if total labour hours available in Department x are 6,200 Hours required to meet the present outside market requirement 5,700 Remaining hours available for producing 400 additional units of Vx 500 After meeting the present outside market requirement (6,200 hours -5,700 hours) Computation of transfer price per unit: (Rs.) Total variable cost on the production of 166.67 units of Vx 2,833 (500 hours / 3 hours) @ Rs.17 per unit by utilizing 500 remaining available hours Total variable cost of 233.33.units of Vx @ Rs.17 per unit 3,967 (400 units – 166.67 units) produced by curtailing the production of Xt product to the tune of 700 hours. Contribution foregone (opportunity cost ) on the diversion of 700 hours of 1,050 Production of Xt for producing 233.33 units of Vx (700 hours x Rs.1.50) Total cost for producing 400 additional units of Vx 7,850 Transfer price for one unit of Vx (Rs.7,850 / 400 units) 19,625 Ans. 32 (i) Statement of contribution (a) When component is purchased by Division B from outside Division A Division B Sales (2000x 400) Less: Cost of Purchase (2000x 200) 400000 Variable costs (200x 150) 300000 Company’s total contribution
(Rs.) Nil 8,00,000 3,80,000
(b) When component is purchased from Division A by Division B Division A Sales (2000x 220) 4,40,000 Less: Variable costs (2000x 190) 7,00,000 Division B Sales (2000x 400) 8,00,000 Less: Variable Costs: Purchase cost in Division A (2000x 220) 440000 Variable cost in Division B (2000x 150) 300000 7,40,000 Company’s total contribution
1,00,000 1,00,000 (Rs.)
60,000
60,000 1,20,000
201
Thus, it will be beneficial for the company as a whole to ask Division B to buy the component from Division A. (ii) Statement of total contribution if Division A could be put to alternative use: Division A: Contribution from alternative use of facilities Division B: 30,000 Sales (2000x 400) 8,00,000 Less: Variable costs: Cost of purchase (2000x 400) 400000 Division B (2000x 150) 300000 7,00,000 1,00,000 Company’s total contribution 1,30,000 Since, the company’s contribution when component is purchased from outside, shows as increase of Rs.30,000 as compared to when there is inter departmental transfer. Hence, it will be beneficial to purchase the component from outside.
(iii) Statement of total contribution when component is available from outside at Rs.185. Division A: Nil Division B: Sales (2000x 400) 8,00,000 Less: Variable costs: Cost of purchase (2000x 185) 370000 Division B (2000x 150) 300000 6,70,000 1,30,000 Company’s total contribution 1,30,000 If the component is purchased by Division B from Division A, the contribution is only Rs.1,20,000 as calculated under (2) above. Hence it will be beneficial to buy the component from outside. (v) Fixations of transfer price (a) When there are no alternative uses of production facilities of Dept. A: In such a case the variable cost i.e. Rs.190 per component will be charged. (b) If facilities of Division A can be put to alternative uses: Variable cost Opportunity cost Transfer price
(Rs.) 190 15 205
(c) If market price gets reduced to Rs.185 and there is no alternative use of facilities of Division A. the variable cost of Rs.190 per component should be charged. Ans. 33 Fastners Limited (a) Present profitability of individual shops and overall profitability Particulars
Welding shop
Painting shop Value Rs.
Qty Unit
2,400 Sale in open market Transfer to painting shop 9,600
12.00 28,800 12.00 1,15,200
9,600
12,000
1,44,000
9,600
Qty. Unit
Total sales : (A)
Rate Rs.
2
202
Less: Variable cost : (B) (12,000 units × 9.50)
1,14,000 (9600 units × Rs.20) 30,000 25,000
Contribution : {(A) – (B)} Less: Fixed cost
1,92,000 48,000 30,000
5,000 18,000 Profit Overall profit for the company (Rs. 5,000 + Rs. 18,000) = Rs. 23,000 (b) (i) When painting shop purchases all its requirement from open market at a price of Rs. 10 per unit Welding shop Rate Qty. Unit Rs. Sale Less: Variable cost
2,400
12.00
Val ue R 28,800
2,400
9.50
22,800
Painting shop Rate Qty Rs. Unit
Value Rs.
9,600
25.00
2,40,000
9,600
18.00*
1,72,800
Contribution
6,000
67,200
Less: Fixed cost
25,000
30,000
Profit/(Loss)
(19,000)
Overall profit for the company
37,200
Rs. 37,200 – Rs. 19,000 = Rs. 18,200
*It is given in the question that cost of painting including transfer price from welding shop is Rs. 20 per unit. The transfer price from welding shop is Rs. 12 per unit. Therefore, the variable cost of Rs. 8 (Rs. 20 – Rs. 12) is incurred by painting shop exclusively. The painting shop will be purchasing its requirement from open market at Rs. 10 per unit. Therefore, the variable cost per unit in painting shop will be Rs. 18 (Rs. 10 + Rs. 8). This point should be noted carefully. (b) (ii) When all the requirements of painting shop is met by transfer from welding shop at a transfer price of Rs. 10 per unit Welding shop Qty. Unit
Rate Rs.
2,400
12.00
28,800
9,600
10.00
96,000
Value Rs.
Painting shop Qty Unit
Rate Rs.
Value Rs.
Sale in the open market
9,600
25.00 2,40,000
Transfer to painting shop Total sales
12,000
1,24,800
Less:Variable cost (12,000 units×Rs.9.50)
1,14,000 (9,600 units×Rs.18)
1,72,800
Contribution
10,800
67,200
Less: Fixed cost
25,000
30,000
(14,200)
37,200
Profit/(Loss)
Overall profit of the company = Rs. 37,200 – Rs. 14,200 = Rs. 23,000 For the purpose of comparison, the results of the three alternatives are summarised below: Welding shop Painting shop Rs. Rs. Profit under (i) 5,000 18,000 Profit/(Loss) under (b)(i) (19,000) 37,200 Profit/(Loss) under (b)(ii) (14,200) 37,200 Rs. The overall profit under
(a)
23,000
203
b(i) b(ii)
18,200 23,000
Alternative (b)(ii) should be accepted due to the following reasons: (a) (b)
It gives a maximum overall profit of Rs. 23,000. The discussion is confined to either b(i) or b(ii). Each shop is treated as a separate cost centre and not a profit centre.
(c)
The policy of overall goal congruence of the company is followed.
Ans. 34 Neither selling price nor total sales is given. Division A of Better Margins Ltd. expects a return of 25% on average assets employed i.e., Rs. 12,00,000. Total sales will be: Rs. (a) Profit (25% of 12,00,000) (b) Fixed overhead (c) Variable cost (2,00,000 × Re. 1) Total sales Sales per unit (Rs. 9,00,000 ÷ 2,00,000 units)
9,00,000 Rs. 4.50
Transfer to Division B sale to outside parties
Sale to outside and parties only
Sales (units)
2,00,000
1,40,000
Sales value (1,40,000 units @ Rs. 4.50) (60,000 units @ Rs. 2.25)
Rs. 6,30,000 1,35,000 7,65,000
Rs. 6,30,000 Nil 6,30,000
2,00,000 5,65,000 4,00,000 1,65,000 12,00,000 13.75%
1,40,000 4,90,000 3,60,000 * 1,30,000 10,00,000 13.00%
Less: Variable cost (Re. 1 per unit) Contribution Less: Fixed overhead Net profit Average assets employed Return on investment
If the component is transferred to Division B as well as sold to outside parties, it is more profitable as the contribution, net profit and return on investment is more than the existing proposal. Therefore selling the components to Division B at Rs. 2.25 per unit is in the overall interest of the company. *Reduction in selling and administration expenses (fixed in nature) by Rs. 40,000.
Ans. 35 Statement showing the contribution to profit for each assuming that all estimates and budgets materialised as expected
Sales Centre (S) New Board Sold – Selling price – Purchase price
Rs.
Rs.
Rs. 35,000 29,000 6,000
204
(ii) Assuming Additional Costs It is noticed that all estimates and budgets are materialised except that repairs undertaken by R took an extra 10 hours and Rs. 100 of materials due to a problem not noticed by B or R. R is responsible for giving correct repair costs and, therefore, he has to bear the additional cost: Rs. Rs. Repair Centre (R)’s contribution 540 Less: Extra cost of materials 100 Extra D.L. variable cost (10 hrs × Rs. 6) 60 160 380 Revised contribution However, full details are not given in the question. ‘B’ is a middleman passing on R’s costs to S and as such should not bear additional costs. Had the item been noticed originally then S would have paid the cost and perhaps it should be passed back. This would be particularly so if R had insufficient opportunity for a complete inspection. In that case extra cost should be: Rs. Material
100
Labour (10 hrs. × Rs. 15)
150 250
Reduced contribution of S = Rs. 3,800 – Rs. 250 = Rs. 3,550 Rs. Original contribution of R
540
Add.: Saving in variable cost [10 hrs × (Rs. 15 – Rs. 6)]
90
Increased contribution of R
630
Note: Other solutions are equally acceptable if well argued and logically justified.
Ans. 36: (a) (i) AB sells product at external market Selling price (Rs.) 30 Less Variable cost 18 Contribution (per unit) 12 Demands (units) 60,000 Total contribution 7,20,000
45 18 27 40,000 10,80,000
60 18 42 20,000 8,40,000
Optimal output is 40,000 units at a selling price of Rs.45 AB transfer at Rs.42 to XY division then contribution of XY
205
Selling price (Rs.) Less Variable cost V+TP (42+60) Contribution (per unit) Demands (units) Total contribution
120
135
150
102 18 15,000 2,70,000
102 33 10,000 3,30,000
102 48 5,000 2,40,000
Manager will choose out put level 10,000 units at a selling price of Rs.135. Overall profit when transfer made at Rs.42 Division AB contribution on 10,000 units [42 – (18 -3)] Division XY contribution 10,000 (135 – 102) Total contribution Division AB contribution from external market sale Total profit (ii)
AB transfer at variable cost Selling price (Rs.) 120 Less Variable cost (15+60) 75 Contribution (per unit) 45 Demands (units) 15,000 Total contribution 6,75,000
135 75 60 10,000 6,00,000
= 2,70,000 = 3,30,000 = 6,00,000 10,80,000 16,80,000 150 75 75 5,000 3,75,000
Optimal is 15,000 units at the rate of 120 per unit. If AB transfer at Variable cost (Rs.15) then no contribution will be generated by AB division XY division choose 15,000 units level gives contribution 15,000 × 45 = 6,75,000 = 10,80,000 Division AB contribution from external market sale = 17,55,000 Total contribution (iii)
Contribution AB division by selling 10,000 units to new external market at Rs.32 and XY division purchasing at Rs.31. Contribution (32 – 18) × 10,000 XY contribution [135 – (31 + 60)] Division AB contribution from external market sale Total contribution
= 1,40,000 = 4,40,000 = 10,80,000 = 16,60,000
Ans. 37 (a) The variable costs per unit of output of sale outside the company are Rs.11 for the intermediate product and rs.49(Rs.10 for A+Rs.39 for B) for the final product. Note that selling and packing expenses are not incurred by the supplying division for the transfer of the intermediate product. It is assumed that the company has sufficient capacity to meet the demand at the various selling prices. Optional output of intermediate product for sale on external market. Selling Price (Rs.) 20 30 Unit contribution (Rs.) 9 19 Demand (units) 15,000 10,000 Total contribution
(Rs.)
40 29 5,000
1,35,000
1,90,000
1,45,000
Optimal output is 10,000 units at a selling price of Rs.30. Optimal output for final product Selling Price (Rs.) 80 Unit contribution (Rs.) 31 Demand (units) 7,200
90 41 5,000
100 51 2,800
206
Total contribution (Rs.) 2,23,200 2,05,000 1,42,800 Optimal output is 7200 unit at a selling price of Rs.80. Optimal output of Division B based on a transfer price of Rs.29. Division B will regard the transfer price as a variable cost. Therefore, total variable cost per unit will be Rs.68(i.e.,29+39) and Division B’s contribution will be as follows: Selling Price (Rs.) 80 90 100 Unit contribution (Rs.) 12 22 32 Demand (units) 7,200 5,000 2,800 Total contribution
(Rs.)
86,400
1,10,000
89,600
The manager of Division B will choose an output level of 5,000 units at a selling price of Rs.90. This is sub-optimal for the company as a whole. Profit for the company as a whole from the sale of the final product are reduced from Rs.2,23,200 (72,00 units) to Rs.2,05,000 (5000 units). Rs.2,05,000 profits would be allocated as follows: Division A Rs.95,000 (5000 units at Rs.19 i.e.,Rs.29-Rs.10) Division b Rs.1,10,000 (b) At a transfer price of Rs.12 the variable cost per unit produced in Division B contribution will be as follows: Selling Price Unit contribution Demand
(Rs.) (Rs.) (units)
Total contribution
(Rs.)
80 29 7,200
90 39 5,000
100 49 2,800
2,08,800
1,95,000
1,37,200
The manager of Division B will choose an output level of 7200 units and a selling price of Rs.80.This is the optimum output level for the company as a whole. Division A would obtain a contribution of Rs.14,400 (7200 units @ Rs.2 (I.e.,Rs.12-Rs.10) from internal transfers of the intermediate product whereas Division B would obtain a contribution of Rs.2,08,800 from converting the intermediate product and selling as a final product. Total contribution for the company as a whole would be Rs.2,23,200. Note that Division A would also earn a contribution of Rs.1,90,000 from the sale of the intermediate product to the external market. Ans. 38: Opticals Ltd manufactures P( lenses) and Q ( swimming goggles ). Division P has option to supply to Division Q or sell to outside market. Division Q has option to buy from Division P or purchase from outside market. However, both divisions have to work within their individual capacity. Variable Cost for product P in Division P = Rs 60. Variable cost for product Q in Division Q ( excluding 2 Nos P's) = Rs 80. Division P has better market price of its product P than the market price offered to Q division. For maximizing profit of the organization :
Rs
P division should optimise its profit by selling maximum units to outside market. Contribution per unit for sale to outside for division P
40
Contribution per unit for Div Q as follows : Sale price - Variable cost ( excluding lenses)
330
Max Contribution per unit ( if procured from P div at its variable cost i.e Rs 60)
210
207
Min Contribution per unit ( if procured at Rs 90 per unit from outside)
150
Contribution per unit at transfer price of Rs 70 i.e minimum market price
190
Option 1 : Division Q buys 5001 units from market @ Rs 70 and meets its capacity. Division P sells 3000 units to outside market @ Rs 100 Sale / Transfer
Contrib. /unit
Contribution in thousand rupees
208
Rs P Div DivP :Sale of 3000 units to outside market @ Rs 100
40
DivQ: Sale of 2500 units with P from market @ Rs 70
190
120
Less : cost of rejection of one unit of product P Total
Q Div
120
Total 120
475
475
-0.07
-0.07
474.93
594.93
Option 2 : Division P sells 3000 units to outside market, transfer 4000 units to div Q and Division Q buys 1000 units from outside market to work within the capacity P Division agrees to a transfer price so that profitability of Q is not affected. To maintain the same profitability of Q, contribution required from 2000 units for Div Q is Rs 400,000 i.e contribution per unit Rs 200 i.e transfer price per unit of P is Rs 65 per unit to make cost of lences Rs 130 Contrib Contribution in Sale / Transfer /unit thousand rupees
209
Rs P Div Div P : Sale of 3000 units to outside market Div P : Transfer of 4000 units to div Q at Rs 65
Q Div Total
40
120
120
5
20
20
Div Q :Sale of 2000 units with P from P div @ Rs 65
200
400
400
Div Q : Sale of 500 units with P from market @ Rs 90
150
75
75
475
615
Total
140
Under Option 1, both divisions worked dis-jointly without caring for capacity utilization resulting lower profitability of the organization. Under Option 2, both divisions worked with mutual advantages for optimizing their individual profits and overall profit for the organization has gone up by effective utilization of capacity. Product P from Division P fetches higher price from open market indicating good quality of product. Moreover, supply from P division is well assured in the long run which is the justification of establishment of two parallel divisions. Hence, Option 2 is suggested. (ii)
(b)
Division functioning as profit centers strive to achieve maximum divisional profits, either by internal transfers or from outside purchase. This may not match with the organisation’s objective of maximum overall profits. Divisions may be commercial to advice overall objects objectives, where divisional decisions are in line with the overall best for the company, and this is goal congruence. Div isions at a disadvantage may be given due weightage while appraising their performance. Goal incongruence defeats the purpose of divisional profit centre system.
In an assignment minimization problem, if one task cannot be assigned to one person, introduce a prohibitively large cost for that allocation, say M, where M has a high the value. Then, while doing the row minimum and column minimum operations, automatically this allocation will get eliminated.
Ans. 39
(a)
Div A
B
B
Rs. / unit
Rs. / unit
Rs. / unit
Direct Material (Other than A)
50
24
Direct Labour
25
14
Variable Overhead (Production)
20
2
Variable Production Cost (excl. A)
95
40
From A
144
From Outside Variable production Cost / unit
____
160
184
200
Selling Price From outside Less: Selling Overhead
40
160
300
13
26
210
Net Selling Price (outside)
147
Net Selling Price to B
144
274
Net Selling Price to S
250
Net Selling Price (outside)
147
274
274
Variable Production Cost
− 95
− 184
−200
Contribution / unit (outside)
52
90
74
(Sale to B & S respectively)
144
250
250
Variable Production Cost
−95
−184
−200
49
66
50
Contribution / unit Best strategy A = Maximise Production; Sell maximum no. of units @ 52 / unit (outside) (To B) remaining units
18,000 × 52 = 9,36,000
2,000 × 49 =
98,000 10,34,000
Total Contribution for A Best strategy for B: Maximise contribution / unit by selling outside and procuring from A 90 / unit Contribution × 2,000 units
Balance units can yield contribution of either 74/ unit for outside or Rs. 50 / unit to S Ltd. Production Capacity = 28,000. Option I
Option II
Outside Sales
Sales to S
20,000 × 74 = 14,80,000
6,000 × 50
Outside Sales × contribution / unit 24,000 × 74 = 17,76,000
= 3,00,000
2,000 × 90 = 1,80,000
2,000 × 90 = 1,80,000
16,60,000 Total Contribution
3,00,000 (16,60,000 + 3,00 ,000)19,60,000
19,56,000
(B) Choose Option I i.e. get 2,000 units from A, sell 6,000 units to S and 20,000 to outside. Make 28,000 units @ full capacity. Total Contribution Rs19,60,000. If A and B are allowed to act independent of the group synergy, Rs. Total contribution
A – 10,34,000 B – 19,60,000 Total contribution for X Ltd. 29,94,000 Cost from X Ltd.’s Perspective Variable Cost of production
Div A
Rs. 95 Div B
Variable cost of production other than A
40
A supplied by Division A – Variable Cost
95
40
211
A purchased Option I
Outside 26,000 units
____
160
135
200
Option II
Outside 20,000 × (274 – 135)
27,80,000
20,000 (274 – 135)
27,80,000
2,000 × (274 – 200)
1,48,000
6,000 (274 – 200)
4,44,000
22,000 S Ltd. 6,000 units (250 – 200)
3,00,000
_________
32,28,000
32,24,000
Choose Option I Contribution = Rs. 32,28,000 for X Ltd. as a whole Transfer
(2,000 units)
Make A transfer all output to B. Sell 6,000 units of B to S and 22,000 units to out side market. This will make X Ltd. better off by 32,28,000 – 29,94,000 = Rs 2,34,000 (i.e. 18,000 units of A sold to outside increases contribution to A by 3 Rs. / unit and decreases contribution to B by 16 Rs. / unit Net negative effect = 13 × 18,000 = Rs.2,34,000).
Ans. 40:
(i)
Division A’s best strategy – 2011 Maximum Manufacturing capacity = 50,000 units Per unit
30,000
15,000
Transfer to B partially < 45,000
Selling price
65
55
55
60
Variable Prod cost
35
35
35
35
Variable Selling cost
10
-
-
-
Total Variable cost
45
35
35
35
Contribution Rs.
20
20
20
25
Demand (units)
External Spl order Market
Transfer to B full 45,000
Transfer to B in full gives maximum contribution. Hence, 45,000 units to be transferred. Balance 5000 will be sold to the external market. Partial fulfilment of Special order will not be possible. Statement of profitability for best strategy in 2011 : Rs Transfer 45000 units to B @ Rs 60 Per Unit : Contribution : 25 x 45000 Supply to external market : Contribution : 20 x 5000 units Total Contribution Annual fixed cost Step fixed cost Fixed selling costs Profit in 2011 (ii) Company’s best strategy for 2010
11,25,000 100000 12,25,000
Rs 4,30,000 Rs 2,00,000 Rs 50,000
6,80,000 5,45,000
212
For Division A Variable cost Price Contribution to Division A Margin for Division B
External Market 45 65 20
Special Order 35 55 20
B – Partial
B - Full
35 45 10 5
35 50 15 0
It is clear from the above table that the Company will have more profitability if A first satisfies external market demand and special order and then supply to B. As quantity for special order and transfer is more than 10,000 units, Div A will always opt for fixed cost of 50,000 instead of variable selling cost of Rs 5 / unit. The company’s strategy for Division A’s production, sales/ Transfer will be :
Strategy I : A’s sale/ transfer (units) Contribution of A & B ( Rs laks) Fixed Cost Rs Lakhs( 4.30 + 1.00 +0.5) Net for company – Rs lakhs Strategy II : from A ( units) Contribution of A & B : RS Lakhs Fixed Cost Rs Lakhs ( 4.30 + 2.00 +0.5) Net for company Rs. Lakhs
External Market 25,000 5.00
25000 5.0
Special Order 10,000 2.00
10000 2.00
B– Partial 5,000 0.75
15000 2.25
Total 40,000 7.75 5.80 1.95 50,000 9.25 6.80 2.45
Thus, the strategy II will be the one for the Company for the year 2010. (iii) B’s negotiating range in 2011 : Upper limit: The effective price of Rs. 60 for procurement from outside source. Lower Limit : Minimum price A will look for i.e Variable cost + Maximum possible contribution from other source + additional fixed cost = Rs ( 35 + 20 + ( 50000/45,000) = Rs 56.11 Thus, Price range for negotiation without changing A’s strategy is Rs 56.11 to Rs 60 per unit.
Ans.: 41
(a) (i) Contribution per unit against sale to outside = Rs ( 200-120-20) = Rs 60 In case of transfer, good units and rejected units are in proportion of 9:1 In case of transfer, contribution per good unit = Rs (190 – 120) = Rs 70 In case of transfer, contribution per rejected unit = Rs (150 – 120-100) = Rs -70 Thus, effective contribution per unit of transfer = Rs (70 x 0.9 – 70x 0.1) = Rs 56 As contribution per unit against outside sale is higher, the best strategy should be to sell maximum number of unit to outside marker. Contribution from outside market from sale of 900 units = Rs 54,000 {Rs.(900 x 60)}
213
(ii)
Contribution from transfer of 300 units to B {Rs (300 x 56)} Total Contribution from best strategy
= =
Rs 16,800 Rs 70,800
If B’s demand is 540 units, total production required (540 /0.9)
=
600 units.
Taking outside market demand of 600, it is within production capacity of 1200 units. Now contribution from 600 units of outside sale Rs (600 x 60 ) = Rs 36,000 Rs (4,200) Contribution from rejected 60 units Rs (60 x – 70) = = Rs 31,800 To keep same level of contribution as in (i), the contribution required from transfer of 540 unit to B (Rs 70,800 – 31,800) = Rs 39,000 Thus, contribution required per unit Rs 39,000 /540 Hence price to be charged p. u. against transfer to B Rs (120 + 72.22)
=
Rs 72.22
=
Rs 192.2
Alternative Solution: Let x be the number of units sold outside and y be the number of units sold to B, before B returns 10% as defectives. Then, x + y = 1,200, is the limitation on production capacity of A. Department A Selling Prices Variable Cost – Production Variable Cost – Sale Total Variable Cost Contribution Contribution on x units sold outside = 60x
Outside Rs. 200 120 ___20 140 60
to B Rs. 190 120 ___-120 70
1
Out of y units to B, 10% = 10 y. 1 = .1y is returned to A. If A scraps, amount got = 30 per unit. If A reworks and sells, it gets 150 – 100 ∴Decision to reworks all defectives. i.e. (.1) (y) Contribution on good units of B = 0.9y × 70 Contribution on reworked units of B = (.1) (y) × 50 Amount of material lost on manufacture of defectives to B ∴Contribution on y gross units transferred to B 63y + 5Y – 12y Total contribution earned by A 56y Where x + y
=
50/unit.
= 63y = 5y =12y(.1)(y)×120 = 56y =
60x
=
1200
To maximize contribution, maximize units sold outside. ∴900 units – sell outside. Balance 300÷1,200 units (gross transfer to B, of which B gives back defectives) Contribution:
Rs.60 (900) + Rs.56 (300) = Rs.54,000 + Rs.16,800
+
214
Contribution Fixed Cost (i) Profit
= Rs.70,800 = Rs.36,000 = Rs.34,800
(ii) Outside demand = 600 units Contribution = 600 × Rs.60 Balance to be got
= Rs.36,000 = Rs.34,800 = Rs.70,800
Out of Rs.34,800, defectives of B will give Rs. 3,000 60 × 50 Rs. 31,800 charge to B for 540 units Contribution to be obtained from 540 units of B Add: Production cost of 600 units @ 120/Amount changed for 540 units
= Rs. 31,800 = Rs. 72,000 = Rs.1,03,800
∴Price to be charged to B = 1,03,800÷540 = 192.22 Per good unit transferred, to maintain the same level of profit as in (a). Ans 42: B will not pay A anything more than 13, because at 13, it will incur additional cost of Rs.2/- to modify it, 13 + 2 = 15, the outside cost.
A
B
C
19
25
Transfer from A
13
13
Modification
2
Divisional variable production
cost
of
Outside sale
Transfer to B & C
7
7
Total Variable Cost of production
7
7
34
38
Selling Price
15
13
40
50
Contribution
8
6
6
12
Option for C, Purchase all units from A @ 13: Any other option is costlier. A
B
C
215
Maximum external demand
3,750
5,000
4,000
Exiting capacity
5,000
2,500
2,500
Maximum capacity that can be added
5,000
1,250
2,250
Total maximum that can be produced
10,000
3,750
4,750
Additional fixed expansion
24,000
6,000
18,700
6,000÷6 = 1,000
18,700÷6 = 1,558.33
cost
Units that must sold/transfer to get amount as contribution
on be this
External demand not covered by existing capacity Decision
24,000÷6 = 4,000
Expand make Expand make Do not expand 10,000 units 2,500 + 1,250 make only 2,500 3,750 – outside = 3,750 units units. 3,750 – B 2,500 – C A
B
C
Outside sale
Transfer to B & C
3,750
3,750 + 2,500 = 6,250
3,750
2,500
Contribution / unit
8
6
6
12
Contribution (Rs.)
30,000
37,500
22,500
30,000
67,500
22,500
30,000
Additional Fixed Cost
24,000
6,000
-
Net revenue addition
43,500
16,500
30,000
Units
Individual strategy is the company’s best strategy.
216
Ans. 43
217
Manager of division X will sell 14,000 units outside at 110 Rs. per unit and earn contribution of Rs. 3.50 lakhs. Excess capacity of 6,000 units can be offered to Y at a price between 70 (the variable manufacturing cost at X) and Rs. 95 (the maximum amount to equa l outside contribution). But Y can get the material outside @ 85. So, y will not pay to X anything above (Rs.85 – 6) = Rs. 79 to match external available price. X will be attracted to sell to Y only in the range of 71 – 79 Rs. per unit at a volume of 6,000 units. At Rs. 70, X will be indifferent, but may offer to sell to Y to use idle capacity. Z will not buy from Y at anything above 135. If X sells to Y at 70 per unit, Y can sell to Z at 134 and earn no contribution, only for surplus capacity and if units transferred by X to Y at Rs. 70 per unit. Y Provided X sells to Y at Rs. 70 per unit
Z
Sell 4,000 units to Z at 134 (Indifferent)
Buy 4,000 units from y at 134 (attracted)
Sell 4,000 units to Z at 135 (willingly for a contribution of Re. 1)
Indifferent, since market price is also 135
For buying from X at 71 – 79 price range, Y will be interested in selling to Z only at prices 136 – 143, which will not interest Z. Thus Y will sell to Z only if X sells to Y at Rs. 70 per unit and Y will supply to Z maximum 4,000 units.
Ans. 44: Capacity of X division = 7000 units X has the following option to sell following number of units: Option
Domestic Market
Export
Transfer
I
6000
800
200
II
5000
800
l200
III
5000
Hiring out (equivalent unit)
2000
IV 5000 800 400 According to the condition given in (iii) for procurement policy of Y,
800
For 7000 units, maximum amount Y is agreeable to pay at market rate i.e Rs 900 per unit = 7000 x Rs 900 = Rs 63,00,000 If X transfers l200 units to Y, It has to incur expenses for 5800 units from market = = 5800 x Rs 920 = Rs 53,36,000 It means for l200 units from X, Y will pay = Rs ( 63,00,000 – 53,36, 000)
218
= Rs 9,64,000 = Rs 803.33 per unit If X transfers 2000 units to Y and Y buys 5000 units,, Y can pay to X only = Rs ( 63,00,000 – 5000 X 920) = Rs l7,00,000 = Rs 850.00 per unit If transfer of less than l000 units to Y, X can claim transfer price of Rs 900 per unit Realization ( Rs) Option I
6000 x l000 + 800 x 900 + 200 x 900
Rs 69,00,000
Option II
5000 x ll20 + 800 x 900 + l200 X 803.33
Rs 72,84,000
Option III
5000 x ll20 + 2000 x 850
Rs 73,00,000
Option IV
5000 x ll20+ 800 x 900 + 400 x 900 plus Rs 66,80,000 plus contribution from hiring out Above table shows that Option III is preferable in comparison to Option I and II . If Option III for X, transfer price will br Rs 850.00 per unit.
For taking a decision on option IV, contribution from equivalent unit from hiring out has to be compared with contribution from minimum sales realization of Rs 775 because sales realization of Rs 775 per unit from equivalent 800 units gives the amount of Rs 6,20,000 which makes up the gap between option III and option IV. In that case, transfer price will be Rs 900 per unit.
219
Decision Making Answer: 11 1. Material A is not yet owned. It would have to be purchased in full at the replacement cost of `6.00 per unit. Relevant cost is therefore 1,000 units at the replacement Cost. 2. Material B is used by the Company regularly. There is already existing a stock of 600 units. If these are used in the contract, a further 400 units would have to be purchased. 3. Material C: 1,000 units of material C are required. 700 units are already in stock. If it is used for the contract, a further 300 units will have to be purchased at a replacement cost of `4.00 each. The existing stock of 700 units will not be replaced. If they are used for the contract, they cannot be used @ `2.50 each unit. The realisable value of these 700 units @ `2.50 per unit represent opportunity cost. 4. Material D is already in stock and will not be replaced. There is an opportunity cost of using D in the contract. It has following two uses: It can be sold to fetch `1,200 i.e. 600 X `2 It can also be used for E, which would cost `1,500 i.e. 300 X `5. Since substitution is more useful, `1,500 is the opportunity cost. Summary of Relevant Costs: Material A Material B Material C Material D Other expenses Total Relevant Cost
1,000 units X `6 1,000 units X `5 700 units X `2.5 300 units X `4 300 units X `5
6,000 5,000 1,750 1,200 1,500 550
`
16,000
Contract should be accepted since offer is of `22,000 in relation to relevant Cost of `16,000. Answer: 12
Variable Costs: (20,000 units @ `0.30 for 3 Years Sale Proceeds of Old Machine Capital Cost of New Machine
Retain Present Machine
Buy New Machine
18,000
12,000
Relative Benefit of Replacement (6,000)
18,000
(4,000) 7,000 15,000
(4,000) 7,000 (3,000)
Thus, it is advantageous to replace the equipment. Note. Depreciation charge and loss on sale of old machine should be ignored for this decision. Answer: 13 Relevant costs of producing one unit of the finished product Cost of material ‘M’ (realisable value) Cost of labour (Being sunk cost) Out-of-pocket expenses
`
80 0 30 110 Allocated overhead is not relevant for the decision. The customer should be charged `110 per unit. Answer: 14
220
(i) The down payment of `2,50,000 represents a sunk cost. The lost profit from subletting the shop of `1,20,000 per annum arrived as: (18,000 × 12) – 96,000 = 1,20,000 is an example of an opportunity cost. The salary amount is not given is also an opportunity cost lost. (ii)
The relevant information for running the shop is: (`)
Net Sales Less: Costs (22,02,000 – 2,50,000) (sunk cost excluded for decision making purpose)
22,20,000 19,52,000
Gross Margin
2,68,000
Less: Opportunity cost from subletting
1,20,000
Profit 1,48,000 As profit is more than opportunity cost, the most profitable decision is to carry on business in the shop. Ans. 15: Analysis of Cost and profit:
Direct material Direct labour Prime cost Overhead: Variable factory overhead Fixed factory overhead Administration overheads Selling commission Fixed selling overheads Total cost Profit Rate of profit on costs (2/18) = 1/9
`(lakhs) 3.60 6.40
`(lakhs) 10.00
2.20 2.60 1.80 1.00 0.40
8.00 18.00 2.00
Overhead absorption rate based on direct wages = (8.00 / 6.40) × 100 = 125% of direct wages Break up of new order: Direct Materials Direct Labour Overheads 125% of direct wages Total costs Profit 1/9 Selling Price The following points emerge:
` 36,000 64,000 80,000 1,80,000 20,000 2,00,000
(i) Factory overheads only are to be recovered on the basis of direct wages. (ii) The special order is a direct order. Hence commission is not payable. (iii) The budgeted sales are achieved. Hence all fixed overheads are recovered. Hence, no fixed overheads will be chargeable to the special order. Based on the above, the factory variable overheads recovery rate may be calculated as under: Total variable factory overheads Direct wages
`2.20 lakhs `6.40 lakhs
221
Factory overhead rate = (2.20 / 6.40) × 100 = 34.375% Applying this rate the cost of the special order will be as under: Direct materials Direct labour Overheads 34.375% of direct wages Total costs Price offered Margin
` 36,000 64,000 22,000 1,22,000 1,50,000 28,000 (more than 1/9)
Hence, the order is acceptable at the price of `1,50,000. Answer: 16 Statement of minimum price which the company can afford to quote for the new customer (based on relevant cost) Cost to be incurred to bring the equipment in its original condition. Opportunity cost of the direct material
29,700 2,250
Direct wages: Dept. A : 15 man days × `120
1,800
Dept. B : 25 man days × `100
2,500
Opportunity cost of contribution lost by department B (`2,500 × `2.30)
8,000
Variable overheads
1,075
25% × (`1,800 + `2,500) Delivery costs
1,350
Supervisory overtime payable for modification
1,050
Control device to be used in another job (Refer to working note 1)
(10,350)
Net loss on material cost savings, in the original equipment (Refer to working note)
11,700
Opportunity cost of remaining materials which can be sold as scrap
11,400
Opportunity cost of sale drawings Total minimum price which may be quoted
1,500 61,975
Working notes: 1. Cost of control device to be used in another job:
` Cost of control device Less: Dismantling & removal cost of control mechanism
10,500 120
(1 man day × `120) Less: Variable cost )25% × `120) Balance cost of control device
30 10,350
2. Net loss on material cost saving of equipment: Loss on material cost saving of equipment
12,000
Less: Conversion cost (2 man days × `120) Less: Variable overheads (25% × `240) Net loss on material cost saving of equipment
240 60 11,700
222
Answer: 17 Working Notes: 1. The book value of Material K `40,000 is a sunk cost and is not relevant for decision making. 2. The Scrap Value of Material K `10,000 will affect the cashflow and is relevant. Alternative I Relevant Costs Material A (Replacement Cost) Direct Labour – Skilled Contribution Lost (Opportunity Cost) Unskilled (not relevant) Variable Overheads Total Relevant Cost Cost per unit Selling Price Profit
= `60000 / 500 units = 500 units (`150 – `120)
(`) 42,000 12,000 4,000 2,000 60,000
(600kgs. X `70) (200 hrs X `6) (2000 X `2)
= `120 p.u. = `150 p.u. = `15,000
Alternative II 1. The Cost of substitute material `8,000 is relevant. 2. The regular profit of a job `6,000 is not relevant. Analysis: From the above analysis it is suggested to convert the materials into a specified product. Answer:18 Working Notes: 1. Relevant cost of labour Grade
: Nil, labour cost for Grade 1 labour as it will not be affected by the decision.
Grade 2
: `20 per hour
2. Relevant cost of material Material A
: `100 per unit, the replacement cost because the material is widely used.
Material B
: `250 per unit, the net realisable value, being the opportunity cost.
3. Statement of loss of contribution from the reduction in the sale of product Y.
` Sales revenue per unit: (A)
` 700
Variable cost per unit Grade 2 labour: (4 hour × `20)
80
Materials relevant variable costs
120
Variable production overheads: (B)
120
320
(4 hours × `30) Contribution per unit: [(A) – (B)]
380
223
Loss of contribution from the reduction in sale of 5,000 units
19,00,000
(5,000 units × `380) Less: Avoidable fixed factory overhead cost
5,90,000
Net Loss
13,20,000
Relevant costs and benefit analysis from the acceptance of the contract. (`’000) Sales revenue: (1)
20,000
(20,000 kgs. × `1,000) Relevant costs: Labour: Grade 1
NIL
Grade 2
2,400
(20,000 kgs. × 6 hours × 20) Material A (20,000 × 2 units × `1,000)
4,000
Material B (20,000 kgs. × 1 litre × `250)
5,000
Variable production overhead (20,000 kgs. × 8 hours × `30)
4,800
Total variable cost Incremental fixed costs
16,200 2,280 18,480
Add: Loss of contribution on product Y (Refer to working note 3) Total relevant cost: (ii) Excess of relevant revenue over relevant cost:
19,800 200
Advice to A Limited: to accept the contract, as it will enhance the pre-tax operating income by `2,00,000 Answer: 19:Working Notes: Calculation of contribution margin The company expects that each per cent point increase in on-time performance will result in revenue increase of `18,000 p.a. Additional revenue increase = `18,000 X 10 = `1,80,000 Contribution margin on additional revenue = `1,80,000 X 45/ 100 = `81,000 Costs incurred annually on the installation of new scheduling and tracking system Additional annual cost Interest Foregone on Fixed (Opportunity Cost) (10% X `2,00,000) deposit Total Costs Expected Savings in costs on the installation of new scheduling and tracking system Contribution margin from additional annual revenue (45% X `1,80,000) Decrease in variable costs due to reduced numbers of (3,000-1,000) X `50 carton lost
(`) 1,50,000 20,000 1,70,000 81,000 1,00,000
(`)
224
Total savings in cost Net saving
(1,81,000 - 1,70,000)
1,81,000 11,000
Suggestion: The expected savings are more than annual costs, hence it is suggested to install a new scheduling and tracking system. Answer: 20 Statement showing Revised Cost Estimates: 1. Steel Sheets (`12/kg. x 5,000kg.) 2. Steel Rods (1,000 kg. @ `17 kg.) 3. Bearing, hardware items, etc. 4. Labour Cost 5. Overheads: Fabrication Shop (500 hrs @ `25) Welding Shop (300 hrs @ `16) Planning engineers cost Design engineers cost Total Estimated Relevant Cost
`60,000 17,000 15,000 Nil 4,800
12,500
Nil Nil 1,09,300
Relevant costs are estimated future costs pertinent to a decision. Imputed costs do not form part of relevant costs. All costs accumulated for stock valuation purposes may not be relevant cost. Reasons for Variation in the Cost Elements 1. Current rate of steel sheets is quite relevant. Past rate of `12 per kg has no impact on the decision and therefore not adopted in the cost estimates. 2. Steel rods purchased five years ago cannot be used (non- moving) and as such it represents sunk cost. This material can now be substituted for alloy steel rods (`17/kg). Alloy rods are cheaper than steel rods and therefore relevant to the decision. 3. Fixed costs are past costs, not relevant to the decision. Labour costs are fixed in nature. 4. It is assumed that Fabrication Shop is working at optimum level. Therefore rate charged from outsiders (`25 per hour) is relevant. 5. It is assumed that Welding shop is not working at full capacity. Therefore variable cost of `16 per machine hour is adopted. 6. Planning and design engineers costs are fixed cost and, therefore, irrelevant. Answer: 21 1. Direct Material:
Revised Cost Estimate - Paper - Ink
2. Direct Labour (Skilled) Normal (250 hrs x `4) Overtime (125 hrs x `1) 3. Variable Overhead (350 hrs x `4) 4. Printing Revised Cost Estimate
2,500 3,000 1,000 125
5,500 1,125 1,400 600 8,625
Working Notes: 1. With no alternative use, the paper would not be replaced; the alternative, therefore, being to scrap the stock receiving proceeds of `2,500. 2. The surplus ink could not be used or sold and therefore the whole cost of the ink purchased should be charged to the cost of the programme. 3. The direct employees are currently usefully employed, therefore, their wage cost is being recovered from an existing customer. Before, transferring them to the work on the programme, the ability of the programme work to bear this cost must be determined.
225
4. The overtime premiums are directly caused by the programme work, which should be able to bear this additional cost. 5. There is no additional cost associated with the employment of the unskilled labour. Current idle time 200 hrs 75 hrs (No additional cost) Printing Work 125 hrs Week-end work 25 hrs Paid time off 50 hrs The 50 hrs of paid time off is more than covered by the 125 hrs of idle time, which is also paid for and, therefore, there is no additional cost. 6. Variable overhead is the incremental cost. 7. The variable overhead and other variable costs associated with running the printing press have been separately dealt with. The additional recovery required is, therefore, the lost contribution associated with 200 printing press hours. 8. Fixed production overheads are not associated with incremental cashflows, and therefore should be ignored. a) The cost of estimating time is a small cost, since it has already been incurred. It does not involve incremental cash flow. Therefore, it has been ignored. b) In short-term decision making, resources usage is best measured by using ‘variable cost’ which change in proportion to changes in output. When variable cost is matched with the sales revenue with which it is associated, the resulting difference or contribution gives a good indication of the expected benefit to the organisation of any course of action. If fixed assets are unaffected by a decision, contribution will be close approximation of cash flow and therefore, it is very real figure which may also be usefully used as a basis for ranking alternatives where limiting factors are involved. c) For evaluating the economic benefit derived from a product, it is necessary to match the revenue generated with he cost incurred. Opportunity cost represents the benefit forgone for taking one course of action rather than alternative. It gives a measure of sacrifice made in order to generate income. Conventional contribution approach normally extracts variable costs from the internal costing records (i.e., stock accounts, etc.). Opportunity costs may be derived from internal or external sources depending on such factors as whether there are alternative uses for internal resources consumed and whether, if used, they would be replaced. Answer:22: Research Project Particulars
Relevancy
Reason
Project cost till date
Not relevant
Sunk cost
Sale price of the project
Relevant
Incremental revenue/opportunity gain
Cost of materials received
Not relevant
Sunk cost
Amount (Rs’000s) 400
Cost of disposal of materials Relevant
Avoidable/opportunity cost
Cost of labour
Not relevant
Common costs
Contribution lost on the alternative use
Relevant
Absorbed Fixed overheads
Not relevant
Opportunity cost [Sales – (Prime cost labour) Sunk cost
Cost of Research Staff
Relevant
Incremental / out of pocket (160)
Redundancy and severance Not relevant pay Share of General Not relevant
Common costs Sunk costs
15 (125)
226
B ildi Total incremental inflow if the project is proceeded with
130
Decision: Better to continue the project. Answer. 23 Statement of cost of product NP Particulars Direct materials A B
(1,00,000 X 2.50) (60,000 X 1.00) (40,000 X 3.00) (1,00,000 X 6.00)
C Direct labour Skilled (25,000 hrs X `3) Unskilled Opportunity loss (25,000 X `2) Variable overhead (1,00,000 X 1.50) Fixed Overheads: Factory overheads: Addl. Overheads- Foreman Supervisor Depreciation: Type P Type Q Total Costs profit Sales
Total cost (100000 units) 2,50,000 60,000 1,20,000 6,00,000
(`) Cost per unit
10,30,000
10.30
1,25,000 1,50,000
1.25 1.50
60,000
0.60
35,000 14,00,000 4,00,000 18,00,000
0.35 14.00. 4.00 18.00
75,000 50,000 36,000 24,000 30,000 5,000
Working Notes: 1. Cost of Direct Material Material A- It is in regular use and hence replacement cost of `2.50 will be charged. Material B- Total requirement is of 1,00,000 units: Stock available 60,000 units opportunity cost `1.00 each 40,000 units purchase price `3.00 each. Material C- Purchase price of `6.00 2. Cost of Direct Labour Skilled Labour: (i) 1,00,000 units at `0.25 per hour (ii) Loss of contribution on existing product opportunity cost 25,000 X 2=`50,000 Unskilled labour: Available in surplus and is to be paid even without work. Hence, not relevant 3. Cost of Additional Staff (`) Foreman 36,000 Supervisor 24,000 Total 60,000 4. Variable Overheads 5. Fixed Overheads 6. Depreciation Type P: Type Q:
`1.50 per unit is relevant cost Not relevant hence excluded The machine is used on other product. Hence, replacement cost is relevant Depreciation =`1,60,000-1,30,000 =`30,000 Since it can be sold if not used resale value is relevant. Depreciation =`22,000-`17,000 =`5,000
227
7. Market Survey Costs: It is a sunk cost. Hence it is not a relevant cost. Answer: 24 Working Notes: 1. Machine manufacturing cost Costs of `50,000 incurred to date in manufacturing the machine is irrelevant for the decision, since It is a sunk cost. The payment of `15,000 received from the customer prior to the liquidation is also not relevant for decision making. 2. Material Cost. The purchase cost of `6,000 of materials bought in the past is irrelevant for decision making. Only the scrap value of materials i.e.`6,000 is relevant for decision making since it is the opportunity cost of materials bought in the past. 3. Labour Costs. Opportunity cost of labour when the workforce, is in short supply, and switched to another job,it could fetch the additional contribution of (`30,000-`8,000-`12,000)=`10,000. 4. Consultancy fees (`) Cost of completing the work 4,000 Cost of canceling the contract 1,500 Incremental cost of completing of work 2,500 5. General Overheads The general overheads are absorbed on allocation and therefore, these costs are not relevant for the decision. Statement showing economics of proposition (`) Revenue from completing work 34,000 Less: Materials (opportunity cost) 2,000 Labour: Actual costs 8,000 10,000 Opportunity costs 18,000 Cost of consultancy (Incremental cost) 2,500 22,500 Additional profit by accepting the offer of new customer in completion of the 11,500 work. In view of incremental profit of `11,500, the offer of new customer can be accepted. Answer: 25: For solving this question, it is necessary to take the following into consideration. SV Ltd. Has two departments A and B. Dept. A is manufacturing FLOTAP, but Dept. B is manufacturing the containers for this product. It also stores this product. This is the existing situation. Now three alternatives are given. Alternative 1.- Close Dept. B and manufacturing & storing may be given to PH Ltd. Alternative 2 – Continue Dept. B and manufacturing may be given to PH Ltd and storing to Dept. B. Alternative 3 – Continue Dept. B, Manufacturing may be done by Dept. B but storing may be given to PH Ltd. Company should either select one of the alternative or continue the existing practice. Working Notes: (i) (`) 4,20,000 Direct Materials including germicide th 1,20,000 Use of germicide (1/5 of `6,00,000) Direct materials other than germicide 3,00,000 This material will be avoidable cost if Division B is to Close-down. (ii) 10% of all materials = 10% of `3, 00,000 (a) Savings: `3, 00,000-`30, 000=`2, 70,000 if manufacture is given to PH Ltd. And storage is with SV Ltd. (b) Savings: 3, 00,000- 90% of `3, 00,000=`30, 000. If manufacture is done by SV Ltd and storage given to PH Ltd. (iii) Direct Labour cost Less: Terminal benefit if B is closed Avoidable cost, if Dept .B is closed (saving)
(`)
3,00,000 45,000 2,55,000
228
If manufacturing is given to PH Ltd. And SV Ltd. continues to store the product, saving on account of labour retrenchment will be only `15,000.(It means in this alterative 3,00,000-15,000=2,85,000 will be spent any way and avoidable cost will be only `15,000). If manufacturing is done by SV Ltd. Then Labour force will continue. It means impact of labour cost in 3rd alternative will be nil. (iv) Supervisory staff will be transferred to another department in the lst alternative. It means cash flow will not be affected. In the second and third alternative, supervisory staff will be retained and it means no additional cash flow or relevant cost due to decision. (v) Depreciation does not affect the cash flow. Therefore it is not relevant for these decisions. (vi) The hire charges of warehouse is `54,000 per annum. The remaining space of the warehouse is idle. It means, when department B is closed, cash outflow of `54,000 will be avoided. Therefore `54,000(and not `27,000) is the avoidable cost for this decision. If Department B continues, this expenditure of `54,000 continue. Therefore cash flow for alternatives 2 and 3 will not be isturbed on this account. (vii) Maintenance of machine is required for manufacturing. If means `21,600 will be avoidable cost for alternative 1 and 2. In 3rd alternative this cost will continue to be there. Besides this machine will not be required in alternative 1 and 2. It will be sold at `1,50,000.It will be a one time cash inflow for alternatives 1 and 2. (viii) Miscellaneous overhead of `94,500 will be avoidable cost for alternative 1. For 2nd alternative 80 % of this i.e `75,600 will be avoidable cost. For 3rd alternative 20% of `94,500 i.e. `18,900 will be avoidable cost. (ix) Germicide- Stock: Stock in 2002 Used last year (1/5th) Balance Stock
(`) 6,00,000 1,20,000 4,80,000
It is given that original price is `3,000 Therefore, `4,80,000/`3,000=160 tonne Germicide is there. (x) Germicide-value Alternative 1 :
Alternative 2 : Alternative 3 :
Storage is done by PH Ltd. Therefore it will be sold at `2,400 per tonne. Cash inflow will be 2,400 X 160=`3,84,000. Note that original price and replacement cost are irrelevant for the decision. 10% of all material will be used. It means 90% of 160 tonne will be sold. Cash inflow will be 160 X 0.90 X `2,400= `3,45,600
In this situation storage is done by PH Ltd. Therefore only 10% of whole quantity of 160 tonne will be sold in market at `2,400 per tonne . Cash inflow will be 16 X `2,400 `38,400. (The replacement cost is irrelevant information in the question and it will be relevant only, when germicide has competing demands.) (xi) Machine is used for manufacturing of containers. It is not required in alternatives 1 and 2. Therefore , it will be sold and there will be one time cash inflow of `1,50,000 under alternatives 1 and 2. Written down value is irrelevant for decision under consideration. (`) Alternative 1 Alternative 2 Alternative 3 Division B Close Continue Continue Manufacture of containers PH Ltd PH Ltd. SV Ltd. Storage of product PH Ltd. SV Ltd. PH Ltd. Cash Inflows (Including avoidable cost)
229
Direct materials other than germicide Direct labour Rent of a part of warehouse Maintenance of machine Miscellaneous overhead Total avoidable cost p.a. (A) Cash outflows Contract fee to PH Ltd. For Manufacturer For packing and storage Total outflow (B) Net Cash outflow p.a. (A-B)-( C ) Total cash outflows for 4 years ( C X 4) One time income Sales of germicide Sale of machine Net cash outflow
3,00,000 2,55,000 54,000 21,600 94,500 7,25,100
2,70,000 15,000 21,600 75,600 3,82,200
30,000 18,900 48,900
7,50,000 1,50,000 9,00,000 (1,74,900) (6,99,600)
7,50,000 7,50,000 (3,67,800) (14,71,200)
1,50,000 1,50,000 (1,01,100) (4,04,400)
3,84,000 1,50,000 (1,65,600)
3,45,600 1,50,000 (9,75,600)
38,400 (3,66,000)
Recommendations: All the alternatives result in net cash outflow. Therefore it is interest of SV Ltd. To continue and to manufacture containers and store them in Division B. Answer: 26: Comparative Statement of Relevant Costs for use of own distribution division or use of Countrywide distributions. (`’000) Particulars Own Distribution Countrywide Distribution 95-96 96-97 97-98 95-96 96-97 97-98 Relevant Cash outflow: Operating Costs 2,100 2,100 2,100 Sub-Contract costs 1,950 1,950 1,950 Total 2,100 2,100 2,100 1,950 1,950 1,950 Less: Relevant cash inflow: Sale of delivery vehicle On 1-4-2002 600 On 31-3-2005 240 Net Relevant Cash outflows: 2,100 +2,100 +1,860 1,350 +1,950 +1,950 Total =6,060 =5,250 Suggestion: From the above comparative statement it is observed that the net relevant cash outflow is more in case of own distribution. Hence, selection of countrywide distributors is recommended. It is based on the assumption that no portion of the common corporate cost of which `3,00,000 is apportioned to distribution division which would be avoided even if, the distribution division is closed down. (b) Reasons for reluctancy to accept countrywide distributors in distribution of Soft Drinks. (1) Loss on Sale of Delivery Vehicles presently owned by the company: (`) Cost of Vehicles Less: Depreciation for 2003-04 Book Value on 1-4-2004 Less: Sales realization Book Loss on sale of Vehicles
(8 Vehicles on 1-4-2003) (8 Vehicles X `75,000)
6. Possibility of reduction in reported income as per Security Analyst’s recommendation Forecast of operating income as per Security Analyst Particulars 1995-96 Estimated Profit when own distribution division is used 630 Net income if the offer of countrywide distributors is accepted 630 Working Notes: Projected Profit for 95-96
19,20,000 4,20,000 15,00,000 6,00,000 9,00,000 (`’000) 1996-97 660 330 (`’000)
660
230
Add; Depreciation avoided Add: Saving in operating cost
420 150 1,230 900 330
(`2,100- `1,950)
Less: Book loss on the disposal of delivery vehicles Net income, if Countrywide distributors selected Analysis: In view of short- run benefit, countrywide distributors can be opted. But when the long-run benefits are recognized, and to focus on customer needs, the company’s own distribution function is recommended. Answer: 27: Statement showing value of total work undertaken by X Ltd. at customer’s price (`’000) Material costs (for appliances covered under agreement)
825
[Rate to working note 1 (i)] Material costs (for appliances not covered under agreement)
275
[Refer to working note 2 (i)] Labor cost (for appliances covered under agreement)
1,000
[Refer to working note 1 (ii)] Labour cost (for appliances not covered under agreement)
240
[Refer to working note 2 (ii)]
_____
Total receipts
2,340
Break up of receipts: Big appliances
60%
1.404
Small appliances
40%
936
Profitability Statement (`’000) Income Big appliances Small appliances Total receipts: (A) Costs: Material Heat, rent, light etc. Management costs Service staff costs Transport costs Total costs: (B) Profit: [(A) – (B)] Recommendation:
Option 1
Option 2
Option 3
129.6 (60%×`216) 936 . 1,065.6
1,404
1.404
86.4 (40%×`216) 1,490.4
936 . 2,340
320 40%×(825+275) 137.5% 125 108 230 25 808 257.6
480 60%×(825+275) 137.5% 50 83 440 220 1,273 217.4
800 (825+275) 137.5% 150 150 750 230 2,080 260
Option 3 is most profitable one. Working Notes: 1.
Material and labour cost (for appliances under after sales agreement):
231
` (i)
Cost of Material per unit charged to customer’s by X Ltd. (`100 + 10% x `100 + 25% x `110) Cost of material charged to customer’s by X Ltd.
137.50
Rs.60,000 × `137.50 Rs.10 (ii)
8,25,000
Cost of labour charged to customer by X Ltd.
Rs.1,00,000 × `100 Rs.10 2.
10,00,000
Material and labour cost (for appliances not covered under sales agreement): ` (i)
Cost of material charged to customer by X Ltd.
Rs.20,000 × `137.50 Rs.10 (ii)
2,75,000
Cost of labour charged to customer by X Ltd.
Rs.36,000 × `100 Rs.15
2,40,000
Answer: 28 Statement of relevant cost of Mahila Griha Udyog Industries If the contract is accepted/rejected Decision
Relevant costs (if contract is accepted) `
Relevant costs (if contract is rejected)
18,00,000
-
-
2,10,000
`
Cash inflows Contract price Sale of material Y
.
.
18,00,000
2,10,000
1,35,000
-
-
27,000
Material Z
3,00,000
-
Replacement of semi-skilled labour by skilled labour
5,70,000
-
3,00,000
-
35,000
-
1,25,000
-
(Refer to working note I) Total cash inflows: (A) Cash outflows Material X substitute (Refer to working note 2) Adaptation required obsolete material X
for
the
use
of
(Refer to working note 3) Non-skilled labour cost (Refer to working note 4) Supervisory staff cost (Refer to working note 5) Avoidable overheads
232
(Refer to working note 6) Total cash outflows: (B)
14,65,000
27,000
Net cash inflows: (A) – (B) 3,35,000 1,83,000 The net benefit on accepting the contract is : `3,35,000 – `1,83,000 = `1,52,000. Conclusion The contract should be accepted as it yields a net incremental cash inflow of `1,52,000. Working notes: 1. Material Y will have to be paid for whether or not the contract is accepted, therefore its cost is irrelevant. The relevant cost figure here is that which has an opportunity cost of `2,10,000. This means that the company can resell material Y at this price. 2. Regarding material X, if the contract is accepted, alterative material will have to be purchased for the other product at a cost of `1,35,000. If the contract is rejected material X will be adapted for a product not included in the list of special range of namkeens at a cost of `27,000. 3. The relevant skilled labour cost of `5,70,000 is the extra cost to the company because of this contract. It is the replacement cost of semi-skilled labour by skilled labour. 4. Non-skilled labour cost is the incremental cost of the contract. 5. If the company accepts the contract it will have to pay `35,000 for the two position that the supervisory staff can replace. 6.
Only `1,25,000 of avoidable overheads are relevant to this contract.
Answer: 29 M/s Ranka Builder’s Statement of relevant costs on the Acceptance of contract form Excel Ltd. (Figure in lakh of `) S.No.
Particulars
1.
Land cost
Basis for cost to relevant
the be
Relevant cost if contract is accepted `
Irrelevant cost if the contract is accepted `
20
(Refer to working note 1) -
7 (Sunk cost)
Incremental
10
-
Cement and sand
Replacement
8
Bricks and Tiles
Opportunity
5
Steel
Incremental
10
2.
Drawings and design
3.
Registration
4.
Materials :
Others
9
(Refer to working note 2) 5.
Labour : Skilled
Opportunity
2
Unskilled
Incremental
8
233
5 (Sunk Cost)
Supervisor’s Salary 6.
Overheads : Relevant (avoidable)
General
4
Depreciation Replacement machine 7.
6 (Sunk Cost)
cost
of
Estimated profit foregone on other project
7 Opportunity foregone
10
Total
93
Decision : Since the offer price of contract is `1 crore and its total relevant cost is `93 lacs; these figures clearly shows that the offer should be accepted. Working notes : 1.
`(Lacs) Total cost of 3 grounds of land
60
Cost of ground of land will be borne by Excel Ltd.
40
Cost of 1 ground of land will be borne by M/s Ranka Builders
20
2. Others material cost is `10 lacs, it includes material worth `2 lacs, relating to interior decoration, which is a sunk cost, this material can be sold for `1 lac, (which is a relevant opportunity cost) and `8 lacs, material is an incremental cost. Hence total relevant cost of others material is `9 lacs. (`8 lacs, incremental + `1 lac, opportunity cost). 3. Since the equipment can also be used on ths contract. Its current replacement price is `32 lacs, and after one year its cost will be `25 lacs. Therefore the relevant opportunity cost of machine is : (`32 lacs – `25 lacs). Answer: 30 Alternative 1 – (Conversion versus immediate sale)
`
`
Sales revenue 900 units at `300 per unit (Refer to working note 1)
2,70,000
Less: Relevant costs Material XY opportunity cost (Refer to working note 2)
21,000
Material A – units @ `90 per unit (Refer to working note 3
54,000
Material B – 1,000 units @ `45 per unit (Refer to working note 4)
45,000
Direct Labour : Unskilled – 5,000 hours @ `3 per hour Semi-skilled Highly skilled – 5,000 hours @ `11 (Refer to
`
15,000 Nil 55,000
70,000
234
working note 5) Variable overheads 15,000 hours @ Re.1 (Refer to working note 6)
15,000
Extra selling and delivery expenses
27,000
Extra advertising
18,000
Fixed advertising
45,000
2,50,000
Nil
(To remain same, not relevant)
.
Excess of relevant revenues
20,000
Alternative 2 – (Adaptation versus Immediate Sale) Saving on purchase of sub-assembly Normal spending – 1,200 units @ `900 per unit
10,80,000
Less: Revised spending – 900 units @ `1,050 per unit (Refer to working note 7)
9,45,000
1,35,000
Less: Relevant costs: Material XY opportunity cost (Refer to working note 2)
21,000
Material C – 1,000 units @ `37 (Refer to working note 8)
37,000
Direct labour Unskilled – 4,000 hours @ `3 per hour Semi-skilled Highly skilled – 4,000 hours @`11 per hour (Refer to working note 5, 6)
12,000 Nil 44,000
Variable Overheads – 9,000 hours @ Re.1/- per hour (Refer to working note 6) Fixed overheads Net relevant savings
56,000 9,000
1,23,000
Nil
. 12,000
Evaluation : The evaluation of two alternatives clearly shows that Alternative 1, yields higher net revenue of `8,000 (`20,000 – `12,000). Hence because of higher net revenue of Alternative 1, it is advisable to convert material XY into a specialized product. Working notes : 1. There will be a additional sales revenue of `2,70,000 if Alternative 1 is chosen. 2. Acceptance of either Alternative 1 or 2 will mean a loss of revenue of `21,000 from the sale of the obsolete material XY and hence it is an opportunity cost for both of the alternatives. The original purchase cost of `75,000 is a sunk cost and thus not relevant. 3. Acceptance of Alternative 1 will mean that material A must be replaced at an additional cost of `54,000. 4. Acceptance of Alternative 1 will mean diversion of material B from the production of product Z. The excess of relevant revenues over relevant cost for product Z is `180 (`390 – `210) and each unit of product Z uses four units of material B. The lost contribution (excluding the cost of material B which is incurred for both alternatives) will therefore be `45 for each unit of material B that is used for converting the obsolete materials into a specialised product.
235
5. Unskilled labour can be matched exactly to the company’s production requirements. Hence acceptance of either alternative 1 or 2 will cause the company to incur additional unskilled labour cost at `3 for each hours. It is assumed that the semi-skilled labour will be able to meet the extra requirements of either alternatives at no extra cost to the company. Hence, cost of semi-skilled labour will not be relevant. Skilled labour is in short supply and can only be obtained by reducing the production of product L, resulting in a loss of contribution of `24 (given) or `6 per hour of skilled labour. Hence the relevant labour cost will be `6 (contribution lost per hour) + `5 (hourly rate of skilled labour) i.e. `11 per hour. 6. It is assumed that for each direct labour of input, variable overhead will increase by Re.1 hence for each alternative using additional direct labour hours, variable overheads will increase. 7. The cost of purchasing the sub-assembly will be reduced by `1,35,000 if the second alternative is chosen and so these savings are relevant to the decision. 8. The company will incur additional variable costs, of `37 for each unit of material C that is manufactured, so the fixed overheads for material C viz. `18/- per unit is not a relevant cost. Ans. 31 Calculation minimum price to be quoted for a quotation, based on relevant costs only Opportunity cost of: (1) Retaining materials already in the original machine - Sale of Brass scrap - Sale of Steel scrap - Balance material , cost of scrapping )saved) (2) Conversion materials - Department M - Department A (3) Conversion work (a) Department M Labour Variable overhead Contribution foregone (b) Department A Labour
60,000 12,000 1,80,000
(`) 1,00,000 25,000 (5,000) 12,000 3,000
2,52,000
Nil
Variable overhead 6,000 57,000 Off-loading cash flow foregone 63,000 (4) Sales proceed of design and specifications 60,000 (5) Incremental fixed overhead-cost of supervision 10,000 Minimum price to be quoted 5,20,000 Note: For the above minimum price of `5,20,000 profit can be added. The existing overheads are committed costs and are not relevant for decision making. Answer: 32 1. Value of Material X in stock : (which can be used as substitute for other materials) = `54,000 X 90 / 100 = `48,600 2. Value of Material X for which firm order has been placed = `76,000 X 90 / 100 = `68,400 3. Value of Material Y in stock = 2 times x `62,000 = `1,24,000 4. Irrelevant Costs: Following costs are irrelevant therefore, they have been ignored • Site manage costs – being fixed costs • Depreciation of plants • Interest on capital • Notional interest in estimated working capital
236
•
Head office expense allocated to contracts.
Comparative statement of Net Benefit resulting from each contract Particulars Material X – in stock Material X – firm orders placed Material X – not yet ordered Material Y - in stock Material Z – not yet ordered Labour – to be paid Travel and other expenses Income from the hire of plant Penalty for rescinding the contract ‘AX’ is relevant Total Cost Contract Price Expected net benefit
(at current cost) (at replacement cost) (future outflow)
Contract AX 48,600 68,400 1,50,000 -
Contract BX
2,15,000 17,000 (15,000) -
2,75,000 14,000
4,84,000 7,20,000 2,36,000
6,61,000 8,80,000 2,19,000
(`)
1,24,000 1,78,000
70,000
Advice- Since the expected net benefit of contract AX, is more than Contract BX, it is suggested to continue with Contract AX. Answer: 33:Relevant Cost of ‘Jeet’ bicycle Material Labour Variable Overhead (0.4 X 300) Cost of Capital (0.15 X 6,00,000) / 25,000
300.00 200.00 120.00 3.60 623.60
If Star Bicycle company accept the offer of making ‘Jeet’ for the chain stores the loss in contribution due to sale of Smart is going down by 1,00,000 units is relevant, which causes a loss of `(899-300-200-120)= `279 The price of Jeet then should be `623.60 + 279 = `902.60. This is higher than the price of `800 as offered by the chain store. So, the offer cannot be accepted. Since the chain store has decided to launch a product like ‘Jeet’, it will do so whether or not Star Bicycle Company accepts the proposal as there is excess capacity in the industry it will be able to do so. In that case, the loss of contribution is `279 is not relevant and Star Bicycle Company can accept the proposal of the chain store. Star Bicycle Company should have a closure look in the market condition and the chain store’s ability to get a replica of ‘Jeet’ from other manufacturer before Star Bicycle Company reaches a final decision. Answer 34: Minimum recommended price per unit of 5,000 units of a product (obsolete model) of ACE Ltd. (i) Historical cost of `11.50 per unit of 5,000 units of a product is irrelevant (as it is a sunk cost) for determining the recommended price per unit. (ii) If at all this model is sold in the market through normal distribution channels it will entail a variable selling and distribution cost of `3 per unit. (iii) If the stock is disposed off by asking someone to take them on “as is where is basis”, the company would have to spend `5,000 over 5,000 units i.e. `1/- per unit. In view of (ii) and (iii) the option of selling 5,000 obsolete units of the model using regular channels will nave a differential cost of `2 (`3 – Re.1) per unit. Recommendation: Hence, if the company can get anything more than `2/- per unit, then it is worthwhile to sell the stock of 5,000 units and earn an additional contribution.
237
Answer: 35 Statement of Increment Cost and Incremental Revenue Capacity in units
Unit cost `
Total cost `
Incremental cost `
Unit price `
Total price `
Incremental revenue `
(a)
(b)
(c)=(a)×(b)
(d)
(e)
(f)=(a)×(e)
(g)
200
40
80,000
-
100
2,00,000
-
3000
35
1,05,000
25,000
95
2,85,000
85,00,000
(`1,05,000 – `80,000) 4000
34
1,36,000
(`2,85,000 `2,00,000) 31,000
94
3,76,000
(`3,76,000 – `2,85,000)
`1,36,000 – 1,05,000) 5,000
32
1,60,000
91,000
24,000
-
-
-
-
-
-
(`1,60,000 – `1,36,000) 6,000
31
1,86,000
26,000 (`1,86,000 – `1,60,000)
Decision: At 4,000 units capacity told sales revenue is `3,76,000 and the total cost is `1,36,000 leaving a profit of `2,40,000. The profit figure at this level clearly shows that the fixed expenses stand fully recovered. Hence, we have to take incremental cost for further level levels of output. For an additional sales of 2,000 units
Rs.50,000 2,000 units
incremental cost is `50,000 (`1,86,000 – `1,36,000) and the cost per unit is `25
Since the price quoted per unit is `28, which is more than `25, therefore, the order should be accepted. Answer: 36 ABC Ltd is facing Direct material constraint and special steel plates are in short supply but the stock is available only 500 M.T. Alternatives available to maximize profit Alternative I: - Manufacture and Supply only 20,000 cylinders at the risk of reduced order in future. Alternative II: - Make 40,00 upper halves, buy 40,000 button halves from outside and supply 40,000 cylinders. Profitability Statement No. of Cylinders Sales Realisation @ `700 Welding and other costs @ 30 Transportation, loading etc. (at `5 per half) Net Differential Income
Alternatives I II 20,000 40,000 140 280 (6) (12) (2) 134 266
Differential Cost 140 (6) (2) 132
The additional net income when 40,000 halves are purchased is `132 lakhs which is the maximum price that ABC Ltd. Can afford to pay keeping for itself at least the contribution it would earn by its own operation (a).
238
i.e. The Price
=
` 120 Lakhs 40,000
=
`330 per bottom half.
Answer: 37 Option 1: Profitability to continue only in season period Particulars Incremental Revenue (i) Differential cost: Cost of Sales Supplies Electricity Charges Total (ii) Incremental revenue over differential cost (i)-(ii) Less: Cost of advertisement Net incremental revenue
Gift shop 6,000 3,300 300 40 3,640 2,360
Working Notes: (1) Incremental revenue Gift shop Restaurant Lodge
(`48,000 X 10/80) (`64,000 X 10/80) (`1,80,000 X 10/90)
(2) Differential cost of sales Gift shop Restaurant
(`6,000 X 55/100) (`8,000 X 55/100)
(3) Differential cost of supplies Gift shop Restaurant Lodge
(`6,000 X 5/100) (`8,000 X 10/100) (`20,000 X 8/100)
(4) Differential cost of Electricity Charges Gift shop Restaurant Lodge
Restaurant 8,000 4,400 800 160 5,360 2,640
(`) Lodge 20,000 1,600 400 2,000 18,000
(`)
7,700 2,700 600 11,000 23,000 12,000 11,000
Total
6,000 8,000 20,000 34,000
Total
(`) 3,300 4,400 7,700 (`)
Total
300 800 1,600 2,700 (`)
(`900-`640) X 10/80) (`3,200 –`1,920)X 10/80) (`13,500-`9,900) X 10/90) Total
Option 2: Profitability to continue throughout the year including season and off season periods (`) Particulars Gift shop Restaurant Lodge Incremental Revenue: Season Period Off Season period 34,200 45,600 80,000 Total (i) 34,200 45,600 80,000 Differential Cost Cost of Sales 19,800 26,400 Supplies 1,800 4,800 12,800 Salaries 9,600 9,600 40,800 Electricity –Fixed 1,280 3,840 13,800 Electricity- Variable 240 960 3,200 Total (ii) 32,720 45,600 70,600 Net incremental Revenue (i)-(ii) 1,480 9,400 Working Notes: (a) Incremental Revenue in off season period
Total 34,000
(`)
40 160 400 600
Total 1,59,800 1,59,800 46,200 19,400 60,000 18,920 4,400 1,48,920 10,880
239
Gift shop Restaurant Lodge (b) Differential Cost of Sales Gift shop Restaurant
(`48,000 X 2 X 30 / 80X 95/100) (`64,000 X 2 X 30 / 80X 95/100 (`1,80,000 X 2 X 40 / 90X 50/100 Total
34,200 45,600 80,000 1,59,800
(`36,000 X 55/100) (`48,000 X 55/100) Total
(`) 19,800 26,400 46,200
(c) Differential cost of supplies Gift shop Restaurant Lodge
(`36,000 X 5/100) (`48,000 X 10/100) (`1,60,000 X 8/100)
(d) Differential cost of Salaries Gift shop Restaurant Lodge
(`4,800 X 2) (`4,800 X 2) (`25,200-`4,800) X 2)
(e) Differential cost of Electricity (Fixed Element) Gift shop (`640 X 2) Restaurant (`1,920 X 2) Lodge (`6,900 X 2)
(`)
Total (`)
Total (`)
Total
(f) Differential cost of Electricity (Variable element) Gift shop (`900-`640) X 30 X2 /80) Restaurant (`3,200 –`1,920) X 30X 2/80) Lodge (`13,500-`9,900) X 40 X 2 /90) Total
(`)
1,800 4,800 12,800 19,400 9,600 4,600 40,800 60,000 1,280 3,840 13,800 18,920 240 960 3,200 4,400
Decision : By adopting the Option 1, the net increase in incremental revenue by `120 (i.e. `11,000-`10,880) over the Option 2.Therefore, Option 1 is suggested to adopt. Incremental profitability by adopting strategies of both advertisement insertions and operating during off season period. (`) Incremental Revenue with Advertisement 11,000 Incremental Revenue with the continue of operations during off season 10,880 Total incremental revenue 21,880 Therefore, both the strategies can be implemented simultaneously for increase of profitability of the organization. Answer: 38 (a) Consequences of undertaking: Nagpur & Delhi Contracts Nagpur Contract Contract revenue Sales of materials held for the Nagpur contract (Note 1) Saving in material purchases by alternative use of materials of Delhi contract (Note2) Hire of plant Incremental costs:
170
48 2 220
(`’000) Delhi Contract
180 24
204
240
Materials to be ordered (Note 3) Project manager’s travel, lodging etc. Local labour Penalty for canceling the other contract Excess of revenue/saving over incremental costs
40 4 70 8
122
34 4 56 16
110
98
Note: (1) If the Delhi job is undertaken sales of materials no longer required for the Nagpur job would be (`) Materials held, at cost Current money value (add 60%) Sales price )x90%) Less: transportation etc. costs (16.67%) Net sales revenue (2) If the Nagpur job is undertaken, the materials for the Delhi job might be refused on a different contract, thereby saving the purchase of additional materials: (`’000) Materials held Contracted for Cost of unwanted materials Saving in purchase on different contract (80%)
94
20 32 28.8 4.8 24.0
24 36 60 48
(3) The materials contracted for to carry out the Delhi job must be paid for whatever happens. Although not yet received, they must be paid for whichever (if either) contract is undertaken. It is therefore not an incremental cost chargeable to the Delhi contract. For similar reason, materials already held are not an incremental cost to their respective contracts. The alternative use of materials not required is , however, significant and this has been taken into account on the revenue side of the analysis. (4) It is assumed that the project manager’ salary is a fixed cost, whichever contract (if either) is undertaken. Incremental labour costs are therefore travel, lodging etc. and local labour. (5) The penalty cost of failing to undertake one contract should be treated as a consequential cost of undertaking the other contract. (6) The excess of revenue/ saving over incremental costs calculated for each contract shows the comparative effect on profits of undertaking each job in preference to the other. The difference between the two figures (`98,000 a and `94,000) shows that there is a difference between the two project of `4,000 in favour of Nagpur job. (c) The approach usef has assumed that one project or the other will be undertaken. Some costs have already been incurred (some materials , plant): other costs have been committed (project manager’s salary, head office administration) and others are notional (interest on plant). These are not relevant to any decision about future action. The only relevant consideration should be: (i) Future revenues or cash savings as a consequence of the decision. (ii) Future costs, incurred as an additional expense as a consequence of the decision. In the solution in part (a), incremental revenues are the revenues from the contract undertaken , alternative uses of materials held but not required and hire of plant. Incremental costs are only those additional costs which would be incurred as a result of the decision to undertake one of the contracts. The cost accounting profit or loss recorded for each contract might be: Nagpur: `1,70,000-`1,60,000 = `10,000 Delhi: `1,80,000-`1,82,000 =(`2,000) There figures are irrelevant to a decision because the costs include past , committed or notional costs, and other revenues and penalty costs to the company are ignored. ( c) Other factors to consider are: (i) The constraints on working which make the contract mutually exclusive. If there is a shortage of labour, funds etc., it might be possible to overcome and carry out both projects: (ii) The likelihood of another contract being offered for the same period of time, which is more profitable than either the Nagpur or Delhi jobs. (iii) Loss of goodwill and future contracts by not undertaking either projects: (iv) Reliability of the prospective customer in each contract:
241
(v) (vi)
Reliability of costs forecasts, lobour availability etc. on both contacts. The net difference between the two jobs, `4,000 is relatively small and sensitivity / risk analysis will be very important: The preference for the Nagpur contract (by `4,000) has assumed that the alternative use for the Delhi contract materials will exist. It is only a likelihood, however. Failure to obtain this saving would shift the preference strongly in favour of accepting the Delhi job.
Answer: 39 Working Notes: Calculation of Balance Capacity Products Units ‘AB’ 5,000 ‘CD’ 10,000 Total At 65% Capacity At 100% Capacity Balance Capacity (i) Statement of Profit for 2003-04 Products Production & Sales (Units) Sales Revenue (i) Variable Costs: Direct Material Direct Labour Products Variable overheads ( 100% on Wages) Total Contribution Less: Fixed Costs Profit
Labour Hours (per unit) 5 4
Total Labur Hours 25,000 40,000 65,000
= 65,000 Labour hours used = Labour hours used would be 1,00,000 = 1,00,000 hours-65,000 hours = 35,000 hours
(ii) (i)-(ii)
Capacity utilized (%) 25 40 65
(`) Total
‘AB’ 5,000 4,00,000 (@`80)
‘CD’ 10,000 10,00,000(@`100)
50,000 (@`10) 1,25 ,000 (@`25)
300000 (@`30) 200000 (@`20)
3,50,000 3,25,000
‘AB’ 1,25,000
‘CD’ 2,00,000
Total 3,25,000
3,00,000 1,00,000
7,00,000 3,00,000
10,00,000 4,00,000 2,25,000 1,75,000
Working Notes: Proposals (1) Utilise balance capacity to Produce ‘AB’ (2) Utilise balance capacity to Produce ‘CD’ (3) Utilise balance capacity to produce a new product ‘EF’ Additional Units= Balance Capacity / Labour hours per unit AB = 35,000 hrs. / 5 hrs = 7,000 units CD = 35,000 hrs. /4 hrs. = 8,750 units 1,400 units Less: Decrease in Efficiency by 16% = 7,350 units EF = 35,000 hrs. / 7 hours 5,000 units
14,00,000
Statement showing utilization of Balance Capacity Products AB - Existing - Additional
Proposal (a0 5,000 7,000
Proposal (b) 5,000 -
Proposal ( c ) 5,000 -
CD – Existing − Additional
12,000 10,000 -
5,000 10,000 7,350
5,000 10,000 -
EF – New Units
10,000 -
17,350 -
10,000 5,000
242
Statement showing contribution per unit of Products ‘AB’ ‘CD’ AND ‘EF’. Product Units Selling Price (i) Variable Costs: Direct Material Direct Labour Variable Overheads (100% of Wages) Total Variable Costs (ii) Contribution (i) – (ii)
Existing 5,000 84.00
AB
Addl. 7,350 104.00
EF New 5,000 145.00
31.50 21.00 21.00
31.50 25.00 25.00
40.00 36.75 36.75
63.00
73.50
81.50
113.50
17.00
30.50
22.50
31.50
Addl. 7,000 80.00
Existing 10,000 104.00
10.50 26.25 26.25
10.50 26.25 26.25
63.00 21.00
CD
Note: 1. The selling price of additional units of Product ‘CD’ is assumed to be `104 as is for existing units. 2. The direct labour cost per unit of additional units of Product ‘CD’ is calculated as below: Time taken for each additional unit of Product ‘CD’ = 35,000 hours/ 7,350 units = 4,762 hours Direct Labour Cost per unit = 4,762 hours x `5.25 per hour = `25000 The variable cost per unit of Products ‘AB’ and ‘CD’ were `60 and `70 respectively in the year 2003-04. In the year 2003-04 it became `63 and `73.50 respectively. Then the differential cost for product ‘AB’ for 5,000 units comes to `3 per unit and for product ‘CD’ for 10,000 units comes to `3.50 per unit. The differential cost per unit for each additional unit produced during unutilised capacity is equal to its variable cost. Profitability Statement using incremental revenue and differential cost approach (`) Products Units Incremental Total Differential Total Difference Revenue per Incremental cost per unit Differential unit revenue cost Proposal (a) AB 5,000 4.00 20,000 3.00 15,000 5,000 7,000 80.00 5,60,000 63.00 4,41,000 1,19,000 CD 10,000 4.00 40,000 3.50 35,000 5,000 Total 6,20,000 4,91,000 1,29,000 Proposal (b) AB 5,000 4.00 20,000 3.00 15,000 5,000 CD 10,000 4.00 40,000 3.50 35,000 5,000 7,350 104.00 7,64,400 81.50 5,99,025 + 1,15,375 50,000 (*) Total 8,24,400 6,99,025 1,25,375 Proposal (c) AB 5,000 4.00 20,000 3.00 15,000 5,000 CD 10,000 4.00 40,000 3.50 35,000 5,000 EF 5,000 145.00 7,25,000 113.50 5,67,500+ 1,27,500 30,000(**) Total 7,85,000 6,47,000 1,37,500 * Selling and Distribution Expenses ** Special Advertising Expenses The Profit as per Statement of Profit for 2003-04 is `1, 75,000. By utilising the Balance capacity 35,000 hours in manufacture of product ‘EF’ the said profit will increase by `1,37,500 Statement of Profit for 2004-05 with the selection of Proposal (C) to Introduce Product ‘EF’ Existing Profit on manufacture of Products ‘AB’ and ‘CD’ Add: Profit from Product ‘EF’ by utilising to balance capacity Total Profit Answer: 40
(`) 1,75,000 1,37,500 3,12,500
243
Differential Cost of the job Increase `
Decrease `
Material cost
50,000
20,000
Labour cost
90,000
22,500
Additional Overheads
10,000
-
-
2,250
1,50,000
44,750
Other expenses Total
Net differential cost of the job : `1,05,250 (`1,50,000 – `44,750) Note: Depreciation, rent, heat and light and power are not going to affect the costs. (b) Full Cost of the jobs: ` Cost as above at (a)
1,50,000
(i.e. increased costs) Depreciation
9,000
Power
1,000
Rent
2,500
Heat & Light
250
Total
1,62,750
(c) Opportunity cost of taking the order: `
`
Sale of Product A
62,500
Less: Material
20,000
Labour
20,500
Power
1,000
Other expenses
2,250
45,750
Total
16,750
(d) Sunk cost of the jobs: ` Depreciation
9,000
Power*
1,000
Rent
2,500
Heat & Light
250
Total
12,750
*If a student treats power as a relevant cost, in that case it would not appear here. Advice regarding the jobs : ZED Ltd. should not accept the job as there will be a chase disadvantage of `42,750/- as computed below: `
`
244
Incremental revenue 5,000 units @ `25 Less: Sale of product A
1,25,000 62,500
62,500
Differential costs (a) Cash disadvantage
1,05,250 42,750
Ans 41:Working Notes: Contribution per hour in manufacturing Product B is as follows: Selling Price Less: Variable Cost Contribution per unit Contribution per machine hour =`40/5 hours =`8
(`per unit)
100 60 40 (`)
Relevant cost per unit 10+(2M.H. X `8) Suppliers price per unit Excess of relevant cost over supplier’s price.
26 25 1
Analysis-The relevant cost of production of component is higher by Re 1 over the purchase price of component part X-100.therefore buy decision is recommended.
`
Ans. 42: Selling price per unit of product ‘A’
50
Less: marginal cost per unit
35
Contribution per unit
15
Contribution per hour of product ‘A’
3
Since one unit of product ‘B’ needs 2 hours, therefore if a unit of B is produced, then the contribution lost by not producing ‘A’ = 2 hours × `3 = `6 Real cost of producing one unit of product ‘B’
` Marginal cost per unit
5
Add: Contribution lost per unit
6
Total cost of producing a unit of Product ‘B’
11
As the suppliers price per unit of product ‘B’ is `10 and that of producing in the factory is `11, therefore it is suggested that it is better to buy product ‘B’ from outside. Ans. 43: Calculation of total number of hour required in department P and Q
Particulars Demand units Department P: Hours per unit Total hour required Particulars Department Q: Hours per unit Total hours required
A 900
Component B 900
C 1350
Total
2 2 1800 1800 Component A B
1.5 2025
5625
C
Total
3 2700
1 1350
6750
3 2700
245
From the above, we can observe that department Q is facing the capacity constraint of 750 hours Statement showing the qualities of components to be purchased to maintain cost Particulars A C Purchase cost 129 70 Less: variable cost of manufacture 99 50 Saving in manufacture 30 20 Hours required per unit in dept. Q 3 1 Saving in manufacture per hour 10 20 Suggestion: since the saving in manufacture per hour is more in case of component C, component A should be purchased from outside. No. of components of A to be purchased from outside =750 hrs/3 hrs =250 units
Ans. 44: (a) Selling price per unit 600 Less: Variable cost of ` Component A 32 Component B 54 Component C 58 Component D 12 Component E 4 Assembly 40 200 Contribution per unit 400 Total contribution for 132 units ` 52800 Less: Fixed cost 132×316 41712 Net profit 11088 (b) The company may buy any one of the components. The number of units that can be produced under the three options: Buy component “A” Buy component “B” Buy component “C” Component Machine Component Machine Component Machine Hrs reqd Hrs reqd Hrs reqd A A 10 A 10 B 14 B B 14 C 12 C 12 C Total machine Hrs/unit 26 22 24 Total machine hours available is 4752 under all options Number of units that can be Number of units that can be Number of units that can be manufactured, if “A” is bought manufactured, if “B” is bought manufactured, if “C” is bought = 4752/22 = 216 units = 4752/24 = 198 units = 4752/26 = 182.77 units Additional capacity that can be Additional capacity that can be Additional capacity that can be created created created (182.77 − 132) ×100 (216 − 132) × 100 (198 − 132) ×100 = 38.5% = 63.6% = 50% 132 132 132 (c) If the increase in demand during the next period is 50% it is not possible to meet it by buying Component “A” as additional capacity created is only 38.5%. Of the remaining two options, the cheaper one has to be accepted. Buy “B” Buy”C” ` `
246
Market price Less: Variable cost if made by the company Additional cost to be incurred Machine hours saved Cost per hour
160 54
125 58
106 14 7.57
67 12 5.58
Since it is cheaper to increase capacity by buying “C” this option has to be exercised. (d) Profitability statement Selling price per unit of equipment Less: Variable cost of: Making A Making B Buying C Making D Making E Assembly
`600 `32 `54 `125 `12 `4 `40 267
267 Contribution per unit 333 Total contribution for 198 units (Note 1) 65934 Less: Fixed cost (as worked out above) 41712 Net profit 27222 Net increase over period for current period 13134 Note: 1. Maximum capacity = 4752 machine hours. Machine hours reqd for one unit of equipment : 36 hours. No. of equipment that can be produced = 4752/36 = 132 Nos. Marketing department of the company anticipates 50% increase in demand during the next period. i.e. 132 + 50% = 198 Nos. Ans. 45: Working Notes: 1. Present demand of components (in batches) from 10,800 (maximum) available machine hours and projected estimates of components demand (in batches) in the next year. Maximum available machine hours
10,800
Machine hours needed to manufacture components. A, B and C (Per batch of ten numbers) of water purifier Components
Total
A
20
Machine hours
B
28
Machine hours
C
24
Machine
72 hours
Present demand (in batches) of components A, B and C (10,800 hours/ 72 hours) 150 Projected estimate of demand of components A, B and C (add 50% increase) in 225 the next year 2. Present and future fixed costs: Present fixed cost of 150 batches @ `200/- per batch
30,000
247
Add: Increase in fixed cost to meet 50% increase in demand
10,000
Total future fixed cost for 225 batches
40,000
3. Expected purchase cost of components View point
Probability
Pessimistic
0.25
Most likely
0.50
Optimistic
0.25
A Expected price
Component B Expected Price
C Expected Price
30 (`120×0.25) 55 (`110×0.50) 20 (`80×0.25) 105
50 (`200×0.25) 65 (`130×0.50) 35 (`140×0.25) 150
40 (`160×0.25) 70 (`140×0.50) 30 (`120×0.25) 140
`
Total
`
`
4. Present contribution (per batch)
` Selling price (per batch)
` 800
Less: Variable production cost
320
Less: Variable assembly cost
50
370
Contribution (per batch)
430
Total Present contribution on 150 batches
64,500
(i) Maximum number of batches that could be produced in 10,800 machine hours each of the three alternatives namely buying A or B or C is considered respectively. (a) Buy component
A (from outside)
No machine hour required
Make component
B
28
Machine hours required
Make component
C
24
Machine hours required
Total
52
Number of batches that could be produced internally 207.69 batches (10,800 hours/52 hours) (b) Buy component
B (from outside)
No machine hour required
Make component
A
20
Machine hours required
Make component
C
24
Machine hours required
Total
44
Number of batches that could be produced internally 245.45 batches (10,800 hours/744 hours) But in view of projected (expected) market demand of 225 batches, production would be restricted to 225 batches only. (c) Buy component
C (from outside)
No machine hours required
Make component
A
20
Machine hours required
Make component
B
28
Machine hours required
248
Total
48
Number of batches that could be produced internally 225 batches (10,800 machine hours 748 hours) (ii) Statement of financial implication when purchases of component A, B and C are made from outside(in view of the fact that production capacity will be limited to 50% increase) Component bought
A
B
C
`
`
`
Total variable cost per batch (I)
64
108
116
Expected purchase cost (II)
105
150
140
Increase I variable cost per batch (III) = (II – I)
41
42
24
Present contribution per batch (IV)
430
430
430
389
388
406
(Refer to working note 3)
(Refer to working note 4) Revised contribution per batch (V) = (IV – III) Total revised contribution
80,791
87,300
91,330
(207.69 batches × `389)
(225 batches × `388)
(225 batches × `406)
Advise: Purchase component C from outside as it gives maximum contribution on manufacturing A and B internally. (iii) Profit Statement (When C is bought from outside and A, B were manufactured internally and extra production is made and sold) Per Batch `
Total (for batches)
225
` Sales revenue: (I)
800.00
1,80,000 (225 batches × `800)
394.00
88.650
Less: Variable costs (`(Per batch) : (II) Production cost of A
`64
Production cost of B
`108
Production cost of D
`24
Production cost of E
`8
Production cost of C
`140
(Refer to working note 3) `344 Assembly cost
`50
(225 batches × `394) Contribution : (III) – (-II)
406.00
91,350
Less: Fixed costs
177.78
40,000
(`40,000 / 225 batches)
249
(Refer to working note 2) Profit
228.22
51.350
Ans: 46:The components are made in a machine shop using three identical machines each of which can make any of the three components. Total machine hours required for 3 components = 4+5+6 = 15 hours Total capacity of 3 machines is 12,000 machine hours per month and is just sufficient to meet the current demand. Hence, the current demand is 12,000/15 = 800 units of product z per month. Profit made by the company for current month. Sale price 300 Less: Variable cost 48+60+80+30= 218 Contribution per unit 82 Total contribution 800 x 82= 65,600 50,000 Less: fixed cost per month Profit for current month RS. 15,600 (a)
From next month onwards, the company expects the demand for z to rise by 25% i.e., 800+25% = 1,000 units per month. One component should be bought from the market. Which component ? Statement of extra cost of component per unit Component A B C Market price 64 75 110 Less: Variable cost 48 60 80 Extra cost of buying one unit 16 15 30 Machine hours required per unit 4 5 6 Extra cost per machine hour 16/4= `4 15/5=`3 30/6=`5 Ranking II I III Because of Ist rank (lowest extra cost), component b should be bought from the market. Manufacturing Hours C 1,000 units x 6 hours = 6,000 A 1,000 units x 4 hours = 4,000 B 400 units x 5 hours = 2,000 (Balance) Total 12,000 Balance 600 units of B should he bought from the market. ( c) Profit made by the company Component Element of cost Cost per unit No. of units A Variable cost 48 1,000 B Variable cost 60 400 B Market price 75 600 C Variable cost 80 1,000 Assembling Variable cost 30 1,000 Total variable cost Add: Fixed cost Total cost Sales 1,000 units at `300 per unit
Amount(`) 48,000 24,000 45,000 80,000 30,000 2,27,000 50,000 2,77,000 3,00,000
250
Profit on 1,000 units
23,000
Ans. 47:i) Statement showing Profit / Loss of company (If it accepts the order of manufacturing moulded toys) Total available machine hours: (A)
18,000
(8 machine × 7.5 hours / day × 300 days) Machine hours required for producing 4,20,000 cans: (B)
14,000
(4,20,000 cans /30 cans) Balance machine hours: {(A) – (B)]
4,000
Total number of production of moulded toys in balance hours
60,000
(4,000 hours × 15 toys / hour) Total contribution on 60,000 moulded toys (`)
6,00,000
(60,000 × `10) Less: Fixed expenses of mould (`) Net profit
2,25,000 (`) 3,75,000
Decision: It is advisable for the company to accept the order of 60,000 moulded toys as it will increase its profit by `3,75,000. (ii)
Statement showing Profit / Loss (If the order of manufacture of cans increase to 5,40,000) If 5,40,000 cans are produced, no machine hours would be available for manufacturing toys
`(Lacs) Total contribution on 5,40,000 cans
32.40
5,40,000 cans × `6) Less: Fixed cost
20.00
Profit
12.40
Alternatively, the production would be 4,20,000 cans and 60,000 moulded toys
`(lacs) A. Profit from 4,20,000 cans: Contribution
25.20
(4,20,000 cans × `6) Less: Fixed cost Profit B. Profit from 60,000 moulded toys
20.00 5.20 3.75
(Refer to (i) above) Total profit: (A + B)
8.95
251
Decisions: The production of 1,20,000 additional cans instead of 60,000 moulded toys will result an additional profit of `3.45 lacs (`12.40 lacs – `8.95 lacs). Therefore, the company is advised not to accept the order of manufacturing moulded toys. (iii) Let the minimum excess capacity needed to justify the manufacturing of any portion of the moulded toys order be x. If toys are manufactured, the profit is
= (`60 – `50) x – `2,25,000
and, if toys are sub-contracted, the profit is = (`60 – `57.50) x Indifference point would be 10x – `2,25,000 = 2.5x or x Toys produced per hour
= 30,000 moulded toys =15 toys
Therefore, 2,000 (30,000 toys / 15 toys) excess machine hours are required to justify manufacturing of toys by the company, instead of sub-contracting. (iv) Profit under existing production plan: (`Lacs) Contribution from 4,50,000 cans
27.00
(4,50,000 × `6) Contribution from 45,000 toys
4.50
(45,000 × `10) Total contribution
31.50
Less: Fixed cost
22.25
(20 lacs + 2.25 lacs) Profit
9.25
Profit from 15,000 sub-contracted toys
0.375
(15,000 × `2.50) Total profit
9.625
If demand was accurately forecasted & 4,80,000 cans were manufactured, excess machine hour capacity available was 2,000 hrs, such excess being the pint of indifference i.e. profit from toys order would be the same by either manufacturing 30,000 toys or sub-contracting them along with the rest of 30,000 toys. (v) Profit under properly negotiated production plan: (`Lacs) Contribution from 4,80,000 cans
28.80
(4,80,000 × `6) Less: Fixed cost
20.00
Profit
8.80
Profit from Toys
1.50
60,000 Nos. sub-contracted (60,000 × `2.5) Total profit
10.30
252
Therefore, the loss for improper prediction and negotiation is `10,30,000 – `9,62,500 or `67,500. Ans. 48: Working Notes: 1. (i) Fixed manufacturing overhead per unit “XY 100”; `3,00,000 / 5,000 units or `60 “XY 200”; `3,00,000 / 12,000 units or `25 (ii) Variable manufacturing overhead per unit “XY 100”; (`180 – `60) or `120 “XY 200”; (`60 – `25) or `35 2. Variable costs of production of “XY 100” and “XY 200” Product
Per unit ‘XY 100’
‘XY 200’
`
`
Direct material
200
200
Variable machine operating costs
150
50
Variable manufacturing overheads
120
35
Total variable costs per unit
470
285
3. (i) machine hours for the production of one unit of each of the two products. “XY 100”; `150/-`100 per hour = 1.5 hours. “XY 200”; `50/- `100 per hour = 0.50 hours. (ii) Total machine hours available 5,000 units × 1.5 hours = 7,500 hours Ranking between manufactured “XY 100” and manufactured “XY 200” Manufactured
Manufactured
“XY 100”
“XY 200”
`
`
470
285
80
60
Total variable cost per unit: (A)
350
345
Selling price per unit: (B)
900
600
Contribution per unit: [(B) – (A)]
350
255
Contribution per hour
233
510
(`3.50/1.5 hrs)
(`255/0.5 hrs)
II
I
Variable cost of production (Refer to working note 2) Variable marketing and administrative cost
[Refer to working note 3(i)] Ranking
Ranking between manufactured “XY 100” and purchased “XY 100” Manufactured
Purchase
253
“XY 100”
“XY 100”
`
`
470
--
--
650
80
40
Total variable cost per unit: (A)
550
690
Selling price per unit: (B)
900
900
Contribution per unit: [(B) – (A)]
350
310
II
I
Variable cost of production (Refer to working note 2) Purchase price Variable marketing and administrative cost
Ranking “XY 200”: 12,000 units × 0.50 hours or 6,000 hours “XY 100”: (7,500 – 6,000) hours = 1,500 hours
Quantity of each product that XYZ Limited should manufacture and / or purchase to maximise operating income Manufactured “XY 200”
12,000 units
Manufactured “XY 100”: 1,500 hours / 1.5 hours
1,000
Purchased “XY 100”
6,000
Maximum number of units Which ABC can supply. Ans. 49: (i)
Profitability as per original Budget Rs (‘000s)
Sales(1,80,000 units × Rs 130)
(A)
23,400
Direct Material (1,80,000 units × Rs 30)
5,400
Component ‘EH’ ( variable cost = Rs 7.20 per unit)
1,296
Direct wages (1,80,000 units × Rs 28)
5,040
Variable factory overheads (1,80,000 units × Rs 24 × 50% )
2,160
Variable selling & distribution (1,80,000 units × Rs 24 × 50% )
2,160
Total variable cost
(B)
Contribution
(A – B)
Fixed factory overheads
Rs(‘000s)
16,056 7,344 2,160
Fixed selling & distribution overheads
720
Component ‘EH’ @2.20
396
Administrative overhead
900
Profit
4,176 3,168
(ii) Export order Rs per Unit
Rs per Unit
254
Direct material
56
Direct labour (10 hours × Rs 7 per hour)
70
Variable factory overhead ( Rs 3 × 10 labour hours)
30
Selling and distribution overheads
14
Total variable cost
170
Selling price (export)
175
Contribution
5
Since the product earns contribution of `5 per unit, it should be accepted. Total units 500(per month)
=
6000 units(per annum)
Therefore additional contribution (6000 units × Rs 5) = `30,000 Total hours on product ‘43 grade’ (1,80,000 units × 4) = 7,20,000 Hrs Total hours on component ‘EH’ (1,80,000 units × 0.5*) = 90,000 Hrs *
Direct Labour cost Rs 52,500 = = No of units produced × Labour rate per hour 15,000 units × Rs 7 per hour
0.5 Hrs Total hours utilised at 90% capacity = 7,20,000 hours + 90,000 hours = 8,10,000 hours 100% capacity hours =
8,10,000 hours × 100 = 9,00,000 Hrs 90
Balance hours available = 90,000 hours p.a Hours required for export order 60,000 hours. Both contribution per unit of export order and availability of capacity confirm its acceptance. (iii) Component ‘EH’ make or buy (per 15,000 units) Make (`) Buy (`) Direct material 30,000 Direct labour 52,500 Variable factory overhead 25,500 Total 1,08,000 1,18,500 Per unit 7.20 7.90 If the company makes the component the out of pocket cost is `7.20 per unit whereas if the component is bought , the out of pocket cost is `7.90. Decision : If the capacity remains idle it is profitable to make. (iv) Alternative use of the spare capacity Units required = 1,80,000 units and hours required = 1,80,000 × 0 .5 = 90,000 Hrs Cost of buying component ‘EH’ = (1,80,000 units × Rs 7.90) =Rs 14,22,000 Cost of making component ‘EH’ = (1,80,000 units × Rs 7.20) = Rs 12,96,000 Hence , excess cost of buying = `1,26,000 Rent income (90,000 hours × Re1) = `90,000 Contribution per unit from making component ‘GYP’ = Rs 8 Rs 0.5 per unit. Direct labour cost per unit of ‘GYP’ =
Rs 1,12,500 = 15,000 Units
Rs 31,500 = `2.10 per unit. 15,000 Units
255
Rs 2.10 = 0.3 Hrs Rs 7 90,000 hours No. of units of ‘GYP’ in 90,000 hours = =3,00,000 0.3 hours Contribution from component ‘GYP’ = 3,00,000 × Rs 0.50 = Rs 1,50,000 No. of labour hours required for one unit of ‘GYP’ =
Since the contribution from ‘GYP’ is greater than the extra variable cost of buying component ‘EH’ , component ‘GYP’ should be manufactured and component ‘EH’ should be purchased.
Hence, accept export order and buy the component. Ans. 50: (i) If the reliable suppliers offered to supply P44E at a guaranteed price of `50 p.u. variable manufacturing cost p.u. Direct material 14 Direct labour 12 Variable overheads 8 Total variable manufacturing cost 34 (`) Purchase price Less: variable manufacturing cost Saving, if manufactured internally
50 34 16
(ii) If the company incur additional inspection and testing charges of `56,000 p.a. = `56,000/`16 p.u. = 3500 units The company can purchase, if yhe requirement of P44E, is less then 3500 units. If the requirement is more then 3500 component, it can manufacture its own requirement. (iii) when the direct labour hours is limiting factor : Calculation of contribution per labour hour Particulars Selling price Cost of purchase of P44E (saving)
Less: variable cost
Own P44E 50 50
manufacture
of Extra sale of another existing product 90 90
34
50
Contribution
(i)
16
40
Labour hours
(ii)
4
8
(i)/(ii)
4
5
II
I
Contribution per labour hour Rank
Analysis: since the labour hours are the limiting factor, it is suggested to opt for extra sale of another existing product then to manufacture component P44E. (iv) The cost of the machine bought last year is a sunk cost and not relevant to the present decision of ‘make or buy’. Book value of the machine is merely an accounting treatment.
Ans. 51: (a)This is a make or buy decision so compare the incremental cost to make with the incremental cost
buy
256
Incremental cost per unit Direct material (`75000 ÷ 10,000) Direct labour (`65000 ÷ 10,000) Variable Overhead (`55000 ÷ 10,000) Supervision (`35,000 ÷ 10,000)
Make the Blades `7.50 `6.50 `5.50 `3.50
Total cost `23.00 Compare the cost to make the blades for 10,000 motors. `23.00, with the cost to buy, `25.00 There is a net loss of `2.00 if ‘X’ chooses to buy the blades. (b)
‘X’ will be indifferent between buying and making the blades when the total costs for making and buying will be equal at the volume level where the variable costs per unit times the volume plus the fixed avoidable costs are equal to the supplier’s offered cost of `25.00 per unit times the volume. (Direct materials + Direct labour + Variable overhead) × Volume + Supervision =, Cost to buy × Volume. Let volume in units = x (7.50 + 6.50 + 5.50) × x + 35,000 = 25.00x 19.50 x + 35,000
= 25.00 x
35,000
= 25.00 × x – 19.50 × x
35,000
= 5.50 × x x = 6,364 units
of blades As volume of production decreases, the average per unit cost of in house production increases. If the volume falls below 6,364 motors, then ‘X’ would prefer to buy the blades from the supplier. (c) If the space presently occupied by blade production could be leased to another firm for `45,000 per year, ‘X’ would face an opportunity cost associated with in house blade production for the 10,000 units of `4.50 per unit. New cost to make = 23.00 + 4.50 = 27.50 Now ‘X’ should buy because the cost to make, 27.50, is higher than the cost to buy, 25.00.
Ans. 52: (i) Deciding whether B Ltd. Should accept the offer from an outside vendor instead of manufacturing chains internally. Price of chain offered by vendor `12 Less: Variable cost of (`5 + `2) 7 Excess of quoted price over variable cost 5 Total excess of quoted price over variable cost (24,000 x `5) `1,20,000 Less: Avoidable cost Inspection, set-up, etc. `24,000 Machine rent 24,000 48,000 Excess of bought –out price over variable cost and avoidable cost 72,000 Decision- B Ltd. Should not accept the offer from outside vendor, because this decision will lead to reduction in profit by `72,000. (ii) Deciding whether the use of internal facilities for upgrading the quality of chains would be useful in comparison to purchase from outside. Incremental revenue per unit
`22
257
Less: Differential cost per cycle Contribution Total Contribution (24,000 x `4) Less: Tooling costs Net contribution
18 4 `96,000 16,000 80,000
Decision – B Ltd. Should accept the offer of alternative use of facilities for upgrading the bicycle. It will lead to increase of `80,000 in contribution. This is more than the excess of bought-out price over variable and avoidable cost [i.e.`72,000 as per (i)]. Thus company will benefit by `8,000 i.e.,(`80,000 – `72,0000) (iii) Deciding whether use of internal facilities for upgrading the bicycle ( chain) internally would be profitable, if batch size becomes 4,000 units in comparison to their purchases from an outside vendor. Bought- out price offered `12 Less: Variable internal cost 7 Excess of bought – out cost over variable cost 5 Total excess of bought – out cost over variable cost (24,000 x `5) `1,20,000 Less: Inspection cost `12,000 Machine rent 24,000 36,000 Excess of bought – out price over variable and avoidable costs 84,000 Decision – If inspection cost (Which varies with batch size) decreases, then excess of bought- out price over variable and avoidable costs would be `84,000. In comparison to this, net contribution from using the internal facilities for upgrading quality of chains will `80,000[refer to (ii).] There fore, if batch size increases and inspection cost reduces, then use of internal facilities of updation of quality of chain is advocated. If decision to update is taken in (ii), it will increase profit by `4,000 (i.e..`84,000 – `80,000) Ans. 53: For taking a make or buy decision, it is necessary to find out the relevant cost of both the decisions, i.e. manufacturing vis-à-vis purchasing the component from outside. Departmental Expenses Budget (`000) Items Total Allocation ratio Gadgets Components Production 24,000 24,000 Variable Costs Direct material 3,840 80 : 20 3,072 768 Direct labour 1,536 75 : 25 1,152 384 Indirect labour 720 80 : 20 576 144 Inspection and testing 480 75 : 25 360 120 Power 480 75 : 25 360 120 7,056 5,520 1,536 Fixed Costs Lighting 40 Insurance 30 Depreciation 96 Misc. Fixed Exp. 54 220 Total cost 7,276 Variable cost per unit `230 `64
258
(i) Variable cost of component is `64 per unit. The purchase price is `70 per unit. For each unit net cash outflow will be `6. Therefore, company should take decision to make. (ii) Evaluation of decision to export Inflow (a) Additional contribution due to export 12,000 units x (`245 – 230) `1,80,000 15,36,000 (b) Saving in variable cost of components (24,000 units x `64) 17,16,000 Less: Outflow Payment to be made to supplier (24,000 units x `70) 16,80,000 36,000 Net Cash Inflow Ans. 54 (a) Demand
52,000 A
48,500 B
26,500 C
30,000 D
Direct Material
64
72
45
56
M/c
48
32
64
24
Other Variable Cost
32
36
44
20
Total Variable Cost
144
140
153
100
Selling Price
162
156
173
118
Contribution (`/u)
18
16
20
18
M/s Hours per unit
6
4
8
3
Contribution (`/ M/c hr.)
3
4
2.5
6
Ranking Cost `/u)
III 146
II 126
IV 155
Cont (`/u) on (Subcontract)
16
30
18
I Sub-Contract 108 8
I Division: It is more profitable to sub-contract B, since contribution is higher sub- contract. 1st Level of Operations: 1,50,000 hours, Produce D as much as possible. Hours required = 30,000 units × 3 = 90,000 hours Balance hours available: 60,000 hours. Produce the next best (i.e. A, Since B is better outsourced) 60,000 hrs = 10,000 units of A. 6 hrs / u 1st Level of Operation: Contribution (units)
Contribution (`)
A
Produce 10,000 units
18
1,80,000
A
Outsource 42,000 units
16
6,72,000
B
48,500 units 30
14,55,000
Outsource fully
259
C
26,500 units Outsource fully
D
18
30,000 units Fully produce
18
5,40,000
Total Contribution:
33,24,000
Less: Fixed cost
10,00,000
Net Gain
23,24,000
2nd Level of Operation: Both A and C increase contribution by own manufacture only by `2/ - per unit. 1,50,000 hrs can produce 25,000 units of A. ∴Contribution increases by 25,000 × 2 = 50,000 (Difference in Contribution sub -contract and own manufacturing) = 2 But increase in fixed Cost = 50,000 At the 2nd level of operation, the increase in contribution by own manufacturing is exactly set up by increase in fixed costs by `50,000/-. It is a point of financial indifference, but other conditions like reliability or possibility of the sub -contractor increasing his price may be considered and decision may them but towards own manufacture. 3rd Level Additional: 1,50,000 hrs available Unit of A that are needed = [52,000 – 25,000 (2 nd Level) – 10,000 (1 st Level)] =
17,000 units × 6 hrs/u = 1,02,000 hrs.
Balance 48,000 hrs are available for C to produce 6,000 units. Increase in Contribution over Level 1 st or 2nd : A:
17,000 × 2
= `34,000
C:
6,000 × 2
= `12,000 = `46,000
Increase in fixed costs
= `50,000
Additional Loss
= `4,000
4th Level Additional 150000 hrs. can give 150000 ÷ 8 = 18,750 unit of C Increase in Contribution 18,750 × 2
= ` 37,500
Increase in Cost
= (`50,000) Level 3rd loss
c/fd
= (` 4,000) Level 1st profit
will order by
=(` 16,500) Advice: Do not
expand capacities; sell maximum No. of units by operating at 1,50,000 hrs. capacity (level 1 st ) and gain `23,24,000. Summary: Product
Produce (Units)
Sub-Contract (Units)
Contribution Contribution (Production) (Sub-Contract)
Total Contribution
A
10,000
42,000
1,80,000
6,72,000
8,52,000
B
-
48,500
-
14,55,000
14,55,000
260
C
-
26,500
-
4,77,000
4,77,000
D
30,000
-
5,40,000
-
5,40,000 33,24,000
Fixed Cost
10,00,000
Profit
23,24,000
Ans. 55 Calculation of contribution per unit Particulars (a) selling cost P.U. Variable cost P.U. Dept. 1 Direct materials Direct labour
EXE 375 58 5 50
WYE 540 100 hours 7.5 75
hours
Variable overheads (5 hrs*`2.40) (7.5 hrs*`2.40)
12 18 (i) 120 193 Dept.2 Direct materials 21 26 Direct labour 90 120 27 (7.5 hrs*`3.60) 36 (10 hrs* `3.60) (ii) 138 182 Total variable cost (i)+(ii) 258 375 Contribution P.U. (a)-(b) 117 165 Calculation of contribution per unit if facilities of Dept.1 were sub-contracted but facilities of Dept.2 used internally (`) Particulars EXE WYE Selling price per unit (a) 375 540 Cost of sub-contracting Dept.1 facilities 138 212 Cost of manufacture in Dept.2 internally 138 182 Total variable manufacturing cost per unit 276 394 Contribution per unit (a)-(b) 99 146
Calculation of contribution per unit if facilities of Dept.1 and Dept.2 are sub-contracted Particulars EXE WYE Selling price per unit (a) 375 540 Cost of sub-contracting P.U. Dept.1 138 212 Dept.2 150 192 Total variable cost P.U. (b) 288 404 Contribution P.U. (a)-(b) 87 136 Statement showing number of units to be produced and sold to earn maximum profit by using own manufacturing capacity Particulars EXE WYE Dept.1 (1,75,000 hrs/5 hrs) 35,000 (1,75,000 hrs/7.5 hrs) 23,333 Dept.2 (2,80,000 hrs/7.5 hrs) 37,333 (2,80,000 hrs/10 hrs) 28,000 Maximum unit can be produced and sold by using facilities of 35,000 23,333
261
both departments. Maximum contribution 40,95,000 (35,000 units* `117) 38,49,945 (23,333 units*`165) Les: fixed cost 15,00,000 15,00,000 (Dept.1 `5,00,000 + Dept.2 `10,00,000) Maximum profit 25,95,000 23,49,945 Suggestion: by production and sale of 35,000 units of EXE is maximum, it is suggestion to manufacture EXE internally. Calculation of profit from EXE (`) 40,95,000 Contribution on internally produced units (35,000 units * `117) 2,30,967 Contribution when Dept.1 services were sub-contracted (2,333 units * `99) 1,01,529 Contribution when Dept.1 & Dept.2 services were sub-contracted (1,167 units * `87) Total contribution of EXE 44,27,496 Less: fixed cost 15,00,000 Profit 29,27,496 Calculation of total contribution of WYE (`) 38,49,945 Contribution on internally produced units (23,333 units * `165) 6,81,382 Contribution when Dept.1 services were sub-contracted (4,667 units * `146) Contribution when Dept.1 and Dept.2 services were sub-contracted (3500 units * `136) 4,76,000 Total contribution of WYE 50,07,327 Less: fixed cost 15,00,000 Profit 35,07,327 Suggestion: profit is maximum for product WYE. Hence 31,500 units of WYE should be produced to yield a sum of `35,07,327 as profit. Ans. 56: Working notes: 1. (a) Total normal and overtime hours available. Department A
B
Normal capacity hours
600
520
Overtime hours
300
260
900
780
(50% of normal hours in each department) Total available hours
(b) Total hours required to meet fully the market demand of 2,500 units of P and 2,000 units of Q. Department Hours required for manufacturing P 2,500 units of Product
Hours required for manufacturing Q 2,000
A
B
250
500
(2,500 Units × 0.1 hour)
(2,500 Units × 0.2 hour)
600
400
262
units of Product (2,000 Units × 0.3 hour)
(2,000 Units × 0.2 hour)
850
900
Total hours required 2. Sub-contracting should be resorted:
To meet the market demand of 2,500 units of product P and 2,000 units of product 850 and 900 hours [Refer to working note 1(b)] are required in departments A and B respectively. In department B only 780 hours are available and thus does not meet fully the requirement of 900 hours. Hence, sub-contracting should be resorted to meet the market demand fully. 3. (i) Contribution per unit; Product
P
Q
Normal hours
Overtime hours
Normal hours
Overtime hours
Director material cost (`)
10.00
10.00
5.00
5.00
Direct labour cost Dept. A (`)
1.00
1.50
3.00
4.50
(`10 × 0.1 hr.)
(`15 × 0.1 hrs.)
(`10 × 0.3 hrs.)
(`15 × 0.3 hrs.)
2.40
3.60
2.40
3.60
(`12 × 0.2 hrs.)
(`18 × 0.2 hrs.)
(`12 × 0.2 hrs.)
(`18 × 0.2 hrs.)
Total variable cost per unit (`) : (A)
13.40
15.10
10.40
13.10
Sub-contract price per unit (`) : (B)
18.00
18.00
12.00
12.00
Contribution / cost saving / (Loss per unit (`)
4.60
2.90
1.60
(1.10)
Dept. B: (`)
(C) = [(B) – (A)] (ii) Contribution per hour Hours required per unit Dept. A
0.1
0.1
0.3
0.3
Dept. B
0.2
0.2
0.2
0.2
46
29
5.33
Loss
(`4.60/0.1 hrs.)
(`2.90/0.1 hr.)
(`1.60/0.3 hrs.)
--
23
14.50
8.0
Loss
(`4.60/0.2 hrs.)
(`2.90/0.2 hr.)
(`1.60/02. Hrs.)
--
Contribution hour Dept. A (`) Dept. B (`)
per
4. Utilization of normal and overtime available hours to meet fully monthly market demand of 2,500 units of P and 2,000 of Q. (i) An analysis of contribution statement (Refer to working note 3) clearly shows that 2,500 units of the product P should be manufactured by utilising the normal capacity hours of departments A and B. The
263
manufacturing of 2,500 units of P will consume 250 normal hours of department A and 500 hours of department B (Refer to working note 1(b). (ii) For manufacturing 2,000 units of product Q, it is beneficial to utilise the remaining normal available hours of departments A and B. The normal available hours in the department B are only 20 hours, [520 hours – 500 hours] and in department A 350 hours [600 hours – 250 hours]. 100 units of product Q can be manufactured by utilising the normal available hours of departments A and B. The manufacturing of 100 units of Q in normal available hours will utilise 30 hours in department A and 20 hours in department B. (iii) Now for manufacturing the remaining 1,900 units of product Q, we have 320 normal hours plus 300 overtime hours in department A and 260 overtime hours in the department B. The manufacturing cost per unit of product Q comes to `11.60 when normal hours of department A and overtime hours of department B are utilized. {`5 (Material Cost) + `3 (Direct Labour in Department A) + `3.60 (Direct Labour in Department B)} On comparing `11.60 with sub-contracting price of `12 per unit, we arrive at a contribution of 0.40 per unit. Hence maximum number of units of product Q should be manufactured by using normal hours of department A and overtime hours of department B. since 0.3 and 0.2 hours are required respectively for manufacturing one unit of product Q in the two departments, therefore, utilising 320 normal hours and 213 overtime hours in departments A and B respectively, 1066.66 units (or say 1,067 units) of product Q are manufactured. (iv) Finally, to manufacture remaining 833 units of Q, the available time is 300 overtime hours and 47 overtime hours in department A and B respectively. According to (working note 1) the available time in department B is short by 120 hours (900 required hours – 780 available hours) therefore 833 units of Q cannot be made internally. But few units can be made by utilising the available overtime hours in departments A and B. The manufacturing cost of 1 unit of Q by utilizing overtime hours in departments A and B comes to `13.10 (Refer to working note 3) which on comparison with subcontract price of `12 gives rise to a situation of loss of `1.10 per unit {`13.10 – `12}. Hence it is advisable not to manufacture the remaining 833 units internally. These 833 units should be sub-contracted at a price of `12/- per unit. (i) Statement of quantity of each product to be manufactured / or to be sub-contracted for fulfilling the market demand in most economical way. Departments A
Available hours working note 1(i)
(Refer
Production 2,500 units of P (Refer to working note 4 (i)) 100 units of Q
Normal time hours
Overtime hours
Normal time hours
Overtime hours
600
300
520
260
250
--
500
--
(2,500 units × 0.1 hrs.) 30
(Refer to working note 4 (ii) 1067 units of Q
--
(100 units × 0.3 hrs.) 320
(Refer to working note 4(iii)) (ii)
to
B
(2,500 units × 0.2 hrs.) 20
(100 units × 0.2 hrs.)
--
(1,067 units × 0.3 hrs.)
--
213
(1,067 units × 0.2 hrs.)
Statement Showing Total Cost (Based on the solution in (i) above) Products
--
264
Particulars
Direct Material Cost
P
Q
Sub contract price
Total
`
`
`
`
25,000
5,835
-
30,855
--
6,000
(2,500 units × `10)
(1,167 units × `5)
Direct Wages: Dept. A
2,500
3,500
(250 hours × `10) Dept. B
(350 hours × `10)
6,000
4,074
(500 hours × `12) Fixed overhead Cost of 833 units @ `12 per unit on subcontracting Total Cost
--
10,075
(20 hours × `12 + 213 hours × `18
18,000
6,400
-
24,400
--
--
9,996
9,996
51,500
19,809
9,996
81,305
Ans. 57: (i) Option Statement of Profit (Loss) (if the firm discontinue all the operations during notice period of 3 months) (`Crores) Products
A
B
C
D
Total
Sales*
-
-
-
-
-
-
-
-
-
-
Manufacturing
1.5
1.2
1.8
1.2
5.7
Admin. & Selling
0.6
0.3
0.9
0.6
2.4
Total allocated overheads during notice period of 3 months
2.1
1.5
2.7
1.8
8.1
(2.1)
(1.5)
(2.7)
(1.8)
(8.1)
Costs: Material & Labour Allocated overheads:
Profit / (Loss)
*The option (i) would not yield any revenue. Conclusion: The option (i) will result in a loss of `8.1 crores due to the committed costs account of 3 months notice period. (ii) Option Working note:
Ascertaining profitable products (if their production is continued during 3 months of notice period) (`Crores) Products
A
B
C
D
Sales (X)
18
13.5
21
15
265
Variable cost: Materials
12.0
7.5
13.5
9.0
Labour
4.5
3.0
7.5
7.5
Total variable costs: (Y)
16.5
10.5
21.0
16.5
Contribution: (X – Y) 1.5 3.0 (1.5) A review of contribution figures in the above statement of four products A, B, C and D clearly reveals that products A and B are only profitable. Statement of Profit (Loss) (If the firm continues the operations of profitable products A and B during 3 months of notice period) (`Crores) Products Contribution (Refer to above working note) Less: total manufacturing administrative overheads (Refer to part (i) above)
&
A
B
Total
1.5
3.0
4.5
selling
8.1
Profit / (Loss)
(3.6)
Conclusion: Under this option the total loss is (`3.6) crores which is less than the loss of option (i). (iii) Option Working Note: Ascertaining profitable products (when notices are issued to the staff and the landlord – only in the manufacturing unit, resort to subcontracting only on profitable products) (`Crores) Products
A
B
C
D
Sales: (X)
72.0
54.0
84.0
60.0
Materials
48.0
30.0
54.0
36.0
Sub-contracting charges
16.0
10.5
27.0
26.0
(20 lacs × `80)
(15 lacs × `70)
(30 lacs × `90)
(20 lacs × `130)
64.0
40.5
81.0
62.0
Variable Cost:
Total variable costs : (Y)
Contribution: (X – Y) 8.0 13.5 3.0 (2.0) A review of contribution figures in the above statement clearly shows that products A, Band C are only profitable. Statement of Profit / (Loss) (If the firm resorts to manufacturing of profitable products by sub-contracting) (`Crores) Product Contribution: (X)
Total
A
B
C
8.0
13.5
3.0
24.5
(Refer to above working note) Total manufacturing overheads of 3 months notice period : (Y) (Refer to option (i) above)
5.7
266
Total administrative & Selling overheads: (Z)
9.6
Profit/(Loss): {X – (Y+Z)}
9.2
Decision: Out of the three options the option (iii) is the most viable one. Not only it will help the company with a turn around, but from the year 2002, the company can look forward to even higher profitability, since the manufacturing overhead would no longer be incurred thereafter.
Ans. 58: Working Notes: 1. FOB price of dismantled kit: FOB price of dismantled kit (in$) FOB price of dismantled kit (in `)
510 24,000
($510 × `47.059) 2. Cost of a dismantled kit to Z Inc. If `120 is the S. P. of kit to Z Inc. then its C `100 Re 1 If `24,000 is the S. P. then C. P. is
= =
Rs.100 Rs.120
Rs.100 Rs.120
× `24,000 = `20,000
3. Cost of local procurements: 140% of the supplies made by Z Inc. or 140% × `10,000* = `14,000 *Being 50% of cost of a dismantled kit to Z Inc. 4. Landed cost of a dismantled kit: ` FOB price
12,000
(50% × `24,000) (Refer to working note 1) Add: Insurance & freight CIF price Add: Customs duty
500 12,500 3,750
(30% × `12,500) Landed cost of a dismantled kit 5. Cost of the standard items procured locally: 48% of the cost of locally procured goods =
48% × `14,000
=
`6,720
6. Royalty payment per computer: Let x = Selling price per unit of personal computer y
= Royalty paid per computer
Since 20% is the margin of profit on S.P. it main a margin of 25% on C.P. Therefore we have
16,250
267
X = 1.25 (`32,250+ `150 + y) Y = 10% {x – (`6,720 + `16,250)} On solving the above equations we get: X = `43,000 Y = `2003.43 or `2,000 (Approx) Statement showing the selling price of a personal computer in India A.
`
Landed cost of a dismantled kit (Refer to working note 4)
B.
16,250
Cost of local procurement (Refer to working note 3)
14,000
C.
Cost of assembly and other overheads per computer
D.
Total cost of manufacture: (A+ B + C)
E.
Technology fee per computer
2,000 32,250 150
(`3,00,00,000 / 2,00,000 computer) F.
Royalty payment per unit (Refer to working note 6)
G.
Total cost (D + E+ F)
34,400
H.
Profit (20% on selling price of 25% of total cost)
I.
Selling price (per computer)
8,600 43,000
Statement of Differential cost
Ans. 59: Capacity Output (units)
FOB cost
Total cost(`)
per unit (`)
Differential cost(`)
Differential cost per unit (`)
70%
70,000
97
67,90,000
−
−
80%
80,000
92
73,60,000
5,70,000
57
90%
90,000
87
78,30,000
4,70,000
47
100%
1,00,000
82
82,00,000
3,70,000
37
Statement showing gain or loss for various export order
If proposal A is accepted the company will suffer a loss of `10,000 with an idle capacity of 5,000 units. If proposals A and B are accepted, the company will suffer a loss of `10,000 with an idle capacity of `5,000 units. If the company accepts all the three proposals, it will earn profit of `80,000 with an idle capacity of 5,000 units.
268
Therefore, the company should accept all three proposals. Ans. 60: Shut down point = Avoidable Fixed cost - Shut down cost P/V Ratio = [120000-40000] - 0 = `400000 1-0.8 Ans. 61: Continue
Shut Down
30,000
-
Fixed expenses at 50% activity Additional shut down cost
2,000
Fixed expenses during shut down
10,000
30,000 Additional fixed cost incurred due to continued operations = 18,000
12,000
If contribution from operation is less than 18,000, a shut down is recommended. i.e. Contribution per unit
<
18,000 5,000
i.e. Contribution
<
Rs 3.60 per unit
i.e Selling price – variable cost
<
Rs 3.60 per unit
or S.P. – 3.6
< Variable cost i.e. 14.00 –
3.60
< Variable Cost or variable
cost is more than Rs 10.40 For a variable cost more than Rs 10.40 per unit, a shut down is recommended. Alternative Contribution from operation must be less than 18,000 `for a shut down. Sales value = 14x5,000 = 70,000 Sales – variable cost < 18,000 or variable cost is more than 70,000-18,000 = 52,000 Variable cost of 5,000 units above `52,000 Or Variable Cost V.C. per unit >
52,000
= `10.40 5,000
For a variable cost per unit above `10.40, shut down is recommended. Ans. 62: Sales Less:Variable Cost Contribution Less:Fixed Cost Additional Cost
If plant is continued
If plant is shutdown
7,60,000
-
5,70,000
-
1,90,00 3,50,000
1,30,00 15,000
269
Operating Loss 1,60,00 1,45,00 A comparison of loss figures indicated as above points out that loss is reduced by (16,000-14,500) `15,000 if plant is shut down. Shut down point
=
3,50,000 - 14,5000 20,500 = = 1,02,500 units 8-6 2
Capacity level of shut down point: 95,000
At 100% level production is
Capacity level at shut down =
= 1,18,750 0.80
1,02,500 = 86.31% 1,18,750
Alternative Solution ` If the plant is shut down, the sunk cost or fixed expenses
1,45,00
If it is working at 80% capacity, the fixed cost
3,50,000
Additional fixed expenses
2,05,000
Contribution (95000*2)
1,90,00 0 15,00
Incremental Loss on Continuing Decision - better to shut down Production at shut-down point 2 x – 350000
=
1,45,000
2x
=
2,05,000
x
=
1,02,500 Units
Capacity %
=
1,02,500/(95,000/0.8) =
Ans. 63:
(a) Contribution per tin = Selling Price – Variable cost = 21 – (7.8 + 2.1+ 2.5 + 0.6) = `8 per tin.
Loss on operation: Fixed cost per annum = 2,00,000 units × 4 per unit = 8 lakhs ∴ Fixed cost for 1 quarter = 8/4 = 2 lakhs
Fixed cost for the quarter Less: Contribution on operation (8 × 10,000) Expected loss on operation Loss on shut down: Unavoidable Fixed Cost Additional shut down cost Loss on shut-down
`
2,00,000 80,000 (1,20,000)
`
74,000 14,000 (88,000)
270
Conclusion: Better to shut down and save `32,000. Shut-down point (number of units) = Avoidable Fixed Cost ÷ Contribution per unit = (2,00,000 − 88,000)/8 = 14,000 units.
Ans. 64: The Directors, XYZ Co. New Delhi Date……. Dear Sir As desired, we have analysed the cost implications of the decision of temporary closure of the trade recession. We find that if the factory is run at 50% capacity and with reduced sales revenue, the loss likely to be incurred in one full year (the estimated period of recession), would be around `200000 as detailed below: `In’000 Direct materials
300
Direct labour
400
Production overhead
240
Administrative o v e r h e a d
120
Selling & distribution overhead
130 1190
Loss
200
Sales
990
If the factory is closed, the following costs will be incurred:
`In ‘000
Fixed costs
220
Settlement cost
150
Maintenance costs Cost of resuming operations
20 80 470 It is obvious from the above, that despite the fact that running at 50% capacity would imply a loss of `200000, it is better not to close down the factory since in that case the loss would be higher. In our views, even if running the factory entailed a somewhat bigger loss as compared to the loss incurred by closing it down temporarily, it may be better to keep the factory in operation. This is because a closure, even if temporary, results in the loss of regular and old customers, suppliers and skilled personal. This, coupled with a loss of goodwill in the market, may give rise to substantial losses at the time of restarting the factory. We trust that the above analysis would be helpful to you in reaching an appropriate decision in the matter. We shall be glad to be of any further assistance that may be required in this regard. Yours faithfully X and Co. Chartered Accountants.
271
Working Note: Production overhead (`Lakhs) (i) (ii) (iii) (iv) (v) (vi)
Amount at 60% Amount at 80% Variable cost for 20% Variable cost for 60% Fixed Cost Amount at 50% (iii×2.5+v)
2.52 2.76 0.24 0.72 1.80 2.40
Admn. overhead (`Lakhs) 1.24 1.32 0.08 0.24 1.00 1.20
Selling overhead (`Lakhs) 1.36 1.48 0.12 0.36 1.00 1.30
Ans. 65: (i) Details Sales Revenue Less: variable cost Contribution Less: fixed cost Profit
M/s supreme Ltd. Comparative statement of sales and profit under marginal costing 2002 `6,00,000 4,50,000 1,50,000 1,20,000 30,000
(ii)
2003 5,62,500 4,50,000 1,12,500 78,750 33,750
Minimum sales required, if the firm decides to shut down in units in 2003: Minimum sales required is the sales which should yield at least the contribution, which is sufficient to meet increase in fixed cost. Increase in fixed costs in 2003 = `78,750 – 60,000 = `18,750 Sales required to yield contribution equal to increase in fixed cost X* P/V retio = `18,750 Or x = `18750 / 0.20 = `93,750 Working notes 1. Computation of variable costs, break even point, profit and fixed cost for the year 2002: Sales revenue `6,00,000 P/V ratio 25% Margin on safety 20% So, margin of safety = sales * 0.20 = `6,00,000 * 0.20 = 1,20,000 We know that margin of safety * P/V ratio = Profit So, Profit: `1,20,000 * 0.25 = `30,000 Total contribution = sales * P/V ratio = `6, 00,000 * 0.25 = `1,50,000 Variable cost = sales – contribution So, variable cost = 6, 00,000 – 1,50,000 = 4,50,000 Fixed cost = contribution – Profit = 1,50,000 – `30, 000 = `1,20,000 Break even sales * P/V ratio = fixed cost So, BES = 1,20,000 / 0.25 = `4,80,000 2. Computation of sales revenue, variable cost, fixed cost and profit in 2003 Let sales revenue for the year 2003 be x. the variable cost for the year 2003 is `4,50,000 (no. change). So, contribution = X – `4,50,000 = 20% (given) We know that P/V retio = contribution Sales Or, 20 100 = X – 4, 50,000 X
272
= `100x – `4, 50, 00,000 = `4, 50, 00,000/80 = 5, 62,500 = 30% (given) = sales * margin of safety ratio = `5, 62,500 * 0.30 = `1, 68,750
Or, 20x Or, x Margin of safety So, margin of safety We know that sales – margin of safety = B.E. sales So, B.E. sales
= `5, 62,500 – `1, 68,750 = `3, 93,750
Ans. 66 (i) Option I
Option II
At 75% in Feb and close in March and April (`)
At 25% each from Feb – April (`)
Direct Material
5,25,000
5,25,000
Direct Labour
5,23,600
5,19,750
10,48,600
10,44,750
Factory Overhead : Indirect Material
8,400
Two months idle
9,800
Indirect Labour
1,01,500
Training cost
65,800
Indirect Exp. : Repairs & Maintenance
28,000
Over hauling cost
14,000
Others Expenses
52,500
Idle × 2 Office overhead:
1,48,400
Idle
1,35,100
Other overheads
28,000
Idle Total overhead cost
22,400
Total cost
1,78,500
84,000 1,02,900
53,200
Staff Salaries 67,550 × 2
14,700
2,94,000 59,850
6,67,100
7,33,950
17,15,700
17,78,700
The more economic course of action is to operate at 75% capacity for a month only, and close the plant for March and April. This option will save (`17,78,700 – `17,15,700) = `63,000. Ans. 68: (i) Statement of Profitability of E Ltd. in Existing Situation A B C Total No. of units 10,000 25,000 20,000 ` ` ` Selling Price per unit 40 75 85 Less: Variable Cost per unit Direct Material 10 14 18 Direct wages 8 12 10 Variable Overhead 8 9 10
273
Contribution per unit Total Contribution Less: Fixed Cost Net Profit
14 1,40,000 1,60,000 -20,000
40 10,00,000 4,50,000 5,50,000
47 9,40,000 4,00,000 5,40,000
20,80,000 10,10,000 10,70,000
Calculation of overall profit under each proposal (ii)(a) If Product A is discontinued and capacity released is utilized for either B, either C or for both B and C Revised contribution of Product B and Product C. B(`) Selling Price per unit 73.50 (75 – 2% of 75) Less: Variable cost per unit Direct Material 15.40 (14 + 10%of 14) Direct Wages 12.00 Variable Overhead 9.00 Contribution per unit
37.10
C (`) 80.75 (85 – 5% of 85) 18.90 (18 + 5%of 18) 10.00 10.00 41.85
Profitability Statement Option 1 Option 2 Option3- Both B and C equally Only B Only C B C No. of Units (as per W.N.1) 6,666 8,000 3,333 4,000 ` ` ` ` Additional contribution 2,47,308.6 3,34,800 1,23,654.3 1,67,400 2,91,054.3 Savings from Fixed Cost of A 1,60,000 1,60,000 1,60,000 Reduction in contribution from A 1,40,000 1,40,000 1,40,000 Net Increase in Profit 267308.6 3,54,800 3,11,054.3 Existing Profit 10,70,000 10,70,000 10,70,000 1337308.6 3,31,054.3 Total Profit 14,24800 Hence, it is better to produce Product C only. (ii)(b) Discontinue Product A and divert the capacity to produce Product D A B C Sales (units) 10,000 25,000 20,000 Labour Hrs. per unit 4 6 5 Total Labour Hours 40,000 1,50,000 1,00,000 Idle Capacity (hours) 2,90,000 * 20 / 80 Capacity released of A Total hours released Hours per unit No. of units that can be produced No. of units Selling Price per unit Less: Variable Cost per unit Direct Material Direct wages Variable Overhead Contribution per unit Additional Contribution (D) Less: Additional Fixed Cost Additional Net Profit Add: Existing Profit (B & C) Total Profit
Profitability Statement
Total 2,90,000 72,500 40,000 1,12,500 4 28,125 28,125 ` 60 28 12 6 14 3,93,750 1,05,500 2,88,250 10,90,000 13,78,250
274
(c) If we hire out the idle capacity Idle hrs. Profit per hour (10,70,000 / 2,90,000) Total Profit Existing Profit Total Profit Decision : Better to produce product C as per proposal (a)
` 72,500 3.69 2,67,500 10,70,000 13,37,500
Working Note-1: Hours release on discontinuation of Product A = 10,000 * 4 Only B Only C B and C equally 40,000 / 6 = 6,666 40,000 / 5 = 8,000 B- 3333 and C- 4000
Ans. 69: 1. Quantity analysis Input in process A – total capacity – given = 2, 00,000 kg Less: loss in process A = 10% of Input = 20,000 kg (NRV at `1/ kg = 20,000) Balance transfer to process B = 1,80,000 kg Less: loss in process B = 5% of Input = 9,000 kg (NRV at `2 / kg = 18,000) Balance good output available for sale = 1,71,000 kg 2. Supplier Evaluation and Decision Supplier P Q R R Condition Max. 1,20,000 kg Max. 1,60,000 kg Any Quantity Qtty = 2,00,000 kg Price 10.00 11.20 11.60 11.00 Var. Transport cost 1.20 1.00 1.00 1.00 Total 11.20 12.20 12.60 12.00 The following can be planned in any of the following ways – Total Purchase = 2, 00,000 kg Purchase entirely from R 2,00,000 kg Purchase first kg. from P(least cost) and balance 80,000 kg from Q (Next least cost) 1,20,000 * `11.20 + 80,000 * `12.20) Cost incurred = (2,00,000 * `12) = 23,20,000 = 24,00,000 Decision: hence the company should Buy 1,20,000 kg from P and 80,000 kg from Q Fixed transport cost being constant is not relevant to the above decision. 3. Customer evaluation and decision Customer k L M Condition Upto 80,000 kg only Upto 1,60,000 kg only All 1,71,000 kg Selling price 65.00 64.00 61.80 Less: discount 2% 1.30 1.28 NIL Net selling price 63.70 62.72 61.80 Less: var. transport cost 2.60 1.44 NIL Net realization 61.10 61.28 61.80 The sales can be made in any of the following way – Total sale Quantity = 1,71,000 kg Sold entirely to M 1, 71,000 kg Amt realized = (1,71,000 * `61.80) = `1,05,67,800 Less: fixed delivery cost NIL Net amount = `1,05,67,800
sell first 1,60,000 kg to L (max. revenue)and Balance 11,000 kg to K (next max. revenue) (1,60,000 * `61.28 + 11,000 * `61.10) = 1,04,76,900 = `60,000 (`5,000 * 12 months) = 1,04,16,900
275
Decision: since revenue is higher, the company should sell the entire quantity to customer M. 4. Statement of process costs Particular Process A Raw materials (`23,20,000 + fixed transport 25,20,000 2,00,000) 22,00,000 Transport from previous process 9,56,000 Direct wages Overheads Total process costs 56,76,000 Less: scrap value of normal loss ( as in WN Above) 20,000 Net process costs transferred to subsequent 56,56,000 process/FG Net profit: sales revenue – costs of production = 1,05,67,800 – 90,83,800 = `14,84,000 Ans. 70: (i)
Process B 56,56,000 21,00,000 13,45,800 91,01,800 18,000 90,83,800
Reorder level
= Safety Stock + lead time consumption = 100 units + (3600 units/12) = 400 units (ii) Anticipated reduction in the value of the average stock investment EOQ
=
2 × Annual consumption × Buying cost per order Cost of carrying one unit of inventory for one year
=
2ab cs
Where a = Annual consumption b= Buying cost per order c= Storage and other inventory carrying cost rate =
2 × 3600 units × Rs. 40 0.2 × Rs.100
The average stock to be held under new system: = minimum lavel + ½Reorder quantity = 100 + ½* 120 = 160 units The average stock investment under new system: = 160 units * `100 = `16,000 The average stock under old system: = Minimum level + ½ EOQ = 0 + ½ (1800 units) = 900 units The average investment under old system = 900 * `100 = `90,000 Therefore, anticipated average reduction in value of average stock investment = `90,000 – `16,000 = `74,000 (iii) The anticipated reduction in total inventory costs (in the first and subsequent years) Under new system: Annual ordering cost ((3,600/120) * `40) = `1,200 Stock holding cost (0.20 * `16,000) = 3,200 Total inventory cost 4,400 Under old system: Annual ordering cost (2 orders * `40) = ` 80 18,000 Stock holding cost (0.20 * `90,000) = Total inventory cost 18,080 Anticipated reduction in subsequent year: Thus anticipated reduction in total inventory cost is `13,680 (i.e., `18,080 – 4,400) in subsequent years. Anticipated reduction in the first year = `13,680 – `10,000 * = `3,680
276
* In the first year 100 units will have to be purchased. Ans. 71: Particular Current Policy A Policy B Policy C Sales 4,50,000 5,00,000 5,40,000 5,65,000 Less: variable cost at 70% 3,15,000 3,50,000 3,78,000 3,95,500 Contribution 1,35,000 1,50,000 1,62,000 1,69,500 Less: fixed cost (given) 10,000 10,000 10,000 10,000 Profit before tax 1,25,000 1,40,000 1,52,000 1,59,500 Less: tax at 40% 50,000 56,000 60,800 63,800 Profit after tax 75,000 84,000 91,200 95,700 Cost of good sold (VC + FC) 3,25,000 3,60,000 3,88,000 4,05,500 Inventory turnover ratio (given) 10 times 8 times 6 times 4 times Average inventory (COGS /T/o ratio) 32,500 45,000 64,667 1,01,375 Carrying cost of inv. At 5% (a) 1,625 2,250 3,233 5,069 Opportunity cost at 20 % of capital blocked in average inventory (b) 6,500 9,000 12,933 20,275 Total cost of inventory holding (a + b) 8,125 11,250 16,166 25,344 Net benefit = total cost of inventory 66,875 72,750 75,034 70,356 Decision: As net benefit is Maximum under policy B, it may be chosen (alternative assumptions exist) Ans. 72: Working Note: Fixed overheads
`
Present sale value: (A)
15,00,000
(15,000 units ×`100) Direct materials
4,50,000
(30% of sale value) Direct labour
3,00,000
(20% of the value) Variable overheads
3,00,000
(`20 per unit)
..
Total variable costs (B)
10,50,000
Contribution: (C) = (A) – (B)
4,50,000
Profit : (D)
2,25,000
(15,000 units × `15)
.
Fixed overheads:
(C) – (D)
2,25,000
(current level) Add: Additional fixed overheads due to price escalation 50,000 Total fixed overheads:
2,75,000 Statement of profitability for various alternatives
Alternatives
I Rejecting the
II
III
IV
Rejecting the proposal for
Accepting the proposal of
Accepting the proposal of the
277
proposal for the purchase of 10,000 units and continuing with present level of sales only
the purchase of 10,000 units from a party and attaining the maximum capacity by incurring additional selling expenditure
the party to take 10,000 units @ `90 per units by installing a balancing equipment and continuing with present level of sales
party to take 10,000 units @ `90 per cent by installing a balancing equipment and attaining sale of maximum available capacity by incurring additional selling expenditure
15,000
20,000
25,000
30,000
`
`
`
`
15,00,000 (15,000 × `100)
20,00,000 (20,000 × `100)
24,00,000 (15,000 × `100+10,000 × `90
29,00,000 (20,00,000 × `100 + 10,000 × `90)
4,95,000
6,60,000
8,25,000*
9,90,000*
Direct Labour
3,75,000
5,00,000
6,25,000*
9,90,000*
Variable overheads
3,00,000
4,00,000
5,00,000
6,00,000
11,70,000
15,60,000
19,50,000
23,40,000
2,75,000
2,75,000
2,75,000
2,75,000
Sale (units) Sales Value: (A)
Variable costs Direct material (33% of sales value)
(@`20 per unit) Total variable costs: (B) Fixed costs Fixed overheads
(Refer to working note) Additional selling expenditure
-
50,000
-
50,000
Depreciation for balancing equipment
-
-
1,00,000
1,00,000
Additional administrative expenses
-
-
50,000
50,000
Total fixed cost : (C)
2,75,000
3,25,000
4,25,000
4,75,000
Total cost D: [(B)+(C)]
14,45,000
18,85,000
23,75,000
28,15,000
Profit: (A)-(D)
55,000
1,15,000
25,000
85,000
Note: For computing the material and labour cost under alternative III & IV the notional sale price of `100 is taken for additional 10,000 units. Recommendation: Alternative II is the best as it gives maximum profit.
278
Ans. 73: Comparative profit Statement (based on Revised Cost Structure)
Total sales revenue (A)
Proposal 1
Proposal 2
Proposal 3
Sell 20,000 units only
Secure orders for 5,000 additional units (unused capacity) and sell 25,000 units
Accept the new order for 10,000 additional units and sell 30,000 units
`
`
`
20,00,000
25,00,000
29,00,000
(`20,000 `100) Director Labour
×
5,00,000
Variable overhead
2,50,000
3,00,000
(25,000 units × `10)
(30,000 `10)
4,40,000
4,40,000
-
-
60,000
-
50,000
-
(`4,00,000 `40,000)
promotion
Depreciation equipment)
(New
(30,000 `33)
(30,000 `10)
units
×
units
×
4,40,000
Add: Sales expenses
×
(`25,000 units × `10)
(20,000 `10)
Administrative
units
7,50,000
2,00,000
Fixed overheads
25,000 `100) 6,25,000
(20,000 `25)
Add: charges
units
units
+
units
+
units
+
+
1,50,000
Total cots (B)
18,00,000
21,90,000
26,90,000
Profit (C) = [(A) – (B)]
2,00,000
3,10,000
2,10,000
Analysis An analysis of the profit figures of M/s Unique products under three proposals clearly shows that it is maximum under proposal 2. Therefore, it is advisable for the concern to produce and sell 25,000 units @ `100/- per unit and utilise its full production capacity.
Ans. 74
(a) Statement of Profitability for the year 1993-94 (as originally envisaged by the company) Products Ethylene EDC VCL Annual Production Capacity (MT) 25,000 30,000 30,000 Annual Planned Productions (MT) (Refer to Note -1) 25,000 25,000 15,000 Cost of production of annual planned production ` ` `
Total
`
279
Variable costs (Refer to Note 2) Fixed cost (Refer to Note 3) Common cost (Refer to Note 4) Cost of Ethylene Cost of Ethylene (Used for EDC) Cost of EDC (25,000 MT) Cost of 10,000 MT of EDC (Refer to Note 5) Cost of 15,000 MT of EDC for (VCL) Cost of Sale (A) Sales Revenue (B) Profit (B-A)
5,00,000 5,00,000 2,50,000 12,50,000
7,50,000 9,00,000 4,50,000
6,00,000 12,00,000 6,00,000
12,50,000 33,50,000 13,40,000
20,10,000 44,10,000 57,50,000 13,40,000 45,00,000 60,00,000 15,00,000 2,50,000 90,000 1,60,000 Note: Only 25,000 metric tonne of ethylene is available and as such 25,000 metric tonne of EDC could be produced. Out of this 15,000 metric tonne of EDC is consumed for VCL production and the balance of 10,000 metric tonne of EDC is sold. Working Note: Note: 1 annual planned production Ethylene EDC VCL Proposed Sale 10,000 15,000 Production: 10,000 15,000 For EDC 10,000 For VCL 15,000 15,000 Total 25,000 25,000 15,000 2. Variable Costs
Ethylene 25,000 MT x `20 =`5,00,000
EDC 25,000 MT x `30 =`7,50,000
VCL 15,000 MT x `40 =`6,00,000
3. Fixed Cost (This will be based on 25,000 MT x 20 Production capacity) =`5,00,000
30,000 MT x 30 =`9,00,000
30,000 MT x40 =`12,00,000
4. Common Cost (This will also be based 25,000 MT x 10 On production capacity =`2,50,000
30,000 MT x 15 =`4,50,000
30,000 MT x 20 =`6,00,000
5. Cost of 25,000 metric tones of EDC = `33,50,000 Cost of one metric ton of EDC = `33,50,000 * 25,000 = `134 Cost of 10,000 metric tones of EDC = 10,000 x `134 = `13,40,000 Cost of 15,000 metric tones of EDC = 15,000 x `134 = `20,10,000 6. Sales Revenue EDC = 10,000 MT x `150 VCL = 15,000 MT x Rs,300 Total
=`15,00,000 =`45,00,000 60,00,000
(b) Revised Statement of Profitability (When the company decides to accept offer of X) Products Ethylene EDC Annual planned productions (MT) 25,000 25,000
VCL 30,000
Total
280
` 12,50,000
` 33,50,000
`
Cost of production Refer (a) Variable cost (30,000 MT x `40) 12,00,000 12,00,000 Production Fixed cost (30,000 MT x `40) 6,00,000 Common Fixed cost (30,000 MT x `20) 6,25,000 Purchases cost of 5,000 MT of EDC @ `125 per MT 39,75,000 Total of EDC used in VCL 39,75,000 Total cost (A) 69,75,000 Total Sales (Refer to note 1 below (B) 80,00,000 Profit (B-A) 10,25,000 Comment – Since the profit has increased the proposal of X should be accepted. Note 1: Total Sales : 20,000 MT of VCL to X @ `250 per MT =`50,00,000 10,000 MT of VCL X `300 (in open Market) =`30,00,000 Hours Available capacity 20,000 16,800 First product D should be produced (2,800 x 6) Balance hours 3,200 Second product A should be produced (2,000 x 1) 2,000 Balance hours 1,200 Third product B should be produced (600 x 2) 1,200 Thus, if 20,000 hours is the limiting factor, all requirements of D and A can be manufactured and only 600 units of product B can be manufactured. The balance requirement of product B. i.e.,3,500-600 =2,900 units will have to be bought – out or manufactured in the second shift. (b) Because purchase price of component c is `52 and cost of manufacturing is `57, it will not be profitable to manufacture C even in second shift. It should be purchased form outside, purchased from outside. The relative position is as follows: Cost of producing 2,900 units of product B in second shift Ans. 75: Solution (a) Working Notes (i) Components Direct expenses Direct hours per unit
Press hours required A B `10 `20 1 2
C `10 1
D `60 6
(ii) Marginal cost per unit vs. bought-out prices per unit Marginal costs: Direct Materials Direct wages Direct expenses Marginal costs Bought – out price Excess of bought out price over marginal cost Process hours per unit
`37 10 10 57 60
`27 8 20 55 59
`25 22 10 57 52
`44 40 60 144 168
3 1
4 2
(5) 1
24 6
281
Excess of bought – out price per unit of limiting factor Ranking
4 3 11
2 111
(5) -
1
The bought – out price of component C is lower than the marginal cost by `5 and for this reason it should be purchased from outside. For the remaining products. Ranking is based on utilization of limiting factor. Optimal product mix has been, calculated as follows: Calculation of optimal product mix `55
Variable Cost Increase in direct wages
2 57 `1,65,300
Total variable cost (2,900 x 57) Additional fixed cost Hours required = 2,900 x 2=5,800 hours Extra fixed cost of 5,800 hours at `500 for each 1,000 hours or part thereof 3,000 Total cost for producing 2,900 units of product B in second shift 1,68,300 Bought- out price for 2,900 units of product B will be 2,900 x `59 1,71,100 Disadvantage in buying B 2,800
For the above-mentioned reasons, it is in the interest of company to manufacture product B in the Second shift instead of buying it from outside market .The disadvantage of the decision to buy product B from outside will be `2,800 . 80,00,000 Ans. 76: Components P Q R S i. Direct wages `17.50 `35.00 `17.50 `105.00 ii. D.L.H. @ `8.75 p.h 2 4 2 12 iii. Variable Mfg. cost `99.75 `96.25 `99.75 `252.00 iv. Purchase Price 105.00 103.00 91.00 294.00 v. Saving if components are manufactured 5.25 6.75 42.00 vi. Saving per hour (5 * 2) 2.625 1.6875 3.50 Ranking 2 3 1 (i) Statement showing product-mix of the components to be manufactured (Available hrs. = 40,000) Component Qty. reqd. Hrs. / unit Production Hrs. Used Balance hrs. S 2,400 12 2,400 28,800 11,200 P 2,400 2 2,400 4,800 6,400 Q 4,800 4 1,600 6,400 Components to be manufactured= Components to be purchased =
*6,400 hrs * 4 = 1,600
S P Q Q R
= = =
= = 1,600 3,200 1,200
2,400 2,400
282
(ii) Statement showing impact of second shift working
Additional quantity of Q required = Hours required to manufacture (3,200 x 4) = Say = Fixed cost (`875 * 1,0000 ) x 13,000 = `11,375 Fixed cost per component Q (11,375 * 3,200) Increase in labour cost (`35 x 25%) Total Saving in cost Loss if component Q is manufactured
3,200 12,800 13,000 =`3.55 8.75 12.30 6.75 5.55
Hence, second shift operation is not recommended • Fixed cost given per 1,000 hours Ans. 77: Since S and Y are produced simultaneously from an input of raw material Z, therefore when additional 60,000 kgs. of Y will be produced then 30,000 of S will also be produced simultaneously. The input of material Z required for these additional 60,000 kgs. of Y and 30,000 kgs. of S will be 90,000 kgs. of material Z. Hence the cost of processing 90,000 kgs. of material will be as follows:
` Cost of Raw material Z
2,70,000
(90,000 kgs. × `3) Variable processing cost
1,80,000
(90,000 kgs. × `2) Total cost of processing
4,50,000
Less: Sales revenue from 60,000 kgs. of Y
2,40,000
(60,000 kgs. × `8) Balance cost to be recovered Current sales revenue from the sale of 3,00,000 kgs. of S
2,10,000 24,00,000
(3,00,000 kgs. × `8) Total sales revenue to be earned from the Sale of S
26,10,000
(3,00,000 kgs. + 30,000 kgs.) Hence minimum reduced price per kg. of S to recover `26.10,000 from
7.91
the sale of 3,30,000 kgs. of S (`26,10,000 / 3,30,000 kgs.) Ans. 78: Working notes: 1. Statement of total available, utilized and surplus capacity hours when 9,000 units of product ‘X’ are produced.
283
Departments
Available Capacity hours
Capacity utilized
Surplus Capacity hours
(in %
(in hours)
(1)
(2)
(3)
(4) = (2)×(3)
(5)=(2)-(4)
A
2,400 (300 days × 8 hours)
75
1,800
600
B
2,400
100
2,400
NIL
C
2,400
70
1,680
720
D
2,400
50
1,200
1,200
2. Statement of total available, utilized and surplus capacity hours when 12,000 units of product ‘X’ are produced. Production Department
Available capacity hours
Capacity utilization on 9,000 units Hours
Balance capacity hours
Unit per hour
Hours required for 3,000 additional units
Surplus capacity hours
(1)
(2)
(3)
(4)=(2)×(3)
(5)
(6)
(7)
(8)=(5)(7)
A
2,400
75
1,800
600
5
600
Nil
B
2,400
100
2,400
Nil
3.75
800
Nil
C
2,400
70
1,680
720
5.36
560
160
D
2,400
50
1,200
1,200
7.5
400
800
9,000 units 1,800 hrs. 9,000 units 2,400 hrs.
9,000 units 1,680 hrs. 9,000 units 1,200 hrs.
Alternative I Statement of net Revenue (Under Alternative I) Production
Surplus capacity hours (Refer to W.N.-1
Hire charges per hour
Total revenue in (`Lacs)
Incremental costs per hour `
Total cost in (`Lacs)
Net revenue in (`)
(a)
(b)
(c)=(a)×(b)
(d)
(e)=(a)×(d)
(f)=(c)-(e)
A
600
2,500
15.00
2,000
12.00
3.00
B
720
1,800
12.96
1,500
10.80
2.16
D
1,200
1,600
19.20
1,200
14.40
4.90
37.20
9.96
Total
47.16
Add: present income (10% of `1,800 lacs) Total return
180.00 189.96
284
Return on investment =
Total return Total investment
× 100 =
189.96 1,800
× 100 = 10.553%
Alternative II Statement of Net Revenue when 12,000 units of product ‘X’ are produced and surplus plant capacity (hours) in departments C and D hired out. Production
Surplus capacity hours (Refer to W.N.-2)
Hire charges per hour
Total revenue in (`Lacs)
Incremental costs per hour `
Total cost in (`Lacs)
Net revenue in (`Lacs)
(1)
(2)
(3)=(1)×(2)
(4)
(5)=(1)×(4)
(6)=(3)-(5)
C
160
1,800
2.88
1,500
2.40
0.48
D
800
1,600
12.80
1,200
9.60
3.20
12.00
3.68
Total
15.68
Add: Revenue (in lacs) earned on 3,000 additional units sale (3,000 units is × `1,600)
48.00
180.00
Add: Present income on investment (10% × `1,800 lacs) Total Return (in lacs)
231.69
Return on investment =
231.68 lacs 2,200 lacs
× 100 = 10.53%
Evaluation of two alternative proposals : Since the return on investment under alternative I is more than that under alternative II; therefore it should be accepted. Ans. 79: (i) Statement of Profitability of three Joint Products resulting from the joint production process of a popular line of colognes. Evergreen
Morning Flower
Evening Flower
Total
`
`
`
`
4,00,000
6,00,000
6,00,000
16,00,000
(10,000 units × `40)
(6,000 units × `100)
(4,000 units × `150)
--
Less: cost after point of split off
2,00,000 (10,000 units × `20)
2,40,000 (6,000 units × `40)
2,00,000 (4,000 units × `50)
6,40,000 --
Net realization value at the point of spilt off
2,00,000
3,60,000
4,00,000
9,60,000
Less: Joint cost apportioned (Refer to working note)
1,16,667
2,10,000
2,33,333
5,60,000
83,333
1,50,000
1,66,667
4,00,000
Sales revenue
Profit
285
Response to the President’s question. Review of the above profitability statement clearly shows that the concern is not selling its largest-volume product viz. evergreen at a loss. It yields a profit of `83,333. In fact the figure of joint cost data given in the statement of the question is misleading. The total joint cost viz. `5,60,000 should have been apportioned ever the three joint products by using net realisable value method. The use of net realisable value method would give joint cost per-unit of three respective joint products as `11,666; `35 and `58.33. (Refer to working note) Working note: Statement of Joint cost apportionment over three products obtained under a joint production process.
Total Joint cost
Joint cost apportionment (One the basis of net realization value i.e. (`2,00,000 : `3,60,000 : `4,00,000 or (5:9:10) Joint cost per unit
Evergreen
Morning Flower
Evening Flower
Total
`
`
`
`
2,80,000
1,68,000
1,12,000
5,60,000
(10,000 units × `28)
(6,000 units × `28)
(4,000 units × `28)
--
1,16,667
2,10,000
2,33,333
5,60,000 --
11,666 (`1,16,667 / 10,000 units)
35 (`2,10,000 / 6,000 units)
58.33 (`2,33,333 / 4,000 units)
(ii) Should the company sell Morning Flower Cologne below cost: To compete successfully with the other company’s product, if the price of Morning Flower Cologne is reduced to `60, it will still contribute `20 per unit (`60 – `40) towards joint cost and profit. On a volume of 6,000 units it will contribute `1,20,000 in total. Hence the company should do so and go ahead to sell Morning Flower below cost. (iii) Response to price reduction: (Refer to working note) A reduction in sales price of Morning Flower fails to maintain a gross margin of 20% on sales of three products obtained from the joint production process of a popular line of colognes. Hence the company cannot reduce the sales price of Morning Flower to `60. A reduction in sale price would result in a loss of revenue of `1,40,000. Working note: ` Total joint cost (20,000 units × `28)
5,60,000
Total cost after split off (10,000 × `20 + 6,000 units × `40 + 4,000 units × `50)
6,40,000
Total cost Add: Profit margin (20% on ales or 25% on total cost
12,00,000 3,00,000
Expected desired sales revenue
15,00,000
Less: Sales revenue of Evergreen and Evening Flower (10,000 units × `40) + (4,000 × `150)
10,00,000
Expected sales revenue from Morning Flower
5,00,000
By reducing sales price of morning flower to `60/- total sale revenue received will be
3,60,000
Loss of revenue resulting from the sale of Morning Flower
1,40,000
(iv) Minimum price for Morning Flower
286
Expected Sales revenue from Morning Flower to maintain a gross margin of 20% of sales: (`)
5,00,000
(Refer to (ii) part Quantity (in units)
6,000
Hence minimum price per unit (`)
83.33
(`5,00,000 / 6,600 units)
Ans. 80: (i) (a)
Statement showing apportionment of joint costs sales value at split-off
Products
Sales in tones (a)
Caustic soda Chlorine Total
2,400 1,600
Selling price per ton (`) (b) 100 150
Sales value (`) (c) = (a) * (b) 2,40,000 2,40,000 4,80,000
Apportioned cost (`) 1,00,000 1,00,000 2,00,000
joint
*Apportioned joint cost = Total joint cost * sale revenue of each product. Total sale value Apportioned joint cost to caustic soda = `2,00,000 * `2,40,000 = 1,00,000 `4,80,000 Apportioned joint cost to chlorine = `2,00,000 * `2,40,000 = `1,00,000 `4,80,000 (b) Statement showing apportionment of joint costs on physical measure (tons) Products Sales in (tons) Caustic soda 2,400 Chlorine 1,600 Total 4,000
Apportioned ** joint costs (`) 1,20,000 80,000 2,00,000
**Apportioned joint cost = Total joint cost * sales of each product (tons) Total sales (tons) Joint cost apportioned to caustic soda = `2,00,000 * 2,400 tons = `1,20,000 `4000 tons Joint cost apportioned to chorine = `2,00,000 * 1,600 tons = `80,000 `4,000 tons (c) Statement showing apportionment of joint costs by using estimated net realizable value method Products
Sales revenue (`)
Caustic soda (2,400 tons * `100) PVC (1,000 tons of PVC * `400) Total
2,40,000
Further cost (`) -
4,00,000
40,000
***Apportioned joint cost =
pro-cessing
Net realizable value (`) 2,40,000
Apportioned ** joint cost (`) 80,000
3,60,000
1,20,000
6,00,000
2,00,000
* Net realizable value of each product. Total joint cost Total net realizable value
Apportioned joint cost for caustic soda = `2,00,000 * `2,40,000 = `80,000 `6, 00,000
287
Apportioned joint cost for chlorine = `2, 00,000 * `3, 60,000 = `1, 20,000 `6, 00,000
(ii) Statement of gross margin percentage of caustic soda and PVC under sales value at split off: physical measure (tons) and estimated net realizable value method Sale value at split off (`) Physical measure (tons) (`) Estimated net realizable value (`) Caustic soda 2,40,000 Sale revenue : (A) 2,40,000 2,40,000 1,00,000 Joint cost allocated : (B) 1,20,000 80,000 1,40,000 Gross margin (C) : (A)-(B) 1,20,000 1,60,000 Gross margin (%) (C) * 100 (A) (b) PVC: Sales revenue (A) Joint cost allocated Further processing cost Total cost Gross margin (c) : (A)-(B) Gross margin (%) (C) *100 (A)
58.33%
50%
66.67%
4,00,000 1,00,000 40,000 1,40,000 2,60,000
4,00,000 80,000 40,000 1,20,000 2,80,000
4,00,000 1,20,000 40,000 1,60,000 2,40,000
65%
70%
60%
(iii) Consequence of the operating income of inorganic chemicals for November, 1998 by accepting the offer of daily swimming pools Ltd. to purchase, 1,600 tons of chlorine Incremental revenue (loss) due to processing of chlorine to PVC (`1, 60,000) (1,600 tons * `150) – (1,000 tons * `400 tons) 40,000 Saving on further processing cost of chlorine into PVC (`1, 20,000) Incremental operating income The operating income of inorganic chemicals will be reduced by `1,20,000 in the month of November, 1998 if it accepts the offer of daily swimming pools Ltd., to purchase 1,600 tons of chlorine in November, 1998 at `150 per ton.
Ans. 81: (i) Statement showing the product to be manufactured and sold and the result contribution Aristocrat
deluxe
Maximum possible production in unit (Note1) S. P. per unit `90.00 `80.00 Less: variable costs: Aristocrat deluxe Direct material `10.00 `10.00 Variable costs: Deptt. A (0.5*`50; 0.3 * `50) 25.00 15 27.00 Deptt. B (0.4 * `60; 0.45 * `60) 24.00 Total variable cost per unit 59.00 52.00 59.00 52.00 Contribution per unit 31.00 28.00 Total contribution per unit 6,800 * `31; 8,500 * `28 `2,10,800 `2,38000 Form the above, it is apparent that sale of `8,500 units of deluxe model produces the maximum contribution of `2,38000 within the capacity and material constraints. Therefore, 8,500 units of deluxe model should be produced. (ii) statement showing the maximum contribution on the sale of aristocrat or deluxe models and hiring out the surplus capacity in departments A and B Aristocrat deluxe Total contribution on sale of maximum possible production as per (i) above `2,10,800 `2,38,000 Contribution on hiring capacity (Note 2):
288
Aristocrat Deluxe Deptt. A Nil 850 * `40 34,000 900 Deptt. B 1,120 * `60 15 * `60 67,200 2,78,000 2,72,900 Total contribution It is noticed that total contribution of the company would be maximum i.e. `2,78,000 on the sale of 6,800 units of aristocrat model and hiring out the surplus capacity of the two departments. (iii) Statement showing total contribution of company when 4,250 units of each product are manufactured and surplus capacity of Deptt. A and/or Deptt. B hired out Aristocrat Deluxe Total (a) Production (units) 4,250 4,250 (b) Contribution per unit as at (i) above `31 `28 Total contribution (a) * (b) `1,31,750 `1,19,000 `2,50,750 Contribution earned on hiring the surplus 13,650* capacity of Deptt. B (Note 3) 2, 64,400 This proposal is less profitable then proposal at (ii) above Working Note: Maximum capacity or production is given in hours. But part (i) required production to be stated in units. The same has been worked out as under: Deptt. A Deptt. B Maximum capacity in hours 3,400 3,840 Aristocrat Deluxe Maximum hour per unit - Deptt. A 0.50 0.30 Deptt. B 0.40 0.45 Maximum possible production (in unit) – constant Maximum capacity Deptt. A: 3,400/0.5; 3,400/0.30 6,800 11,333 Deptt. B 3,840/0.40; 3,840/0.45 9,600 8,533 Maximum possible production (in unit) – constant Available material 17,000 kgs/2 kgs 17,000/2 kgs 8,500 8,500 Maximum possible production considering both Capacity and material constants 6,800 8,500 2. Surplus capacities (a) Maximum possible hours (b) Capacity used when 6,800 units of aristocrat model are produced (0.50 * 6,800; 0.40 * 6,800) (c) surplus capacity with aristocrat model (d) Capacity used when 8,500 units of deluxe model are produced (0.3 * 8,500; 0.45 * 8,500) (e) Surplus capacity with deluxe model (a)-(d) 3. Maximum possible hour as in unit Note 1 Hour utilized aristocrat 4,250 * 0.50; 4,250 * 0.45 Deluxe Surplus capacity (hours)
Deptt.A 3,400
Deptt. B 3.840
3,400 NIL
3,840 1,120
2,550 850 Deptt. A 3,400 (-) 2,125 (-) 1,275 NIL
3,825 15 Deptt. B 3,840 (-) 1,700 (-) 1912.5 NIL
Ans. 82:
Brightly Unit price
`
Contrib ution per unit
`
Volume Units
Total contributi on (`in 000)
Increment al contributi on (`000)
Labou r hours
Increme ntal labour hours
Increment al contributi on per labour hour
`
Rank
289
276
176
12000
2112
2112
2400 0
24000
88
2
272
172
14000
2408
296
2800 0
4000
74
6
268
168
16000
2688
280
3200 0
4000
70
7
264
164
18000
2952
264
3600 0
4000
66
8
260
160
20000
3200
248
4000 0
4000
62
9
254
154
22000
3388
188
4400 0
4000
47
10
Lightly Unit price
Contribution per unit
Volume
Total contribution (`in 000)
Incremental contribution (`000)
Labour hours
Incremental labour hours
Incremental contribution per labour hour
Rank
163
103
40,000
4120
4,120
40,000
40,000
103
1
162
102
42,000
4284
164
42,000
2,000
82
3
161
101
44,000
4444
160
44,000
2,000
80
4
160
100
46,000
4600
156
46,000
2,000
78
5
156
96
48,000
4608
8
48,000
2,000
4
11
152
92
50,000
4600
(8)
50,000
2,000
(4)
Loss
As the labour time is scarce source (time available 78,000 hours), the decision has to be taken on the basis of ranks based upon incremental contribution per labour hour. Price
Incremental volume
Incremental labour hours
Balance hours
Incremental Contribution (in 000 `)
Lightly
163
40,000
40,000
38,000
4120
Brightly
276
12,000
24,000
14,000
2112
Lightly
162
2,000
2,000
12,000
164
Lightly
161
2,000
2,000
10,000
160
Lightly
160
2,000
2,000
8,000
156
Brightly
272
2,000
4,000
4,000
296
Brightly
268
2,000
4,000
Product
280
Total
7,288
Hence product mix is Brightly – 16,000 units and Lightly 46,000 units Optimal contribution per month
`72,88,000
Fixed costs per month
`60,00,000
Optimal profit per month
`12,88,000
Working Notes: Brightly Variable cost (p.u.) Fixed cost (`)
(38,00,000 − 34,00,000) = Rs. 100 (16,000 − 12,000)
Lightly
(66,80,000 − 62,00,000) = Rs. 60 ( 48,000 − 40,000)
22,00,000
Contribution = Unit selling price less variable cost per unit.
38,00,000
290
Ans. 83: Statement showing computation of selling price per unit Months 1-3 4-9 10-12 Total number of unit `60,000 `33,750 Produced (Note 4) `28,125 Variable cost `2,81,250 `6,00,000 `3,37,500 Labour cost (Note 2) 3,00,000 6,00,000 3,37,500 Overheads 1,12,500@ 2,40,000@ 1,35,000@ Total sami variable overheads (Note 3) Fixed overheads Total costs Add: profit: (20% on selling price or 25% on cost) Sales revenue Selling price per unit ( `40,10,063/1,21,875 on cost)
Working notes 1. Average installed capacity per month (in units): = Total annual installed capacity/12 month (in units): = 1, 50,000 units/ 12 months = 12,500 units per month. 2. Total labour cost at different capacity utilization: Capacity utilization 75% Expected production per month ( in units) 9,375 Labour cost of expected production (`) 93,750 Minimum lqbour cost per month (`) 1, 00,000 Capacity utilization (in months) 3 Total labour cost at different capacity levels `3, 00,000
80% 10,000 1, 00,000 1, 00,000 6 `6, 00,000
Total 1,21,875 `12,18,750 12,18,750 4,87,500 72,000# 1, 92,300 32, 08,050 8, 02,013 40, 10,063 32.90
90% 11,250 1, 12,500 1, 12,500 3 `3, 37,500
@28125 × `4; 60000 × `4; 33750 × `4 #This can also be taken based on average capacity utilization i.e. ( 121875÷150000) × 100 = 81.25%. Therefore, semivariable overheads can also be taken as 68000 (refer note 3). In that case, selling price will be `32.87. Ans. 84: Part A
Part B
Target Price (`) Less : Variable Cost p.u. (`) Material(1.6 kg. @ `12.5 p.kg.) (`) Variable OH Machine A (0.6/0.25 hrs @ `80 p.h.) (`) Variable OH: Machine B (0.5/0.55 hrs @ `100 p.h.) (`) Total Variable Cost p.u. (`) Contribution p.u. (`)
145
115
20 48 50 118 27
20 20 55 95 20
Number of parts can be manufactured on the basis of: Alloy Available (13000kg ÷ 1.6/1.6) Machine A (4000 hrs ÷ 0.6/0.25) Machine B (4500 hrs ÷ 0.5/0.55) Maximum units that can be manufactured
8,125 6,666 9,000 6,666
8,125 16,000 8,181 8,125
179,982
162,500
Total Contribution (6,666 units × 27; 8,125 × 20) Hence it is recommended to produce Part A. (b) Parts A to be Manufactured
6,666 units Hours utilized Idle hours Machine A usage (6,666 × 0.6) 3,999.6 0.4 Machine B usage 3,333 1167 Compensation for unutilized machine hour (1167.4 @ Rs 60/ hour) `70,044 Revised contribution after reduction of 10% in S.P. [6,666 × (145 × 0.9 – 118)] `83,325
291
`153,369
Total Contribution Ans. 85:
Cutting 10,000
Capacity (units) Selling Price 1000 Material Cost 400 Throughput contribution 600 `/u. (i)
Throughput Contribution
600
Subcontracting changes
400
Finishing 5,000
200 Increase in throughput contribution = 200 x 5000 = 10,00,000 (ii) Already cutting has surplus capacity. It is not a bottleneck. Do not outsource as there will be no benefit, instead there will be reduction of or throughput contribution of outsourced. (iii) Cutting has surplus capacity. Do not increase non-bottleneck capacity. Ans. 86: Contribution analysis: Product X
Product Y
`
`
288
432
Selling price Variable costs: Direct materials
40
80
Direct Labour:
48
72
24
48
72
−
−
96
Variable overheads
32
28
Total variable costs
216
324
Contribution per unit 72 108 The direct labour hours required to manufacture the two products in each of the four departments at the wage rate of `8 per hour are as under: Department
Product X
Product Y
Wage cost
Hours/unit
Wage cost
Hours/unit
1
48
6
72
9
2
24
3
48
6
3
72
9
−
−
4
−
−
96
12
Department 3 is used only for product X and department 4 is used only for product Y. Hence, these two departments will determine the maximum production of these two products as under: Department 3 : Maximum available hours: Workers
×
Hours/day
×
Days/year
27
×
8
×
300
=
64,800 hours
292
Maximum possible production of product X:
64,800 = 7,200 units 9 hrs per unit
Department 4 : Maximum available hours: Workers
×
Hours/day
×
Days/year
36
×
8
×
300
Maximum possible production of product Y:
=
86,400 hours
86,400 = 7,200 units 12 hrs per unit
The company can produce 7,200 units each of products X and Y provided departments 1 and 2 have capacity to process this quantity of output. We can check the capacity of departments 1and 2 as under: Department 1: Maximum available hours: Workers
×
Hours/day
×
days/year
45
×
8
×
300
=
1,08,000 hours
Hours required to produce 7,200 units each of X and Y: Product X
7,200 × 6 hours
=
43,200 hours
Product Y
7,200 × 9 hours
=
64,800 hours
=
1,08,000 hours
Total
Department 1 has capacity to produce 7,200 units each of products X and Y. Department 2 : Maximum available hours: Workers
×
Hours/day
×
days/year
24
×
8
×
300
=
57,600 hours
Hours required to produce 7,200 units each of X and Y: Product X
7,200 ×3 hours
=
21,600 hours
Product Y
7,200 × 6 hours
=
43,200 hours
=
64,800 hours
Total
Department 2 has scarce capacity. Since department 2 capacity is scarce, link the contribution to the key factor of department 2 hours as under: Contribution per unit Department 2 hours per unit Hours Contribution per hour of Department 2 Rank Optimal product mix:
Product X 72 3
Product Y 108 6
24 1
18 2
`
Product
Max. units
Lab. Hours/unit
Prod. units
Hours used
Balance hours
Cont./unit
`
`
X
7,200
3
7,200
21,600
36,000
72
5,18,400
Y
7,200
6
6,000
36,000
−
108
6,48,000
Total optimal contribution
Total cont.
11,66,400
Fixed costs
5,00,000
Optimal profit
6,66,400
Alternative Solution:
293
The maximum possible production of product X is 7,200 units and that of product Y is 7,200 units. The following two methods shall be used to determine the optimal profit: (a) Produce 7,200 units of product X and use the balance capacity to produce product Y. (b) Produce 7,200 units of product Y and use the balance capacity to produce product X. Profitability based on (a): Direct labour hours are scarce in Department 2. Maximum available hours in Department 2
57,600
Product X requires 7,200×3=
21,600 hours
Balance hours on Y
36,000
Production of Y 36,000 ÷ 6=
6,000 units
Contribution: @ `72 @ `108
X 7,200 units
`5,18,400
Y 6,000 units
`6,48,000
Total
`11,66,400
Fixed costs
`5,00,000
Profit
`6,66,400
Profitability based on (b): Maximum available hours in Department 2 Product Y requires 7,200×6=
57,600
43,200 hours
Balance hours on X
14,400
Production of X 14,400 ÷ 3=
4,800 units
Contribution:
X 4,800 × 72
`3,45,600
Y 7,200 × 108
`7,77,600
Total
`11,23,200
Fixed costs
`5,00,000
Profit
`6,23,200
Profitability of (a) is better. Ans. 87: (a) Statement of Cash Receipts, Disbursements and cumulative difference in Cash flows for four years taken together under both alternatives (`in thousands) Alternatives
Keep old machine nd
rd
Buy new machine
Year 1
2 3 & 4th year each
All 4 years
Year 1
2nd 3rd & 4th year each
All 4 years
150
150
600
150
150
600
-
-
-
8
-
8
Receipts Sales revenue Self
of
old
Cumulative difference in cash flows for four years taken together
294
equipment Total receipts : (A)
150
150
600
158
150
608
Annual operating cost
15
15
60
9
9
36
Other cash costs
110
110
440
110
110
440
Purchase cost of “old” machine
20
-
20
20
-
20
Purchase of “new” machine
-
-
-
24
-
24
145
125
520
163
119
520
5
25
80
(5)
31
88
Disbursements
Total disbursements (B)
:
Net cash inflows: (A)-(B)
08
(b) Statement of income for each of the four years and cumulative difference in operating income. Alternatives
Keep old machine st
nd
rd
Buy new machine
1 ,2 3 & 4th year each
All years
Year 1
2nd 3rd & 4th year each
All 4 years
Sales revenue
150
600
150
150
600
Total revenue : (A)
150
600
150
150
600
15
60
9
9
36
110
440
110
110
440
5
20
6
6
24
-
-
12
-
12
Total costs: (B)
130
520
137
125
512
Operating (A)-(B)
20
80
13
25
88
Cumulative difference operating income
Income
Costs: Annual cost
operating
Other cash costs Depreciation (Refer to working note 1) Loss on disposal of machine
the old
(Refer to working note 2) income:
08
(c) The purchase of cost old machine `20,000; the sale revenue `1.50,000 and other cash costs of `1,10,000 as irrelevant items for the presentation in requirements (a) and (b) above. These items are irrelevant because their amounts are common to both the alternatives. (d) The net difference in requirements under (a) and (b) will not change if the cost of ‘old’ machine becomes `10,00,000 instead of `20,000. This is so because the cost of old machine is common for both the alternatives. (e) In the decision about eh replacement of machine the book value of the machine is irrelevant because it is a past (historical) cost. All past costs are down the drains. Nothing can change what has already happened. As apparent from (a) and (b) above; we can completely ignore the cost of old machine i.e. `20,000 and still have a correct analysis.
295
Working note: 1. Depreciation (according to straight line method): Old machine (i) cost of machine (`)
20,000
(ii) Terminal disposal value
Zero
(iii) Useful life
4
(i) - (ii) ` (iii)
Depreciation
New machine 24,000 Zero 4
5,000
5,000
2. Loss on the disposal of old machine:
`
`
Purchase price of old machine
20,000
Disposal value
10,000
Less: Removal cost
2,000
8,000 12,000
Ans. 88: Evaluation of Make or Buy proposal (All figures are in lakhs in rupees) Year
(a)
P.V. factors at 10%
(b)
When the manufactured
component
is
When the component is bought from an outside supplier
Cash outflow (Capital cost + manufacturing cost + opportunity cost)
Present Value
Cash outflow (Buying cost)
Present Value
`
`
`
`
(c)
(d)=(b)×(c)
(e)
(f)=(b)×(e)
0
1.000
4
4.000
-
-
1
0.909
6+2
7.272
9
8.181
2
0.826
7+2
7.434
10
8.260
3
0.751
8+2
7.510
11
8.261
4
0.683
10+2
8.196
14
9.562
Total
34.412
Saving in cash outflow (when brought from outside)
24.264
Total present value of total present value of cash outflow, when the cash outflow, when the − = component is manufactured component is bought from outside. internally
= `24.412 – `34.264 = `0.148 (lakhs) Conclusion: Since there is a saving of `0.148 (lakhs) in buying the component from outside, therefore, we should stick to this decision.
296
Note: The loss of `2 lakhs cash inflow for each of the four years due to the inability of the firm to operate another machine if it manufactures the component has been treated as an opportunity cost. Ans. 89: Proposal I Year (a)
Statement of sales revenue of mild Quantity of mild in Price per metric metric tonnes (b) tonne (c)
1 2 3 4 5
15,000 15,000 15,000 15,000 15,000
950 900 850 800 750
Total amt of sales in (`Lacs) (d) = (b) * (c) 142. 5 135.0 127. 5 120.0 112. 5
Discount factor @ 12% (e) 0.89 0.79 0.71 0.64 0. 57
NPV of sales (`In lacs) (f) = (d) * (e) 126.825 106.65 90. 525 76.800 64.125 464. 925
Proposal II Year (a)
Quantity of Price per Variable Net price per Net sales Discount PV of net sales medium in metric cost per metric tone (`) revenue in factor @ revenue metric tones metric tone (e) =(c)– (d) tone (`Lacs.) (f) = 12% (g) (`Lacs.) (h) = (b) (c) (`) (d) (b) * (e) (f) * (g) 1 1,000 1,200 200 1,000 10 0.89 8.90 2 2,000 1,300 200 1,100 22 0.79 17.38 3 3,000 1,400 200 1,200 36 0.71 25.56 4 4,000 1,500 200 1,300 52 0.64 33.28 5 5,000 1,600 200 1,400 70 0.57 39.90 Total 125.02 Note: since the selling price of medium is not given after second year, therefore an individual is free to talk any selling price after second year. In view of this assumption the answer of each case may differ. Year (a)
1 2 3 4 5
Quantity of mild in metric tones (b) 14,000 13,000 12,000 11,000 10,000
Price per metric tone (`) (c) 950 900 850 800 750
Sales revenue in (`Lacs) (d) = (b) * (c) 133 177 102 88 75
Discount factor @ 12% (e) 0.89 0.79 0.71 0.64 0.57
PV of sales revenue in (`Lacs) (f) = (d) * (e) 118.37 92.43 72.42 56.32 42.75
Total 382.29 Total present value of sales of medium and mild under proposal II (`Lacs) 507.31 (`125.02 lacs – `382.29 lacs) Total net present value under proposal II (`507.31 lacs – `30 lacs) The net present value under proposal I is `464.925 lacs, and that under proposal II is `477.31 lacs. A comparison of the net present value under two proposal clearly shows that the proposal II is better as it yield a higher net present value of revenue, therefore it should be accepted.
Ans: 90 (i) 15,000 tins scrapped per month can be converted into 75,000 lids. (Each rejected tin can be converted into 5 lids) unusable tins are sold as scrap at `8 per unit. Hence, `8 can be taken as raw material cost for conversion into lids. 15,000 tines at `8 1,20,000 Add: Conversion cost `50 per 100 pieces. i.e. 50 paise per piece. 15000 x 5 = 75,000 lids x 0.50 = 37,500
297
Total cost of 75,000 lids 1,57,500 Less: Value of scrapped lids and off-cuts. Weight of tins: 15,000 kgs. 75,000 x 120 gms = 1,000 9,000 kgs. Weight of scrap 6,000 kgs. Sales value of scrap 6,000 x 5 30,000 Net cost of 75,000 lids 1,27,500 Cost of each lid 1,27,500 / 75,000 `1.70 Cost of buying one lid `2.00 Hence, there will be a saving of 30 paise on each lid converted instead of buying from outside. In view of saving , the proposal should be accepted. `lakhs (ii) Saving in year: Buying 1,00,000 lids x 12 Months x `2.00 24.00 Less: Conversion cost: 75,000 lids x 12 months x 1.70 = Cost of buying the balance lids = 25,000 lids x 12 months x 2.00 = Saving in a year
15.30 6.00
21.30 2.70
Or else, 75,000 lids x 12 months = 9,00,000 lids at Re. 0.30 each = `2,70,000 savings in a year accrue to the company if the proposal is accepted. Ans. 91: Order Qty Order Qty 100-140 (`) 141-200 (`) 30,000 30,000 Selling Price `/u Commission @ 10% 3,000 3,000 Sales revenue p. u. 33,000 33,000 Less: Variable purchase cost Contribution / unit 29,000 26,000 4,000 7,000 (before shipping) Less: Shipping cost > 110 units 5,000 Contribution/ units after Shipping 2,000 (i) Upto 110 units, Reference will earn a contribution of `4,000/u. (ii) Between 110 & 140 units, contribution of 4,000 will be wiped out by 5,000 on shipping costs. Hence we should not consider 110 – 140 range. (iii) 101 – 110 not to be considered since additional fixed costs 2,25,000 will not be covered by 10 units. (iv) Valid consideration, 100 units or 141 to 190 units. Fixed cost of box of 50 cameras is `2,25,000
298
Units
141
150
190
B
2 3 4,50,000 6,75,000
3 6,75,000
4 9,00,000
Contribution (Rs/u) `4,000
C
400,000
Contribution (`) first 110 units @ 7,000/u
D
7,70,000
7,70,000
No. of Camera Boxes Cost of Cameras (`)
100 A
7,70,000
62,000 80,000 1,60,000 E Contribution (`) Balance units @ 2,000/u 4,00,000 8,32,000 8,50,000 9,30,000 F Total Contribution (F - 50 000 1 57 000 1 75 000 30 000 Best strategy buy 150 units from Comp. sell 110 at store and 40 outside. BEP should be between 151 – 191 units Extra Camera box cost beyond 150 units
= 2,25,000
Less: Profit for 150 units
= 1,75,000
Extra profit acquired
= 50,000
No. of units to cover this additional costs at contribution 2000 `/u =25 ∴BEP = 150 + 25 = 175 units
299
Miscellaneous Theory Chapters Ans. 6: (a) Calculation of cost of per 100 units of good components: (A)
X Ltd.
Y Ltd.
10,000
10,000
300
500
(3%)
(5%)
If not inspected Units required Estimated defectives
Cost Purchase price (Rs.) Production damage (Rs.)
(B)
Rs.
Rs.
18,000
17,400
540
900
Total Cost (Rs.) Good component (units)
18,540
18,300
Cost per 100 good component (Rs.)
9,700
9,500
191.13
192.63
Defectives not detected
30
50
Defectives detected
270
450
Components paid for
9,730
9,550
Rs.
Rs.
17,514 2,400
16,61 7 2,400
54
90
If inspected
Cost Purchase cost Inspection cost Production damage Total cost Good components Cost per 100 good components (Rs.)
19,968
19,107
9,700
9,500
205.86
201.3
Decision: (i)
On the basis of the cost per 100 good component calculated at (A) and (B) above, it is concluded that inspection at the point of receipt is not justified.
(ii) It will be advantageous to purchase the component from X Ltd. Ans. 7: 1. a. Percentage of defective units shipped
2003 400 = 4% 10,000
2004 330 11000
b. Customer complaints as a percentage of units shipped c. On-time delivery
500 = 5% 10000 8500 = 85% 10000
517 11000 9900 11000
=4.7%
d. Percentage of units reworked during production
600 10000
627 11000
=5.7%
=6%
= 3%
= 90%
300
2. The calculations in requirement I indicate that ESC’s performance on both quality and timeliness has improved. Quality has improved because (a) percentage of defective units shipped has decreased from 4% to 3%,(b) customer complaints have decreased from 5% to 4.7% , and (c) percentage of units reworked during production has decreased from 6% to 5.7% . Timeliness has improved as on –time delivery has increased from 85 % to 90% . Of course , there is a relationship between the improvements in quality and timeliness. Better quality and less rework reduces delays in production and enables faster and on-time delivery to customers. 2003
3a. The output per labor- hour Between 2003 and 2004 Can be calculated as follows
2004 11000 =0.10 110000
10000 =0.11 90000
3b . Output per labor-hour may have declined from 2003 and 2004 either because workers were less productive or more likely because the initial implementation of the quality program may have resulted in lost production time as employees were trained and became more adept at solving production quality problems. As workers implement good quality practices and defects and rework decrease over time, it is possible that both quality and productivity (output per labor-hour) will increase. 3c. it is not clear that the lower output per labor-hour will decrease operating income in 2004. the higher labor costs in 2004 could pay off in many ways. Higher quality and lower defects will likely result in lower material costs because of lower defects and rework. Internal and external failure costs will also be lower, resulting in lower customer returns and warranty costs. Customer satisfaction will likely increase, resulting in higher sales, higher prices, and higher contribution margins. Indeed the 10% increase in the number of units produced and sold in 2004 may well have been due to quality improvements. Overall, the benefits of higher quality in 2004 may very well exceed the higher labor costs per unit of output. Ans. 8: (i) Classification of Quality Costs 2007 Sales Prevention Quality training Appraisal Product Inspection Materials Inspection Internal Failure Scrap Rework External Failure Product warranty
% of sales
6,000 75
6,000 1.25
200 80 280 600 500 1100
Figures Rs. ’000 % of 2008 sales
150
2.5
240 4.67
60 300
5
18.33
300 400 700
11.67
300 5 150 2.5 1755 29.25 1300 21.67 (ii) Cost reduction was effected by 7.58% (29.25 – 21.67) of sales, which is an increase in profit by Rs.4,55,000. (6 Marks) Nov/08-NC& ICWA-June/03 [Adapted] Ans. 9: Had there been no defectives for production of 1,00,000 pieces of P 1,00,000X5=5,00,000 units of raw material would be required. In case of high quality material , defective being 10% total raw material required is 5,00,000 units/0.90 =5,55,556 units. In case of lower quality material, defective being 20%, total raw material requirement is 5,00,000 units/0.08 =6,25,000 units. Similarly labour and variable overhead requirement are to be adjusted accordingly. Ascertainment of Total cost I. Using high quality materials (scrap 10%) (Rs) Material (5,00,000 units/0.90X Rs.1.05) 5,83,333 Labour (2,50,000 hours/0.90X Rs.0.50) 1,38,889 Variable overhead (Rs.1,00,000/0.90) 1,11,111
301
Fixed overhead Less: Scrap
50,000 8,83,333 16,667 8,66,666
(5,00,000/0.90)-5,00,000)XRe.0.30
Cost of 1,00,000 pieces of P II. Using lower quality materials Material Labour Variable overhead Fixed overhead Machine and Tooling cost Additional laboour Additional overhead for additional labour
(scrap 10%) (5,00,000 units/0.80X Rs.0.80) (2,50,000 hours/0.80X Rs.0.50) (Rs.1,00,000/0.80)
(Rs) 5,00,000 1,56,250 1,25,000 50,000 3,000 2,500
(1,00,000units X 0.5hours XRe.0.50) (1,00,000 units x 0.5 hours)X (Rs.1,00,000/2,50,000 hours)
20,000 8,79,250 5000 8,74,250
Less: Realizable value of scrap Cost of 1,00,000 pieces of P Analysis: Hence the high quality material should be used.
Ans. 10:-Let the defectives be’d’ (I) If each components is tested before being sent to the agents for sales No: of components in a batch Rs.2000 Cost of testing each components Rs.20 Cost of rectification before dispatch Rs.200 Total Cost Rs.(2000x25)+200d (II) If components dispatch without pre-testing and defectives received back for rectification under warranty. Total Cost 400d In difference point of two alternatives (2000x25)+200d 400d 400d-200d 2000x25 200d 50,000 D 50000/20 250 Defective Components 250 components Percentage of defectives to total components 250/2000*100 =12.5% Analysis: If defectives exceed 12.5% of the total number of components per-testing is recommended. Present Position (Based on 1,000 units Production) Ans. 11: Cost per unit. Direct material Direct wages (8 hours @ Re.0.50) Overheads (8 hours @ Rs.1.75) Total Per unit Particular Sales price Firsts 30 Seconds 20 Thirds 10
Units Profit / Loss 2 (-) 8 (-) 18
900 50 50
Reprocessing of Inferior units (a) Additional expenditure for reprocessing per unit Direct Material Direct Wages 8 hrs. Variable overhead @ 0.875 Total expenditure for 100 units Rs.1,500
(Rs.) 10 4 14 28 Total Profit 1,800 1,800 Net Profit
Loss 400 900 1,300 500 (Rs.) 4 4 7 15
302
. (b) Additional Revenue Second (Rs.30-Rs.20)x50units Thirds (Rs.30-Rs.10)x50
(Rs.) 500 1000 1500
Note: No change in the profit position hence this need not be considered. Ans. 12: (a)
i.
Total production (Preinspection)
Existing
After TQM Programme
5,000
5,000
units
Total sales requirements Specification losses 5% Downgrading
at
12.5 × 5,250 87.5
250
inspection
5,250
5,125
750
416
6,000
5,541
Purchase of material ‘X’(Sq Mtr) Material required to meet pre inspection production requirement 6,000 × 8 SqMtr Processing loss
Scrapped
48,000 SqMtr
4 × 48,000 96
Input to the process material
44,328 SqMtr
1,137 2.5 × 44,328 97.5
50,000
45,465
2,632
1,406
5 × 95
Total purchases
5,541×8 SqMtr
2,000
3 × 45,465 97
50,000
iii
125
7.5 × 5,125 92.5
Total units before inspection ii
2.5%
52,632
46,871
Gross Machine Hours Initial requirements 6,000 × 0.6 Idle time
20 × 3,600 80
Gross time (b)
3,600
5,541 × 0.5
2,771
900
12.5 × 2,771 87.5
396
4,500
3,167
Profit and loss statement Rs
Rs
Sales revenue 5,000 Units× Rs 1,000
50,00,00 0
50,00,000
Sales downgraded
5,25,000
416 Units × Rs 700
2,91,200
303
750 Units×Rs 700 55,25,00 0
52,91,200
Costs: Material 52,632 Sq Mtr ×Rs 40
21,05,28 0
46,871Sq Mtr × Rs 40
18,74,840
Inspection and storage costs 52,632 Sq Mtr ×Re 1
52,632
Machine cost 4,500 Hrs × Rs 400
18,00,00 0
3,167 Hrs× Rs 400
Inspection and other cost
2,50,000
2,50,000 × 60%
1,50,000
Product liability (3% × 50,00,000
1,50,000
1% × 50,00,000
50,000
Sundry cost of selling, distribution and administration.
6,00,000
6,00,000 × 90%
5,40,000
Preventive programme cost
2,00,000
6,00,000
51,57,91 2
45,28,511
3,67,088
7,62,689
Net profit
46,871Sq Mtr × Re 1
46,871 12,66,800
Ans. 13: (a) (i) Units Components worked on in the process 6120 Less: planned defective units 612 replacements to customer (2% X 5400) 108 Components invoiced to customers 5400 Therefore actual result agree with planned results (ii) Planned components cost = (3 X Rs.18 for material A) + (2 X Rs.9 for material B) + Rs.15 variable cost =Rs.87 Comparing with the data in appendix: Materials = Rs.440 640/6120 =Rs.72 Variable overhead = Rs.91 800/6120 = Rs.15 This indicates that prices were at the planned levels. (b) Internal failure costs = Rs.53 244(612 units X Rs.87) External failure costs = Rs.9396 (108 units X Rs.87) (c) (i) Period 2 (units) Period 3 (units) Components invoiced to customers 5500 5450 Planned replacement (2%) 110 109 Unplanned replacement 60 (170-110) -69 (40-109) Components delivered to customers 5670 5490 Planned process defects (10% of worked on in the process) 620 578 Unplanned defects (difference to agree with with final row) -90 -288 Components worked on in the process 6200 5780 (ii) Period 2(Rs.) Period 3(Rs.) Internal failure costs 46,110 (620-90) XRs. 87 25,230 (578-288) X Rs.87 External failure costs 14,790 (110+60) X Rs.87 3,480 (109-69) X Rs.87 Appraisal costs 10,000 15,000 Prevention costs 5,000 8,000 (iii) The following points should be included in the report:
304
1. Insufficient detail is provided in the statistics shown in the appendix thus results in the need to for an improvement in reporting. 2. The information presented in (c) (i) indicate that free replacement to customers were 60 greater than planned in period 2 but approximately 70 less than planned in period 3. in contrast, the in process defects were 90 less than planned (approximately 15%) in period 2 and 288 less than plan (approximately 50%) in period 3. 3. Internal failure costs show a downward trend from period 1-3 with a substantial declined in period 3.External failure costs increased in period 2 but declined significantly in period 3. 4. The cost savings arising in period 2 and 3 are as follows: Period 2(Rs.) Period 3(Rs.) Increase /decrease from previous period: Internal failure costs -1734(Rs.53244-Rs.46110) -20880(Rs.46110-Rs.25230) External failure +5394(Rs.9396-Rs.14790) -11310(Rs.14790-Rs.3480) Total decrease -1740 -32190 The above savings should be compared against the investment of Rs.10000 appraisal cost and Rs.5000 prevention cost for period 2 and Rs.15,000 and Rs.8,000 respectively in period 3. it can be seen that the cost exceed the savings in period 2 but the savings exceeds the cost in period 3. There has also been an increase in the external failure cost from period 1 to period 2. Investigations should me made relating to the likely time lag from incurring prevention/appraisal costs and their subsequent benefits. 5. The impact on customer goodwill from the reduction in replacements should also be explained. Ans. 27:
Return of 12% net (after tax of 40%) on capital employed is equivalent to 12%÷(1-0.4) = 20% (gross) on capital employed. Let selling price per unit to be ‘x’ Since Total sales = Total cost + profit i.e., 80,000x = 14,60,000+20% (12,00,000+0.5×80,000×) Or, 80,000x = 14,600+2,40,000+8,000x Or, 72,000x = 17,00,000
Or, ‘x’ =
17,00,000 = Rs. 23.61 72,000
Hence selling price per unit will be Rs. 23.61 Ans. 28:
(i) Statement showing price of Product Z Direct Material Direct Labour Variable overhead
Deptt. A
30
Deptt. B
25
Deptt. A
30
Deptt. B
40
Deptt. A 3×6
18
Deptt B 4×3
12
Variable selling and distribution overhead 30,000/1,500 Total Variable Cost per unit Total hours required for a target of 1,500 units of product Z
55 70 30 20 175
305
Deptt. A1500 × 3
4500 hours
Deptt. B1500 × 4
6000 hours 10500 hours
10500 hours represent 30% capacity So total capacity per month 10500 / 0.30 = 35000 hours. Yearly capacity is 35000 × 12 = 420000 hours. Fixed capital employed in both department
= 40.00 Lakhs
(25 lakhs + 15 Lakhs) Expected return
= 0.21 × 40,00,000
= 840000
Contribution per hour
= 840000 / 4200000
= 2.00 per hour
Working Capital
= 0.21 × 400000
= 84000
Contribution per unit 84000 / 18000 unit
= 4.67 per unit
Total contribution required
Rs.
To cover fixed cost 3 hours of A and 4 of B = 7 × 2
= 14.00
To working capital
= 4.67 18.67
Fixed charges recovery is based on usage. Full capacity is not being used by product Z and departments are also producing other products using same plant and machinery. Price of Product = Variable cost + contribution required = 175 + 18.67 = 193.67 per unit. (ii)
Price of product when product is well established in market: Variable Cost Fixed Cost (24 + 16) Total price
175 40 215
The product is first time launched in the market, and then variable cost Rs.175 should form the basis for price fixation. Ans. 29: (a)
Rs./u of alloy Materials: Iron 10kg @ Rs.5/-
50
Copper 5 kg @ Rs.8/-
40
90
Wages X : 3 hrs @ 15 Rs./Hr.
45
Y : 5 hrs @ 12 Rs./Hr
60
Variable OH (Production) X : 8 hrs × 3 hrs
24
Y : 5 hrs × 5 hrs
25
105
49
306
20
Variable OH – Selling
264
Total Variable Cost Fixed Off: X : 8/hrs × 3 hrs.
24
Y : 5/hrs × 5 hrs
25
49
313 Total Cost (i) If pricing strategy is to penetrate the market, the minimum price for a new product should be the variable cost i.e. Rs.264/-. In some circumstances, it can also be sold below the variable cost, if it is expected to quickly penetrate the market and later absorb a price increase. Total Variable Cost is the penetration price. (ii)
When the alloy is well established, the minimum selling price will be the total cost – including the fixed cost i.e. Rs.313 per unit. Long run costs should cover at least the total cost.
Ans. 30: XYZ Ltd. Sales in X (rearranged for the purpose of ranking) Rank Category Stock(Rs.’000) 1 OTC 175 2 Toiletries 150 3 Photo 125 4 Food/ Drink 100 5 Baby 50 5 San. Prod. 50 5 Other 50 8 Foot Care 30 9 Cosmetics 25 10 Hair-care 25 11 Perfume 20
Cum. Sales(Rs.’000) 175 325 450 550 600 650 700 730 755 780 800
% 21.9 40.6 56.3 68.8 75.0 81.3 81.3 91.3 94.4 97.5 100.0
Stock in X (rearranged for the purpose of ranking) Rank Category Stock(Rs.’000) 1 Toiletries 60 2 Cosmetics 40 3 OTC 35 4 Photo 20 4 Food/ Drink 20 6 Other 13 7 Baby 10 7 San. Prod. 10 7 Hair 10 7 Perfume 10 11 foot care 2
Cum. Sales(Rs.’000) 60 100 135 155 175 188 198 208 218 228 230
% 26.1 43.5 58.7 67.4 76.1 81.7 86.1 90.4 94.8 99.1 100.0
Sales in Z (Rearranged for ranking) Rank Category Stock(Rs.’000) 1 OTC 120 2 Toiletries 100 3 Food/ Drink 75 4 Photo 60 5 Cosmetics 30 6 Baby 25 6 San. Prod. 25 6 Other 25 9 Foot care 20 10 Hair 10 11 Perfume 10
Cum. Sales(Rs.’000) 120 220 295 355 385 410 435 460 480 490 500
% 24 44 59 71 77 82 87 92 96 98 100
307
Sales in Z (Rearranged for ranking) Rank Category Stock (Rs.’000) 1 Toiletries 65 2 Cosmetics 45 3 OTC 40 4 Food/ Drink 20 5 Photo 12.5 6 Perfume 7.5 7 Baby 5 7 San. Prod. 5 7 foot care 5 7 Hair 5 7 Other 5
Cum. Sales(Rs.’000) 65 110 150 170 182.5 190 200 200 205 210 215
Ans. 46:Annual Relevant Costs of Current Production System and JIT Production Corporation. Relevant Costs under Current Production Relevant Items System Annual tooling costs Required return on investment: 12% per year x Rs.9,00,000 of average inventory per year Rs.1,08,000 12% per year x Rs.2,00,000 of average inventory per year Insurance , space, materials handling , and setup costs 2,00,000 Rework costs 3,50,000 Incremental revenues from higher selling prices Total net incremental costs Rs.6,58,000 Annual difference in favor of JIT production Rs.1,54,000
% 30.2 51.2 69.8 79.1 84.9 88.4 93.0 93.0 95.3 97.7 100.0 System for Evans Relevant Costs under JIT Production System Rs.1,50,000 24,000 1,40,000a 2,80,000b (90,000)c Rs.5,04,000
a
Rs. 200,000 (1-0.30) = Rs.140,000 Rs. 350,000 (1-0.20) = Rs.280,000 c Rs. 3x30,000 units = Rs.90,000 b
(a) Personal observation by production line workers and managers is more effective in JIT plants than in traditional plants. A JIT plant’s production process layout is streamlined. Operations are not obscured by piles of inventory or rework. As a result, such plants are easier to evaluate by personal observation than cluttered plants where the flow of production is not logically laid out. Besides personal observation, non financial performance measures are the dominant methods of control. Non financial performance measures provide most timely and easy to understand measures of plant performance. Examples of non financial performance measures of time, inventory, and quality include: • Manufacturing lead time • Units produced per hour • Machine setup time / manufacturing time4 • Number of defective units / number of units completed. In addition to personal observation and non financial performance measures. Financial performance measures are also used. Examples of financial performance measures include. • Cost of rework • Ordering costs • Stock out costs • Inventory turnover (3b) The success of a JIT system depends on the speed of information flows from customers to manufactures to suppliers. The Enterprise Resource Planning (ERP) system has a single database, and gives lower-level managers, workers, customers, and suppliers access to operating information. This benefit, accompanied by tight coordination across business function, enables the ERP system to rapidly transmit information in response to changes in supply and demand so that manufacturing and distribution plans may be revised accordingly. Ans. 47: (i) Comparative Statement of cost for purchasing from Y Co Ltd under current policy & JIT
308
Particulars Purchasing cost Ordering cost Opportunity carrying cost Other carrying cost(Insurance, material handling etc) Stock out cost
Current Policy Rs 18,20,000 (13,000 × 140) 26 (2×13 orders) 10,500.00 (1/2×1000×140×15%)
JIT Rs 18,20,260 (13,000 × 140.02) 260 (2×130 orders) 1,050.15 (1/2×100×140.02×15%)
1,550.00 (1/2×1000×3.10)
155
200 (4 × 50) Total relevant cost 18,32,076 18,21,925.15 Comments: As may be seen from above, the relevant cost under the JIT purchasing policy is lower than the cost incurred under the existing system. Hence, a JIT purchasing policy should be adopted by the company. (ii) Statement of cost for purchasing from Z Co Ltd. Particulars Purchasing cost Ordering Cost Opportunity Carrying Cost Other Carrying Cost Stock out Cost Inspection Cost Customer Return Cost
Rs. 1,76,800 (13,000x13.60) 260 (2x130 orders) 102 (1/2×100×13.60× 15%) 150 (1/2×100×3.00) 2,880 (8x360) 650 (13,000 x .05) 6,500.00 ( 13,000 x 2% x 25) 1,87,342
Total Relevant Cost Comments : The comparative costs are as follows, Under current policy Rs 18,32,076.00 Under purchase under JIT Rs 18,21,925.10 Under purchase from Z Co Ltd Rs 1,87,342.00 Packages should be bought from Z Co as it is the cheapest.
309
Linear Programming Ans:7 The problem may be summarized as follows: Chemical A Supplier X
1
Supplier X2 Units required
Chemical B
4 1
2 1
80
60
Cost per mix Rs. 10 4
Let x1 be the number of mixes to be purchased from supplier X1 and x2 be of those to be purchased from supplier X2. The conditions of the problem when symbolised, take the form: Minimize Z = 10 x1 + 4 x2 Subject to the restrictions x1 ≥ 0, x2 ≥ 0 4x1 + x2 ≥ 80, 2x1 + x2 ≥ 60. For the line 4x1 + x2 = 80, let x1 = 0,so that x2 = 80; let x2 = 0,so that x1 = 20. For the line 2x1 + x2 = 60, let x1 = 0,so that x2 = 60; let x2 = 0,so that x1 = 30.
Feasible region is shaded in the diagram which appears to be unbounded. We now try to determine the additional hidden conditions in the problem for which the feasible region becomes bounded. The column vector for the values of the objective function is given by
310
Since 260 is the smallest element in EC, the minimum value is reached at the extreme point E2, whose coordinates are (10,40). Thus, to honour the contract and yet to minimize cost, the company should purchase 10 mixes from X1 and 40 mixes from X2. Ans.8: Maximize
z = 80x + 100y subject to
x + 2y ≤ 720 5x + 4y ≤ 1800 3x + y ≤ 900 x≥0y≥0
where
x = No. of units of A y = No. of units of B
By the addition of slack variables s1, s2 and s3 the inequalities can be converted into equations. The problem thus become z = 80x + 100y subject to
x + 2y + s 1 = 720 5x + 4y + s 2 = 1800 3x + y +s 3 = 900
and x ≥ 0,
y ≥ 0,
s 1 ≥ 0, s 2 ≥ 0, s 3 ≥ 0
Table I
S1
Profit/unit 0
Qty. 720
80 X Ι
S2
0
1800
5
4
0
1
0
900
3 80
Ι 100
0 0
0 0
1 0
S3 0 Net evaluation row 1800 – 720 ×4/2 = 360
100 Y 2
0 S1 1
0 S2 0
0 S3 0
900 - 720×1/2 = 540
5 – I×2 = 3
3 - 1× ½ = 5/2
4 – 2 × 2 =0
I – 2 ×1/2 = 0
0 - I×2 = - 2
0 – I ×1/2 =- 1/2
I - 0×2 = I
0 – 0 ×1/2 = 0
0 - 0×2 = 0
I- 0×1/2 = I
Table 2: Program
Profit/unit
Qty.
80 X
100 Y
0 S1
0 S2
0 S3
720 = 360 2 1800/4 = 450 900/1 = 900
311
Y
100
360
½
I
½
0
0
360÷1/2=720
S2 S3
0 0
360 540
3 5/2
0 0
1 0
0 I
360÷3=120 540÷5/2=216
30
0
−2 −1/ 2 −50
0
0
Net evaluation row 360 – 360 × 1/6 = 300 ½ - 3 ×1/6 = 0 1- 0× 1/6=1 ½ - -2 × 1/6 = 5/6 0 – 1 ×1/6 = - 1/6 0 – 0 ×1/6 = 0
540 – 360 × 5/6 = 240 5/2 –3 × 5/6 = 0 0 – 0 × 5/6 = 0 -1/2 - -2 ×5/6 = 7/6 0 – 1 × 5/6 = -5/6 1-0 × 5/6 = 1
Table 3:
80
100
0
0
0
Program
Profit/unit
Qty.
X
Y
S1
S2
S3
Y
100
300
0
I
5/6
-1/6
0
X
80
120
I
0
−2/3
1/3
0
S3
0
240
0
0
7/6
-5/6
I
0
0
-500/6
+100/6
+160/3
-80/3
Net evaluation row
=
180 6
= −
0
60 6
All the values of the net evaluation row of Table 3 are either zero or negative, the optimal program has been obtained. Here X = 120,
y = 300 and the maximum profit = 80×120 + 100× 300 = 9600 + 30,000 = Rs. 39,600.
Ans. 9: Formulation of Linear Programming (LP) model : Let X 1 and X 2 be the units of products A and B respectively which were manufactured and sold (within sales constraints) by the company in a month, by utilizing monthly available budgeted capacity in department A and B so as to maximize the profit of the company. The formulated LPP based on the given data is as under : Max Z = 80 x 1 + 100 x 2
(Refer to working note)
2 x 1 + 4x 2 < 1,400
--
Department P Constraint
5x 1 + 4x 2 < 2,000
--
Department Q constraint
X 1 < 400
--
Product A Sales constraint
312
X 2 < 400
--
Product B sales constraint
X 1 , X2 > 0 Graphical Solution : Draw the above four constraints by selecting X1 and X2 axes as shown in the diagram.
X2 - AXIS X1 < 400
(0,500)
X2 < 400
(0,350)
P (200, 250)
0
(400,0)
(700,0)
Put x 2 = 0 in (i), then x 1 = 700 Put x 1 = 0 in (i), then x 2 = 350 Put x 2 = 0 in (ii); then x 1 = 400 Put x 1 = 0 in (ii); then x2 = 500 The point of intersection of (i) and (ii) viz, P is given by (200, 250) The marked area represents the feasible area (common to all of the four constraints). The corner points of the identified feasible region are (0,0); (400,0); (200,250) and (0,350). According to Dantzig, the objective function is maximum or minimum at the corner points of the feasible region.
313
Z (0,0)
=
0,0
Z (400, 0)
=
32,000
Z (0, 350)
=
35,000
Z (200, 250)
=
41,000
The objective function has maximum contribution viz, Rs. 41,000 at the point (200, 250). Hence, the concern should manufacture and sell 200 units of A and 250 units of B product. Optimal contribution (Rs) (200 units x Rs. 80 + 250 units x Rs. 100)
41,000
Less : Fixed costs (Rs. 14,000 + Rs. 20,000)
34,000 _____ 7,000
Optimal profit Working note : Product A
Product B
Selling price per unit : (i)
300
200
Variable manufacturing costs
160
60
60
40
220
100
80
100
Sales commission Total variable cost per unit : (ii) Contribution per unit : (ii – I)
Ans. 11:
Let x1, x 2 x 3 be the number of units produced of products A, B and C respectively. Then the profit gained by the industry is given by Z = 3x 1 + 8x 2 + 2x 3 Here it is assumed that all the units of products A and B are sold. In first operation, A takes 3 h of manufacturer’s time and B takes 4 h of manufacturer’s time. Therefore, total number of hours required in first operation becomes. 3x 1 + 4x 2 In second operation, per unit of A takes 2 h of manufacturer’s time and per unit B takes 5 h of manufacturer’s time. Therefore, the total number of hours used in second operation becomes 3x 1 + 5x 2 Since there are 18 h available in first operation and 21 h in second operation, the restrictions become 3x 1 + 4x 2 ≤ 18
…… (1)
314
3x 1 + 5x 2 ≤ 21
…… (2)
Since the maximum number of units of C that can be sold is 5, therefore, X3 ≤ 5
…… (3)
Further, the company gets three units of by product C for every unit of product B produced, therefore X 3 = 3x 2
…… (4)
Now, the allocation problem of the industry can be finally put in the following linear programming problem: Maximise Z = 3x 1 + 8x 2 + 2x 3 Subject to the constraints 3x 1 + 4x 2 ≤ 18 3 x 1 + 5x 2 ≤ 21 x 3 ≤ 5, x 3 = 3x 2 x1, x2, x3 ≥ 0
Ans. 15:
Let X 1 , X 2 and X 3 respectively be the amounts in tons of grades A, B, and C used. The constraints are
(i)
Phosphorus content must not exceed 0.03% .02 X 1 + .04X 2 + 0.3 X 3 ≤ .03 (X 1 + X 2 + X 3 ) 2X 1 + 4 X 2 + 3X 3 ≤ 3 (X 1 + X 2 + X 3 ) or – X 1 + X 2 ≤ 0
(ii) Ash content must not exceed 3% 3X 1 + 2 X 2 + 5 X 3 ≤ 3 (X 1 + X 2 + X 3 ) or – X 2 + 2X 3 ≤ 0 (iii) Total quantity of fuel required is not more than 100 tons. X 1 + X 2 + X 3 ≤ 100 The Mathematical formulation of the problem is Maximize Z = 12 X 1 + 15X 2 + 14 X 3 Subject to the constraints: - X1 + X2
≤
0
- X2 + X3 ≤
0
X1 + X2 + X3
≤
X1, X2, X3 >
0
100
Introducing slack variable X 4 >0, X 5 >0, X 6 >0 12
15
14
0
0
0
Cb
Yb
Xb
Y1
Y2
Y3
Y4
Y5
Y6
0
Y4
0
-1
1*
0
1
0
0
0
Y5
0
0
-1
2
0
1
0
0
Y6
100
1
1
1
0
0
1
-12
-15
-14
0
0
0
Y1
Y2
Y3
Y4
Y5
Y6
Z Cb
Yb
Xb
315
15
Y2
0
-1
1
0
1
0
0
0
Y5
0
-1
0
2
1
1
0
0
Y6
100
2*
0
1
-1
0
1
-14
15
0
0
Z
-27
Cb
Yb
Xb
Y1
Y2
Y3
Y4
Y5
Y6
15
Y2
50
0
1
1/2
1/2
0
1/2
0
Y5
50
0
0
5/2*
1/2
1
1/2
12
Y1
50
1
0
1/2
-1/2
0
1/2
0
0
-1/2
3/2
0
27/2
Z Cb
Yb
Xb
Y1
Y2
Y3
Y4
Y5
Y6
15
Y2
40
0
1
0
2/5
-1/5
2/5
14
Y3
20
0
0
1
1/5
2/5
1/5
12
Y1
40
1
0
0
-3/5
-1/5
2/5
Z 0 0 0 8/5 1/5 The optimum solution is X 1 = 40, X 2 = 40 and X 3 = 20 with maximum Z = 1360.
68/5
Ans.16: 40
Cj Cj
Variable
0 0 0
X3 X4 X5 Zj Zj-Cj
Qty
Variable X3 X4 X2 Zj Zj-Cj
0
Ratio
X1
X2
X3
X4
X5
36 60 60
3 5 2
3 2 6
1 0 0
0 1 0
0 0 1
0
0 -40
0 -60
0 0
0 0
0 0
40
60
Table 2 0 0
0
X1 2 13/3 1/3 20 -20
X2 0 0 1 60 0
Cj Cj 0 0 60
Table 1 0 0
60
Qty 6 40 10 600
Cj
40
X3 1 0 0 0 0 Table 3 60
X4 0 1 0 0 0
X5 -½ -1/3 1/6 10 10
0
12 30 10
Ratio
3 120/13 30
0
0
316
Cj 40 0 60
Qty
Variable X1 X4 X2 Zj Zj-Cj
X1 1 0 0 40 0
3 27 9 660
X2 0 0 1 60 0
X3 ½ -13/6 -1/6 10 10
X4 0 1 0 0 0
X5 -1/4 3/4 1/4 5 5
Since all Zj –Cj are positive or zero, this is the optimum solution with, X1 =40 & X2 = 60 and optimum Z = 660. Note: Alternatively, Cj-Zj may be used whereby maximum positive value may be considered. Ans. 18: Under the usual notations where S1, S2, S3 are stock Variables, A4 = the artificial variable S4 = Surplus Variable We have, Max. Z = 100x 1 + 80x2 + 0S1 + 0S2 + 0S3 + 0S4 – M A4. S.t. 3x1 + 5x2 + S1 =
150
x2 + S2 =
20
8x1 + 5x2 + S3 =
300
x1 + x2 + - S4 + A4 = x1 x2 S1 Basis
Cj CB
S4
A4
100
80
0
0
0
0
-M
0
3
5
1
0
0
0
0
150
√
S2
0
0
1
0
1
0
0
0
20
√
S3
0
8
5
0
0
1
0
0
300
√
A4
-M
1
1
0
0
0
-1
1
25
√
-M
-M
0
0
0
M
-M
-25M
√
0
0
0
-M
0
Cj-Zj
(i)
S3
S1
Zj
Ans.20:
25 S2
100+M 80+M
√
Simplex Table Basis
Cj →
8
6
0
0
CB
x1
x2
s1
s2
(1 mark)
317
x1
8
1
0
x2
6
0
1
Zj
→
6
6
5
0
−5
Cj - Zj
NER
0
-⅙ ⅓ ⅔ -⅔
⅓ -⅙ 3 3
2 marks 1 marks
Note: Zj values are obtained by multiplying each row with cost and adding the values of the respective column as under: X1
X2
S1
X1
8X1=8
8X0=0
8 X 1/3 = 2.2/3
X2
6X0=0
6X1=6
6 X - 1/6 = - 1
Adding Zj
8
6
5/3
S2 6 8 X - 1/ = 1.1/3 6 X 1/3 = 2/3 2
Net Evaluation Row (NER) is obtained by deducting Zj from Cj as under: 8–8=0
6–6=0
0 – 5/3 = - 5/3 0 – 2/3 = - 2/3
Since the values of NER ar≤e 0, the solution represented by this tableau is optimal. (ii) X1 MI 60 X2 M II 48 Total optimal contribution Ans.21:
x x
S1 5/3 -
S2 2/3
Rs. 100 32 132
Let pi dj be the variable to denote the number of units of product from the ith plant to the jth destination, so that P1d1 = transport from plant P 1 to D1 P2d2 = transport from plant P 2 to D2 etc. Objective function Minimize z = 400 p1d1 + 600 p1d2 + 800 p1d3 + 1000 p2d1 + 1200 p2d2 + 1400 p2d3 + 500 p3d1 + 900 p3d2 + 700 p3 d3. Subject to: p1d1 + p1d 2 + p1d 3 ≤ 65 p 2 d1 + p 2 d 2 + p 2 d 3 ≤ 24 (Plant constraints) p 3 d1 + p 3 d 2 + p 3 d 3 ≤ 111
and
p1d1 + p 2 d1 + p 3 d1 ≥60 p1d 2 + p 2 d 2 + p 3 d 2 ≥ 65 (destination constraints)
318
p1d 3 + p 2 d 3 + p 3 d 3 ≥ 75 all pidj ≥ 0
Ans.22: Route I Residence HO
600
400
300
180
500
300
200
40
4
10
20
80
80
100
Residence Route II Residence Br. Residence No. of vehicles Max. capacity No. of passengers
220 260
Let i be the ith route, and j be the type of vehicle, so that S11 = no. of vans (vehicles on Route I, Type I) S12 = no. of 8 seater cars on Route I S13 = no. of 5 seater cars on Route I S21 = no. of vans ─ on Route II S22 = no. of 8 seater cars on Route II S 23 = no. of 5 seater cars on Route II Ans. 23:
Formulation. Let xi be the number of times cutting alternative i (j = 1,2, .....6) is employed. Minimise (waste produced) Z = 1x3 + 1x4 + 1x5 + 1x6 subject to 6x1 + 1x3 + 4x6
≤ 3000
3x1 + 3x2 + 1x3 + 4x5+ 2x6
≤ 2000
2x2 + 1x3 + 2x4 + 1x5+ 1x6
≤ 1500
1x3 + 1x4
≤ 1000
xj
≥ 0, for all j
Ans.24:
The profits for each arrangement are: Economy = 6.00 – 4 (0.20) – 2(0.25) – 8 (0.15)
= Rs. 3.50
May time
= 8.00 – 8 (0.20) – 5 (0.25) – 10 (0.15) – 4 (0.22)
= Rs. 2.77
Spring colour Deluxe rose
= 10.00 – 9 (0.20) – 10 (0.15) – 9 (0.20) – 6 (0.22) = 12.00 – 12 (0.20) – 12 (0.20) – 12 (0.22)
= Rs. 3.58 = Rs. 4.56
Let x1, x2, x3, x4 be number of units arrangements of type Economy, May time, Spring colour & Deluxe rose. Then the objective is Maximise Z = 3.5x1 + 2.77x2 + 3.58x3 + 4.56x4 subject to
4x 1 + 9x3 + 12x4
≤ 800
319
2x 1 + 5x2
≤ 456
8x 1 + 10x2 + 10x3
≤ 4000
8x
2
+ 9x+3 12x
≤ 920
4x 2 + 6x3 + 12x4
≤ 422
All xi's ≥ 0
Ans. 26: The information given in the question can be presented in the following tabular form. X1
X2
X3
Selling price (per kg)
Y1
1/2
1/4
1/4
Rs.90
Y2
3/7
2/7
2/7
Rs.100
Y3
--
2/3
1/3
Rs.120
Cost of raw material (Per kg)
Rs.30
Rs.50
Rs.120
Availability of raw material
20 kg
15 kg
10 kg
Products
Raw material (in kg) required to produce one kg of product
From the above table, the cost of producing 1 kg of Y 1 , Y 2 and Y 3 can be calculated as given below: Cost to produce 1 kg of Y 1
=
½ Rs.30 + ¼ Rs.50 + Rs.120
=
Rs.15 + Rs.12.50 + Rs.30
=
Rs.57.50
∴ Profit per kg of Y 1
=
Rs.90 – Rs.57.50 = Rs.32.50
Similarly, cost to produce 1 kg of Y 2
=
3/7 Rs.30 + 2/7 Rs.50 + Rs.120
=
1/7 (Rs.90 + Rs.100 + Rs.240)
=
Rs.430/7 = Rs.61.43
Profit per kg of Y 2 = Rs.100 – Rs.61.43 = Rs.38.57 and cost to produce 1 kg of Y 3 = 2/3 Rs.50 + 1/3 Rs.120 = Rs.220/3 = Rs.73.33 Profit per kg of Y 3 = Rs.120 – Rs.73.33 = Rs.46.67 Let the manufacturer produce y 1 , y 2 and y 3 units of the products Y 1 , Y 2 and Y 3 respectively. Since the manufacturer wants to maximise the profit, the objective function is given by Maximise Z = 32.50 y 1 + 38.57 y 2 + 46.67 y 3 ½ y 1 + 3/7 y 2 ≤ 20 or 7 y 1 + 6 y 2 ≤ 280 ¼ y 1 + 2/7 y 2 + 2/3 y 3 ≤ 15 or 21 y 1 + 24 y 2 + 56 y 3 ≤ 1,260 ¼ y 1 + 2/7 y 2 + 1/3 y 3 ≤ 10 or 21 y 1 + 24 y 2 + 28 y 3 ≤ 840 where Y 1 , Y 2 and Y 3 ≥ 0 Ans. 27: Let
x 1 = No. of units of product 1 produced X 2 = No. of units of product 2 produced
320
X 3 = Amount of money borrowed The profit contribution per unit of each product is given by the selling price minus the variable cost of production. Total profit ay be computed by summing up the profits from producing the two products minus the cost associated with borrowed funds (if any):The objective function is thus stated as Maximize Z = (14 – 10 ) x 1 + (11 – 8) X 2 - 0.05 X 3 = 4 x 1 + 3 X 2 - 0.05 X 3 (Note that the interest rate is 20% per annum, hence 5% for a period of three months) Subject to the following constraints: The production capacity constraints for each department, as given by table 1 are: 0.5x 1 + 0.3X 2 ≤ 500 0.3x 1 + 0.4X 2 ≤ 400 0.2x 1 + 0.1X 2 ≤ 200
……….(1) ……….(2) ……….(3)
The funds available for production include both Rs.3,00,000 cash that the firm possesses and any borrowed funds maximum up to Rs.2,0,000. Consequently production costs. The constraint expressing this relationship is Funds required for production ≤ Funds available. ≤ Rs. 3,00,000 + X 3 i.e 10x 1 + 8X 2 ≤ Rs. 3,00,000 or 10x 1 + 8X 2 - X 3
……….(4)
The borrowed funds constraint (from condition (iii) of the Question) is X 3 ≤ Rs. 2,00,000 ……….(5) The constraint based on the acid-test condition is developed as follows:Surplus cash on hand after production + Accounts receivable Bank Borrowings + Interest accrued thereon i.e. (3,00,000 +X 3 - 10x 1 – 8X 2 ) + 14x 1 + 11X 2 (X 3 + 0.05X 3 )
≥1
≥1
or, 3,00,000 +x3 +4x1 +3x2 > (x3 +0.05x3) Or, - 4x 1 - 3X 2 + 0.05X 3 ≤ 3,00,000
……….(6)
Thus, the linear programming problem is given by Maximize Z = 4x 1 + 3X 2 - 0.05X 3 Subject to
0.5x 1 + 0.3X 2 ≤ 500 0.3x 1 + 0.4X 2 ≤ 400 0.2x 1 + 0.1X 2 ≤ 200 10x 1 + 8X 2 - X 3 ≤ Rs. 3,00,000 X 3 ≤ Rs. 2,00,000 - 4x 1 – 3X 2 + 0.05X 3 ≤ Rs. 3,00,000
……….(1) ……….(2) ……….(3) ………..(4) ……….(5) ……….(6)
321
Where x 1 X 2 X 3 ≥ 0. Ans. 28: Let x 1 , x 2 and x 3 be the number of acres allotted for cultivating radish, mutter and potato respectively. Since the average yield of radish is 1,500 kg per acre, and the selling price for radish is Rs.5/kg hence the selling amount which the agriculturist gets from one acre is: Rs.5 × 1,500 = Rs.7,500 To produce 100 kg of radish, the manure cost is Rs.12.50, so the manure cost per acre will be Rs.12.50 × 1,500/100 = Rs.12.50 × 15. Labour cost per acre for radish = Rs.40 × 6 = Rs.240 Profit per acre for radish = Rs.7,500 – Rs.12.50 × 15 – Rs.240 = Rs.7,072.50 Similarly, the selling price, manure cost, labour cost and profit per acre of land for mutter and potato are also calculated and presented in the following table. Per acre
Radish
Mutter
Potato
Selling price
Rs.5 × 1,500 = Rs.7,500
Rs.4 × 1,800 = Rs.7,200
Rs.5 × 1,200 = Rs.6,000
Manure cost
Rs.12.50× 1,500
Rs.12.50× 1,800
Rs.12.50× 1,200
100
100
80
Labour cost
Rs.40 × 6 = Rs.240
Rs.40 × 5 = Rs.200
Rs.40 × 6 = Rs.240
Profit
(Rs.7,500-Rs.187.50 – Rs,240) = Rs. 7,072.50
(Rs.7,200 – Rs.255 Rs.200) = Rs.6,775
Rs.6,000–Rs.187.50 – Rs.240) = Rs. 5572.50
Since, the agriculturist wants to maximise the total profit, hence the objective function of the problem is given by: Maximise Z = 7,072.5x 1 + 6,775x 2 + 5572.5x 3 Subject to following constraints: x 1 + X 2 + X 3 ≤ 125 …… (1) (land constraint) 6x 1 + 5x 2 + 6x 3 ≤ 500 Where x 1 , x 2 and x 3 ≥ 0 Ans. 29: Maximize Z
= 60 (9x 1 + 5x2) + 90 (7x 1 + 9x2) = 1170x1 + 1110x2
Subject to 9x1 + 5x2 ≥ 500 commitment for A 7x1 + 9x2 ≥ 300 commitment for B 5x1 + 3x2 ≤ 1500 availability of Q
…… (2) (man day constraint)
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7x1 + 9x2 ≤ 1900 availability of P 2x1 + 4x2 ≤ 1000 availability of R and x1 ≥ 0, x2 ≥ 0. Ans. 30: Let x 1 , X 2 and X 3 denote the number of P III, P II and Celeron Computers respectively to the manufactured in the company. The following data is given: P III
P II
Celeron
Selling Price per unit (Rs.)
3,000
5,000
15,000
Labour, Material and other Variable Costs p.u. (Rs.)
2,000
4,000
8,000
Profit per unit (Rs.)
1,000
1,000
7,000
From the data given for time required for various models and the total number of hours available for machine time and assembly time, we get the following constraints: 20x 1 + 15x 2 + 12x 3 ≤ 1,000 (Machine Time Restriction) 5x 1 + 4x 2 + 3x 3 ≤ 1,500 (Assembly Time Restriction) The level of operations in the company is subject to availability of cash next month i.e.; the cash required for manufacturing various models should not exceed the cash available for the next month. The cash requirements for x 1 units of P III, x 2 units of P II and x 3 units of Celeron computers are: 2,000x 1 + 4,000 x 2 + 8,000x 3
…… (1)
The cash availability for the next month from the balance sheet is as below: Cash availability (Rs.)
Cash balance (Rs. 2,10,000)
Loan to repay to Nationalized bank (Rs. 50,000) Interest on loan from XYZ cooperative bank and Nationalized bank (Rs. 1500)
0.18 × 2,00,000 Interest on long term loans 12 Salary to staff (Rs. 15,000) Or, Cash availability
= Rs. 2,10,000-(Rs. 50,000 + Rs. 1,500 + Rs. 3,000 + Rs. 15,000)
= Rs. 1,40,500
..…. (2)
Thus, from (1) and (2), 2000 X1 + 4000 X2 + X3 < Rs. 1,40,500 The company has also promised to deliver 3 P III, 2 P II and 5 Celeron computers to M/s. Kingspen Ltd. Hence, X1 > 3, X2 > 2, X3 > 5 Since the company wants to maximize the profit, hence the objective function is given by: Maximize Z = 1000X1 + 1000X2 + 7000X3- (Rs. 15000 + Rs. 3000 + Rs. 1500) The LP formulation of the given problem is as follow: Maximize Z = 1000 X1 + 1000X2 + 7000 X3 – (Rs. 15000 + Rs.15000) Subject to the constraints: 20X1 + 15X2 + 12X3 < 1000 5X1 + 4X2 + 3X3 < 1500
323
2000 X1 + 4000 x2 + 8000 X3 < Rs. 1,40,500 X1 > 3, X2 > 2, X3 > 5 X1, X2 and X3 can take only positive integral values. Ans. 31: Let the firm produce x 1 units of product A, x 2 units of products B and x 3 units of product C. The profit per unit of products A, B and C is Rs. 50, and Rs. 80 respectively. Since the objective of the firm is to maximize the profit, therefore, the objective function is given by Maximize Z = 50x 1 +50x 2 +80x 3 The firm uses two types of raw materials I and II of which 5,000 and 7,500 units respectively are available. As per the given data, the raw material constraints can be formulated as given below: 3x 1 +4x 2 +5x 3 < 5,000 and 5x 1 +3x 2 +5x 3 < 7,500
………….. (i) (ii)
The labour time for each unit of product A is twice that of product B and three times that of product C. Also the entire labour force can produce the equivalent of 3,000 units. ∴ X1 +
X2 X3 < 3,000 + 2 3
or, 6x 1 +3x 2 +2x 3 < 18,000
(iii)
The minimum demand of the three products is 600, 650 and 500 units respectively. Hence, x 1 > 600, x 2 > 650 and x 3 > 500 Since the ratios of the number of units produced must be equal to 2:3:4, therefore, ½ x 1 = 1/3 x 2 , and 1/3 x 2 = ¼ x 3 or, 3x 1 = 2x 2 and 4x 2 =3x 3
(iv)
The linear programming model can be formulated as follows: Maximize Z = 50x 1 +50x 2 +80X 3
(v)
Subject to the constraints: 3x 1 +4x 2 +5x 3 < 5,000 5x 1 +3x 2 +5x 3 < 7,500 6x 1 +3x 2 +2x 3 < 18,000 3x 1 = 2x 2 and 4x 2 =3x3 x 1 >600, x 2 > 650 & x 3 > 500. Ans. 32: Renco Foundries has to decide the amount of funds to be allocated to projects A, B, C, D, E and money market instruments. Let us define the decision variables as
324
a b c d e Si (for i = 0,1,2)
: : : : : :
Rs. Invested in investment A Rs. Invested in investment B Rs. Invested in investment C Rs. Invested in investment D Rs. Invested in investment E Rs. Invested in money market instruments at time i
The objective of Renco Foundries is to draw up the capital budget in such a way that will “maximize cash on hand at time 3”. Now at time 3, the cash on hand for Renco Foundries will be the sum of all cash inflows at time 3. Since the firm earns interest at 8% p.a. by parking the un-invested funds in money market instruments, hence Rs. S 0 which are invested in these instruments at time 0 will become 1.08 S 0 at time 1. Similarly an investment of Rs. S1 at time 1 will become 1.08 S 1 at time 2, and an investment of Rs. S 2 at time 2 will become 1.08 S 2 at time 3. From the table giving the description of various investments, it can be computed that at time 3, Cash on hand
= a×Re. 0+b×Re.1+c× Re. 0+d× Rs.1.9+ e× Rs. 1.5+ 1.08S 2 = Rs. (b+1.9d+1.5e+1.08S 2 )
The objective of Renco Foundries is to maximize the cash on hand at time 3. hence the objective function will be Maximize Z = b+ 1.9d+ 1.5e +1.08 S 2 …………….(i)
t ………..(ii)
It may be noted that Cash available for investment at time t = cash on hand at time
At time 0, funds to the tune of Rs. 1,00,000 are available for investment. From the table, it can be seen that funds are invested in investment A, C, D and S 0 at time 0. Hence, a+c+d+S 0 = 1,00,000………………….(iii) At time 1, Rs. 0.5 a, Rs. 1.2 c and Rs. 1.08 S0 will be the available returns as a result of investments made at time 0. From the table Rs. B and Rs. S1 are invested in investment B and money market instruments respectively at time 1. Using equation (ii), we get 0.5a+ 1.2c+ 1.08S 0 = b+ S 1 ……………….(iv) At time 2, Re. 1 a, Rs. 0.5 b and Rs. 1.08S 1 will be available for investment. However, Rs. E and Rs. S2 are invested at time 2………………………………..(v) Further, since the firm will not commit an investment exceeding Rs. 75,000 in any project, we get the following constraints:
325
a b c d e
< < < < <
75,000 75,000 75,000 75,000 75,000
(vi) (vii) (viii) (ix) (x)
Also a, b, c, d, e and Si (for i = 0, 1, 2) are all > 0 Combining all the constraints, the linear programming model for the Renco Foundries is as given below: Maximize Z = b+ 1.9d+ 1.5e+ 1.08S 2 Subject to following constraints a+c+d+S0 = 1,00,000 0.5a +1.2c +1.08 S 0 = b+S 1 1a+ 0.5b +1.08S 1 = e+ S 2 a b c d e
< < < < <
75,000 75,000 75,000 75,000 75,000
a, b, c, d, e and si (I =0, 1, 2) are all > 0 Ans. 33: Let x 1 and x 2 be the amount to be invested in first and second stock portfolio respectively. The average rate of return for first portfolio is 10% and for second portfolio, it is 20%. Since the company wishes to maximize the return from investment, the objective function is as given below: Maximise Z = 0.1x 1 + 0.2x 2 The maximum amount available for investment is Rs.1,00,000. Hence, x 1 + x 2 ≤ 1,00,000
…… (1)
Further, the maximum investment allowed in either portfolio set is Rs.75,000. Therefore, x 1 ≤ 75,000
…… (2)
and x 2 ≤ 75,000
…… (3)
The first portfolio has a risk rating of 4 (on a scale from 0 to 10) and the second has 9. The company will not accept a risk factor above 6. Therefore, 4x 1 + 9x 2 ≤ 6 (x 1 +x 2 )
…… (4)
Further, the company will not accept an average rate of return below 12%. Hence, 0.1x 1 + 0.2 x 2 ≥ 0.12 (x 1 + x 2 )
…… (5)
Also, x 1 and x 2 ≥ 0
…… (6)
The linear programming model for the given problem can now be formulated as follows: Maximise Z = 0.1x 1 + 0.2x 2 Subject to the constraints x 1 +x 2 ≤ 1,00,000
…… (1)
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x 1 ≤ 75,000
…… (2)
x 2 ≤ 75,000
…… (3)
4x 1 + 9x 2 ≤ 6 (x 1 + x 2 ) or – 2x 1 + 3x 2 ≤ 0
…… (4)
0.1x 1 + 0.2x 2 ≥ 0.12 (x 1 +x 2 ) or – 0.02x 1 + 0.08x 2 ≥ 0
…… (5)
where x 1 , x 2 ≥ 0 The problem is solved graphically below:
The point of intersection for the lines - 2x 1 + 3x 2 = 0 and x 1 + x 2 = 1,00,000 is given by B (60,000, 40,000) The point of intersection for the lines X 1 = 75,000 and x 1 + x 2 = 1,00,000 is given by C (75,000, 25,000) Similarly, the lines x 1 = 75,000 and – 0.02x 1 + 0.08x 2 = 0 intersect at point D (75,000, 18,750) Thus, the feasible region is bounded by ABCDA and feasible points are A (0, 0); B(60,000, 40,000); C(75,000, 25,000) and D(75,000, 18,750). Value of the objective function at the above mentioned feasible points is calculated below: At A, Z=0 At B, Z=0.1 × 60,000 + 0.2 × 40,000 = 6,000 + 8,000 = Rs.14,000 At C, Z=0.1 × 75,000 + 0.2 × 25,000 = 7,500 + 5,000 = Rs.12,500
327
At D, Z=0.1× 75,000 + 0.2 × 18,750 = 7,500 + 3,750 = Rs.11,250 We find that the value of the objective function is maximum (Rs.14,000) at point B(60,000, 40,000). Hence, the company should invest Rs.60,000 in first portfolio and Rs.40,000 in second portfolio to achieve the maximum average rate of return of Rs.14,000. Ans. 35: Contribution analysis: Products
A
B
(Rs.)
(Rs.)
500
450
Direct Materials
100
100
Direct Labour
80
40
Painting
30
60
Variable Overheads
190
175
Total variable costs (B)
400
375
Contribution (A – B)
100
75
Selling price (A) Variable costs:
Direct Material per unit
100/25 = 4 kg.
100/25 = 4 kg.
Direct Labour hour per unit
80/20 = 4 hours
40/20 = 2 hours
Painting hour per unit
30/30 = 1 hour
60/30 = 2 hours
Let A be the units to be produced of product A and B be the units to be produced of product B. LP Problem formulation: Z Max
100A + 75B
Maximisation of contribution
Subject to: 4A + 4B ≤ 480
Raw material constraint
4A + 2B ≤ 400
Direct Labour hour constraint
A + 2B ≤ 200
Painting hour constraint
A, B ≥ 0
Non negativity constraint
Raw Material Constraint :
Put B = 0, A = 120 Put A = 0, B = 120
Direct Labour Constraint :
Put B = 0, A = 100 Put A = 0, B = 200
328
Painting Constraint
:
Put B = 0, A = 200 Put A = 0, B = 100
The graphical representation will be as under:
Q Intersects 4A + 2B = 400
(1)
and 4A + 4B = 480
(2)
Subtracting (2) from (1), we get −2B = −80 ⇒ B = 80/2 = 40 Putting value of B in (1), we get 4A + 2 × 40 = 400 ⇒ A=
400 − 80 = 80 4
R Intersects 4A + 4B = 480 2B = 200
(3) and A +
(4) Multiplying (4) by (2) and then subtracting
from (3), we get 2A = 80 ⇒ A = 40 Putting the value of A in (4), we get 2B = 200 – 40 ⇒ B = 80.
329
Evaluation of corner points: Point
Products A
Contribution B
Total Contribution
A (Rs.)
B (Rs.)
100 per unit
75 per unit
Rs.
P
0
100
0
7,500
7,500
Q
80
40
8,000
3,000
11,000
R
40
80
4,000
6,000
10,000
S
100
0
10,000
0
10,000
Optimal product mix is Q Product
Units
Contribution Rs.
A
80
8,000
B
40
3,000
Total contribution
11,000
Less: Fixed costs 400 D.L. Hrs. × Rs. 17.50
7,000
Optimal Profit
4,000
(iii) If the painting time can be sold at Rs. 40 per hour the opportunity cost is calculated as under: A
B
(Rs.)
(Rs.)
Income from sale per hour
40
40
Painting variable cost per hour
30
30
Opportunity cost
10
10
Painting hours per unit
1
2
Opportunity cost
10
20
100 – 10 = 90
75 – 20 = 55
Revised contribution
Hence, modification is required in the objective function. Re-formulated problem will be:
330
Z Max.
90A + 55B
Maximisation of contribution
4A + 4B ≤ 480
Raw Material constraint
4A + 2B ≤ 400
Direct Labour hour constraint
A + 2B ≤ 200
Painting hour constraint
A, B ≥ 0
Non-negativity constraint
Subject to:
Ans 40: Dual: Minimise
140u1 + 120u2 + 50u3
S.T.
6u1 + 10u2 + 10u 3 ≥ 100 4u1 + 10u2 + 12u 3 ≥ 90 8u1 + 2u2 + 6u3 ≥ 40 4u1 + 6u2 + 2u3 ≥ 60 u 1, u 2 u 3 u 4 ≥ 0
331
Transportation Ans. 6 (a) 3 4 8
20 20 ---
20
4
6
----
20
---
40
30
60
6
30
3
40 (ii)
--
9
50
5
120
30
Initial allocation under NW corner rule is as above. Initial cost: 20×3 = 60 20×4 = 80 20×4 = 80 30×3 = 90 150 30×5 = 460
(a) 3 4 8
20 20 ---
--
9
20
4
40
50
1
1
4
----
20
3
---
40
0
0
2
30
60
2
2
2
6
30
3
6
5 30
1 1
1
1 Initial solution
20×3 20×4 50×3 20×6 10×5
1 = = = = =
60 80 150 120 __100 __460
Checking for optimality 3 4
6 3
V1 =3
U1 = 0
v2 = 3
5 v3 = 5
U2 = 1 U3 = 0
332
Ui+ vj
3
5
0
4
1
3 3
0 3
5
∆ij = Cij- (ui-vj)
5 ∆ij > 0
6 0
1 ∴ Solution is optimal
Conclusion: The solution under VAM is optimal with a zero in R 2 C 2 which means that the cell C 2 R 2 which means that the cell C 2 R 2 can come into solution, which will be another optimal solution. Under NWC rule the initial allocation had C 2 R 2 and the total cost was the same Rs. 460 as the total cost under optimal VAM solution. Thus, in this problem, both methods have yielded the optimal solution under the 1st allocation. If we do an optimality test for the solution, we will get a zero for ∆ij in C 3 R 2 indicating the other optimal solution which was obtained under VAM. Ans. 8 The new transportation costs table, which consists of both production and transportation costs, is given in following table. Store
Factories
P
Q
R
S
Supply
A
2+2=4
4+2=6
6+2=8
11+2=13
50
B
10+3=13
8+3=11
7+3=10
5+3=8
70
C
13+1=14
3+1=4
9+1=10
12+1=13
30
D
4+5=9
6+5=11
8+5=13
3+5=8
50
Demand
25
35
105
20
200 185
Since the total supply of 200 units exceeds the total demand of 185 units by 200-185 =15 units of product, there fore a dummy destination (store) is added to absorb the excess supply. The associated cost coefficients in dummy store are taken as zero as the surplus quantity remains lying in the respective factories and is, in fact, not shipped at all. The modified table is given below. The problem now becomes a balanced transportation one and it is a minimization problem. We shall now apply Vogel’s Approximation method to fine an initial solution.
333
P A
Q
25
5 4
B
R 20
Dummy
Supply
Difference
13
0
50/25/20/0
42225
8
0
70/0
822222
10
13
0
30/0
46____
15
20
15
50/35/15/0
811335
6
13
S 8
11
70 10
C
14
30 4
D
9
11
13
8
0
Demand
25/0
35/5/0
105/85/15/0 20/0
15/0
Difference
5
2
2
0
0
5
2
2
0
-
5
5
2
0
-
-
5
2
0
-
-
-
2
0
-
200
The initial solution is shown in above table. It can be seen that 15 units are allocated to dummy store from factory D. This means that the company may cut down the production by 15 units at the factory where it is uneconomical. We will now test the optimality of the solution. The total number of allocations is 8 which is equal to the required m+n-1 (=8) allocation. Introduce u i’s, v j’ s, i= (1,2,- - - - -4) and j =(1,2,- - - -5) ∆ ij =c ij -(u i +v j ) for allocated cells. We assume that u 4 =0 and remaining u j’ s, v j’ s and ∆ ij ’s are calculated below” P A
Q
25
5 4
B
13
11
14
D
70
30
9 0
8
10
11
0
13
15
+12
13
Ui
50
U 1 = -5
70
U2 =
30
U 3 = -7
50
U4 = 0
+3 0
20
Supply
+5
+3
+4
0
0 +10
10
4
Dummy
13 8
+3
+1
S
20 6
+7 C
R
+7 15
8
0
Demand
25
35
105
20
15
Vj
V 1 =9
2
2
0
0
Please not that figures in top left hand corners of the cell represent the cost and the one in the bottom right hand corner of the non basic cell are the values of ∆ ij =c ij -[(u i +v j )] Since opportunity cost in all the unoccupied cells is positive, therefore initial solution is an optimal solution also. The total cost (transportation and production together) associated with this solution is Total cost
= 4×25+6×5+8×20+10×70+4×30+13×15+8×20+0×15 = 100+30+160+700+120+195+160 = Rs.1,465/-
Ans.9:
334
The given problem is an unbalanced transportation problem since the availability of trailers (= 10+4+6+5=25) is less than the requirement (=13+10+6+6=35). Therefore, it is first converted into a balanced problem by adding a dummy terminal with an availability of 10 trailers and cost elements for various plants as zero. The problem becomes as given below. Plants Terminals
A
B
C
D
Availability
U
20
36
10
28
10
V
40
20
45
20
4
W
75
35
45
50
6
X
30
45
40
25
5
Dummy
0
0
0
0
10
Requirement
13
10
6
6
The objective of the company is to minimize transportation cost. To achieve this objective, let us find an initial feasible solution by applying Vogel’s Approximation Method to the above matrix. Plants Terminals U
A
B
C
3
D
6 20
V
Difference
1
36
10
28
10/4/1/0
10/10/8/8
20
45
20
4/0
0/0/0/-
35
45
50
6/0
10/10/15/15
4 40
W
6 75
X Dummy
Availability
5 30
35
40
25
5/0
5/5/5/5
0
0
0
0
10/0
0/-/-/-
10
Requirement
13/3/0
10/6/0
6/0
6/1/0
Difference
20
20
10
20
10
15
30
5
10
15
0
5
10
0
-
5
The initial solution is as given below which is tested for optimality.
335
Plants Terminals U
A
B
C
3
D
6 20
V
1
36
10
28
10
20
45
20
4
35
45
50
6
4 40
W
6 75
X Dummy
Availability
5 30
35
40
25
5
0
0
0
0
10
10
Requirement
13
10
6
6
The number of allocation is 7 which is one less than the required m+n-1 (=8) allocations. Introduce a very small quality e in the least cost independent cell (Dummy, B0. Let us also introduce u j , v j ; I- (1,2 – 5) j = (1,2,3,4) such that ∆ ij = cij-(u1+v j ) for allocation cells. We assume that u1=0 and remaining u i ’s, v j ’s and ∆ ij’ ’s are calculated as below: Terminals U
A 3
B +θ
16
20
4
40
-θ
6
13 10
-θ 0
vj’s
20
45 40 10
50
15
25
-3
0
-20
-8
0 20
0
5
35 +θ
20 7
33
e
0
+θ
45
35 18
28 -8
20
30 Dummy
35
u i ’s -θ
10
20
75 X
1
36
40 W
D
6
20 V
C
0 10
28
Since some of the ∆ ij’ ’s are negative, the above solution is not optimal. Introduce in the cell (V,D) with the most negative ∆ ij an assignment θ. And the reallocated solution as obtained from above is given below. The values of u i ’s and v j’ ’s and ∆ ij’ ’s also calculated.
336
Terminals U
A
B
4
16
20
3
40 5 9
40 10 0
20
0
50
15
25
5
0
-20
0
0
20
20
5
35
0 v j ’s
45 25
1
0
15
35
30 Dummy
45 20
10
28 1
20
75 X
10 35
6
u i ’s
8
36
40 W
D
6
20 V
C
10
20
-20
Since all ∆ Ij’s for non basic cells are positive, therefore, the solution obtained above is an optimal one. The allocation of terminals to plants and their cost is given below. Terminal Plant Cost U
A
4 × Rs.20
= Rs.80
U
C
6 × Rs.10
= Rs.60
V
B
3 × Rs.20
= Rs.60
V
D
1 × Rs.20
= Rs.20
W
B
6 × Rs.35
= Rs.210
X
D
5 × Rs.25
= Rs.125 = Rs.555
Ans. 10:
Answer (a) The problem may be treated as an assignment problem. The solution will be the same even if prices are halved. Only at the last stage, calculate the minimum cost and divide it by 2 to account for fall in oil prices. A
B
C
X
15
9
6
Y
21
12
6
Z
6
18
9
Subtracting Row minimum, we get A
B
C
X
9
3
0
Y
15
6
0
Z
0
12
3
Subtracting Column minimum,
337
A
B
C
No of lines required to cut Zeros = 3 Cost / u Allocation:
Units
Cost
Revised
X
B
9
10
90
45
Y
C
6
10
60
30
Z
A
6
10
60
30
210
105
Minimum cost = 105 Rs. Alternative Solution I Least Cost Method
X–BY–CZ–A
Test for optimality No. of allocation = 3 No. of rows m =3, no. of column = 3
Cost
338
m+n–1=3+3–1=5 2 very small allocation are done to 2 cells of minimum costs, so that , the following table is got : A
e
6
21
12
10
6
6
18
15
Y 10
10
C
9
X
Z
B
9
e
m +n–1=5 Now testing for optimality ui 9
e 6
6 vj 6 ui + vj for unoccupied cells
e 9
0 0
6
A
B
C
X
6
-
-
Y
6
9
-
Z
-
9
-
A
B
C
X
9
-
-
Y
15
3
-
Z
-
9
-
Diff = Cij – (ui + vj)
All Δij > 0, Hence this is the optimal solution.
0
339
Original Costs
Reduced Costs due to Oil Price
Qty.
Cost
X–B
9
4.5
10
45
Y–C
6
3
10
30
Z–A
6
3
10
30 105
Total cost of transportation is minimum at Rs.105 Alternative Solution II
No. of rows + no. of column – 1 m+n–1=5 No. of allocation = 3
340
Hence add ‘e’ to 2 least cost cells so that
Now m + n – 1 = 5 Testing for optimality, ui, vj table A
B
X
C 4.5
ui e
Y
0
3
Z
3
vj 3 ui + vj for unoccupied cells
0
e 4.5
0
3
3
-
-
3
4.5
-
-
4.5
-
Cij
u i+vj
7.5
-
-
3
-
-
11.5
6
-
3
4.5
-
-
-
4.5
-
9 Δij = Cij – (ui + vj) 4.5
-
-
11.5
1.5
-
8.5 4.5 All Δij > 0. Hence the solution is optimal. Qty.
Cost/u
Total Cost
X–B
10
4.5
45
Y–C
10
3
30
Z–A
10
3
30
Total minimum cost at revised oil prices
105
341
Ans.11:
The concept tested in this problem is Degeneracy with respect to the transportation problem. Total of rows and columns = (4 + 5) = 9. Hence, the number of allocations = 9 – 1 = 8. As the actual number of allocation is 7, a ‘zero’ allocation is called for. To resolve this, an independent cell with least cost should be chosen. R4C2 has the least cost (cost = 3), but this is not independent. The next least cost cell R4C3 (cost = 5) is independent. 9
2
5
6
2
C1
C2
C3
C4
C5
8
0R1
11
6
2
8
6
2
9
12
9
6
7
7
10
0R2
9
8
−2R3
7
6
3
2
0R4 Total
0
2
9
3
5
6
11
12
8
8
8
4
Total 4 18 10 8
4 40
Forming Equations through allocated cells Basic equation
Setting R1 = 0 other values
R1 + C2 = 2
Setting R1 = 0, C2 = 2
R1 + C4 = 6
C4 = 6
R1 + C5 = 2
C5 = 2
R2 + C1 = 9
R2 = 0
R3 + C3 = 3
R3 = −2
R4 + C1 = 9
C1 = 9
R4 + C3 = 5
C3 = 5
R4 + C4 = 6
R4 = 0
Evaluate unallocated cells R1C1 = 11 − 0 − 9 = 2
R3C1 = 7 + 2 − 9 = 0
R1C3 = 8 − 0 − 5 = 3
R3C2 = 6 + 2 − 2 = 6
R2C2 = 9 − 0 − 2 = 7
R3C4 = 7 + 2 − 6 = 7
R2C3 = 12 − 0 − 5 = 7
R3C5 = 7 + 2 − 2 = 7
R2C4 = 9 − 0 − 6 = 3
R4C2 = 3 − 0 − 2 = 1
R2C5 = 6 − 0 − 2 = 4
R4C5 = 11 − 0 − 2 = 9
Since all the evaluation is 0 or +ve, the optimal solution is obtained. Optimal cost = (8 × 2) + (6 × 6) + (4 × 2) + (10 × 9) + (8 × 3) + (2 × 9) + (0 × 5) + (2 × 6) = 16 + 36 + 8 + 90 + 24 + 18 + 10 + 12 = Rs. 204. Note: As regards allocation of the zero values, the solution to the above problem is also obtained by allocating the zero value in other independent cells such as R1C3, R2C2, R2C3, R3C1, R3C2, R3C4,
342
R3C5. In such situation there will be one more iteration.
Ans. 12 The optimum distribution for this company to minimize shipping costs Availabilities
= 160 +150 +190 = 500
Requirements
= 80 +90 +110 +160 = 440
Availabilities –Requirement
= 500 – 440 = 60
Therefore, a dummy warehouse H is introduced, and initial solution is obtained below by VAM in just one table. D
E
F
G
H
Available
160 A
42
48
38
B
40
e
37
80
0
10 49
52
160/0
37/1/1/1
150/90/10/0
48*/9/11*/1
60 51
90
Diff.
0
100
C
39
38
40
43
0
Reg.
80/0
90/0
110/10/0
160/0
60/0
Diff.
0
0
0
0
0
1
10*
2
6*
0
190/100/0
38/1/1/3
since there are only 6 (one less than m+n –1) allocations, an infinitesimally small allocation e is placed in the least cost and independent cell (1, 5). This solution is tested for optimality below. (N.B.: if allocations were m +n –2 we would place two e’s, e , which e2 are virtually zero in the 2 least cost independent cells). This device enables us to apply to optimality test on (m +n –1) allocations. Vj 37 40
52 38
40
Vj
50
40
52
50
37
0
0
52
(ui + vj) matrix 37 25
–1 11
0
–12
28 –2
0
40
50
2
0
–12
–14 14 18
12
Δ ij m atrix
Since there are –ve Äij ‘s the initial solution is not optimal. Reallocation is done below by ticking the most -ve Äij cell (1, 3) and involving it in the loop. θ mx
343
√ 160 e ⎧e − θ = 0 ⎫ ⎪ ⎪ min ⎨10 − θ = 0 ⎬ ⎪ ⎪ ⎩= e
80
10 90
60
100
⎭ e
80
Note that the maximum that can be tansferred to the ticked cell is e. Since e is infinitestimally small it leaves other corner allocations unaffected. (Intermediate i.e. non corner allocations are never altered in the process of reallocations). 160
10 90
Reallocation
60
100
This solution is tested for optimally below : 38 40
37
38
52 38
-12
0
40 -1
-52
36
–14
50
51
28
(ui+vj) matrix)
39
16
52
40
-2 26
0
–12
12
14
–1
0
11
Δ j matrix
4
12
Since there are –ve ΔØ, this solution too is not optimal. Reallocation is done below : 160
⎛10 − θ = 0 ⎞ ⎟ ⎝ 90 − θ = 0 ⎠
θmax = min ⎜
80
√
10–θ
90–θ
100+θ
e 80
60
160
10
60
80
Reallocation
110
Since there are –ve Δij this solution too is not optimal. Reallocation is done below. This solution is tested for optimality below: u 38 40 40
0
-3 8 49
40 51
i
–13
49
0 Vi
37
0 –11
50
0
344
27
26
–13 51
50
29
( v i + v j)
39
15
–11
12
13 1
1
10
Δ ij m a t rix
4
11
Since all Δij’s are +ve, this solution is optimal.
j
Ans. 15: The initial solution is found by VAM below: Factory Godown 1 2 3 4 1 7 20 5 7 7
5 5
6 40 3
Availability Diff. 60/40/0
2/4/0 1/3
2
10 9
11
10 6
11
∞
5
20/10/0
3
11
10
30 6
20 2
40 2
8
90/70/30/0 0/4/2/5
4
50 9
10
9
6
9
12
50/0
60 50 0 2
20 0
40 10 0 0/1
20 0
40 0
40 0
4
3
2
Demand Diff.
5
3/0
The above initial solution is tested for optimality. Since there are only 8 allocations and we require 9(m+n-1 =9) allocations, we put a small quantity in the least cost independent cell (2, 6) and apply the optimality test. Let u= 0 and3 then we calculate remaining ui and v vj ui Factory Godowns 1 2 3 4 5 6 1 7 20 40 -2 5 7 7 5 3 2 10 10 e 0 9 11 6 11 ∞ 5 3 30 20 40 0 11 10 6 2 2 8 4 50 9 10 9 6 9 12 0 Vj 9 7 6 2 2 5 Now we calculate Δij = cij – (ui +vj) for non basic cells which are given in the table below: 0
3 4
2
7
5
9
∞
3 3
3 3
4 Δ ij matrix
7
7
345
Since all Δij are positive, the initial solution found by VAM is an optimal solution. The final allocations are given below: Factory
to
Godown
Unit
Cost
Value
1
2
20
5
100
1
6
40
3
120
2
1
10
9
90
2
3
10
6
60
3
3
30
6
180
3
4
20
2
40
3
5
40
2
80
4
1
50
9
450
Total cost Rs.
=
1,120
The above solution is not unique because the opportunity cost of cell (1,2) is zero. Hence alternative solution exists. Students may find that the alternative solution is as given below: Factory 1 1 1 2 2 3 3 3 4
to
Godown 1 2 6 3 6 3 5 4 1
Unit 10 20 30 10 10 30 40 20 50
Cost 7 5 3 6 5 6 2 2 9 Total cost (Rs.)
Value 70 100 90 60 50 180 80 40 450 1,120
Ans. 16 The given problem is a balanced minimization transportation problem. The objective of the company is to minimize the cost. Let us find the initial feasible solution using Vogel’s Approximation method (VAM) Outlets Plants
A
B
X
D
400 4
Y
300 6
50 3
Z
C 8 2
400 9
700/300/0
2200
400/50/0
1200
600/200/0
2240
5 200
3
Difference
6
350 5
Capacity
6
Requirement 400/0
450/400/0
350/0
500/300/0
Difference
0
1
4
0
0
1
-
0
-
1
-
0
The initial feasible solution obtained by VAM is given below:
346
Outlets Plants
A
B
X
C
D
400
300
4 Y
6 50
8
6 400
5
2
5
400
200 3
Requirement
700
350
3 Z
Capacity
9
400
600
6
450
5
350
500
Since the number of allocations = 6= (m+n-1), let us test the above solution for optimality. Introduce u i (i=1,2,3) and v j (1,2,3,4) such that ∆ ij = C ij – (u i +v j ) for allocated cells. We assume u 1 =0, and rest of the u i ’s, vj’s and ∆i j ’s are calculated as below: Outlets Plants X
A
B
0
400
0
50
400
Vj
4
6 0
5
-1
2
5
4
3
0
8 350
4
200
9 6
Ui
300
6
3 Z
D
5
4 Y
C
-1
6
5
3
6
On calculating ∆i j ’s for non-allocated cells, we found that all the ∆i j ≥0, hence the initial solution obtained above is optimal. The optimal allocations are given below. Plants
Outlet
Units
Cost
Total Cost
X
→B
400
×
6
=
2,400
X
→D
300
×
6
=
1,800
Y
→B
50
×
5
=
250
Y
→C
350
×
2
=
700
Z
→A
400
×
3
=
1,200
Z
→D
200
×
5
=
1,000 7,350
The minimum cost = 7,350 thousand rupees. Since some of the ∆i j ’s = 0, the above solution is not unique. Alternative solutions exist. Ans.17: The given problem is a transportation problem. The profit matrix for various factories and sales counters is calculated below:
347
Factory
Sales Centres
Capacity (kgms)
1
2
3
A
3
2
4
100
B
0
-1
1
20
C
4
3
5
60
D
2
1
3
80
Demand (kgms) 120 140 60 Since this is an unbalanced transportation problem (demand > capacity), let us introduce a dummy factory with profit as Rs.0 per unit for various sales centres and capacity equal to sixty units. The resulting matrix would be as below: Factory
Sales Centres
Capacity (kgms)
1
2
3
A
3
2
4
100
B
0
-1
1
20
C
4
3
5
60
D
2
1
3
80
Dummy
0
0
0
60
Demand (kgms)
120
140
60
The above profit matrix can be converted into a loss matrix by subtracting all its elements from the highest payoff of the matrix i.e. 5. The loss matrix so obtained is given below: Factory
Sales Centres
Capacity (kgms)
1
2
3
A
2
3
1
100
B
5
6
4
20
C
1
2
0
60
D
3
4
2
80
Dummy
5
5
5
60
Demand (kgms)
120
140
60
The initial solution is obtained by applying Vogel’s approximation method. Factory
Sales Centres 1
A
2
Difference
3
100 2
B
3
1
100/0
11-
4
20/0
111
60/0
1--
20 5
6
C D
Capacity
60 1
2
20
60
0
348
3
4
Dummy
2
80/60/0
111
5
60/0
000
60 5
5
Demand
120/20/0
140/120/60/0
60/0
Difference
1
1
1
1
1
-
2
1
-
The solution obtained by VAM is as given below: Factory A B C D Dummy Vj
Sales Centres
Ui
1
2
3
100
0
E
2
3
1
0
20
0
5
6
4
0
0
60
1
2
0
20
60
0
3
4
2
1
60
2
5
5
5
-1
0
2
3 6 2 4 5
Since all ∆ ij ≥ 0 for the non allocated cells, hence the solution given by above matrix is optimal. The optional solution for the given problem is given below: From Factory
To Sales Centre
Quantity
Profit per unit (Rs.)
Total Profit (Rs.)
A
1
100
3
300
B
2
20
-1
-20
C
3
60
5
300
D
1
20
2
40
D
2
60
1
60
Dummy
2
60
0
0
Total Profit =
660
(Note: since some of the ∆ ij’s are equal to zero, alternative solutions also exist.) Ans.18: The given problem is an unbalanced transportation problem which is converted into a balanced on by adding a dummy investment as given below:
349
Year
Net Return data (in paise) of Investment
Dummy
Amount Payable
P
Q
R
S
1
95
80
70
60
0
70
2
75
65
60
50
0
40
3
70
45
50
40
0
90
4
90
40
40
30
0
30
Maximum Investment
40
50
60
60
20
The values in the table represent net return on investment of one rupee till the end of the fourth year. The objective of the company is to maximize the net return. For achieving this objective, let us convert this maximization problem into minimization problem by subtracting all the elements of the above payoff matrix from the highest payoff i.e. 95, and apply Vogel’s approximation method for finding the initial feasible solution. Year
Loss Matrix – Investment type P
1
Q
40
Dummy
R
S
Amount Available
Difference
30 0
2
15 20
25
3 5
9 5
70/30/0
15/10 _ _
35
4 5
9 5
40/20/0
10/5/5/10
20
20
30
3
40 25
50
50
45
4
5 5 10
35
90/50/0
9 5
30/20/0
20
55
55
6 5
Maximum Investment
40/0
50/20/0
60/40/0
60/10/0
20/0
Difference
20
15
10
10
0
-
15
10
10
0
-
20
10
10
0
-
-
10
10
0
solution obtained by VAM is as given below
9 5
10/40/20 /0/0
10/3/0
350
Year
Loss Matrix – Investment type P
1
Q
40
Dummy
R
S
30 0
2
15 20
20
25
35
95
70
35
45
95
40
55
95
90
95
30
20 30
3
40 25
50
50
45
4
10 35
Maximum Investment
Amount Available
40/0
20
55
55
65
50/20/0
60/40/0
60/10/0
20/0
This initial solution is tested for optimality. There are 8 (=m+n-1) independent allocations. Let us introduce u i, v j, i=(1,2,3,4); = (1,2,3,4,5 such that Dij = cij = (u i +v j ) for allocation cell. We assume u1 = 0 and remaining u1’s vj’s and Dij’s are calculated. Year
Loss Matrix – Investment type P
1
Q
40
2
5
10
0
55 10
55 15
95
15
95
25
95
35
20
55 20
0
10
45
5
0
45 50
50
95 20
35 40
35 v j ’s
35 0
30
Amount Available
35
25 20
25 4
5
15 20
0
S
5
20 3
R
30 0
Dummy
65 30
60
On calculating A ij s for non-allocated cells, we found that their values are positive, hence the initial solution obtained above is optimal. The optimal allocations are given below: Year 1
Invest in Invest Rs 40 lacs in investment P
Net Return 0.95xRs.40 lacs = Rs. 38,00,000
351
2
3 4
Rs 30 lacs in investment Q
0.80xRs.30 lacs = Rs. 24,00,000
Invest Rs 20 lacs in investment Q
0.65xRs.20 lacs = 13,00,000
Rs 20 lacs in investment R
0.60xRs.20 lacs = 12,00,000
Invest Rs 40 lacs in investment R
0.50xRs.40 lacs = Rs. 20,00,000
Rs 50 lacs in investment S
0.40xRs.50 lacs = Rs. 20,00,000
Invest Rs.10 lacs in investment S
0.30xRs.10 lacs = Rs.3,00,000
Total Rs.130,00,000 Ans. 19: The given information can be tabulated in following transportation problem: Profit Sales offices Plant 1 2 3 4 5 1 9 11 6 5 5 2 -1 3 1 9 1 3 8 9 10 14 4 Demand 80 100 75 45 125
Capacity in units 150 200 125
Where entries in the cells of the above table indicate profit per unit received by selling one unit of item from plant i (1 =1,2,3) to the sales office (i=1,2,3,4,5). The profit per unit is calculated using the following formula. Profit = sales price –(production cost +Shipping cost) The objective of the company is to maximize the profit. For achieving this objective, let us convert this maximization problem into minimization problem by subtracting all the elements of the above payoff matrix from the highest payoff i.e. Rs. 14. Loss matrix Sales offices
Capacity in units
Plant 1 2 3 4 5 1 5 3 8 9 9 150 2 15 11 13 5 13 200 3 6 5 4 0 10 125 Demand 80 100 75 45 125 The problem is an unbalanced transportation problem since capacity (=475 units) is 50 units more than the demand. Hence a dummy sales office is added with cost equal to zero for all plants and demand equal to 50 units. Now, let us apply Vogel’s Approximation method to the resultant balanced matrix for finding the initial feasible solution.
352
Plant 1 2
1 50 5
25 5
3
2 100 3
15
11
6
Demand
8
5
9
4
Dummy
50
10
Difference
150/50/0
3/3/2/2/4
200/150/125/0 5/11/2/2/2/2
0
13
0
Capacity
0
9
125
13 5 45
75
80/30 /25/0 1 1 1 1 1
differ
Sales offices 4 5
3
0
125/80/5/0
100/0
75/0
45/0
125/0
50/0
2 2 2 2 --
4 4 4 ---
5 -----
1 1 1 1 1
0 0 ----
0/4/1/1/4/4
The initial solution obtained by VAM is given below which is tested for optimality. Plant
1
1
50
2
25
3
15 5
Demand in units
2 5
3
100
5
3
8
9
11
13
5
6
6
80
4
75
100
45
4 75
Dummy
9
125
50
13
0
0
10
45
125
Capacity in units 150
0
200
6
125
50
These are m +n –1 =8 independent allocations. Let us now introduce ui, vj, I = (1,2,3); j = (1,2-----6) such that ∆ ij = Cij –(ui +vj) for allocation cells. We assume u2 = 0 and remaining ui’s vj’s and ∆ij’s are calculated as below:
Plant 1
50
1 5
100
25
-θ
3
15 5
11 +θ 1 6 15
5
3 -2
2
V j ’s
2
Sales offices 3 4 10 8 9
10
5 13
13
75
4 13
5
6
9 + 125
-4 θ 45 9
0
5 - 6 θ
Dummy 10 0 13 10
13
50 9 0
U i ’s -10
0
0
0
-9
353
Since some of the Δ ij ’s are negative, therefore, the above solution is not optimal. Introduce in the cell (2,4) with the most negative Δ ij , an assignment. The value of θ and reallocated solution as obtained from above is given below. The reallocated solution is again tested for optimally. Hence, the values u i ’s v j ’s and Δ ij ’s are again calculated.
Plant 1
50
2
4
3
30
Vj’s
1 5 15 11
6
100
Sales offices 3 4 5 10 8
2
3 2
11
1 9
5
4
13
75 9
4
25
9 5
20 5
0
5
2
9
125
13
2 13
10
Dummy 6 0 50 5 0
Ui’s -6
0
0
0
-5
Since all Δ ij ’s for non-basic cells are positive, therefore, the solution obtained above is an optimal one. The allocation of plants to sales officers and their profit amount is given below: Plant 1 1 2 2 2 3 3 3
Sales Office 1 2 4 5 Dummy 1 3 4
units
profit per unit 9 11 9 1 0 8 10 14 Total
50 100 25 125 50 30 75 20
profit 450 1,100 225 125 0 240 750 280 3,170
Ans.20: Convert the given profit matrix into a loss matrix by subtracting each element of the matrix from the highest value viz.44.The resulting loss matrix is as follows: Loss Matrix
Factory P Q R Demand
Customer -----------------------------------------------A B C 4 0 6 40
19 9 6 20
22 14 16 60
D
supply
11 14 14 30
100 30 70 150/200
The loss matrix, obtained as above is an unbalanced one, We introduce a dummy column to make it a balanced one.
354
Loss Matrix
Factory
Customers ______________________________________ A B C D
P Q R Demand
4 0 6 40
19 9 6 20
22 14 16 60
11 14 14 30
Dummy 0 0 0 50
Supply 100 30 70 200/200
By using Vogal’s approximation method, the following initial feasible solution is found Factory
A
P
10
B
Customers C
60
D
30
Dummy
e
Supply
100
4 19 22 11 0 -------------------------------------------------------------------------------------------------------------Q 30 30 0 9 14 14 0 ---------------------------------------------------------------------------------------------------------------R 20 50 70 6 6 16 14 0 ----------------------------------------------------------------------------------------------------------------Demand 40 20 60 30 50 200/200
Since the number of allocation’s in the initial feasible solution are 6 and for applying optimality test they should be equal to (m+n-1)=7, therefore we enter a very small assignment equal to e in the minimum cost so that no loop is formed. Let us introduce the variables Ui and Vj such that Ui + Vj = Cij for allocated cells. We thus have the following relations: U2 + V1 = 0 U1 + V1 = 4 U 1 + V 3 = 22 U3 + V2 = 6 U 1 + V 4 = 11 U3 + V5 = 0 U1 + V5 + 0 Put U 1 = 0,we get V 1 = 4;V 3 = 22; V 4 = 11; V 5 = 0; U 3 = 0;V 2 = 6 and U 2 = (-4) Compute: Cij – (Ui + Vj) for non-allocated cells. U 1 V 2 =19 - (0 + 6) = 13 U 2 V 2 = 9 - (- 4 + 6) =7
355
U 2 V 3 = 14 - ( - 4 + 22) = (-4) U 2 V 4 = 14 - (- 4 + 11) = 7 U 2 V 5 = 0 - (- 4 + 0) = 4 U 3 V 1 = 6 - (0 + 4) = 2 U 3 V 3 = 16 - (0 + 22) = (-6) U 3 V 4 = 14 - (0 + 11) = 3 Since the value of Cij - (Ui + Vj)is negative in two cells therefore the initial solution is not optimal, Introduce an assignment 0 in the cell U3V3 and construct a loop shown as below, after adjusting.
Customers Factory A B C D Dummy Supply Ui ------------------------------------------------------------------------------------------------------------------------------P 10 60-0 30 e+0 100 U1 = 0
Q (-4) R 0 Demand Vj
30
4
19
0
22
20
9
0
11
14
6
6
16
40
20
60
V1= 4
V2 = 6
V 3 = 22
14
0
30 V 4 =11
U2 =
70
U3 =
0
50-0
14
30
0 50
200/200
V5 = 0
Maximum value of 0 = 50 Apply optimality test once again. Introduce U i and V j’ s and determine their values Compute C ij - (U i + V j ) for non-allocated cells, since it comes out to be negative for U 2 V 3 cell, therefore we repeat the aforesaid process by introducing 0 in U 2 V 3 cell, the minimum value 0f 0 is 10.
356
Customers
Factory P
A
B
10+θ 4
Q
19
6
V1
V 1 =4
30 22
Dummy
Supply
50
100
11
Ui U 1 =0
0 U2 =(-4)
30 14
20
40
10-θ
9
R 6)
Demand
D
0
30-θ 0
C
14
0
50 6
70 16
20 V 2 =12
14
60
30
V 3 =22
V 4 =11
U3 = ( -
0 50
200/ 200
V 5 =0
The second improved solution obtained is as under: Apply optimality test to the solution once again after determining the values of U i and V j . Since C ij - (U i + V j ) for non-allocated cell is positive, therefore the following solution is optimal one. Customers Factory A B C D Dummy Supply Ui ----------------------------------------------------------------------------------------------------------------------------P 20 30 50 100 U1=0 4 Q
19
22
11
0
20
30 0
9
R
Demand
10
14 20
14
0
50
6
6
40
20
U2=(-4)
70 U3=(-2) 16 60
14
0
30
50
200/200
357
Vj
V1=4
V2=8
V3=18
V4+11
V5=0
Transferring the solution to the original profit matrix, we get;
Customers Factory A B C D Dummy ------------------------------------------------------------------------------------------------P 20 30 50 40 Q
25
22
20
33
R
35 20
38 Demand
40
30 30
30
0
50 38 20
100
0
10 44
Supply
70 28
30
60
30
0 50
Maximum profit =20 Rs.40+30Rs.33+20*Rs.44+10*Rs.30+20*Rs.38+50*Rs.28+50*Rs.0 =Rs.800+Rs.990+Rs.880+Rs.300+Rs.760+Rs.1,400
=Rs.5,130 Ans. 21 The given information can be tabulated in following transportation problem: Project Auditor
1 2 3 Time Required (Hours)
1
2
3
(Rs.) 1,200 1,400 1,600
(Rs.) 1,500 1,300 1,400
(Rs.) 1,900 1,200 1,500
130
140
Time available (Hours)
160 160 160
160
The given problem is an unbalanced transportation problem. Introducing a dummy project to balance it, we get
358
Auditor
1
2
1 2 3 Time Required (hrs.)
1,200 1,400 1,600 130
1,500 1,300 1,400 140
Project
3
Dummy
1,900 1,200 1,500 160
0 0 0 50
Time available (Hours) 160 160 160 480
The objective here is to maximize total billing amount of the auditors. For achieving this objective, let us convert this maximization problem into a minimization problem by subtracting all the elements of the above payoff matrix from the highest payoff i.e. Rs. 1900. Auditor 1 2 3 Time required (Hrs)
1 700 500 300 130
2 400 600 500 140
Project
3 0 700 400 160
Dummy 1900 1900 1900 50
Time available 160 160 160 480
Now, let us apply Volgel’s Approximation Method to the above matrix for finding the initial feasible solution.
Auditor
1
1
7
2
5
130
3
3 130/0
Difference
2/2/-/-
Time Required
Project (Figure of payoff’s in Rs. 00’s) 2 3 Dummy
110 30
4 6
5 140/110/0 1/1/1/1
160
0 7
50
19 19
4 160/0
19 50/0
4/-/-
0/0/0
Time Available
Difference
160/0
4/-/-/-
160/50/0
1/1/13/13
160/30/0
1/2/14/-
The initial solution is given below. It can be seen that it is a degenerate solution since the number of allocation is 5. In order to apply optimality test, the total number of allocations should be 6 (= m + n -1). To make the initial solution a non-degenerate, we introduce a very small quantity in the least cost independent cell which is cell of Auditor 3, Project 3.
359
Auditor
1
2
1
7
4
2
5
110
Project 160
3 0
6
Dummy
Time Available
19
160
19
160
50
7
130 30 e 3 3 5 4 19 160 Time 130 140 160 50 Required Introduce u i’s and v j’s such that ∆ ij = C ij – (u i +v j ) (for I, = 1 to 3; j = 1,2,3, dummy). To determine the values of u i’s and v j’s we assume that u 3 = 0, values of other variables i.e. u i’s , v j’s and … are calculated as follows: Project Auditor
1
2
3
Dummy
1
8
3
160
5
7 2
1
4 110
5 3
130
2 6
30 3
0
19
U 1 =-4
19
U 2 =1
19
U 3 =0
50 7
e 5
U j ’s
1 4
V j ’s v 1 =3 v2= 5 v 3 =4 v 4 =18 Since all for non basic cells are positive, therefore the initial solution obtained above is optimal. The allocation of projects to auditors and their billing amount is given below: Here an auditor may be involved in more one project as apparent from the following solutions. Auditor 1 2 3 3
Project 3 2 1 2 Total billing
Billing amount (Rs.) 160xRs. 1900 = 3,04,000 110xRs. 1300 = 1,43,000 130xRs. 1600 = 2,08,000 30xRs. 1400 = 42,000 = 6,97,000
Hence, the maximum total billing during the next month will be Rs. 6,97,000
360
Assignment Ans. 1: I 16 26 76 38
1 2 3 4 Step 1:
II 52 56 38 52
III 34 8 36 48
IV 22 52 30 20
Subtract the smallest element of each row from every element of the corresponding row I II III IV 1 0 36 18 6 2 18 48 0 44 3 46 8 6 0 4 18 32 28 0 Step 2: Subtract the smallest element of each column from every element in that column I
II
III
IV
1
0
28
18
6
2
18
40
0
44
3
46
0
6
0
4
18
24
28
0
Step 3: Drew minimum number of horizontal and vertical lines to cover all the zeros I
II
III
IV
1
0
28
18
6
2
18
40
0
44
3
46
0
6
0
4
18
24
28
0
The optimal assignment is 1
─
I
=
16
2
─
III
=
8
3
─
II
=
38
4
─
IV
=
20 82 hours
Minimum time taken
=
82 hours
Ans. 2: (a) Consider the following assignment problem:
Division N
E
W
S
361
Marketing Executives
A
14
20
11
19
B
12
10
15
9
C
16
19
18
15
D
17
13
15
14
Step 1 Select the minimum element of first row and subtract it from all the elements of the row. On repeating the step with all the rows of the above matrix, we get the following
Marketing Executives
Step 2
N
Division E
A
3
B
W
S
9
0
8
3
1
6
0
C
1
4
3
0
D
4
0
2
1
Select the minimum element of first column and subtract it from all the elements of the column. On repeating this step with all the columns of the above matrix; we get the following Division
Marketing Executives
N
E
W
S
A B
2 2
9 1
0 6
8 0
C D
0 3
4 0
3 2
0 1
N
E
W
S
A B
2 2
9 1
0 6
8 0
C
0
4
3
0
Step 3 On drawing the minimum number of lines in the above matrix, so as to cover at the zeros, we get the following matrix. Division
Marketing Executives
D 3 0 2 1 Since the minimum number of lines drawn under the step is equal to number of marketing executives or number of divisions, therefore we go over to the final step for determining the required optimal solution. Step 4 For determining the optimal solution scan each row in turn for a single uncovered zero in it, encircle it and pass a line in its column.
362
Division
Marketing Executives
N
E
W
S
A B
2 2
9 1
0 6
8 0
C
0
4
3
0
D
3
0
2
1
The optimal assignment obtained in this case is as under: Marketing Executive A B C D Total minimum cost
Division
Cost Rs. 11 09 16 13 49
W S N E
Ans. 5: Using the information that the factory works effectively 7 hours (=420 minutes) a day and the time required by each operator for producing each of the products, we obtain the following production and profit matrices: Production Matrix (units) Operator
Profit Matrix (in Rs.)
Product
Operator
A
B
C
D
P
70
42
30
35
Q
60
84
140
R
70
60
S
21
42
Product A
B
C
D
P
210
84
120
35
105
Q
180
168
560
105
42
42
R
210
120
168
42
28
28
S
63
84
112
28
In order to apply the assignment algorithm for minimizing losses, let us first convert this profit matrix to a loss matrix by subtracting all the elements of the given matrix from its highest element which is equal to Rs.560. The matrix so obtained is given below: Operator
Product A
B
C
D
P
350
476
440
525
Q
380
392
0
455
R
350
440
392
518
S
497
476
448
532
Now apply the assignment algorithm to the above loss matrix. Subtracting the minimum element of each row from all elements of that row, we get the following matrix:
363
Operator P Q R S
Product A 0 380 0 49
B 126 392 90 28
C 90 0 42 0
D 175 455 168 84
Now subtract the minimum element of each column from the elements of that column to get the following matrix: Operator
Product A
B
C
D
P
0
98
90
91
Q
380
364
0
371
R
0
62
42
84
S
49
0
0
0
Draw the minimum number of lines to cover all zeros. The minimum number of lines to cover all zeros is three which is less than the order of the square matrix (i.e.4) thus the above matrix will not give the optimal solution. Subtract the minimum uncovered element (=62) from all uncovered elements and add it to the elements lying on the intersection of two lines, we get the following matrix: Operator
Product A
B
C
D
P
0
36
90
29
Q
380
302
0
309
R
0
0
42
22
S
111
0
62
0
The minimum number of lines which cover all zeros is 4 which is equal to the order of the matrix, hence, the above matrix will give the optimal solution. Specific assignments in this case are as below: Operator
Product A
B
C
D
P
0
36
90
29
Q
380
302
0
309
R
0
0
42
22
S
111
0
62
0
Ans. 8:
Operator
Product
Profit (Rs.)
P
A
210
Q
C
560
R
B
120
S
D
28
Total
Profit (Rs.)
918
364
(i) 4
12
16
8
20
28
32
24
36
44
48
40
52
60
64
56
Subtracting minimum element – each row. 0
8
12
4
0
8
12
4
0
8
12
4
0
8
12
4
Subtracting minimum element – each column, 0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Minimum no. of lines to cover all zeros = 4 = order of matrix. Hence optional assignment is possible. Minimum cost = 4 + 28 + 48 + 56 = 136. = AR1 + BR2 + CR3 + DR4 Since all are zeros, there are 24 solutions to this assignment problem. Viz.
A
B
C
D
R1
R2
R3
R4
R2
R3
R4
R1
R3
R4
R1
R2
R4
R1
R2
R3
R1
R3
R4
R2
etc.
A can be assigned in 4 ways, B in 3 ways for each of A’s 4 ways. (ii) SP – VC = 100 Rs. A
B
C
D
R1
96
88
84
92
R2
80
72
68
76
R3
64
56
52
60
R4
48
40
36
44
Subtracting the highest term 0
8
12
4
16
24
28
20
32
40
44
36
48
56
60
52
Subtracting minimum term of each row.
365
0
8
12
4
0
8
12
4
0
8
12
4
0
8
12
4
Which is the same as the earlier matrix Maximum contribution = Rs. (96 + 72 + 52 + 44) = Rs. 264. Alternative Solution: Maximisation of contribution is same as minimizing cost. Hence, same assignments as in (i) will be the optional solution. Maximum Contribution Rs. (400 – 136) = Rs. 264 (iii) (a)
The relative cost of assigning person i to region r does not change by addition or subtraction of a constant from either a row, or column or all elements of the matrix.
(b)
Minimising cost is the same as maximizing contribution. Hence, the assignment solution will be the same, applying point (i) above.
(c)
Many zero’s represent many feasible least cost assignment. Here, all zeros mean maximum permutation of a 4 × 4 matrix, viz. 4 × 3 × 2 × 1 = 24 solutions are possible.
Ans. 9: Reducing minimum from each column element (figure in ’000s) Step 1
Step 2
R1
R2
R3
R4
C1
1
1
−
−
C2
−
0
−
C3
0
−
C4
−
−
R1
R2
R3
R4
C1
0
0
−
−
0
C2
−
0
−
0
0
−
C3
0
−
0
−
2
1
C4
−
−
1
0
Number of lines to connect all zeros nos. is 4 which is optional. Alternatively you may also reduce the minimum from each row. Step 1
Step 2
R1
R2
R3
R4
C1
0
1
−
−
C2
−
0
−
C3
1
−
C4
−
−
R1
R2
R3
R4
C1
0
1
−
−
0
C2
−
0
−
0
0
−
C3
0
−
0
−
0
1
C4
−
−
0
0
Number of lines to connect all zeros nos. is 4 which is optional. All diagonal elements are zeros and are chosen. The minimum cost is Rs.15,000 C 1 – R 1 4,000; C 2 – R 2 4,000; C 3 – R 3 2,000; C 4 – R 4 5,000; (Total) = 15,000. Ans.10:
Let us first formulate the preference ranking assignment problem. MANAGERS
366
M1
Room No.
M2
M3
M4
M5
301 – 4 2 – 1 302 1 1 5 1 2 303 2 – 1 4 – 304 3 2 3 3 3 305 – 3 4 2 – We have to find an assignment so that total preference ranking is minimum. In a cell (-) indicates that no assignment is to be made in that particular cell. Let us assign a very large ranking value M to all such cells. Step 1 : From each row, subtract the minimum element of that row, from all the elements of that row to get the following matrix. MANAGERS M1 M 0 1
Room No 301 302 303
M2 3 0 M
M3 1 4 0
M4 M 0 3
M5 0 1 M
304 1 0 1 1 1 305 M 1 2 0 M Draw the minimum number of lines in the above table to cover all zeros. In this case the number of such lines is five, so the above matrix will give the optimal solution. The assignment is made as below: Rooms No.
MANAGERS M4
M1
M2
M3
M5
301
M
3
1
M
0
302
0
0
4
0
1
303 304 305
1 1 M
M 0 1
0 1 2
3 1 0
M l M
Thus, the assignment is M1 → 302, M2 → 304, M3 → 303, M4 → 305, M5 → 301 and the total minimum ranking = 1 + 2 + 1 + 2 + 1 = 7 Ans. 11:
Dummy machine (M5) is inserted to make it a balanced cost matrix and assume i ts installation cost to be zero. Cost of install at cell M3 (J) and M2 (L) is very high marked as é. J
K
L
M
N
M1
18
22
30
20
22
M2
24
18
é
20
18
M3
é
22
28
22
14
M4
28
16
24
14
16
M5 (Dummy)
0
0
0
0
0
Step 1 Subtract the minimum element of each row from each element of that row J
K
L
M
N
367
M1
0
4
12
2
4
M2
6
0
é
2
0
M3
é
8
14
8
0
M4
14
2
10
0
2
M5 (Dummy)
0
0
0
0
0
Step 2 Subtract the minimum element of each column from each element of that column J
K
L
M
N
M1
0
4
12
2
4
M2
6
0
é
2
0
M3
é
8
14
8
0
M4
14
2
10
0
2
M5 (Dummy)
0
0
0
0
0
Step 3 Draw lines to connect the zeros as under: J
K
L
M
N
M1 M2
0 6
4 0
12 é
2 2
4 0
M3
é
8
14
8
0
M4
14
2
10
0
2
M5 (Dummy)
0
0
0
0
0
There are five lines which are equal to the order of the matrix. Hence the solution is optimal. We may proceed to make the assignment as under: J
K
L
M
N
M1
0
4
12
2
4
M2
6
0
e
2
0
M3
e
8
14
8
0
M4
14
2
10
0
2
M5 (Dummy)
0
0
0
0
0
The following is the assignment which keeps the total cost at minimum: Machines
Location
Costs Rs.
M1
J
18
M2
K
18
368
M3
N
14
M4
M
14
M5 (Dummy)
L
0
Total
64
Ans. 12: Since the Executive Director of the 5 star hotel is interested in maximizing the revenue of the hotel, therefore, the objective of the given problem is to identify the preferences of marriage parties about halls so that hotel management could maximize its profit. To solve this problem first convert it to a minimization problem by subtracting all the elements of the given matrix from its highest element which is equal to Rs. 10,000. The matrix so obtained which is known as loss matrix is given below: Marriage party A B C D
1
2
0 2000 3000 0
1000 0 0 2000
Loss matrix/Hall 3 M 2000 4000 M
4 M 5000 2000 M
Now apply the assignment algorithm to the above loss matrix. Subtracting the minimum element of each column from all elements of that column, we get the following matrix. Marriage party A B C D
1 0 2000 3000 0
Loss matrix/Hall 2 1000 0 0 2000
3 M 0 2000 M
4 M 3000 0 M
The minimum number of lines to cover all zeros is 3 which is less than the order of the square matrix (i.e. 4), the above matrix will not give the optimal solution. Subtracting the minimum uncovered element (= 1000) from all uncovered elements and add it to the elements lying on the intersection of two lines, we get the following matrix Marriage party A B C D
1 0 3000 4000 0
2 0 0 0 1000
3 M 0 2000 M
4 M 3000 0 M
Since the minimum number of lines to cover all zeros is 4 which is equal to the order of the matrix, the above matrix will give the optimal solution which is given below: Marriage party A B C D
1 0 3000 4000 0
2 0 0 0 1000
3 M 0 2000 M
4 M 3000 0 M
369
and the optimal schedule is : Marriage party
A B C D
Revenue (Rs.) Hall 2 9,000 Hall 3 8,000 Hall 4 8,000 Hall 1 10,000 Total 35,000
→ → → →
Ans. 14: The following matrix gives the cost incurred if the typist (i = A, B, C, D, E) executes the job (j = P, Q, R, S, T). Job Typist
P
Q
R
S
T
A
85
75
65
125
75
B
90
78
66
132
78
C
75
66
57
114
69
D
80
72
60
120
72
E
76
64
56
112
68
Subtracting the minimum element of each row from all its elements in turn, the above matrix reduces to Job Typist P Q R S T A 20 10 0 60 10 B 24 12 0 66 12 C 18 9 0 57 12 D 20 12 0 60 12 E 20 8 0 56 12 Now subtract the minimum element of each from all its elements in turn, and draw minimum number of lines horizontal or vertical so as to cover all zeros . All zeros can be covered by four lines as given below: 2
2
0
4
0
6
4
0
10
2
0
1
0
1
2
2
4
0
4
2
2
0
0
0
2
Since there are only 4 lines ( 0.67] σe 6 But Z = 0.67 from the normal distribution is 0.2514. Thus, the probability of not meeting the due date is 25.14%. Ans. 28: The required network is drawn below:
382
The expected time marked in the above network diagram for various activities is calculated in the table below: Activity
Time (in weeks)
Expected time (weeks) t e = (t 0 + 4t m + tp) / 6
t p − t0 Variance σ 2 = 6
Optimistic (t o )
Most likely (t m )
Pessimistic (t p )
1-2
3
3
3
3
0
2-3
3
6
9
6
1
2-4
2
4
6
4
4/9
3-5
4
6
8
6
4/9
4-6
4
6
8
6
4/9
5-6
0
0
0
0
0
5-7
3
4
5
4
1/9
6-7
2
5
8
5
1
2
(i) Variance of each of the activities has been calculated in the last column of the above table. (ii) Critical path is given by 1 – 2 – 3 – 5 – 6 – 7 and the expected project length is 20 weeks. (iii) Variance of the critical path = σ² = 0 + 1 + 4/9 + 0 + 1 = 22/9 = 2.444 Mean = x = 20 weeks To calculate the probability of completing the project in 23 weeks, we will first calculate the normal Z as below: Z=
D−x
σ
=
23 − 20 2.444
= 1.92
P (x < 23) = P (z < 1.92) = 0.9726
(from the normal table)
Thus, the probability that the project will be completed in 23 weeks is 97.26%.
Ans. 29:
383
The network for the given problem is drawn below: 17.67
17.83
2
17.83
3
5
19
7
22.83
9
16. 67
1
4
17
8
6
20
In the table below, we have calculated the expected duration and variance of each activity. Activity
Time
Expected duration {(a+4m+b)÷6}
Variance {(b-a)÷6}2 3.36 1.36
Optimistic
Most Likely
Pessimistic
a
m
b
1-2
14
17
25
2-3
14
18
21
2-4
13
15
18
2-8
16
19
28
3-4
-
-
-
3-5
15
18
27
4-6
13
17
21
5-7
-
-
-
17.83 17.83 15.17 20 19 17 17.67 22.83
5-9
14
18
20
16.67
6-7
-
-
-
6-8
-
-
-
7-9
16
20
41
4
17.36 20.08
384
8-9
14
16
Variance paths are: 1-2-3-5-7-9
22
77.49
1-2-3-5-9 1-2-3-4-6-7-9 1-2-3-4-6-8-9 1-2-8-9 1-2-4-6-8-9 1-2-4-6-7-9
72.33 75.49 69.33 54.5 66.67 72.83
Hence the critical path is 1-2-3-5-7-9 with duration of 77-49 days or 78 days approximately. Variances of various activities on critical path have been calculated in the last column of the above table. Hence standard deviation of critical path = √ 26.08 = 5.12 Now we want to find out that within how many days the project should be completed so as to provide 95% probability of break even. Z 0.95 = 1.65 Hence, 1.65 = {(D-77.49)÷5.12} Or, D = 1.65× 5.12+77.49 = 85.94 or 86 days The fixed cost of the project is Rs. 8 lakhs and the variable cost is Rs. 9,000 per day. Thus, amount to bid
= Rs. 8 lakhs+ Rs. 9,000×86 = Rs. 8 lakhs + Rs. 7,74,000 = Rs. 15,74,000
Ans. 34: (a) Critical Paths: All are critical paths:
385
(i)
1–2–5–6
2+8+5
= 15
(ii)
1–3–5–6
3+7+5
= 15
(iii) 1 – 4 – 5 – 6
4+6+5
= 15
(iv) 1 – 3 – 4 – 5 – 6
3+1+6+5
= 15
(i)
Choose 5 – 6, common path; Crash by 1 day
(ii)
Choose: 1 – 2, 1 – 3, 1 – 4 Or
(iii) Choose: 1 – 2, 3 – 5, 4 – 5 Or (iv) Choose: 2 - 5 , 3 – 5, 4 – 5
Or
(v) Choose: 1 – 3, 1 – 4, 2 - 5 Ans. 35: (i)
Assuming that the duration of activity 3 – 5 is 4 weeks.
The various critical paths are: 1-2-5-8-9 15 weeks 1-3-4-7-8-9 15 weeks 1-3-4-6-7-8-9 15 weeks 1-3-5-8-9 15 weeks (ii) Note: Since the duration for activity 3-5 is not specified it is open for you to assume the duration. Depending upon the duration assume three possibilities emerge. 1. 2. 3.
If the duration assumed is more than 4 weeks then that path (13, 35, 58, 89) alone will be critical. In that case you can choose any of the activity in the critical path. If the duration assumed is exactly 4 weeks then it will be one of the 4 critical paths and the various possibilities are given below. If the duration assumed is less than 4 weeks then the solution should be based on 3 of the critical paths namely 12,589, 1346789 and 134789. This has 16 combinations. Reduce in the following ways, the project duration is. Since all the paths are critical, reduction is possible by combining activities. The activities can be independent, common to few paths and common to all the paths. The various categories are as follows: 1. Common to all the paths. 8-9 2. Independent : Combination 1. 1-2,3-5,4-6 and 4-7. Combination 2. 2-5,3-5,4-6 and 4-7. 3. Combination 4. Activities common to two of the paths. Combination 1. Combination 2. Combination 3. Combination 4.
Combination
3.
1-2,3-5,4-7, 6-7. 2-5,3-5,4-7, 6-7. 1-2,1-3. 1-3,2-5. 3-4,5-8. 5-8,7-8.
386
4.
Activities common to two of the paths and two independent activities. Combination 1. 1-2,3-4,3-5. Combination 2. 1-2,3-5,7-8. Combination 3. 2-5,3-4,3-5. Combination 4. 2-5,3-5,7-8. Combination 5. 4-6,4-7,5-8. Combination 6. 4-7,5-8,6-7. (Any three of the above combination.) Ans. 36: (i) Project network based on the given activities is as under :
(ii) A review of the above network clearly shows that there are four paths 1 – 4 – 5; 1 – 2 –5 ; 1 –2 – 3 – 5;& 1 – 3 – 5 of duration 10 days; 11 days; 13 days and 4 days respectively. The longest path of 13 days viz,. 1 – 2 – 3 – 5 is the critical path of the drawn network. (iii) The optimum duration of a project is that duration of the project for which the total cost (direct & indirect) will be minimum. The cost corresponding to optimal duration is known as resultant cost of the project. To determine optimum duration and resultant cost of the project based on the given activities we proceed as follows: Activity
Normal Time (days)
Crash Time (days)
Normal Cost Rs.
Crash Cost Rs
Cost slope per day Rs.
1–2
4
3
1,500
2,000
500
1–3
2
2
1,000
1,000
--
1–4
5
4
1,875
2,250
375
387
2–3
7
5
1,000
1,500
250
2–5
7
6
2,000
2,500
500
3–5
2
1
1,250
1,625
375
4–5 Total direct cost
5
4
1,500 10,125
2,125
625
The normal total cost (direct & Indirect) of completing the project in 13 days is : Normal direct cost : (Rs)
10,125
Indirect cost 13 days x Rs. 500
6,500 ______ 16,625
Total normal cost : (Rs)
To determine the optimum duration and resultant cost we crash activities on the critical path by properly selecting them as under : Activities
1–2
2–3
3–5
1
2
1
Cost slope per day (Rs)
500
250
375
Indirect cost per day (Rs)
500
500
500
Saving in cash
--
250
125
Ranking
--
1
2
No. of available crash days
The above ranking clearly shows that we should select the activity 2 – 3 and crash it for one day, as it results in maximum saving of Rs. 250 per day. Let us crash 2 – 3 by 2 days.
Rs. 10,125
Normal direct cost Cost slope (2 days x Rs. 250)
500
Indirect cost (11 days x Rs. 500)
5,500 ______ 16,125
Total cost After crashing the activity 2 – 3 we are left with the following paths as under : 1–2
2–3
3–5
of 11 days duration
1–2
2–5
of 11 days duration
1–4
4–5
of 10 days duration
388
1–3
3–5
of 4 days duration
1 – 2 is a common activity in the first two paths with cost slope of Rs. 500/- per day. There is no profit or loss in crashing this actively. Hence crash it by one by. Rs. 10,125
Normal direct cost Total cost slope (Rs. 500 + 1 day x Rs. 500) Indirect cost (10 days x Rs. 500)
1,000 5,000 ______ 16,125
Total cost Now we have the following four paths are as under : 1–2
2–3
3–5
of 10 days duration
1–2
2–5
of 10 days duration
1–4
4–5
of 10 days duration
1–3
3–5
of 4 days duration
To reduce the duration of project further, we are required to select the activities on all the three paths. These activities may be 3 – 5, 2 – 5, and 1 – 4. if all of these activities are crash by even 1 day each, then the total increase in cost would be (Rs. 375 + Rs. 500 + Rs. 375) or Rs. 1,250/- for saving Rs. 500. At this stage, we stop the process of crashing. Hence optimal project duration
10 days
Resultant project cost/optimal cost : (Rs)
16,125
Ans. 38: (i)
The required network is given below:
The various paths in the network are:
389
1 – 2 – 4 – 5 with project duration = 16 days 1 – 4 – 5 with project duration = 17 days 1 – 3 – 4 – 5 with project duration = 20 days The critical path is → 1 3 → 4 → 5. The normal length of the days.
project is 20 days and minimum project length is 12
(ii) Since the present schedule consumers more time than the minimum project length, the duration can be reduced by crashing some of the activities. Also, since the project duration is controlled by the activities lying on the critical path, the duration of some of the activities lying on critical path can be reduced. It is given that overhead cost is Rs.60 per day. Step I: First, the crashing cost of activity (3, 4) being minimum, the duration of this activity can be compressed from 10 days to 9 days. The total cost for 19 day’s schedule = Rs.15 + Rs.19 × 60 = Rs.1,155 Step II: Since the critical path remains unchanged, the duration of activity (3, 4) can be further reduced from 9 days to 8 days resulting in an additional cost of Rs.15 so that total cost for 18 days schedule = Rs.30 + Rs.60 × 18 = Rs.30 + Rs.1,080 = Rs.1,110. Step III: Continue this procedure till the minimum project length schedule. The calculations are given below: Normal Project length (days)
Job crashed
Crashing Cost (Rs.)
Overhead cost @ Rs.60 / day
Total Cost. (Rs.)
20
--
--
20×60
1,200
19
3–4
1 × 15 = 15
19×60
1,155
18
3–4
2 × 15 = 30
18×60
1,110
17
3–4
3 × 15 = 45
17×60
1,065
16
4–5
3×15+1×40 = 85
16×60
1,045
15
3–4, 1–4
4×15+1×40+1×30= 130
15×60
1,030
14
1–3, 1–4, 2–4
130+1×30+1×25+1×10=195
15×60
1,035
13
1–3, 1–4, 2–4
195+1×25+1×30+1×10=260
13×60
1,040
12
1–3, 1–4, 1–2
260+25+30+20=335
12×60
1,055
(iii) Since the total cost starts increasing from 14 days duration onwards, the minimum total cost of Rs.1,030 for the optimum project duration of 15 days occurs for optimum duration of each job as given below: Job: Optimum: Duration (day)
(1,2)
(1,3)
(1,4)
(2,4)
(3,4)
(4,5)
9
8
14
5
6
1
390
Path 1 → 2 → 4 → 5 = 9 + 5 + 1= 15 days Path 1 → 4 → 5 = 14 + 1 = 15 days Path 1 → 3 → 4 → 5 = 8 + 6 + 1 = 15 days. Hence, the optimum duration of the project is 15 days. Ans. 39 : (a) (i) Net work diagram
Critical Path is 1-2-5-6-7-8 = 32 weeks Associated Cost = 4220 + 32×50 = 5820 (ii) Total floats Activity
Duration weeks
Early start
Latest start
Early finish
Latest finish
Total float
391
1-2
3
0
0
3
3
0
2-3
3
3
4
6
7
1
2-4
7
3
5
10
12
2
2-5
9
3
3
12
12
0
3-5
5
6
7
11
12
1
4-5
0
10
12
10
12
2
5-6
6
12
12
18
18
0
6-7
4
18
18
22
22
0
6-8
13
18
19
31
32
1
7-8
10
22
22
32
32
0
(iii) Calculation of crashing Activity
Nt
Nc
Ct
Cc
Slop = (Cc-Nc) / (Nt-Ct)
1-2
3
300
2
400
100
2-3
3
30
3
30
0
2-4
7
420
5
580
80
2-5
9
720
7
810
45
3-5
5
250
4
300
50
4-5 5-6
0 6
0 320
0 4
0 410
0 45
6-7
4
6-8 7-8
13
400 780 1000
3 10 9
470 900 1200
70 40 200
10
The critical path activities are
1-2
2-5
5-6
6-7
7-8
Slope
100
45
45
70
200
Two activities cost slope cost is minimum (2-5 and 5-6) but activity 5-6 is common and critical, it also continuing so reduce by 2 weeks, then reduce activity 2 -5 by one week. Activity
From-to
Project durations
Cost
I
5-6
6-4 weeks
32-2 = 30
4220 + (2×45) + (30×50) = 5810
II
2-5
9-8
30-1 = 29
4220+90+(1×45)+(29×50) = 5805
After this reduction now two paths are critical 1-2-3-5-6-7 = 28 and 1-2-5-6-7 = 28 So
1-2
3-5
6-7
392
2-5 Slope cost
100
50+45=95
70
As cost per week for every alternative is greater than Rs.50 (overhead cost p er week). Therefore, any reduction in the duration of project will increase the cost of project completion. Therefore, time for projects is 29 weeks, minimum cost is Rs.5805. Answer 40: The network is given below:
(i)
The critical path of the project is ACEG or 1-2-3-4-6-7 with normal duration of 25 days. The minimum duration of the project is 18 days.
(ii)
The cost slope for various activities is given below: Activity A (1-2)
Normal Duration 7
Crash duration 5
Normal cost (Rs.) 500
Crash cost (Rs.) 900
B (2-4)
4
2
400
600
C (2-3)
5
5
500
500
D (2-5)
6
4
800
1,000
E (4-6)
7
4
700
1,000
F (5-6)
5
2
800
1,400
G (6-7)
6
4
800
1,600
Cost slope (Rs.)
900 − 500 = 200 7−5 600 − 400 = 100 4−2
N.A.
1,000 − 800 = 100 6−4 1,000 − 700 = 100 7−4 1,400 − 800 = 200 5−4
1,600 − 800 = 400 6−4
393
Total
4,500
Step –1: Various paths of the network are given below: 1-2-3-4-6-7 With duration = 25 days 1-2-4-6-7 With duration = 24 days 1-2-3-5-6-7 With duration = 23 days 1-2-5-6-7 With duration = 24 days In order to determine the cost of completing the project in 21 days, let us crash that activity on the critical path, which has minimum cost slope. It can be seen that the minimum cost slope of Rs.100 corresponds to activity E (4-6) and it lies on the critical path. Hence, we crash activity E (4 –6) by 1 day at an additional cost of Rs. 100. Step- 2: Various paths now are: 1-2-3-4-6-7 1-2-4-6-7 1-2-4-6-8 1-2-4-6-9
With duration = 24 days With duration = 23 days With duration = 23 days With duration = 24 days
An examination of the above four paths clearly points out that there are two critical paths namely 1-2-3-4-6-7 and 1-2-5-6-7, each with duration = 24 days. To reduce the project duration by three days more, there are following possible combination of activities. 1.
Crash activities 4-6 on the path 1-2-3-4-6-7 and 5-6 on the path 1-2-5-6-7 by one day each at an addition cost of Rs. 100 +Rs. 200 = Rs. 300.
2.
Crash activities 4-6 on path 1-2-3-4-6-7 and 2-5 on path 1-2-5-6-7 by one day each at an additional cost of Rs. 100 +Rs. 100 = Rs. 200
3.
Crash activity 1-2 by one day at an additional cost of Rs. 200.
It can be observed that the additional cost of reducing the project duration by one day in combination 2 as well as combination 3 is Rs. 200. Hence any of these two can be selected for crashing. However, since crashing activity 1-2 by 1 day reduces the duration of all the paths by1 day, we will crash it by I day. The project duration becomes = 23 days at an additional cost = Rs. 200. Step 3: Crash activity 1-2 by 1 day further, it would reduce the project duration to 22 days at an additional cost = Rs. 200. Step 4: Activity 1-2 can not be crashed further. So, we now select the combination 2 stated above for crashing. Crash activities 4-6 and 2-5 by one day each at an additional cost of Rs. 100 +Rs. 100 = Rs. 200. Hence, in order to complete the project in 21 days, an additional cost of Rs. 100 +Rs. 200 +Rs. 200 +Rs. 200 = Rs. 700 will be incurred. The normal cot of completing the project in 25 days =Rs. 4,500. Hence, the percentage increase in cost to complete the project in 21 days
394
=
Rs.700 ×100 = 15.5%. Rs.4,500
Answer 42 The requires network based on the given activities and duration is drawn below : The critical path of the network is 1-3-4-5-6 i.e. B-E-G-H. The duration of the project is 14 weeks. E=4 L=6
2
A 4
3
D
C 3
E=9 L=9
1
E = 14 L = 14
6
4
E=0 L=0
B
E
3
2
7
G 2
5
F 3
H
E = 11
2
L = 11
E=7 L=7 The time scale diagram for various activities along the resource accumulation table showing the number of workers required on each day are drawn on next page. C(2) 3 A(4)
2
4
7
D(4) 3
2
B(2)
E(6) 3
1 7
G(3)
4 2
5 2
Crew size
6 3
F(3) 2
H(4)
2
395
6
1
6
2 6
3 6
4 6
6
6
6
5 8 -2 6
6 8 -2 6
7 8 -2 6
8 9
9 9
10 3
9
9
3
11 3 3
12 4 +2 6
13 4 +2 6
14 4 +2 6
It can be seen that the demand on the resources is not even. On the 8th and 9th week, the demand of workers is as high as 9 whereas on the 10th and 11th week, it is only three. If 9 workers are to be hired for the entire project duration of 14 weeks, then during most of the days they will be idle. We will attempt to re-schedule our activities in such away so as to utilize the workers in a fairly uniform manner. As can be seen from the above network diagram, activity C has a float of 7 weeks and activity F has a float of 2 weeks. The maximum demand on the resources occurs during 5th week to 7th week. (i.e. 8 workers) and during 8th to 9th week (i.e. 9 workers). We will shift activity C by seven weeks so that it starts on 12th week instead of 5ht week. This reduces the demand of the workers from 8 to 6 during 5th to 7th weeks. The modified resource requirements are shown in the last row of the above table. Activity F has a float of two weeks. It is shifted by two weeks so that it starts on 10th week instead of 9th workers required earlier. The modified resource accumulation table is given: Crew size 1 6
2 6
3 6
4 6
5 8
6 8
7 8
6
6
6
6
6
6
6
8 9 -3 9
9 -3 9
9
10 3 +3 6
11 3 +3 6
12 4
13 4
14 4
6
6
6
It is evident from the last row of the above table that there is a uniform demand of 6 workers throughout the duration of the project. Ans. 46: The network diagram is drawn below:
E= 4 L=4 2 4 E=0 L=0
8 4
1
6 6 4
3
3
E=8 L=8
5
E = 14 L = 14
396
4
E=3 L=4 The critical path is 1-2-4-5. The total floats of all the activities are calculated below:
Activity 1-2 1-3 1-4 2-4 2-5 3-4 3-5 4-5 (b)
Duration 4 3 6 4 8 4 4 6
Total float 0 1 2 0 2 1 7 0
The resource allocation table is given below: Starting day Equipment X job done No. of men required day completed Equipment Y Job done No. of men required Day completed Equipment Z Job done No. of men required Day completed Total no. of men
1st (1,2) 30 4 (1,3) 20 3
50
4th (1,2) 30 4
5th (2,4) 30 8
(1,4) 20 9 50
(1,4) 20 9 50
9th
10th
(3,4) 20 12 (1,4) 20 9 40
(3,4) 20 12 (2,5) 20 17 40
13th (4,5) 30 18
(2,5) 20 17 50
18th (4,5) 30 18 (3,5) 20 21
21st
(3,5) 20 21
50
20
Explanation:
This is basically a problem of resource-leveling whereby the main constraint would be on the resources. It the maximum demand on any resource is not to exceed a certain limit, the activities will have to be rescheduled so that the total demand on the resources at any time will be within the limit and consequent the project duration time is exceeded. The criterion to be followed in such a case is to delay the job with a large float. In this way we tend to absorb the float and cutdown the demand on the resource. If two or more jobs are competing Ans. 47:
397
Paths 1-2-5-7-8 1-2-4-7-8 1-4-7-8 1-3-4-7-8 1-3-6-7-8 1-3-6-8 Critical path = 1-3-6-7-8 = 47 days
Duration 7+16+9+8 = 40 7+12+19+8 = 46 6+19+8 = 33 8+6+19+8 =41 8+24+7+8 =47 8+24+4 = 36
398
Simulation Ans. 6 The numbers 00-99 are allocated in proportion to the probabilities associated with each event as given below: Daily Demand
Probability
Cumulative Probability
Random Numbers Allocated
0
0.01
0.01
00-00
10
0.20
0.21
01-20
20
0.15
0.36
21-35
30
0.50
0.86
36-85
40
0.12
0.98
86—97
50
0.02
1.00
98-99
Let us simulate the demand for the next 10 days using the given random numbers in order to find out the stock position if the owner of the bakery decides to make 30 breads every day. We will also estimate the daily average demand for the bread on the basis of simulated data. Day
Random Number
Simulated Demand
Stock if 30 breads are prepared every day
1
48
30
0
2
78
30
0
3
19
10
20
4
51
30
20
5
56
30
20
6
77
30
20
7
15
10
40
8
14
10
60
9
68
30
60
10
9
10
80
Total
220
Daily average demand of the basis of simulated data = 22 Ans. 7: The random numbers are established as in Table below: Production Per day 196 197 198 199 200 201 202 203
probability 0.05 0.09 0.12 0.14 0.20 0.15 0.11 0.08
cumulative probability 0.05 0.14 0.26 0.40 0.60 0.75 0.86 0.94
Random number 00-04 05-13 14-25 26-39 40-59 60-74 75-85 86-93
399
204 0.06 1.00 94-99 Based on the 15 random numbers given we simulate the production per day as above in table 2 below. Random No.
Estimated Production Per day
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
82 89 78 24 53 61 18 45 04 23 50 77 27 54 10
No. of mopeds waiting Opening Balance
202 203 202 198 200 201 198 200 196 198 200 202 199 200 197
No. of empty spaces in the lorry
current current Total excess short waiting Production production
-2 5 7 5 5 6 4 4 0 0 0 2 1 1
2 3 2 ---1 ---------2 ------
-----2 ---2 -4 2 --1 -3 Total
2 5 7 5 5 6 4 4 0 0 -2 1 1 _-42
-----------------2 --------__2 __4
Average number of mopeds waiting
=
=
2.80
Average number of empty spaces in lorry
=
42 15 4 15
=
0.266
Ans. 8: If the numbers 00-99 are allocated in proportion to the probabilities associated with each category of work, then various kinds of dental work can be sampled, using random number table :Type
Probability
Filling Crown Cleaning Extraction Checkup
Random Numbers
0.40 0.15 0.15 0.10 0.20
00-39 40-54 55-69 70-79 80-99
Using the given random numbers, a work sheet can now be completed as follows :FUTURE EVENTS PATIENT SCHEDULED ARRIVAL
1 2 3
8.00 8.30 9.00
RN
40 82 11
CATEGORY
Crown Checkup Filling
SERVICE TIME
60 minutes 15 minutes 45 minutes
400
4 5 6 7 8
9.30 10.00 10.30 11.00 11.30
34 25 66 17 79
Filling Filling Cleaning Filling Extraction
45 minutes 45 minutes 15 minutes 45 minutes 45 minutes
Now, let us simulate the dentist’s clinic for four hours starting at 8.00 A.M. STATUS
Time
Event
Number of the patient being served (time to go)
1st
1st(60) 1st(30)
2nd
2nd(15) 3rd(45) 3rd(30)
3rd 4th
4th(45) 4th(15) 5th(45) 5th(30)
5th 5th & 6th 6th 6th & 7th
6th(15) 7th(45) 7th(30) 8th(45)
7th & 8th 8th 8th -
patient arrives 2 “ arrives 1st departs 3rd “ arrives nd 2 departs 4th “ arrives departs 3rd 5th “ arrives 6th “ arrives 4th departs 7th “ arrives departs 5th 8th “ arrives 6th departs End -
8.0 8.30 9.00
nd
9.15 9.30 10.00 10.30 10.45 11.00 11.30 11.45 12.00 12.30
Patients waiting
The dentist was not idle during the entire simulated period :The waiting times for the patients were as follows :Patient
Arrival
1 2 3 4 5 6 7 8
8.00 8.30 9.00 9.30 10.00 10.30 11.00 11.30
Service Starts
Waiting (Minutes)
8.00 9.00 9.15 10.00 10.45 11.30 11.45 12.30 Total
285 15
The average waiting time of a patient was
=
0 30 15 30 45 60 45 60 285 35.625 minutes.
Ans. 9: Random allocation tables are as under: Time Arrival (Mts) (Proba.)
Arrivals cumulative Probability
Random No. allocated
Time (Mts)
Service (Proba.)
Service Random Cumulative No. Probability allocated
401
1 2 3 4 5 6
0.05 0.20 0.35 0.25 0.10 0.05
0.05 0.25 0.60 0.85 0.95 1.00
00-04 05-24 25-59 60-84 85-94 95-99
Simulation of ten trails: R. No. Arrival Mts. Time Start
60 16 08 36 38 07 08 59 53 03
4 2 2 3 3 2 2 3 3 1 Total
9.04 9.06 9.08 9.11 9.14 9.16 9.18 9.21 9.24 9.25
1 2 3 4 5
0.10 0.20 0.40 0.20 0.10
R. No. Time Mts. Finish Time
9.04 9.06 9.08 9.11 9.14 9.16 9.18 9.22 9.25 9.29
09 12 18 65 25 11 79 61 77 10
1 2 2 3 2 2 4 3 4 2
9.05 9.08 9.10 9.14 9.16 9.18 9.22 9.25 9.29 9.31
0.10 0.30 0.70 0.90 1.00
00-09 10-29 30-69 70-89 90-99
Waiting Time Clerk 4 1 − 1 − − − −
Passanger
1 1 4 6
_ 6
In half an hour trial, the clerk was idle for 6 minutes and the passengers had to wait for 6 minutes. Ans. 10: From the frequency distribution of arrivals and service times, probabilities and cumulat ive probabilities are first worked out as shown in the following table: Time between arrivals
Frequency Probability
Cum. Prob.
Service Time
Frequency
Prob.
Cum. Prob.
1
5
0.05
0.05
1
1
0.10
0.10
2
20
0.20
0.25
2
2
0.20
0.30
3
35
0.35
0.60
3
4
0.40
0.70
4
25
0.25
0.85
4
2
0.20
0.90
5
10
0.10
0.95
5
1
0.10
1.00
6
5
0.05
1.00
6
0
0.00
1.00
Total 100 10 The random numbers to various intervals have been allotted in the following table: Time between arrivals
Probability
Random numbers allotted
Service Time
Probability
Random numbers allotted
402
1
0.05
00-04
1
0.10
00-09
2
0.20
05-24
2
0.20
10-29
3
0.35
25-59
3
0.40
30-69
4
0.25
60-84
4
0.20
70-89
5
0.10
85-94
5
0.10
90-99
6
0.05
95-99
6
0.00
-
Simulation Work Sheet Random Time till Number next arrival
Arrival Time a.m.
Service Random Service begins number time a.m.
Service Clerk Customer Ends Waiting waiting a.m. Time time
Time spend by customer in system
Length of waiting line
64
4
11.04
11.04
30
3
11.07
04
-
3
-
04
1
11.05
11.07
75
4
11.11
-
2
6
1
02
1
11.06
11.11
38
3
11.14
-
5
8
2
70
4
11.10
11.14
24
2
11.16
-
4
6
2
03
1
11.11
11.16
57
3
11.19
-
5
8
2
60
4
11.15
11.19
09
1
11.20
-
4
5
2
16
2
11.17
11.20
12
2
11.22
-
3
5
2
18
2
11.19
11.22
18
2
11.24
-
3
5
2
36
3
11.22
11.24
65
3
11.27
-
2
5
1
38
3
11.25
11.27
25
2
11.29
-
2
4
1
07
2
11.27
11.29
11
2
11.31
-
2
4
1
08
2
11.29
11.31
79
4
11.35
-
2
6
1
59
3
11.32
11.35
61
3
11.38
-
3
6
1
53
3
11.35
11.38
77
4
11.42
-
3
7
1
01
1
11.36
11.42
10
2
11.44
-
6
8
2
62
4
11.40
11.44
16
2
11.46
-
4
6
2
36
3
11.43
11.46
55
3
11.49
-
3
6
2
27
3
11.46
11.49
52
3
11.52
-
3
6
1
97
6
11.52
11.52
59
3
11.55
-
-
3
-
86
5
11.57
11.57
63
3
12.00
2
-
3
-
20
57
6
56
Average queue length =
54 Number of customers in waiting line 26 = 1.3 = 20 Number of arrivals
Average waiting time per customer = Average service time =
26
56 = 2.8 minutes 20
54 = 2.7 minutes 20
Ans. 11: Cumulative frequency distribution for Ramu is derived below. Also fitted against it are the eight given random numbers. In parentheses are shown the serial numbers of random numbers.
403
10
4
01 (2)
20
10
30
20
40
40
50
80
44 (4)
60
91
82 (6)
70
96
95 (3)
80
100
00 (7)
03 (8)
14 (1) 61 (5)
Thus the eight times are: 30, 10, 70, 50, 60, 10 and 10 respectively. Like wise we can derive eight times for Raju also. Col-1
Col-2
Col-3
(2× Col-2)
10
4
8
20
9
18
30
15
30
25 (4)
40
22
44
36 (1)
34 (8)
50
32
64
55 (3)
56 (7)
60
40
80
76 (2)
70
46
92
80
50
100
41 (6)
97 (5)
(Note that cumulative frequency has been multiplied by 2 in column 3 so that all the given random numbers are utilized). Thus, Raju’s times are: 40, 60, 50, 30, 80 40, 50 and 40 seconds respectively. Ramu’s and Raju’s times are shown below to observe for waiting time, if any. 1
2
3
4
Ramu
Cum. Times
Raju Initial
Raju’s cumulative time with included
30
30
40
70
10
40
60
130
70
110
50
180
50
160
30
210
50
210
80
290
60
270
40
330
10
280
70
400
10
290
40
440
30 seconds
Since col. 4 is consistently greater than Co.2, no subsequent waiting is involved.
Ans. 12: The numbers 00-99 are allocated in proportion to the probabilities associated with each event. If it rained on the previous day, the rain distribution & the random no allocation are given below:
404
Event
Probability
Cumulative Probability
Random numbers Assigned
No rain 1 cm rain 2 cm rain 3 cm rain 4 cm rain 5 cm rain
0.50 0.25 0.15 0.05 0.03 0.02
0.50 0.75 0.90 0.95 0.98 1.00
00-49 50-74 75-89 90-94 95-97 98-99
Table 1 – Rain on previous day Similarly, if it did not rain the previous day, the necessary distribution and the random number allocation is given below: Event Probability Cumulative Random Probability numbers Assigned No rain 1 cm rain 2 cm rain 3
0.75 0.15 0.06 0.04
0.75 0.90 0.96 1.00
00-74 75-89 90-95 96-99
Table 2- No rain on previous day Let us now simulate the rain fall for 10 days using the given random numbers. For the first day it is assumed that it had not rained the day before: Day 1 2 3 4 5 6 7 8 9 10
Random Numbers 67 63 39 55 29 78 70 06 78 76
Event No rain No rain No rain No rain No rain 1 cm rain 1 cm rain No rain 1 cm rain 2 cm rain
(from table 2) (from table 2) (from table 2) (from table 2) (from table 2) (from table 2) (from table 1) (from table 1) (from table 2) (from table 1)
Hence, during the simulated period, it did not rain on 6 days out of 10 days. The total rain fall during the period was 5 cm. Ans.13: The probabilities of occurrence of A, B and C defects are 0.15, 0.20 and 0.10 respectively. So, tile numbers 00-99 are allocated in proportion to the probabilities associated with each of the three defects Defect-A Defect-B Defect-C Exists Random Exists? Random Exists? Random Numbers numbers numbers Assigned assigned assigned Yes 00-14 yes 00-19 yes 00-09 No 15-99 No 20-99 no 10-99
405
Let us now simulate the output of the assembly line for 10 items using the given random numbers in order to determine the number of items without any defect, the number of items scrapped and the total minutes of rework time required: Item RN for RN for RN for whether Rework Remarks No. defect A defect B defect C any defect time (in Exists minutes) 1 48 47 82 none --2 555 36 95 none --3 91 57 18 none --4 40 04 96 B 15 -5 93 79 20 None --6 01 55 84 A -Scrap 7 83 10 56 B 15 --8 63 13 11 B 15 --9 47 57 52 None --10 52 09 03 B,C 15+30 =45 -During the simulated period, 5 out of the ten items had no defects, one item was scrapped and 90 minutes of total rework time was required by 3 items. Answer 14: The question is not happily worded, if we go by the language of the question, the following solution can be worked out: First of all, random numbers 00-99 are allocated in proportion to the probabilities associated with demand as given below: Demand
Probability
Cum. Probability
Random Nos.
0
0.05
0.05
00-04
1
0.10
0.15
05-14
2
0.30
0.45
15-44
3
0.45
0.90
45-89
4
0.10
1.00
90-99
Based on the ten random numbers given, we simulate the demand per day in the table given below. It is given that stock n hand = 8 and stock on order = 6 (expected next day). Let us now consider both the options stated in the question. Option A: Order 5 Books, when the inventory at the beginning of the day plus orders outstanding is less than 8 books: Day
Random No.
Sales Demand
Op. Stock in hand
Qty. Order
Qty. Recd. At end of the day
Total Qty. on order
Closing Stock
1
89
3
8
-
-
6
5
2
34
2
5
-
6
-
9
3
78
3
9
-
-
-
6
4
63
3
6
5
-
5
3
406
5
61
3
3
-
6
81
3
0
0
7
39
2
8
16
2
9
13
1
10
73
3
-
5
0
Now on day 6, there is stock out position since 5 units will be received at the end of the day and demand occurring during the day can not be met. Hence, it will into be possible to proceed further and we will have to leave the answer at this stage. Random No.
Sales Demand
Opening Stock in hand
Qty. Order
Qty. Recd. At end of the day
Total Qty. on order
Closing Stock
1
89
3
8
--
--
6
5
2
34
2
5
--
6
--
9
3
78
3
9
--
--
--
6
4
63
3
6
8
--
8
3
5
61
3
3
--
--
8
0
6
81
3
0
--
8
--
7
39
2
8
16
2
9
13
1
10
73
3
Now on day 6, there is stock out position since 8 units will be received at the end of the day and demand occurring during the day can not be met. Hence, it is not possible to proceed further and we may leave the answer at this stage. Alternatively, if we assume that the demand occurring during the day can be met out of stock received at the end of the day, the solution will be as follows: Stock in hand = 8 and stock on order = 6 (expected next day) Random No.
Sales Demand
Opening Stock in hand
Qty. Order
Qty. Recd. At end of the day
Total Qty. on order
Closing Stock
1
89
3
8
--
--
6
5
2
34
2
5
--
6
--
9
3
78
3
9
--
--
--
6
4
63
3
6
5
--
5
3
5
61
3
3
--
--
5
0
6
81
3
0
5
5
5
2
7
39
2
2
5
--
10
0
8
16
2
0
--
5
5
3
9
13
1
3
--
5
--
7
10
73
3
7
5
--
5
4
407
Carrying Cost = 39 × 0.50 = Rs.19.50 Ordering Cost = 4 × 10 = Rs.40.00 Total Cost = Rs.59.50 Option B: Order 8 Books, when the inventory at the beginning of the day plus orders outstanding is less than 8 books: Random No.
Sales Demand
Opening Stock in hand
Qty. Order
Qty. Recd. At end of the day
Total Qty. on order
Closing Stock
1
89
3
8
--
--
6
5
2
34
2
5
--
6
--
9
3
78
3
9
--
--
--
6
4
63
3
6
8
--
8
3
5
61
3
3
--
--
8
0
6
81
3
0
--
8
--
5
7
39
2
5
8
--
8
3
8
16
2
3
--
--
8
1
9
13
1
1
--
8
--
8
10
73
3
8
--
--
--
5
Carrying Cost = 45 × 0.50 = Rs.22.50 Ordering Cost = 2 × 10 = Rs.20.00 Total Cost = Rs.42.50 Since Option B has lower cost, Manager should order 8 books.
Ans.15 Demand (Tons) 1 2 3 4 Option-I RN Demand 88 41 67 63 48 74 27 16 11 64 49 21
3 2 3 3 3 3 2 2 1 3 3 2
Probability 0.15 0.30 0.45 0.10 Opening Stock 8 5 9 6 3 0 2 0 3 7 4 1
Cumulative Probability 0.15 0.45 0.90 1.00 Receipts 6 5 5 5 5
Closing Stock 5 9 6 3 0 2 0 3 7 4 1 4
Op.Stock on Order 5 5 5 10 5 5 5 5
Random Nos. Allocated 00-14 15-44 45-89 90-99 Order 5 5 5 5 5 -
Cl.Stock on Order 6 5 5 10 10 10 5 5 5 10 5
408
44 (Rs.) No of order placed 5 Ordering cost Closing Stock Carrying cost Total Option-II RN Demand 88 41 67 63 48 74 27 16 11 64 49 21
3 2 3 3 3 3 2 2 1 3 3 2
(5x1000) 44 (44x50)
Opening Stock 8 5 9 6 3 0 5 3 1 8 5 2
No of orders 3 Closing stock 47
Receipts 6 8 8 -
5,000 2,200 7,200
Closing Stock 5 9 6 3 0 5 3 1 8 5 2 0 47
Op.Stock on Order 8 8 8 8 8 8
Order 8 8 8 -
(Rs.) 3,000 2,350 5,350
Ordering cost 3 x 1000 Carrying cost 47x50 Total
Analysis: Since the cost of inventory is less in Option II, it is suggested to implement. Ans. 16 (i)
Allocation of random numbers Demand 0 7,56,000 or x > 50.4 Alternative Solution: Total cost / unit of capacity 20,000 = 60.3 Weighted average selling price > 80.4 i.e.
5,000 × 100 + 15,000 x > 60.3 20,000
= 5,00,000 + 15,000 x > 60.3 × 20,000 = 15,000 x > 12,06,000 – 5,00,000 Or 15,000 x > 7,06,000 x > 47.06 Minimum price to cover production Cost = 47.06 Minimum price to cover same amount of profit = 50.40 (refer to W orking Note 1) Working Note 1 (− 47.06 + 50.04) × 15,000 units = Rs. 50,000
Ans. 14:
Units
Average/ hrs/u.
1
2,000
2
1,600
4
1,280
8
1,024
Material Cost / u
= 10,000
Variable cost
= 2,000
Variable Cost
= 12,000
Option I If both the orders came together, learning rate 80% applies and 8 units can be made, with average time of 1,024 hours per unit. Cost to PQ: Variable cost excl. labour
= Rs.12,000
Labour cost 1,024 hrs × 4 Rs./hr
= Rs. 4,096
413
= Rs.16,096 In this case, Y
X
Selling Price p. u.
Rs.17,200
Rs.16,500
Variable Cost p. u.
Rs.16,096
Rs.16,096
Contribution p. u.
Rs.1,104
Rs.404
4
4
4416
1616
No. of units Contribution (Rs.) Option II
→ (under option I)
6032
If X Ltd supplies its labour. 80% learning curve will apply to 4 units each of PQ & X. Hence: hrs/ u = 1280 Y
X
Selling Price
Rs.17,200
Rs.14,000
Variable Cost (excl. labour)
Rs.12,000
Rs.12,000
Labour cost: 1280 × 4
Rs.5,120
1280 × 1
.
Rs.1280
Rs.17,120
Rs.13,280
Rs.80
Rs.720
4
4
Total Variable Cost Contribution Units
Contribution (Rs.) 320 2,880 PQ should not take labour from X Ltd. It should choose option I. Ans. 16:
3,200
Working notes :
(1) By the theory of learning curve YX = KX5 ……………………… (i) Here X is the cumulative number of units or lots produced, Y is the cumulative average unit time of those X units. K is the average time of the first unit or lot, s is the improvement exponent or the learning coefficient or the index of learning. Taking log on both sides of relation (i) we have Log YX = log K + s log X ……………(ii) (2) Time required for 30 units order (when the time required for the first unit is 40 hours) Log 40 + (-0.322) log 30 0.4756 Anti log of 1.1264 Hence hours required Per unit
= 1.6021 + (- 0.322) (1.4771) = 1.6021 – = 1.1264 = 13.38 = 13.38
Total time required for 30 units = 30 units x 13.38 hours = 401.40
414
(3) Time required for 50 units order (When the time required for first unit is 40 hours) log 40 + (-0.322) log 50 = 1.6021 + (-0.322) 1.6990 = 1.055 Anti log of 1.055 = 11.35 Hence hours required per unit 11.35 hours Total time required for 50 units = 11.35 x 50 units = 567.5 hours (4) Fixed overhead recovery rate per labour hour Total labour hours 10 men x 25 days x 8 hours Less : 25% downtime (in hours)
2,000 500 _____ 1,500 7,500 5
Total effective hours Total fixed overheads per month (Rs.) Fixed overhead recovery rate per labour hour (Rs) (Rs. 7,500/1,500 hours) (i)
Computation of cost per unit of the first order of 30 units Direct material cost (30 units x Rs. 60) Direct labour cost (401.4 hours x Rs. 6) Variable overheads (401.40 hours x Re 1) Fixed overheads (401.4 hours x Rs. 5) Total cost of 30 units Cost per unit (Rs. 6,616.80/30 units)
(ii)
Rs. 1,800.00 2,408.40 401.40
2,007.00 6,616.80 220.56
Cost per unit, when a repeat order for 20 units is also placed. Direct material cost (20 units x Rs. 60) Direct labour (567.5 hours – 401.40 hours) x Rs. 6 Variable overheads (1.66.1 hours x Re 1) Fixed overheads (166.1 hours x Rs. 5) Total cost of 20 additional units
Rs. 1,200.00 996.60 166.10 830.50
________ 3,193.20
Cost per unit (Rs. 3,193.20/20 units) Price to be quoted to yield a profit of 25% on selling price
159.66
415
If selling price is Rs. 100 then profit is Rs. 25 and cost is Rs. 75 Hence selling price per unit = 100 x 159.66 75 = Rs. 212.88 Ans. 18 (i)
Price per unit for first order of 100 units Rs
Rs
Direct material Direct labour
500.00 Dept A 20 Hrs @ 10 = 200
800.00
Dept B 40 Hrs @ 15 = 600 Variable Overhead
20% of Rs 800
160.00
Fixed Overhead
Dept A 20 Hrs @ 8 = 160
360.00
Dept B 40 Hrs @ 5 = 200 Total cost
1,820.00
Profit 25%
455.00
Selling price per unit
2,275.00
(ii) Price per unit for second order of 60 units Learning will be applicable only in department B. Cumulative output becomes 100 units + 60 units = 160 units i.e 1.6 times for which learning is 86.1 % from the tables. Therefore Total Hrs for 160 units = 160 units × 40 × .861 = 5,510.4 Hrs Therefore Hrs for 60 units = Hrs for 160 units less Hrs for 100 units Or 5510.4 less 40 × 100 = 1510.4 Hrs Therefore Hrs per unit =
1510.4 = 25.17 60
Calculation of selling price per unit Direct materials Direct labour Variable Overhead Fixed Overhead
Dept A 20 Hrs @ 10 = 200 Dept B 25.17 Hrs @ 15 = 377.55 20% of 577.55 Dept A 20 Hrs @8= 160 Dept B 25.17 Hrs @5=125.85
Total cost Profit 25% Selling price per unit (iii) Price per unit for third order of 40 units
Rs 500.00 577.55 115.51 285.85 1,478.91 369.73 1,848.64
Cumulative output becomes 100 + 60 + 40 = 200 units i.e. 2 times for which learning is 80% from the table
416
Total Hrs for 200 units = 200 × 40 × .80 = 6,400 Hrs Hrs for 40 units = Hrs for 200 units less Hrs for 160 units Or 6,400 less 5510.4 = 889.6 Hrs Therefore Hrs per unit =
889.6 = 22.24 40
Calculation of selling price per unit Direct materials Direct labour Variable Overhead Fixed Overhead Total cost Profit 25% Selling price per unit
Dept A 20 Hrs @ 10 = 200.00 Dept B 22.24 @ 15 = 333.60 20% of 533.60 Dept A 20 Hrs @ 8 = 160 Dept B 22.24 Hrs @ 5 = 111.20
Rs 500.00 533.60 106.72 271.20 1,411.52 352.88 1,764.40
