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SUPPLEMENT 7 C A PA C I T Y P L A N N I N G
S U P P L E M E N T
Capacity Planning
DISCUSSION QUESTIONS 1. Design capacity is the theoretical maximum output of a system in a given period. Effective capacity is the capacity a firm can expect to achieve given its current product mix, methods of scheduling, maintenance, and standards of quality. 2. The fundamental assumptions of breakeven analysis are
Fixed costs do not vary with volume Unit variable costs do not vary with volume Unit revenues do not vary with volume
3. The manager obtains data for use in breakeven analysis from
Cost data: industrial engineering and accounting Demand and revenue data: marketing
4. Revenue data, when plotted, do not fall on a straight line because of volume discounts, etc. 5. Lagging is preferred when shortterm options like overtime and subcontracting are relatively low cost and/or easy to use. Leading is preferred when a firm cannot afford to lose customers for lack of product availability, and overtime, etc., are not available. 6. NPV determines the discounted or time value of money, comparing cost and income streams over periods of time. Process decisions may incur much of their expense early in the life of the equipment, but the stream of revenues may follow for decades. NPV is the appropriate analytical tool for that situation. 7. Effective capacity is the capacity a firm can expect to achieve given its current product mix, methods of scheduling, maintenance, and standards of quality. 8. Efficiency is the actual output as a percent of effective capacity. Efficiency = actual output/effective capacity 9. Expected output = effective capacity efficiency
ACTIVE MODEL EXERCISES ACTIVE MODEL S7.1: Productivity 1. Due to an anticipated decrease in demand the firm is considering dropping one of its shifts. What will be the capacity if they do so? 134,400 2. Another option would be to maintain 3 shifts but only work on weekdays. What will be the capacity if they select this option? 144,000 3. As the effective capacity rises, how does this affect both the utilization and efficiency. Utilization is unaffected but the efficiency drops.
4. As the actual output rises, how does this affect both the utilization and efficiency? Both utilization and efficiency rise.
ACTIVE MODEL S7.2: Breakeven Analysis 1. Use the scrollbars to determine what happens to the breakeven point as the fixed costs increase? The variable costs increase? The selling price increases? If the fixed or variable costs increase then the breakeven point increases, while if the selling price increases then the breakeven point decreases. 2. What is the percentage increase (over 5,714) to the breakeven point if the fixed costs increase by 10% to $11,000? If the variable costs increase by 10% to $2.48? If the price per unit increases by 10% to $4.40? If the fixed costs rise by 10% the break even point rises by 10%. In this case if the variable costs rise by 10% then the BEP rises by 15%. If the price per unit increases by 10% then the breakeven point FALLS by 19%. 3. In order to cut the breakeven point in half, by how much would the FIXED costs have to decrease? The variable costs? How much would the selling price have to increase? Fixed costs – $5,000; Variable costs by $1.75 from $2.25 to $.50; The selling price would need to increase by the same $1.75.
END-OF-CHAPTER PROBLEMS S7.1 Utilization =
actual output 6,000 = = 0.857 85.7% design capacity 7,000
S7.2 Efficiency =
actual output 4,500 = = 0.692 or 69.2% effective capacity 6,500
S7.3 Expected output = (effective capacity) (efficiency) (6,500)(.88) 5,720 S7.4 Efficiency =
actual (expected) output 800 = = 88.9% effective capacity 900
S7.5 Efficiency =
actual output 400 or 0.80 = effective capacity effective capacity
Thus, effective capacity =
400 500 0.80
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SUPPLEMENT 7 C A PA C I T Y P L A N N I N G
S7.6 Expected output = (effective capacity) (efficiency) = 90 0.90 = 81 chairs
S7.10 In 2006, Eye Associates has 8 machines @ 2500. In year 2011 it needs capacity of 20,100.
S7.7 Actual (expected) output = hours efficiency = 8 hr 5 days 2 shifts 4 machines 0.95 = 320 0.95 = 304 hrs S7.8 Design: 93,600 0.95 = 88,920 Fabrication: 156,000 1.03 = 160,680 Finishing: 62,400 1.05 = 65,520
(a) Therefore, if it adds 3,000 to capacity in 2006, total capacity in 2011 will be 23,000 lenses, more than adequate. Exceeds by 2,900. (b) If it buys the standard machine in 2006, its capacity in 2011 will be 22,500 lenses, still more than adequate; the smaller machine will suffice. Exceeds by 2,400. S7.11 Where:
S7.9 Year
X
1996 1997 1998 1999 2000 2001 2002 2003 2004 2005
1 2 3 4 5 6 7 8 9 10 X 5 = 5
X2
Y 15.00 15.50 16.25 16.75 16.90 17.24 17.50 17.30 17.75 18.10 Y 168.2 = 9
X 2 =
1 4 9 16 25 36 49 64 81 100 38 5
XY
XY =
15.00 31.00 48.75 67.00 84.50 103.44 122.50 138.40 159.75 181.00 951.3 4
Regression Output Constant X Coefficient Std err of Y est R squared No. of observations Degrees of freedom Std err of coef.
15.11 0.312 0.301 0.916 8 10 8 0.033
x 5.5 n y Y 16.829 n 25.745 b 0.312 82 a 16.829 0.312 5.5 15.11 X
Year 2006 = a + bx11, therefore 15.11 + 0.312 11 = 15.11 + 3.43 = 18.54, or 18,540 lenses Year 2008 = a + bx13, therefore 15.11 + 0.312 13 = 15.11 + 4.056 = 19.17, or 19,160 lenses Year 2010 = a + bx15, therefore 15.11 + 0.312 15 = 15.11 + 4.68 = 19.79, or 19,790 lenses (a) 2006 capacity needs = 18.54 thousand 2008 capacity needs = 19.17 thousand 2010 capacity needs = 19.79 thousand (b) Requirements in 2010 are for 19.79( 1000) lenses. Therefore, Eye Associates will need 8 machines (19,790/2,500 = 7.9, round up to 8).
Design Capacity = 2,000 students Effective Capacity = 1,500 students Actual Output = 1,450 students Therefore: Utilization
actual output 1,450 72.5% design capacity 2,000
Efficiency
actual output 1,450 96.7% effective capacity 1,500
S7.12 (a) Proposal A breakeven in units is: Fixed cost $50,000 $50,000 6,250 units SP VC 20 12 8 (b) Proposal B breakeven in units is: Fixed cost $70,000 $70,000 7,000 units SP VC 20 10 10 S7.13 (a) Proposal A breakeven in dollars is: Fixed cost 1 VC SP
$50,000 $10,000 1 12 20
$60,000 $150,000 0.40
(b) Proposal B breakeven in dollars is: BEP$ =
Fixed cost $70,000 $10,000 = 1 VC 1 10 SP 20
$80,000 $160,000 0.50
S7.14 Set Proposal A = Proposal B (SPA VC A ) X A FA (SPB VCB ) X B FB (20 12)X 50,000 (20 10)X 70,000 (8)X 50,000 (10)X 70,000 (8)X + 20,000 (10)X 20,000 10 X 8 X 20,000 2 X 10,000 X 20,000 1,667 pizzas; 14 2 30,000 BEPB 2,353 pizzas 14 1.25
S7.15 (a) BEPA
(b & c) For both quantities, oven A is slightly more profitable (but oven B is catching up).
SUPPLEMENT 7 C A PA C I T Y P L A N N I N G
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S7.15 (cont’d) Oven A Fixed cost Revenue Variable cost
$20,000.00 $14.00 $2.00
Oven B
Unit Sales of
$30,000.00 $14.00 $1.25
$9,000 $12,000
(d) 20,000 + 2Xa = 30,000 + 1.25Xb .75X = 10,000 X = 13,333 pizzas S7.16 Given: Price ( P) = $8 unit Variable cost (V ) = $4 unit Fixed cost (F ) = $50,000 (a) Breakeven in units is given by: BEPx
Profit A – $88,000 $124,000
Breakeven is given by: (a) BEPx
F 325,000 325,000 32,500 units P V 30 20 10
(b) BEP$
F 325,000 325,000 $975,000 1 0.667 1 VP 1 20 30
S7.20 Option A: Stay as is Option B: add new equipment Units Price VC FC = Profit
Profit A = 30,000 1.00 0.50 14,000
F 50,000 50,000 12,500 units PV 84 4
= $1,000
Profit B = 50,000 1.00 0.60 20,000
(b) Breakeven in dollars is given by: BEP$
F 50,000 50,000 $100,000 1 0.50 1 48 1 VP
(c) Profit is given by: Profit Volume Contribution Fixed cost 100,000 8 4 50,000
= $0 Therefore, the company should stay with the present equipment. S7.21 Option A: Stay as is Option B: Add new equipment, raise selling price Units Price VC FC = Profit
Profit A = 30,000 1.00 0.50 14,000
400,000 50,000 $350,000
= $1,000
S7.17 Given: Price ( P ) = $0.05 unit Variable cost (V ) = $0.01 unit Fixed cost ( F ) = $15,000 Breakeven is given by: BEP$
Profit B – $84,750 $123,000
F 15,000 15,000 $18,750 0.01 1 0.2 1 VP 1 0.05
F 15,000 15,000 P V 0.05 0.01 0.04 375,000 copies
BEPx
S7.18 Given: Price ( P ) = $30 unit Variable cost (V ) = $20 unit Fixed cost ( F ) = $250,000 Breakeven is given by: BEP$
F 250,000 250,000 $750,000 20 1 0.667 1 VP 1 30
BEPx
F 250,000 250,000 25,000 units P V 30 20 10
S7.19 Given: Price (P) $30 unit Variable cost (V ) $20 unit Fixed cost (F ) $250,000 $75,000 $325,000
Profit B = 45,000 1.10 0.60 20,000 = $2,500
Therefore, the company should choose option B: add the new equipment and raise the selling price. S7.22 Where: FC = $37,500 VC = $1.75 P = 2.50 (a) Breakeven quantity for the manual process in units:
F 37,500 50,000 bags P V 2.50 1.75
(b) Revenue at the breakeven quantity: 50,000 2.50 $125,000 and 37,500 BEP$ V 1 P 37,500 $125,000 1.75 1 2.50 (c) Breakeven quantity for the mechanized process: where: F = 75,000 P = 1.25 75,000 BEPu 60,000 bags 2.50 1.25 (d) Revenue at the breakeven quantity for the mecha nized process: 60,000 × 2.50 = $150,000 75,000 and = $150,000 1.25 1 2.50
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SUPPLEMENT 7 C A PA C I T Y P L A N N I N G
(e) Monthly profit or loss of the manual process if they expect to sell 60,000 bags of lettuce per month: Profit = 2.50(60,000) – 37,500 – 1.75(60,000) = $7,500
S7.24 (a) Breakeven volume: Total fixed cost = 1800 rent, utilities, etc. + 2000 entertainment = 3800
(f) Monthly profit or loss of the mechanized process if they expect to sell 60,000 bags of lettuce per month 2.50(60,000) – 75,000 – 1.25(60,000) = 0.0 (breakeven) (g) They should be indifferent to the process selected at 75,000 bags. 37,500 1.75 X 75,000 1.25 X 37,500 .5 X 75,000 X (h) The manual process be preferred over the mechanized process below 75,000 bags. The mechanized process be preferred over the manual process above 75,000 bags.
Selling Price Volume Revenue Drinks Meals Desserts/etc. Sandwiches
1.50 10.00 2.50 6.25
P Drinks 1.50 Meals 10.00 Desserts 2.50 Lunch 6.25
BEP$
30000 10000 10000 20000
Percent of Total Revenue
45000 100000 25000 125000 295000
0.153 0.339 0.085 0.423 1.00 0
V
V/P
1–V/P
Wi
1– (V/P)Wi
0.75 5.00 1.00 3.25
0.50 0.50 0.40 0.52
0.50 0.50 0.60 0.48
0.153 0.339 0.085 0.423 1.00 0
0.077 0.170 0.051 0.203 0.501
F
i
1 VPi
Wi
3800 $7,584.83 0.501
(b) Number of meals per day at breakeven = 9 S7.23 (a) Yes, Total profit now: [40,000 (2.00 – 0.75)] – $20,000 = $30,000 Total profit with new machine: [50,000 (2.00 – .50)] – $25,000 = $50,000 (b) The equipment choice changes at 20,000 units. .75x 20,000 .50 x 25,000 .25x 5,000 x 20,000 units
Fraction BE Units BE Selling of Total Dollar per Units Price Revenue Volume Month per Day Drinks 1.50 Meals 10.00 Desserts/et 2.50 c. Sandwiches 6.25
0.153 0.339 0.085
1160.48 2571.26 644.71
774 258 258
26 9 8
0.424
3208.28
514
18
S7.25 (a) Breakeven volume: Total fixed cost = 1800 rent, utilities, etc. + 2000 entertainment = 3800 Selling Price Drinks Meals Desserts/et c. Sandwiches
Volume Revenue
1.50 10.00 2.50
30000 10000 10000
45000 100000 25000
0.153 0.339 0.085
6.25
20000
125000 29500 0
0.424 1.00 0
Total Variable Food Cost Cost Factor*
(c) At a volume of 15,000 units, the current process should be used. Drinks
Percent of Total Revenue
0.75
1.10
Total Variable Cost 0.83
SUPPLEMENT 7 C A PA C I T Y P L A N N I N G
Meals Desserts/etc. Lunch/Sandwich es
5.00 1.00 3.25
1.43 1.10 1.43
7.15 1.10 4.65
* The total variable cost factor for meals and sandwiches is developed as: 1.00 food cost 0.33 labor, at twothirds of food cost 0.10 variable expenses at 10% of food costs 1.43
102
Total sales at breakeven × 25% of sales Price of wine 986.19 × 0.25 = = 140.9 servings $1.75
(b) No. of wine servings = at breakeven 103
SUPPLEMENT 7 C A PA C I T Y P L A N N I N G
The total variable cost factor for drinks and desserts/wines is developed as: 1.00 food cost 0.10 variable expenses at 10% of costs 1.10 total variable expense
Drinks Meals Dessert s Lunch
BEP$
P
V
V/P
1–V/P
Wi
[1– (V/P)Wi
1.50 10.00 2.50
0.83 7.15 1.10
0.55 0.72 0.44
0.45 0.28 0.56
0.153 0.339 0.085
0.069 0.095 0.048
6.25
4.65
0.74
0.26
0.423 1.000
0.110 0.322
F
1 Vi Pi
Wi
3800 $11,801.24 0.322
Selling Price
Fraction of Total Revenue
1.50 10.00 2.50
0.153 0.339 0.085
1805.59 4000.62 1003.11
1204 401 402
6.25
0.424
5003.73
810
Drinks Meals Desserts/Win e Lunch/ Sandwiche s
S7.27 (a)
Dollar Volume BEP Units
(b) Branch B which represents Option BModernize 2nd floor, has the highest expected value, $74,000. S7.28
(b) Monthly breakeven, to include a profit of $35,000 per year Total Fixed Cost = 1800 rent, utilities, etc. + 2000 entertainment + 2917 (35,000 /12) profit = 6717 BEP$
F
V
i
1 Pi
Wi
6717 $20,860.25 0.322
Selling Price
Fraction of Total Revenue
1.50 10.00 2.50
0.153 0.339 0.085
3191.62 7071.62 1773.12
2128 708 710
6.25
0.424
8844.75
1516
Drinks Meals Desserts/Win e Lunch/ Sandwiche s
Dollar Volume BEP Units
Prefer to build a large line. Large line has a payoff of $100,000. Small line has a payoff of $66,666 + 0 = $66,666.
S7.26 (a) Breakeven volume, where total fixed cost = labor (at $250) + booth rental (at 5 $50) = $500.
Item Soft Drinks Wine Coffee Candy Totals
Selling Price 1.00 1.75 1.00 1.00
Variable Var. Cost Total Cost Factor (%) Var. Cost 0.65 0.95 0.30 0.30
1.1 1.1 1.1 1.1
Breakeven = TFC/wt. contribution = 500/0.507 = $986.19
0.715 1.045 0.330 0.330
Estimated Contributio Percent n 1 Revenue Weighted (vc/sp) Revenue 0.285 0.403 0.670 0.670
0.25 0.25 0.30 0.20 1.0 0
0.071 0.101 0.201 0.134 0.50 7
SUPPLEMENT 7 C A PA C I T Y P L A N N I N G
S7.29
* NPV factor from Table S7.1.
Initial investment = $75,000 Salvage value = $45,000 Fiveyear return = $15,000 Cost of capital = 12% NPV annuity factor 5 years @ 12% = 3.605 Present value = 3.605 15,000 = $54,075 Present value of salvage: 0.567 45,000 = $25,515 Net present value = 54,075 + 25,515 – 75,000 = $4,590 S7.30 Initial investment = $65,000 Eightyear return = $16,000 per year Cost of capital = 10% NPV annuity factor 8 years @ 10% = 5.33 Present value = 5.33 $16000 = $85,280 Net present value = $85,280 – $65,000 = $20,280
P
F (1 i) N
2000 (1 0.09)3
NPV for Machine A is –$22,988; NPV for Machine B is – $27,026. Therefore, Machine A should be recommended. S7.34 Expense
2000 $1,544.40 1.2950
or from Table S7.1 NPV = F PVF9%, 3 = 2000 = 0.772 = $1,544
Two Large Ovens
3750 750
5000 0
750
400
750
1000
Three Small Ovens NPV Factor*
Now 1 2 3 4 5
Expense Expense Expense Expense Expense Expense
3750 1500 1500 1500 1500 1500
1.000 0.877 0.769 0.675 0.592 0.519
5
Salvage revenue
750
0.519
S7.32
NPV –3750 –1316 –1154 –1013 –888 –779 –8900 +389 –8511
P
F (1 i)
N
5600 15
(1.08)
* NPV factor from Table S7.1.
5600 $1,765.35 3.17
Two Large Ovens NPV Factor*
or from Table S7.1
Year
NPV = F PVF8%, 15 = 5600 0.315 = $1,764
Now 1 2 3 4 5
Expense Expense Expense Expense Expense Expense
5000 400 400 400 400 400
1.000 0.877 0.769 0.675 0.592 0.519
5
Salvage revenue
1000
0.519
S7.33 Expense Original cost Labor per year Maintenance per year Salvage value
Machine A
Machine B
10000 2000 4000 2000
20000 4000 1000 7000
Year
NPV Factor*
NPV –10000 –5358 –4782 –4272 –24412 +1424
Now 1 2 3
Expense Expense Expense Expense
10000 6000 6000 6000
1.000 0.893 0.797 0.712
3
Salvage revenue
2000
0.712
–22988 * NPV factor from Table S7.1. Machine B Year
NPV –5000 –351 –308 –270 –237 –208 –6374 +519 –5855
Machine A
3
Three Small Ovens
Original cost Excess labor per year Maintenance per year Salvage value
Year
S7.31
Now 1 2 3
104
NPV Factor*
NPV
Expense Expense Expense Expense
20000 5000 5000 5000
1.000 0.893 0.797 0.712
Salvage revenue
7000
0.712
–20000 –4465 –3985 –3560 –32010 +4984 –27026
* NPV factor from Table S7.1.
(a) NPV of the three small ovens = –$8,511; NPV of the two large ovens = –$5,855. Therefore, you should recommend that the firm purchase the two large ovens. (b) The basic assumptions made with regard to the ovens are: The ovens are of equal quality The ovens are of equivalent production capacity (c) The basic assumptions made with regard to methodology are: Future interest rates are known Payments are made at the end of each time period
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SUPPLEMENT 7 C A PA C I T Y P L A N N I N G
S7.35
F 300 100 crepes (a) BEPx1 P –V 4–1 0 F2 0 0 (b) BEPx 2 P – V2 4–(1+1.5) 1.5
S7.39 (a) Proposal A: Profit at 8,500 units Profit = (SP VC )X F @ 8,500 for Proposal A: (20 12)8,500 50,000 = 18,000 @ 8,500 for Proposal B: (20 10)8,500 70,000 = 15,000
If fixed costs are zero, and V
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