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Cost volume behavior analysis...
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Chapter 7
Cost-Volume-Profit Analysis
Chapter 7 Cost-Volume-Profit Analysis Quick Check Answers: QC-1. d QC-2. c
QC-3. b QC-4. c
QC-5. a QC-6. c
QC-7. b QC-8. b
QC-9. c QC-10. d
Short Exercises (5-10 min.) S7-1 a.
Sales price per passenger……………………. Less: Variable cost per passenger………….. Contribution margin per passenger…………
$ 50 20 $ 30
b.
Contribution margin per passenger………… Divided by sales price per passenger………. Contribution margin ratio……………………..
$30 ÷ 50 60%
c.
Total contribution margin (11,000 × $30)…... Less: Fixed expenses………………………….. Operating income……………………………….
$330,000 210,000 $120,000
d.
Total contribution margin ($490,000 × 60%) ………………………….. Less: Fixed expenses………………………….. Operating income……………………………….
$294,000 210,000 $84,000
(5 min.) S7-2 The unit contribution margin tells managers how much income is earned on each unit of sales before considering fixed costs. Each sale contributes its unit contribution margin towards covering fixed costs and generating a profit. Therefore, if the number of dinner cruises sold increases by 600 and each sale generates $30 of contribution margin, operating income will increase (or operating loss will decrease) by $18,000 (= 600 passengers × $30 per passenger).
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(5-10 min.) S7-3 Units sold (to break even)
Fixed expenses + Operating income Contribution margin per unit (passenger)
=
$210,000 + 0 $30*
= =
7,000 passengers
*Contribution margin per passenger
=
$50 sales price
−
$20 variable expense per passenger
Number of passengers to break even*……………. Sales price per passenger…………………………... Sales revenue to break even………………………..
7,000 × $50 $350,000
* from earlier calculation
(5 min.) S7-4 Sales in units
= = =
Fixed expenses + Operating income Contribution margin per unit $210,000 + $45,000 $30 8,500 dinner cruise tickets
Or, using the equation approach: Sales revenue
−
Variable expenses
−
Fixed expenses
=
Operating income
Sale price Units per unit × sold
−
Variable cost Units per unit × sold
−
Fixed expenses
=
Operating income
[($50 × Units sold)
−
($20 × Units sold)] [($50 − $20) × Units sold]
− $210,000 − $210,000 Units sold
= $45,000 = $45,000 = 8,500 tickets
To earn target income of $45,000, the cruiseline must sell 8,500 dinner cruise tickets.
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Chapter 7
Cost-Volume-Profit Analysis
(5-10 min.) S7-5
(5 min.) S7-6 a. b. c. d. e. f. g. h. i. j.
Fixed expense line Total expense line Sales revenue line Dollars (vertical axis) Units (horizontal axis) Operating loss area Operating income area Breakeven point 150 $300
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(10 min.) S7-7
Req. 1 If the sales price declines to $40, then the new unit contribution margin is $20 ($40 − $20). The new breakeven point in units is: Fixed expenses + Operating income = Sales in units Contribution margin per unit $210,000 + $0 $20
= =
10,500 dinner cruise passengers
To achieve breakeven, sales revenue needs to be $420,000 (10,500 passengers × $40 sales price per passenger). Also can be calculated as: Fixed expenses + Operating income = Sales in $ Contribution margin ratio $210,000 + $0 0.50*
= =
$420,000 dinner cruise revenue *CM ratio = $20/$40 = 0.50
Or, using the equation approach: Sales revenue
−
Sale price Units per unit × sold
−
Variable expenses Variable cost per unit ×
($40 × Units sold) − [($40 − $20) × Units sold]
Units sold
($20 × Units sold)
−
Fixed expenses
=
Operating income
−
Fixed expenses
=
Operating income
− $210,000 − $210,000 Units sold
10,500 passengers × $40 = $420,000 Alternatively, Contribution margin ratio
= Sales in dollars
Contribution margin per unit Sale price per unit
= =
$40 − $20 $20 0.50 Fixed expenses + Operating income Contribution margin ratio
= = =
= $0 = $0 = 10,500 passengers
$210,000 + $0 0.50 $420,000
All else being constant, a decrease in sales price will decrease the contribution margin per unit and the contribution margin ratio. The breakeven point will therefore increase. Increases in sales price will have the opposite effect. 7-4
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Chapter 7
Cost-Volume-Profit Analysis
(continued) S7-7 Req. 2 If the variable cost decreases to $10, then the new unit contribution margin is $40 ($50 − $10). The new breakeven point in units is: Fixed expenses + Operating income = Sales in units Contribution margin per unit $210,000 + $0 $40
= =
5,250 dinner cruise passengers
To achieve breakeven, sales revenue needs to be $262,500 (5,250 passengers × $50 sales price per ticket). Or, using the equation approach: Sales revenue
−
Variable expenses
−
Fixed expenses
=
Operating income
Sale price Units per unit × sold
−
Variable cost Units per unit × sold
−
Fixed expenses
=
Operating income
($50 × Units sold) − [($50 − $10) × Units sold]
($10 × Units sold)
− $210,000 − $210,000 Units sold
= $0 = $0 = 5,250 passengers
5,250 passengers × $50 = $262,500 Alternatively, Contribution margin ratio
= = Sales in dollars
Contribution margin per unit Sale price per unit
=
$50 − 10 $50 0.80 Fixed expenses + Operating income Contribution margin ratio
= = =
$210,000 + $0 0.80 $262,500
All else being equal, a decrease in variable costs will increase the contribution margin per unit and the contribution margin ratio. The breakeven point will therefore decrease. An increase in variable costs will have the opposite effect.
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(5-10 min.) S7-8 Req. 1 The decline in fixed costs does not affect the $30 unit contribution margin calculated in S7-1. The new breakeven point in units is: Fixed expenses + Operating income = Sales in units Contribution margin per unit $180,000 + $0 $30
= =
6,000 dinner cruise passengers
Or, using the equation approach: Sales revenue
−
Sale price Units per unit × sold
−
Variable expenses Variable cost per unit ×
($50 × Units sold) − [($50 − $20) × Units sold]
Units sold
($20 × Units sold)
−
Fixed expenses
=
Operating income
−
Fixed expenses
=
Operating income
− $180,000 − $180,000 $30 × Units sold Units sold
6,000 passengers × $50 = $300,000 Alternatively, Contribution margin ratio
= = Sales in dollars
$50 − 20 $50 0.60 Fixed expenses + Operating income Contribution margin ratio
= = =
7-6
Contribution margin per unit Sale price per unit
=
$180,000 + $0 0.60 $300,000
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= = = =
$0 $0 $180,000 6,000 passengers
Chapter 7
Cost-Volume-Profit Analysis
(continued) S7-8
Req. 2 The breakeven point is lower than in S7-3. By cutting fixed costs, the cruiseline was able to decrease its breakeven point by 1,000 passengers (7,000 - 6,000). All else being equal, a decrease in fixed costs will decrease the breakeven point, while an increase in fixed costs will increase the breakeven point.
(5-10 min.) S7-9 Weighted-Average Contribution Margin per Unit Regular Executive Cruise Cruise Sale price per ticket $ 50 $130 Less: Variable expense per ticket 20 40 Contribution margin per ticket $ 30 $ 90 Sales mix in units × 4 × 1 Contribution margin $120 $ 90 Weighted-average contribution margin per unit ($210 / 5)
Total
5 $210 $ 42.00
A simple average contribution margin would be $60 [(30 + 90) / 2]. The weighted-average is less than the simple average because the cruiseline sells more regular cruises (with the lower contribution margin) than executive cruises. The weighted average contribution margin ($42.00) is higher than the contribution margin of regular cruises ($30) because the cruiseline sells some executive cruises, and executive cruises have a higher contribution margin ($90) than regular cruises. Because the new sales mix creates a higher weighted average contribution margin, the cruiseline will need to sell fewer cruises, in total, to breakeven than when it just sold regular cruises.
(5-10 min.) S7-10 a. Sales in total tickets
= =
Fixed expenses + Operating income Weighted-average contribution margin per unit $210,000 + $0 $42.00*
= 5,000 passengers *Weighted-average contribution margin per unit from S7-9. b. Breakeven sales of regular cruises (5,000 × 4/5)……… Breakeven sales of executive cruises (5,000 × 1/5)...... Total cruise passengers.................................………..
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4,000 1,000 5,000
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(5-10 min.) S7-11 a.
Margin of safety in units
Expected sales in units
= =
8,750 – 7,000*
=
1,750 passengers
Breakeven sales in units
−
*(from S7-3) b.
Margin of safety in dollars
Target level sales dollars
= =
$437,500a - $350,000b
=
$87,500 a
-
Breakeven sales dollars
8,750 x $50 = $437,500 7,000 x $50 = $350,000
b
c.
Margin of safety as a percentage of expected sales
Margin of safety in dollars Expected sales in dollars
=
$87,500 $437,500
= =
20%
(5-10 min.) S7-12 a.
Contribution margin (8,750 × $30 / cruise passenger)…………………………………...... Less: Fixed expenses…………………………. Operating income……………………………….. Operating Leverage Factor
$262,500 210,000 $52,500 =
Contribution margin Operating income
=
$262,500 $52,500
=
5.0
b.
If volume increases 10%, operating income will increase 50% (operating leverage factor of 5.0 multiplied by 10%).
c.
If volume decreases by 5%, operating income will decrease by 25% (operating leverage factor of 5.0 multiplied by 5%).
(5-10 min.) S7-13 a. 7-8
Margin of safety
=
Expected sales
−
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Breakeven sales
Chapter 7 in units
Cost-Volume-Profit Analysis
in units =
1,500 – 750*
=
750 posters
in units
*Breakeven in units = $15,000/($45-$25) = 750 units b.
Margin of safety in dollars
Target level sales dollars
= =
$67,500** - $33,750***
=
$33,750
-
Breakeven sales dollars
** Expected sales in dollars = 1,500 x $45 = $67,500 *** Breakeven in dollars = 750 x $45 = $33,750 c.
Margin of safety as a percentage of expected sales
Margin of safety in dollars Expected sales in dollars
=
= =
33,750 67,500 50%
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(5-10 min.) S7-14 Contribution margin (1,500 × $20 / poster)……. Less: Fixed expenses…………………………. Operating income……………………………….. Operating Leverage Factor
$30,000 15,000 $15,000
=
Contribution margin Operating income
=
$30,000 $15,000
= 2.0 If volume increases 20%, operating income will increase 40% (operating leverage factor of 2.0 multiplied by 20%). Proof: Original volume (posters) ………………………….. Add: Increase in volume (20% × 1,500) ……… New volume (posters) …………………………….... Multiplied by: Unit contribution margin…………. New total contribution margin…………………….. Less: Fixed expenses……………………………... New operating income……………………………… Less: Operating income before change in
1,500 300 1,800 × $20 $36,000 (15,000 ) $21,000
volume (from above)……………………….....
(15,000 )
Increase in operating income……………………...
$6,000
Percentage change ($6,000 / $15,000) ……………..
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40%
Chapter 7
Cost-Volume-Profit Analysis
(5-10 min.) S7-15
Req. 1 Product: Cupcakes Selling price per unit Less: Variable cost per unit CM
$ $ $
6.00 4.00 2.00
To find the indifference point, you need to set the costs of Option 1 equal to the costs of Option 2: $2,600 = $1,700 + [($6 x .05) x CUPCAKES] Then solve for CUPCAKES: CUPCAKES = 3,000 Proof: Lease costs under Option 1: Fixed costs Variable costs (none) Total costs under Option 1
$ 2,600 0 $ 2,600
Lease costs under Option 2: Fixed costs Variable costs per unit ($6 x .05) Times # of units at pt of indifference (3,000)
$
0.30
$ 1,700
3,000
Total variable costs Total costs under Option 2
900 $2,600
Since the number of units is 2,200 and is less than the 3,000 point of indifference, option 2 would be the lowest cost option. Option 1 costs = $2,600 Option 2 costs = $1,700 + ($6 x 0.05) x 2,200) = $2,360 Req. 2 Option 1 is the better option for 4,500 units Option 1 costs = $2,600 Option 2 costs = $1,700 + (($6 x 0.05) x 4,500) = $3,050
(5-10 min.) S7-16 1. Integrity - Mitigate actual conflicts of interest, regularly communicate with business associates to avoid apparent conflicts of interest. Advise all parties of any potential conflicts. 2. Competence - Maintain an appropriate level of professional expertise by continually developing knowledge and skills. 3. Competence - Perform professional duties in accordance with relevant laws, regulations, and technical standards. 4. Confidentiality - Keep information confidential except when disclosure is authorized or legally required. 5. Credibility - Disclose all relevant information that could reasonably be expected to influence an intended user's understanding of the reports, analyses, or recommendations.
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Exercises (Group A) (15 min.) E7-17A Req. 1 Global Travel Contribution Margin Income Statements Sales revenue Less: Variable expenses (30% of sales revenue*) Contribution margin (70% of sales revenue**) Fixed expenses Operating income (loss) __________ *$120,000 / $400,000 = 0.30 **$280,000 / $400,000 = 0.70 (CM ratio)
$270,000 81,000 189,000 170,800 $ 18,200
$410,000 123,000 287,000 170,800 $ 116,200
Req. 2 Breakeven sales
=
$170,800 + $0 1 − 0.30
=
$170,800 + $0 0.70
= $244,000
(10-15 min.) E7-18A This problem involves working backwards through the shortcut contribution margin formula and then working backwards through the contribution margin income statement to find the missing data. First, fill in the given data in the short cut contribution margin formula, and solve for the contribution margin ratio: Sales needed to breakeven $48,000 Contribution margin ratio Contribution margin ratio
=
Fixed expenses Contribution margin ratio
=
$24,000 Contribution margin ratio
=
$24,000 $48,000
= .50
Next, fill in the given data in the contribution margin income statement: Sales…………………………. Less: Variable expenses…. Contribution margin………. Less: Fixed expenses…….. Operating income…………..
7-12
$ ? 42,000 ? 24,000 $ ?
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Chapter 7
Cost-Volume-Profit Analysis
(continued) E7-18A Because the contribution margin ratio 50% of sales revenue. Therefore: Variable expenses $ 42,000 $ 84,000 Or alternatively: Sales − $42,000 Sales − 50% Sales 50% Sales Sales Sales
is 50% of sales revenue, the variable expenses must be = = =
50% × Sales revenue 50% × Sales revenue Sales revenue
= = = =
50% Sales $42,000 $42,000 $42,000 50% $84,000
=
Once sales revenue is found, the rest of the income statement follows: Sales………………………………. $ 84,000 Less: Variable expenses………. 42,000 Contribution margin……………. $ 42,000 Less: Fixed expenses………….. 24,000 Operating income………………. $ 18,000 Therefore, at the current level of operations, the company’s sales revenue is $84,000 and its operating income is $18,000.
(15 min.) E7-19A Req. 1 Contribution margin per unit: Sale price....................................………….. Less: Variable expenses.................................…. Contribution margin per unit.................... Contribution margin ratio: Contribution margin per unit Sale price per unit
$1.80 0.90 $0.90
=
$0.90 $1.80
=
0.50
Req. 2 Breakeven sales in units
= =
Fixed expenses + Operating income Contribution margin per unit $90,000 + $0 $0.90
= 100,000 packages
Breakeven sales in dollars
= =
Fixed expenses + Operating income Contribution margin ratio $90,000 + $0 0.50
= $180,000
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(continued) E7-19A Req. 3 Sales in units
= =
Fixed expenses + Operating income Contribution margin per unit $90,000 + $18,000 $0.90
= 120,000 packages
(5-10 min.) E7-20A New contribution margin per unit: Sales price....................................………….. Less: Variable expenses.................................…. Contribution margin per unit.................... Sales in units
= =
$1.80 0.80 $1.00
Fixed expenses + Operating income Contribution margin per unit $105,000 + $18,000 $1.00
= 123,000 packages The company would have to sell 3,000 more packages of socks (123,000 − 120,000 from E719A) to earn $18,000 of operating income. The increase in fixed costs was not completely offset by the decrease in variable costs at the prior target profit volume of sales. Therefore, the company will need to sell more units in order to achieve its target profit level.
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Chapter 7 Req. 1 Contribution margin ratio
(10-15 min.) E7-21A Contribution margin per unit Sales price per unit
= = =
Breakeven sales in dollars
Cost-Volume-Profit Analysis
$5.25 − $2.10 $5.25 0.60 Fixed expenses + Operating income Contribution margin ratio
= = =
$7,500 + $0 0.60 $12,500
Req. 2 If franchisees require a monthly operating income of $7,500 Target sales Fixed expenses + Operating income = in dollars Contribution margin ratio = =
$7,500 + $7,050 0.60 $24,250
Yes, the franchising concept is a good idea. Most locations are expected to sell more ($25,000) than the sales required to earn the target profit ($24,250).
(10- 15 min.) E7-22A Req. 1 Prior to changes, the average restaurant location had the following operating income: Contribution margin per unit ($5.25 - $2.10) $ 3.15 Average sales volume units………………… × 6,500 Contribution margin………………………….. $20,475 Less: Fixed expenses………………………. (7,500) Operating income……………………………... $12,975 Req. 2 After the price cut and advertising fees, the average restaurant location will have the following operating income: New contribution margin per unit ($4.75 sales price – $2.10 variable cost……………………………………. $ 2.65 New sales volume (units)…………. × 7,000 Contribution margin………………... $18,550 Less: New fixed expenses ($7,500 + $600 advertising fee)…… (8,100) New operating income…………….. $ 10,450 Assuming volume increases according to plan, cutting the sales price and advertising will allow the franchise owners to continue to reach their target profits of $7,050 per month. However, their operating income will not be as high as before the changes.
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(10-15 min.) E7-23A Req. 1 Breakeven sales in dollars
Fixed expenses + Operating income Contribution margin ratio
= = =
$630,000 + $0 0.70 $900,000
Req. 2 Grover’s Steel Parts Operating Income Projections at Different Sales Levels Sales revenue $ 520,000 × Contribution margin ratio 0.70 Contribution margin 364,000 Less: Fixed expenses 630,000 Operating income (loss) $(266,000)
$1,010,000 0.70 707,000 630,000 $ 77,000
Req. 3 Yes, the income projections at the two different sales levels make sense given the breakeven sales level ($900,000) computed in Req. 1. Req. 2 shows that if the company’s revenue is only $520,000 (short of the revenue required to breakeven) the company incurs a loss. On the other hand, if revenue is $1,010,000 (higher than the revenue required to breakeven), the company earns a profit.
(15 min.) E7-24A Req. 1 Target sales in dollars
= = =
Fixed expenses + Operating income Contribution margin ratio $630,000 + $77,000 0.40 $1,767,500
Req. 2 Fixed expenses + Operating income Contribution margin ratio
Sales in dollars
=
$1,010,000
=
$404,000
=
Fixed expenses + $77,000
$327,000
=
Fixed expenses
Fixed expenses + $77,000 0.40
Fixed expenses can only be $327,000 to maintain the prior profit level of $77,000 per month. Therefore, Grover will have to save at least $303,000 per month in fixed costs ($630,000 − $327,000) by moving operations overseas if he plans to maintain his prior profit level.
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Chapter 7
Cost-Volume-Profit Analysis
(15-20 min.) E7-25A
Req. 1 (Fixed expenses + Operating income) / CM per unit = Breakeven in units ($240,000 + $0) / ($2,400 - $1,000 - $200) = 200 units
(Fixed expenses + Operating income) / CM ratio = Breakeven in sales dollars CM ratio = ($2,400 - $1,000 - $200) / $2,400 = .50 ($240,000 + $0) / .50 = $480,000 Req. 2 Total CM ($2,400 - $1,000 - $200) x 410 = $492,000 Projected operating income = $492,000 - $240,000 = $252,000 Req. 3 New fixed expenses = $240,000 + $120,000 = $360,000 New CM = $2,400 – ($1,000 - $240) - $200 = $1,440 (Fixed expenses + Operating income) / CM per unit = Breakeven in units ($360,000 + $0) / ($2,400 – ($1,000 - $240) - $200) = 250 units (Fixed expenses + Operating income) / CM ratio = Breakeven in sales dollars CM ratio = ($2,400 – ($1,000 - $240) - $200) / $2,400 = .60 ($360,000 + $0) / .60 = $600,000 Req. 4 Total CM ($2,400 – ($1,000 - $240) - $200) x 410 = $590,400 Projected operating income = $590,400 - $360,000 = $230,400 Req. 5 Based purely on the financial analysis presented above (operating income for Req. 1 is more than the operating income for Req. 4), the company should not implement the software control system. However, the new control system would reduce waste and contribute to the company’s sustainability objectives. The company should take into account not only the financial measures such as operating income, breakeven point, and operating leverage, but also the sustainability impact of the decision. Student answers may vary for Req. 5.
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(5-10 min.) E7-26A Use the short cut contribution margin formula to determine the company’s current level of fixed expenses: Fixed expenses Sales needed to breakeven = Contribution margin ratio Fixed expenses .20
$350,000
=
$350,000 × .20
=
Fixed expenses
$70,000
=
Fixed expenses
After buying the equipment, the company’s fixed expenses will be $125,000 ($70,000 + $55,000 increase). Calculate breakeven (in sales) at the new level of fixed expenses: Fixed expenses Sales needed to breakeven = Contribution margin ratio = =
$125,000 .20 $625,000
The company will now have to generate $625,000 of sales revenue to breakeven.
(5-10 min.) E7-27A Sales price per unit……………….. Contribution margin ratio………... Contribution margin per unit…….
$24.00 × .625 $15.00
Find the number of scarves needed to breakeven on (or pay for) the extra entrance fee cost of $120 (= $1,200 × 10% increase): Fixed expenses Breakeven in units = Contribution margin per unit
Alternatively: Breakeven in sales revenue
=
$120 $15.00
=
8 scarves Fixed expenses Contribution margin ratio
= =
$120 .625
= $192 in sales revenue Dividing $192 in sales revenue by the price per scarf ($24) yields 8 scarves. The owner will have to sell an additional 8 scarves next year to cover the increase in entrance fees.
(15-20 min.) E7-28A 7-18
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Chapter 7
Cost-Volume-Profit Analysis
Weighted-Average Contribution Margin per Unit Twig Sale price per unit $15.00 Less: Variable cost per unit 2.50 Contribution margin per unit $12.50 Multiply by: Sales mix in units × 4 Contribution margin $50.00
Oak $35.00 10.00 $25.00 × 1 $25.00
Weighted-average contribution margin per unit ($75 / 5 units) Sales in total units: = =
Total
5 $75.00 $15.00
Fixed expenses + Operating income Weighted-average contribution margin per unit
$300 + $0 $15
= 20 units Breakeven sales of twig stands (20 × 4/5)……………… Breakeven sales of oak stands (20 × 1/5).………………
16 units 4 units
By charging her husband part of the craft fair entrance fees, the wife’s fixed costs will decrease. Therefore, the wife will need to sell fewer scarves to breakeven than before her husband decided to share her craft booths.
(15-20 min.) E7-29A Weighted-Average Contribution Margin per Unit Standard Chrome Sales price per unit $60 $75 Less: Variable cost per unit 45 55 Contribution margin per unit $15 $20 Multiply by: Sales mix in units × 3 × 2 Contribution margin $45 $40 Weighted-average contribution margin per unit ($110 / 5 units)
Total
5 $ 85 $ 17
Sales in total units: Fixed expenses + Operating income Weighted-average contribution margin per unit
= =
$18,700 + $0 $17
= 1,100 units Breakeven sales of standard scooters (1,100 × 3/5)……………… Breakeven sales of chrome scooters (1,100 × 2/5).………………..
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660 units 440 units
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(continued) E7-29A
Sales in total units:
Fixed expenses + Operating income Weighted-average contribution margin per unit
=
$18,700 + $13,600 $17
=
= 1,900 units Target sales of standard scooters (1,900 × 3/5)........……………… Target sales of chrome scooters (1,900 × 2/5)............…................
1,140 units 760 units
(20-30 min.) E7-30A This is a challenging exercise that requires students to work backwards. Use the weightedaverage contribution margin per unit chart, in conjunction with the shortcut formula, to work backwards to find the contribution margin of the Classic. Sales price per unit................……….. Less: Variable expense per unit. ($125 + $35) Contribution margin per unit..…….. Multiply by: Sales mix in units..........…………….. Contribution margin..........…………. Weighted-average contribution margin per unit..........…………….. a
Classic 215 × 3 645
Sales in total units
=
Fixed expenses + Operating income Weighted-average contribution margin per unit
2,100
=
$195,000 + $36,000 Weighted-average contribution margin per unit
Weighted-average contribution margin per unit
= =
7-20
Digital $225 160 65 x7 $455
$231,000 2,100 $110 / unit
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Total
10 1,100 $ 110
Chapter 7
Cost-Volume-Profit Analysis
(continued) E7-30A b
c
Weighted-average contribution margin per unit
Contribution margin per Classic watch
Total sales mix contribution margin Total sales mix units
=
$455 + X 10
$110
=
$1,100
=
$455 + X
X
=
$645
3
=
$645
=
$215
×
Contribution margin per Classic watch
(15 min.) E7-31A Req. 1 The company’s operating income can be computed as follows: Sales revenue……………………………………. Less: Variable expenses……………………… Contribution margin……………………………. Less: Fixed expenses……($2,600,000 - $1,088,000) Operating income……………………………….. Req. 2 Contribution margin ratio
5,712,000 6,800,000
= =
$6,800,000 1,088,000 5,712,000 1,512,000 $4,200,000
84%
Req. 3 Breakeven in sales dollars
1,512,000 84%
= =
$1,800,000
Req. 4 If the company embarks on this advertising campaign, sales revenue and variable costs will rise by 14%, which will cause the contribution margin to increase by 14%. Fixed costs will rise by only $250,000 due to the advertising campaign. Overall operating income will increase by $549,680 See the computations to follow. The change in operating income can be computed as follows: Current contribution margin Percentage increase Increase in contribution margin Less: Increase in fixed costs of advertising campaign Increase in operating income
$5,712,000 × 14% 799,680 250,000 $549,680
(15 min.) E7-32A Copyright © 2015 Pearson Education, Inc.
7-21
Managerial Accounting 4e Solutions Manual Req. 1 Contribution margin ratio
Breakeven sales in dollars
=
1.00 – 0.60
=
0.40
= = Target sales in dollars
Margin of safety
Req. 2 Margin of safety as a percentage of target sales
Fixed expenses + Operating income Contribution margin ratio
=
$12,000 + $0 0.40 $30,000 Fixed expenses + Operating income Contribution margin ratio
= =
$12,000 + $20,000 0.40
=
$32,000 0.40
=
$80,000
=
$80,000 − $30,000
=
$50,000
=
$50,000 $80,000
= 0.625 or 62.5% of target sales Req. 3 Target sales……………………... Contribution margin ratio…….. Contribution margin…………… Less: Fixed expenses……….. Operating income………………. Operating Leverage Factor
$80,000 × .40 $32,000 12,000 $20,000 =
Contribution margin Operating income
=
$32,000 $20,000
=
1.60
Req. 4 If volume decreases 12%, operating income will decrease 19.20% (operating leverage factor of 1.60 multiplied by 12%).
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(10 min.) E7-33A First, find the company’s contribution margin: Sales……………………………… Contribution margin ratio…….. Contribution margin……………
$60,000 × .35 $21,000
Then, work backwards to find the company’s operating income: Contribution margin Operating leverage factor = Operating income =
$21,000 Operating income
Operating income
=
$21,000 1.40
Operating income
= $15,000
1.40
Finally, finish the income statement to find the fixed expenses: Contribution margin…….. $21,000 Less: Fixed expenses…. Unknown Operating income……….. $15,000 Therefore, fixed expenses must be $6,000.
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(10-15 min.) E7-34A Req. 1 Selling price $30 Less: Variable costs ($6 + $3 + $3) 12 CM per unit $18 Lease costs under Option A: Fixed costs Variable costs (none) Total costs under Option A
$ 3,000 0 $ 3,000
Lease costs under Option B: Fixed costs Total variable costs (10% x $30 x 250) Total costs under Option B
$ 1,650 750 $ 2,400
The more attractive lease option is Option B because it results in the lowest total lease costs. Req. 2 To solve the question, you need to set the costs of Option A equal to the costs of Option B: $3,000 = $1,650 + (10% x $30 x CANDLES) Then solve for CANDLES: CANDLES = 450 Req. 3 The lease option that is more attractive for the company if the company plans to sell 600 candles a month is option A, the fixed lease payment because the sales volume is more than the indifference point.
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Chapter 7
(20-25 min.) E7-35A
Req. 1 Breakeven in units
Fixed expenses Contribution margin per unit
= = =
*
Req. 2 2a.
2b.
Cost-Volume-Profit Analysis
Selling price Less: variable cost per unit CM per unit
Sales in units to reach desired profit
Sales in dollars to reach desired profit
$600 $30* 20 grooming kits
$62 $32 $30
Fixed expenses + Operating Income Contribution margin per unit
= =
$600 + $900 $30
=
$1,500 $30
=
50 grooming kits
=
breakeven units x selling price per unit
=
50 units x $62/each
=
$3,100
2c. Condensed Income Statement Sales Less: variable expenses (50 x $32)
$3,100
Contribution margin
$1,500
Less: fixed expenses
$600
Operating income
$900
$1,600
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(continued) E7-35A Req. 3 Margin of safety in dollars: Sales at target level: Sales at B/E level: Margin of safety in dollars Margin of safety in units: Sales at target level: Sales at B/E level: Margin of safety in units Margin of safety in %: Margin of safety in dollars: Sales at target level: $1,860/$3,100 =
$3,100 $1,240* $1,860
50 20 30
$1,860 $3,100 60.00%
*Sales at B/E level: 20 kits x $62 = $1,240
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(20-25 min.) E7-36A Req. 1 Total Sales
Per Unit
%
$81,250
$25
100%
48,750
15
60%
Contribution Margin
$32,500
$10
40%
Less: Fixed expenses
13,000
Less: Variable expenses
Operating income
$19,500
1a) Total contribution margin is $32,500. 1b) Per unit contribution margin is $10. 1c) Operating income is $19,500. 1d) Units sold = Total sales / sales price = $81,250 / $25 = 3,250 units Req. 2 2a. Breakeven in units
= =
$13,000 $10
=
1,300 units
2b. Breakeven sales in dollars
Fixed expenses Contribution margin per unit
= = =
Fixed expenses + Operating income Contribution margin ratio $13,000 + 0 0.40 (from req. 1) $32,500
Req. 3 3a. Sales in units to reach desired profit
=
Fixed expenses + Operating Income Contribution margin per unit
=
$13,000 + $53,000 $10
=
$66,000 $10
=
6,600 units
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(continued) E7-36A 3b. Budgeted Sales Units
3,250
Less: Breakeven Sales Units
1,300
Margin of Safety in Units
1,950
3c. Budgeted Sales
$81,250
Less: Breakeven Sales Volume
$32,500
Margin of Safety in Dollars 3d.
$48,750
Margin of Safety in Dollars
$48,750
Divided by: Budgeted Sales Dollars
$81,250
Margin of Safety %
60.0%
(20-25 min.) E7-37A 1.
Sales price per unit............................................. Less: Variable cost per unit (7.30+6+2.60+2.10)......................................... Contribution margin per unit .............................
$25.00 $18.00 $ 7.00
Contribution margin ratio
=
$7.00 $25.00
Sales revenue (140,000 × $25.00)……………… Less: Variable expenses (140,000 × $18.00)… Contribution margin……………………………..
=
.28
=
28%
$ 3,500,000 (2,520,000) $ 980,000
2.
Sales volume (units)……………………………… Unit contribution margin………………………… Contribution margin……………………………… Less: Fixed expenses………($292,000 + $447,200) Operating income………………………………….
170,000 x $7.00 $1,190,000 (739,200) $450,800
3.
Sales revenue……………………………………… Contribution margin ratio……………………….. Contribution margin……………………………… Less: fixed expenses……………………………. Operating income………………………………….
$4,500,000 x 28% $1,260,000 (739,200) $ 520,800
4.
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B/E sales in units
=
$739,200 $7.00
=
B/E sales in dollars
=
$739,200 28%
=
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105,600 units $2,640,000
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Cost-Volume-Profit Analysis
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(continued) E7-37A 5. 6.
$739,200 + $269,500 $7.00
=
Original contribution margin per unit.................. Less: Increase in direct labor cost per unit ($6.00 x 10%).......................................................... New contribution margin per unit………………...
$0.60 $6.40 $739,200 24,000
New fixed expenses…………………………………
$763,200 $763,200 $6.40
=
8.
Increase in volume…………………….. × Operating leverage factor………….. New fixed expenses……………………
9.
Margin of safety
$ 240,800
Sales − Sales at breakeven $3,500,000 − $2,640,000 (from part 1) (from part 4) $860,000
= Margin of safety as a percentage =
$860,000 $3,500,000
16 GB $25 18 $ 7 × 6 $42
=
=
.25 (rounded )
32 GB
Total
$50 22 $28 ×1 $28
7 $70
Weighted-average contribution margin per unit Sales in units
4.07 = (rounde d)
$980,000
8% 4.07 32.6% (rounded)
=
Sales price…………….. Less: Variable cost………….. Contribution margin…. Sales mix………………. Multiply by: Contribution margin….
119,250 Units
$980,000 (739,200) $ 240,800 =
=
$739,200 + $269,500 $10
Smaller 16 GB: 100,870 × 6/7………………….. Larger 32 GB: 100,870 × 1/7….………………….
7-30
=
Contribution margin (from part 1)………………... Less: Fixed expenses……………………………... Operating income…………………………………… Operating Leverage factor
10.
$7.00
Original fixed expenses……………………………. Plus: Increase in fixed expenses………………..
New breakeven in units 7.
144,100 units
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25% = (rounded )
$10.00
=
100,870 units
86,460 units (rounded) 14,410 units (rounded)
Chapter 7
Cost-Volume-Profit Analysis
The target profit volume is lower than before (Req. 5) because now the company is selling a product with a much higher unit contribution margin.
Exercises (Group B) (15 min.) E7-38B Req. 1 Contribution Margin Income Statements Sales revenue Less: Variable expenses (35% of sales revenue*) Contribution margin (65% of sales revenue**) Fixed expenses Operating income (loss) __________ *$192,500 / $550,000 = 0.35 **$357,500 / $550,000 = 0.65 (CM ratio)
$190,000 66,500 123,500 176,800 $ (53,300)
$420,000 147,000 273,000 176,800 $ 96,200
Req. 2 Breakeven sales
=
$176,800 + $0 1 − 0.35
=
$176,800 + $0 0.65
= $272,000
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(10-15 min.) E7-39B This problem involves working backwards through the shortcut contribution margin formula and then working backwards through the contribution margin income statement to find the missing data. First, fill in the given data in the short cut contribution margin formula, and solve for the contribution margin ratio: Sales needed to breakeven $40,000 Contribution margin ratio
=
Fixed expenses Contribution margin ratio
=
$30,000 Contribution margin ratio
=
$30,000 $40,000
Contribution margin ratio
= .75
Next, fill in the given data in the contribution margin income statement: Sales…………………………. Less: Variable expenses…. Contribution margin………. Less: Fixed expenses…….. Operating income…………..
$ ? 45,000 ? 30,000 $ ?
Because the contribution margin ratio is 75% of sales revenue, the variable expenses must be 25% of sales revenue. Therefore: Variable expenses $ 45,000 $180,000
= = =
25% × Sales revenue 25% × Sales revenue Sales revenue
Sales − $45,000 Sales − 75% Sales 25% Sales Sales
= = = =
Sales
=
75% Sales $45,000 $45,000 $45,000 25% $180,000
Or alternatively:
Once sales revenue is found, the rest of the income statement follows: Sales………………………………. Less: Variable expenses………. Contribution margin……………. Less: Fixed expenses………….. Operating income……………….
$180,000 45,000 $135,000 30,000 $ 105,000
Therefore, at the current level of operations, the company’s sales revenue is $180,000, and its operating income is $105,000.
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(15 min.) E7-40B
Req. 1 Contribution margin per unit: Sale price....................................………….. Less: Variable expenses.................................…. Contribution margin per unit.................... Contribution margin ratio: Contribution margin per unit Sale price per unit
$1.60 0.80 $0.80
=
$0.80 $1.60
=
0.50
Req. 2 Breakeven sales in units
= =
Fixed expenses + Operating income Contribution margin per unit $80,000 + $0 $0.80
= 100,000 packages
Breakeven sales in dollars
= =
Fixed expenses + Operating income Contribution margin ratio $80,000 + $0 0.50
= $160,000 Req. 3 Sales in units
= =
Fixed expenses + Operating income Contribution margin per unit $80,000 + $25,000 $0.80
= 131,250 packages
(5-10 min.) E7-41B New contribution margin per unit: Sale price....................................………….. Less: Variable expenses.................................…. Contribution margin per unit.................... Sales in units
= =
$1.60 0.60 $1.00
Fixed expenses + Operating income Contribution margin per unit $95,000 + $25,000 $1.00
= 120,000 packages
(continued) E7-41B
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Managerial Accounting 4e Solutions Manual The company would have to sell 11,250 fewer packages of socks (120,000 − 131,250 from E740B) to earn $25,000 of operating income.
(10-15 min.) E7-42B Req. 1 Contribution margin ratio
= = Breakeven sales in dollars
Contribution margin per unit Sales price per unit
=
$6.25 − $2.50 $6.25 0.60 Fixed expenses + Operating income Contribution margin ratio
= = =
$8,250 + $0 0.60 $13,750
Req. 2 If franchisees require a monthly operating income of $6,600 Target sales Fixed expenses + Operating income = in dollars Contribution margin ratio = =
$8,250 + $6,600 0.60 $24,750
No, the franchising concept is not a good idea. The sales required to earn the target profit ($24,750) are more than the expected sales generated ($24,000).
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(10- 15 min.) E7-43B
Req. 1 Prior to changes, the average restaurant location had the following operating income: Contribution margin per unit (from E7-42B) $ 3.75 Average sales volume units………………… × 5,500 Contribution margin………………………….. $20,625 Less: Fixed expenses………………………. (8,250) Operating income……………………………... $12,375
Req. 2 After the price cut and advertising fees, the average restaurant location will have the following operating income: New contribution margin per unit ($5.75 sales price – $2.50 variable cost……………………………………. New sales volume (units)…………. Contribution margin………………... Less: New fixed expenses ($8,250 + $500 advertising fee)…… New operating income……………..
$ 3.25 × 6,000 $19,500 (8,750) $ 10,750
Assuming volume increases according to plan, cutting the sales price and advertising will allow the franchise owners to reach their target profits of $6,600 per month.
(10-15 min.) E7-44B Req. 1 Breakeven sales in dollars
= = =
Fixed expenses + Operating income Contribution margin ratio $620,000 + $0 0.80 $775,000
Req. 2
Sales revenue × Contribution margin ratio Contribution margin Less: Fixed expenses Operating income (loss)
Operating Income Projections at Different Sales Levels $ 520,000 0.80 416,000 620,000 $(204,000)
$1,020,000 0.80 816,000 620,000 $ 196,000
Req. 3 Yes, the income projections at the two different sales levels make sense given the breakeven sales level ($775,000) computed in Req. 1. Req. 2 shows that if the company’s revenue is only $520,000 (short of the revenue required to breakeven) the company incurs a loss. On the other hand, if revenue is $1,020,000 (higher than the revenue required to breakeven), the company earns a profit.
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(15 min.) E7-45B Req. 1 Sales in dollars
= = =
Req. 2
Fixed expenses + Operating income Contribution margin ratio $620,000 + $196,000 0.50 $1,632,000
Fixed expenses + Operating income Contribution margin ratio
Sales in dollars
=
$1,020,000
=
$510,000
=
Fixed expenses + $196,000
$314,000
=
Fixed expenses
Fixed expenses + $196,000 0.50
Fixed expenses can only be $314,000 to maintain the prior profit level of $196,000 per month. Therefore, the company will have to save at least $306,000 per month in fixed costs ($620,000 − $314,000) by moving operations overseas if it plans to maintain its prior profit level.
(15-20 min.) E7-46B Req. 1 (Fixed expenses + Operating income) / CM per unit = Breakeven in units ($294,000 + $0) / ($2,100 - $520 - $110) = 200 units (Fixed expenses + Operating income) / CM ratio = Breakeven in sales dollars CM ratio = ($2,100 - $520 - $110) / $2,100 = .700 ($294,000 + $0) / .700 = $420,000 Req. 2 Total CM = ($2,100 - $520 - $110 ) x 290 = $426,300 Projected operating income = $426,300 - $294,000 = $132,300 Req. 3 New fixed expenses = $294,000 + $126,000 = $420,000 New CM = ($2,100 – ( $520 - $210) - $110) = $1,680 (Fixed expenses + Operating income) / CM per unit = Breakeven in units ($420,000 + $0) / $1,680) = 250 units (Fixed expenses + Operating income) / CM ratio = Breakeven in sales dollars CM ratio = $1,680 / $2,100 = .800 ($420,000 + $0) / .800 = $525,000 Req. 4 Total CM ($2,100 – ($520- $210) - $110) x 290 = $487,200 Projected operating income = $487,200 - $420,000 = $67,200
(continued) E7-46B 7-36
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Cost-Volume-Profit Analysis
Req. 5 However, the new control system would reduce waste and contribute to the company’s sustainability objective. The company should take into account not only the financial measures such as operating income, breakeven point, and operating leverage, but also the sustainability impact of the decision. Student answers may vary.
(5-10 min.) E7-47B Use the short cut contribution margin formula to determine the company’s current level of fixed expenses: Fixed expenses Contribution margin ratio
Sales needed to breakeven
=
$500,000
=
$500,000 × .50
=
Fixed expenses
$250,000
=
Fixed expenses
Fixed expenses .50
After buying the equipment, the company’s fixed expenses will be $300,000 ($250,000 + $50,000 increase). Calculate breakeven (in sales) at the new level of fixed expenses: Sales needed to breakeven
Fixed expenses Contribution margin ratio
= = =
$300,000 .50 $600,000
The company will now have to generate $600,000 of sales revenue to breakeven.
(5-10 min.) E7-48B Sales price per unit……………….. Contribution margin ratio………... Contribution margin per unit…….
$14.00 × .625 $8.75
Find the number of scarves needed to breakeven on (or pay for) the extra entrance fee cost of $350 (= $1,400 × 25% increase): Fixed expenses Breakeven in units = Contribution margin per unit = =
$350 $8.75 40 scarves
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Managerial Accounting 4e Solutions Manual Alternatively: Breakeven in sales revenue
(continued) E7-48B Fixed expenses Contribution margin ratio
= =
$350 .625
= $560 in sales revenue Dividing $560 in sales revenue by the price per scarf ($14) yields 40 scarves. The owner will have to sell an additional 40 scarves next year to cover the increase in entrance fees.
(15-20 min.) E7-49B Weighted-Average Contribution Margin per Unit Twig Sales price per unit $18.00 Less Variable cost per unit 3.00 Contribution margin per unit $15.00 Multiply by: Sales mix in units × 4 Contribution margin $60.00 Weighted-average contribution margin per unit ($90 / 5 units)
Oak $38.00 8.00 $30.00 × 1 $30.00
Total
5 $90.00 $18.00
Sales in total units: Fixed expenses + Operating income Weighted-average contribution margin per unit
= =
$360 + $0 $18
= 20 units Breakeven sales of twig stands (20 × 4/5)……………… Breakeven sales of oak stands (20 × 1/5).………………
16 units 4 units
By charging her husband part of the craft fair entrance fees, the wife’s fixed costs will decrease. Therefore, the wife will need to sell fewer scarves to breakeven than before her husband decided to share her craft booths.
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(15-20 min.) E7-50B Weighted-Average Contribution Margin per Unit Standard Chrome Sales price per unit $65 $85 Less: Variable cost per unit 55 65 Contribution margin per unit $10 $20 Multiply by: Sales mix in units × 3 × 2 Contribution margin $30 $40 Weighted-average contribution margin
Total
5 $70 $ 14
Sales in total units to breakeven: Fixed expenses + Operating income = Weighted-average contribution margin per unit =
$9,800 + $0 $14
= 700 units Breakeven sales of standard scooters (700 × 3/5)……………… Breakeven sales of chrome scooters (700 × 2/5).………………..
420 units 280 units
Sales in total units to achieve target operating income: Fixed expenses + Operating income = Weighted-average contribution margin per unit =
$9,800 + 8,400 $14
= 1,300 units Target sales of standard scooters (1,300 × 3/5)........…………… Target sales of chrome scooters (1,300 × 2/5)............….............
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780 units 520 units
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Managerial Accounting 4e Solutions Manual
(20-30 min.) E7-51B This is a challenging exercise that requires students to work backwards. Use the weightedaverage contribution margin per unit chart, in conjunction with the shortcut formula, to work backwards to find the contribution margin of the Classic. Digital $250 170 80 × 8 $640
Sales price per unit................……….. Less: Variable expense per unit. ($120 + $50) Contribution margin per unit..…….. Multiply by: Sales mix in units..........…………….. Contribution margin..........…………. Weighted-average contribution margin per unit..........…………….. a
2,200
=
$200,000 + $75,000 Weighted-average contribution margin per unit $275,000 2,200
=
Weighted-average contribution margin per unit
Contribution margin per Classic watch
$125 / unit Total sales mix contribution margin Total sales mix units
=
$640 + X 10
$125
=
$1,250
=
$640 + X
X
=
$610
2
=
$610
=
$305
×
10 1,250 $ 125
Fixed expenses + Operating income Weighted-average contribution margin per unit
Contribution margin per Classic watch
7-40
c
=
=
c
305 × 2 610
Total
Sales in total units
Weighted-average contribution margin per unit
b
Classic
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Chapter 7
Cost-Volume-Profit Analysis
(15 min.) E7-52B Req. 1 The company’s operating income can be computed as follows: Sales revenue……………………………………. Less: Variable expenses……………………… Contribution margin……………………………. Less: Fixed expenses………($2,590,000 - $1,342,000) Operating income………………………………..
$6,100,000 1,342,000 4,758,000 1,248,000 $3,510,000
Req. 2 Contribution margin ratio
= Req. 3 Breakeven in sales dollars
$4,758,000 $6,100,000
=
=
78%
$1,248,000 78%
= $1,600,000 The company will have to generate $1,600,000 in sales in order to break even. Req. 4 If the company embarks on this advertising campaign, sales revenue and variable costs will rise by 16%, which will cause the contribution margin to increase by 16%. However, fixed costs will rise by $260,000 dollars due to the advertising campaign. The change in operating income can be computed as follows: Current contribution margin Percentage increase Increase in contribution margin Less: Increase in fixed costs of advertising campaign Increase in operating income
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$4,758,000 × 16% 761,280 260,000 $501,280
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Managerial Accounting 4e Solutions Manual Req. 1 Contribution margin ratio
Breakeven sales in dollars
(15 min.) E7-53B =
1.00 − 0.40
=
0.60
= = Target sales in dollars
Req. 2 Margin of safety as a percentage of target sales
$7,500 + $0 0.60 $12,500
=
Fixed expenses + Operating income Contribution margin ratio
=
$7,500 + $30,000 0.60
=
Margin of safety
Fixed expenses + Operating income Contribution margin ratio
=
$37,500 0.60
=
$62,500
=
$62,500 − $12,500
=
$50,000
=
$50,000 $62,500
= 0.80 or 80% of target sales Req. 3 Target sales……………………... Contribution margin ratio…….. Contribution margin…………… Less: Fixed expenses……….. Operating income………………. Operating Leverage Factor
$62,500 × .60 $37,500 7,500 $30,000 =
Contribution margin Operating income
=
$37,500 $30,000
=
1.25
Req. 4 If volume decreases 12%, operating income will decrease 15.0% (operating leverage factor of 1.25 multiplied by 12%).
(10 min.) E7-54B First, find the contribution margin: 7-42
Copyright © 2015 Pearson Education, Inc.
Chapter 7 Sales……………………………… Contribution margin ratio…….. Contribution margin……………
Cost-Volume-Profit Analysis
$45,000 × .20 $ 9,000
Then, work backwards to find operating income: Contribution margin Operating leverage factor = Operating income =
$9,000 Operating income
Operating income
=
$9,000 1.60
Operating income
= $5,625
1.60
Finally, finish the income statement to find the fixed expenses: Contribution margin…….. $9,000 Less: Fixed expenses…. Unknown Operating income……….. $ 5,625 Therefore, fixed expenses must be $3,375.
(10-15 min.) E7-55B Req. 1 Selling price $45 Less: Variable costs ($10 + $4 + $2) CM per unit $29
16
Lease costs under Option A: Fixed costs Variable costs (none) Total costs under Option A
$ 3,600 0 $ 3,600
Lease costs under Option B: Fixed costs Total variable costs (20% x $45 x 190) Total costs under Option B
$ 990 1,710 $2,700
The more attractive lease option is Option B because it results in the lowest total lease costs. Req. 2 To solve the question, you need to set the costs of Option A equal to the costs of Option B: $3,600 = $990 + (20% x $45 x CANDLES) Then solve for CANDLES: CANDLES = 290 Req. 3 The lease option that is more attractive for the company if the company plans to sell 490 candles a month is option A, the fixed lease payment because the sales volume is more than the indifference point. Lease costs under option A: #3,600 Lease costs under option B: $990 + (20% x $45 x 490) = $5,400
(20-25 min.) E7-56B Req. 1 Breakeven in units
=
Fixed expenses Contribution margin per unit
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Managerial Accounting 4e Solutions Manual = = *
Req. 2 2a.
2b.
Selling price Less: variable cost per unit CM per unit
Sales in units to reach desired profit
Sales in dollars to reach desired profit
$720 $40* 18 grooming kits
$73 $33 $40 Fixed expenses + Operating Income Contribution margin per unit
= =
$720 + $1,080 $40
=
$1,386 $40
=
45 grooming kits
=
target units x selling price per unit
=
45 units x $73/each
=
$3,285
2c. Condensed Income Statement Sales (45 x $73) Less: variable expenses (45 x $33)
$3,285
Contribution margin
$1,800
Less: fixed expenses Operating income
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$1,485 $720 $1,080
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Cost-Volume-Profit Analysis
(continued) E7-56B
Req. 3 Margin of safety in dollars: Sales at target level Sales at B/E level: ($720 / 40) x $73 Margin of safety in dollars
$3,285 $1,314 $1,971
Margin of safety in units: Sales at target level: Sales at B/E level: ($720 / 40) Margin of safety in units
45 18 27
Margin of safety in %: Margin of safety in dollars: Sales at target level: $1,971/ $3,285
$1,971 $3,285 60.0%
(20-25 min.) E7-57B Req. 1 Total Sales
Per Unit
%
$115,000
$50
100%
57,500
25
50%
Contribution Margin
$57,500
$25
50%
Less: Fixed expenses
11,500
Less: Variable expenses
Operating income
$46,000
1a) Total contribution margin is $57,500. 1b) Per unit contribution margin is $25. 1c) Operating income is $46,000. 1d) Units sold = Total sales / sales price = $115,000 / $50 = 2,300 units
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(continued) E7-57B
Req. 2 2a. Breakeven in units
=
Fixed expenses Contribution margin per unit
=
$11,500 $25
=
460 units
2b. Breakeven sales in dollars
= = =
Req. 3 3a.
Sales in units to reach desired profit
Fixed expenses + Operating income Contribution margin ratio $11,500 + 0 0.50 (from req. 1) $23,000
Fixed expenses + Operating Income Contribution margin per unit
= =
$11,500 + $58,000 $25
=
$69,500 $25
=
2,780 units
3b. Budgeted Sales Units
2,300
Less: Breakeven Sales Units Margin of Safety in Units
460 1,840
3c. Budgeted Sales
$115,000
Less: Breakeven Sales
$23,000
Margin of Safety in Dollars
$92,000
3d. Margin of Safety in Dollars Divided by Budgeted Sales Dollars Margin of Safety %
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$92,000 $115,000 80.0%
Copyright © 2015 Pearson Education, Inc.
Chapter 7
Cost-Volume-Profit Analysis
(20-25 min.) E7-58B 1.
Sales price per unit....................................... Less: Variable cost per unit ($8.40+$8+$3.70+ $1.90)................................... Contribution margin per unit.............................
$25.00 $22.00 $ 3.00
Contribution margin ratio
=
$3.00 $25.00
=
.12
=
12%
Sales Revenue (100,000 × $25.00)………… Less: Variable exp. (100,000 × $22.00) Contribution margin……………….………..
$ 2,500,000 (2,200,000) $ 300,000
2.
Sales volume (units)………………………… Unit contribution margin…………………… Contribution margin………………………… Less: Fixed expenses ($121,800+$167,100)……………………… Operating income……………………………
130,000 x $25.00 $390,000 (288,900) $101,100
3.
Sales revenue………………………………… Contribution margin ratio………………….. Contribution margin………………………… Less: Fixed expenses ($121,800+$167,100)……………………… Operating income……………………………
$4,000,000 x 12% $480,000 (288,900) $ 191,100
4.
5.
B/E sales in units
=
$288,900 $3.00
B/E sales in dollars
=
$288,900 12%
$288,900 + $260,100 $3.00
Copyright © 2015 Pearson Education, Inc.
=
= =
96,300 units $2,407,500 183,000 units
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Managerial Accounting 4e Solutions Manual
(continued) E7-58B 6.
Original contribution margin per unit.................. Less: Increase in Direct labor cost per unit ($8.00 x 10%).......................................................... New contribution margin per unit………………...
$3.00 $0.80 $2.20
Original fixed expenses……………………………. Plus: Increase in fixed expenses………………. New fixed expenses………………………………… New breakeven in units 7.
$288,900 23,500 $312,400 $312,400 $2.20
=
=
Contribution margin (from part 1)………………... Less: Fixed expenses…………………………….. Operating income…………………………………… Operating leverage factor
8.
Increase in volume…………………….. × Operating leverage factor………….. New fixed expenses……………………
9.
Margin of safety
$300,000
=
$11,100
=
Sales − Sales at breakeven $2,500,000 − $2,407,500 (from part 1) (from part 4) $92,500
Margin of safety as a percentage = 16 GB $25 22 $ 3 × 9 $27
92,500 2,500,000
=
.037
32 GB $50 27 $23 ×1 $23
=
$121,800 + $167,100 + $260,100 $5.00
Smaller 16 GB: 109,800 × 9/10………………… Larger 32 GB: 109,800 × 1/10….………………
=
3.7%
Total
10 $50
Weighted-average contribution margin per unit Sales in units
27.03 (rounded)
3% 27.03 81.1% (rounded)
=
Sales price…………….. Less: Variable cost………….. Contribution margin…. Multiply by: Sales mix………………. Contribution margin….
$300,000 (288,900) $11,100 =
=
10.
142,000 Units
$5.00 109,800 units =
98,820 units 10,980 units
The target profit volume is lower than before (Req. 5) because now the company is selling a product with a much higher unit contribution margin.
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Copyright © 2015 Pearson Education, Inc.
Chapter 7
Cost-Volume-Profit Analysis
Problems (Group A) (30-45 min.) P7-59A Req. 1 Cost-Volume-Profit Analysis Companies Q, R, S, T
Target sales Less: Variable expenses Less: Fixed expenses Operating income Units sold Contribution per unit
margin
Q $625,000 125,000 370,000 $130,000 80,000 $
COMPANY R $445,000 178,000 159,000 $ 108,000 106,800
6.25
Contribution margin 0.80 ratio Computations (top to bottom for each company) Q:
$
2.50
S $236,000 118,000 94,000 $ 24,000 12,500 $
0.60
9.44 0.50
T $780,000 156,000 493,000 $131,000 16,000 $
39.00 0.80
Sales − Variable expenses − Operating income = Fixed expenses $625,000 − $125,000 − $370,000 = $130,000 Sales − Variable expenses = Contribution margin; Contribution margin / Unit contribution margin = Units sold $625,000 − $125,000 = $500,000; $500,000 / $6.25 = 2,048 units Contribution margin / Sales = Contribution margin ratio $500,000 / $625,000 = 0.80
R:
Sales × Contribution margin ratio = Contribution margin; Sales − Contribution margin = Variable expenses ($445,000 × 0.60) = $267,000; $445,000 − $267,000 = $178,000 Sales − Variable expenses − Fixed expenses = Operating income $445,000 − $178,000 − $159,000 = $108,000 Contribution margin / Units sold = Contribution margin per unit $267,000 / 106,800 = $2.50
S:
Units sold × Unit contribution margin = Contribution margin; Sales − Contribution margin = Variable expenses 12,500 × $9.44 = $118,000; $236,000 − $118,000 = $118,000 Sales − Variable expenses − Fixed expenses = Operating income $236,000 − $118,000 − $94,000 = $24,000 Contribution margin / Sales = Contribution margin ratio $118,000 / $236,000 = 0.50
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Managerial Accounting 4e Solutions Manual
(continued) P7-59A T:
Units sold × Unit contribution margin = Contribution margin; Contribution margin + Variable expenses = Sales 16,000 × $39 = $624,000; $624,000 + $156,000 = $780,000 Sales − Variable expenses − Operating income = Fixed expenses $780,000 − $156,000 − $131,000 = $493,000 Contribution margin / Sales = Contribution margin ratio $624,000 / $780,000 = 0.80
Req. 2 Breakeven Sales: Q
B/E
=
$370,000 0.80
=
$462,500
R:
B/E
=
$159,000 0.60
=
$265,000
S:
B/E
=
$94,000 0.50
=
$188,000 Lowest breakeven point
T:
B/E
=
$493,000 0.80
=
$616,250
Company S’s low breakeven point is primarily due to its low fixed expenses.
(30-45 min.) P7-60A Req. 1 Revenue per show: 1,200 tickets × $55 / ticket........................……………
$66,000
Variable expenses per show: Programs: 1,200 guests × $9 / guest....................… Cast: 60 cast members × $320 / cast member......... Total variable expenses per show.......................…..
$ 10,800 19,200 $30,000
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Copyright © 2015 Pearson Education, Inc.
Chapter 7
Cost-Volume-Profit Analysis
(continued) P7-60 Sales revenue
−
Variable expenses
− Fixed expenses
=
Operating income
=
Operating income
=
$0
Revenue per show
×
Number of shows
−
Variable Number exp. per × of − Fixed expenses show shows
$66,000
×
Number of shows
−
$30,000 ×
Number of − $969,000 shows
($66,000 – $30,000) × Number of shows $36,000 × Number of shows Number of shows Breakeven number of shows Req. 3 Contribution margin
= $1,224,000 = = =
$1,224,000 $1,224,000 $36,000 34 shows
= $66,000 − $30,000 = $36,000 Fixed expenses + Target operating income Contribution margin per unit
Target number of shows
=
Target number of shows
=
$1,224,000 + $3,888,000 $36,000
Target number of shows
=
$5,112,000 $36,000
Target number of shows
= 142 shows
This profit goal is unrealistic since the show currently performs 115 times a year. Req. 4 Fiddler on the Roof Contribution Margin Income Statement For the Year Ended December 31 Sales revenue (115 × $66,000) Less: Variable expenses (115 × $30,000) Contribution margin Less: Fixed expenses Operating income
Copyright © 2015 Pearson Education, Inc.
$7,590,000 3,450,000 4,140,000 1,224,000 $2,916,000
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Managerial Accounting 4e Solutions Manual Req. 1 Sales Revenue Sale price × Units sold per unit
(30-45 min.) P7-61A −
−
Variable expenses Variable cost × per unit
Units sold
− Fixed expenses
= Operating income
− Fixed expenses
= Operating income
($16.50 × Units sold) − ($6.50 × Units sold) − $1,095,000 ($13.50 − $3.50) × Units sold $10.00 × Units sold Units sold Breakeven sales in units Req. 2
= $0 = $1,095,000 = $1,095,000 =
$1,095,000 $10.00
= 109,500 cartons
Contribution margin = $16.50 − $6.50 = $10.00 Contribution margin ratio = $10.00 / $16.50 = 0.61 (rounded) Target sales in dollars = Target sales in dollars = =
Fixed expenses + Target operating income Contribution margin ratio $1,095,000 + $308,000 0.61 $1,403,000 0.61
= $2,300,000 Req. 3 Team Spirit Calendars Contribution Margin Income Statement Month Ended June 30 Sales revenue (450,000 × $16.50) Less Variable expenses: Cost of goods sold (450,000 × $6.50 × 0.68) $1,989,250 Operating expenses (450,000 × $3.50 × 0.32) 936,000 Contribution margin Less: Fixed expenses Operating income
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Copyright © 2015 Pearson Education, Inc.
$7,425,000 2,925,000 4,500,000 1,095,000 $3,405,000
Chapter 7 Req. 4 Margin of Margin of Margin of Margin of
Cost-Volume-Profit Analysis
(continued) P7-61A safety safety safety safety
Operating leverage factor Operating leverage factor Operating leverage factor
= = = =
Sales − Sales at breakeven $7,425,000 − (109,500 cartons × $16.50 per carton) $7,425,000 − $1,806,750 $5,618,250 Contribution margin Operating income $4,500,000 = $3,405,000 = 1.322 (rounded) =
Req. 5 If volume increases 16%, then operating income will increase 21.15% (operating leverage factor of 1.322 multiplied by 16%). Proof: Original volume (cartons)…..…………………... 450,000 Add: Increase in volume (16% × 450,000)… 72,000 New volume (cartons)………………………... 522,000 Multiplied by: Unit contribution margin……… $10.00 New total contribution margin……………… $5,220,000 Less: Fixed expenses………………………. (1,095,000) New operating income………………………. $4,125,000 vs. Operating income before change in volume…………………………………….. 3,405,000 Increase in operating income………………. $ 720,000 Percentage change ($720,000 / $3,405,000)
21.15% (rounded)
(30-45 min.) P7-62A Req. 1 Contribution margin ratio
= 0.75 (computed as 1.00 − 0.12 − 0.04 − 0.06)
0.03 −
Monthly fixed expenses = $9,000 (computed as $2,700 + $280 + $250 + $600 + $650 + $4,520) Fixed expenses + Operating income Contribution margin ratio
Breakeven sales in dollars = =
$9,000 + $0 0.75
= $12,000 Breakeven sales in units = (trades)
$12,000 $500
= 24 trades
(continued) P7-62A Req. 2 Copyright © 2015 Pearson Education, Inc.
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Managerial Accounting 4e Solutions Manual Sales revenue − Variable expenses − Fixed expenses
=
Target operating income
Sales revenue − 0.25 Sales revenue − $9,000 = $5,250 0.75 Sales revenue = $14,250 Sales revenue =
$14,250 0.75
Sales revenue = $19,000 Req. 3
Req. 4 Breakeven sales in dollars (from Req. 1)
=
$12,000
Breakeven sales in units (trades)
=
$12,000 $300
=
40 trades
The decrease in the average trade revenue increases the breakeven point from 24 to 40 trades.
(25-35 min.) P7-63A Req. 1 Westlake Coffee Weighted-Average Contribution Margin per Unit Small Large 7-54
Copyright © 2015 Pearson Education, Inc.
Total
Chapter 7 Sales price per unit Less: Variable expense per unit Contribution margin per unit Multiply by: Sales mix in units Contribution margin per unit
Cost-Volume-Profit Analysis
$3.00 1.50 $1.50 × 3 $4.50
$5.00 2.50 $2.50 × 1 $2.50
Weighted-average contribution margin per unit ($7.00 / 4 units) Breakeven sales in total units: Fixed expenses + Operating income Weighted-average contribution margin per unit
=
4 $7.00 $1.75
$28,000 + $0 $1.75
Breakeven sales of small coffees (16,000 × ¾)........ Breakeven sales of large coffees (16,000 × ¼)........
=
16,000 units
12,000 units 4,000 units
Proof: Westlake Coffee Contribution Margin Income Statement Month Ended February 29 Sales revenue [(12,000 × $3) + (4,000 × $5)] Less: Variable expenses [(12,000 × $1.50) + (4,000 × $2.50)]
$56,000 28,000 28,000 28,000 $ 0
Contribution margin Less: Fixed expenses Operating income Req. 2 Margin of safety
=
Actual sales − Breakeven sales
Margin of safety
=
$126,000 − $56,000*
= $70,000 *Breakeven sales from proof in Req. 1.
Copyright © 2015 Pearson Education, Inc.
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Managerial Accounting 4e Solutions Manual Req. 3 Operating leverage factor
(continued) P7-63A = Contribution Margin Operating income = $63,000 $35,000 = 1.80
A 15% increase in volume will lead to 27% increase in operating income (15% multiplied by the operating leverage factor of 1.80). Therefore, the new operating income will be $44,450 ($35,000 old operating income × 1.27). Proof: Westlake Coffee Effect on Operating Income of 15% Increase in Sales Volume Increase in sales revenue ($126,000 × 0.15) $18,900 Increase in variable expenses ($63,000 × 0.15)
Increase in contribution margin Change in fixed expenses Operating income before sales increase Operating income after sales increase
9,450 9,450 0 35,000 $44,450
Alternatively, Westlake Coffee Effect on Operating Income of 15% Increase in Sales Volume Sales revenue ($126,000 × 1.15) $144,900 Variable expenses ($63,000 × 1.15)
72,450
Contribution margin
72,450
Fixed expenses
28,000
Operating income
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$ 44,450
Copyright © 2015 Pearson Education, Inc.
Chapter 7
Cost-Volume-Profit Analysis
Problems (Group B) (30-45 min.) P7-64B Req. 1 Cost-Volume-Profit Analysis Companies Q, R, S, T
Q $757,500 242,400 340,000 $ 175,100 85,000
Target sales Less: Variable expenses Less: Fixed expenses Operating income Units sold Contribution per unit
margin
Contribution ratio
margin
$
COMPANY R $445,000 178,000 159,000 $ 108,000 106,800
6.06 0.68
$
2.50
S $162,500 32,500 81,000 $ 49,000 15,625 $
0.60
8.32 0.80
T $1,000,000 360,000 488,000 $152,000 20,000 $
32.00 0.64
Computations (top to bottom for each company) Q:
Sales − Variable expenses − Operating income = Fixed expenses $757,500 − $242,400 − $175,100 = $340,000 Sales − Variable expenses = Contribution margin; Contribution margin / Unit contribution margin = Units sold $757,500 − $242,400 = $515,100; $515,100 / $6.06 =85,000 units Contribution margin / Sales = Contribution margin ratio $515,500 / $757,500 = 0.68
R:
Sales × Contribution margin ratio = Contribution margin; Sales − Contribution margin = Variable expenses ($445,000 × 0.60) = $267,000; $445,000 − $267,000 = $178,000 Sales − Variable expenses − Fixed expenses = Operating income $445,000 − $178,000 − $159,000 = $108,000 Contribution margin / Units sold = Contribution margin per unit $267,000 / 106,800 = $2.50
S:
Units sold × Unit contribution margin = Contribution margin; Sales − Contribution margin = Variable expenses 15,625 × $8.32 = $130,000; $162,500 − $130,000 = $32,500 Sales − Variable expenses − Fixed expenses = Operating income $162,500 − $32,500 − $81,000 = $49,000 Contribution margin / Sales = Contribution margin ratio $130,000 / $162,500 = 0.80
Copyright © 2015 Pearson Education, Inc.
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(continued) P7-64B T:
Units sold × Unit contribution margin = Contribution margin; Contribution margin + Variable expenses = Sales 20,000 × $32.00 = $640,000; $640,000 + $360,000 = $1,000,000 Sales − Variable expenses − Operating income = Fixed expenses $1,000,000 − $640,000 − $152,000 = $208,000 Contribution margin / Sales = Contribution margin ratio $640,000 / $1,000,000 = 0.64
Req. 2 Breakeven Sales: Q:
B/E
=
$340,000 0.72
=
$500,000
R:
B/E
=
$159,000 0.60
=
$265,000
S:
B/E
=
$81,000 0.80
=
$101,250
$488,000 0.64
=
T:
B/E
=
Lowest breakeven point
$762,500
Company S’s low breakeven point is primarily due to its low fixed expenses.
(30-45 min.) P7-65B Req. 1 Revenue per show: 1,400 tickets × $65 / ticket........................…………
$91,000
Variable expenses per show: Programs: 1,400 guests × $6 / guest....................… Cast: 65 cast members × $320 / cast member......... Total variable expenses per show.......................…..
$ 8,400 20,800 $29,200
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Chapter 7
Cost-Volume-Profit Analysis
(continued) P7-65B
Req. 2 Sales revenue −
Variable expenses
− Fixed expenses
=
Operating income
=
Operating income
=
$0
Revenue Number per × of show shows
−
Variable Number exp. per × of − Fixed expenses show shows
Number of shows
−
$29,200 ×
$91,000 ×
Number of − $2,163,000 shows
($91,000 – $29,200) × Number of shows $61,800 × Number of shows Number of shows Breakeven number of shows Req. 3 Contribution margin
=
$2,163,000
=
$2,163,500
= =
$2,163,500 $61,800 35 shows
= $91,000 − $29,200 = $61,800 Fixed expenses + Target operating income Contribution margin per unit
Target number of shows
=
Target number of shows
=
$2,163,000 + $3,708,000 $61,800
Target number of shows
=
$5,871,000 $61,800
Target number of shows
= 95 shows
This profit goal is realistic. The show already performs 100 times a year. Req. 4 Wicked Contribution Margin Income Statement For the Year Ended December 31 Sales (100 x $91,000) Less: Variable expenses (100 × $29,200) Contribution margin Less: Fixed expenses Operating income
Copyright © 2015 Pearson Education, Inc.
$9,100,000 2,920,000 6,180,000 2,163,000 $4,017,000
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(30-45 min.) P7-66B Req. 1
Sales Revenue −
Sale price × Units sold per unit
−
Variable expenses Variable cost × per unit
Units sold
− Fixed expenses
= Operating income
− Fixed expenses
= Operating income
($19.50 × Units sold) − ($4.50 × Units sold) − $1,125,000 ($19.50 − $4.50) × Units sold $15.00 × Units sold Units sold Breakeven sales in units
= $0 = $1,125,000 = $1,115,000 =
$1,125,000 $15.00
= 75,000 cartons
Req. 2 Contribution margin = $19.50 − $4.50 = $15.00 Contribution margin ratio = $15.00 / $19.50 = 0.77 (rounded) Target sales in dollars = Target sales in dollars = =
Fixed expenses + Target operating income Contribution margin ratio $1,125,000 + $338,000 0.77 $1,463,000 0.77
= $1,900,000 Req. 3 Dudley Calendars Contribution Margin Income Statement Month Ended June 30 Sales revenue (475,000 × $19.50) Less variable expenses: Cost of goods sold (475,000 × $4.50 × 0.74) $1,581,750 Operating expenses (475,000 × $4.50 × 0.26) 555,750 Contribution margin Less: fixed expenses Operating income
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Copyright © 2015 Pearson Education, Inc.
$9,262,500 2,137,500 7,125,000 1,125,000 $6,000,000
Chapter 7 Req. 4 Margin of Margin of Margin of Margin of
Cost-Volume-Profit Analysis
(continued) P7-66B safety safety safety safety
Operating leverage factor Operating leverage factor Operating leverage factor
= = = =
Sales − Sales at breakeven $9,262,500− (75,000 cartons × $19.50 per carton) $9,262,500− $1,462,500 $7,800,000 Contribution margin Operating income = $7,125,000 / $6,000,000 = 1.188 (rounded) =
Req. 5 If volume increases 13%, then operating income will increase 15.44% (operating leverage factor of 1.188 multiplied by 13%). Proof: Original volume (cartons)…..……………… Add: Increase in volume (13% × 475,000) New volume (cartons)……………………… Multiplied by: Unit contribution margin… New total contribution margin……………… Less: Fixed expenses……………………… New operating income……………………… vs. Operating income before change in volume……………………………………. Increase in operating income……………… Percentage change ($926,250 / $6,000,000)
Copyright © 2015 Pearson Education, Inc.
475,000 61,750 536,750 $15.00 $8,051,250 (1,125,000) $6,926,250 6,000,000 $ 926,250 15.43% (rounded)
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(30-45 min.) P7-67B Req. 1
Contribution margin ratio
= 0.60 (computed as 1.00 − 0.10 − 0.05 − 0.23)
0.02 −
Monthly fixed expenses = $6,000 (computed as $2,500 + $260 + $250 + $600 + $640 + $1,750) Fixed expenses + Operating income Contribution margin ratio
Breakeven sales in dollars = =
$6,000 + $0 0.60
= $10,000 Breakeven sales in units = (trades)
$10,000 $500
= 20 trades Req. 2 Sales revenue − Variable expenses − Fixed expenses
=
Target operating income
Sales revenue − 0.40 Sales revenue − $6,000 = $5,400 0.60 Sales revenue = $11,400 Sales revenue =
$11,400 0.60
Sales revenue = $19,000
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Chapter 7
Cost-Volume-Profit Analysis
(continued) P7-67B Req. 3
Req. 4
Breakeven sales in dollars (from Req. 1)
=
$10,000
Breakeven sales in units (trades)
=
$10,000 $400
=
25 trades
The decrease in the average trade revenue increases the breakeven point from 20 to 25 trades.
Copyright © 2015 Pearson Education, Inc.
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Managerial Accounting 4e Solutions Manual
(25-35 min.) P7-68B
Req. 1
Margot Coffee Weighted-Average Contribution Margin per Unit Small Large Sale price per unit $3.00 $5.00 Less: Variable expense per unit 1.50 2.50 Contribution margin per unit $1.00 $2.50 Multiply by: Sales mix in units × 3 × 1 Contribution margin per unit $4.50 $2.50 Weighted-average contribution margin per unit ($5.00 / 4 units) Breakeven sales in total units: Fixed expenses + Operating income Weighted-average contribution margin per unit
=
Total
4 $7.00 $1.75
$42,000 + $0 $1.75
Breakeven sales of small coffees (24,000 × ¾)........ Breakeven sales of large coffees (24,000 × ¼)........
=
24,000 units
18,000 units 6,000 units
Proof: Margot Coffee Contribution Margin Income Statement Month Ended February 29 Sales revenue [(18,000 × $3) + (6,000 × $5)] Less: Variable expenses [(18,000 × $1.50) + (6,000 × $2.50)] Contribution margin Less: Fixed expenses Operating income Req. 2 Margin of safety
=
Actual sales − Breakeven sales
Margin of safety
=
$154,000 − $84,000*
$84,000 42,000 42,000 42,000 $ 0
= $70,000 *Breakeven sales from proof in Req. 1. Req. 3 Operating leverage factor: = Contribution margin Operating income = $77,000 $35,000 = 2.2 A 15% increase in volume will lead to 33% increase in operating income (15% multiplied by the operating leverage factor of 2.2). Therefore, the new operating income will be $46,550 ($35,000 old operating income × 1.33).
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Chapter 7
Cost-Volume-Profit Analysis
(continued) P7-68B
Proof:
Margot Coffee Effect on Operating Income of 15% Increase in Sales Volume Increase in sales revenue ($154,000 × 0.15) $23,100 Increase in variable expenses ($77,000 × 0.15)
Increase in contribution margin Change in fixed expenses Operating income before sales increase Operating income after sales increase
11,550 11,550 0 35,000 $46,550
Alternatively, Hemingway Coffee Effect on Operating Income of 15% Increase in Sales Volume Sales revenue ($154,000 × 1.15) $177,100 Variable expenses ($77,000 × 1.15)
88,550
Contribution margin
88,550
Fixed expenses
42,000
Operating income
$ 46,550
Copyright © 2015 Pearson Education, Inc.
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Discussion & Analysis Questions A7-69 1. Define breakeven point. Why is the breakeven point important to managers? The breakeven point is the sales level at which operating income is zero; total revenues equal total expenses. The breakeven point is important to managers because they know the volume that needs to be sold in order to cover costs. Anything below that point results in a loss; anything above the point results in a profit. 2. Describe four different ways cost-volume-profit analysis could be useful to management. C-V-P is useful to managers because it helps them determine: 1. 2. 3. 4.
the breakeven point the volume needed to reach target profit how changes in costs, sales price, and volume affect the company’s profit and the firm’s risk level.
3. The purchasing manager for Rockwell Fashion Bags has been able to purchase the material for its signature handbags for $2 less per bag. Keeping everything else the same, what effect would this reduction in material cost have on the breakeven point for Rockwell Fashion Bags? Now assume that the sales manager decides to reduce the selling price of each handbag by $2. What would the net effect of both of these changes be on the breakeven point in units for Rockwell Fashion Bags? A decrease in the material costs, and keeping everything else the same, would lower the variable expenses for each handbag, which would increase the contribution margin per bag. This would, in turn, lower the breakeven point. If the manager reduces the selling price by $2 along with the $2 decrease in variable costs, the contribution margin would stay the same and so would the breakeven point. 4. Describe three ways that cost-volume-profit concepts could be used by a service organization. C-V-P can be used by a service organization to help them determine: 1. the breakeven point 2. the volume needed to reach target profit and 3. how changes in costs, sales price, and volume affect the company’s profit. 5. “Breakeven analysis isn’t very useful to a company because companies need to do more than break even to survive in the long run.” Explain why you agree or disagree with this statement. It’s true that companies need to do more than break even to survive in the long run, but breakeven analysis allows the manager to see the level that must be reached to cover costs. This becomes the starting point for determining target profits and analyzing how changes in selling prices, costs, and volume will affect profits. 6. What conditions must be met for cost-volume-profit analysis to be accurate? The following conditions must be met for C-V-P analysis to be accurate: 7-66
A change in volume is the only factor that affects costs. Managers can classify each cost (or the components of mixed costs) as either variable or fixed. These costs are linear throughout the relevant range of volume. Revenues are linear throughout the relevant range of volume. Inventory levels will not change. Copyright © 2015 Pearson Education, Inc.
Chapter 7
Cost-Volume-Profit Analysis
The sales mix of products will not change. Sales mix is the combination of products that make up total sales. If profits differ across products, changes in sales mix will affect CVP analysis.
7. Why is it necessary to calculate a weighted-average contribution margin ratio for a multiproduct company when calculating the breakeven point for that company? Why can’t all of the products’ contribution margin ratios just be added together and averaged? A company that sells more than one product must calculate each product’s contribution margin. It then uses the weighted average of all products, which is each unit’s contribution margin times the relative number of units sold. Since the sales volume for each unit is different and its contribution margin is different, the ratio must be weighted to reflect its volume in conjunction with the other units sold. 8. Is the contribution margin ratio of a grocery store likely to be higher or lower than that of a plastics manufacturer? Explain the difference in cost structure between a grocery store and a plastics manufacturer. How does the cost structure difference impact operating risk? The contribution margin ratio of a grocery store is more likely to be lower than that of a manufacturer because a grocery store would most likely have higher variable costs where the manufacturer would have higher fixed costs due to the plant and equipment needed to make a product. Operating risk is less for a company with fewer fixed costs to cover because they are at less risk of incurring a loss should sales decline. 9. Alston Jewelry had sales revenues last year of $2.4 million, while its breakeven point (in dollars) was $2.2 million. What was Alston Jewelry’s margin of safety in dollars? What does the term margin of safety mean? What can you discern about Alston Jewelry from its margin of safety? Alston’s margin of safety is the difference between sales and breakeven point, so it would be $200,000 ($2.4 million - $2.2 million). This means that Alston could suffer a drop in sales of $200,000 without incurring a loss. 10. Rondell Pharmacy is considering switching to the use of robots to fill prescriptions that consist of oral solids or medications in pill form. The robots will assist the human pharmacists and will reduce the number of human pharmacy workers needed. This change is expected to reduce the number of prescription filling errors, to reduce the customer’s wait time, and to reduce the total overall costs. How does the use of the robots affect Rondell Pharmacy’s cost structure? Explain the impact of this switch to robotics on Rondell Pharmacy’s operating risk. Using robotics would likely decrease the pharmacy’s variable costs (fewer human labor hours, fewer errors, etc.) and increase the fixed costs (depreciation and maintenance of the robots). This would result in a higher contribution margin (less labor cost) for the pharmacy and a higher breakeven point due to the higher fixed costs (robots). The pharmacy’s risk will be higher than before due to the higher level of fixed costs. 11.Suppose a company can replace the packing material it currently uses with a biodegradable packing material. The company believes this move to biodegradable packing materials will be well received by the general public. However, the biodegradable packing materials are more expensive than the current packing materials, and the contribution margin ratios of the related products will drop. What are the arguments for the company to use the biodegradable packing materials? What are the arguments for the company to not use the biodegradable materials? What do you think the company should do? Student answers will vary. Copyright © 2015 Pearson Education, Inc.
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Managerial Accounting 4e Solutions Manual 12.
How can CVP techniques be used in supporting a company’s sustainability efforts? Conversely, how might CVP be a barrier to sustainability efforts? CVP analysis is often used by managers to determine how sustainability initiatives will impact the company’s operating income. Sustainability initiatives often result in both cost savings and additional costs. These costs and cost savings may be fixed or variable in nature. Managers use CVP analysis to determine how these initiatives will impact the volume needed to achieve the company’s operating income goals. CVP techniques can be used to quantify the environmental savings of a sustainable initiative. However, as mentioned above, CVP analysis will also uncover the costs associated with sustainable initiatives. These added costs may overshadow the environmental savings.
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Chapter 7
Cost-Volume-Profit Analysis
Application & Analysis A7-70 Select one product that you could make yourself. Examples of possible products could be cookies, birdhouses, jewelry, or custom t-shirts. Assume that you have decided to start a small business producing and selling this product. You will be applying the concepts of cost-volumeprofit analysis to this potential venture. Note: This is a sample solution. Student answers will vary. CVP for a Product Basic Discussion Questions 1.
Describe your product. What market are you targeting this product for? What price will you sell your product for? Make projections of your sales in units over each of the upcoming five years. I make beaded necklaces for women who are interested in unique, yet affordable accessories to their wardrobes. The necklaces will sell for an average of $100 each. Sales Projections 2012 150
2.
2013 175
2014 200
1 25 10 30 inches 1
$15 $6 $3 $2 $1 $27
Make a list of all of the equipment you will need to make your product. Estimate the cost of each piece of equipment that you will need. Equipment Tools Storage boxes for materials Beading boards Miscellaneous supplies TOTAL
4.
2016 250
Make a detailed list of all of the materials needed to make your product. Include quantities needed of each material. Also include the cost of the material on a per-unit basis. Materials per Necklace Pendants Beads Silver findings Wire Clasp TOTAL
3.
2015 225
$100 $75 $50 $50 $275
Make a list of all other expenses that would be needed to create your product. Examples of other expenses would be rent, utilities, and insurance. Estimate the cost of each of these expenses per year. Rent Utilities Insurance TOTAL
$1,800 $120 $50 $1,970 Copyright © 2015 Pearson Education, Inc.
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Managerial Accounting 4e Solutions Manual 5. Now classify all of the expenses you have listed as being either fixed or variable. For mixed expenses, separate the expense into the fixed component and the variable component. Rent Utilities Insurance
Fixed Fixed Fixed
6. Calculate how many units of your product you will need to sell to breakeven in each of the five years you have projected. Fixed expenses / Unit contribution margin = Unit breakeven point $1,850 / ($100 - $27) = 26 necklaces 7.
Calculate the margin of safety in units for each of the five years in your projection. Margin of Safety = Projected Sales – Breakeven Sales 2012 2013 2014 150-26=124 175-26=149 200-26=174 $15,000$17,500 $20,000 $2,600 $2,600 $2,600 $12,400 $14,900 $17,400
8.
2015 225-26=199 $22,500 $2,600 $19,900
2016 250-26=224 $25,000 $2,600 $22,400
Now decide how much you would like to make in before-tax operating income (target profit) in each of the upcoming five years. Calculate how many units you would need to sell in each of the upcoming years to meet these target profit levels. Fixed expenses + Target profit / Unit CM = Yearly sales volume $1,850 + $12,000 / ($100 - $27) = 190 necklaces
9.
How realistic is your potential venture? Do you think you would be able to break even in each of the projected five years? How risky is your venture (use the margin of safety to help answer this question). Do you think your target profits are achievable? The venture looks realistic. The breakeven point is only 26 necklaces, which means I would need to sell on average less than three necklaces a month. The margin of safety is promising as long as the projected sales can be made. The target profits appear achievable, but will require implementing a solid marketing plan. Student answers will vary.
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Chapter 7
Cost-Volume-Profit Analysis
(30 min.) A7-71 Ethics Mini-Case 1.
a. The ethical issues in this situation are: Competence: “Provide decision support information and recommendations that are accurate, clear, concise, and timely.” In his initial report, Greg Michaels’ had an inaccuracy. It was a mistake, but ignoring the mistake is a breach of this principle. Confidentiality: “Keep information confidential except when disclosure is authorized or legally required.” Greg Michaels’ disclosure of the internal report to Beth Sparrow, an employee of a competing company, is neither authorized nor legally required. As a result, this is a clear ethical violation. Integrity: “Abstain from engaging in or supporting any activity that might discredit the profession.” Ignoring errors in reports which affect real business decisions could discredit the profession. Credibility: “Disclose all relevant information that could reasonably be expected to influence an intended user’s understanding of the reports, analyses, or recommendations.” It is reasonable to expect that the undisclosed error, if disclosed, would affect the understanding of the report. Thus, by not reporting this inaccuracy, Greg Michaels is violating this ethical principle. b. Greg Michaels’ responsibilities as a management accountant are to be honest, fair, objective, and responsible. He should seek to correct the mistake he had made by reporting it to his immediate supervisor. He is also responsible for maintaining confidential information, so he should not disclose confidential information to his friend, however much he may trust her. c. John Hammond is responsible for reviewing the reports which are given to him before signing off on them, especially in the case of interns or junior employees. It is not sufficient that a report looks professional, but he has a duty to also verify that it is accurate. d. Beth Sparrows is responsible for making ethical decisions. Since she is employed by a competing company, she should not look at Greg Michaels’ report, as it could result in unethical behavior. She should encourage Greg to take his concerns to his supervisor. She may give him general advice but should not examine anything which is confidential. 2. By omitting the fixed monthly sales staff salaries from the report, breakeven sales are reported as lower than they actually are. This error would certainly influence the decision about proceeding with the new proposal, since it would make the proposal look favorable and more profitable than it actually is. 3. First, Greg should report the mistake with his immediate supervisor. If he has concerns about his employment with the firm after this mistake, he should take these concerns to the HR department to get an objective third party which is not involved in this incident.
(20-25 min.) A7-72 Real-life Mini Case 1. Is the cost of down a fixed cost or a variable cost for a jacket manufacturer such as Lands’ End? Down is a variable cost to jacket manufacturers because more down is required for each additional unit (jacket) produced. 2. If the cost of down increases, what happens to the breakeven point for a downfilled jacket product line at Land’s End? If the cost of down increases, the breakeven point will also increase because the contribution margin will decrease.
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Managerial Accounting 4e Solutions Manual 3. What is the percentage increase in the cost of down per pound from 2010 to 2012 at Land’s End? Would you expect the breakeven units to change by this same percentage? Why or why not? The price of down increased by about 77% [($23 - $13)/$13]. The breakeven units will not change by this same percentage because down is only one material that goes into the cost of the jacket. If we assume that the other costs are assumed to have stayed the same, the actual total cost of making the jacket will increase by a smaller total percentage. Therefore, the breakeven in units will increase by a smaller amount than 77%. 4. If down increases by a certain percentage, will the selling price of a down-filled jacket need to change by that same percentage to maintain the same profit margin? Explain. No. Again, down is only one component of the jacket. The other materials in the jacket will help to lessen the impact of the percentage increase in the cost of down (assuming those other materials remain at a constant cost.) Therefore, the selling price will not have to be increased by 77 percent to cope with the 77 percent increase in the cost of down. 5. Assume that a Land’s End down jacket selling for $100 uses 12 ounces of down. Further assume that Lands’ End has $250,000 of fixed costs related to the down jacket line and its other variable manufacturing costs total $60 per jacket. As stated in the story, the cost per pound of down was $13 and $23 in October 2010 and October 2012, respectively. Calculate the breakeven number of jackets both in (a) October 2010; and (b) October 2012. Do these breakeven numbers agree with your answers to the prior questions? October 2010 breakeven: $250,000 / ($100 – ($60 + ($13 x 12/16))) = 8,264 jackets (rounded) October 2012 breakeven: $250,000 / ($100 – ($60 + ($23 x 12/16))) = 10,989 jackets (rounded) Yes, these numbers agree to answers to the prior questions. 6. Assume now the same set of facts as in Question 5 but that Lands’ End raises the selling price of each jacket by $10 in October 2013. Does the contribution margin percentage remain the same? No, the contribution margin would increase, this is because Lands’ End only uses 12 ounces of down in each jacket and the price per pound of down went up $10. Therefore, the $10 increase in price will overcompensate for the variable cost per unit increase of the jacket. October 2010 contribution margin: $100 – ($60 + ($13 x 12/16)) = $69.75 October 2010 contribution margin ratio: $69.75 / $100 = 69.75% October 2012 contribution margin: $110 – ($60 + ($23 x 12/16)) = $87.25 October 2012 contribution margin ratio: $87.25 / $110 = 79.32%
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