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(1)

Chapter 7 Cost-Volume-Profit Analysis

Quick Check

Answers: QC-1. d QC-3. b QC-5. a QC-7. b QC-9. c QC-2. c QC-4. c QC-6. c QC-8. b QC-10. d

Short Exercises

(5-10 min.) S7-1

a. Sales price per passenger………. $ 50

Less: Variable cost per passenger………….. 20

Contribution margin per passenger………… $ 30

b. Contribution margin per passenger………… $30

Divided by sales price per passenger………. ÷ 50

Contribution margin ratio……….. 60%

c. Total contribution margin (11,000 × $30)…... $330,000

Less: Fixed expenses……….. 210,000

Operating income………. $120,000

d. Total contribution margin

($490,000 × 60%) ……….. $294,000

(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).

(2)

(5-10 min.) S7-3

Units sold ₌ Fixed expenses + Operating income

(to break even) Contribution margin per unit (passenger) = $210,000 + 0_$30*

= 7,000 passengers

*Contribution margin ₌ $50 sales ₋ $20 variable expense

per passenger price per passenger

Number of passengers to break even*………. 7,000

Sales price per passenger………... × $50

Sales revenue to break even……….. $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 − _expensesFixed = Operating_income Sale price Units

per unit × sold − Variable cost Unitsper unit × sold − expensesFixed = Operatingincome [($50 × Units sold) − ($20 × Units sold)] − $210,000 = $45,000

[($50 − $20) × Units sold] − $210,000 = $45,000 Units sold = 8,500 tickets To earn target income of $45,000, the cruiseline must sell 8,500 dinner cruise tickets.

(3)

(5-10 min.) S7-5

(5 min.) S7-6

a. Fixed expense line

b. Total expense line c. Sales revenue line d. Dollars (vertical axis) e. Units (horizontal axis) f. Operating loss area g. Operating income area h. Breakeven point

i. 150 j. $300

(4)

(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:

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:

per unit × sold − Variable cost Unitsper unit × sold − expensesFixed = Operatingincome ($40 × Units sold) − ($20 × Units sold) − $210,000 = $0

[($40 − $20) × Units sold] − $210,000 = $0

Units sold = 10,500 passengers 10,500 passengers × $40 = $420,000

Alternatively,

Contribution ₌ Contribution margin per unit

margin ratio Sale price per unit

= $40 − $20_$20 = 0.50

Sales ₌ Fixed expenses + Operating income

in dollars Contribution margin ratio

= $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.

(5)

(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:

= $210,000 + $0_$40

To achieve breakeven, sales revenue needs to be $262,500 (5,250 passengers × $50 sales price per ticket).

per unit × sold − Variable cost Unitsper unit × sold − expensesFixed = Operatingincome ($50 × Units sold) − ($10 × Units sold) − $210,000 = $0

[($50 − $10) × Units sold] − $210,000 = $0 Units sold = 5,250 passengers 5,250 passengers × $50 = $262,500 Alternatively, Contribution

= Contribution margin per unit

= $50 − 10_$50 = 0.80

= $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:

= $180,000 + $0_$30

per unit × sold −

Variable cost Units ₋ Fixed ₌ Operating per unit × sold expenses income ($50 × Units sold) − ($20 × Units sold) − $180,000 = $0

[($50 − $20) × Units sold] − $180,000 = $0 $30 × Units sold = $180,000 Units sold = 6,000 passengers 6,000 passengers × $50 = $300,000 Alternatively,

= $50 − 20_$50 = 0.60

= $180,000 + $0_0.60 = $300,000

(7)

(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 Total

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 5

Contribution margin $120 $ 90 $210

Weighted-average contribution

margin per unit ($210 / 5) $ 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

= Fixed expenses + Operating income in total tickets 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)……… 4,000

Breakeven sales of executive cruises (5,000 × 1/5)... 1,000 Total cruise passengers...……….. 5,000

(8)

(5-10 min.) S7-11

a. Margin of safety ₌ Expected sales ₋ Breakeven sales

in units in units in units

= 8,750 – 7,000* = 1,750 passengers *(from S7-3)

b. Margin of safety ₌ Target level _- Breakeven

in dollars sales dollars sales dollars

= $437,500a_{- $350,000}b

= $87,500

a_{8,750 x $50 = $437,500} b_{7,000 x $50 = $350,000}

c. Margin of safety ₌ Margin of safety in dollars as a percentage Expected sales in dollars of expected sales

= _$437,500$87,500 = 20%

(5-10 min.) S7-12

a. Contribution margin (8,750 × $30 / cruise

passenger)………... $262,500

Less: Fixed expenses………. 210,000

Operating income……….. $52,500

Operating Leverage Factor = 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%).

(9)

in units in units in units = 1,500 – 750*

= 750 posters

*Breakeven in units = $15,000/($45-$25) = 750 units

b. Margin of safety ₌ Target level _- Breakeven

in dollars sales dollars sales dollars

= $67,500** - $33,750*** = $33,750

** Expected sales in dollars = 1,500 x $45 = $67,500 *** Breakeven in dollars = 750 x $45 = $33,750 c. Margin of safety ₌ Margin of safety in dollars

as a percentage Expected sales in dollars of expected sales

= 33,750

67,500 = 50%

(10)

(5-10 min.) S7-14

Contribution margin (1,500 × $20 / poster)……. $30,000

Less: Fixed expenses………. 15,000

Operating Leverage Factor ₌ 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)

……….. 1,500

Add: Increase in volume (20% × 1,500)

……… 300

New volume (posters)

……….... 1,800

Multiplied by: Unit contribution

margin…………. × $20

New total contribution

margin……….. $36,000

Less: Fixed

expenses………... (15,000)

New operating

income……… $21,000

Less: Operating income before change in

volume (from above)………... (15,000₎

Increase in operating

income………... $6,000

Percentage change ($6,000 / $15,000)

(11)

(5-10 min.) S7-15

Req. 1

Product: Cupcakes

Selling price per unit $ 6.00

Less: Variable cost per unit $ 4.00

CM $ 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 $ 2,600

Variable costs (none) 0

Total costs under Option 1 $ 2,600

Lease costs under Option 2:

Fixed costs $ 1,700

Variable costs per unit ($6 x .05) $ 0.30 Times # of units at pt of indifference (3,000)

3,000

Total variable costs 900

Total costs under Option 2 $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.

(12)

Exercises (Group A)

(15 min.) E7-17A

Req. 1

Global Travel

Contribution Margin Income Statements

Sales revenue $270,000 $410,000

Less: Variable expenses (30% of sales revenue*) 81,000 123,000 Contribution margin (70% of sales revenue**) 189,000 287,000

Fixed expenses 170,800 170,800

Operating income (loss) $ 18,200 $ 116,200

__________ *$120,000 / $400,000 = 0.30 **$280,000 / $400,000 = 0.70 (CM ratio) 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 = Fixed expenses _{Contribution margin ratio}

$48,000 = $24,000_{Contribution margin ratio}

Contribution margin ratio = $24,000_$48,000 Contribution margin ratio = .50

Next, fill in the given data in the contribution margin income statement:

Sales………. $ ?

Less: Variable expenses…. 42,000

Contribution margin………. ?

Less: Fixed expenses…….. 24,000

(13)

(continued) E7-18A

Because the contribution margin ratio is 50% of sales revenue, the variable expenses must be 50% of sales revenue. Therefore:

Variable expenses = 50% × Sales revenue $ 42,000 = 50% × Sales revenue $ 84,000 = Sales revenue Or alternatively: Sales − $42,000 = 50% Sales Sales − 50% Sales = $42,000 50% Sales = $42,000 Sales = $42,000 50% Sales = $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...………….. $1.80 Less: Variable expenses...…. 0.90 Contribution margin per unit... $0.90 Contribution margin ratio:

Contribution margin per unit ₌ .90$0

Sale price per unit $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

(14)

(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...………….. $1.80 Less: Variable expenses...…. 0.80 Contribution margin per unit... $1.00

= $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 E7-19A) 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.

(15)

(10-15 min.) E7-21A

Req. 1

margin ratio Sales price per unit

= $5.25 − $2.10_$5.25 = 0.60

Breakeven sales ₌ Fixed expenses + Operating income

= $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

= $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.

(16)

(10-15 min.) E7-23A

Req. 1

= $630,000 + $0_0.70 = $900,000

Req. 2

Grover’s Steel Parts Operating Income Projections

at Different Sales Levels

Sales revenue $ 520,000 $1,010,000

× Contribution margin ratio 0.70 0.70

Contribution margin 364,000 707,000

Less: Fixed expenses 630,000 630,000

Operating income (loss) $(266,000) $ 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

Sales in dollars = Fixed expenses + Operating income_{Contribution margin ratio}

$1,010,000 = Fixed expenses + $77,000_0.40

$404,000 = Fixed expenses + $77,000

$327,000 = Fixed expenses

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.

(17)

(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.

(18)

(5-10 min.) E7-26A

Use the short cut contribution margin formula to determine the company’s current level of fixed expenses:

Sales needed to breakeven = _{Contribution margin ratio}Fixed expenses

$350,000 = Fixed expenses_.20

$350,000 × .20 = 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:

= $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……….. $24.00

Contribution margin ratio………... × .625 Contribution margin per unit……. $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):

Breakeven in units = _{Contribution margin per unit}Fixed expenses

= $120

$15.00 = 8 scarves Alternatively:

Breakeven in sales revenue ₌ 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.

(19)

Twig Oak Total

Sale price per unit $15.00 $35.00

Less: Variable cost per unit 2.50 10 .00

Contribution margin per unit $12.50 $25.00

Multiply by: Sales mix in units × 4 × 1 5

Contribution margin $50.00 $25 .00 $75 .00

Weighted-average contribution margin per unit ($75 / 5

units) $15 .00

Sales in total units:

Weighted-average contribution margin per unit

= $300 + $0

$15 = 20 units

Breakeven sales of twig stands (20 × 4/5)……… 16 units

Breakeven sales of oak stands (20 × 1/5).……… 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

Standard Chrome Total

Sales price per unit $60 $75

Less: Variable cost per unit 45 55

Contribution margin per unit $15 $20

Contribution margin $45 $40 $ 85

Weighted-average contribution margin per unit ($110 / 5 units)

$ 17

Weighted-average contribution margin per unit = $18,700 + $0

$17 = 1,100 units

Breakeven sales of standard scooters (1,100 × 3/5)……… 660 units Breakeven sales of chrome scooters (1,100 × 2/5).……….. 440 units

(20)

(continued) E7-29A

= _{Weighted-average contribution margin per unit}Fixed expenses + Operating income

= $18,700 + $13,600_$17 = 1,900 units

Target sales of standard scooters (1,900 × 3/5)...……… 1,140 units Target sales of chrome scooters (1,900 × 2/5)...…... 760 units

(20-30 min.) E7-30A

This is a challenging exercise that requires students to work backwards. Use the weighted-average contribution margin per unit chart, in conjunction with the shortcut formula, to work backwards to find the contribution margin of the Classic.

Digital Classic Total Sales price per unit...……….. $225

Less: Variable expense per unit. ($125 + $35) 160

Contribution margin per unit..…….. 65 215

Multiply by: Sales mix in units...……….. x 7 × 3 10

Contribution margin...…………. $455 645 1,100

margin per unit...……….. $ 110

a_{Sales in}

total units Weighted-average contribution margin per unit

2,100 = $195,000 + $36,000

Weighted-average contribution margin per unit Weighted-average

= $231,000_2,100 contribution

margin per unit

(21)

(continued) E7-30A

b_{Weighted-average}

Total sales mix contribution margin Total sales mix units

contribution =

margin per unit

$110 = $455 + X₁₀ $1,100 = $455 + X X = $645 c_Contribution × 3 = $645 margin per Classic watch Contribution margin ₌ _$215

per Classic watch

(15 min.) E7-31A

Req. 1

The company’s operating income can be computed as follows:

Sales revenue………. $6,800,000

Less: Variable expenses……… 1,088,000

Contribution margin………. 5,712,000

Less: Fixed expenses……($2,600,000 - $1,088,000) 1,512,000

Operating income……….. $4,200,000

Req. 2

Contribution margin ratio = 5,712,000_6,800,000

= 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 $5,712,000

Percentage increase × 14 %

Increase in contribution margin 799,680

Less: Increase in fixed costs of advertising campaign 250,000

Increase in operating income $549,680

(22)

Req. 1

Contribution margin ratio = 1.00 – 0.60 = 0.40

= $12,000 + $0_0.40 = $30,000

= $12,000 + $20,000 0.40 = $32,000_0.40 = $80,000 Margin of safety = $80,000 − $30,000 = $50,000 Req. 2 Margin of safety as _{= $50,000} $80,000 a percentage of target sales

= 0.625 or 62.5% of target sales

Req. 3

Target sales………... $80,000

Contribution margin ratio…….. × .40

Contribution margin……… $32,000

Operating Leverage Factor ₌ 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%).

(23)

(10 min.) E7-33A

First, find the company’s contribution margin:

Sales……… $60,000

Then, work backwards to find the company’s operating income: Operating leverage factor = Contribution margin_{Operating income}

1.40 = _{Operating income} $21,000

Operating income = $21,000_1.40

Operating income = $15,000

Finally, finish the income statement to find the fixed expenses: Contribution margin…….. $21,000

Less: Fixed expenses…. Unknown

(24)

(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 $ 3,000

Total costs under Option A $ 3,000

Lease costs under Option B:

Fixed costs $ 1,650

Total variable costs (10% x $30 x 250) 750

Total costs under Option B $ 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.

(25)

(20-25 min.) E7-35A

Req. 1

= $600 $30* = 20 grooming kits * Req. 2 2a.

Sales in units to reach desired

profit = Fixed expenses + Operating IncomeContribution margin per unit

= $600 + $900 $30 = $1,500 $30 = 50 grooming kits 2b.

Sales in dollars to reach desired

profit = breakeven units x selling price per unit = 50 units x $62/each

= $3,100 2c.

Condensed Income Statement

Sales $3,100

Less: variable expenses (50 x

$32) $1,600

Contribution margin $1,500

Less: fixed expenses $600

Operating income $900

Selling price $62

Less: variable cost

per unit $32

(26)

(continued) E7-35A

Req. 3

Margin of safety in dollars:

Sales at target level: $3,100

Sales at B/E level: $1,240*

Margin of safety in dollars $1,860

Margin of safety in units:

Sales at target level: 50

Sales at B/E level: 20

Margin of safety in units 30

Margin of safety in %:

Margin of safety in dollars: $1,860

$1,860/$3,100 = 60.00%

(27)

(20-25 min.) E7-36A

Req. 1

Total Per Unit %

Sales _$81,250 _$25 _100%

Less: Variable expenses _48,750 ₁₅ _60%

Contribution Margin _$32,500 _$10 _40%

Less: Fixed expenses _13,000

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 = _{Contribution margin per unit}Fixed expenses = $13,000

$10 = 1,300 units 2b.

Breakeven sales in dollars = Fixed expenses + Operating income Contribution margin ratio

= $13,000 + 0

0.40 (from req. 1) = $32,500

Req. 3

3a.

profit =

Fixed expenses + Operating Income Contribution margin per unit = $13,000 + $53,000

$10

= $66,000

$10 = 6,600 units

(28)

(continued) E7-36A

3b.

3c.

3d.

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... $25.00 Less: Variable cost per unit

(7.30+6+2.60+2.10)... $18.00 Contribution margin per unit ... $ 7.00

Contribution margin ratio = $7.00_$25.00 = .28

= 28%

Sales revenue (140,000 × $25.00)……… $ 3,500,000

Less: Variable expenses (140,000 × $18.00)… (2,520,000)

Contribution margin……….. $ 980,000

2. Sales volume (units)……… 170,000

Unit contribution margin……… x $7.00

Contribution margin……… $1,190,000

Less: Fixed expenses………($292,000 + $447,200) (739,200)

3. Sales revenue……… $4,500,000

Contribution margin ratio……….. x 28%

Contribution margin……… $1,260,000

Less: fixed expenses………. (739,200)

4.

B/E sales in units = $739,200_$7.00 = 105,600_units

B/E sales in dollars = $739,200 = $2,640,000

Budgeted Sales Units _3,250

Less: Breakeven Sales Units _1,300

Margin of Safety in Units _1,950

Budgeted Sales _$81,250

Less: Breakeven Sales Volume _$32,500

(29)

(30)

(continued) E7-37A

5. $739,200 + $269,500 ₌ _{144,100 units}

$7.00

6. Original contribution margin per unit... $7.00 Less: Increase in direct labor cost per unit ($6.00 x

10%)... $0.60

New contribution margin per unit………... $6.40

Original fixed expenses………. $739,200

Plus: Increase in fixed expenses……….. 24,000

New fixed expenses……… $763,200

New breakeven in units = $763,200_$6.40 = 119,250_Units

7. Contribution margin (from part 1)………... $980,000

Less: Fixed expenses………... (739,200)

Operating income……… $ 240,800

Operating Leverage factor = $980,000 =

4.07 (rounde

d) $ 240,800

8. Increase in volume……….. 8%

× Operating leverage factor………….. 4.07

New fixed expenses……… 32.6%

(rounded)

9. Margin of safety = 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 = .25 (rounded ) = 25% (rounded ) 10. 16 GB 32 GB Total Sales price……….. $25 $50

Less: Variable cost………….. 18 22

Contribution margin…. $ 7 $28

Sales mix………. × 6 × 1 7

Multiply by: Contribution margin…. $42 $28 $70

$10.00

Sales in units = $739,200 + $269,500_$10 = 100,870_units

Smaller 16 GB: 100,870 × 6/7……….. 86,460 units_(rounded) Larger 32 GB: 100,870 × 1/7….………. 14,410 units_(rounded)

(31)

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 $190,000 $420,000

Less: Variable expenses (35% of sales revenue*) 66,500 147,000 Contribution margin (65% of sales

revenue**) 123,500 273,000

Fixed expenses 176,800 176,800

Operating income (loss) $ (53,300) $ 96,200

__________ *$192,500 / $550,000 = 0.35 **$357,500 / $550,000 = 0.65 (CM ratio) Req. 2 Breakeven sales = $176,800 + $0_{1 − 0.35} = $176,800 + $0_0.65 = $272,000

(32)

(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 = Fixed expenses _{Contribution margin ratio}

$40,000 = $30,000_{Contribution margin ratio}

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…. 45,000

Contribution margin………. ? Less: Fixed expenses…….. 30,000

Operating income………….. $ ?

Because the contribution margin ratio is 75% of sales revenue, the variable expenses must be 25% of sales revenue. Therefore:

Variable expenses = 25% × Sales revenue $ 45,000 = 25% × Sales revenue $180,000 = Sales revenue Or alternatively: Sales − $45,000 = 75% Sales Sales − 75% Sales = $45,000 25% Sales = $45,000 Sales = $45,000 25% Sales = $180,000

Once sales revenue is found, the rest of the income statement follows:

Sales………. $180,000

Less: Variable expenses………. 45,000

Contribution margin………. $135,000

Less: Fixed expenses………….. 30,000

Therefore, at the current level of operations, the company’s sales revenue is $180,000, and its operating income is $105,000.

(33)

(15 min.) E7-40B

Req. 1

Contribution margin per unit:

Sale price...………….. $1.60 Less: Variable expenses...…. 0.80 Contribution margin per unit... $0.80 Contribution margin ratio:

Contribution margin per unit ₌ .80$0

Sale price per unit $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

= $80,000 + $0_0.50 = $160,000

Req. 3

= $80,000 + $25,000_$0.80 = 131,250 packages

(5-10 min.) E7-41B

New contribution margin per unit:

Sale price...………….. $1.60 Less: Variable expenses...…. 0.60 Contribution margin per unit... $1.00

= $95,000 + $25,000_$1.00 = 120,000 packages

(34)

The company would have to sell 11,250 fewer packages of socks (120,000 − 131,250 from E7-40B) to earn $25,000 of operating income.

(10-15 min.) E7-42B

Req. 1

margin ratio Sales price per unit

= $6.25 − $2.50_$6.25 = 0.60

Breakeven sales ₌ Fixed expenses + Operating income

= $8,250 + $0 0.60 = $13,750

Req. 2

If franchisees require a monthly operating income of $6,600 Target sales

= $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).

(35)

(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……….

$ 3.25

New sales volume (units)…………. × 6,000

Contribution margin………... $19,500

Less: New fixed expenses

($8,250 + $500 advertising fee)…… (8,750)

New operating income……….. $ 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

= $620,000 + $0_0.80 = $775,000

Req. 2

Operating Income Projections at Different Sales Levels

Sales revenue $ 520,000 $1,020,000

× Contribution margin ratio

0.80 0.80

Contribution margin 416,000 816,000

Less: Fixed expenses 620,000 620,000

Operating income (loss) $(204,000) $ 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.

(36)

(15 min.) E7-45B

Req. 1

Sales in dollars = Fixed expenses + Operating income_{Contribution margin ratio}

= $620,000 + $196,000_0.50 = $1,632,000

Req. 2

Sales in dollars = Fixed expenses + Operating income

Contribution margin ratio

$1,020,000 = Fixed expenses + $196,000_0.50

$510,000 = Fixed expenses + $196,000

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

(37)

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:

$500,000 = Fixed expenses_.50

$500,000 × .50 = Fixed expenses

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:

= $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……….. $14.00

Contribution margin ratio………... × .625 Contribution margin per unit……. $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):

= $350

$8.75 = 40 scarves

(38)

(continued) E7-48B

Alternatively:

Breakeven in sales revenue ₌ 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

Twig Oak Total

Sales price per unit $18.00 $38.00

Less Variable cost per unit 3.00 8 .00

Contribution margin $60.00 $30 .00 $90 .00

Weighted-average contribution margin per unit ($90 / 5

units) $18 .00

= _{Weighted-average contribution margin per unit}Fixed expenses + Operating income

= $360 + $0_$18 = 20 units

Breakeven sales of twig stands (20 × 4/5)……… 16 units

Breakeven sales of oak stands (20 × 1/5).……… 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.

(39)

(15-20 min.) E7-50B

Standard Chrome Total

Sales price per unit $65 $85

Less: Variable cost per unit 55 65

Contribution margin per unit $10 $20

Contribution margin $30 $40 $70

Weighted-average contribution margin $ 14

Sales in total units to breakeven:

Weighted-average contribution margin per unit = $9,800 + $0

$14 = 700 units

Breakeven sales of standard scooters (700 × 3/5)……… 420 units Breakeven sales of chrome scooters (700 × 2/5).……….. 280 units Sales in total units to achieve target operating income:

= $9,800 + 8,400

$14 = 1,300 units

Target sales of standard scooters (1,300 × 3/5)...……… 780 units Target sales of chrome scooters (1,300 × 2/5)...…... 520 units

(40)

(20-30 min.) E7-51B

This is a challenging exercise that requires students to work backwards. Use the weighted-average contribution margin per unit chart, in conjunction with the shortcut formula, to work backwards to find the contribution margin of the Classic.

Digital Classic Total Sales price per unit...……….. $250

Less: Variable expense per unit. ($120 + $50) 170

Contribution margin per unit..…….. 80 305 c

Multiply by: Sales mix in units...……….. × 8 × 2 10

Contribution margin...…………. $640 610 1,250

margin per unit...……….. $ 125

a_{Sales in}

total units Weighted-average contribution margin per unit 2,200 = _{Weighted-average contribution margin per unit}$200,000 + $75,000 Weighted-average

= $275,000_2,200 contribution

margin per unit

= $125 / unit

b_{Weighted-average}

Total sales mix contribution margin Total sales mix units

contribution =

margin per unit

$125 = $640 + X₁₀ $1,250 = $640 + X X = $610 c_Contribution × 2 = $610 margin per Classic watch Contribution margin ₌ _$305

(41)

(15 min.) E7-52B

Req. 1

The company’s operating income can be computed as follows:

Sales revenue………. $6,100,000

Less: Variable expenses……… 1,342,000

Contribution margin………. 4,758,000

Less: Fixed expenses………($2,590,000 - $1,342,000) 1,248,000

Operating income……….. $3,510,000

Req. 2

Contribution margin ratio = $4,758,000_$6,100,000

= 78%

Req. 3

Breakeven in sales dollars = $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 $4,758,000

Percentage increase × 16 %

Increase in contribution margin 761,280

Less: Increase in fixed costs of advertising campaign 260,000

(42)

(15 min.) E7-53B

Req. 1

Contribution margin ratio = 1.00 − 0.40 = 0.60

= $7,500 + $0_0.60 = $12,500

= $7,500 + $30,000 0.60 = $37,500_0.60 = $62,500 Margin of safety = $62,500 − $12,500 = $50,000 Req. 2 Margin of safety as _{= $50,000} $62,500 a percentage of target sales

= 0.80 or 80% of target sales

Req. 3

Target sales………... $62,500

Operating Leverage Factor ₌ 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:

(43)

Sales……… $45,000 Contribution margin ratio…….. × .20

Contribution margin……… $ 9,000

Then, work backwards to find operating income:

Operating leverage factor = Contribution margin_{Operating income}

1.60 = _{Operating income} $9,000

Operating income = $9,000_1.60

Operating income = $5,625

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) 16

CM per unit $29

Lease costs under Option A:

Fixed costs $ 3,600

Total costs under Option A $ 3,600

Lease costs under Option B:

Fixed costs $ 990

Total variable costs (20% x $45 x 190) 1,710

Total costs under Option B $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

(44)

= $720 $40* = 18 grooming kits * Req. 2 2a.

profit = Fixed expenses + Operating IncomeContribution margin per unit = $720 + $1,080 $40 = $1,386 $40 = 45 grooming kits 2b.

Sales in dollars to reach desired

profit = target units x selling price per unit = 45 units x $73/each

= $3,285 2c.

Condensed Income Statement

Sales (45 x $73) $3,285

Less: variable expenses (45 x

$33) $1,485

Contribution margin $1,800

Less: fixed expenses $720

Operating income $1,080

Selling price $73

Less: variable cost

per unit $33

(45)

(continued) E7-56B

Req. 3

Margin of safety in dollars:

Sales at target level $3,285

Sales at B/E level:

($720 / 40) x $73 $1,314

Margin of safety in dollars $1,971

Margin of safety in units:

Sales at target level: 45

Sales at B/E level:

($720 / 40) 18

Margin of safety in units 27

Margin of safety in %:

Margin of safety in dollars: $1,971

$1,971/ $3,285 60.0%

(20-25 min.) E7-57B

Req. 1

Total Per Unit %

Sales _$115,000 _$50 _100%

Less: Variable expenses _57,500 ₂₅ _50%

Contribution Margin _$57,500 _$25 _50%

Less: Fixed expenses _11,500

Operating income _$46,000

1a) Total contribution margin is $57,500. 1b) Per unit contribution margin is $25. 1c) Operating income is $46,000.

(46)

(continued) E7-57B

Req. 2

2a.

Breakeven in units = _{Contribution margin per unit}Fixed expenses = $11,500

$25 = 460 units 2b.

= _{0.50 (from req. 1)}$11,500 + 0 = $23,000

Req. 3

3a.

profit =

Fixed expenses + Operating Income Contribution margin per unit = $11,500 + $58,000 $25 = $69,500 $25 = 2,780 units 3b. 3c. 3d.

Margin of Safety in Dollars _$92,000

Divided by Budgeted Sales Dollars _$115,000

Margin of Safety % _80.0%

Budgeted Sales Units _2,300

Less: Breakeven Sales Units ₄₆₀

Margin of Safety in Units _1,840

Budgeted Sales _$115,000

Less: Breakeven Sales _$23,000

(47)

(20-25 min.) E7-58B

1. Sales price per unit... $25.00

Less: Variable cost per unit ($8.40+$8+$3.70+

$1.90)... $22.00

Contribution margin per unit... $ 3.00 Contribution margin ratio = _$25.00 $3.00 = .12

= 12%

Sales Revenue (100,000 × $25.00)………… $ 2,500,000

Less: Variable exp. (100,000 × $22.00) (2,200,000)

Contribution margin……….……….. $ 300,000

2. Sales volume (units)……… 130,000

Unit contribution margin……… x $25.00

Less: Fixed expenses ($121,800+$167,100)……… (288,900)

Operating income……… $101,100

3. Sales revenue……… $4,000,000

Contribution margin ratio……….. x 12%

Less: Fixed expenses ($121,800+$167,100)……… (288,900)

Operating income……… $ 191,100

4. _{B/E sales in units} ₌ $288,900 ₌ 96,300

$3.00 units

B/E sales in dollars = $288,900_12% = $2,407,500

5. $288,900 + $260,100 ₌ _{183,000 units}

(48)

(continued) E7-58B

6. Original contribution margin per unit... $3.00

Less: Increase in Direct labor cost per unit ($8.00 x

10%)... $0.80

New contribution margin per unit………... $2.20

Original fixed expenses………. $288,900

Plus: Increase in fixed expenses………. 23,500

New fixed expenses……… $312,400

New breakeven in units = $312,400_$2.20 = 142,000_Units

7. Contribution margin (from part 1)………... $300,000

Less: Fixed expenses……….. (288,900)

Operating income……… $11,100

Operating leverage factor = $300,000 = _(rounded)27.03 $11,100

8. Increase in volume……….. 3%

× Operating leverage factor………….. 27.03

New fixed expenses……… 81.1%

(rounded)

9. Margin of safety = Sales − Sales at breakeven

= $2,500,000 − $2,407,500_{(from part 1) (from part 4)} = $92,500

Margin of safety as a percentage

= 92,500 _2,500,000 = .037 = 3.7%

10. 16 GB 32 GB Total

Sales price……….. $25 $50

Less: Variable cost………….. 22 27

Contribution margin…. $ 3 $23

Multiply by: Sales mix………. × 9 × 1 10

Contribution margin…. $27 $23 $50

Weighted-average contribution margin per

unit $5.00

Sales in units = $121,800 + $167,100 +$260,100 = 109,800 units $5.00

Smaller 16 GB: 109,800 × 9/10……… 98,820 units

Larger 32 GB: 109,800 × 1/10….……… 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.

(49)

Problems (Group A)

(30-45 min.) P7-59A

Req. 1 Cost-Volume-Profit Analysis Companies Q, R, S, T COMPANY Q R S T Target sales $625,000 $445,000 $236,000 $780,000

Less: Variable expenses 125,000 178,000 118,000 156,000

Less: Fixed expenses 370,000 159,000 94,000 493,000 Operating income $130,000 $ 108,000 $ 24,000 $131,000 Units sold 80,000 106,800 12,500 16,000 Contribution margin per unit $ 6.25 $ 2.50 $ 9.44 $ 39.00 Contribution margin ratio 0.80 0.60 0.50 0.80

Computations (top to bottom for each company)

Q: 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

(50)

(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...… $ 10,800 Cast: 60 cast members × $320 / cast member... 19,200 Total variable expenses per show...….. $30,000

(51)

(continued) P7-60

Sales revenue − Variable expenses − Fixed expenses = Operating income

Revenue Number Variable Number

per × of − exp. per × of − Fixed expenses = Operating income

show shows show shows

Number Number $66,000 × of − $30,000 × of − $969,000 = $0 shows shows ($66,000 – $30,000) × Number of shows = $1,224,000 $36,000 × Number of shows = $1,224,000 Number of shows = $1,224,000_$36,000

Breakeven number of shows = 34 shows

Req. 3

Contribution margin = $66,000 − $30,000 = $36,000

Target number of shows = Fixed expenses + Target operating income Contribution margin per unit

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) $7,590,000

Less: Variable expenses (115 × $30,000) 3,450,000

Contribution margin 4,140,000

Less: Fixed expenses 1,224,000

(52)

(30-45 min.) P7-61A

Req. 1

Sales Revenue − Variable expenses − Fixed expenses = Operating income

Sale Variable

price × Units sold − cost × Units sold − Fixed expenses = Operating income per

unit per unit

($16.50 × Units sold) − ($6.50 × Units sold) − $1,095,000 = $0

($13.50 − $3.50) × Units sold = $1,095,000 $10.00 × Units sold = $1,095,000 Units sold = $1,095,000_$10.00 Breakeven sales in units = 109,500 cartons

Req. 2

Contribution margin = $16.50 − $6.50 = $10.00

Contribution margin ratio = $10.00 / $16.50 = 0.61 (rounded)

Target sales in dollars = Fixed expenses + Target operating income_{Contribution margin ratio}

Target sales in dollars = $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) $7,425,000

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 2,925,000

Contribution margin 4,500,000

Less: Fixed expenses 1,095,000

(53)

(continued) P7-61A

Req. 4

Margin of safety = Sales − Sales at breakeven

Margin of safety = $7,425,000 − (109,500 cartons × $16.50 per carton) Margin of safety = $7,425,000 − $1,806,750

Margin of safety = $5,618,250

Operating leverage factor = Contribution margin_{Operating income} Operating leverage factor = $4,500,000_$3,405,000

Operating leverage factor = 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 − 0.03 − 0.06)

Monthly fixed expenses = $9,000 (computed as $2,700 + $280 + $250 + $600 + $650 + $4,520)

Breakeven sales in dollars = Fixed expenses + Operating income Contribution margin ratio = $9,000 + $0

0.75 = $12,000 Breakeven sales in units = $12,000

(trades) $500 = 24 trades

(continued) P7-62A

(54)

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

(55)

Sales price per unit $3.00 $5.00 Less: Variable expense per unit 1 .50 2 .50

Contribution margin per unit $4 .50 $2 .50 $7.00

Weighted-average contribution margin per unit ($7.00 / 4 units)

$1.75

Breakeven sales in total units:

Fixed expenses + Operating income

= $28,000 + $0 = 16,000 units

Weighted-average contribution $1.75

margin per unit

Breakeven sales of small coffees (16,000 × ¾)... 12,000 units Breakeven sales of large coffees (16,000 × ¼)... 4,000 units

Proof:

Westlake Coffee

Contribution Margin Income Statement Month Ended February 29

Sales revenue [(12,000 × $3) + (4,000 × $5)] $56,000

Less: Variable expenses [(12,000 × $1.50) + (4,000 × $2.50)]

28,000

Contribution margin 28,000

Less: Fixed expenses 28,000

Operating income $ 0

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.