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Managerial Accounting 3e Solutions ManualChapter 7 Cost-Volume-Profit (CVP) Analysis

Chapter 7

Cost-Volume-Profit (CVP) Analysis

Quick Check

Answers:

1. d3. c5. a7. d9. d

2. b4. c6. b8. a10. c

Short Exercises

(5-10 min.) S 7-1

a.Sales price per passenger.$ 120

Less: Variable cost per passenger.. (48)

Contribution margin per passenger$ 72

b.Contribution margin per passenger$72

Divided by sales price per passenger. 120

Contribution margin ratio..60%

c.Total contribution margin (10,000 $72)...$720,000

Less: Fixed expenses.. 270,000

Operating income.$450,000

d.Total contribution margin

($650,000 60%) ..$390,000



(5 min.) S 7-2

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 300 and each sale generates $72 of contribution margin, operating income will increase (or operating loss will decrease) by $21,600 (= 300 passengers $72 per passenger).

(5-10 min.) S 7-3

Units sold=Fixed expenses + Operating income

(to break even)Contribution margin per unit (passenger)

=$270,000 + 0

$72*

=3,750 passengers

*Contribution margin=$120 sale$48 variable expense

per passenger priceper passenger

Number of passengers to break even*.3,750

Sales price per passenger... $120

Sales revenue to break even..$450,000

* from earlier calculation

(5 min.) S 7-4

Sales in units =Fixed expenses + Operating income

Contribution margin per unit

=$270,000 + $97,200

$72

=5,100 dinner cruise tickets

Or, using the equation approach:

Sales revenueVariable expensesFixed=

expensesincome

Sale price Units

per unit sold Variable cost UnitsFixed=Operating

per unit soldexpensesincome

($120 Units sold)($48 Units sold)$270,000=$97,200

[($120 $48) Units sold]$270,000=$97,2000

$72Units sold=$367,200

Units sold=5,100 tickets

To earn target income of $97,200, Luxury Cruiseline must sell 5,100 dinner cruise tickets.

(5-10 min.) S 7-5

(5 min.) S 7-6

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

(10 min.) S 7-7

Req. 1

If the sales price declines to $96, then the new unit contribution margin is $48 ($96 $48). The new breakeven point in units is:

=Fixed expenses + Operating income

Sales in unitsContribution margin per unit

=$270,000 + $0

$48

=5,625 dinner cruise passengers

To achieve breakeven, sales revenue needs to be $540,000 (5,625 passengers $96 sales price per passenger).

(continued) S 7-7


Sales revenueVariable expensesFixed=Operating

expensesincome

Sale price Units



($96 Units sold)($48 Units sold)$270,000=$0

[($96 $48) Units sold]$270,000=$0


Units sold=5,625 passengers

5,625 passengers $96 = $540,000

Alternatively,

Contribution=Contribution margin per unit

margin ratioSale price per unit

=$96 $48

$48

=0.50

Sales=Fixed expenses + Operating income

in dollarsContribution margin ratio

=$270,000 + $0

0.50

=$540,000

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.

Req. 2

If the variable cost decreases to $30, then the new unit contribution margin is $90 ($120 $30). The new breakeven point in units is:



=$270,000 + $0

$90


To achieve breakeven, sales revenue needs to be $360,000 (3,000 passengers $120 sales price per ticket).

(continued) S 7-7



expensesincome

Sale price Units




[($120 $30) Units sold]$270,000=$0



3,000 passengers $120 = $360,000

Alternatively,



=$120 30

$90

=0.75

Sales =Fixed expenses + Operating income


=$270,000 + $0

0.75

=$360,000

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.

(5-10 min.) S 7-8

Req. 1

The decline in fixed costs does not affect the $60 unit contribution margin calculated in S 7-1. The new breakeven point in units is:



=$180,000 + $0

$72


(continued) S 7-8



expensesincome

Sale price Units




[($120 $48) Units sold]$180,000=$0



2,500 passengers $120 = $300,000Alternatively,



=$120 48

$120

=0.60



=$180,000 + $0

0.60

=$300,000

Req. 2

The breakeven point is lower than in S 7-3. By cutting fixed costs, Luxury Cruiseline was able to decrease their breakeven point by 750 passengers (3,750 - 3,000).

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.) S 7-9

Luxury Cruiseline

Weighted-Average Contribution Margin per Unit

RegularExecutive

CruiseCruiseTotal

Sale price per ticket$ 120$240

Deduct: Variable expense per ticket (48) (180)

Contribution margin per ticket$ 72$ 60

Sales mix in units 4 1 5

Contribution margin$288$ 60$348

Weighted-average contribution

margin per unit ($348 / 5)$ 69.60

(continued) S 7-9A simple average contribution margin would be $66 [(72 + 60) / 2]. The weighted-average is more than the simple average because Luxury Cruiseline sells more regular cruises (with the higher contribution margin) than executive cruises.

The weighted-average contribution margin ($69.60) is lower than the contribution margin of regular cruises ($72) because Luxury Cruiseline sells some executive cruises, and they have a lower contribution margin ($60) than regular cruises.

Because the new sales mix creates a lower-weighted average contribution margin, Luxury Cruiseline will need to sell more cruises, in total, to break even than when they just sold regular cruises.

(5-10 min.) S 7-10

a.


in total ticketsWeighted-average contribution margin per unit

=$270,000 + $0

$69.60*

=3,880 (rounded) passengers

*Weighted-average contribution margin per unit from S 7-9.

b.

Breakeven sales of regular cruises (3,880 4/5)3,104

Breakeven sales of executive cruises (3,880 1/5)......776

Total cruise passengers...................................3,880

(5-10 min.) S 7-11

a.Margin of safety=Expected salesBreakeven sales

in unitsin unitsin units

=10,000 3,750*

=6,250 passengers

*(from S 7-3)

b.Margin of safety=Target level-Breakeven

in dollarssales dollarssales dollars

=$1,200,000 - $450,000

=$750,000

(continued) S 7-11

c.Margin of safety=Margin of safety in dollars

as a percentageExpected sales in dollars

of expected sales

=$750,000

$1,200,000

=62.5%

(5-10 min.) S 7-12

a.Contribution margin (12,000 $72 / cruise

passenger)......$864,000

Less:Fixed expenses. (270,000)

Operating income..$594,000

Operating Leverage Factor=Contribution margin

Operating income

=$864,000

$594,000

=1.45

b.If volume increases 10%, operating income will increase 14.5% (operating leverage factor of 1.45 multiplied by 10%).

c.If volume decreases by 5%, operating income will decrease by 7.25% (operating leverage factor of 1.45 multiplied by 5%).

(5-10 min.) S 7-13

a.Margin of safety=Expected salesBreakeven sales

in unitsin unitsin units

=1,000 600

=400 posters

b.Margin of safety=Target level-Breakeven

in dollarssales dollarssales dollars

=$31,000 - $18,600

=$12,400

(continued) S 7-13

c.Margin of safety=Margin of safety in dollars

as a percentageExpected sales in dollars

of expected sales

=12,400

31,000

=40%

(5-10 min.) S 7-14

Contribution margin (1,000 $10 / poster).$10,000


Operating income..$ 4,000

Operating Leverage Factor =Contribution margin

Operating income

=$10,000

$ 4,000

=2.5

If volume increases 10%, operating income will increase 25% (operating leverage factor of 2.5 multiplied by 10%).

Proof:

Original volume (posters)..1,000

Add:Increase in volume (10% 1,000)+ 100

New volume (posters)....1,100

Multiplied by:Unit contribution margin. $10

New total contribution margin..$ 11,000

Less:Fixed expenses... (6,000)

New operating income$ 5,000

vs.Operating income before change in

volume (from above).....4,000

Increase in operating income...$ 1,000

Percentage change ($600 / $2,400)..25%

(5-10 min.) S 7-15

Req. 1

Product: Cupcakes

Selling price per unit$ 5.00

Variable cost per unit$ 2.00

CM$ 3.00

Option 1: Lease the store space for a monthly fixed fee

Fixed costs$ 2,500

Option 2: Monthly lease of X plus % of monthly sales revenue

Fixed costs$ 1,000

Variable % of net sales20%

Point of indifference (in units):1,500

Proof:

Lease costs under Option 1:

Fixed costs$ 2,500

Variable costs (none)0

Total costs under Option 1$ 2,500


Fixed costs$ 1,000

Variable costs per unit$ 1.00

Times # of units at pt of indifference1,500.00

Total variable costs1,500.00

Total costs under Option 2$2,500.00

Req. 2

Option 2 is the better option for 1,000 units because it is below the indifference point of 1,500 units as calculated in Requirement 1

(5-10 min.) S 7-16

1.

Costs under Option #1= Costs under Option #2

Variable Costs + Fixed Costs= Variable Costs + Fixed Costs

(# Units Var. cost per unit) + Fixed Costs= (# Units Var. cost per unit) + Fixed Costs

(# Units $0) + $1,200= (# Units $11) + $0

# Units $3.50= $700

$1,200= # Units $11

# Units= 90.90 units

2.

They would prefer Option #2 because they will have a higher operating income under Option #2 than Option #1. Option #2 has a lower operating leverage (no fixed costs, but more variable costs), meaning that it is a less risky cost structure than Option #1.Exercises (Group A)

(15 min.) E 7-17A

Req. 1

Western Travel

Contribution Margin Income Statements

Sales revenue$255,000$363,000

Variable expenses

(20% of sales revenue*) 51,000 72,600

Contribution margin (80% of sales

revenue**) 204,000 290,400

Fixed expenses 174,000 174,000

Operating income (loss) $ (30,000)$ 116,400

__________

*$100,000 / $500,000 = 0.20

**$400,000 / $500,000 = 0.80 (CM ratio)

Req. 2

Breakeven sales=$174,000 + $0

1 0.20

=$174,000 + $0

0.80

=$217,500

(10-15 min.) E 7-18A

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

$42,000=25,500


Contribution margin ratio=$25,500

$42,000

Contribution margin ratio=.60

Next, fill in the given data in the contribution margin income statement:(continued) E 7-18A

Sales.$ ?

Less: Variable expenses.32,000

Contribution margin. ?

Less: Fixed expenses..25,500

Operating income..$ ?

Because the contribution margin ratio is 60% of sales revenue, the variable expenses must be 40% of sales revenue. Therefore:

Variable expenses=40% Sales revenue

$ 32,000=40% Sales revenue

$ 80,000=Sales revenue

Or alternatively:

Sales $32,000=60% Sales

Sales 60% Sales=$32,000

40% Sales =$32,000

Sales=$32,000

40%

Sales =$80,000

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

Sales.$ 80,000

Less: Variable expenses. 32,000

Contribution margin.$ 48,000


Operating income.$ 22,800

Therefore, at the current level of operations, Bentfield Drycleaners sales revenue is $80,000 and its operating income is $22,800.

(15 min.) E 7-19A

Req. 1

Contribution margin per unit:

Sale price......................................$5.00

Variable expenses.................................. 3.50

Contribution margin per unit....................$1.50

Contribution margin ratio:

Contribution margin per unit=$1.50

Sale price per unit$5.00

=0.30

(continued) E 7-19A

Req. 2

Breakeven sales in units=Fixed expenses + Operating income


=$150,000 + $0

$1.50

=100,000 packages

Breakeven sales in dollars=Fixed expenses + Operating income


=$150,000 + $0

0.30

=$500,000

Req. 3

Sales in units=Fixed expenses + Operating income


=$150,000 + $22,500

$1.50

=115,000 packages

(5-10 min.) E 7-20A

New contribution margin per unit:

Sale price......................................$5.00





=$160,000 + $22,500

$2.00

=91,250 packages

Happy Feet would have to sell 23,750 fewer packages of socks (91,250 115,000 from E 7-19) to earn $22,500 of operating income. The increase in fixed costs was completely offset by the decrease in variable costs at the prior target profit volume of sales. Therefore, Happy Feet will need to sell fewer units in order to achieve their target profit level.

(10-15 min.) E 7-21A

Req. 1



=$5.75 $2.30

$5.75

=0.60

Breakeven sales=Fixed expenses + Operating income


=$8,400 + $0

0.60

=$14,000

Req. 2

If franchisees require a monthly operating income of $8,750

Target sales=Fixed expenses + Operating income


=$8,400 + $6,000

0.60

=$24,000

Yes, Wongs franchising concept is a good idea. She expects most locations could sell more ($26,000) than the sales required to earn the target profit ($24,000).

(10- 15 min.) E 7-22A

Req. 1

Prior to changes, the average Global Chopsticks location had the following operating income:

Contribution margin per unit (from E 7-21) $ 3.45

Average sales volume units 6,000

Contribution margin..$20,700


Operating income...$12,300

Req. 2

After the price cut and advertising fees, the average Global Chopsticks location will have the following operating income:

New Contribution margin per unit ($5.25 sales price $2.30 variable cost.$ 2.95

New sales volume (units). 6,500

Contribution margin...$19,175

Less:New fixed expenses

($8,400 + $400 advertising fee) (8,800)

New operating income..$ 10,375

(continued) E 7-22A

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 $6,000 per month. However, their operating income will not be as high as before the changes ($12,300).

(10-15 min.) E 7-23A

Req. 1



=$640,000 + $0

0.80

=$800,000

Req. 2

Stewarts Steel Parts

Operating Income Projections

at Different Sales Levels

Sales revenue$ 530,000$1,050,000

Contribution margin ratio 0.80 0.80

Contribution margin424,000840,000


Operating income (loss)$(216,000)$ 200,000

Req. 3

Yes, the income projections at the two different sales levels make sense given the breakeven sales level ($800,000) computed in Req. 1. Req. 2 shows that if Stewarts revenue is only $530,000 (short of the revenue required to breakeven) the company incurs a loss. On the other hand, if revenue is $1,050,000 (higher than the revenue required to breakeven), the company earns a profit.

(15 min.) E 7-24A

Req. 1

Sales in dollars=Fixed expenses + Operating income


=$640,000 + $200,000

0.70

=$1,200,000

(continued) E 7-24A

Req. 2



$1,050,000=Fixed expenses + $200,000

0.70

$735,000=Fixed expenses + $200,000

$535,000=Fixed expenses

Fixed expenses can only be $535,000 to maintain the prior profit level of $200,000 per month. Therefore, Stewart will have to save at least $105,000 per month in fixed costs ($640,000 $535,000) by moving operations overseas if he plans to maintain his prior profit level.

(15-20 min.) E 7-25A

Expected number of units to be sold400

Average selling price per premium garage door$ 1,500

Average variable manufacturing cost per door$ 600

Average variable selling cost per door$ 150

Total annual fixed costs$ 240,000


CM per door$ 750

Req. 1

B/E in units320

B/E in dollars (selling price B/E in units)$ 480,000

Req. 2

Operating income if they do NOT develop software control system:

Total contribution margin (Selling price VC) * # of units$ 300,000

Less fixed costs$ 240,000

Projected operating income$ 60,000

Req. 3

Revised situation

Increase in annual FC$ 60,000

Decrease in avg var mfg cost per door$ 50

New B/E375

(continued) E 7-25A

Req. 4

Operating income if they develop software control system:




Req. 5

Based purely on the financial analysis presented above Kingston Garage Doors should not implement the software control system. However, the new control system would reduce waste and contribute to the companys sustainability objective. Kingston 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.

(15-20 min.) E 7-26AReq. 1

(continued) E 7-26A

Req. 2

Breakeven computation:


expensesincome

Sale price Units



($30 Units sold)($5 Units sold)$32,000,000=$0

[($30 5) Units sold]$32,000,000=$0

$25Units sold=$32,000,000

Units sold=1,280,000

tickets

In dollars:

1,280,000 tickets $30 per ticket = $38,400,000

(5-10 min.) E 7-27A

Use the short cut contribution margin formula to determine Empires current level of fixed expenses:




.40

$400,000 .40=Fixed expenses


After buying the equipment, Empires fixed expenses will be $215,000 ($160,000 + $55,000 increase). Calculate breakeven (in sales) at the new level of fixed expenses:



=$215,000

.40

=$537,500

Bevil will now have to generate $537,500 of sales revenue to breakeven.

(5-10 min.) E 7-28A

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):

Breakeven in units=Fixed expensesContribution margin per unit

=$350

$8.75

=40 scarves

ALTERNATIVELY:Breakeven in sales revenue=Fixed expensesContribution margin ratio

=$350.625

=$560 in sales revenue

Dividing $560 in sales revenue by the price per scarf ($14) yields 40 scarves. Elizabeth will have to sell an additional 40 scarves next year to cover the increase in entrance fees.

(15-20 min.) E 7-29A

Johns Plant Stands


TwigOakTotal

Sale price per unit$18.00 $38.00

Deduct: Variable expense per unit 3.00 8.00

Contribution margin per unit$15.00 $30.00

Sales mix in units 4 15

Contribution margin$60.00 $30.00$90.00

Weighted-average contribution margin

per unit ($90 / 5 units)$18.00

(continued) E 7-29A

Sales in total units:


Weighted-average contribution margin per unit

=$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, Elizabeths fixed costs will decrease. Therefore, Elizabeth will need to sell fewer scarves to breakeven than before her husband decided to share her craft booths.

(15-20 min.) E 7-30A

Rally Scooters


StandardChromeTotal

Sale price per unit$50 $60

Deduct: Variable expense per unit 35 40

Contribution margin per unit$15 $20


Contribution margin$45 $40$ 85


per unit ($110 / 5 units)$ 17




=$14,450 + $0

$17

=850 units

Breakeven sales of standard scooters (850 3/5)510 units

Breakeven sales of chrome scooters (850 2/5)...340 units

(continued) E 7-30A




=$14,450 + $11,900

$17

=1,550 units

Target sales of standard scooters (1,550 3/5)........930 units

Target sales of chrome scooters (1,550 2/5)............................620 units

(20-30 min.) E 7-31A

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.

DigitalClassicTotal

Sale price per unit..................$230

Deduct:Variable expense per unit. 150

Contribution margin per unit.... 80 190c

Sales mix in units............ 6 4 10

Contribution margin...........$480760 1,240


margin per unit............$ 124a

aSales in =Fixed expenses + Operating income

total unitsWeighted-average contribution margin per unit

2,500=$220,000 + $90,000


Weighted-average=$310,000

2,500

contribution

margin per unit

=$124 / unit

(continued) E 7-31A

bWeighted-averageTotal sales mix contribution margin

Total sales mix units

contribution=

margin per unit

$124=$480 + X

10

$1,240=$480 + X

X =$760

cContribution4=$760

margin per

Classic watch

Contribution margin=$190

per Classic watch

(15 min.) E 7-32A

Req. 1

Ghents operating income can be computed as follows:

Sales revenue. $6,300,000

Less:Variable expenses - 1,260,000

Contribution margin. 5,040,000

Less: Fixed expenses. - 940,000

Operating income.. $4,100,000

Req. 2

Contribution margin ratio=5,040,000

6,300,000

=80%

Req. 3

Breakeven in sales dollars=940,000

80%

=$1,175,000

Req. 4

If Ghents embarks on this advertising campaign, sales revenue and variable costs will rise by 20%, which will cause the contribution margin to increase by 20%. However, fixed costs will rise by $200,000 dollars due to the advertising campaign.

The change in operating income can be computed as follows:

Current contribution margin$5,040,000

Percentage increase 20%

Increase in contribution margin1,008,000

Less:Increase in fixed costs of advertising campaign 200,000

Increase in operating income$808,000

(5 min.) E 7-33A

Margin of safety=Expected sales Sales at breakeven

$10,500=$18,000 Sales at breakeven

Sales at breakeven=$ 7,500

Vs. actual sales=$17,050

Difference=$ 9,550

Actual sales exceeded breakeven sales by $9,550.

(15 min.) E 7-34A

Req. 1

Contribution margin ratio=1.00 0.50

=0.50



=$7,000 + $0

0.50

=$14,000

Target sales in dollars=Fixed expenses + Operating income


=$7,000 + $10,500

0.50

=$17,500

0.50

=$35,000

Margin of safety=$35,000 $14,000

=$21,000

(continued) E 7-34A

Req. 2

Margin of safety as =$21,000

$35,000

a percentage of target sales

=0.60 or 60% of target sales

Req. 3

Target sales...$35,000

Contribution margin ratio.. .50

Contribution margin$17,500

Less:Fixed expenses.. (7,000)



Operating income

=$17,500

$10,500

=1.67

Req. 4

If volume decreases 9%, operating income will decrease 15.03% (operating leverage factor of 1.67 multiplied by 9%).

(10 min.) E 7-35A

First, find Guintys contribution margin:

Sales$50,000



Then, work backwards to find Guintys operating income:

Operating leverage factor=Contribution margin

Operating income

1.50= $15,000

Operating income

Operating income=$15,000

1.50


Finally, finish the income statement to find the fixed expenses:


Less:Fixed expenses.Unknown

Operating income..$10,000

Therefore, fixed expenses must be $5,000.(10-15 min.) E 7-36A



CM$ 11.00


Fixed costs$ 2,500


Fixed costs$ 1,200


Point of indifference (in units):650

Proof:


Fixed costs$ 2,500




Fixed costs$ 1,200


Times # of units at pt of indifference650.00



Option 2 is the better option for 500 units because it is below the indifference point of 650 units

(10-15 min.) E 7-37A

Product: HeadbandsSelling price per unit$ 10.00


CM$ 6.00

Option 1

Fixed costs$ 1,000


Option 2

Fixed costs$ 2,000


1,000 + (.2*10*X) = 2,000 + (.1*10*X)

1,000 _ 2X = 2,000 + 1X

1X = 1,000

(c8 - c12)*SP1.00

(C11 - C7)$ 1,000

(c11 - c7)/(c8 - c12)1,000.00

Point of indifference (in units):1,000

Proof:


Fixed costs$ 1,000

Variable costs$2,000.00



Fixed costs$ 2,000


Times # of units at pt of indifference1,000.00



Option 1 is the better option for 1,500 units because it is above the indifference point of 1,000 units

(20-25 min.) E 7-38A

Req. 1


=$880

$55*

=16 grooming kits

Selling price$84

less VC per unit$29

CM per unit$55

*

(continued) E 7-38A

Req. 2

2a)

Sales in units to reach desired profit=Fixed expenses + Operating IncomeContribution margin per unit

=$880 + $1,320

$55

=$2,200

$55

=40 grooming kits

2b)Sales in dollars to reach desired profit=breakeven units x selling price per unit

=40 units x $84/each

=$3,360

2c)

Condensed Income Statement

Sales$3,360

less VC $1,160

CM$2,200

less FC$880

NI$1,320

Req. 3

Margin of safety in dollars:

Sales at target level:$3,360

Sales at B/E level:$1,344*

Margin of safety in dollars$2,016

Margin of safety in units:

Sales at target level:40

Sales at B/E level:16

Margin of safety in units24

Margin of safety in %:

Margin of safety in dollars:$2,016


divide top/bottom:60.00%

*Sales at B/E level: 16 kits x $84 = $1,344

(20-25 min.) E 7-39A

Req. 1

TotalPer Unit%

Sales$116,000$40100%

Variable expenses87,0003075%

Contribution Margin$29,000$1025%

Fixed expenses11,000

Operating income$18,000

1a) Total contribution margin is $29,000.

1b) Per unit contribution margin is $10.

1c) Operating income is $18,000.

1d) Units sold = Total sales / sale price = $116,000 / 40 = 2,900 Units

Req. 2

2a.


=$11,000

$10

=1,100 units

2b.



=$11,000 + 0

0.25 (from req. 1)

=$44,000

Req. 3

3a)


=$11,000 + $55,000

$10

=$62,000

$10

=6,600 units

(continued) E 7-39A

3b)

Budgeted Sales Units2,900

Breakeven Sales Units- 1,100

Margin of Safety in Units1,800

3c)

Budgeted Sales $116,000

Breakeven Sales Volume$44,000

Margin of Safety in Dollars$72,000

3d)


Budgeted Sales Dollars $116,000

Margin of Safety %62.1%

(20-25 min.) E 7-40A

1.Sales price per unit.............................................$20.00

Variable cost per unit.........................................$16.00

Contribution margin per unit.............................$ 4.00

Contribution margin ratio=$4.00=.20

$20.00

=20%

Sales Revenue (120,000 $20.00)$ 2,400,000

Less: Variable expenses (120,000 $16.00)(1,920,000)

Contribution margin..$ 480,000

2.Sales volume (units) 150,000

Unit contribution margin x $4.00


Less: Fixed expenses (449,000)


3.Sales revenue$4,000,000

Contribution margin ratio.. x 20%


Less: fixed expenses. (449,000)


4.B/E sales in units=$449,000=112,250

$4.00units

B/E sales in dollars=$449,000=$2,245,000

20%

(continued) E 7-40A

5.$449,000 + $260,000=177,250 units

$4.00

6.Original contribution margin per unit..................$4.00

Less:Increase in Direct labor cost per unit ($7.00 x 10%)..........................................................$0.70

New contribution margin per unit...$3.30

Original fixed expenses.$449,000

Plus:Increase in fixed expenses.. 28,500

New fixed expenses$477,500

New breakeven in units=$477,500=144,697

$3.30Units

7.Contribution margin (from part 1)...$480,000

Less: Fixed expenses... (449,000)

Operating income$ 31,000

Operating Leverage factor=$480,000=15.48

$ 31,000

8.Increase in volume..5%

Operating leverage factor..15.48

New fixed expenses77.4%

9.Margin of safety=Sales Sales at breakeven

=$2,400,000 $2,245,000

(from part 1) (from part 4)

=$155,000

Margin of safety as a percentage=155,0002,400,000=.06=6%

(continued) E 7-40A

10.16 GB32 GBTotal

Sales price.. $20$45

Variable cost.. (16)(21)

Contribution margin. $ 4$24

Sales mix. 3 1 4

Contribution margin.$12$24$36

Weighted-average contribution margin per unit 36

4 $9.00

Sales in units=$449,000 + $260,000=78,778 units (rounded)

$9

Smaller 16 GB: 78,778 3/4..59,084 units (rounded)

Larger 32 GB: 78,778 1/4..19,695 units (rounded)

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.) E 7-41B

Req. 1

Worldwide Travel

Contribution Margin Income Statements

Sales revenue$220,000$361,000

Variable expenses

(40% of sales revenue*)88,000 144,400

Contribution margin (60% of sales

revenue**) 132,000 216,600


Operating income (loss) $ (42,000)$ 42,600

__________

*$126,600 / $316,500 = 0.40

**$189,900 / $316,500 = 0.60 (CM ratio)

Req. 2

Breakeven sales=$174,000 + $0

1 0.40

=$174,000 + $0

0.60

=$290,000

(10-15 min.) E 7-42B

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:



$44,000=$33,000


Contribution margin ratio=$33,000

$44,000

Contribution margin ratio=.75

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

Sales.$ ?

Less: Variable expenses.37,500

Contribution margin. ?

Less: Fixed expenses..33,000

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

$ 37,500=25% Sales revenue

$150,000=Sales revenue

Or alternatively:

Sales $44,000=75% Sales

Sales 75% Sales=$37,500

25% Sales =$37,500

Sales=$37,500

25%

Sales =$150,000

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

Sales.$150,000

Less: Variable expenses. 37,500

Contribution margin.$112,500



Therefore, at the current level of operations, Aldermans sales revenue is $150,000, and its operating income is $79,500.

(15 min.) E 7-43B

Req. 1

Contribution margin per unit:

Sale price......................................$2.00



Contribution margin ratio:

Contribution margin per unit=$0.80

Sale price per unit$2.00

=0.40

Req. 2

Breakeven sales in units=Fixed expenses + Operating income


=$85,000 + $0

$0.80

=106,250 packages



=$85,000 + $0

0.40

=$212,500

Req. 3



=$85,000 + $26,000

$0.80

=138,750 packages

(5-10 min.) E 7-44B

New contribution margin per unit:

Sale price......................................$2.00





=$90,000 + $26,000

$1.00

=116,000 packages

(continued) E 7-44B

Trendy Toes would have to sell 22,750 fewer packages of socks (138,750 116,000 from E 7-43B) to earn $26,000 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, Trendy Toes will need to sell more units in order to achieve their target profit level.

(10-15 min.) E 7-45B

Req. 1



=$4.50 $1.80

$4.50

=0.60

Breakeven sales=Fixed expenses + Operating income


=$9,000 + $0

0.60

=$15,000

Req. 2

If franchisees require a monthly operating income of $7,350

Target sales=Fixed expenses + Operating income


=$9,000 + $7,350

0.60

=$27,250

No, Longs franchising concept is not a good idea. The sales required to earn the target profit ($27,250) are more than the expected sales generated ($23,000).

(10- 15 min.) E 7-46B

Req. 1

Prior to changes, the average Oriental Express location had the following operating income:

Contribution margin per unit (from E 7-45B) $ 2.70

Average sales volume units 6,500



Operating income...$8,550

(continued) E 7-46B

Req. 2

After the price cut and advertising fees, the average Oriental Express location will have the following operating income:

New Contribution margin per unit ($4.00 sales price $1.80 variable cost.$ 2.20

New sales volume (units). 7,000

Contribution margin...$15,400

Less:New fixed expenses

($9,000 + $500 advertising fee) (9,500)

New operating income..$ 5,900

Assuming volume increases according to plan, cutting the sales price and advertising will not allow the franchise owners to continue to reach their target profits of $7,350 per month. However, their operating income will not be as high as before the changes ($8,550).

(10-15 min.) E 7-47B

Req. 1



=$660,000 + $0

0.75

=$880,000

Req. 2

Rodgers Steel Parts

Operating Income Projections

at Different Sales Levels

Sales revenue$ 560,000$1,030,000

Contribution margin ratio 0.75 0.75



Operating income (loss)$(240,000)$ 112,500

Req. 3

Yes, the income projections at the two different sales levels make sense given the breakeven sales level ($880,000) computed in Req. 1. Req. 2 shows that if Rogers revenue is only $560,000 (short of the revenue required to breakeven) the company incurs a loss. On the other hand, if revenue is $1,030,000 (higher than the revenue required to breakeven), the company earns a profit.

(15 min.) E 7-48B

Req. 1



=$660,000 + $112,500

0.60

=$1,287,500

(continued) E 7-48B

Req. 2



$1,030,000=Fixed expenses + $112,500

0.60

$618,000=Fixed expenses + $112,500


Fixed expenses can only be $505,500 to maintain the prior profit level of $112,500 per month. Therefore, Roger will have to save at least $154,500 per month in fixed costs ($660,000 $505,500) by moving operations overseas if he plans to maintain his prior profit level.

(15-20 min.) E 7-49B

Expected number of units to be sold450

Average selling price per premium garage door$ 1,300

Average variable manufacturing cost per door$ 550

Average variable selling cost per door$ 150



CM per door$ 600

Req. 1

B/E in units400

B/E in dollars (selling price B/E in units)$ 520,000

Req. 2

Operating income if they do NOT develop software control system:




Req. 3

Revised situation

Increase in annual FC$ 61,000

Decrease in avg var mfg cost per door$ 00

New B/E430

(continued) E 7-49B

Req. 4

Operating income if they develop software control system:




Req. 5

Based purely on the financial analysis presented above Kingston Garage Doors should not implement the software control system. However, the new control system would reduce waste and contribute to the companys sustainability objective. Kingston 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.

(15-20 min.) E 7-50B

Req. 1

(continued) E 7-50B

Req. 2

Breakeven computation:


expensesincome

Sale price Units



($35 Units sold)($5 Units sold)$24,000,000=$0

[($35 5) Units sold]$24,000,000=$0

$30Units sold=$24,000,000

Units sold=800,000

tickets

In dollars:

800,000 tickets $30 per ticket = $24,000,000

(5-10 min.) E 7-51B

Use the short cut contribution margin formula to determine Edwards current level of fixed expenses:




.20

$300,000 .20=Fixed expenses


After buying the equipment, Edwards fixed expenses will be $100,000 ($60,000 + $40,000 increase). Calculate breakeven (in sales) at the new level of fixed expenses:



=$100,000

.20

=$500,000

Edward Industries will now have to generate $500,000 of sales revenue to breakeven.

(5-10 min.) E 7-52B

Sales price per unit..$20.00

Contribution margin ratio... .625

Contribution margin per unit.$12.50

Find the number of scarves needed to breakeven on (or pay for) the extra entrance fee cost of $50 (= $500 10% increase):(continued) E 7-52B


=$50

$12.50

=4 scarves

ALTERNATIVELY:

Breakeven in sales revenue=Fixed expensesContribution margin ratio

=$50.625

=$80 in sales revenue

Dividing $80 in sales revenue by the price per scarf ($20) yields 4 scarves. Ramona will have to sell an additional 4 scarves next year to cover the increase in entrance fees.

(15-20 min.) E 7-53B

Mikes Plant Stands


TwigOakTotal

Sale price per unit$14.00 $40.00

Deduct: Variable expense per unit 2.00 18.00

Contribution margin per unit$12.00 $22.00


Contribution margin$48.00 $22.00$70.00


per unit ($70 / 5 units)$14.00




=$350 + $0

$14

=25 units

Breakeven sales of twig stands (25 4/5)20 units

Breakeven sales of oak stands (25 1/5). 5 units

By charging her husband part of the craft fair entrance fees, Ramonas fixed costs will decrease. Therefore, Ramona will need to sell fewer scarves to breakeven than before her husband decided to share her craft booths.

(15-20 min.) E 7-54B

Zippy Scooters


StandardChromeTotal

Sale price per unit$45 $65

Deduct: Variable expense per unit 30 35

Contribution margin per unit$15 $30


Contribution margin$45 $60$105


per unit ($105 / 5 units)$ 21




=$17,850 + $0

$21

=85units

Breakeven sales of standard scooters (850 3/5)510 units

Breakeven sales of chrome scooters (850 2/5)...340 units




=$17,850 + 14,700

$21

=1,550 units

Target sales of standard scooters (1,550 3/5)........930 units

Target sales of chrome scooters (1,550 2/5).........................620 units

(20-30 min.) E 7-55B

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.

DigitalClassicTotal

Sale price per unit..................$225

Deduct:Variable expense per unit. 155

Contribution margin per unit.... 70145 c

Sales mix in units............ 6 4 10

Contribution margin...........$420580b 1,000


margin per unit............$ 100a

(continued) E 7-55B

aSales in =Fixed expenses + Operating income

total unitsWeighted-average contribution margin per unit

2,500=$180,000 + $70,000


Weighted-average=$250,000

2,500

contribution

margin per unit

=$100 / unit

bWeighted-averageTotal sales mix contribution margin

Total sales mix units

contribution=

margin per unit

$100=$420 + X

10

$1,000=$420 + X

X =$580

cContribution4=$580

margin per

Classic watch

Contribution margin=$145

per Classic watch

(15 min.) E 7-56B

Req. 1

Heltons operating income can be computed as follows:

Sales revenue. $6,500,000

Less:Variable expenses - 1,560,000

Contribution margin. 4,940,000

Less: Fixed expenses. - 1,140,000

Operating income.. $3,800,000

Req. 2

Contribution margin ratio=$4,940,000

$6,500,000

=76%

(continued) E 7-56B

Req. 3

Breakeven in sales dollars=$1,140,000

76%

=$1,500,000

Heltons will have to generate $1,500,000 in sales in order to break even.

Req. 4

If Heltons embarks on this advertising campaign, sales revenue and variable costs will rise by 10%, which will cause the contribution margin to increase by 10%. However, fixed costs will rise by $230,000 dollars due to the advertising campaign.

The change in operating income can be computed as follows:

Current contribution margin$4,940,000

Percentage increase 10%

Increase in contribution margin494,000

Less:Increase in fixed costs of advertising campaign 230,000

Increase in operating income$264,000

(10 min.) E 7-57B

Margin of safety=Expected sales Sales at breakeven

$11,700=$20,000 Sales at breakeven

Sales at breakeven=$ 8,300

Vs. actual sales=$18,400

Difference=$ 10,100

Actual sales exceeded breakeven sales by $10,100.

(15 min.) E 7-58B

Req. 1

Contribution margin ratio=1.00 0.50

=0.50



=$10,000 + $0

0.50

=$20,000

(continued) E 7-58B

Target sales in dollars=Fixed expenses + Operating income


=$10,000 + $12,500

0.50

=$22,500

0.50

=$45,000

Margin of safety=$45,000 $20,000

=$25,000

Req. 2

Margin of safety as =$25,000

$45,000

a percentage of target sales

=0.56 or 56% of target sales

Req. 3

Target sales...$45,000



Less:Fixed expenses.. (10,000)



Operating income

=$22,500

$12,500

=1.80

Req. 4

If volume decreases 8%, operating income will decrease 14.40% (operating leverage factor of 1.80 multiplied by 8%).

(10 min.) E 7-59B

First, find Welchs contribution margin:

Sales$60,000



(continued) E 7-59B

Then, work backwards to find Welchs operating income:


Operating income

1.25= $15,000

Operating income


1.25


Finally, finish the income statement to find the fixed expenses:


Less:Fixed expenses.Unknown

Operating income..$ 12,000

Therefore, fixed expenses must be $3,000.

(10-15 min.) E 7-60A



CM$ 13.00


Fixed costs$ 2,000


Fixed costs$ 1,500



Proof:


Fixed costs$ 2,000




Fixed costs$ 1,500



Total variable costs500.00


Option 2 is the better option for 300 units because it is below the indifference point of 400 units

(10-15 min.) E 7-61A

Product: HeadbandsSelling price per unit$ 20.00


CM$ 8.00

Option 1

Fixed costs$ 1,200


Option 2

Fixed costs$ 2,400


(c8 - c12)*SP2.00

(C11 - C7)$ 1,200

(c11 - c7)/(c8 - c12)600.00


Proof:


Fixed costs$ 1,200

Variable costs$3,000.00



Fixed costs$ 2,400





Option 1 is the better option for 1,000 units because it is above the indifference point of 600 units

(20-25 min.) E 7-62B

Req. 1


=$759

$33*

=23 grooming kits

Selling price$70

less VC per unit$37

CM per unit$33

*

(continued) E 7-62B

Req. 2

2a)


=$759 + $627

$33

=$1,386

$33

=42 grooming kits (round UP to the nearest whole unit)

2b)

Sales in dollars to reach desired profit=breakeven units x selling price per unit

=42 units x $70/each

=$2,940

2c)

Condensed Income Statement

Sales (42 x $70)$2,940

less VC (42 x $37)$1,554

CM$1,386

less FC$759

NI$627

Req. 3

Margin of safety in dollars:

Sales at target level$2,940

Sales at B/E level:

($759 / 33) x $70$1,610

Margin of safety in dollars$1,330

Margin of safety in units:

Sales at target level:42

Sales at B/E level:

($759 / 33)23

Margin of safety in units19

Margin of safety in %:

Margin of safety in dollars:$1,330


divide top/bottom:45.23%

(20-25 min.) E 7-63B

Req. 1

TotalPer Unit%

Sales$110,000$20100%

Variable expenses82,5001572%

Contribution Margin$27,500$525%



1a) Total contribution margin is $27,500.

1b) Per unit contribution margin is $5.

1c) Operating income is $13,500.

1d) Units sold = Total sales / sale price = $110,000 / $20 = 5,500 Units

Req. 2

2a.


=$14,000

$5

=2,800 units

2b.



=$14,000 + 0

0.25 (from req. 1)

=$56,000

Req. 3

3a)


=$14,000 + $52,000

$5

=$66,000

$5

=13,200 units

(continued) E 7-63B

3b)

Budgeted Sales Units5,500

Breakeven Sales Units- 2,800

Margin of Safety in Units2,700

3c)

Budgeted Sales $110,000

Breakeven Sales$56,000


3d)


Budgeted Sales Dollars $110,000

Margin of Safety %49%

(20-25 min.) E 7-64B

1Sales price per unit.......................................$20.00

Variable cost per unit...................................$15.00

Contribution margin per unit.............................$ 5.00

Contribution margin ratio=$5.00=.25

$20.00

=25%

Sales Revenue (130,000 $20.00)$ 2,600,000

Less: Variable exp. (130,000 $17.00) (1,950,000)

Contribution margin...$ 650,000

2Sales volume (units) 160,000

Unit contribution margin x $5.00


Less: Fixed expenses (479,000)


3Sales revenue$4,000,000

Contribution margin ratio.. x 25%

Contribution margin$1,000,000

Less: fixed expenses. (479,000)


4B/E sales in units=$479,000=95,800

$5.00units

B/E sales in dollars=$479,000=$1,916,000

25%

5$479,000 + $260,000=147,800 units

$5.00

(continued) E 7-64B

6.Original contribution margin per unit..................$5.00

Less:Increase in Direct labor cost per unit ($5.00 x 10%)..........................................................$0.50

New contribution margin per unit...$4.50

Original fixed expenses.$479,000

Plus:Increase in fixed expenses. 27,000

New fixed expenses$506,000

New breakeven in units=$506,000=115,000

$4.50Units

7.Contribution margin (from part 1)...$650,000

Less: Fixed expenses.. (479,000)


Operating Leverage factor=$650,000=3.80

$171,000

8.Increase in volume..5%

Operating leverage factor..3.80

New fixed expenses19%

9.Margin of safety=Sales Sales at breakeven

=$2,600,000 $1,916,000

(from part 1) (from part 4)

=$684,000

Margin of safety as a percentage= 684,0002,600,000=.26=26%

10.16 GB32 GBTotal

Sales price.. $20$45

Variable cost.. (15)(20)

Contribution margin. $ 5$25

Sales mix. 3 1 4

Contribution margin.$15$25$40

Weighted-average contribution margin per unit (40)

(4) $10.00

Sales in units=$479,000 + 260,000=73,900 units

10

Smaller 16 GB: 73,900 6/755,425 units

Larger 32 GB: 73,900 1/7.18,475 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.

Problems (Group A)

(30-45 min.) P 7-65A

Req. 1

Cost-Volume-Profit Analysis

Companies Q, R, S, T

COMPANY

QRST

Target sales$720,000$328,750$190,000$900,000

Variable expenses216,00065,75076,000270,000

Fixed expenses 350,000 153,000 90,000497,000

Operating income $154,000 $ 110,000 $ 24,000 $133,000

Units sold84,000131,50012,00018,000

Contribution

margin per unit$ 6.00 $ 2.00$ 9.50$ 35.00

Contribution

margin ratio0.70 0.800.600.70

Computations (top to bottom for each company)

Q:Sales Variable expenses Operating income = Fixed expenses

$720,000 $216,000 $154,000 = $350,000

Sales Variable expenses = Contribution margin;

Contribution margin / Unit contribution margin = Units sold

$720,000 $216,000 = $504,000; $504,000 / $6 = 84,000 units

Contribution margin / Sales = Contribution margin ratio

$504,000 / $720,000 = 0.70

R:

Sales Contribution margin ratio = Contribution margin;

Sales Contribution margin = Variable expenses

($328,750 0.80) = $263,000; $328,750 $263,000 = $65,750

Sales Variable expenses Fixed expenses = Operating income

$328,750 $65,750 $153,000 = $110,000

Contribution margin / Units sold = Contribution margin per unit

$263,000 / 131,500 = $2.00

S:

Units sold Unit contribution margin = Contribution margin;


12,000 $9.50 = $114,000; $190,000 $114,000 = $76,000


$190,000 $76,000 $90,000 = $24,000


$114,000 / $190,000 = 0.60

(continued) P 7-65A

T:


Contribution margin + Variable expenses = Sales

18,000 $35 = $630,000; $630,000 + $270,000 = $900,000

Sales Variable expenses Operating income = Fixed expenses

$900,000 $270,000 $133,000 = $497,000


$630,000 / $900,000 = 0.70

Req. 2

Breakeven Sales:

QB/E=$350,000=$500,000

0.70

R:B/E=$153,000=$191,250

0.80

S:B/E=$90,000=$150,000

0.60

Lowest breakeven point

T:B/E=$497,000=$710,000:

0.70

Company Ss low breakeven point is primarily due to its low fixed expenses.

(30-45 min.) P 7-66A

Req. 1

Revenue per show:

1,000 tickets $60 / ticket........................$60,000

Variable expenses per show:

Programs: 1,000 guests $9 / guest....................$ 9,000

Cast: 75 cast members $300 / cast member......... 22,500

Total variable expenses per show.........................$31,500

(continued) P 7-66A

Req. 2

Sales revenueVariable expensesFixed expenses=Operating income

RevenueNumberVariableNumber

perofexp. perofFixed expenses=Operating income

showshowsshowshows

NumberNumber

$60,000of$31,500of$969,000=$0

showsshows

($60,000 $31,500) Number of shows = $969,000

$28,500 Number of shows= $969,000

Number of shows = $969,000

$28,500

Breakeven number of shows= 34 shows

Req. 3

Contribution margin=$60,000 $31,500

=$28,500

Target number of shows=Fixed expenses + Target operating income


Target number of shows=$969,000 + $3,078,000

$28,500

Target number of shows=$4,047,000

$28,500

Target number of shows=142 shows

This profit goal is realistic. In fact, the goal is low. The show currently performs 120 times a year.

Req. 4

Jersey Boys

Contribution Margin Income Statement

For the Year Ended December 31

Sales revenue (120 $60,000)$7,200,000

Variable expenses (120 $31,500) 3,780,000

Contribution margin 3,420,000

Fixed expenses 969,000

Operating income$2,451,000

(30-45 min.) P 7-67A

Req. 1

Sales RevenueVariable expensesFixed expenses=Operating income

SaleVariable

priceUnits soldcostUnits soldFixed expenses=Operating income

per unitper unit

($13.50 Units sold) ($3.50 Units sold) $1,065,000= $0

($13.50 $3.50) Units sold = $1,065,000

$10.00 Units sold = $1,065,000

Units sold =$1,065,000

$10.00

Breakeven sales in units=106,500 cartons

Req. 2

Contribution margin=$13.50 $3.50

=$10.00

Contribution margin ratio=$10.00 / $13.50

=0.74 (rounded)

Target sales in dollars=Fixed expenses + Target operating income


Target sales in dollars=$1,065,000 + $304,000

0.74

=$1,369,000

0.74

=$1,850,000

Req. 3

University Calendars


Month Ended June 30

Sales revenue (470,000 $13.50)$6,345,000

Variable expenses:

Cost of goods sold (470,000 $3.50 0.65)$1,069,250

Operating expenses (470,000 $3.50 0.35) 575,750 1,645,000


Fixed expenses: 1,065,000


(continued) P 7-67A

Req. 4

Margin of safety=Sales Sales at breakeven

Margin of safety=$6,345,000 (106,500 cartons $13.50 per carton)

Margin of safety=$6,345,000 $1,437,750

Margin of safety=$4,907,250


Operating income

Operating leverage factor=$4,700,000

$3,635,000

Operating leverage factor=1.293

Req. 5

If volume increases 12%, then operating income will increase 15.52% (operating leverage factor of 1.293 multiplied by 12%).

Proof:

Original volume (cartons).....470,000

Add: Increase in volume (12% 470,000) 56,400

New volume (cartons)...526,400

Multiplied by:Unit contribution margin$10.00

New total contribution margin$5,264,000

Less:Fixed expenses. (1,065,000)

New operating income.$4,199,000


volume.. 3,635,000

Increase in operating income.$ 564,000

Percentage change ($564,000 / $3,635,000)15.52%

(30-45 min.) P 7-68A

Req. 1

Contribution margin ratio =0.70 (computed as 1.00 0.14 0.07 0.03 0.06)

Monthly fixed expenses=$9,100 (computed as $2,100 + $260 + $280 + $600 + $640 + $5,220)



=$9,100 + $0

0.70

=$13,000

Breakeven sales in units=$13,000

(trades)$520

=25 trades

(continued) P 7-68A

Req. 2

Sales revenue Variable expenses Fixed expenses=Target operating

income

Sales revenue 0.30 Sales revenue $9,100=$3,640

0.70 Sales revenue=$12,740

Sales revenue=$12,740

0.70


Req. 3

(continued) P 7-68A

Req. 4

Breakeven sales in dollars (from Req. 1)=$13,000

Breakeven sales in units (trades)=$13,000

$425

=31 trades

The decrease in the average trade revenue increases the breakeven point from 25 to 31 trades.

(25-35 min.) P 7-69A

Req. 1

Pepperpike Coffee


SmallLargeTotal

Sale price per unit$3.00$5.00

Deduct:Variable expense per unit 1.50 2.50

Contribution margin per unit$1.50$2.50


Contribution margin per unit$4.50$2.50 $7.00


per unit ($7.00 / 4 units) $1.75

Breakeven sales in total units:

Fixed expenses + Operating income=$42,000 + $0=124,000 units

Weighted-average contribution$1.75

margin per unit

Breakeven sales of small coffees (24,000 )........18,000 units

Breakeven sales of large coffees (24,000 )........6,000 units

Proof:

Pepperpike Coffee


Month Ended February 29

Sales revenue [(18,000 $3) + (6,000 $5)]$84,000

Variable expenses [(18,000 $1.50) + (6,000 $2.50)] 42,000

Contribution margin 42,000


Operating income$ 0

(continued) P 7-69A

Req. 2

Margin of safety=Actual sales Breakeven sales

Margin of safety=$103,000 $84,000*

=$19,000

*Breakeven sales from proof in Req. 1.

Req. 3

Operating leverage factor

= Contribution Margin

Operating income

= $62,000

$20,000

= 3.10

A 15% increase in volume will lead to 4.65% increase in operating income (15% multiplied by the operating leverage factor of 3.10). Therefore, the new operating income will be $29,300 ($20,000 old operating income 1.465).

Proof:

Pepperpike Coffee

Effect on Operating Income of 15% Increase in Sales Volume

Increase in sales revenue ($103,000 0.15)$14,450

Increase in variable expenses ($41,000 0.15)6,150


Change in fixed expenses0

Operating income before sales increase 20,000

Operating income after sales increase$29,300

Alternatively,

Proof:

Pepperpike Coffee


Sales revenue ($103,000 1.15)$118,450

Variable expenses ($41,000 1.15)47,150

Contribution margin71,300


Operating income $ 29,300

Problems (Group B)

(30-45 min.) P 7-70B

Req. 1

Cost-Volume-Profit Analysis

Companies Q, R, S, T

COMPANY

QRST

Target sales$687,500$480,000$171,875$780,000

Variable expenses192,500216,00061,875156,000

Fixed expenses 405,000165,000 88,000493,000

Operating income $ 90,000 $ 99,000 $ 22,000 $131,000

Units sold75,000110,00011,00016,000

Contribution

margin per unit$ 6.60 $ 2.40$ 10.00$ 39.00

Contribution

margin ratio0.72 0.550.640.80

(30-45 min.) P 7-70B

Computations (top to bottom for each company)

Q:Sales Variable expenses Operating income = Fixed expenses

$687,500 $192,500 $90,000 = $405,000

Sales Variable expenses = Contribution margin;

Contribution margin / Unit contribution margin = Units sold

$687,500 $192,500 = $495,000; $495,000 / $6.60 =75,000 units


$495,000 / $687,500 = 0.72

R:

Sales Contribution margin ratio = Contribution margin;


($480,000 0.55) = $264,000; $480,000 $264,000 = $216,000


$480,000 $216,000 $165,000 = $99,000

Contribution margin / Units sold = Contribution margin per unit

$264,000 / 110,000 = $2.40

S:



11,000 $10.00 = $110,000; $171,875 $110,000 = $61,875


$171,875 $61,875 $88,000 = $22,000


$110,000 / $171,875 = 0.64

(continued) P 7-70B

T:


Contribution margin + Variable expenses = Sales

16,000 $39.00 = $624,000; $624,000 + $156,000 = $780,000

Sales Variable expenses Operating income = Fixed expenses

$780,000 $156,000 $131,000 = $493,000


$624,000 / $780,000 = 0.80

Req. 2

Breakeven Sales:

Q:B/E=$405,000=$565,500

0.72

R:B/E=$165,000=$300,000

0.55

S:B/E=$88,000=$137,500

0.64

Lowest breakeven point

T:B/E=$493,000=$616,250

0.80

Company Ss low breakeven point is primarily due to its low fixed expenses.

(30-45 min.) P 7-71B

Req. 1

Revenue per show:

1,000 tickets $45 / ticket........................$45,000

Variable expenses per show:

Programs: 1,000 guests $9 / guest....................$ 9,000

Cast: 45 cast members $300 / cast member......... 13,500

Total variable expenses per show.........................$22,500

(continued) P 7-71B

Req. 2

Sales revenueVariable expensesFixed expenses=Operating income

RevenueNumberVariableNumber

perofexp. perofFixed expenses=Operating income

showshowsshowshows

NumberNumber

$45,000of$22,500of$787,500=$0

showsshows

($45,000 $22,500) Number of shows = $787,500

$22,500 Number of shows= $787,500

Number of shows = $787,500

$22,500

Breakeven number of shows= 35 shows

Req. 3

Contribution margin=$45,000 $22,500

=$22,500

Target number of shows=Fixed expenses + Target operating income


Target number of shows=$787,500 + $2,362,500

$22,500

Target number of shows=$3,150,000

$22,500

Target number of shows=140 shows

This profit goal is realistic. The show currently performs 120 times a year. By adding one more show every other week, they would be able to reach their goal.

Req. 4

Shrek


For the Year Ended December 31

$5,400,000

Variable expenses (120 $22,500) 2,700,000

Contribution margin 2,700,000



(30-45 min.) P 7-72B

Req. 1

Sales RevenueVariable expensesFixed expenses=Operating income

SaleVariable

priceUnits soldcostUnits soldFixed expenses=Operating income

per unitper unit

($18.50 Units sold) ($6.00 Units sold) $1,115,000= $0

($18.50 $6.00) Units sold = $1,115,000

$12.50 Units sold = $1,115,000

Units sold =$1,115,000

$12.50

Breakeven sales in units=89,200 cartons

Req. 2

Contribution margin=$18.50 $6.00

=$12.50

Contribution margin ratio=$12.50 / $18.50

=0.68 (rounded)

Target sales in dollars=Fixed expenses + Target operating income


Target sales in dollars=$1,115,000 + $330,000

0.68

=$1,445,000

0.68

=$2,125,000

Req. 3

College Calendars


Month Ended June 30

Sales revenue (455,000 $18.50)$8,417,500

Variable expenses:

Cost of goods sold (455,000 $6.00 0.67)$1,829,100

Operating expenses (455,000 $6.00 0.33) 900,900 2,730,000


Fixed expenses: 1,115,000


(continued) P 7-72B

Req. 4

Margin of safety=Sales Sales at breakeven

Margin of safety=$8,417,500 (89,200 cartons $18.50 per carton)

Margin of safety=$8,417,500 $1,650,200

Margin of safety=$6,767,300


Operating income

Operating leverage factor=$5,687,500$4,572,500

Operating leverage factor=1.244 (rounded)

Req. 5

If volume increases 11%, then operating income will increase 13.68% (operating leverage factor of 1.244 multiplied by 11%).

Proof:

Original volume (cartons)..455,000

Add:Increase in volume (11% 455,000) 50,050

New volume (cartons)505,050

Multiplied by:Unit contribution margin$12.50

New total contribution margin$6,313,125

Less:Fixed expenses (1,115,000)

New operating income$5,198,125


volume. 4,572,500

Increase in operating income$ 625,625

Percentage change ($625,625 / $4,572,500)13.68%

(30-45 min.) P 7-73B

Req. 1

Contribution margin ratio =0.80 (computed as 1.00 0.10 0.05 0.02 0.03)

Monthly fixed expenses=$7,600 (computed as $2,900 + $330 + $280 +$690 + $700 + $2,700)



=$7,600 + $0

0.80

=$9,500

Breakeven sales in units=$9,500

(trades)$475

=20 trades

Req. 2

Sales revenue Variable expenses Fixed expenses=Target operating

income

Sales revenue 0.20 Sales revenue $7,600=$3,040

0.80 Sales revenue=$110,640


0.80


(continued) P 7-73B

Req. 3

Req. 4

Breakeven sales in dollars (from Req. 1)=$9,500

Breakeven sales in units (trades)=$9,500

$375

=26 trades (round UP to the nearest whole unit)

The decrease in the average trade revenue increases the breakeven point from 20 to 26 trades. Note: with breakeven analysis always round up the next whole-number.

(25-35 min.) P 7-74B

Req. 1

Hemingway Coffee


SmallLargeTotal

Sale price per unit$2.00$4.00

Deduct:Variable expense per unit 1.00 2.00

Contribution margin per unit$1.00$2.00


Contribution margin per unit$3.00$2.00 $5.00


per unit ($5.00 / 4 units) $1.25

Breakeven sales in total units:

Fixed expenses + Operating income=$30,000 + $0=24,000 units

Weighted-average contribution$1.25

margin per unit

Breakeven sales of small coffees (24,000 )........18,000 units

Breakeven sales of large coffees (24,000 )........6,000 units

Proof:

Hemingway Coffee


Month Ended February 29

Sales revenue [(18,000 $2) + (6,000 $4)]$60,000

Variable expenses [(18,000 $1.00) + (6,000 $2.00)] 30,000

Contribution margin 30,000


Operating income$ 0

Req. 2

Margin of safety=Actual sales Breakeven sales

Margin of safety=$94,000 $60,000*

=$34,000

*Breakeven sales from proof in Req. 1.

Req. 3

Operating leverage factor

= Contribution Margin

Operating income

= $54,000

$24,000

= 2.25

A 15% increase in volume will lead to 33.75% increase in operating income (15% multiplied by the operating leverage factor of 2.25). Therefore, the new operating income will be $32,100 ($24,000 old operating income 1.3375).

(continued) P 7-74B

Proof:

Hemingway Coffee


Increase in sales revenue ($94,000 0.15)$14,100

Increase in variable expenses ($40,000 0.15)6,000


Change in fixed expenses0

Operating income before sales increase 24,000

Operating income after sales increase$32,100

Alternatively,

Proof:

Hemingway Coffee


Sales revenue ($94,000 1.15)$108,100

Variable expenses ($40,000 1.15)46,000

Contribution margin62,100



Discussion & Analysis Questions

Discussion & Analysis Questions A7-75

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. the breakeven point

2. the volume needed to reach target profit

3. how changes in costs, sales price, and volume affect the companys profit and

4. the firms 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?

(continued) A7-75

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 companys profit.

5. Breakeven analysis isnt 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.

Its 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:

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.

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 cant all of the products contribution margin ratios just be added together and averaged?

A company that sells more than one product must calculate each products contribution margin. It then uses the weighted average of all products, which is each units 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 Jewelrys 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?

Alstons 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.

(continued) A7-75

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 customers wait time, and to reduce the total overall costs. How does the use of the robots affect Rondell Pharmacys cost structure? Explain the impact of this switch to robotics on Rondell Pharmacys operating risk.

Using robotics would likely decrease the pharmacys 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 pharmacys 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.

12. How can CVP techniques be used in supporting a companys 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 companys 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 companys 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.

Application and Analysis

Application & Analysis

A7-76 CVP for a Product

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-volume-profit analysis to this potential venture.

Note: This is a sample solution. Student answers will vary.

Basic Discussion Questions

1. Describe your product. What market are you targeting this product for? What price will you sell your product for? Ma

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Documents

unit of sales

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income sales

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