Solution Manual, Managerial Accounting Hansen Mowen 8th Editions_ch 11

CHAPTER 11 COST-VOLUME-PROFIT ANALYSIS: A MANAGERIAL PLANNING TOOL QUESTIONS FOR WRITING AND DISCUSSION 1. CVP analysis allows managers to focus on selling prices, volume, costs, profits, and sales mix. Many different “what if” questions can be asked to assess the effect on profits of changes in key variables.

$30,000/$25 = 1,200 packages, or 2,400 units of A and 1,200 units of B.

2. The units-sold approach defines sales volume in terms of units of product and gives answers in these same terms. The salesrevenue approach defines sales volume in terms of revenues and provides answers in these same terms. 3. Break-even point is the level of sales activity where total revenues equal total costs, or where zero profits are earned. 4. At the break-even point, all fixed costs are covered. Above the break-even point, only variable costs need to be covered. Thus, contribution margin per unit is profit per unit, provided that the unit selling price is greater than the unit variable cost (which it must be for break-even to be achieved). 5. Profit = $7.00 × 5,000 = $35,000

12.

Profit = 0.60($200,000 – $100,000) = $60,000

13.

A change in sales mix will change the contribution margin of the package (defined by the sales mix) and, thus, will change the units needed to break even.

14.

Margin of safety is the sales activity in excess of that needed to break even. The higher the margin of safety, the lower the risk.

15.

Operating leverage is the use of fixed costs to extract higher percentage changes in profits as sales activity changes. It is achieved by increasing fixed costs while lowering variable costs. Therefore, increased leverage implies increased risk, and vice versa.

16.

Sensitivity analysis is a “what if” technique that examines the impact of changes in underlying assumptions on an answer. A company can input data on selling prices, variable costs, fixed costs, and sales mix and set up formulas to calculate break-even points and expected profits. Then, the data can be varied as desired to see what impact changes have on the expected profit.

17.

By specifically including the costs that vary with nonunit drivers, the impact of changes in the nonunit drivers can be examined. In traditional CVP, all nonunit costs are lumped together as “fixed costs.” While the costs are fixed with respect to units, they vary with respect to other drivers. ABC analysis reminds us of the importance of these nonunit drivers and costs.

6. Variable cost ratio = Variable costs/Sales. Contribution margin ratio = Contribution margin/Sales. Contribution margin ratio = 1 – Variable cost ratio. 7. Break-even revenues = $20,000/0.40 = $50,000 8. No. The increase in contribution is $9,000 (0.30 × $30,000), and the increase in advertising is $10,000. 9. Sales mix is the relative proportion sold of each product. For example, a sales mix of 3:2 means that three units of one product are sold for every two of the second product. 10.

Packages of products, based on the expected sales mix, are defined as a single product. Selling price and cost information for this package can then be used to carry out CVP analysis.

11.

Package contribution margin: (2 × $10) + (1 × $5) = $25. Break-even point =

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18.

JIT simplifies the firm’s cost equation since more costs are classified as fixed (e.g., direct labor). Additionally, the batch-level variable is gone (in JIT, the batch is one unit). Thus, the cost equation for JIT includes fixed costs, unit variable cost times the number of units sold, and unit product-level cost times the number of products sold (or related cost

driver). JIT means that CVP analysis approaches the standard analysis with fixed and unit-level costs only.

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EXERCISES 11–1 1.

Direct materials Direct labor Variable overhead Variable selling expenses Variable cost per unit

$3.90 1.40 2.10 1.00 $ 8.40

2.

Price Variable cost per unit Contribution margin per unit

3.

Contribution margin ratio = $5.60/$14 = 0.40 or 40%

4.

Variable cost ratio = $8.40/$14 = 0.60 or 60%

5.

Total fixed cost = $44,000 + $47,280 = $91,280

6.

Breakeven units = (Fixed cost)/Contribution margin = $91,280/$5.60 = 16,300

$14.00 8.40 $5.60

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11–2 1.

Price Less: Direct materials Direct labor Variable overhead Variable selling expenses Contribution margin per unit

$12.00 $1.90 2.85 1.25 2.00

8.00 $4.00

2.

Breakeven units = (Fixed cost)/Contribution margin = (44,000 + $37,900)/$4.00 = 20,475

3.

Units for target

4.

Sales (22,725 × $12) Variable costs (22,725 × $8) Contribution margin Fixed costs Operating income

= (44,000 + $37,900 + $9,000)/$4 = $90,900/$4 = 22,725 $ 272,700 181,800 $ 90,900 81,900 $ 9,000

Sales of 22,725 units does produce operating income of $9,000.

11–3 1.

Units = Fixed cost/Contribution margin = $37,500/($8 – $5) = 12,500

2.

Sales (12,500 × $8) Variable costs (12,500 × $5) Contribution margin Fixed costs Operating income

3.

Units = (Target income + Fixed cost)/Contribution margin = ($37,500 + $9,900)/($8 – $5) = $47,400/$3 = 15,800

$100,000 62,500 $ 37,500 37,500 $ 0

350

11–4 1.

Contribution margin per unit = $8 – $5 = $3 Contribution margin ratio = $3/$8 = 0.375, or 37.5%

2.

Variable cost ratio = $75,000/$120,000 = 0.625, or 62.5%

3.

Revenue = Fixed cost/Contribution margin ratio = $37,500/0.375 = $100,000

4.

Revenue = (Target income + Fixed cost)/Contribution margin ratio = ($37,500 + $9,900)/0.375 = $126,400

11–5 1.

Break-even units = Fixed costs/(Price – Variable cost) = $180,000/($3.20 – $2.40) = $180,000/$0.80 = 225,000

2.

Units = ($180,000 + $12,600)/($3.20 – $2.40) = $192,600/$0.80 = 240,750

3.

Unit variable cost = $2.40 Unit variable manufacturing cost = $2.40 – $0.32 = $2.08 The unit variable cost is used in cost-volume-profit analysis, since it includes all of the variable costs of the firm.

351

11–6 1.

Before-tax income = $25,200/(1 – 0.40) = $42,000 Units = ($180,000 + $42,000)/$0.80 = $222,000/$0.80 = 277,500

2.

Before-tax income = $25,200/(1 – 0.30) = $36,000 Units = ($180,000 + $36,000)/$0.80 = $216,000/$0.80 = 270,000

3.

Before-tax income = $25,200/(1 – 0.50) = $50,400 Units = ($180,000 + $50,400)/$0.80 = $230,400/$0.80 = 288,000

11–7 1.

Contribution margin per unit = $15 – ($3.90 + $1.40 + $2.10 + $1.60) = $6 Contribution margin ratio = $6/$15 = 0.40 or 40%

2.

Breakeven Revenue = Fixed cost/Contribution margin ratio = ($52,000 + $37,950)/0.40 = $224,875

3.

Revenue = (Target income + Fixed cost)/Contribution margin ratio = ($52,000 + $37,950 + $18,000)/0.40 = $269,875

4.

Breakeven units = $224,875/$15 = 14,992 (rounded) Or Breakeven units = $89,950/$6 = 14,992 (rounded)

5.

Units for target income = $269,875/$15 = 17,992 (rounded) Or Units for target income = $107,950/$6 = 17,992 (rounded)

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11–8 1.

Sales mix is 2:1 (Twice as many videos are sold as equipment sets.)

2. Product Videos Equipment sets Total

Price $12 15

Variable – Cost $4 6

=

CM $8 9

×

Sales Mix 2 1

= Total CM $16 9 $25

Break-even packages = $70,000/$25 = 2,800 Break-even videos = 2 × 2,800 = 5,600 Break-even equipment sets = 1 × 2,800 = 2,800 3.

Switzer Company Income Statement For Last Year Sales ........................................................................................... Less: Variable costs ................................................................. Contribution margin.................................................................. Less: Fixed costs ...................................................................... Operating income ................................................................

$ 195,000 70,000 $ 125,000 70,000 $ 55,000

Contribution margin ratio = $125,000/$195,000 = 0.641, or 64.1% Break-even sales revenue = $70,000/0.641 = $109,204

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11–9 1.

Sales mix is 2:1:4 (Twice as many videos will be sold as equipment sets, and four times as many yoga mats will be sold as equipment sets.)

2. Product Videos Equipment sets Yoga mats Total

Price $12 15 18

–

Variable Cost $4 6 13

=

CM $8 9 5

×

Sales Mix 2 1 4

= Total CM $16 9 20 $45

Break-even packages = $118,350/$45 = 2,630 Break-even videos = 2 × 2,630 = 5,260 Break-even equipment sets = 1 × 2,630 = 2,630 Break-even yoga mats = 4 × 2,630 = 10,520 3.

Switzer Company Income Statement For the Coming Year Sales ........................................................................................... Less: Variable costs ................................................................. Contribution margin.................................................................. Less: Fixed costs ...................................................................... Operating income ................................................................

$555,000 330,000 $225,000 118,350 $106,650

Contribution margin ratio = $225,000/$555,000 = 0.4054, or 40.54% Break-even revenue = $118,350/0.4054 = $291,934

11–10 1.

Variable cost per unit = $5.60 + $7.50 + $2.90 + $2.00 = $18 Breakeven units = $75,000/($24 – $18) = 12,500 Breakeven Revenue = $24 × 12,500 = $300,000

2.

Margin of safety in sales dollars = ($24 × 14,000) – $300,000 = $36,000

3.

Margin of safety in units = 14,000 units – 12,500 units = 1,500 units

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11–11 1. $35,000

$30,000

$25,000

$20,000

$15,000

$10,000

$5,000

$0 0

500

1,000

1,500

2,000

2,500

3,000

3,500

Units Sold

Break-even point = 2,500 units; + line is total revenue and x line is total costs.

355

11–11 Continued 2.

a. Fixed costs increase by $5,000:

$40,000 $35,000 $30,000 $25,000 $20,000 $15,000 $10,000 $5,000 $0 0

500

1,000

1,500

2,000

Units Sold

Break-even point = 3,750 units

356

2,500

3,000

3,500

4,000

11–11 Continued b. Unit variable cost increases to $7:

$50,000

$40,000

$30,000

$20,000

$10,000

$0 0

500

1,000

1,500

2,000

2,500

Units Sold

Break-even point = 3,333 units

357

3,000

3,500

4,000

11–11 Continued c. Unit selling price increases to $12:

$50,000

$40,000

$30,000

$20,000

$10,000

$0 0

500

1,000

1,500

2,000

2,500

Units Sold

Break-even point = 1,667 units

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3,000

3,500

4,000

11–11 Continued d.

Both fixed costs and unit variable cost increase:

$70,000 $60,000 $50,000 $40,000 $30,000 $20,000 $10,000 $0 0

1,000

2,000

3,000

4,000

5,000

Units Sold

Break-even point = 5,000 units

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6,000

7,000

8,000

11–11 Continued 3.

Original data:

$10,000

$0 0

500

1,000

1,500

2,000

-$10,000

Break-even point = 2,500 units

360

2,500

3,000

3,500

4,000

11–11 Continued a. Fixed costs increase by $5,000:

$15,000

$0 0

500

1,000

1,500

2,000

-$15,000

Break-even point = 3,750 units

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2,500

3,000

3,500

4,000

11–11 Continued b. Unit variable cost increases to $7:

$10,000

$0 0

500

1,000

1,500

2,000

-$10,000

Break-even point = 3,333 units

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2,500

3,000

3,500

4,000

11–11 Continued c. Unit selling price increases to $12:

$10,000

$0 0

500

1,000

1,500

2,000

-$10,000

Break-even point = 1,667 units

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2,500

3,000

3,500

4,000

11–11 Concluded d. Both fixed costs and unit variable cost increase:

$15,000

$0 0

1,000

2,000

3,000

4,000

5,000

6,000

7,000

-$15,000

Break-even point = 5,000 units 4. The first set of graphs is more informative since these graphs reveal how costs change as sales volume changes.

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11–12 1.

Darius: $100,000/$50,000 = 2 Xerxes: $300,000/$50,000 = 6

2.

Darius X = $50,000/(1 – 0.80) X = $50,000/0.20 X = $250,000

Xerxes X = $250,000/(1 – 0.40) X = $250,000/0.60 X = $416,667

Xerxes must sell more than Darius to break even because it must cover $200,000 more in fixed costs (it is more highly leveraged). 3.

Darius: 2 × 50% = 100% Xerxes: 6 × 50% = 300% The percentage increase in profits for Xerxes is much higher than the increase for Darius because Xerxes has a higher degree of operating leverage (i.e., it has a larger amount of fixed costs in proportion to variable costs as compared to Darius). Once fixed costs are covered, additional revenue must cover only variable costs, and 60 percent of Xerxes revenue above breakeven is profit, whereas only 20 percent of Darius revenue above break-even is profit.

11–13 1.

Breakeven units = $10,350/($15 – $12) = 3,450

2.

Breakeven sales dollars = $10,350/0.20 = $51,750

3.

Margin of safety in units = 5,000 – 3,450 = 1,550

4.

Margin of safety in sales dollars = $75,000 – $51,750 = $23,250

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11–14 1.

Variable cost ratio = Variable costs/Sales = $399,900/$930,000 = 0.43, or 43% Contribution margin ratio = (Sales – Variable costs)/Sales = ($930,000 – $399,900)/$930,000 = 0.57, or 57%

2.

Break-even sales revenue = $307,800/0.57 = $540,000

3.

Margin of safety = Sales – Break-even sales = $930,000 – $540,000 = $390,000

4.

Contribution margin from increased sales = ($7,500)(0.57) = $4,275 Cost of advertising = $5,000 No, the advertising campaign is not a good idea, because the company’s operating income will decrease by $725 ($4,275 – $5,000).

11–15 1.

Income 0 0 $570,000 P

= Revenue – Variable cost – Fixed cost = 1,500P – $300(1,500) – $120,000 = 1,500P – $450,000 – $120,000 = 1,500P = $380

2.

$160,000/($3.50 – Unit variable cost) = 128,000 units Unit variable cost = $2.25

3.

Margin of safety = Actual units – Breakeven units 300 = 35,000 – breakeven units Breakeven units = 34,700 Breakeven units = Total Fixed Cost/(Price – Variable cost per unit) 34,700 = Total Fixed Cost/($40 – $30) Total Fixed Cost = $347,000

366

11–16 1.

Contribution margin per unit = $5.60 – $4.20* = $1.40 *Variable costs per unit: $0.70 + $0.35 + $1.85 + $0.34 + $0.76 + $0.20 = $4.20 Contribution margin ratio = $1.40/$5.60 = 0.25 = 25%

2.

Break-even in units = ($32,300 + $12,500)/$1.40 = 32,000 boxes Break-even in sales = 32,000 × $5.60 = $179,200 or = ($32,300 + $12,500)/0.25 = $179,200

3.

Sales ($5.60 × 35,000) Variable costs ($4.20 × 35,000) Contribution margin Fixed costs Operating income

4.

Margin of safety = $196,000 – $179,200 = $16,800

5.

Break-even in units = 44,800/($6.20 – $4.20) = 22,400 boxes

$ 196,000 147,000 $ 49,000 44,800 $ 4,200

New operating income = $6.20(31,500) – $4.20(31,500) – $44,800 = $195,300 – $132,300 – $44,800 = $18,200 Yes, operating income will increase by $14,000 ($18,200 – $4,200).

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11–17 1.

Variable cost ratio = $126,000/$315,000 = 0.40 Contribution margin ratio = $189,000/$315,000 = 0.60

2.

$46,000 × 0.60 = $27,600

3.

Break-even revenue = $63,000/0.60 = $105,000 Margin of safety = $315,000 – $105,000 = $210,000

4.

Revenue = ($63,000 + $90,000)/0.60 = $255,000

5.

Before-tax income = $56,000/(1 – 0.30) = $80,000

Note: Tax rate = $37,800/$126,000 = 0.30 Revenue = ($63,000 + $80,000)/0.60 = $238,333 Sales ................................................................................ Less: Variable expenses ($238,333 × 0.40) .................. Contribution margin....................................................... Less: Fixed expenses .................................................... Income before income taxes ......................................... Income taxes ($80,000 × 0.30) ....................................... Net income ................................................................

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$ 238,333 95,333 $ 143,000 63,000 $ 80,000 24,000 $ 56,000

11–18 1.

Contribution margin/unit = $410,000/100,000 = $4.10 Contribution margin ratio = $410,000/$650,000 = 0.6308 Break-even units = $295,200/$4.10 = 72,000 units

Break-even revenue = 72,000 × $6.50 = $468,000 or = $295,200/0.6308 = $467,977* *Difference due to rounding error in calculating the contribution margin ratio. 2.

The break-even point decreases: X = $295,200/(P – V) X = $295,200/($7.15 – $2.40) X = $295,200/$4.75 X = 62,147 units Revenue = 62,147 × $7.15 = $444,351

3.

The break-even point increases: X = $295,200/($6.50 – $2.75) X = $295,200/$3.75 X = 78,720 units Revenue = 78,720 × $6.50 = $511,680

4.

Predictions of increases or decreases in the break-even point can be made without computation for price changes or for variable cost changes. If both change, then the unit contribution margin must be known before and after to predict the effect on the break-even point. Simply giving the direction of the change for each individual component is not sufficient. For our example, the unit contribution changes from $4.10 to $4.40, so the break-even point in units will decrease. Break-even units = $295,200/($7.15 – $2.75) = 67,091 Now, let’s look at the break-even point in revenues. We might expect that it, too, will decrease. However, that is not the case in this particular example. Here, the contribution margin ratio decreased from about 63 percent to just over 61.5 percent. As a result, the break-even point in revenues has gone up. Break-even revenue = 67,091 × $7.15 = $479,701

369

11–18 Concluded 5.

The break-even point will increase because more units will need to be sold to cover the additional fixed expenses. Break-even units = $345,200/$4.10 = 84,195 units Revenue = $547,268

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PROBLEMS 11–19 1.

Operating income (0.20)Revenue (0.20)Revenue (0.40)Revenue Revenue

= Revenue(1 – Variable cost ratio) – Fixed cost = Revenue(1 – 0.40) – $24,000 = (0.60)Revenue – $24,000 = $24,000 = $60,000

Sales ................................................................................ Variable expenses ($60,000 × 0.40) .............................. Contribution margin....................................................... Fixed expenses .............................................................. Operating income .....................................................

$ 60,000 24,000 $ 36,000 24,000 $ 12,000

$12,000 = $60,000 × 20% 2.

If revenue of $60,000 produces a profit equal to 20 percent of sales and if the price per unit is $10, then 6,000 units must be sold. Let X equal number of units, then: Operating income 0.20($10)X $2X $4X X 0.25($10)X $2.50X $3.50X X

= (Price – Variable cost) – Fixed cost = ($10 – $4)X – $24,000 = $6X – $24,000 = $24,000 = 6,000 buckets = $6X – $24,000 = $6X – $24,000 = $24,000 = 6,857 buckets

Sales (6,857 × $10) ......................................................... Variable expenses (6,857 × $4) ..................................... Contribution margin....................................................... Fixed expenses .............................................................. Operating income .....................................................

$68,570 27,428 $41,142 24,000 $17,142

$17,142* = 0.25 × $68,570 as claimed *Rounded down.

Note: Some may prefer to round up to 6,858 units. If this is done, the operating income will be slightly different due to rounding.

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11–19 Concluded 3.

Net income = 0.20Revenue/(1 – 0.40) = 0.3333Revenue 0.3333Revenue 0.3333Revenue 0.2667Revenue Revenue

= Revenue(1 – 0.40) – $24,000 = 0.60Revenue – $24,000 = $24,000 = $89,989

11–20 1.

Unit contribution margin = $1,060,000/50,000 = $21.20 Break-even units = $816,412/$21.20 = 38,510 units Operating income = 30,000 × $21.20 = $636,000

2.

CM ratio = $1,060,000/$2,500,000 = 0.424 or 42.4% Break-even point = $816,412/0.424 = $1,925,500 Operating income = ($200,000 × 0.424) + $243,588 = $328,388

3.

Margin of safety = $2,500,000 – $1,925,500 = $574,500

4.

$1,060,000/$243,588 = 4.352 (operating leverage) 4.352 × 20% = 0.8704 0.8704 × $243,588 = $212,019 New operating income level = $212,019 + $243,588 = $455,607

5.

Let X = Units 0.10($50)X = $50.00X – $28.80X – $816,412 $5X = $21.20X – $816,412 $16.20X = $816,412 X = 50,396 units

6.

Before-tax income = $180,000/(1 – 0.40) = $300,000 X = ($816,412 + $300,000)/$21.20 = 52,661 units

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11–21 1.

Unit contribution margin = $825,000/110,000 = $7.50 Break-even point = $495,000/$7.50 = 66,000 units CM ratio = $7.50/$25 = 0.30 Break-even point = $495,000/0.30 = $1,650,000 or = $25 × 66,000 = $1,650,000

2.

Increased CM ($400,000 × 0.30) Less: Increased advertising expense Increased operating income

3.

$315,000 × 0.30 = $94,500

4.

Before-tax income = $360,000/(1 – 0.40) = $600,000 Units = ($495,000 + $600,000)/$7.50 = 146,000

5.

Margin of safety = $2,750,000 – $1,650,000 = $1,100,000 or = 110,000 units – 66,000 units = 44,000 units

6.

$825,000/$330,000 = 2.5 (operating leverage) 20% × 2.5 = 50% (profit increase)

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$ 120,000 40,000 $ 80,000

11–22 1.

Sales mix: Squares: $300,000/$30 = 10,000 units Circles: $2,500,000/$50 = 50,000 units Product Squares Circles Package

P $30 50

–

V* $10 10

=

P–V $20 40

×

Sales Mix 1 5

=

Total CM $ 20 200 $220

*$100,000/10,000 = $10 $500,000/50,000 = $10 Break-even packages = $1,628,000/$220 = 7,400 packages Break-even squares = 7,400 × 1 = 7,400 Break-even circles = 7,400 × 5 = 37,000 2.

Contribution margin ratio = $2,200,000/$2,800,000 = 0.7857 0.10Revenue = 0.7857Revenue – $1,628,000 0.6857Revenue = $1,628,000 Revenue = $2,374,216

3.

New mix: Product Squares Circles Package

P $30 50

–

V $10 10

=

P–V $20 40

×

Sales Mix 3 5

Break-even packages = $1,628,000/$260 = 6,262 packages Break-even squares = 6,262 × 3 = 18,786 Break-even circles = 6,262 × 5 = 31,310 CM ratio = $260/$340* = 0.7647 *(3)($30) + (5)($50) = $340 revenue per package 0.10Revenue = 0.7647Revenue – $1,628,000 0.6647Revenue = $1,628,000 Revenue = $2,449,225

374

=

Total CM $ 60 200 $260

11–22 Concluded 4.

Increase in CM for squares (15,000 × $20) Decrease in CM for circles (5,000 × $40) Net increase in total contribution margin Less: Additional fixed expenses Increase in operating income

$ 300,000 (200,000) $ 100,000 45,000 $ 55,000

Gosnell would gain $55,000 by increasing advertising for the squares. This is a good strategy. 11–23 1. Product Scientific Business Total

Price* – $25 20

Variable Cost = $12 9

*$500,000/20,000 = $25 $2,000,000/100,000 = $20 X = ($1,080,000 + $145,000)/$68 X = $1,225,000/$68 X = 18,015 packages 18,015 scientific calculators (1 × 18,015) 90,075 business calculators (5 × 18,015) 2.

Revenue = $1,225,000/0.544* = $2,251,838 *($1,360,000/$2,500,000) = 0.544

375

CM $13 11

×

Units in Mix 1 5

=

Package CM $13 55 $68

11–24 1.

Currently: Sales (830,000 × $0.36) Variable expenses Contribution margin Fixed expenses Operating income

$ 298,800 224,100 $ 74,700 54,000 $ 20,700

New contribution margin = 1.5 × $74,700 = $112,050 $112,050 – promotional spending – $54,000 = 1.5 × $20,700 Promotional spending = $27,000 2.

Here are two ways to calculate the answer to this question: a. The per-unit contribution margin needs to be the same: Let P* represent the new price and V* the new variable cost. (P – V) = (P* – V*) $0.36 – $0.27 = P* – $0.30 $0.09 = P* – $0.30 P* = $0.39 b. Old break-even point = $54,000/($0.36 – $0.27) = 600,000 New break-even point = $54,000/(P* – $0.30) = 600,000 P* = $0.39 The selling price should be increased by $0.03.

3.

Projected contribution margin (700,000 × $0.13) Present contribution margin Increase in operating income

$91,000 74,700 $16,300

The decision was good because operating income increased by $16,300. (New quantity × $0.13) – $54,000 = $20,700 New quantity = 574,615 Selling 574,615 units at the new price will maintain profit at $20,700.

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11–25 1.

Contribution margin ratio = $487,548/$840,600 = 0.58

2.

Revenue = $250,000/0.58 = $431,034

3.

Operating income 0.08R/(1 – 0.34) 0.1212R 0.4588R R

4.

$840,600 × 110% = $353,052 × 110% =

= CMR × Revenue – Total fixed cost = 0.58R – $250,000 = 0.58R – $250,000 = $250,000 = $544,900 $924,660 388,357 $536,303

CMR = $536,303/$924,660 = 0.58 The contribution margin ratio remains at 0.58. 5.

Additional variable expense = $840,600 × 0.03 = $25,218 New contribution margin = $487,548 – $25,218 = $462,330 New CM ratio = $462,330/$840,600 = 0.55 Break-even point = $250,000/0.55 = $454,545 The effect is to increase the break-even point.

6.

Present contribution margin Projected contribution margin ($920,600 × 0.55) Increase in contribution margin/profit

$ 487,548 506,330 $ 18,782

Fitzgibbons should pay the commission because profit would increase by $18,782.

377

11–26 1.

One package, X, contains three Grade I and seven Grade II cabinets. 0.3X($3,400) + 0.7X($1,600) = $1,600,000 X = 748 packages Grade I: 0.3 × 748 = 224 units Grade II: 0.7 × 748 = 524 units

2.

Product Grade I Grade II Package

P $3,400 1,600

–

Direct fixed costs—Grade I Direct fixed costs—Grade II Common fixed costs Total fixed costs

V $2,686 1,328

=

P–V $714 272

×

Mix 3 7

=

Total CM $2,142 1,904 $4,046

P–V $956 392

×

Mix 3 7

=

Total CM $2,868 2,744 $5,612

$ 95,000 95,000 35,000 $ 225,000

$225,000/$4,046 = 56 packages Grade I: 3 × 56 = 168; Grade II: 7 × 56 = 392 3.

Product Grade I Grade II Package Package CM Package CM $21,400X X

P $3,400 1,600

–

V $2,444 1,208

=

= 3($3,400) + 7($1,600) = $21,400 = $1,600,000 – $600,000 = 47 packages remaining

141 Grade I (3 × 47) and 329 Grade II (7 × 47) Additional contribution margin: 141($956 – $714) + 329($392 – $272) Increase in fixed costs Increase in operating income

$73,602 44,000 $29,602

Break-even: ($225,000 + $44,000)/$5,612 = 48 packages 144 Grade I (3 × 48) and 336 Grade II (7 × 48)

378

11–26 Concluded The new break-even point is a revised break-even for 2004. Total fixed costs must be reduced by the contribution margin already earned (through the first five months) to obtain the units that must be sold for the last seven months. These units are then be added to those sold during the first five months: CM earned = $600,000 – (83* × $2,686) – (195* × $1,328) = $118,102 *224 – 141 = 83; 524 – 329 = 195 X = ($225,000 + $44,000 – $118,102)/$5,612 = 27 packages In the first five months, 28 packages were sold (83/3 or 195/7). Thus, the revised break-even point is 55 packages (27 + 28)—in units, 165 of Grade I and 385 of Grade II. 4.

Product Grade I Grade II Package

P $3,400 1,600

New sales revenue

–

V $2,686 1,328

=

P–V $714 272

×

Mix 1 1

=

Total CM $714 272 $986

$1,000,000 × 130% = $1,300,000

Package CM = $3,400 + $1,600 $5,000X = $1,300,000 X = 260 packages Thus, 260 units of each cabinet will be sold during the rest of the year. Effect on profits: Change in contribution margin [$714(260 – 141) – $272(329 – 260)] Increase in fixed costs [$70,000(7/12)] Increase in operating income

$66,198 40,833 $25,365

X = F/(P – V) = $295,000/$986 = 299 packages (or 299 of each cabinet) The break-even point for 2006 is computed as follows: X = ($295,000 – $118,102)/$986 = $176,898/$986 = 179 packages (179 of each) To this, add the units already sold, yielding the revised break-even point: Grade I: 83 + 179 = 262 Grade II: 195 + 179 = 374

379

11–27 1.

R = F/(1 – VR) = $150,000/(1/3) = $450,000

2.

Of total sales revenue, 60 percent is produced by floor lamps and 40 percent by desk lamps. $360,000/$30 = 12,000 units $240,000/$20 = 12,000 units Thus, the sales mix is 1:1. Product Floor lamps Desk lamps Package

P $30.00 20.00

–

V* $20.00 13.33

=

P–V $10.00 6.67

×

Mix 1 1

=

Total CM $10.00 6.67 $16.67

X = F/(P – V) = $150,000/$16.67 = 8,999 packages Floor lamps: 1 × 8,999 = 8,999 Desk lamps: 1 × 8,999 = 8,999 Note: packages have been rounded up to ensure attainment of breakeven. 3.

Operating leverage

= CM/Operating income = $200,000/$50,000 = 4.0

Percentage change in profits = 4.0 × 40% = 160%

380

11–28 1.

Break-even units = $300,000/$14* = 21,429 *$406,000/29,000 = $14 Break-even in dollars = 21,429 × $42** = $900,018 or = $300,000/(1/3) = $900,000 The difference is due to rounding error. **$1,218,000/29,000 = $42

2.

Margin of safety = $1,218,000 – $900,000 = $318,000

3.

Sales Variable costs (0.45 × $1,218,000) Contribution margin Fixed costs Operating income

$ 1,218,000 548,100 $ 669,900 550,000 $ 119,900

Break-even in units = $550,000/$23.10* = 23,810 Break-even in sales dollars = $550,000/0.55** = $1,000,000 *$669,900/29,000 = $23.10 **$669,900/$1,218,000 = 55%

381

11–29 1.

The annual break-even point in units at the Peoria plant is 73,500 units and at the Moline plant, 47,200 units, calculated as follows: Unit contribution calculation: Selling price Less variable costs: Manufacturing Commission G&A Unit contribution

Peoria $150.00

Moline $150.00

(72.00) (7.50) (6.50) $ 64.00

(88.00) (7.50) (6.50) $ 48.00

Fixed costs calculation: Total fixed costs = (Fixed manufacturing cost + Fixed G&A) × Production rate per day × Normal working days Peoria = [$30.00 + ($25.50 – $6.50)] × 400 × 240 = $4,704,000 Moline = [$15.00 + ($21.00 – $6.50)] × 320 × 240 = $2,265,600 Break-even calculation: Break-even units = Fixed costs/Unit contribution Peoria = $4,704,000/$64 = 73,500 units Moline = $2,265,600/$48 = 47,200 units 2.

The operating income that would result from the divisional production manager’s plan to produce 96,000 units at each plant is $3,628,800. The normal capacity at the Peoria plant is 96,000 units (400 × 240); however, the normal capacity at the Moline plant is 76,800 units (320 × 240). Therefore, 19,200 units (96,000 – 76,800) will be manufactured at Moline at a reduced contribution margin of $40 per unit ($48 – $8). Contribution per plant: Peoria (96,000 × $64) Moline (76,800 × $48) Moline (19,200 × $40) Total contribution Less: Fixed costs Operating income

$ 6,144,000 3,686,400 768,000 $ 10,598,400 6,969,600 $ 3,628,800

382

11–29 Concluded 3.

If this plan is followed, 120,000 units will be produced at the Peoria plant and 72,000 units at the Moline plant. Contribution per plant: Peoria (96,000 × $64) Peoria (24,000 × $61) Moline (72,000 × $48) Total contribution Less: Fixed costs Operating income

$ 6,144,000 1,464,000 3,456,000 $ 11,064,000 6,969,600 $ 4,094,400

383

11–30 1.

Break-even dollars (in thousands) X = Variable cost of goods sold + Current fixed costs + Fixed cost of hiring + Commissions X = 0.45aX + $6,120b + $1,890c + 0.1X + 0.05(X – $16,000) = 0.60X + $6,120 + $1,890 – $800 = $18,025 a

$11,700/$26,000 = 45% Current fixed costs (in thousands): Fixed cost of goods sold Fixed advertising expenses Fixed administrative expenses Fixed interest expenses Total c Fixed cost of hiring (in thousands): Salespeople (8 × $80) Travel and entertainment Manager/secretary Additional advertising Total b

$2,870 750 1,850 650 $6,120 $ 640 600 150 500 $1,890

2.

Break-even formula set equal to net income (in thousands): 0.6(Sales – Var. COGS – Fixed costs – Commissions) = Net income 0.6(X – 0.45X – $6,120 – 0.23X) = $2,100 0.192X – $3,672 = $2,100 0.192X = $5,772 X = $30,063

3.

The general assumptions underlying break-even analysis that limit its usefulness include the following: all costs can be divided into fixed and variable elements; variable costs vary proportionally to volume; and selling prices remain unchanged.

384

MANAGERIAL DECISION CASES 11–31 1. Break-even point = F/(P – V) First process: $100,000/($30 – $10) = 5,000 cases Second process: $200,000/($30 – $6) = 8,333 cases 2.

I X($30 – $10) – $100,000 $20X – $100,000 $100,000 X

= X(P – V) – F = X($30 – $6) – $200,000 = $24X – $200,000 = $4X = 25,000

The manual process is more profitable if sales are less than 25,000 cases; the automated process is more profitable at a level greater than 25,000 cases. It is important for the manager to have a sales forecast to help in deciding which process should be chosen. 3.

The divisional manager has the right to decide which process is better. Danna is morally obligated to report the correct information to her superior. By altering the sales forecast, she unfairly and unethically influenced the decisionmaking process. Managers do have a moral obligation to assess the impact of their decisions on employees, and to be fair and honest with employees. However, Danna’s behavior is not justified by the fact that it helped a number of employees retain their employment. First, she had no right to make the decision. She does have the right to voice her concerns about the impact of automation on employee well-being. In so doing, perhaps the divisional manager would come to the same conclusion even though the automated system appears to be more profitable. Second, the choice to select the manual system may not be the best for the employees anyway. The divisional manager may have more information, making the selection of the automated system the best alternative for all concerned, provided the sales volume justifies its selection. For example, the divisional manager may have plans to retrain and relocate the displaced workers in better jobs within the company. Third, her motivation for altering the forecast seems more driven by her friendship for Jerry Johnson than any legitimate concerns for the layoff of other employees. Danna should examine her reasoning carefully to assess the real reasons for her behavior. Perhaps in so doing, the conflict of interest that underlies her decision will become apparent.

385

11–31 Concluded 4. Some standards that seem applicable are III-1 (conflict of interest), III-2 (refrain from engaging in any conduct that would prejudice carrying out duties ethically), and IV-1 (communicate information fairly and objectively).

11–32 1.

Number of seats sold (expected): Seats sold = Number of performances × Capacity × Percent sold

Dream Petrushka Nutcracker Sleeping Beauty Bugaku

Type of Seat B 3,024 3,024 15,120 6,048 3,024 30,240

A 570 570 2,280 1,140 570 5,130

C 3,690 3,690 19,680 7,380 3,690 38,130

Total revenues = ($35 × 5,130) + ($25 × 30,240) + ($15 × 38,130) = $179,550 + $756,000 + $571,950 = $1,507,500 Segmented revenues (Seat price × Total seats):

Dream Petrushka Nutcracker Sleeping Beauty Bugaku

A $19,950 19,950 79,800 39,900 19,950

B $ 75,600 75,600 378,000 151,200 75,600

386

C $ 55,350 55,350 295,200 110,700 55,350

Total $150,900 150,900 753,000 301,800 150,900

11–32 Continued Segmented variable-costing income statement: Sales Variable costs Contribution margin Direct fixed costs Segment margin Sales Variable costs Contribution margin Direct fixed costs Segment margin Common fixed costs Operating (loss) 2.

Dream $ 150,900 42,500 $ 108,400 275,500 $(167,100)

Petrushka $150,900 42,500 $108,400 145,500 $ (37,100)

Nutcracker $753,000 170,000 $583,000 70,500 $512,500

Sleeping Beauty $ 301,800 85,000 $ 216,800 345,000 $(128,200)

Bugaku $ 150,900 42,500 $ 108,400 155,500 $ (47,100)

Total $ 1,507,500 382,500 $ 1,125,000 992,000 $ 133,000 401,000 $ (268,000)

Contribution margin per ballet performance:

Dream Petrushka Nutcracker Sleeping Beauty Bugaku

$108,400/5 = $21,680 $108,400/5 = $21,680 $583,000/20 = $29,150 $216,800/10 = $21,680 $108,400/5 = $21,680

Segment break-even point: X = F/(P – V)

Dream Petrushka Nutcracker Sleeping Beauty Bugaku

$275,500/$21,680 = $145,500/$21,680 = $70,500/$29,150 = $345,000/$21,680 = $155,500/$21,680 =

387

13 7 3 16 8

11–32 Continued 3.

Weighted contribution margin (package): Mix: 1:1:4:2:1 $21,680 + $21,680 + 4($29,150) + 2($21,680) + $21,680 = $225,000 X = F/(P – V) X = ($992,000 + $401,000)/$225,000 = 6.19 or 7 (rounded up) 7 Dream, Petrushka, and Bugaku; 14 Sleeping Beauty; 28 Nutcracker Provided the community will support the number of performances indicated in the break-even solution, I would alter the schedule to reflect the break-even mix.

4.

Additional revenue per performance: 114 × $30 × 80% = $ 2,736 756 × $20 × 80% = 12,096 984 × $10 × 80% = 7,872 $ 22,704 Increase in revenues ($22,704 × 5) Less: Variable costs ($8,300 × 5) Increase in contribution margin

$113,520 41,500 $ 72,020

New mix 1:1:4:2:1:1 Contribution margin per matinee: $72,020/5 = $14,404 Adding the matinees will increase profits by $72,020. New break-even point: X = F/(P – V) = ($992,000 + $401,000)/($225,000 + $14,404) = $1,393,000/$239,404 = 5.82 packages, or 6 (rounded up) 6 Dream, Petrushka, Bugaku, and Nutcracker matinees 12 Sleeping Beauty 24 Nutcracker

388

11–32 Concluded 5.

Current total segment margin Add: Additional contribution margin Add: Grant Projected segment margin Less: Common fixed costs Operating (loss)

$ 133,000 72,020 60,000 $ 265,020 401,000 $ (135,980)

No, the company will not break even. This is a very thorny problem faced by ballet companies around the world. The standard response is to offer as many performances of The Nutcracker as possible. That action has already been taken here. Other actions that may help include possible increases in prices of the seats (particularly the A seats), offering additional performances of some of the other ballets, cutting administrative costs (they seem somewhat high), and offering a less expensive ballet (direct costs of Sleeping Beauty are quite high).

RESEARCH ASSIGNMENT 11–33 Answers will vary.

389

390