mba 504 ch4 solutions

Chapter 4Cost-Volume-Profit Analysis

QUESTIONS

1. Variable costs are costs that change in response to changes in activity (e.g., production or

sales activity). Fixed costs are costs that do not change in response to changes in activity.

2. A mixed cost is a cost that has a fixed cost component and a variable cost component. Forexample, the amount paid for telecommunication services would be a mixed cost if therewas a fixed monthly fee plus a charge for use.

3. Discretionary fixed costs are those fixed costs that management can easily change in theshort-run (e.g., advertising). Committed fixed costs are those fixed costs that cannot beeasily changed in the short-run (e.g., rent).

4. Commissions paid to salespersons and direct materials are examples of variable costs.

5. Rent and insurance expenses are examples of fixed costs.

6. Salespersons are paid a base salary plus commissions. The base amount is fixed andcommissions are variable. Thus, total compensation paid to the sales force is mixed.

7. With telecom, there is likely to be a basic service charge (fixed) plus a charge for use(which will be variable if use increases with business activity).

8. The horizontal axis would be production.

9. With account analysis, managers use judgment to classify costs as either fixed or variable.The total of the costs classified as variable can then be divided by a measure of activity tocalculate the variable cost per unit of activity. The total of the costs classified as fixedprovides the estimate of fixed cost.

10. With the high-low method, you use the highest and lowest levels of activity.

11. The relevant range is the range of activity for which estimates of costs are likely to beaccurate.

Jiambalvo Managerial Accounting4-2

12. The contribution margin is equal to the selling price minus variable cost. The contributionmargin ratio is the contribution margin per dollar of sales.

13. The profit equation states that profit is equal to revenue (selling price times quantity) minusvariable cost (variable cost per unit times quantity) minus total fixed cost.

Profit = SP (x) - VC (x) - TFC

14. It would not be appropriate to focus on weighted average contribution margin per unit if theunits were dissimilar (e.g., pencils and computers at an office supply warehouse).

15. The assumptions in C-V-P- analysis are:1. Costs can be separated into fixed and variable components.2. Fixed costs remain fixed and variable costs per unit do not change.3. When performing multiproduct C-V-P, an important assumption is that the mix

remains constant.

16. Companies that have relatively higher fixed costs are said to have higher operatingleverage. Thus, a software company with a large investment in research and development(a fixed cost) would likely have higher operating leverage compared to a manufacturingcompany that used little equipment but expensive labor (a variable cost).

17. When there is a constraint, focus on the contribution margin per unit of the constraint.

Chapter 4 Cost-Volume-Profit Analysis 4-3

EXERCISES

E1. With high fixed costs, a business is quite risky. This follows because if salesfail to meet expectations, the company may have a large loss.

Paul may be able to make rent a variable expense—pay the mall owner apercent of total revenue rather than a fixed monthly amount. This type of

arrangement is quite common in shopping malls. He may also be able to payemployees relatively low base salaries with bonuses tied to sales. This would

make salary expense more of a variable expense.

E2. The cost structure at Microsoft is heavily weighted toward fixed cost (e.g.,

research and development). Consider the variable cost associated with sellingan additional unit of the product “Office” through the OEM (original

equipment manufacturer) channel. The product sells for well over $100 but

the incremental cost (ignoring tax) is probably less than $1. With highoperating leverage, it’s not surprising that profit grew faster than sales.

E3. At the Men’s Warehouse, the gross margin is equal to net sales less cost of

goods sold, including buying and occupancy costs. Since store occupancy cost

is primarily a fixed cost, dividing the gross margin by sales is not likely toprovide a good estimate of the contribution margin ratio.

At Best Buy, the gross profit is equal to revenues less cost of goods sold.

Since cost of goods sold is the company’s primary variable cost, dividing

gross profit by revenues may yield a relatively good estimate of the firm’sweighted average contribution margin ratio.


E4. Depreciation appears to be a fixed cost.

Direct labor appears to be a variable cost.


Telecommunications appears to be a mixed cost. Note that the intercept is$10,000.

E5. ($20,000 - $8,000) ÷ (8,000 - 2,000) = $2 per machine hour of variable repair cost

$8,000 - ($2 x 2,000) = $4,000 per month of fixed repair cost.

E6. a. The highest level of activity is sales of $28,000 with cost of $23,800. The

lowest level of activity is sales of $19,000 with cost of $18,400.

($23,800 - $18,400) ÷ ($28,000 - $19,000) = $.60 of variable cost per dollar ofsales.

$23,800 – ($.60 x $28,000) = $7,000 per month of fixed cost.

Thus, Cost = $7,000 + ($.60 x Sales).

b. For $1 of sales, there will be $.60 of variable cost and $.40 (i.e., $1 - $.60)of contribution margin. That is, the contribution margin for a dollar of

sales (known as the contribution margin ratio) is $1 - $.60.

c. For a sales increase of $50,000, profit will increase by $20,000 (i.e.,$50,000 - ($.60 x $50,000) = $20,000).


d. The regression indicates that variable cost per dollar of sales is $.52289and fixed costs are $8,950 per month. However, care must be exercisedsince, as indicated in the graph of costs and sales, costs in April ($23,400)appear to be extreme given that sales were only $21,000.

Using the regression, for a sales increase of $50,000, profit will increase by$23,855.50 (i.e., $50,000 - ($.52289 × $50,000) = $23,855.50).

Note—This output was generated using the regression function in Excel (in Excel, goto tools, then data analysis, and then regression).

SUMMARY OUTPUT

Regression Statistics

Multiple R 0.75838256

R Square 0.5751441

Adjusted R Square 0.53265851

Standard Error 1382.7356

Observations 12

ANOVA

df SS MS F

Regression 1 25882922.54 25882922.5 13.5373925

Residual 10 19119577.46 1911957.75

Total 11 45002500

Coefficients Standard Error t Stat P-value

Intercept 8950 3386.996675 2.64245904 0.0246298

Sales 0.52288732 0.142115224 3.67931958 0.00425115


E7. a.

b. The relation appears to be approximately linear (note that R – Square is

.89). There are no obvious outliers.

E8. a. Arguably, the only variable costs in human resources are staff salaries andoffice supplies (and a case could be made that even staff salaries are fixed).

In this case, variable costs are $504 per hire [($25,000 + $200) ÷ 50 hires].

Fixed costs are $8,800.

b. The estimated cost for June with 60 new hires is:

$8,800 + ($504 × 60) = $39,040.

c. The incremental cost associated with 10 more employees is $5,040 (i.e.,$504 × 10).


E9. a. Arguably, the only variable costs are cleaning supplies ($800) andemployee wages ($15,800). In this case, variable costs per dollar of sales

are:

Cleaning supplies $ 800Employee wages 15,800

Total variable costs 16,600Divided by sales 28,000

Variable cost per dollar of sales $ .5929

Fixed costs per month are:

Rent $ 800

Utilities 600

Depreciation 200Owner’s salary 5,600

Fixed costs per month $7,200

b. The contribution margin ratio = $1 - .5929 = .4071. In other words, if the

company has approximately 59 cents of variable costs for every dollar of

sales, then it must have approximately 41 cents of contribution margin perdollar of sales.


E10. a. Variable costs are:

Material $ 30,000

Direct labor 20,000

Other utilities (80% variable) 2,240Supervisory salaries (20% variable) 2,200

Equipment repair (90% variable) 4,500Indirect materials 400

Factory maintenance (10% variable) 560

Total variable costs $59,900Divided by units produced 1,000

Variable cost per unit $ 59.90

Fixed costs per month are:

Depreciation $10,000

Phone 200 Other utilities (20% fixed) 560

Supervisory salaries (80% fixed) 8,800

Equipment repair (10% fixed) 500Factory maintenance (90% fixed) 5,040

Total fixed costs per month $25,100

b. The incremental costs of producing 100 units is $5,990 (i.e., $59.90variable cost per unit × 100 units).


E11. a. The break-even point equals fixed cost divided by the contribution marginper unit. Thus, the break-even point is 100 pairs of speakers [i.e., $50,000

÷ ($800 - $300) = 100 pairs of speakers].

b. The company must sell 140 pairs to earn a profit of $20,000.

($50,000 + $20,000) ÷ ($800 - $300) = 140 pairs of speakers

E12. a. Given that variable cost per dollar of sales is $.80, the contribution margin

per dollar of sales (i.e., the contribution margin ratio) is $.20. The break-even point equals fixed cost divided by the contribution margin ratio. Thus,

the break-even point is $1,000,000 [i.e., $200,000 ÷ $.20 = $1,000,000].

b. ($200,000 + $60,000) ÷ $.20 = $1,300,000

c. The expected level of profit is:

($1,400,000 × $.20) - $200,000 = $80,000.

E13. a. The contribution margin is $500 (i.e., $800 - $300).

b. The effect on profit of selling 5 more pairs of speakers is $2,500 (i.e., $500

× 5).

E14. a. The contribution margin ratio is 0.625.

Contribution margin ratio = contribution margin ÷ sales

= $500 ÷ $800 = 0.625.

b. The effect on profit of additional sales of $5,000 is $3,125 (i.e., $5,000 ×0.625).


E15. a. Expected profit is $800 (120) - $300 (120) - $50,000 = $10,000.

b. Breakeven sales are $50,000 ÷ $0.625 = $80,000.

Expected sales are $120 × $800 = $96,000.

The margin of safety is equal to expected sales - break-even sales =$96,000 -$80,000 = $16,000.

E16. Expected profit is $1,000 (120) - $300 (120) - $50,000 = $34,000.

E17. a. The weighted average contribution margin per unit is $178,000 ÷ 5,000 =$35.60.

b. The break-even point is $103,000 ÷ $35.60 = 2,893 units.

c. The number of Smashers would be (1,000 ÷ 5,000) × 2,893 = 579.

The number of Bashers would be (2,000 ÷ 5,000) × 2,893 = 1,157.

The number of Dinkers would be (2,000 ÷ 5,000) × 2,893 = 1,157.

E18. a. The weighted average contribution margin ratio is $178,000 ÷ $300,000 =0.59333

b. ($103,000 + $100,000) ÷ 0.59333 = $342,137.

c. The sales of Smashers would be ($100,0000 ÷ $300,000) × $342,137 =$114,046.

The sales of Bashers would be ($120,0000 ÷ $300,000) × $342,137=$136,855.

The sales of Dinkers would be ($80,0000 ÷ $300,000) × $342,137 =$91,236.


E19. a. The weighted average contribution margin ratio is $679,000 ÷ $2,015,000= 0.336973.

b. ($237,000 + $500,000) ÷ .336973 = 2,187,121.

c. The contribution margin ratios of the three departments are:

Department A .60

Department B .40

Department C .20

All else equal, Department A should be emphasized in the weekly

advertisement because this department earns $.60 on each incrementaldollar of sales (more than either of the other departments).

E20. a. Currently, profit as a percent of sales is $442,000 ÷ $2,015,000 = .21935.

b. The contribution margin ratio is $679,000 ÷ $2,015,000 = 0.336973.

Thus, if sales increase by 20% ($2,015,000 × .2 = $403,000), profit will

increase by:

Increase in sales $403,000

Times contribution margin ratio .336973

Increase in profit $135,800

The new sales level will be ($2,015,000 + $403,000 ) = $2,418,000.

The new profit level will be ($442,000 + $135,800 ) = $577,800.

Thus, profit as a percent of sales will be .23896 (i.e., $577,800 ÷ $2,418,000).

When sales increase, variable costs increase, but fixed costs do not increase.

Thus, when sales increase, profit as a percent of sales will also increase.


E21.a. Product A Product BSelling price $80 $70

Variable costs 20 40Contribution margin 60 30

÷ Hours to produce 1 item 5 2

Contribution margin per hour $12 $15

The company should produce just Product B. With 320 hours available, this

product will generate $4,800 of contribution margin ($15 × 320 hours) while

Product A will generate just $3,840 ($12 × 320).

b. If the company obtains additional labor, it should produce more Product B.

The incremental benefit of 10 labor hours is $150 ($15 contribution marginper hour x 10 hours).

As an aside, note that if production of Product A requires 5 labor hours and

variable costs are only $20 per unit, workers at Howard Products must bepaid less than $4 per hour because part of the variable costs are material

costs! Perhaps production is taking place in a third-world country!


PROBLEMS

P1. a. Depreciation—fixedb. Salaries of restaurant staff—mixed (a minimum number is required in slow

months plus additional people are required from November through

February)c. Salaries of administrative staff—fixed

d. Soap, and other toiletries (variable)e. Laundry—mixed (part is variable and part is fixed, e.g., depreciation on

laundry equipment)

f. Food and beverage—variableg. Grounds maintenance—fixed


P2. a. Variable costsComponent costs $68,000

Supplies 1,540Assembly labor 22,800

Shipping 1,400

Total $93,740

Variable cost per disc play

($93,740 ÷ 140) $669.57

Fixed costsRent $2,000

Supervisor salary 5,000Electricity 200

Telephone 220

Gas 100Advertising 2,000

Administrative costs 12,500

Total $22,020

b. Expected cost in August = $122,455.50.

$669.57 (150) + $22,020 = $122,455.50

c. Contribution margin = Selling price less variable cost = $1,200 - $669.57 =$530.43.

d. Estimated profit at 150 units = $57,544.50.

$1,200 (150) - $669.57 (150) - $22,020 = $57,544.50.

e. The special order will increase profit by $13,043.

($800 - 669.57) × 100 = $13,043.


P3. a. Production CostHigh 165 $134,700

Low 125 107,670 40 $ 27,030

Variable cost per unit = $27,030 ÷ 40 = $675.75.

Total cost at 165 units $134,700Less variable costs

(165 × $675.75) 111,499

Fixed cost $ 23,201

b. Break-even sales in units = 44.

$23,201 ÷ ($1,200 - $675.75) = approximately 44 units.

c. Margin of safety = 150 - 44 = 106 units.

d. Total profit = $55,436.50.

$1,200 (150) - $675.75 (150) - $23,201 = $55,436.50.

e. A major limitation of the high-low method is that it estimates variable andfixed costs using extreme values. Also, the approach uses only two

observations. A better approach would be to use regression analysis.


P4. a. Note—This output was generated using the regression function in Excel (inExcel, go to tools, then data analysis, and then regression).

Regression Statistics

Multiple R 0.958354089R Square 0.918442559

Adjusted R. Square 0.910286815

Standard Error 2326.339027

Observations 12

ANOVA

df SS MS F

Regression 1 609444867.3 609444867.3 112.6129696

Residual 10 54118532.67 5411853.267

Total 11 663563400

Coefficients Standard Error t Stat P-value

Intercept 25699.20792 8688.960364 2.957685021 0.014344813

Production 643.2475248 60.6155316 10.61192582 9.19871E-07

Based on the regression, fixed costs are $25,699.21 and variable costs are

$643.25 per unit.

b. Comparison of estimates:

Variable cost Fixed costAccount analysis $669.57 $21,220.00High-low $675.75 $23,201.00

Regression $643.25 $25,699.21

The regression approach arguably provides the best estimates because it usesmore data and is less subjective. However, in this case, all three of the

estimates are reasonably close.


P5. a. Number of trips(6 per week x 52 weeks) 312

Total revenue $312,000

Revenue per trip($312,000 ÷ 312) $1,000

Variable costs:

Fuel $ 99,840

Maintenance 124,800$224,640

Variable costs per trip($224,640 ÷ 312) $720

Contribution margin per trip($1,000 - $720) $280

Fixed costs:Salary $ 34,000

Depreciation of plane 20,000Depreciation of office equipment 600

Rent 24,000

Insurance 5,000Miscellaneous 2,000

$ 85,600

Breakeven number of trips is 306 ($85,600 ÷ $280 = 305.71).

b. If David draws a salary of $80,000, fixed costs will increase by $46,000 to$131,600. In this case, the breakeven number of trips is 470 ($131,600 ÷$280). Note that this number of trips is not feasible if David can only flyone round trip per day.


c. The average before tax profit per round trip is $1,760 ÷ 312 = $5.64.

d. The incremental profit associated with adding a round trip is thecontribution margin per trip, which is $280.

P6 a. Account Analysis

Fixed cost per month (April data)

Day manager salary $ 4,000Night manager salary 3,500

Depreciation 10,000

$17,500

Variable costs per room (April data):Cleaning staff $15,000

Continental breakfast 4,500

19,500Number of rooms 1,500

Variable costs per room $ 13

b. High-Low Method($38,600 – $37,000) ÷ 300 rooms = $5.33 per occupied room of variablecost.

$37,000 – $5.33 x (1,500 rooms) = $29,005 of fixed costs per month.

c. $85.00 – $5.33 = $79.67 contribution margin per occupied room.

P7. a Income will only be proportional to sales if all costs are variable. Thatassumption is wrong (for example, the registration fee and the pay to JaneKramer are fixed).


b. Sales $18,624.00Less cost of sales (60% of sales in prior year) 11,174.40

Gross margin 7,449.60Less other expenses:

Registration fee 1,000.00

Booth rental (5% of sales) 931.20 Salary of Jane Kramer 300.00

Before tax profit $ 5,218.40

P8.

Sales $1,000,000.00 $1,100,000.00 $1,200,000.00 $1,300,000.00 $1,400,000.00

Less cost of components 700,000.00 770,000.00 840,000.00 908,000.16 964,000.16

Gross margin 300,000.00 330,000.00 360,000.00 391,999.84 435,999.84

Less:

Staff salaries 180,000.00 180,000.00 180,000.00 180,000.00 180,000.00

Rent 24,000.00 24,000.00 24,000.00 24,000.00 24,000.00

Utilities 3,600.00 3,600.00 3,600.00 3,600.00 3,600.00

Advertising 2,000.00 2,000.00 2,000.00 2,000.00 2,000.00

Operating profit before

bonuses 90,400.00 120,400.00 150,400.00 182,399.84 226,399.84

Staff bonuses 36,160.00 48,160.00 60,160.00 72,959.94 90,559.94

Profit before taxes

and owner “draw” $ 54,240.00 $ 72,240.00 $ 90,240.00 $ 109,439.90 $ 135,839.90

In the prior year, cost of components was 70% of sales. In the coming year,prices will be reduced by 20% on all purchases over $900,000. Purchasesof $900,000 corresponds to sales of $1,285,714. ($900,000 ÷ .7). Thus, thecalculation of cost of components when sales are $1,300,000 is:

$900,000 + [($1,300,000 – $1,285,714) x .7 x .8] = $908,000.16.


P9. a. Production costs:($95,000 - $78,500) ÷ (150 – 95) = $300 variable cost per unit

$95,000 – ($300 x 150) = $50,000 fixed cost per month.

Selling and administrative costs:

($16,000 - $13,800) ÷ (150 – 95) = $40 variable cost per unit

$16,000 – ($40 x 150) = $10,000 fixed cost per month.

b. Sales (1,400 units x $800) $1,120,000Less production costs ($50,000 x 12) + ($300 x 1,400) 1,020,000Less selling and adm. ($10,000 x 12) + ($40 x 1,400) 176,000Income (loss) ($ 76,000)

P10. a. Audio Video CarContribution margin $1,080,000 $ 460,000 $ 570,000Sales 3,000,000 1,800,000 1,200,000

Contribution margin ratio (CM ÷ sales) 0.3600 0.2556 0.4750

b. A $100,000 increase in Audio sales would increase profit by $36,000 while

the effect for Video would be $25,560 and $47,500 for the Car productline. All else equal, it would be better to increase sales of Car products.

c. The weighted average contribution margin ratio is $2,110,000 ÷

$6,000,000 = .3516667

The break-even level of sales is:

(Direct fixed + common fixed) ÷ contribution margin ratio = $4,123,222.

($760,000 + 690,000) ÷ .3516667 = $4,123,222


d. Sales need to achieve a profit of $1,500,000 is ($1,500,000 + $760,000 + $690,000) ÷ .3516667 = $8,388,625.

e. Audio sales = ($3,000,000 ÷ 6,000,000) × $8,388,625 = $4,194,313

Video sales = ($1,800,000 ÷ 6,000,000) × $8,388,625 = $2,516,587

Car sales = ($1,200,000 ÷ 6,000,000) × $8,388,625 = $1,677,725

P11. a. The contribution margin ratio is $493,000 ÷ $1,200,000 = 0.410833.

Thus, if sales increase by 20% ($1,200,000 × .2 = $240,000), profit willincrease by:

Increase in sales $240,000

Times contribution margin ratio .410833Increase in profit $ 98,600

Thus, profit will increase by 42.87% ($98,600 ÷ $230,000)

Profit increases at a faster rate than sales because some costs are fixed anddo not increase with sales.

b. If the owner of RealTimeService wanted to focus on the contribution

margin per unit, he would, most likely, treat hours worked (on consulting,training, or repair services) as the unit of service. For example, if in the

past fiscal year the company worked 6,000 hours, the contribution marginper hour would be $82.17 (i.e., $493,000 ÷ 6,000 hours).


P12. a. Sercon has the highest operating leverage (note that it has $50,000,000 offixed costs versus only $20,000,000 for Zercon.

b. For a 10% change in sales, Sercon’s profit will change by 60% while

Zercon’s profit will change by only 30%.

Sercon ZerconChange in contribution margin $6,000,000 $3,000,000Previous profit 10,000,000 10,000,000

% change 60% 30%

c. Sercon is more risky. Note that if sales decrease by only 10%, profit willdecline by 60% (versus a 30% decline for Zercon).

P13. a. Jens is not approaching this problem in a proper manner. Instead of

focusing on profit per assembly hour, he should focus on the contributionmargin per assembly hour.

For sales of 2,000 units, the contribution margin is $1,000,000. To earn

this contribution margin required 8,000 assembly hours. Thus, thecontribution margin per assembly hour is $125 per hour.

If four hours were available, profit would increase by $125 × 4 = $500

(which is the contribution margin per unit).

b. Jens is underestimating the benefit of more assembly time. By focusing on

profit per hour, he estimates an average benefit of $50 per hour. However,

the real benefit is $125 per hour.

c. If Jens pays workers $25 per hour of overtime premium, he will still make

an incremental $100 per hour ($125 - $25).


P14. a. The Finisher has the highest contribution per hour of assembly time.Therefore, only the minimum number of Masters should be produced and

the remaining assembly time should be devoted to Finishers.

Production of 2,000 Masters requires 4,000 assembly hours. This leaves106,000 hours for production of Finishers indicating that 70,667 pairs of

Finishers can be produced (106,000 ÷ 1.5 hours = 70,667).

The contribution margin for Masters is $110 per unit and the contribution

margin for Finishers is $85 per unit.

Contribution margin of Masters ($110 × 2,000) $ 220,000

Contribution margin of Finishers

($85 × 70,667) 6,006,695Total $6,226,695

b. Production of 4,000 Masters requires 8,000 assembly hours. This leaves102,000 hours for production of Finishers indicating that 68,000 pairs of

Finishers can be produced (102,000 ÷ 1.5 hours = 68,000).

Contribution margin of Masters ($110 × 4,000) $ 440,000

Contribution margin of Finishers

($85 × 68,000) 5,780,000Total $6,220,000

Note that the total contribution margin has declined by $6,695. Thus, the

opportunity cost of requiring that at least 4,000 pairs of the Master beproduced is $6,695.


P15. Increase in sales at normal prices $2,500,000 Less 20% discount 500,000

Increase in sales after discount 2,000,000 Less incremental costs

.58897387 x $2,500,000 1,472,435

Incremental profit $ 527,565

Note that since the regression was estimated using normal selling prices,the incremental costs must be calculated using normal selling prices.

mba 504 ch4 solutions

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