**Chapter 4 Cost-Volume-Profit Analysis**

**QUESTIONS**

1. A mixed cost is a cost that has a fixed cost component and a variable cost component. For example, the amount paid for telecommunication services would be a mixed cost if there was a fixed monthly fee plus a charge for use.

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

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

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

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

6. 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 to calculate the variable cost per unit of activity. The total of the costs classified as fixed provides the estimate of fixed cost.

7. The relevant range is the range of activity for which estimates of costs are likely to be accurate.

8. The contribution margin is equal to the selling price minus variable cost. The contribution margin ratio is the contribution margin per dollar of sales, i.e., the contribution margin per unit divided by the sales price per unit.

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

10. Companies that have relatively higher fixed costs are said to have higher operating leverage.

Thus, a software company with a large investment in research and development (a fixed cost) would likely have higher operating leverage compared to a manufacturing company that used little equipment but expensive labor (a variable cost).

**EXERCISES**

E1. LO 5 a. As sales declines, variable costs will be reduced as well. Fixed costs, however, will remain constant. If large portion of costs in the cost structure are fixed the higher the operating leverage. When sales decline, profit will decline even faster because a small portion of the cost declines with sales (variable costs) but the fixed costs remain unchanged. b.

John can turn fixed costs into variable costs by outsourcing some services–for example, human resources. If the employees that provide services to building construction projects are salaried employees, John could replace them with independent contractors who are paid for work completed.

E2. LO 4 Oakland Hills Golf Course is more likely to focus on contribution margin per unit in Cost Volume Profit (CVP) analysis since each unit sold (a round of golf) is the same. Brook’s Men’s Clothing, however, is more likely to focus on contribution margin ratio in CVP analysis since each unit (an article of clothing) is very different (e.g., a shirt, suit, tie) and, as a result, a per unit contribution margin would only be an average over the different types of products.

E3. LO 4 The Coca-Cola Income Statement for 2010 (in million) is as follows: Net Sales$28,857 Cost of goods sold10,406 Gross Profit18,451 Selling and Administrative 10,945 Other 254 Operating income$ 7,252 The contribution margin ratio is 63. 94% ($18,451 ? $28,857). To increase gross profit by $2 billion Coca-Cola would have to increase sales by $3. 128 billion ($2 billion ? .6394). E4. LO 1 Depreciation appears to be a fixed cost. [pic]

Direct labor appears to be a variable cost. [pic] Telecommunications appears to be a mixed cost. Note that the intercept is $75,000. [pic] E5. LO 2 ($20,500 – $8,500) ? (900,000 – 300,000) = $0. 02 per copy of variable repair cost $20,500 – ($0. 02 ? 900,000) = $2,500 per month of fixed repair cost. E6. LO 2 and Appendix a. The highest level of activity is sales of 32,000 tickets with cost of $230,000. The lowest level of activity is sales of 17,000 tickets with cost of $155,000. ($230,000 ? $155,000) ? (32,000 ? 17,000) = $5 of variable cost per ticket sold. $230,000 – ($5 ? 32,000) = $70,000 per month of fixed cost.

Thus, cost = $70,000 + ($5 ? No. of tickets sold). b. For a sales increase of 14,000 tickets, profit will increase by $280,000 (i. e. , ($25 ? 14,000) ? ($5 ? 14,000) = $280,000). c. The regression indicates that variable cost per ticket sold is $4. 392894 and fixed costs are $86,438. 04 per month. However, care must be exercised since, as indicated in the graph of costs and sales, costs in November ($207,000) appear to be low given that ticket sales were only 30,000. Using the regression, for a sales increase of 14,000 tickets, profit will increase by $288,499. 48 (i. e. , ($25 ? 14,000) ? $4. 392894 ( 14,000) = $288,499. 48). Note—This output was generated using the regression function in Excel (in Excel, go to tools, then data analysis, and then regression). |SUMMARY OUTPUT | | | | | | | | | | |Regression Statistics | | | | |Multiple R |0. 61552136 | | | | |R Square |0. 92458251 | | | | |Adjusted R Square |0. 917040761 | | | | |Standard Error |5867. 692252 | | | | |Observations |12 | | | | | | | | | |ANOVA | | | | | | |Df |SS |MS |F | |Regression |1 |4220931043 |4220931043 |122. 5952381 | |Residual |10 |344298123. |34429812. 36 | | |Total |11 |4565229167 | | | | | | | | | | |Coefficients |Standard Error |t Stat |P-value | |Intercept |86438. 04172 |10176. 36198 |8. 494002266 |6. 94063E-06 | |X Variable 1 |4. 92894561 |0. 396747299 |11. 07227339 |6. 20264E-07 | [pic] E7. LO 2 a. [pic] b. The relation appears to be approximately linear (note that R – Square is . 90). There are no obvious outliers. E8. LO 2 a. Arguably, the only variable costs in human resources are salaries and office supplies (and a case could be made that even salaries are fixed). In this case, variable costs are $555 per hire [($33,000 + $300) ? 60 hires]. Fixed costs are $10,400. b. The estimated cost for June with 70 new hires is: $10,400 + ($555 ( 70) = $49,250. c.

The incremental cost associated with 10 more employees is $5,550 (i. e. , $555 ( 10). E9. LO 2 & 3 a. Arguably, the only variable costs are wages ($147,200). In this case, variable costs per ticked sold are: Total variable costs (wages)$147,200 Divided by tickets sold 40,000 Variable cost per ticket sold $ 3. 68 Fixed costs per month are: Rent$60,000 Author royalties/fees80,000 Utilities7,000 Depreciation — theater equipment14,000 Owner’s salary 10,000 Fixed costs per month$171,000 b. The contribution margin per unit = $25 ? $3. 68 = $21. 32. Thus, the contribution margin ratio = $21. 32 ? $25 = 0. 528. In other words, the company has approximately 85 cents of contribution margin per dollar of sales. E10. LO 2 a. Variable costs are: Material$ 50,400 Direct labor19,200 Other utilities (80% variable)3,360 Supervisory salaries (25% variable)6,300 Equipment repair (80% variable)6,000 Indirect materials540 Factory maintenance (20% variable) 600 Total variable costs$86,400 Divided by units produced 1,200 Variable cost per unit$ 72 Fixed costs per month are: Depreciation$ 9,000 Phone300 Other utilities (20% fixed)840 Supervisory salaries (75% fixed)18,900 Equipment repair (20% fixed)1,500

Factory maintenance (80% fixed) 2,400 Total fixed costs per month$32,940 b. The incremental cost of producing 300 units is $21,600 (i. e. , $72 variable cost per unit ( 300 units). E11. LO 3 a. The break-even point equals fixed cost divided by the contribution margin per unit. Thus, the break-even point is 22 cakes [i. e. , $7,700 ? ($600 – $250) = 22 cakes]. b. The company must sell 51 cakes to earn a profit of $10,000. ($7,700 + $10,000) ? ($600 ? $250) = 51 cakes E12. LO 3 a. Given that variable cost per dollar of sales is $. 40, the contribution margin per dollar of sales (i. e. the contribution margin ratio) is $0. 60. The break-even point equals fixed cost divided by the contribution margin ratio. Thus, the break-even point is $500,000 [i. e. , $300,000 ? 0. 60 = $500,000]. b. ($300,000 + $60,000) ? 0. 60 = $600,000 c. The expected level of profit is: ($1,000,000 ( 0. 60) ? $300,000 = $300,000. E13. LO 3 a. The contribution margin is $600 (i. e. , $900 – $300). b. The effect on profit of selling 6 more pairs of speakers is $3,600 (i. e. , $600 ( 6). c. The contribution margin ratio is $600 ? $900 = . 6667 d. $7,000 ? .6667 = $4,667 E14. LO 3 a. Expected profit is $900 (130) ? 300 (130) ? $60,000 = $18,000. b. The contribution margin ratio is $600 ? $900 = 0. 6667 Breakeven sales are $60,000 ? 0. 6667 = $89,996. Expected sales are $130 ( $900 = $117,000. The margin of safety is equal to expected sales ? break-even sales = $117,000 ? $89,996 = $27,004. E15. LO 3 Expected profit is $1,200 (130) ? $300 (130) ? $60,000 = $57,000. E16. LO 4 a. The weighted average contribution margin ratio is $695,000 ? $2,035,000 = 0. 3415. b. ($255,000 + $600,000) ? .3415 = 2,503,660. c. The contribution margin ratios of the three departments are: Department A ($160,000 ? 270,000). 59 Department B ($335,000 ? $855,000). 39 Department C ($200,000 ? $910,000). 22 All else equal, Department A should be emphasized in the weekly advertisement because this department earns $. 59 on each incremental dollar of sales (more than either of the other departments). E17. LO 4 & 5 a. Currently, profit as a percent of sales is $440,000 ? $2,035,000 = . 21622. b. The contribution margin ratio is $695,000 ? $2,035,000 = 0. 3415. Thus, if sales increase by 15%, profit will increase by: Increase in sales ($2,035,000 ( 15%)$305,250 Times contribution margin ratio . 3415

Increase in profit$104,243 The new sales level will be ($2,035,000 + $305,250) = $2,340,250. The new profit level will be ($440,000 + $104,243) = $544,243. Thus, profit as a percent of sales will be . 2325 (i. e. , $544,243 ? $2,340,250). 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. E18. LO 6 a. Stand AStand B Selling price$90$80 Variable costs 30 44 Contribution margin6036 ? Hours to produce 1 item 6 3 Contribution margin per hour$10$12 The company should produce just stand B.

With 15 hours available, this stand will generate $180 of contribution margin ($12 ( 15 hours) while stand A will generate just $150 ($10 ( 15). b. If the company obtains additional labor, it should produce more of stand B. The incremental benefit of 15 labor hours is $180 ($12 contribution margin per hour x 15 hours). As an aside, note that if production of stand A requires 6 labor hours and variable costs are only $30 per unit, workers at Dvorak Music must be paid less than $5 per hour because part of the variable costs are material costs! Perhaps production is taking place in a third-world country!

**PROBLEMS**

P1. LO 1 a. Depreciation of the building—fixed b. 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, shampoo, and other toiletries in rooms (variable) e. Laundry costs—mixed (part is variable and part is fixed, e. g. , depreciation on laundry equipment) f. Food and beverage costs—variable g. Grounds maintenance—fixed P2. LO 2 & 3 a. Variable costs Component costs $68,000 Supplies2,500 Assembly labor 24,650 Shipping 2,000 Total$97,150

Variable cost per disc player ($97,150 ? 145) = $670 Fixed costs Rent $2,300 Supervisor salary5,600 Electricity 350 Telephone280 Gas300 Advertising2,600 Administrative costs 15,000 Total$26,430 b. Expected cost in August = $670 (165) + $26,430 = $136,980 c. Contribution margin = Selling price less variable cost = $1,300 ? $670 = $630. d. Estimated profit at 165 units = $1,300 (165) ? $670 (165) ? $26,430 = $77,520. e. The special order will increase profit by ($950 ? 670) ( 120 = $33,600. P3. LO 2 & 3 a. ProductionCost High170$143,910 Low130 116,990 40$ 26,920 Variable cost per unit = $26,920 ? 40 = $673.

Total cost at 170 units$143,910 Less variable costs ($673 * 170) 114,410 Fixed cost$ 29,500 b. Break-even sales in units = $29,500 ? ($1,300 ? $673) = approximately 47 units. c. Margin of safety = 165 ? 47 = 118 units. d. Total profit = ($1,300 * 165) ? ($673 * 165) ? $29,500 = $73,955. e. A major limitation of the high-low method is that it estimates variable and fixed costs using extreme values. Also, the approach uses only two observations. A better approach would be to use regression analysis. P4. (LO 2 and Appendix) a. Note—This output was generated using the regression function in Excel which is an “add-in” to Excel.

In Excel, go to Tools, then Data Analysis, and then Regression. If Data Analysis is not available under Tools or if Regression is not available within Data Analysis, “add-in” this function through Excel’s Add-in process. |SUMMARY OUTPUT | | | | | | | | | | |Regression Statistics | | | | |Multiple R |0. 98433139 | | | | |R Square |0. 996868734 | | | | |Adjusted R Square |0. 996555607 | | | | |Standard Error |460. 0103314 | | | |Observations |12 | | | | | | | | | | |ANOVA | | | | | | |df |SS |MS |F | |Regression |1 |673679196. 6 |67367196. 6 |3183. 96109 | |Residual |10 |2116095. 05 |211609. 505 | | |Total |11 |675795291. 7 | | | | | | | | | | |Coefficients |Standard Error |t Stat |P-value | |Intercept |28968. 56436 |1777. 912568 |16. 29358208 |1. 57514E-08 | |Units |676. 2970297 |11. 8611658 |56. 42336492 |7. 41768E-14 | Based on the regression, fixed costs are $28,968. 56 and variable costs are $676. 30 per unit. b. Comparison of estimates: Variable costFixed cost Account analysis$670$26,430 High-low$673$29,500 Regression$676$28,969 The regression approach arguably provides the best estimates because it uses more data and is less subjective. P5. LO 3 a. Number of trips (6 per week ? 52 weeks)312 Revenue per trip ($360 x 4 passengers)$1,440 Total revenue ($1,440 per trip x 312 trips)$449,280 Variable costs: Fuel$147,976 Maintenance 127,920 Total variable costs$275,896

Variable costs per trip ($275,896 ? 312)$884. 28 Contribution margin per trip ($1,440 ? $884. 28)$555. 72 Fixed costs: Salary$ 70,000 Depreciation of plane25,000 Depreciation of office equipment2,800 Rent40,000 Insurance20,000 Miscellaneous 7,500 Total fixed costs$165,300 Breakeven number of trips is ($165,300 ? $555. 72) = 297 trips. b. If Michael draws a salary of $110,000, fixed costs will increase by $40,000 to $205,300. In this case, the breakeven number of trips is ($205,300 ? $555. 72) 369. Note that this number of trips is not feasible if Michael can only fly one round trip per day, unless he adds a seventh day. . The average before tax profit per round trip is $8,084 ? 312 = $25. 91. d. The incremental profit associated with adding a round trip is the contribution margin per trip, which is $555. 72. P6LO 2 & 3 a. Account Analysis Fixed cost per month (April ? June data) Day manager salary$ 4,500 Night manager salary3,900 Depreciation 12,500 $20,900 Variable costs per room (April data): Cleaning staff$15,960 Complimentary continental breakfast 4,760 Total variable costs20,720 Divided by number of rooms 1,600 Variable costs per room $ 12. 95 b. High-Low Method ($42,580 – $41,620) ? 300 rooms = $3. 0 per occupied room of variable cost. $41,620 – $3. 20 x (1,600 rooms) = $36,500 of fixed costs per month. c. $120. 00 – $3. 20 = $116. 80 contribution margin per occupied room. P7. LO 2 & 3 a. Income will only be proportional to sales if all costs are variable. That assumption is wrong (for example, the registration fee and the pay to Mindy Orwell are fixed). b. Sales$23,520 Less cost of sales (55% of sales in prior year) 12,936 Gross margin10,584 Less other expenses: Registration fee1,800 Booth rental (6% of sales)1,411 Salary of Mindy Orwell 450 Before tax profit$ 6,923 P8. LO 1, 2, 3 Sales |$1,600,000 |$1,700,000 |$1,800,000 |$1,900,000 |$2,000,000 | |Less cost of | 1,032,000 | 1,084,000 | 1,136,000 | 1,188,000 | 1,240,000 | |components | | | | | | |Gross margin |568,000 |616,000 |664,000 |712,000 |760,000 | |Less: | | | | | | | Staff salaries |266,000 |266,000 |266,000 |266,000 |266,000 | | Rent |40,000 |40,000 |40,000 |40,000 |40,000 | | Utilities |8,000. 00 |8,000. 00 |8,000. 00 |8,000. 00 |8,000. 00 | | Advertising | 7,000. 00 | 7,000. 00 | 7,000. 00 | 7,000. 00 | 7,000. 0 | |Operating profit | | | | | | |before bonuses |247,000 |295,000 |343,000 |391,000 |439,000 | |Staff bonuses | 74,100 | 88,500 | 102,900 | 117,300 | 131,700 | |Profit before taxes | | | | | | | and owner “draw” | $ 172,900 | $ 206,500 | $ 240,100 | $ 273,700 | $ 307,300 | In the prior year, cost of components was 65% of sales. In the coming year, prices will be reduced by 20% on all purchases over $1,000,000. Purchases of $1,000,000 corresponds to sales of $1,538,462. ($1,000,000 ? 0. 65).

Thus, the calculation of cost of components when sales are $1,600,000 is: $1,000,000 + [($1,600,000 – $1,538,462) ? 0. 65 ? 0. 8] = $1,032,000. P9. LO 2 a. Production costs: ($112,978 ? $83,007) ? (138 – 97) = $731 variable cost per unit $112,978 – ($731 ? 138) = $12,100 fixed cost per month. Selling and admin costs: ($28,030 ? $22,495) ? (138 – 97) = $135 variable cost per unit $28,030 – ($135 ? 138) = $9,400 fixed cost per month. b. Sales (1,550 units ? $900)$1,395,000. 00 Less production costs ($12,100 ? 12) + ($731 ? 1,550)1,278,250. 00 Less selling and admin. ($9,400 ? 12) + ($135 ? 1,550) 322,050. 00 Income (loss)($205,300. 00) P10. LO 2 & 3 a.

The high point is June with 310 loans and $55,725 in costs; the low point is December with 160 loans and $48,600 in costs. To find the variable cost per loan processed: Variable cost per loan = Change in cost ? Change in loans Variable cost per loan = ($55,725 – $48,600) ? (310 – 160) Variable cost per loan = $47. 50 To find the fixed cost, substitute in the line equation using the high point: Total cost = Fixed cost + (Variable cost ? Number of loans) $55,725 = Fixed cost + ($47. 50 ? 310) Fixed cost = $41,000 Therefore, the cost function will be: Total cost = $41,000 + $47. 50(X) where X = activity level b. Contribution margin per loan = $500 – $47. 50 = $452. 50 Breakeven = Fixed costs ?

Contribution margin per loan Breakeven = $41,000 ? $452. 50 = 91 loans (round up to the nearest whole unit when calculating breakeven) c. Total cost = $41,000 + $47. 50(X) Substitute 275 for X, then: Total cost = $41,000 + $47. 50(275) Total cost = $54,063 (rounded) |Sales (275 loans @ $500 each) |$137,500 | |Less costs (calculated above) | 54,063 | |Estimated profit |$ 83,437 | d. [pic] e. It appears that the high-low method will give a reasonable estimate of variable and fixed costs. The points generally have a linear relationship.

If you were to draw a line between the high point and the low point, the line would be generally representative of the rest of the data, but it would not fit perfectly. P11. LO 3 a. | |Total |Per unit |Percent | |Sales ($1,200 x 1,500 apps) |$1,800,000 |$1,200 |100. 00% | |Less variable expenses |1,110,000 |$740 |61. 67% | |Contribution margin |690,000 |$460 |38. 3% | |Less fixed expenses | 300,000 | | | |Operating income |$ 390,000 | | | Breakeven point (in number of apps) = $300,000 ? $460 = 652 units (rounded) Contribution margin ratio = $460 ? $1,200 = 38. 33% Breakeven point (in sales dollars) = $300,000 ? 38. 33% = $782,677 (rounded) b. Margin of safety in units = 1,500 – 652 = 848 units Margin of safety in dollars = $1,800,000 – $782,677 = $1,017,326 c. Target profit (in units) = ($300,000 + $450,000) ? $460 = 1,630 units (rounded) Target profit (in dollars) = ($300,000 + $450,000) ? 38. 33% = $1,956,692 (rounded) d. New income statement: |Total |Per unit |Percent | |Sales |$2,124,000 |$1,200 |100% | |Less variable expenses |1,309,800 |$740 |61. 67% | |Contribution margin | 814,200 |$460 |38. 33% | |Less fixed expenses | 380,000 | | | |Operating income |$ 434,200 | | Yes, they should increase their advertising, since their operating income will rise to $434,200 from $390,000 in the original scenario. P12. LO 4 a. AudioVideoCar Contribution margin$1,120,000$ 460,000$ 614,400 Sales3,200,0001,920,0001,280,000 Contribution margin ratio (CM ? sales) 0. 35000. 23950. 4800 b. A $125,000 increase in Audio sales would increase profit by $43,750 while the effect for Video would be $29,938 and $60,000 for the Car product line. All else equal, it would be better to increase sales of Car products. c. The weighted average contribution margin ratio is $2,194,400 ? $6,400,000 = . 42875 The break-even level of sales is: (Direct fixed + common fixed) ? contribution margin ratio = $4,360,190. ($785,000 + 710,000) ? .342875 = $4,360,190 d. Sales need to achieve a profit of $1,800,000 is ($1,800,000 + $785,000 + $710,000) ? .342875 = $9,609,916. e. Audio sales = ($3,200,000 ? 6,400,000) ( $9,609,916 = $4,804,958 Video sales = ($1,920,000 ? 6,400,000) ( $9,609,916 = $2,882,975 Car sales = ($1,280,000 ? 6,400,000) ( $9,609,916 = $1,921,983 P13. LO 4 & 5 a. The weighted-average contribution margin ratio is $618,100 ? $1,500,000 = 0. 412067. Thus, if sales increase by 10% ($1,500,000 ( . 1 = $150,000), profit will increase by:

Increase in sales$150,000 Times weighted-average contribution margin ratio . 412067 Increase in profit$ 61,810 Thus, profit will increase by 18. 12% ($61,810 ? $341,100) Profit increases at a faster rate than sales because some costs are fixed and do not increase with sales. b. If the owner of ComputerGuard wanted to focus on the contribution margin per unit, she 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 7,500 hours, the weighted-average contribution margin per hour would be $82. 41 (i. e. , $618,100 ? 7,500 hours). P14. LO 4 a. |Smasher |Basher |Dinker |Total | | |Units sold |1,500 |3,000 |3,000 |7,500 |Weighted Avg % | |Sales |$150,000 |$180,000 |$120,000 |$450,000 | | |Less variable costs |80,000 |75,000 |35,000 |190,000 | | |Contribution margin |$ 70,000 |$105,000 |$ 85,000 |260,000 |57. 78% | |Less common fixed costs | | |140,000 | | |Profit | | | |$120,000 | | The weighted average contribution margin per unit is $34. 67 [($46. 67 ? 1. 5) + ($35 ? 3) + ($28. 33 ? 3)] ? (1. 5 + 3 + 3) b. The breakeven point in total units will be: $140,000 ? $34. 67 = 4,038 (rounded) c. To calculate each product’s share of the breakeven sales volume in units: |Smasher |Basher |Dinker |Total | |Breakeven sales in units (total) |4,040 |4,040 |4,040 | | |Multiply by breakeven sales |20. 00% |40. 00% |40. 00% | | |Breakeven sales in units by product |808 |1,616 |1,616 |4,040 | |(Note: rounding error will be present. ) | | | | d.

The weighted average contribution margin ratio is $260,000 ? $450,000 = 57. 77%. e. The amount in total sales dollars need to achieve a profit of $125,000 will be: ($140,000 + $125,000) ? 57. 77% = $458,716 (rounded) f. To calculate each product’s share of the breakeven sales volume: | |Smasher |Basher |Dinker |Total | |Sales (original level) |$150,000 |$180,000 |$120,000 |$450,000 | |Relative weight |33. 33% |40. 00% |26. 67% |100. 0% | |Multiply by target sales level |$458,716 |$458,716 |$458,716 | | |Breakeven sales by product |$152,890 |$183,486 |$122,340 |$458,716 | |(Note: rounding error will be present. ) | | | | P15. LO 5 a. Equillion has the highest operating leverage (note that it has $60,000,000 of fixed costs versus only $25,000,000 for Stoichran. b. For a 20% change in sales, Equillion’s profit will change by 60% while Stoichran’s profit will change by only 30%. EquillionStoichran Change in contribution margin$15,000,000$8,000,000 Previous profit15,000,00015,000,000 % change100%53% c. Equillion is more risky.

Note that if sales decrease by only 20%, profit will decline by 100% (versus a 53% decline for Stoichran). P16. LO 6 a. Jurgis is not approaching this problem in a proper manner. Instead of focusing on profit per assembly hour, he should focus on the contribution margin per assembly hour. For sales of 2,500 units, the contribution margin is $1,500,000. To earn this contribution margin required 12,500 assembly hours. Thus, the contribution margin per assembly hour is $120 per hour. If five hours were available, profit would increase by $120 ( 5 = $600 (which is the contribution margin per unit). b. Jurgis is underestimating the benefit of more assembly time.

By focusing on profit per hour, which includes fixed costs that will not change, he estimates an average benefit of $78 per hour. However, the real benefit is $120 per hour. c. If Jurgis pays workers $39 per hour of overtime premium, he will still make an incremental $81 per hour ($120 ? $39). P17. LO 6 a. The Mx100 has the highest contribution per hour of assembly time. Therefore, only the minimum number of Nx100s should be produced and the remaining assembly time should be devoted to Mx100s. Production of 3,000 Nx100s requires 9,000 assembly hours. This leaves 191,000 hours for production of Mx100s indicating that 95,500 pairs of Mx100s can be produced (191,000 ? 2 hours = 95,500).

The contribution margin for Nx100s is $115 per unit and the contribution margin for Mx100s is $95 per unit. Contribution margin of Nx100s ($115 ( 3,000)$ 345,000 Contribution margin of Mx100s ($95 ( 95,500) 9,072,500 Total$9,417,500 b. Production of 5,000 Nx100s requires 15,000 assembly hours. This leaves 185,000 hours for production of Mx100s indicating that 92,500 pairs of Mx100s can be produced (185,000 ? 2 hours = 92,500). Contribution margin of Nx100s ($115 ( 5,000)$ 575,000 Contribution margin of Mx100s ($95 ( 92,500) 8,787,500 Total$ 9,362,500 Note that the total contribution margin has declined by $55,000. Thus, the opportunity cost of requiring that at least 5,000 pairs of the Nx100 be produced is $55,000. P18. LO 2 and Appendix) Increase in sales at normal prices$3,000,000 Less 20% discount 600,000 Increase in sales after discount2,400,000 Less incremental costs .54762019 x $3,000,000 1,642,860 Incremental profit$ 757,140 Note that since the regression was estimated using normal selling prices, the incremental costs must be calculated using normal selling prices. Case 4-1, LO 1, 3 ROTHMUELLER MUSEUM Summary A museum is trying to estimate the financial impact of a new exhibition. •Links C-V-P analysis and decision making. Questions to ask students 1. What’s the situation at Rothmueller Museum? 2. What is the financial impact of the Ansel Adams exhibition?

Is offering the exhibition a good decision from a financial standpoint? 3. How many people must attend the exhibition to break-even? Discussion I begin by asking a student to summarize the situation. Rothmueller Museum is planning an Ansel Adams exhibit. Alice Morgan, the photographic curator, wants to estimate its financial impact. The financial impact is a positive $67,840 as follows: |Incremental revenue: | | |10,000 ? $15 |$ 150,000 | |8,000 ? $6 |48,000 | |. 2 ? 8,000 ? $8 ? 3 | 3,840 | | | 201,840 | |Incremental costs: | | |Lease of photos |100,000 | |Packing |5,000 | |Insurance |4,000 | |Guard |12,000 | |Installation |2,000 | |Advertising |7,000 | |Programs | 4,000 | | | 134,000 | | | | |Incremental profit |$ 67,840 | | | | 6,639 people must attend the exhibition in order for its financial impact to be profit neutral (i. e. , the museum will not be better off nor worse off financially). Incremental costs$134,000 Divided by average incremental revenue ($201,840 ? 10,000)20. 184 Number who must attend6,639

Offering the exhibition appears to be a good decision in that it will more than cover its incremental costs. It may be, however, that a different exhibition would have contributed even more “profit. ” That is, there may be some opportunity cost. Case 4-2, LO 3 MAYFIELD SOFTWARE, CUSTOMER TRAINING Summary An internal report shows that the customer training center is losing money. The manager wants to know how many classes must be offered to break-even. •Shows how allocated costs can make a valuable operation appear unprofitable. Questions to ask students 1. What’s the situation at the customer training center for Mayfield Software? 2. What will be the impact on company profit if the training center is closed? 3.

How many classes must be offered to break-even given the current room configuration and approach to allocation? 4. What happens to break-even if the amount paid to instructors is reduced to $3,500 per class? 5. What will be the impact on group profit if version 4. 0 of “CustomerTrack” is released? Discussion If the customer training operation is shut down, Mayfield Software will lose $1,179,250 per year (i. e. , profit before central charges). Note that the central charges are not likely to change as a result of closing the customer training center. Given the current room configuration and approach to allocation of central charges (20 percent of revenue), Marie must offer approximately 889 classes to break-even on the Report of Operating Results. Revenue per class | |$ 7,200 | |Variable costs: | | | | Trainer cost |$ 4,000 | | | Operating manuals |600 | | | Postage |15 | | | Central charges |1,440 | 6,055 | | Contribution margin | | 1,145 | | | | | |Fixed costs: | | | Director salary | | 180,000 | | Receptionist | |60,000 | | Office manager | |80,000 | | Utilities | |38,000 | | Lease expense | |400,000 | | Rent | |100,000 | | Advertising | | 160,000 | |Total | |$1,018,000 | $1,145. 00 (X) ? $1,018,000 = 0. X = 889. 08. If the amount paid to instructors is reduced to $3,500 per class, the break-even point drops to 619.

Marie should give serious consideration to this option since it will have a very significant impact on profitability and the break-even point. $1,645. 00 (X) ? $1,018,000 = 0. X = 618. 84. Finally, the impact of 30 sessions related to “CustomerTrack” is $34,350. $1,145. 00 (30) = $34,350 Case 4-3, LO 2, 4 KROG’S METALFAB, INC. Summary Company is trying to estimate lost profit, related to fire damage, so it can submit an insurance claim. •Focuses on cost estimation. •Demonstrates the effect of operating leverage—why profit does not increase or decrease at the same rate as sales. Questions to ask students 1. What is the situation facing Krog’s Metalfab? 2.

What are your estimates of lost profit? 3. What is wrong with Peter Newell’s analysis? Discussion I begin the discussion the same way I begin the discussion of almost all cases, by asking a student to summarize the situation. Krog had a fire at the beginning of 2010 that reduced capacity and profit during 2010. The company has insurance to cover lost profit, but what is the amount of lost profit during 2010? At this point, I generally ask 5-10 students to simply give me their lost profit estimates and I put them on the board. If students have large estimates (say greater than $700,000) I’ll play the role of the insurance company and argue that their estimates are highly inflated.

After all, the company only had profit of approximately $110,000 in 2009 (the year before the fire). I may go so far as to argue that the company should have ceased operations during the period of reconstruction to avoid having such high losses. In response, a sharp student will bring up the idea that this would have been the end of the business. And the company is surely worth more than $700,000 since it generates more than $300,000 per year in income from operations. (Note that the calculations for expected profit in 2010, without the fire, show annual expected profit of $336,979 using the regression approach and $398,446 using the high-low method. )

At this point, I may fall back on Peter Newell’s analysis, and argue that as long as the insurance company is willing to pay the excess operating costs ($250,000) plus the $34,184 estimated by Peter, Krog should be happy. This reimburses the company for the average profit per dollar of sales ($. 02 per dollar of sales). This should lead to a discussion of the fundamental flaw in Peter’s analysis. When sales decline, profit will not decline by the average profit per dollar of sales. It will decline by a higher percent since when sales decline, fixed costs will not decline (and as we will see, Krog Metalfab has high fixed costs). This drives home the concept of operating leverage and its link to fluctuations in profit.

Now it’s on to reviewing the calculation of lost profit. The answer depends on how the students estimate fixed and variable costs. Below, I’ll review calculations based on cost estimates using regression, the high-low method, and account analysis. Regression analysis suggests that fixed costs are $260,589 per month and variable costs are $. 3641 per dollar of sales. Thus, the estimate of lost profit is $1,064,815. Regression Expense = $260,589 + . 3641 ( Sales R squared = . 60 Sales in 2009$5,091,094 Predicted sales with 7% increase$5,447,471 Predicted expense ($260,589 ( 12) + (. 3641 ( $5,447,471) 5,110,492 Predicted profit336,979 Less actual loss 727,836 Lost profit$1,064,815

A student who has carefully reviewed the problem will note that February of 2009 is an outlier (expenses are higher than sales in this month). Without February in the data set, the regression indicates that fixed costs are $221,277 and variable costs are $. 4363 per dollar of sales. With these estimates, lost profit is $1,143,251. Regression Expense = $221,277 + . 4363 ( Sales R squared = . 99 Sales in 2009$5,091,094 Predicted sales with 7% increase$5,447,471 Predicted expense ($221,277 ( 12) + (. 4363 ( $5,447,471) 5,032,056 Predicted profit415,415 Less actual loss 727,836 Lost profit$1,143,251 This estimate clearly shows the flaw in Peter’s analysis. Cost increase by $0. 363 per dollar of sales. That means that profit increases by $0. 5637 per dollar of sales (the contribution margin ratio). Sales are off by $1,589,972 compared to predicted sales and this means that profit is off by $896,267. In addition the company had $246,984 of excess expenses. Thus, it is easy to see why profit is off by more than $1,100,000. High-Low Approach If students use the high-low method, they will estimate variable costs as $0. 4381 per dollar of sales and fixed costs as $221,874 per month. August April HighLowChange Sales$603,210$303,685$299,525 Expense$486,140$354,931$131,209 Variable cost per dollar of sales ($131,209 ? $299,525) = $0. 4381

Fixed cost per month ($486,140 – $. 4381 ( $603,210) = $221,874 In this case, lost profit is estimated as $1,126,282. Sales in 2009$5,091,094 Predicted sales with 7% increase$5,447,471 Predicted expense ($221,874 ( 12) + (. 4381 ( $5,447,471) 5,049,025 Predicted profit398,446 Less actual loss 727,836 Lost profit$1,126,282 Account Analysis If students use account analysis, they are likely to classify cost of goods sold as variable and selling and administrative costs as fixed. Using annual totals this suggests that variable costs are $. 8875 per dollar of sales and fixed costs are $463,124. Cost of goods sold$4,518,475 Sales$5,091,094 Cost of goods sold ? sales$0. 8875

Selling expense$217,124 Administrative expense 246,000 Total$463,124 Use of these values results in estimated lost profit of $877,552. Estimated lost profit is lower here because estimated fixed costs are lower and estimated variable costs are higher. Sales in 2009$5,091,094 Predicted sales with 7% increase$5,447,471 Predicted expense $463,124 + $. 8875 ( $5,447,471 5,297,755 Predicted profit149,716 Less actual loss 727,836 Lost profit$ 877,552 This estimate seriously underestimates lost profit. The assumption that cost of goods sold is completely variable is at odds with the data (see the regression analysis) which indicates a large fixed cost component.