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Module 15
Cost-Volume-Profit Analysis and Planning
DISCUSSION QUESTIONS
Q3-1. Cost-volume-profit analysis is a technique used to examine the relationships among the total volume of some independent variable, total costs, total revenues, and profits during a time period. It is particularly useful in the early stages of planning when it provides a framework for discussing planning issues.
Q3-2. The important assumptions that underlie cost-volume-profit analysis are:
1. All costs are classified as fixed or variable with unit-level activity cost drivers.
2. The total cost function is linear within the relevant range.3. The total revenue function is linear within the relevant range.4. The analysis is for a single product, or the sales mix of multiple
products is constant.5. There is only one activity cost driver: unit or dollar sales
volume.
Q3-3. The use of a single variable in cost-volume-profit analysis is most reasonable when analyzing the profitability of a specific event or the profitability of an organization that produces a single product or service on a continuous basis.
Q3-4. In a contribution income statement, costs are classified according to behavior as variable or fixed, and the contribution margin (the difference between total revenues and total variable costs) that goes toward covering fixed costs and providing a profit is emphasized. In a functional income statement, costs are classified according to function (rather than behavior), such as manufacturing and selling and administrative. This is the type of income statement typically included in corporate annual reports.
Q3-5. The unit contribution margin is equal to the difference between the unit selling price and the unit variable costs. In computing the unit break-even point, the fixed costs are divided by the unit contribution margin.
Q3-6. The contribution margin ratio is the portion of each dollar of sales revenue contributed toward covering fixed costs and earning a profit. It is especially useful in situations involving several products or when unit sales information is not available.
Q3-7. The desired profit is added to the fixed costs, increasing the sales volume required to cover both.
Q3-8. A profit-volume graph contains only one line showing the relationship between volume and profits, while a cost-volume-profit graph contains two lines – one for total revenues and one for total costs. A profit-volume graph is most likely to be used when management is primarily interested in the impact on profits of changes in sales volume and less interested in the related revenues and costs.
Q3-9. Income taxes increase the sales volume required to earn a desired after-tax profit.
Q3-10. Other things being equal, the higher the degree of operating leverage, the greater the opportunity for profit with increases in sales. Conversely, a higher degree of operating leverage magnifies the risk of large losses with a decrease in sales.
15-2 Financial & Managerial Accounting for MBAs, 3rd Edition
MINI EXERCISES
M15-11
a. Break-even point = $120,000/(1 0.40) = $200,000
b. Margin of safety = $240,000 $200,000 = $40,000
c. Sales volume for desired profit = ($120,000 + $70,000) = $316,667(1 0.40)
M15-12
a. 1. Total variable costs2. Total revenue3. Total costs4. Variable costs5. Fixed costs6. Total costs7. Contribution margin8. Break-even unit sales volume9. Loss area10. Profit area
b. Line CC Line OR Break-Even Point1. Shift downward No change Shift left (decrease)2. No change Increase slope Shift left (decrease)3. Increase slope No change Shift right (increase)4. Shift upward Decrease slope Shift right (increase)5. Shift downward and No change Shift left (decrease)
a. 1. Loss area2. Profit area3. Break-even point4. Axis on which profit and loss are measured5. Fixed costs6. Profit at volume E
b. Line CF Break-Even Point1. Increase slope Shift left (decrease)2. Decrease slope Shift right (increase)3. Shift upward Shift left (decrease)4. Shift downward and Shift right (increase) decrease slope5. Shift upward and Can't tell; the two changes
15-4 Financial & Managerial Accounting for MBAs, 3rd Edition
M15-14 (concluded)
b.
c. It is most appropriate to use a profit-volume graph when management is primarily interested in the impact on profits of changes in sales volume and less interested in the related revenues and costs.
a. Selling price $5.00 per hot dogVariable costs 3.50 per hot dogContribution margin $1.50
Break-even point = $750,000/$1.50 = 500,000 hot dogs
b.
c.
d. It is easier to determine profit or loss at any volume with a profit-volume graph than with a cost-volume-profit graph. This is especially true in situations, such as this, where the unit contribution margin is small and the scale of activity is large. Although a profit-volume graph provides a clear illustration of profits, it does not illustrate revenues and costs. Hence, a manager using a profit-volume graph does not see the relationship between revenues, costs, and profits.
Contribution Income StatementFor the Month of May 2012
Sales (6,000 x $40) $240,000Less variable costs:
Direct materials (6,000 x $10) $ 60,000Direct labor (6,000 x $2) 12,000Manufacturing overhead (6,000 x $5) 30,000Selling and administrative (6,000 x $5) 30,000 (132,000)
Contribution margin 108,000Less fixed costs:
Manufacturing overhead 40,000Selling and administrative 20,000 (60,000)
Profit $ 48,000
b.
Note: The instructor might extend this assignment in class, computing the break-even point, the margin of safety, and the impact on profits of a change in sales.
a. Contribution margin $ 380,000Sales 1,000,000 Contribution margin ratio 0.38
Break-even point in sales dollars = $285,000/0.38= $750,000
b. Current sales $1,000,000Break-even sales (750,000 ) Margin of safety $ 250,000
c. Current fixed costs $285,000Impact of increase 57,000New fixed costs $342,000
Revised break-even point = $342,000/0.38= $900,000
d. Required before-tax income = $200,000/(1 0.36)= $312,500
Sales volume required to provide an after-tax income of $200,000:($285,000 + $312,500)/0.38 = $1,572,368
e. Sales $1,572,368Variable costs (62% of sales) (974,868 ) Contribution margin (38% of sales) 597,500Fixed costs (285,000 ) Net income before taxes 312,500Income taxes (36%) (112,500 ) Net income after taxes $ 200,000*
15-10 Financial & Managerial Accounting for MBAs, 3rd Edition
E15-20
a. Fixed costs $12,500,000Contribution [($8,000 $1,000) 1,500] $10,500,000Endowments and grants 250,000 (10,750,000 ) Required from other sources $ 1,750,000
Paper Mate should use the labor-intensive method if sales are less than 290,000 units and use the capital-extensive method if sales are above 290,000 units.
c. 1. Operating leverage is a measure of the responsiveness of income to changes in sales. The higher a firm's operating leverage, the more sensitive are its profits to changes in sales volume. It is also an indication of an organization's cost structure. The higher the portion of an organization's fixed costs (in comparison with variable costs), the higher its operating leverage.
2. Capital- Labor-
Intensive IntensiveUnit contribution margin $ 14.00 $ 8.00Unit sales volume x 250,000 x 250,000Contribution margin 3,500,000 2,000,000Fixed costs (2,940,000) (1,200,000)Net income $ 560,000 $ 800,000
Contribution Income StatementFor the Year Ended December 31, 2012
Sales (45,000 $90) $4,050,000Variable costs (45,000 $80) (3,600,000 ) Contribution margin 450,000Fixed costs 275,000 ) Net income $ 175,000
b. Operating leverage = Contribution margin/Net income= $450,000/$175,000= 2.57
c. Percentage change in profits = % decrease in sales x Operating leverage= 10 x 2.57= 25.7 percent decrease
Profits should decrease by 25.7 percent to $130,025, computed as: [$175,000 ($175,000 x 0.257)].
d. Contribution margin [45,000 ($90 $77.50)] $ 562,500Fixed costs (375,000 ) Net income $ 187,500
Operating leverage ($562,500/$187,500) 3
The acquisition of the berry-picking machines will reduce variable costs, thereby increasing the contribution margin. It will also increase fixed costs, thereby increasing the difference between the contribution margin and net income. The net effect would be an increase in operating leverage.
15-14 Financial & Managerial Accounting for MBAs, 3rd Edition
E15-23
a. Unit Sales Selling MixProduct Price (units) WeightStandard $ 50 x 1,750/2,500 $35Multiform 125 x 500/2,500 25Complex 250 x 250/2,500 25Average unit selling price $85
Unit Sales Contribution Mix Product Margin (units)* Weight Standard $ 20 x 1,750/2,500 $14Multiform 50 x 500/2,500 10Complex 100 x 250/2,500 10Average unit contribution margin $34
Contribution margin ratio = $34/$85 = 0.40
Break-even sales volume = $45,000/0.40 = $112,500
b. Actual sales volume = 2,500 $85 = $212,500Break-even sales volume 112,500 Margin of safety $100,000
Required population = 440 customers / 0.04 customers in population = 11,000
E15-27 A
a. Minimum order size to break even on order = $200 = $2,500(0.10 – 0.02)
b. Annual sales to break-even on average customer = ($200 x 4 orders) + $1,000 = $22,500
(0.10 – 0.02)
c. Average order size = $22,500/4 = $5,625
d. Order-level costs ($200 4 orders 100 customers) $ 80,000Customer-level costs ($1,000 100 customers) 100,000Facility-level costs 60,000Total costs $ 240,000Contribution margin ratio 0.08 Minimum annual sales to break even $3,000,000
e. Average order size = $3,000,000/(4 orders 100 customers) = $7,500
f. Part (a) considers only order-level costs while part (c) also considers customer-level costs, and part (e) adds facility-level costs. In order for a company to break even on an order, it need only cover order-level costs. To break even on a customer, the company must cover order-level and customer-level costs. Finally, to achieve true break-even, all costs must be covered.
15-18 Financial & Managerial Accounting for MBAs, 3rd Edition
PROBLEMS
P15-28
a. Unit contribution margin: $35 $25 = $10
Total contribution (20,000 $10) $200,000Fixed costs 110,000 Net income before taxes 90,000Net income after taxes 54,000 Income taxes 36,000Net income before taxes $90,000 Tax rate 0.40
b. Required before-tax income = $90,000/(1 0.40)= $150,000
Volume required to provide an after-tax income of $90,000:($110,000 + $150,000)/$10 = 26,000 units
c. Contribution marginCurrent $10.00Impact of reduction in variable costs 2 .50 New $12 .50
Fixed costs:Current $110,000Impact of increase in fixed costs 20,000New $130,000
Volume required to provide an after-tax income of $90,000:($130,000 + $150,000)/$12.50 = 22,400 units
The reduction in variable costs was more than enough to offset the increase in fixed costs. Consequently, the volume required to achieve an after-tax profit of $90,000 declined from 26,000 units to 22,400 units.
d. Requirements (a) through (c) assume that taxable income and accounting income are equal and that the tax rate is constant.
Revenues per patient-day $300Variable costs per patient-day (100)*Contribution margin per patient-day $200
*$6,000,000 total 2011 revenues/$300 revenue per patient-day equals 20,000 patient-days for 2011.
$2,000,000 total 2011 variable costs / 20,000 patient-days = $100 variable costs per patient-day
Break-even point in patient-days = $3,380,000/$200= 16,900 patient-days
b.Pediatrics
Schedule of Change in Earnings from Rental of 20 Additional BedsFor the Year Ending June 30, 2012
Increase in revenues (20 beds 90 days $300/ day) $ 540,000Increase in expenses:
Fixed charges by Melford Hospital:Annual charge per bed ($2,900,000/60) $ 48,333Number of additional beds 20 Total increase in fixed charges 966,660
Variable charges by Melford Hospital($100/patient-day 90 days 20 beds) 180,000 (1,146,660)
Net decrease in earnings $ (606,660)
(Note that the break-even on the additional 20 beds is 4,834 bed days ($966,660/$200), or 242 days for each of the 20 additional beds. This is an increase of 3,034 bed days (or 152 days for each bed) above the estimated demand of 90 days for each of the 20 beds.)
*Because only one product will be produced the product-level costs and the facility-level costs are combined: $130,000 + $150,000 for Sure Foot and $50,000 + $150,000 for Trail Runner.
b. Required sales for identical before-tax profit:
d. Without further analysis it is apparent that at a volume of 13,000 pairs the Trail Runner is preferred. Trail Runner requires fewer sales to achieve a $30,000 after-tax profit and the profits of both products are not identical until a total of 16,000 pairs of either product are sold. This answer can also be demonstrated analytically:
15-24 Financial & Managerial Accounting for MBAs, 3rd Edition
P15-33 (concluded)
e. Required Sure Foot variable costs for identical profit at 13,000 pairs:
Because before-tax and after-tax profits will be the same for either product, it is simpler to develop a solution based on identical before-tax profits with X representing the required Sure Foot variable costs per pair.
d. The equations assume linear cost behavior, stable prices, and a stable cost structure.
Netflix reported a 2009 operating profit of $191,939,000, $13,406,500 more than the amount predicted using equations based on 2007 and 2008 data, an error of approximately 7 percent. This under-prediction likely occurred because of changes in Netflix’s cost structure, higher fixed costs and lower variable costs, as the number of Netflix customers increase with greater use of streaming video. See the opening vignette for Chapter 3.
15-26 Financial & Managerial Accounting for MBAs, 3rd Edition
P15-35 A
a. Annual break-even point in sales dollars:Break-even point = $360,000/(1 0.75 0.05) = $1,800,000
b. Annual break-even point in units:Break-even point = $360,000/{$120 [$120(0.75 + 0.05)]} = 15,000 units(or $1,800,000/$120 = 15,000)
c. On new books the contribution to other costs is 25 percent (1.00 less 0.75 to the publisher) of the suggested retail price. On used books the contribution to other costs is 50 percent of the suggested retail price (0.75 less 0.25 cost of the book). Shifting towards more used books and fewer new books will increase bookstore profitability with the same unit sales.
d. Publisher project break-even point:Note: Solution is in terms of wholesale price to bookstore, not retail price to final buyer.
Project break-even point = $325,000/(1 0.20 0.15) = $500,000
e. Profitability analysis of sales of 8,000 new books:1. Bookstore’s unit-level contribution
Contribution margin ratio = $400,000/$1,050,000 = 0.38095
Break-even point = $240,000/0.38095 = $630,004
b. Unit contribution margin and break-even point:
Average unit contribution margin = $400,000/2,500 = $160
Unit break-even point = $240,000/$160 = 1,500 units
c. The current average unit contribution margin is $160.
Current unit contribution margin of individual products:Cozy Kitchen $100,000/1,000 units $100All-House $300,000/1,500 units $200
Shifting the mix to 80:20 will change the average unit contribution margin:
($100 0.80) + ($200 0.20) = $120
Contribution with proposed plan = 3,000 units $120 = $360,000
The current contribution margin is $400,000. The contribution margin with a shift in the mix, even with a 500-unit sales increase, is only $360,000. Hence, profits will decrease if the projected shift occurs. In the absence of capacity constraints, sales reps should emphasize increased sales of the product with the higher unit contribution margin.
Long-run break-even point = $28,760/0.525 = $54,781
b. Answers to requirement (b) will vary. Two possible recommendations are as follows:
Do not introduce the sandwich. There is too much risk. Introducing the sandwich causes a short-run loss, a permanent decline in the contribution ratio, and an increase in the break-even point. If the predicted increase in sales does not occur, the company will be in serious difficulty. Also, it is unclear what the time period is for the short run.
Introduce the sandwich. While there is a short-run loss, a permanent decline in the contribution ratio, and an increase in the break-even point, these negatives are more than offset by the long-run increase in volume. Introducing the sandwich is taking the business to the next level of size and profitability.
15-32 Financial & Managerial Accounting for MBAs, 3rd Edition
MANAGEMENT APPLICATIONS
MA15-39
It is important for senior management to set the ethical climate for the organization. In this case, perhaps out of a true concern for employees, or perhaps out of a desire for a “big bonus,” the plant manager is proposing an unethical (illegal?) speedup of the assembly line.
We do not know if New City Automotive has a code of ethics. If it does, Art Conroy should refer to it for guidance. Because Art is a management accountant, he should also refer to the Standards of Ethical Conduct for Management Accountants, published by the Institute of Management Accountants.
Art has followed these standards so far. Faced with an issue that concerned him, he went to the appropriate company official. At this point, he should follow the procedures for resolution of ethical conflict. In particular, he needs to further discuss the situation with Paula, expressing his concern about what may happen if the speedup is detected (strikes, legal action, mistrust, plant closure) and what he believes are the advantages of facing the situation directly.
He might recommend a general meeting with all employees and suggest that in this meeting financial information be shared. Employees should be made aware of the likelihood of closing the plant if financial performance is not improved. They should also be shown how a small increase in productivity will make a big difference in financial performance. They might even be invited to offer their own suggestions for increasing productivity. They should be treated as team members, rather than as adversaries. Finally Art might conclude his comments by noting how the careers of all plant employees, including management, will be adversely affected if the speedup is detected or if productivity is not improved. In this case, including employees in the decision is less risky than the alternative.
a. Using a unit-level analysis, develop a graph with two lines, (1) representing Homestead Telephone’s cost structure in the 1940s and (2) representing Homestead Telephone’s cost structure in the late 1990s. Be sure to label the axes and lines.
b. With sales revenue as the independent variable, the likely impact of the changed cost structure on Homestead Telephone’s:
Contribution margin percent: Because variable costs decrease, the contribution margin percent will INCREASE
Break-even point With an increase in fixed costs and a decrease in variable costs, the impact on the break-even point CANNOT BE DETERMINED. If there is a change, the BEP will likely increase because of downward pressure on prices.
c. The shift from human operators to mechanical devices increased Homestead’s operating leverage, which means that if sales increase, the percentage increase in before-tax profits will exceed the percentage increase in sales. Conversely, if sales decrease, the percentage decrease in profits will exceed the percentage decrease in sales.
15-34 Financial & Managerial Accounting for MBAs, 3rd Edition
MA15-41
a. To determine the break-even point, you must first find the contribution margin as a percent of sales and the fixed costs per period. Because there are no taxes at the break-even point, our analysis is based on before-tax information:
Variable costs as a percent of sales =
Change in total costs = $4,857,900 $4,430,000 = 0.823Change in Sales $5,520,000 $5,000,000
d. The method used for determining the cost equation for Regional Distribution with the available data was the high-low method, which used only two data points. There was not sufficient information to determine whether those two data points were representative of the larger population of data points. Also, it was not possible to determine the possible effects of inflation on the data from 2010 to 2011. Also, if Regional Distribution has multiple products and or departments that have varying cost structures, using aggregate data for the company as a whole to estimate its costs and break-even point may not produce accurate results. The cost-volume-profit model works best when there is a single cost driver and all costs are either variable or fixed with respect to that cost driver. For that reason, the model is generally more effective for analyzing smaller segments of a business, such as a particular product line.