# Cost-volume-profit analysis and the contribution margin approach to decision-making

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```					Chapter 22 - Cost-volume-profit analysis and the contribution margin approach to decision-making
CHAPTER OVERVIEW
In Chapter 21 you learned about a particular type of management accounting concerned with manufacturing businesses where direct materials are converted into finished goods. We now turn our attention to a closer examination of costs and how costs change relative to changes in output. The interaction of cost and volume results in changes in profits (or losses). The learning objectives for this chapter are to: 1. 2. 3. 4. 5. 6. 7. 8. Identify different cost behaviour patterns. Use a contribution margin statement of financial performance to make business decisions. Calculate break-even sales. Calculate the sales level needed to earn a target net profit. Graph a set of cost-volume-profit relationships. Calculate a margin of safety. Use the sales mix in CVP analysis. Calculate profit using variable costing and absorption costing.

CHAPTER REVIEW Objective 1 - Identify different cost behaviour patterns.
Cost behaviour is the way that costs change in response to changes in business activity. A cost driver is any factor that affects costs. The three patterns of cost behaviour are variable, fixed, and mixed. Variable costs change in direct proportion to changes in volume or level of activity. Examples of variable costs include direct materials, sales commissions, and delivery expense. Suppose CDs have a cost of \$6 per disk when purchased for resale. If a retailer sells 1,000 CDs, cost of goods sold will be \$6,000. However, if 2,000 CDs are sold, cost of goods sold will be \$12,000. Thus, the more CDs the retailer sells, the higher the cost of goods sold will be since the \$6 variable cost per unit is constant. Fixed costs do not change as volume changes. Examples of fixed costs include expenses such as rent and depreciation. Suppose the rent for a store is \$5,000 per month. The store owner will pay \$5,000 per month whether sales increase, decrease, or remain the same. Mixed costs (also called semivariable costs) are part variable and part fixed. The monthly telephone bill, for example, is based both on fixed line rental cost and a service cost. The monthly line charge is a fixed cost, while the amount for calls made is a variable cost. Therefore, the total telephone bill is a mixed cost. Study the graphs in your text illustrating cost behaviour patterns (Exhibits 22-1, 22-2, and 22-3). The variable cost graph begins at the origin (zero volume, zero cost). Variable cost increases in a straight line, the slope of which equals the variable cost per unit. As the slope of the line gets steeper, the more the variable cost per unit increases. The fixed cost graph is a horizontal line that intersects the cost (vertical) axis at the fixed cost level. The mixed cost graph intersects the cost axis at the level of the fixed cost component, and its slope equals the variable cost per unit.

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When budgeting costs, companies use the relevant range concept. Relevant range is the band of activity or volume of operations within which relationships between costs and volume can be predicted. These relationships will be different in other ranges. See Exhibit 22-4 in your text. The conventional statement of financial performance focuses on the perspective of external users of financial statements. It has the format: Sales Cost of Goods Sold Gross Profit (Margin) Operating Expenses Net Profit

= =

Note that the conventional statement of financial performance classifies expenses according to the value chain, such as cost of goods sold or operating expenses. The contribution margin statement of financial performance focuses on the contribution margin, the excess of sales over variable expenses. It classifies expenses according to cost behaviour, which will be either variable or fixed. It has the format: Sales Variable Expenses Contribution Margin Fixed Expenses Net Profit

= =

Exhibit 22-5 presents the two formats. Note the end result ‘net profits’ is the same in both.

Objective 2 - Use a contribution margin statement of financial performance to make business decisions.
The contribution margin statement of financial performance is a useful management tool. Once fixed expenses are covered, the balance of the contribution margin ‘contributes’ to profits. Since fixed expenses remain constant, when the contribution margin changes, profits will change by the same amount. Remember that, in general, variable expenses will change proportionately with sales. Thus, if sales increase by 10%, variable expenses will increase by 10%, and the contribution margin will increase by 10%. Using the contribution margin statement of financial performance, it is possible to calculate exactly how a change in sales will affect profit. Similar analysis using the conventional statement of financial performance is not possible. The following assumptions underlie CVP analysis: 1. 2. 3. 4. 5. 6. 7. Expenses can be classified as either variable or fixed. Cost-volume-profit relationships are linear over a wide range of production and sales. Sales prices, unit variable costs, and total fixed expenses are constant. Volume is the only cost driver. The relevant range of volume is specified. Inventory levels will be unchanged. The sales mix of products will not change during the period.

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Objective 3 - Calculate break-even sales.
Cost-volume-profit analysis is often called break-even analysis. The break-even point is the sales level at which net profits or losses are zero. If sales are below the break-even point, the result is a loss. If sales are above the break-even point, the result is a profit. Decision makers use cost-volume-profit analysis to answer questions such as, ‘How much do we need to sell to break even?’ or ‘If our sales are some specific amount, what will our profit be?’ Two approaches used in cost-volume-profit (or CVP) analysis are the equation approach and the contribution margin approach. With either approach, start by separating total expenses into variable expenses and fixed expenses. The equation approach is: Sales - Variable Expenses - Fixed Expenses = Net Profit Net profit is zero at break-even. The equation shows how many units must be sold (and the total dollar amount of the sales) in order to break even. The contribution margin approach is: Contribution Margin = Sales - Variable Costs The contribution margin receives its name because it contributes to the payment of fixed costs and profits. The contribution margin may be expressed on a per-unit basis, or as a percentage or ratio: Contribution Margin Per Unit = Sales Price Per Unit - Variable Expense Per Unit Contribution Margin Percentage or Ratio = Contribution Margin Selling Price Break-even sales in units is computed by dividing fixed expenses by the contribution margin per unit: Break-even Sales in Units = Fixed Expenses in Units Contribution Margin Per Unit

Break-even sales in dollars is calculated by dividing fixed expenses by the contribution margin ratio: Break-even Sales in Dollars = Fixed Expenses Contribution Margin Ratio

Review the examples in the text so that you know what will happen to the break-even point if a fixed cost is changed, if the sale price is changed, or if the variable cost per unit is changed. If fixed costs or variable cost increase, break-even increases. If the sale price increases, break-even decreases.

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Objective 4 - Calculate the sales level needed to earn a target net profit.
The profit that a business wishes to earn is called the target profit. Target Sales In Units = Fixed Expenses + Target Profit Contribution Margin Per Unit Fixed Expenses + Target Profit Contribution Margin Ratio

Target Sales In Dollars

=

Notice that the only difference between calculating break-even sales and target sales is that with target sales, the target profit amount is added to fixed expenses.

Objective 5 - Graph a set of cost-volume-profit relationships.
Often, a business is interested in knowing the amount of operating profit or operating loss to expect at various levels of sales. One convenient way to provide this information is to prepare a cost-volumeprofit graph. In order to familiarise yourself with the components of the CVP graph, study these steps and review Exhibit 22-7 in the textbook:    Step l: Draw a sales line from the origin through a preselected sales volume. Step 2: Draw the fixed expense line. Step 3: Draw the total expense line by computing the variable expenses at your preselected sales volume (Step 1), then plot them beginning at your fixed expense line. Step 4: Identify the break-even point (where sales and total expenses intersect). Step 5: Identify the net profit and net loss areas.

Objective 6 - Calculate a margin of safety.
The margin of safety is the excess of expected or actual sales over break-even sales. It tells a business how much sales can drop before a loss is incurred. The margin of safety may be calculated in terms of either dollars or units: Margin of Safety = Expected Sales - Break-even Sales

Objective 7 - Use the sales mix in CVP analysis.
One of the basic assumptions underlying CVP analysis is that the sales mix, the combination of products that make up total sales, does not change. Break-even questions involving multiple products can be answered using either the contribution margin approach or the equation approach. Regardless of approach, you begin by establishing the sales mix (for instance 3 units of one product for every 2 of a second product, or 3:2). The sales mix is then 5 units, the total of 3 and 2. Determine 4 Chapter 22

the contribution margin for this mix, then divide the result into total fixed expenses. The result is break-even for the ‘mix’ (3 of one product and 2 of a second). Multiply the break-even by each component in the mix for break-even in sales units.

Objective 8 - Calculate profit using variable costing and absorption costing.
Absorption costing assigns both variable and fixed manufacturing costs to products (the term refers to the products absorbing the costs). Absorption costing has been assumed in the financial statements presented throughout this discussion because it conforms to GAAP requirements. However, there is an alternative approach called variable costing, although it can be used only for internal purposes. Variable costing assigns variable manufacturing costs to products, but fixed manufacturing costs (property taxes on the factory, depreciation on the building, etc.) are treated as period costs and reported on the statement of financial performance when incurred. The argument for the variable costing approach is that fixed manufacturing costs will be incurred regardless of production levels and should therefore be treated as period costs. Carefully review Exhibit 22-9 in your text. Notice that the only difference between these two approaches is the treatment of fixed manufacturing costs. However, this difference will affect net profits, as illustrated in Exhibit 22-10 in your text. Because absorption costing assigns fixed manufacturing costs to inventory, these costs will not appear on the statement of financial performance until the units are actually sold, whereas under variable costing all fixed manufacturing costs are included on the statement of financial performance when they are incurred. The general rule is that when inventories are increasing, absorption costing profits will be higher than variable costing profits. The reverse is true when inventories are declining. Study Tip: Review the Decision Guidelines (p. 980) comparing absorption and variable costing in your textbook. Remember, variable costing is only used internally - external reports and statements use absorption costing.

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TEST YOURSELF
All the self-testing materials in this chapter focus on information and procedures that your instructor is likely to test in quizzes and examinations.

I. Matching
_____ 1. _____ 2. _____ 3. _____ 4. _____ 5. _____ 6. _____ 7.

Match each numbered term with its lettered definition. _____ 8. _____ 9. _____ 10. _____ 11. _____ 12. _____ 13. _____ 14. margin of safety relevant range variable costing sales mix CVP analysis absorption costing period costs

cost behaviour variable cost fixed cost mixed cost break-even point contribution margin target profits

A. B. C. D. E. F. G. H. I. J. K. L. M. N.

a costing method that assigns all manufacturing costs to products a costing method that assigns only variable manufacturing costs to products the description of how costs change in response to a shift in the volume of business activity the excess of sales price over variable expenses a band of activity or volume in which actual operations are likely to occur a cost that does not change in total as volume changes the excess of expected (or actual) sales over break-even sales a cost that is part variable and part fixed a cost that changes in total in direct proportion to changes in volume or activity the desired profit a business wishes to earn costs reported on the statement of financial performance as incurred the combination of products that make up total sales the amount of unit sales or dollar sales at which revenues equal expenses a part of the budgeting system that helps managers predict the outcome of their decisions by analysing relationships between costs, volume, and profit or loss.

II. Multiple Choice

Use the following information for questions 1 to 4: CD Cales sells blank CDs. Last year CD Cales sold 5,500 cases at \$26 per case. The variable cost per case was \$14.00 and fixed costs amounted to \$38,400. 1. The break-even point in cases of CD’s was: A. 1,200 B. 2,000 C. 3,200 D. 5,500

2. The break-even point in sales dollars was: A. \$66,000 B. \$83,200 C. \$24,000 D. \$14,400

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3. The margin of safety in dollars was: A. \$59,800 B. \$48,000 C. \$51,000 D. \$0

4. If CD Cales wished to earn a net profit of \$34,800, how many cases of CDs would have to be sold? A. 3,600 B. 4,400 C. 5,500 D. 6,100

5. Dividing break-even sales dollars by the unit selling price results in the: A. variable cost per unit B. break-even point in dollars C. break-even point in units D. variable cost ratio

6. Which of the following will decrease the break-even point? A. decreasing fixed costs B. increasing fixed costs C. increasing variable costs per unit D. decreasing selling price

7. Which of the following will increase the break-even point? A. decreasing fixed costs B. increasing fixed costs C. decreasing variable cost per unit D. decreasing selling price

Use the following graph to answer Questions 8 to 10: B C G E

F H

I D

A 8. Line D must be: A. the sales line B. total expense line C. fixed expense line D. cannot be determined

9. If E is the total expense line then I must be: A. net profit area B. variable expense area C. net loss area D. cannot be determined

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10. If C is the sales line and E is the total expense line then F must be: A. break-even point B. total units C. total dollars D. cannot be determined

III. Completion Complete each of the following.
1. Variable costing reports only ____________________ costs as __________________ costs on the statement of financial performance. 2. A convenient way to determine net profit or loss at various levels of sales is to prepare a ________________________________. 3. _______________________ and _______________________ change proportionately with sales. are examples of costs that

4. The__________________________ is the combination of products that make up total sales.

5. Two approaches used in CVP analysis are the _______________________ approach and the ________________________ approach. 6. _______________________________tells a decision-maker how much sales can drop before an operating loss is incurred.

For questions 7 to 10, complete the sentence with increase, decrease, or not affect. 7. An increase in direct material cost will _______________________ the contribution margin. 8. An increase in direct labour cost will ____________________________ the break-even point. 9. A decrease in direct materials costs will ___________________________the break-even point. 10. An increase in fixed plant insurance will ___________________________the break-even point.

11. Absorption costing reports all ___________________ costs as ___________________ costs on the statement of financial performance. 12. The __________________________ is equal to the selling price per unit minus the variable expenses per unit.

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IV. Daily Exercises
1. Classify each of the following costs as fixed, variable, or mixed (assume a relevant range and current period). Cost a. b. c. d. e. f. g. h. i. j. land taxes direct materials depreciation on office equipment advertising expense office salaries expense direct labour manufacturing overhead rent expense insurance expense supplies expense Classification

2. Bola’s Basketry has fixed costs of \$420,000. Variable costs are 20% of sales. Assuming each basket sells for \$10, what is the break-even point in unit sales?

3. Manuel’s Manufacturing sells a product for \$8 per unit. If the variable cost is \$5 per unit, and break-even is 48,000 units, what are Manuel’s fixed costs?

4. If variable costs are 60% of sales and fixed costs are \$230,000 what is the break-even point in sales dollars?

5. Gayle’s Greetings sells boxes of greeting cards and packages of gift-wrap. Boxes sell for \$5.00 and packages sell for \$2.20. Variable costs are \$2.50 for boxes and \$1.00 for packages. Gayle expects to sell 1,500 boxes of greeting cards and 750 packages of gift-wraps. Fixed costs are \$2,350. What is the break-even point?

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V. Exercises
1. A monthly statement of financial performance for Bijan’s Batburgers appears as follows: Sales Cost of Goods Sold Gross Profit Operating Expenses: Marketing Expense General Expense Net Profit \$280,000 120,000 160,000 \$35,000 75,000

110,000 \$ 50,000

Cost of Goods Sold is a variable expense. Marketing expense is 70% variable and 30% fixed. General Expense is half fixed and half variable. In the space below, present a contribution margin statement of financial performance for the month.

2. Review the information in Exercise 1 above, and calculate the following: a. contribution margin ratio

b. break-even point in sales

c. If the frozen burritos sell for \$2 per package, what is the break-even point in units?

d. By what amount would net profit decrease if sales dropped by 20%?

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3. Using the form below and the information in Exercise 1 above, graph Bijan’s Burritos total expense (both fixed and variable) and sales, showing clearly the break-even point calculated in Exercise 2 above.
300,000 280,000 240,000

Sales

200,000 160,000 120,000 80,000 40,000 20,000 60,000 100,000 140,000 180,000

Units

4. A manufacturer of rubber exercise balls provides the following cost information: Variable cost per ball Fixed monthly expenses Selling price per ball \$ 9.50 \$15,000 \$ 20.00

a. What is the manufacturer’s contribution margin per ball and contribution margin ratio?

b. What is the manufacturer’s break-even point in units and dollars?

c. Prove the accuracy of your answers in (b) above by presenting a statement of financial performance at break-even.

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d. Assuming the manufacturer’s targeted net profit is \$12,000 per month, and the company is subject to a 40% tax rate, calculate the sales necessary to achieve the targeted net profit (after tax).

5. Review the information in Exercise 4 above, assuming the manufacturer achieves the \$12,000 targeted net profit, after tax. The owner is considering an advertising campaign to increase sales. The cost of the ads would be \$5,000 per month. By what amount, expressed in units and dollars, would sales need to increase to justify the advertising expenditure?

VI. Beyond the Numbers
Review Daily Exercise 1. How would your answers change if output remains within the relevant range but the costs listed are classified over a long period? Cost a. b. c. d. e. f. g. h. i. j. land taxes direct materials depreciation on office equipment advertising expense office salaries expense direct labour manufacturing overhead rent expense insurance expense supplies expense Classification

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VII. Demonstration Problems
Demonstration Problem #1 The Ganji Game Company is planning to introduce a new video game. The relevant range of output is between 10,000 and 40,000 units. Within this range, fixed expenses are estimated to be \$325,000 and variable expenses are estimated at 35% of the \$30 selling price. Required: 1. Using the contribution margin approach, calculate break-even sales in units and in dollars. 2. If targeted net profit (pre-tax) is \$120,000, how many games must be sold? 3. Prepare a graph showing profit and loss areas from 0 to 40,000 games, assuming a selling price of \$30. Identify the break-even sales level and the sales level needed to earn net profit of \$120,000. 4. If the company increases the selling price to \$36, how many games must be sold to earn net profit of \$60,000?

Requirement 1 (Break-even sales in units and dollars)

Requirement 2 (Targeted profit)

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Requirement 3 (Graph)

\$1,200,000

\$900,000

\$600,000

\$300,000

0

10

20 Units (in thousands)

30

40

Requirement 4 (Effect of change in selling price)

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Demonstration Problem #2 Bega Deluxe Ice Cream Company manufactures top of the line premium ice cream. The product, in a variety of styles, is available in one, two and four litres. Past experience has shown that 4 two litres are sold for each four litres and 5 one litres are sold for two litres. Selling prices and variable costs for the product line are as follows: One Litre \$1.50 \$0.60 Two Litres \$2.75 \$1.15 Four Litres \$5.25 \$2.25

Selling price Variable cost

Fixed costs average \$900,000 per month. Of this amount, approximately 2/3 is manufacturing overhead and 1/3 is operating expense. Variable costs consist entirely of direct materials (ingredients and packaging) and direct labour. Part A 1. Determine the sales mix. 2. Calculate break-even in units and sales. 3. Assuming the company pays taxes at the rate of 40% of pre-tax profits, calculate the sales needed to earn after-tax profits of \$1,200,000 annually. Part B The company is considering an increase in price and, at the same time, eliminating the manufacture of the four litre size. Research indicates the elimination of the four litre would result in a 25% increase in two litre sales but have no impact on one litre sales. Assuming the decision is made to eliminate the four litre and increase the selling price of one and two litre to \$1.75 and \$3.00 respectively, answer the following: 1. Which variable and fixed costs are likely to change as a result of this decision? 2. What is the new sales mix? 3. Assuming variable and fixed costs remain the same, what is the new break-even point in units and sales? 4. Assuming variable costs remain the same but the elimination of four litre results in a one-time restructuring charge of \$750,000 and a 20% reduction in fixed manufacturing costs, what is the effect on net profits and profits from ordinary activities? Part A 1. Determine the sales mix.

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2. Calculate break-even in units and sales.

3. Targeted profit

Part B 1. Effects on variable and fixed costs

2. New sales mix

3. New break-even point in units and dollars

4. Effect on net profits and profits from ordinary activities

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SOLUTIONS I. Matching
1. C 2. I 3. F 4. H 5. M 6. D 7. J 8. G 9. E 10. B 11. L 12. N 13. A 14. K

II. Multiple Choice
1. 2. 3. 4. 5. C B A D C \$38,400 / (\$26.00 - \$14.00) = 3,200 \$26  3,200= \$83,200 (5,500 boxes - 3,200 boxes)  \$26.00 = \$59,800 (\$34,800 + \$38,400) / \$12 = 6,100 BE\$ = Break-even sales dollars. BEu = Break-even in units. \$Pu = Unit selling price. BE\$ = BEu  \$Pu BE\$ / \$Pu = Beu BE\$ = Break-even sales dollars. BEu = Break-even in units. \$Pu = Unit selling price. FC = Fixed Cost VCu = Variable cost per unit. Recall that BEu = FC / (\$Pu - VCu) Of the answers listed, only A, ‘decreasing fixed costs’, will decrease the break-even point. D Refer to 6 above. Note that answer D, ‘decreasing selling price’, will decrease the or contribution margin and increase the break-even point. B Study Tip: If you have difficulty with 5 to 7, consider the formula for the break-even point in units: 7. Fixed Expenses / Contribution Margin Per Unit = Break-even in Units If the numerator increases, or the denominator decreases, the break-even point increases. If the numerator decreases, or the denominator increases, the break-even point decreases. 8. 9. C B The sales and total expense line slope upward; only the fixed expense line is flat. The variable expense area is the difference between the total expense line and the fixed expense line. Total units and total dollars are the A and B axis. F is the break-even point where sales intersect total expenses.

6.

A

10.

A

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III. Completion
1. 2. 3. 4. 5. 6. 7. 8. variable, product (order important) cost-volume-profit graph Cost of goods sold, selling commission (other answers may be acceptable) sales mix equation, contribution margin The margin of safety decrease (An increase in direct materials is an increase in the variable cost per unit. This decreases the contribution margin.) increase (An increase in direct labour cost is an increase in the variable cost per unit. This decreases the contribution margin. As the contribution margin decreases, the break-even point increases.) decrease (A decrease in direct materials cost is a decrease in variable cost per unit. This increases the contribution margin. As the contribution margin increases, the break-even point decreases. Contrast with #8.) increase (An increase in plant insurance is an increase in fixed costs. An increase in fixed costs increases the break-even point.) manufacturing, product (order important) contribution margin per unit

9.

10. 11. 12.

IV. Daily Exercises
1. Cost a. b. c. d. e. f. g. land taxes direct materials depreciation on office equipment advertising expense office salaries expense direct labour manufacturing overhead Classification fixed variable fixed fixed fixed variable mixed (because some are fixed, such as rent, depreciation, etc., whereas others are variable - indirect materials, electricity, for instance) fixed fixed variable

h. rent expense i. insurance expense j. supplies expense

2. If VC = 20% of sales, then CM = 80% of sales, or \$8 per unit. Fixed expenses Contribution margin \$420,000 \$8 = Break-even point

=

52,500 units

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3. Fixed expenses Contribution margin FE \$3.00 or 48,000  \$3 FE = \$144,000 = Break-even point

=

48,000

4. If VC = 60% of sales, then CM = 40% of sales. Fixed costs Contribution margin ratio \$230,000 40% = Break-even in sales

=

\$575,000

5. Boxes greeting cards Sales price per unit Variable expense per unit Contribution margin per unit Estimated sales in units Estimated contribution margin per unit Weighted-average contribution margin per unit (\$4,620 / 2,250) Break-even sales in units = \$5.00 \$2.50 \$2.50  1,500 \$3,750 + Packages gift wrap Total

\$2.20 \$1.00 \$1.20  750 \$900 =

2,250 \$4,650

\$2.07 Fixed expenses Weighted-average contribution margin = \$2,350 \$2.07 = 1,136 (rounded)

Break-even sales of boxes of greeting cards = 1,136  (1,500 / 2,250) = 757 boxes Break-even sales of packages of gift wraps = 1,136  (750 / 2,250) = 379 packages

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V. Exercises
1. Sales Less: Variable Expenses Cost of Goods Sold Marketing Expense General Expense Contribution Margin Less: Fixed Expenses Marketing Expense General Expense Net Profit \$280,000 \$120,000 24,500 37,500

182,000 98,000

10,500 37,500

48,000 \$ 50,000

2. a. contribution margin ratio = = = = = contribution margin / sales 100,500 / 280,000 = 35.9% (rounded) \$0 net profit fixed expense / contribution margin ratio \$45,500 / 35.9% = \$126,741

b. break-even point in sales

c. \$126,741 / \$2 each = 63,371 packages d. Sales [(\$280,000 - 20%(\$280,000)] Less: Variable Expenses Cost of Goods Sold Marketing Expense General Expense Contribution Margin Less: Fixed Expenses Net Profit \$224,000 \$96,000 19,600 28,000

143,600 80,400 45,500* \$ 34,900

Fixed expenses remain the same, regardless of sales level (assuming no change in the relevant range).

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3. 300,000 280,000 240,000 Sales (\$) 200,000 160,000 120,000 80,000 Fixed Expense 40,000 20,000 60,000 100,000 Units 140,000 180,000 Break-even Sales Variable Cost

4. a. contribution margin = = = = = = = = sales - variable costs \$20 - \$9.50 = \$10.50 contribution margin / sales \$10.50 / \$20.00 = 52.5% fixed expenses / contribution margin \$15,000 / \$10.50 = 1,428.5714 units fixed expenses / contribution margin ratio \$15,000 / 52.5% = \$28,571 (rounded)

contribution ratio

b. break-even (units)

break-even (sales)

c. Sales Less: Variable Costs (1,428.5714 units  \$9.50 ea) Contribution Margin Less: Fixed Expenses Net Profits \$28,571 13,571 (rounded) 15,000 (rounded) 15,000 -0-

d. Since the targeted net profit (\$12,000) is after-tax, first we have to calculate the pre-tax target profit. pre-tax profit targeted sales = = = = \$12,000 / 60% = \$20,000 (fixed expenses + net profit before tax) / contribution margin (\$15,000 + \$20,000) / 52.5% \$35,000 / 52.5% = \$66,667 (rounded)

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5. The advertising cost is a fixed expense so replace the \$15,000 amount with \$20,000, then solve as follows: target sales (dollars) target sales (units) = = (\$20,000 + \$20,000) / 52.5% = \$76,190 (rounded) (\$20,000 + \$20,000) / \$10.50 = 3,810 units

VI. Beyond the Numbers
a. b. c. d. e. f. g. h. i. j. fixed (while land taxes will probably rise over the long run, they still are a fixed cost) variable fixed mixed (the business will always advertise, but the amount will vary over the long run) fixed variable variable mixed possibly mixed (a portion fixed regardless of output with add-ons to reflect changes in output) variable

VII. Demonstration Problems
Demonstration Problem #1 Solved and Explained Requirement 1 To compute break-even in dollars and in units, we need to find the contribution margin per unit and the contribution margin ratio: Contribution Margin Per Unit Contribution Margin Percentage or Ratio = Sales Price Per Unit = Variable Cost Per Unit

Contribution Margin Sales Price Per Unit

Since the variable costs are 35% (0.35) of sales, the contribution margin per unit is: \$30 - (0.35  30) = \$30 - \$10.50 = \$19.50 The contribution margin ratio is: \$19.50 / 30 = 0.65

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The calculation of break-even sales in units is: Break-even Sales in Units = Fixed Expenses Contribution Margin Per Unit

\$325,000 / \$19.50 = 16,667 games The break-even point in units is 16,667 games. The calculation of break-even sales in dollars is: Break-even Sales in Dollars = Fixed Expenses Contribution Margin Percentage

\$325,000 / 0.65 = \$500,000 The break-even point in dollars is \$500,000. Requirement 2 The target net profit is given as \$120,000. The number of games that must be sold to earn a target profit of \$120,000 is: Target Sales in Units = Fixed Expenses + Target Net Profit Contribution Margin Per Unit

(\$325,000 + \$120,000) / \$19.50 = 22,821 games To achieve the target net profit of \$120,000, 22,821 games must be sold.

Requirement 3 (Graph) \$1,200,000 \$120,000 targeted profit (Requirement 2)

900,000 Break-even 600,000 325,000 300,000 operating loss 0 10 20 30 Games (in thousands) 40 operating profit Total Expenses Fixed Expenses

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Requirement 4 To find the solution to Requirement 4, you must first determine exactly what item changes. No change in fixed expenses is indicated, and the target net profit of \$120,000 remains the same. However, the selling price increases from \$30 to \$36, an increase of \$6. Since variable expenses are 35% of the selling price, the new variable costs is \$12.60 (35%  \$36). Since the selling price of the game has changed, we must find the new contribution margin per unit in order to use the formula for target sales in Requirement 2. The new contribution margin per unit is: \$36 - \$12.60 = \$23.40 Since the contribution margin per unit has increased to \$23.40, the new target sales in units will be: (\$325,000 + \$60,000) / \$23.40 = 16,453 games Target sales in units have decreased to 16,453 units. This is due to the increase in the selling price and the resulting increase in the contribution margin per unit.

Demonstration Problem #2 Solved and Explained Part A 1. Determine the sales mix. The sales mix is the combination of products that make up total sales. In this problem the sales mix is: one ‘four litre’ = 4 ‘two litre’ = 20 ‘one litre’ (5 one litre are sold for each two litre). Another way of expressing this relationship is to convert the ‘mix’ to percentages. Doing so results in 4% 16% 80% 100% 2. Calculate break-even in units and sales. To do this, we first calculate the weighted-average contribution margin, as follows: Four litre Selling price Less variable cost Contribution margin  weight Weighted-average contribution margin Break-even Sales in Units = \$5.25 2.25 3.00  1 \$3.00 Two litre \$2.75 1.15 1.60  4 \$6.40 One litre \$1.50 0.60 0.90  20 \$18.00 = = \$27.40 = 32,847 units Four litre (1/25) Two litre (4/25) One litre (20/25)

Fixed Expenses Weighted-average Contribution Margin

\$900,000 \$27.40

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Chapter 22

or Four litre 32,847  1 32,847 Two litre One litre 32,847  4 131,388 32,847  20 656,940

Now apply the unit selling price to each result to obtain break-even sales (or convert the weightedaverage contribution margin to a ratio). Four litre 32,847  \$5.25 Total break-even sales \$1,519,174 = \$172,447 + Two litre 131,388  \$2.75 \$361,317 + One litre 656,940  \$1.50 \$985,410

Remember, fixed expenses were given as monthly, so both of the above results are monthly.

3.

Targeted net profit: Sales = Fixed Expenses + Target Net Profit Contribution Margin Ratio \$10,800,000* + \$2,000,000 ** 59.3% (rounded)

Sales

=

*

If fixed expenses are \$900,000 monthly, then they are \$10,800,000 (\$900,000  12) annually. If the tax rate is 40%, the pre-tax profit is \$2,000,000 (\$1,200,000 / 0.6).

**

Sales needed to achieve after-tax profits of \$1,200,000 are \$21,585,160 annually or \$1,798,763 monthly.

Part B 1. In the short run, neither variable nor fixed costs will change. In the longer run, variable costs will not change either (the problem states all variable costs are prime costs). However, fixed costs should decrease as facilities (equipment, etc.) needed to produce the four litre are eliminated (see #4 below). 2. The new sales mix is 5 two litres to 20 one litre or 20% two litre and 80% one litre.

Cost-volume-profit analysis and the contribution margin approach to decision-making

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3. Two litre Selling price Less variable cost Contribution margin  weight Weighted-average contribution margin Fixed Expenses Contribution Margin Two litre 27,907  5 139,535 units In sales: Two litre 139,535  \$3.00 \$418,605 Again, these are monthly amounts. One litre 558,140  \$1.75 \$976,745 = \$3.00 1.15 1.85  5 \$9.25 One litre \$1.75 0.60 1.15  20 + \$23.00 = \$32.25

\$900,000 \$32.25

= 27,907 units

One litre 27,907  20 558,140 units

= \$1,395,350

4. Net profits would be affected by the \$750,000 restructuring charge, because, although it may be an extraordinary item, it is listed as part of net profits. The problem states that 2/3 of the fixed expenses are manufacturing overhead, or \$600,000 (2/3  \$900,000). A 20% reduction would, therefore, result in an increase in profits from ordinary activities of \$120,000 (20%  \$600,000). (This is more complex than you may have expected unless you remember back to Chapter 15.)

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Chapter 22

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Description: In Chapter 21 you learned about a particular type of management accounting concerned with manufacturing businesses where direct materials are converted into finished goods. We now turn our attention to a closer examination of costs and how costs change relative to changes in output. The interaction of cost and volume results in changes in profits (or losses). The learning objectives for this chapter are to: 1. Identify different cost behaviour patterns. 2. Use a contribution margin statement of financial performance to make business decisions. 3. Calculate break-even sales. 4. Calculate the sales level needed to earn a target net profit. 5. Graph a set of cost-volume-profit relationships. 6. Calculate a margin of safety. 7. Use the sales mix in CVP analysis. 8. Calculate profit using variable costing and absorption costing.