CHAPTER 3

PROFITABILITY ANALYSIS AND PLANNING

Learning Objectives

After completing this chapter, you should be able to:

1 Discuss the uses and limitations of traditional cost-volume-profit analysis.

2 Prepare and contrast contribution and functional income statements.

3 Use cost-volume-profit analysis to find a break-even point and for preliminary profit planning without and with income taxes.

4 Analyze the profitability of a multiple product firm with a constant sales mix.

5 Use operating leverage to analyze profit opportunities and the risk of loss.

6 Analyze the profitability of organizations that operate with unit and nonunit cost drivers.

Chapter Review Introduction. Effective profitability analysis and planning require a framework for determining the relationships among costs, activity levels, and income. These cost-volume-profit relationships can significantly impact a firm’s profitability when activity levels change. Although technology firms such as Inktomi, Microsoft, Cisco, Yahoo, Amazon, and Webvan have very different products, services, and management strategies, managers at each firm have seen their firm’s performance affected – in some cases severely affected -- by these cost-volume-profit relationships. This chapter examines the relationships of three key profitability variables: volume, prices, and costs.

1 Profitability Analysis with Unit Cost Drivers. Profitability analysis involves analyzing the relationships among revenues, costs, and the resulting profit. Managers often use this type of analysis in the economic evaluation of an existing or potential product or service.

a Two general approaches to profitability analysis are possible:

1 A unit level approach assumes that the only cost driver is the number of units sold or the level of sales dollars.

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1 A cost hierarchy approach incorporates both unit level and nonunit cost drivers.

b The traditional approach to profitability analysis -- cost-volume-profit analysis (CVP) -- examine the relationships among volume of activity, total costs, total revenues, and profit during a specific time period. This technique is helpful for short-term planning.

c Managers find CVP analysis helpful in the early stages of planning because it provides a framework for organizing relevant information.

d CVP relies on several assumptions that limit the applicability of this model.

1 All costs may be classified as fixed or variable with unit level activity drivers.

1 The total cost function is linear within the relevant range.

1 The total revenue function is linear within the relevant range.

1 The analysis is for a single-product firm or a multiple-product firm with a constant sales mix.

1 There is a single activity cost driver - sales volume (measured in units or dollars).

e The accuracy of CVP analysis decreases as the scope of operations being examined increases.

f CVP applies a profit formula in many different ways.

1 The basic profit formula is:

Profit = (Total revenues - Total costs)or

p = R - Y

where:p = ProfitR = Total revenuesY = Total costs

1 The revenue portion of this formula may be expanded since revenue is a function of sales volume and selling price. The cost component may also be expanded since total cost include both fixed costs and the variable costs of the units sold. Therefore:

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R = pXY = a + bX

where:p = Unit selling pricea = Fixed costsb = Unit variable costsX = Unit sales

1 Given these relationships, the basic profit formula may be expanded as follows:

p = pX - (a + bX)

g Possible variable costs include direct materials, direct labor, variable manufacturing overhead, and variable selling and administrative costs.

1 Direct materials include the primary raw materials converted into finished products.

1 Direct labor includes the wages earned by production employees for converting the raw materials into finished goods.

1 Variable manufacturing overhead includes all other variable costs of the conversion process. Items such as electricity or general supplies are usually considered variable manufacturing overhead costs.

1 Variable selling and administrative costs include variable costs not associated with the primary conversion process of the business. Sales commissions and outbound transportation costs are variable selling and administrative cost because they are variable in nature but not related to the primary conversion of raw materials to finished goods.

h Possible fixed costs include fixed manufacturing overhead and fixed selling and administrative costs.

1 Fixed manufacturing overhead costs include all fixed costs associated with the conversion process. Property taxes and insurance on factory buildings represent fixed manufacturing costs.

1 Fixed selling and administrative costs include all fixed costs outside the conversion process. Salaries of employees in

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a firm’s legal department represent fixed selling and administrative costs.

2 Contribution and Functional Income Statements. To provide detailed information for managers, an income statement may be presented in either a contribution or functional format.

a In a contribution income statement, costs are organized by their behavior: either variable or fixed.

1 The contribution income statement presents a modified income statement format for internal reporting purposes.

1 The contribution income statement follows the general format:

Sales revenue- Variable costs

= Contribution margin- Fixed costs

= Profit

1 The contribution margin equals the difference between total revenues and total variable costs. This margin goes toward covering fixed costs and providing profit

Contribution margin = (Total revenue - Variable costs)

b A functional income statement organizes costs according to a functional classification such as manufacturing or selling and administrative.

1 The functional income statement follows the general format:

Sales revenue- Cost of Goods Sold

= Gross margin- Other Expenses

= Profit

1 A functional income statement format is the one used for external reporting. Cost of Goods Sold includes both variable and fixed manufacturing costs while Other Expenses includes both variable and fixed selling and administrative costs.

c Because costs are organized by their behavior, the contribution income statement is often used in profitability analysis.

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d The contribution margin can be expressed several ways: total contribution margin dollars, unit contribution margin, or contribution margin ratio (contribution margin ¸ total revenue).

e The contribution margin is used in sensitivity analysis where managers study the responses of CVP results to changes in one or more of the independent variables.

3 Break-Even Point and Profit Planning. The profit planning process often begins with the determination of a firm’s break-even point and margin of safety.

a The break-even point is the unit or dollar sales volume where total revenues and total costs are equal.

b The margin of safety is the amount by which actual or planned sales exceed the break-even point.

c Solving the profit equation for the break-even quantity reveals a specialized form of the profit equation. At the break-even point:

Total revenue = Total costsor

pX = a + bX

d Solving for the sales level X, the following relationship emerges.

X = a ¸ (p - b)

e Since selling price minus variable cost (p - b) equals the unit contribution margin, the break-even formula may be expressed as:

Break-even unit sales volume = (Fixed costs ¸ Unit contribution margin)

f Profit planning often examines the relationship between sales units and the resulting profit. A profit planning equation may also be derived from the general profit formula by setting desired profit equal to total revenue minus total costs. This equation may also be solved for sales units, and the following relationship emerges:

Target unit sales volume = ([Fixed Costs + Desired profit] ¸ Unit contribution margin)

g A cost-volume-profit graph displays relationships among costs, revenue, activity level, and profit. Text Exhibit 3-3 exemplifies a CVP graph.

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h A profit-volume graph illustrates the relationship between volume of activity and profit. The contribution margin determines the slope of the profit line. An example of a profit volume graph appears in text Exhibit 3-4.

i CVP equations assume that the calculated profit is profit before taxes.

1 If management’s profit objectives are described in after- tax dollars, these targets must be converted to their before-tax equivalents in order to use CVP analysis.

1 The conversion equation appears in two forms:

After-tax profit = Before-tax profit x (1 - Tax rate) or

Before-tax profit = After-tax profit ¸ (1 - Tax rate)

1 When taxes are involved in a profit planning analysis, managers should determine the desired level of after tax profit, compute the equivalent level of before-tax profit, and use the before-tax profit to solve for the required sales unit level.

4 Multiple Product Cost-Volume-Profit Analysis. Multiple-product CVP analysis relies on the assumption of a constant sales mix and the use of the contribution margin ratio.

Dollar break-even point = (Fixed costs ¸ Contribution margin ratio)

Target dollar sales volume = ([Fixed costs + Desired profit] ¸ Contribution margin ratio)

a Because the analysis uses the contribution margin ratio, the break-even point and target sales volume calculations are made in sales dollars rather than sales units.

b The variable cost ratio equals variable costs at a specific sales volume divided by sales revenue at that same volume.

c Since total revenue minus variable costs equals contribution margin, the variable cost ratio and the contribution margin ratio must always add to 1.00. (Every dollar of sales can be divided into an amount to cover variable costs -- the variable cost ratio -- and an amount remaining as contribution margin -- the contribution margin ratio.)

5 Operating Leverage. Operating leverage refers to the amount of fixed costs included in an organization’s cost function.

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a The degree of operating leverage measures the portion of fixed costs in the cost function.

Degree of operating leverage = (Contribution margin ¸ Income before taxes)

b The higher the degree of operating leverage, the greater the opportunity for profits as sales increase beyond the break-even point.

c Operating leverage is also a measure of risk since fixed costs must be covered. Significant losses will occur if the organization does not achieve break-even sales levels.

d Managers interested in lowering their level of risk would likely reduce operating leverage by shifting away from fixed costs and toward variable costs. Managers interested in greater potential profitability along with greater risk would likely accept greater levels of fixed costs.

6 Profitability Analysis with Unit and Nonunit Cost Drivers. CVP analysis is limited by the exclusive focus on unit-level activity cost drivers.

a Managers may incorporate nonunit cost drivers through the development of a multi-level contribution income statement. This statement, for example, could incorporate unit, order, customer, and facility-level costs.

b Income statements such as this must be constructed carefully to assure that they reflect to appropriate levels of cost drivers encountered by the firm.

Practice Questions on the Major Concepts

For each of the following multiple choice questions, select the answer or answers you believe are correct. Because they are practice questions, there is often more than one correct answer. Study each option carefully and select all the correct statements. Suggested answers may be found at the end of the exercises for this chapter.

1 When beginning the process of profitability analysis, managers should select:a Only a unit level approach with one cost driver.b Only a cost hierarchy approach with unit and nonunit cost drivers.c Either a unit level or a cost hierarchy approach.d An approach that focuses on costs levels rather than cost drivers.

2 Traditional cost-volume-profit analysis is valuable to managers:a When they are planning for the short-term.b When they are planning for the entire business.c After detailed budget planning has been done.

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d Prior to the introduction of a new product or service.

3 CVP analysis relies on which of the following assumptions?a Firms must produce or sell a single product.b Volume of activity is the cost driver.c Long-term activity levels must be predictable.d Cost and revenue functions must be linear within the relevant range.

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4 Categories of variable cost could include:a Direct materials.b Direct labor.c Manufacturing overhead.d Selling and administration.

5 Direct labor cost include:a Production workers hourly wages only.b Salaries of all managers in the firm.c Wages for all hourly employees of the firm.d Both wages and salaries of all clerical and administrative personnel.

6 Which of the following costs would be included in variable and fixed manufacturing overhead?

a Insurance on delivery vehicles.b Property taxes on the factory.c Electricity used in the conversion process.d Sales commissions paid to outside sales personnel.

7 Managers must remember that contribution margin represents:a The amount of revenue remaining after the firm covers both variable and

fixed costs.b Just another name for gross margin.c The amount of revenue remaining after fixed costs are covered.d The amount of revenue remaining to cover fixed costs and provide for a

profit.

8 What is the contribution margin for a firm selling 25,000 units for $10 each with $80,000 of total fixed costs and $150,000 of total variable costs?

a $20,000b $100,000c $230,000.d $170,000.

9 Which of the following would be a component of Cost of Goods Sold?a Fixed selling and administrative costs.b Fixed manufacturing overhead costs.c Direct labor costs. d Direct materials costs.

10 What are the contribution margin per unit and contribution ratio for a firm selling 25,000 units for $10 per unit with $80,000 of total fixed costs and $150,000 of total variable costs?

a $0.08 and 0.08.b $9.20 and 0.92.c $4 and 0.4.d $6.80 and 0.68.

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11 For managers in a multiple-product firm, the margin of safety represents:a The degree of operating leverage the firm may accept.b The amount by which actual or planned sales exceeds the break-even

level.c The potential change in the sales mix that can be absorbed by the firm.d The amount by which total contribution margin exceeds fixed costs.

12 At what activity level will a firm with a selling price of $12 per unit, variable costs of $9 per unit, and $75,000 of fixed costs break even?

a 14,583 units.b 8,333 units.c 6,250 units.d 25,000 units.

13 At what activity level will a firm with a selling price of $36 per unit, variable costs of $30 per unit, and $120,000 of fixed costs earn a desired profit of $45,000? (Ignore taxes.)

a 20,000 units.b 5,500 units.c 35,000 units.d 27,500 units.

14 At what activity level will a multiple-product firm with sales of $450,000, variable costs of $342,000, and $150,000 of fixed costs break even?

a $625,000b 49,200 units.c 62,500 units.d $492,000.

15 At what activity level would a multiple-product firm with sales of $600,000, variable costs of $360,000, and fixed costs of $200,000 earn a desired profit of $150,000? (Ignore taxes.)

a $500,000.b $875,000.c $375,000.d $710,000.

16 At what activity level would a firm with sales of 50,000 units at $15 per unit, variable costs of $10 per unit, and fixed costs of $250,000 earn a desired profit of $97,500 after taxes of 35%?

a $80,000.b $69,500. c 80,000 units.d 69,500 units.

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17 Managers who wish to take advantage of operating leverage should remember that:

a The firm will have a higher proportion of fixed costs in the cost function.b Higher variable costs are the key to this operating strategy.c The strategy creates less operating risk.d This strategy can produce significant losses below the break-even point.

18 For a firm with sales of $500,000, variable costs of $350,000, fixed costs of $100,000, and a tax rate of 40%, the degree of operating leverage is:

a 5.0.b 3.0.c 10.0.d 7.0.

19 Which types of cost drivers are considered in CVP analysis?a Structural cost drivers.b Organizational cost drivers.c Activity cost drivers.d Any of the three, but only one at a time.

20 When preparing a multi-level contribution income statement, a senior manager’s support team would likely:

a Rely on the prescribed GAAP format.b Include both unit and nonunit cost drivers.c Still include only one contribution margin.d Include facilities cost that are often fixed.

Review Exercises and Short Cases

Please provide answers to the following exercises. The most effective practice will come from attempting each problem and working out all calculations before checking your work. Suggested answers appear after the final exercise.

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1 Comparing Income Statement Formats . Managers of The River Bend Remanufacturing Company are beginning the process of profitability analysis for the upcoming year. The firm purchases used automobile engines in need of repair, disassembles them, and reassembles them using new parts as needed. Support staff has assembled the following revenue and cost information:

Revenue or Cost Category AmountRevenue per engine $1,400Direct materials per engine $650Direct labor per engine $400Variable manufacturing overhead per engine $200Fixed manufacturing overhead per year $90,000Variable selling and administrative costs per engine $50Fixed selling and adminstrative costs per year $85,000

Please assist the operating managers in their profitability analysis for the next operating period when the firm believes that 2,500 engines will be remanufactured.

a Prepare a projected functional income statement for the next operating period.

b Prepare a projected contribution income statement for the next operating period.

c Compare the suitability of these two income statement for profitability analysis.

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2 Developing and Using a Contribution Income Statement : The Cirrus Kite Company manufactures a special-design kite that is easy to fly. In a recent month, 15,000 kites were manufactured and sold for $8 each with the following costs:

Cost Category AmountSelling and administrative: Fixed $20,000 per month Variable $1 per kiteManufacturing overhead: Fixed $13,000 per month Variable $0.50 per kiteDirect materials $1.50 per kiteDirect labor $2.00 per kite

Please assist Cirrus managers by answering the following questions:

a What was the contribution income statement for this recent month? (Ignore taxes.)

b What was the contribution margin per unit and the contribution ratio?

c What is the break-even point and how many kites must be sold to produce an income of $18,000 before taxes?

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3 Using CVP Analysis with Taxes : Country Outfitters is a multi-store retail firm that specializes in outdoor clothing and equipment. Although the firm is growing, the sales mix is very stable. The firm operates with a “low overhead” strategy that makes prices very competitive and keeps fixed costs down. In the most recent period, the firm had total sales revenue of $950,000 with variable costs of $646,000 and fixed costs of $125,000. Country Outfitters operates in a state where the combined federal and state income taxes are 40%.

a What are Country Outfitters’ most recent contribution margin, contribution margin ratio, and after-tax profit?

b What is Country Outfitters’ break-even point?

c What sales level must Country Outfitters achieve in order to earn a desired profit of $135,000 after taxes?

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4 Performing Sensitivity Analysis : The Sweet Grove Citrus Company buys a variety of citrus fruit from growers and then processes the fruit into a product line of fresh fruit, juices, and fruit flavorings. The most recent year’s sales revenue was $4,200,000 with variable costs averaging 60%. Fixed costs last year were $1,300,000.

Sweet Grove management is evaluating several cost alternatives designed to enhance profitability. One staff member has proposed that Sweet Grove purchase more automated processing equipment. This strategy would increase fixed costs by $300,000 but decrease variable costs to 54% of sales. Another staff member has suggested that Sweet Grove rely more on outsourcing for fruit processing. This would reduce fixed costs by $300,000 but increase variable costs to 65%. Please assist Sweet Grove managers by answering the following questions:

a What are Sweet Grove’s current break-even point, profit before taxes, and degree of operating leverage?

b Assuming sales are constant, what would be Sweet Grove’s break-even point, profit before taxes, and degree of operating leverage for the automation alternative? The outsourcing alternative?

c Briefly describe the strengths and weaknesses of the automation and outsourcing alternatives.

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5 Analyzing Profitability with Both Unit and Nonunit Cost Drivers . Cape Cod Catering provides meals for a variety of formal luncheon functions throughout its region. Cape Cod charges customers $25 per lunch, and the firm has traditionally analyzed profitability using the number of lunches as a single unit activity cost driver. Using this approach, the staff estimates a variable cost of $20 for each lunch with fixed facilities costs of $2,500 per month.

Recently, the firm’s management team has decided to analyze operations based on a multi-level approach. Managers concluded that the actual variable cost of a lunch was only $15, but other costs included $100 per event and $50 per customer in addition to the $2,500 facilities cost per month. Cape Cod averages 20 events and a total of 10 different customers per month.

Please assist the management team by answering the following questions:

a What is the firm’s monthly break-even point in sales dollars and units using a unit activity cost driver approach?

b What is the firm’s monthly break-even point in sales dollars and units using a multi-level cost driver approach assuming 20 events for a total of 10 customers during the period?

c What would be the estimated profit associated with serving 700 meals at 14 events involving a total of 6 customers? (Compare the results of both the single driver and multi-level driver approaches.)

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Suggested Answers to Questions, Exercises, and Short Cases

The following suggested answers provide not only the recommended choices but also the underlying reasoning behind the choices.

Multiple Choice Questions:

1 Answer (c) is correct. Managers may approach profitability analysis from either a unit level or cost hierarchy perspective. Answers (a) and (b) imply that managers are restricted to one approach; this conclusion is untrue. Answer (d) is also incorrect since effective profitability analysis must focus on some definition of cost drivers.

2 Answers (a) and (d) are correct. Traditional CVP analysis is helpful for short-term planning situations with existing or proposed products. Answer (b) is incorrect since CVP accuracy deteriorates as the analysis expands to an entire business. Answer (c) is incorrect since CVP analysis should take place prior to the budgeting process.

3 Answers (b) and (d) are correct. Volume is assumed to be the cost driver, and the model is based on linear cost and revenue relationships. Answers (a) and (c) are incorrect since the model does work for multiple-product firms with a constant sales mix and should not be used in long-term situations.

4 Answers (a), (b), (c), and (d) are all correct. Direct materials and direct labor are usually considered variable costs. Manufacturing overhead and selling and administrative costs usually include some variable components. Therefore, each of these cost categories may be included in variable costs.

5 Answer (a) is correct. Direct labor cost includes the wages paid to production workers engaged in the conversion process of the firm. Answers (b), (c), and (d) are incorrect since they each include at least some wages or salaries that would be classified as selling and administrative costs.

6 Answers (b) and (c) are correct. Variable and fixed manufacturing overhead include all indirect conversion costs including electricity used in conversion and factory property taxes. Insurance on delivery vehicles and sales commissions are selling and administrative costs, and, therefore, answers (a) and (d) are incorrect.

7 Answer (d) is correct. Contribution margin equals total revenues minus variable costs. This amount covers fixed costs and provides for a profit. Answers (a) and (c) are incorrect since they imply that contribution margin remains after fixed costs are covered. Contribution margin is measured before fixed costs are deducted. Answer (b) is incorrect since gross margin and contribution margin are very different measures.

8 Answer (b) is correct. The contribution margin = $250,000 (total revenue) - $150,000 (variable costs) = $100,000.

9 Answers (b), (c), and (d) are correct. Cost of Goods Sold includes costs of the conversion process including direct materials, direct labor, variable overhead, and fixed overhead. Answer (a) is incorrect since both variable and fixed selling and administrative costs are included as a separate category of cost.

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10 Answer (c) is correct. The contribution margin per unit = $10 (revenue per unit) - $6 (variable cost per unit; $150,000 ¸ 25,000 = $6) = $4. The contribution margin ratio = $4 (contribution margin) ¸ $10 (sales price) = 0.4.

11 Answer (b) is correct. For both single-product and multiple-product firms, margin of safety is the amount by which sales exceed the break-even point. Answer (a) is incorrect since operating leverage and margin of safety are different ideas. Answers (c) and (d) are incorrect since they are not related to the definition of margin of safety.

12 Answer (d) is correct. The break-even activity level = $75,000 (fixed costs) ¸ $3 (contribution margin; $12 - $9 = $3) = 25,000 units.

13 Answer (d) is correct. The activity level necessary to earn the desired $45,000 profit = ($120,000 [fixed costs] + $45,000 [desired profit]) ¸ $6 (contribution margin; $36 - $30 = $6) = 27,500 units.

14 Answer (a) is correct. The break-even activity level = $150,000 (fixed costs) ¸ 0.24 (contribution margin ratio; [$450,000 - $342,000] ¸ $450,000 = 0.24) = $625,000.

15 Answer (b) is correct. The activity level necessary to earn the desired $150,000 profit = ($200,000 [fixed costs] + $150,000 [target profit]) ¸ 0.4 (contribution margin ratio; [$600,000 - $360,000] ¸ $600,000 = 0.4) = $875,000.

16 Answer (c) is correct. The before-tax equivalent of $97,500 after taxes = ($97,500 ¸ [1 - 0.35]) = $150,000. The activity level necessary to earn $150,000 before taxes = ($250,000 [fixed costs] + $150,000 [desired profit]) ¸ $5 (contribution margin per unit; $15 -$10 = $5) = 80,000 units.

17 Answers (a) and (d) are correct. Operating leverage does involve higher fixed costs and can produce significant losses below the break-even point. Higher variable costs and less risk, answers (b) and (c), are incorrect since variable costs would be lower and risk would be higher with greater operating leverage.

18 Answer (b) is correct. The degree of operating leverage = $150,000 (contribution margin) ¸ $50,000 (income before taxes; $500,000 - $350,000 - $100,000 = $50,000) = 3.

19 Answer (c) is correct. CVP analysis considers only activity cost drivers (and often only unit level activity drivers). It is a short-term model that assumes that structural and organizational cost driver decisions, answers (a) and (b), have already been made.

20 Answers (b) and (d) are correct. A multi-level contribution income statement would likely include both nonunit cost drivers and facility costs. Answers (a) and (c) are incorrect since the statement does not follow GAAP format and would likely have multiple contribution margins.

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Review Exercises and Short Cases:

1 Comparing Income Statement Formats .

a Functional Income Statement:

Sales (2,500 x $1,400) $3,500,000Less cost of goods sold: Direct materials (2,500 x $650) $1,625,000 Direct labor (2,500 x $400) 1,000,000 Variable manufacturing overhead (2,500 x $200) 500,000 Fixed manufacturing overhead 90,000 3,215,000Gross margin $285,000Less other expenses Variable selling and administrative (2,500 x 50) $125,000 Fixed selling and administrative 85,000 210,000Profit $75,000

b Contribution Income Statement:

Sales (2,500 x $1,400) $3,500,000Less variable costs: Direct materials (2,500 x $650) $1,625,000 Direct labor (2,500 x $400) 1,000,000 Manufacturing overhead (2,500 x $200) 500,000 Selling and administrative (2,500 x $50) 125,000 3,250,000 Contribution margin $250,000Less fixed costs Manufacturing overhead $90,000 Selling and administrative 85,000 175,000Profit $75,000

c Suitability for Profitability Analysis:

The two income statement are similar although not identical. Consider the difference between gross margin and contribution margin -- a difference that results from the different placement of fixed manufacturing overhead and variable selling and administrative costs. Contribution income statements provide better information for internal decision makers. The relationships among volume, costs, and profit are more evident with the contribution format. The functional format, however, is the one most often presented in corporate annual reports since it conforms to US GAAP.

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2 Developing and Using a Contribution Income Statement .

a Contribution Income Statement:

In this version of a contribution income statement, the variable costs are summed to $5 per kite (Variable costs = $1.50 + $2 + $0.50 + $1 = $5).

Sales (15,000 x $8) $120,000Less variable costs (15,000 x $5) (75,000)Contribution margin $45,000Less fixed costs (33,000)Profit $12,000

b Contribution Margin per Unit and Contribution Ratio:

Contribution margin per unit = Total contribution margin ¸ Units; $45,000 ¸ 15,000 Units = $3

(Alternatively: Contribution margin per unit = Unit selling price - Unit variable cost) $8 - $5 = $3)

Contribution margin ratio = Contribution ¸ Sales

Totals: $45,000 ¸ $120,000 = 0.375Units: $3 ¸ $8 = 0.375

c Break-Even Point and Desired Profit Unit Sales Volume:

Break-even point = Fixed costs ¸ Unit contribution margin $33,000 ¸ $3 = 11,000 kites

Desired profit unit sales volume = (Fixed costs + Desired profit) ¸ Unit contribution margin; ($33,000 + $18,000) ¸ $3 = 17,000 kites

3 Using CVP Analysis with Taxes .

a Contribution Margin, Contribution Margin Ratio, and After-Tax Profit:

Contribution margin = Total revenue - Variable cost; $950,000 - $646,000 = $304,000

Contribution margin ratio = Contribution margin ¸ Total revenue; $304,000 ¸ $950,000 = 0.32

After-tax profit:

Total revenue - Total costs = Before-tax profit; $950,000 - ($646,000 + $125,000) = $179,000

Before-tax profit x (1 - Tax rate) = After-tax profit; $179,000 x 0.6 = $107,400

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b Break-Even Point:

Break-even point = Fixed costs ¸ Contribution margin ratio; $125,000 ¸ 0.32 = $390,625

c Sales Level to Achieve Desired After-Tax Profit:

Before-tax profit = After-tax profit ¸ (1 - Tax rate); $135,000 ¸ 0,6 = $225,000

Desired profit dollar sales volume = (Fixed costs + Desired profit) ¸ Contribution margin ratio; ($125,000 + $225,000) ¸ 0.32 = $1,093,750

4 Performing Sensitivity Analysis :

Formulas for Parts (a) and (b):Break-even point = Fixed costs ¸ Contribution margin ratioBefore-tax profit = Total revenue - Total costsDegree of operating leverage = Contribution margin ¸ Before-tax profit

a Current Situation:

Break-even point = $1,300,000 ¸ 0.4 = $3,250,000Profit = $4,200,000 - ($2,520,000 + $1,300,000) = $380,000Degree of operating leverage = $1,680,000 ¸ $380,000 = 4.42

b Automation and Outsourcing Alternatives:

Automation:

Break-even point = $1,600,000 ¸ 0.46 = $3,478,260Profit = $4,200,000 - ($2,268,000 + $1,600,000) = $332,000Degree of operating leverage = $1,932,000 ¸ 332,000 = 5.82

Outsourcing:

Break-even point = $1,000,000 ¸ 0.35 = $2,857,143Profit = $4,200,000 - ($2,730,000 + $1,000,000) = $470,000Degree of operating leverage = $1,470,000 ¸ $470,000 = 3.13

c Strengths and Weaknesses:

Automation: This alternative is attractive if sales increase. The higher operating leverage will magnify profits. The weaknesses are the higher risk, higher break-even point, and lower profit at current level of activity.

Outsourcing: This alternative is attractive at the current level of activity since it offers less risk, a lower break-even point, and greater immediate profitability. It will not, however, magnify profit as much as the other alternative as sales grow since the degree of operating leverage is lower.

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5 Analyzing Profitability with Both Unit and Nonunit Cost Drivers .

a Break-even using a unit cost driver approach:

Break-even sales dollars = Fixed facilities costs ¸ contribution margin ratio

The contribution margin ratio = ($25 - $20) ¸ $25 = 0.2Therefore, the break-even sales dollars = $2,500 ¸ 0.2 = $12,500 The break-even units would be $12,500 ¸ $25 per lunch = 500 lunches

b Break-even using multilevel cost drivers:

Break-even sales dollars = (Events costs + Customer costs + Fixed facilities costs) ¸ Contribution margin ratioWith an average of 20 events and 10 customers, break-even sales would be:([20 x $100] + [10 x $50] + $2,500) ¸ ([$25 - $15] ¸ $25)$5,000 ¸ 0.4 = $12,500On a units basis; $12,500 ¸ $25 per lunch = 500 lunches

(These results match those determined in part (a) and might cause management to falsely conclude that the multi-level approach is no better than the unit approach. In this situation, the two break-even sales level are the same because management’s unit-based estimate of $20 variable cost per lunch includes an extra $5 that is not really variable. This additional cost is really made up of the average step costs for events and customers expressed as an additional $5 per lunch.

For a catering firm that experiences costs based on the number of events and customers as well as lunches, a simple unit-based analysis can lead to faulty managerial conclusions as part (c) illustrates.)

c Profitability Estimate with 700 Lunches, 14 Events, and 6 Customers:

Unit Approach: (700 x $25) - ([700 x $20] + $2,500) = $1,000

Multi-level Approach: (700 x $25) - ([700 X $15] + [14 X $100] + [6 X $50] + $2,500) = $2,800

(Notice that this time, the unit and multi-level approaches produced very different profit estimates. Changing the estimated number of lunches, events, or customers can significantly alter the results. The unit approach continues to use static information on the relationship among lunches, events, and customers, and the $20 cost per lunch that included some step costs is no longer accurate. The multi-level approach treats genuine variable costs and step costs separately and, therefore, produces more useful management information.)

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Chapter Three

Chapter Notes

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