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PART 5 © Getty Images Managerial Decision Making Chapter 11: Cost-Volume-Profit Analysis: A Managerial Planning Tool Chapter 12: Tactical Decision Making Chapter 13: Capital Investment Decisions Chapter 14: Inventory Management chapter 11 Cost-Volume-Profit Analysis: A Managerial Planning Tool l e a r n i n g o b j e c t i v e s After studying this chapter, you should be able to: 1. Determine the number of units that must be sold to break even or to earn a targeted profit. 2. Calculate the amount of revenue required to break even or to earn a targeted profit. 3. Apply cost-volume-profit analysis in a multiple-product setting. 4. Prepare a profit-volume graph and a cost-volume-profit graph, and explain the meaning of each. 5. Explain the impact of risk, uncertainty, and changing variables on costvolume-profit analysis. 6. Discuss the impact of activity-based costing on cost-volume-profit analysis. Scenario For years, Janet McFarland’s friends and family raved about her homemade jellies and salsas. Janet traditionally canned several gallons of salsa, ladled it into decorative pint jars, wrapped them, and sent them as gifts. Her friends said, “You ought to sell this stuff—you’d make a fortune!” So, Janet decided to give it a try. First, she decided to concentrate on one product, a green cactus salsa that had gotten rave reviews. She scouted sources of jars, lids, and labels. In addition, Janet got in touch with her local agricultural extension office and learned a considerable amount about laws regulating food sales. One source of surprise was that she was required to obtain an expert confirmation of the ingredients in her salsa. Usually, Janet added a little of this and a little of that until it tasted right. She found out that this casual approach would not work. Foods were required to be labeled with the name of each ingredient in order of amount. Suddenly, it mattered whether ancho or poblano chilis were used and in what proportion. Janet needed a standardized recipe. She located a professional food chemist to analyze the recipe and certify the proportion of ingredients. Janet traveled to a number of grocery stores and gift shops in the area. Several were willing to stock her product on consignment, placing a few jars by the cash register; others guaranteed shelf space but required a shelf charge for it. She figured that traveling to the stores, checking on sales and stock, and visiting prospective customers would take about one day a week. Before starting production, Janet consulted with her family accountant, Bob Ryan. Janet outlined her business plan. Since her product was new on the market, she thought a price of $4.50 would be reasonable. Bob took the proposed price and the costs she had estimated, and did some quick break-even analysis. Then he looked up and gave Janet the bad news; at a price of $4.50 per jar, she would lose money. Even worse, increasing the quantity sold would just make the loss larger. As a friend and business advisor, Bob decided to help Janet reconsider her proposed methods of making the salsa, to see if the variable costs could be reduced. If she could not find a way to get her variable costs below price, her business could never succeed. Questions to Think About 1. What kinds of variable and fixed costs do you think Janet will incur? 2. Given Bob’s initial assessment that the variable costs are higher than the price, what is wrong with Janet’s thought that selling more is the way to go? 3. How important is break-even analysis to a firm? Do you suppose that large companies do break-even analysis as well as small companies? 4. Why is the concept of breaking even important? Doesn’t Janet want to make a profit? 5. Janet doesn’t know what price to charge. How could she get a better idea? 472 Pa r t 5 / M a n a g e r i a l D e c i s i o n M a k i n g Cost-volume-profit analysis (CVP analysis) is a powerful tool for planning and decision making. Because CVP analysis emphasizes the interrelationships of costs, quantity sold, and price, it brings together all of the financial information of the firm. CVP analysis can be a valuable tool to identify the extent and magnitude of the economic trouble a division is facing and to help pinpoint the necessary solution. For example, Microsoft’s Xbox 360 was sold for a retail price of $399 during its late2005 debut. However, that price did not allow a profit. In fact, Microsoft lost about $126 per unit. Didn’t they know that? Yes, it was a deliberate business strategy to sell the console at a loss, but to make a profit on the software—the games.1 CVP analysis can address many other issues as well, such as the number of units that must be sold to break even, the impact of a given reduction in fixed costs on the break-even point, and the impact of an increase in price on profit. Additionally, CVP analysis allows managers to do sensitivity analysis by examining the impact of various price or cost levels on profit. While this chapter deals with the mechanics and terminology of CVP analysis, you should keep in mind that CVP analysis is an integral part of financial planning and decision making. Every accountant and manager should be thoroughly conversant with its concepts, not just the mechanics. Break-Even Point in Units Objective 1 Determine the number of units that must be sold to break even or to earn a targeted profit. Since we are interested in how revenues, expenses, and profits behave as volume changes, it is natural to begin by finding the firm’s break-even point in units sold. The break-even point is the point where total revenue equals total cost, the point of zero profit. To find the break-even point in units, we focus on operating income. We will first discuss the way to find the break-even point and then see how our approach can be expanded to determine the number of units that must be sold to earn a targeted profit. The firm’s initial decision in implementing a units-sold approach to CVP analysis is the determination of just what a unit is. For manufacturing firms, the answer is obvious. Procter & Gamble may define a unit as a bar of Ivory soap; Janet McFarland (from the opening scenario) would define a unit as a jar of salsa. Service firms face a more difficult choice. Southwest Air Lines may define a unit as a passenger mile or as a one-way trip. A second decision centers on the separation of costs into fixed and variable components. CVP analysis focuses on the factors that effect a change in the components of profit. Because we are looking at CVP analysis in terms of units sold, we need to determine the fixed and variable components of cost and revenue with respect to units. (This assumption will be relaxed when we incorporate activity-based costing into CVP analysis.) It is important to realize that we are focusing on the firm as a whole. Therefore, the costs we are talking about are all costs of the company—manufacturing, marketing, and administrative. Thus, when we say variable cost, we mean all costs that increase as more units are sold, including direct materials, direct labor, variable overhead, and variable selling and administrative costs. Similarly, fixed cost includes fixed overhead and fixed selling and administrative expenses. Using Operating Income in CVP Analysis The income statement is a useful tool for organizing the firm’s costs into fixed and variable categories. The income statement can be expressed as a narrative equation: Operating income  Sales revenues  Variable expenses  Fixed expenses 1 Arik Hesseldahl, “Microsoft’s Red-Ink Game,” Business Week Online (November 22, 2005), http:// businessweek.com/technology/content/nov2005/tc20051122_410710.htm, accessed March 31, 2006. C h a p t e r 1 1 / C o s t -Vo l u m e - P ro f i t A n a l y s i s : A M a n a g e r i a l P l a n n i n g To o l Managers Decide CVP Analysis Important to Ford CVP analysis can be a valuable tool to identify the extent and magnitude of the economic trouble a company is facing and to help pinpoint the necessary solution. Ford Motor Company’s North American automobile business had been profitable in 2003 and 2004. But the next two years saw increasing materials and energy costs and plunging market share. The division was well below the break-even point. To reverse the slide, Ford announced a restructuring plan that would make extensive cuts in both variable and fixed costs. For example, North American manufacturing capacity is to be reduced by 26 percent (1.2 million vehicles); 14 manufacturing plants are to be closed and up to 30,000 employees laid off; and reductions are to be made in the number of salaried employees and corporate officials. On the revenue side, the company plans to adjust its sales mix by increasing the number of hybrid gas-electric vehicles. These hybrids, with their higher prices, will include the Ford Five Hundred, Mercury Montego, Ford Edge, and Lincoln MKX. If the plan works as expected, Ford’s North American operations are expected to return to profitability by 2008. ■ Sources: Bill Vlasic, “Ford to Shut Wixom and 13 Other Plants,” Detroit News (January 23, 2006), http://www.detnews.com/ apps/pbcs.dll/article?AID/20060123/ AUTO01/601230407; “Ford Statement on Restructuring,” Detroit News (January 23, 2006), http://www.detnews.com/apps/pbcs .dll/article?AID/20060123/AUTO01/ 601230419, accessed March 31, 2006. Note that we are using the term operating income to denote income or profit before income taxes. Operating income includes only revenues and expenses from the firm’s normal operations. Net income is operating income minus income taxes. Once we have a measure of units sold, we can expand the operating-income equation by expressing sales revenues and variable expenses in terms of unit dollar amounts and number of units. Specifically, sales revenue is expressed as the unit selling price times the number of units sold, and total variable costs are the unit variable cost times the number of units sold. With these expressions, the operatingincome equation becomes: Operating income  (Price
Number of units sold)  (Variable cost per unit
Number of units sold)  Total fixed cost Suppose you were asked how many units must be sold in order to break even, or earn a zero profit. You could answer that question by setting operating income to zero and then solving the operating-income equation for the number of units. Let’s use the following example to solve for the break-even point in units. Assume that Whittier Company manufactures a mulching lawn mower. For the coming year, the controller has prepared the following projected income statement: Sales (1,000 units @ $400) Less: Variable expenses Contribution margin Less: Fixed expenses Operating income $400,000 325,000 $ 75,000 45,000 $ 30,000 We see that for Whittier Company, the price is $400 each, and the variable cost per unit is $325 ($325,000/1,000 units). Fixed cost is $45,000. At the break-even point, then, the operating-income equation would take the following form: 473 474 Pa r t 5 / M a n a g e r i a l D e c i s i o n M a k i n g 0  ($400
Units)  ($325
Units)  $45,000 0  ($75
Units)  $45,000 $75
Units  $45,000 Units  600 Therefore, Whittier must sell 600 lawn mowers to just cover all fixed and variable expenses. A good way to check this answer is to formulate an income statement based on 600 units sold. Sales (600 units @ $400) Less: Variable expenses Contribution margin Less: Fixed expenses Operating income $240,000 195,000 $ 45,000 45,000 $ 0 Indeed, selling 600 units does yield a zero profit. An important advantage of the operating-income approach is that all further CVP equations are derived from the variable-costing income statement. As a result, you can solve any CVP problem by using this approach. Shortcut to Calculating Break-Even Units We can more quickly calculate break-even units by focusing on the contribution margin. The contribution margin is sales revenue minus total variable cost. At breakeven, the contribution margin equals the fixed expenses. For example, Apple’s iTunes charges $0.99 to download a song. Its variable costs, including payments to the record companies and others, total approximately $0.95. This means that iTunes earns a contribution margin of $0.04 for every song purchased and downloaded. The low contribution margin per unit, which must cover all fixed costs, means that iTunes is virtually a break-even business.2 If we substitute the unit contribution margin for price minus unit variable cost in the operating-income equation and solve for the number of units, we obtain the following fundamental break-even equation: © PR Newswire APPLE COMPUTER, INC. Apple understands the importance of contribution margin in setting prices for its iTunes unit. While iTunes does not contribute much to profit, it does cover expenses and allows Apple to focus on the iPod. Number of units  Fixed cost/Unit contribution margin Using Whittier Company as an example, we can see that the contribution margin per unit can be computed in one of two ways. One way is to divide the total contribution margin by the units sold for a result of $75 per unit ($75,000/1,000). A second way is to compute price minus variable cost per unit. Doing so yields the same result, $75 per unit ($400  $325). To calculate the break-even number of units for Whittier Company, use the fundamental break-even equation as follows: Number of units  $45,000/($400  $325)  $45,000/$75  600 Of course, the answer is identical to that computed using the income statement. 2 Roger O. Crockett, “Major Hangups Over the iPod Phone,” Business Week Online (March 24, 2005), http://yahoo .businessweek.com/technology/content/mar2005/tc20050324_7462_tc024.htm, accessed March 31, 2006. C h a p t e r 1 1 / C o s t -Vo l u m e - P ro f i t A n a l y s i s : A M a n a g e r i a l P l a n n i n g To o l Unit Sales Needed to Achieve Targeted Profit While the break-even point is useful information, most firms would like to earn operating income greater than zero. CVP analysis gives us a way to determine how many units must be sold to earn a particular targeted income. Targeted operating income can be expressed as a dollar amount (for example, $20,000) or as a percentage of sales revenue (for example, 15 percent of revenue). Both the operating-income approach and the contribution margin approach can be easily adjusted to allow for targeted income. Targeted Income as a Dollar Amount Assume that Whittier Company wants to earn operating income of $60,000. How many mulching lawn mowers must be sold to achieve this result? Let’s use the income statement to find out: $60,000  ($400
Units)  ($325
Units)  $45,000 $105,000  $75
Units Units  1,400 If, instead, we use the fundamental break-even equation, we simply add targeted profit of $60,000 to the fixed cost and solve for the number of units: Units  ($45,000  $60,000)/($400  $325) Units  $105,000/$75 Units  1,400 Whittier must sell 1,400 lawn mowers to earn a before-tax profit of $60,000. The following income statement verifies this outcome: Sales (1,400 units @ $400) Less: Variable expenses Contribution margin Less: Fixed expenses Operating income $560,000 455,000 $ 105,000 45,000 $ 60,000 Another way to check this number of units is to use the break-even point. As just shown, Whittier must sell 1,400 lawn mowers, or 800 more than the break-even volume of 600 units, to earn a profit of $60,000. The contribution margin per lawn mower is $75. Multiplying $75 by the 800 lawn mowers above breakeven produces the profit of $60,000 ($75
800). This outcome demonstrates that contribution margin per unit for each unit above breakeven is equivalent to profit per unit. Since the break-even point had already been computed, the number of lawn mowers to be sold to yield a $60,000 operating income could have been calculated by dividing the unit contribution margin into the target profit and adding the resulting amount to the break-even volume. In general, assuming that fixed costs remain the same, the impact on a firm’s profits resulting from a change in the number of units sold can be assessed by multiplying the unit contribution margin by the change in units sold. For example, if 1,500 lawn mowers instead of 1,400 are sold, how much more profit will be earned? The change in units sold is an increase of 100 lawn mowers, and the unit contribution margin is $75. Thus, profits will increase by $7,500 ($75
100). Targeted Income as a Percent of Sales Revenue Assume that Whittier Company wants to know the number of lawn mowers that must be sold in order to earn a profit equal to 15 percent of sales revenue. Sales revenue is price multiplied by the quantity sold. Thus, the targeted operating income is 15 percent of price times quantity. Using the income statement (which is simpler in this case), we have the following: 475 476 Pa r t 5 / M a n a g e r i a l D e c i s i o n M a k i n g 0.15($400)(Units)  ($400
Units)  ($325
Units)  $45,000 $60
Units  ($400
Units)  ($325
Units)  $45,000 $60
Units  ($75
Units)  $45,000 $15
Units  $45,000 Units  3,000 Does a volume of 3,000 lawn mowers achieve a profit equal to 15 percent of sales revenue? For 3,000 lawn mowers, the total revenue is $1.2 million ($400
3,000). The profit can be computed without preparing a formal income statement. Remember that above breakeven, the contribution margin per unit is the profit per unit. The break-even volume is 600 lawn mowers. If 3,000 lawn mowers are sold, then 2,400 (3,000  600) lawn mowers above the break-even point are sold. The before-tax profit, therefore, is $180,000 ($75
2,400), which is 15 percent of sales ($180,000/$1,200,000). After-Tax Profit Targets When calculating the break-even point, income taxes play no role. This is because the taxes paid on zero income are zero. However, when the company needs to know how many units to sell to earn a particular net income, some additional consideration is needed. Recall that net income is operating income after income taxes and that our targeted income figure was expressed in before-tax terms. As a result, when the income target is expressed as net income, we must add back the income taxes to get operating income. In general, income taxes are computed as a percentage of income. The after-tax profit is computed by subtracting the tax from the operating income (or before-tax profit). Net income  Operating income  Income taxes  Operating income  (Tax rate
Operating income)  Operating income (1  Tax rate) or Operating income  Net income/(1  Tax rate) Thus, to convert the after-tax profit to before-tax profit, simply divide the after-tax profit by (1
Tax rate). Suppose that Whittier Company wants to achieve net income of $48,750 and its tax rate is 35 percent. To convert the after-tax profit target into a before-tax profit target, complete the following steps: $48,750  Operating income  (0.35
Operating income) $48,750  0.65 (Operating income) $75,000  Operating income In other words, with an income tax rate of 35 percent, Whittier Company must earn $75,000 before income taxes to have $48,750 after income taxes.3 With this conversion, we can now calculate the number of units that must be sold: Units  ($45,000  $75,000)/$75 Units  $120,000/$75 Units  1,600 Let’s check this answer by preparing an income statement based on sales of 1,600 lawn mowers. Sales (1,600 @ $400) $640,000 Less: Variable expenses 520,000 Contribution margin $120,000 Less: Fixed costs 45,000 Operating income $ 75,000 Less: Income taxes (35% tax rate) 26,250 Net income $ 48,750 3 To practice the after-tax to before-tax conversion, calculate how much before-tax income Whittier would need to have $48,750 after-tax income if the tax rate were 40 percent. [Answer: $81,250] C h a p t e r 1 1 / C o s t -Vo l u m e - P ro f i t A n a l y s i s : A M a n a g e r i a l P l a n n i n g To o l 477 Break-Even Point in Sales Dollars Objective 2 Calculate the amount of revenue required to break even or to earn a targeted profit. © Getty Images/PhotoDisc In some cases when using CVP analysis, managers may prefer to use sales revenues as the measure of sales activity instead of units sold. A units-sold measure can be converted to a sales revenue measure simply by multiplying the unit selling price by the units sold. For example, the break-even point for Whittier Company was computed at 600 mulching lawn mowers. Since the selling price for each lawn mower is $400, the break-even volume in sales revenue is $240,000 ($400
600). Any answer expressed in units sold can be easily converted to one expressed in sales revenues, but the answer can be computed more directly by developing a separate formula for the sales revenue case. In this case, the important variable is sales dollars, so both the revenue and the variable costs must be expressed in dollars instead of units. Since sales revenue is always expressed in dollars, measuring that variable is no problem. Let’s look more closely at variable costs and see how they can be expressed in terms of sales dollars. To calculate the break-even point in sales dollars, variable costs are defined as a percentage of sales rather than as an amount per unit sold. For example, suppose that price is $10, and variable cost is $6. Of course, the remainder is contribution margin of $4 ($10  $6). If 10 units are sold, total variable costs are $60 ($6
10 units). Alternatively, since each unit sold earns $10 of revenue and has $6 of variable cost, we could say that 60 percent of each dollar of revenue earned is attributable to variable cost ($6/$10). Thus, focusing on sales revenue, we would expect total variable costs of $60 for revenues of $100 (0.60
$100). The variable cost ratio (in this example, 60 percent) is the proportion of each sales dollar that must be used to cover variable costs. The variable cost ratio can be computed by using either total data or unit data. Of course, the percentage of sales dollars remaining after variable costs are covered is the contribution margin ratio. The contribution margin ratio is the proportion of each sales dollar available to cover fixed costs and provide for profit. So if the variable cost ratio is 60 percent of sales, then the contribution margin ratio must be the remaining 40 percent of sales. It makes sense that the complement of the variable cost ratio is the contribution margin ratio. After all, the proportion of the sales dollar left after variable costs are covered should be the contribution margin component. Just as the variable cost ratio can be computed using total or unit figures, the contribution margin ratio, forty percent in our exhibit, can also be computed in these two ways. That is, one can divide the total contribution margin by total sales ($40/$100), or one can use the unit contribution margin divided by price ($4/$10). Naturally, if the variable cost ratio is known, it can be subtracted from 1 to yield the contribution margin ratio (1  0.60  0.40). Where do fixed costs fit into this? Since the contribution margin is revenue remaining after variable costs are covered, it must be the revenue available to cover fixed costs and contribute to profit. There are three possibilities: fixed cost can equal contribution margin; fixed cost can be less than contribution margin; or fixed cost can be greater than contribution margin. If fixed cost equals contribution margin, then operating income, or profit, is zero and the company is at breakeven. If fixed cost is less than contribution margin, the company earns a profit (or positive operating income). Finally, if fixed cost is greater than contribution margin, the company faces an operating loss. The manufacturer of this riding mower had both variable and fixed costs. These had to be considered in determining the number of units to produce and the price to charge. 478 Pa r t 5 / M a n a g e r i a l D e c i s i o n M a k i n g Now let’s turn to a couple of examples based on Whittier Company to illustrate the sales-revenue approach. Restated below is Whittier Company’s variable-costing income statement for 1,000 lawn mowers. Dollars $400,000 325,000 $ 75,000 45,000 $ 30,000 Sales Less: Variable costs Contribution margin Less: Fixed costs Operating income Percent of Sales 100.00% 81.25 18.75% Notice that sales revenue, variable costs, and contribution margin have been expressed as a percent of sales. The variable cost ratio is 0.8125 ($325,000/$400,000); the contribution margin ratio is 0.1875 (computed either as 1  0.8125 or as $75,000/$400,000). Fixed costs are $45,000. Given the information in this income statement, how much sales revenue must Whittier earn to break even? Operating income  Sales  Variable costs  Fixed costs 0  Sales  (Variable cost ratio
Sales)  Fixed costs 0  Sales (1  Variable cost ratio)  Fixed costs 0  Sales (1  0.8125)  $45,000 Sales (0.1875)  $45,000 Sales  $240,000 Thus, Whittier must earn revenues totaling $240,000 in order to break even. (You might want to check this answer by preparing an income statement based on revenue of $240,000 and verifying that it yields zero profit.) Note that (1  0.8125) is the contribution margin ratio. We can skip a couple of steps by recognizing that Sales  (Variable cost ratio
Sales) is equal to Sales
Contribution margin ratio. What about the fundamental break-even equation used to determine the breakeven point in units? We can use that approach here as well. Recall that the formula for the break-even point in units is: Break-even units  Fixed cost/(Price  Unit variable cost) If we multiply both sides of this equation by price, the left-hand side will equal sales revenue at breakeven: Break-even units
Price Break-even sales Break-even sales Break-even sales     Price
[Fixed cost/(Price  Unit variable cost)] Fixed cost
[(Price/(Price  Unit variable cost)] Fixed cost
(Price/Contribution margin) Fixed cost/Contribution margin ratio Again using Whittier Company data, the break-even sales dollars would be computed as ($45,000/0.1875), or $240,000. Same answer, just a slightly different approach. Profit Targets and Sales Revenue Consider the following question: How much sales revenue must Whittier generate to earn a before-tax profit of $60,000? (This question is similar to the one we asked earlier in terms of units, but it phrases the question directly in terms of sales revenue.) To answer the question, add the targeted operating income of $60,000 to the $45,000 of fixed cost and divide by the contribution margin ratio: Sales  ($45,000  $60,000)/0.1875  $105,000/0.1875  $560,000