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Cost-Volume-Profit Explain the features of costvolume-profit (CVP) analysis
2. Determine the breakeven point and output level needed to achieve a target operating income
3. Understand how income taxes
affect CVP analysis 4. Explain CVP analysis in decision making and how sensitivity analysis helps managers cope with uncertainty
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5. Use CVP analysis to plan variable and fixed costs
6. ~ p p CVP analysis to a company ~ y
producing multiple products
Tiffany Tinkers with Its Sales Mix-and Takes a Cost-Volume-Profit Gamble1
In the late 1990s, Tiffany's managers decided to create cheaper silver jewelry to address the then-emerging trend toward "affordable" luxury. Middle-class consumers were becoming increasingly brand-conscious. And silver had emerged as the "it" metal. Tiffany's 1997 introduction of the silver "Return to Tiffany" collection, which offered jewelry inscribed with the Tffany name for just over $100, was a huge hit. Teens jammed Tiffany's hushed stores, clamoring for the $110 must-have fashion accessory. Even Elle Woods, the ditzy law student in the 2001 hit movie Legally Blonde, accessorized her string bikini with a Tiffany charm bracelet and matching necklace. From 1997 to 2002, the company's profits more than doubled. But Tiffany's managers were worried. On the one hand, they knew the cheaper, silver jewelry had become a fad that could eventually erode Tiffany's brand name and the sales of its higher-priced products, which were relatively more expensive to produce. On the other hand, any effort to curb lower-end silver could dramatically slow sales and affect profitability. Nonetheless, in a dramatic gamble, Tfiany decided to slow down its "golden goose" by hiking prices on the fast-growing, highly profitable line while simultaneously introducing pricier jewelry collections.
7. Adapt CVP analysis to situations in
which a product has more than one cost driver
' Source: Ellen Byron, "Fashion Victim: To Refurbish Its Image, Tiffany's Rlsks Profits," The Wall
StreetJournal, January 10, 2007, p. A l .
By 2005 the craze died down, sales of silver iewelrv and other ~ i e c e s under $500 declined, but with it the company's earnings and stock price. But by 2007, Tiffany could boast that its store sales were up in 2006, and that its biggest sales growth had come from --
?%-+ = ,
> :*:,2~*$~ .
=----+% - ,<
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iewelrv items costina over $20.000 a ~ i e c eThe . jury is still out on whether the daring move has worked. The company's profit marqins and stock price have vet to reach the highs of years past. As you read this chapter, you will begin to understand Tiffany's challenges and the actions it would have had to take to sustain profitability as sales of lower-end jewelry declined. A key task in the face of declining sales is to reduce fixed costs. Many capital intensive companies, such as US Airways and United Airlines in the airlines industry and Global Crossing and WorldCom in the telecommunications industry, had t o file for bankruptcy because, when sales declined at these companies during 2001 and 2002, fixed costs remained high. The methods of CVP analysis described in this chapter help management accountants alert managers to such risks.
Essentials of CVP Analysis
Cost-volume-profit (CVP) analysis examines the behavior of total revenues, total costs, and operating income as changes occur in the units sold, the selling price, the variable cost per unit, or the fixed costs of a product. Let's consider an example to illustrate CVP analysis.
Example: Mary Frost is considering selling Do-All Software, a home-office software package, at a computer convention in Chicago. Mary knows she can purchase this software from a computer software wholesaler at $120 per package, with the privilege of returning all unsold packages and receiving a full $120 refund per package. She also knows that she would pay $2,000 to Computer Conventions, Inc., for the booth rental at the convention. She will incur no other costs. She must decide whether she should rent a booth.
Explain the features of cost-volume-profit (CVP) analysis
. . . how operating income changes with changes in output level. selling prices, variable costs, or fixed costs
Mary, like most managers who face such a situation, works through a series of steps. 1. Identify the problem and uncertainties. The decision to rent the booth hinges critically on how M a r y resolves two important uncertainties-the price she can charge and the number of packages she can sell at that price. Every decision deals with selecting a
CHAPTER 3 COST-VOLUME-PROFIT ANALYSIS
course of action. The outcome of the chosen action is uncertain and will only be known in the future. 2. Obtain information. When faced with uncertainty, managers obtain information that might help them understand the uncertainties better. For example, Mary gathers information about the type of individuals likely to attend the convention and other software that might be sold at the convention. She also gathers data on her past experiences selling Do-A11 Software at conventions very much like the Chicago convention. 3. Make predictions about the future. Using all the information available to them, managers make predictions. Mary predicts that she can charge a price of $200 for Do-All Software. At that price she is reasonably confident that she will be able to sell 30 packages and possibly as many as 60. In making these prcdictions, Mary like most managers, must exercise considerable judgment. Her predictions rest on the belief that her experience at the Chicago convention will be similar to her experience at the San Francisco convention four months earlier. Yet, Mary ponders several questions. Is this comparison appropriate? Have conditions and circumstances changed over the last four months? Are there any biases creeping into her thinking? She is keen on selling at the Chicago convention because sales in the last couple of months have been lower than expected. Is this experience making her predictions overly optimistic? Has she ignored some of the competitive risks? Will the other software vendors at the convention reduce their prices? Mary reviews her thinking. She retests her assumptions. She also explores these questions with John Mills, a close friend, who has extensive experience selling software like Do-All. In the end, she feels quite confident that her predictions are reasonable and carefully thought through. 4. Make decisions by choosing among alternatives. Mary uses CVP analysis, described just below, and decides to rent the booth at the Chicago convention.
5. Implement the decision, evaluate performance, and learn. Thoughtful managers never stop learning. They compare their actual performance to predicted performance to understand why things worked out the way they did and what they might learn. At the end of the Chicago convention, for example, Mary would want to evaluate whether her predictions about price and the number of packages she could sell were correct. Such feedback would be very helpful to Mary as she makes decisions about renting booths at subsequent conventions.
How does Mary use CVP analysis in Step 4 to make her decision? Mary begins by identifying what costs are fixed and what costs are variable. The booth-rental cost of $2,000 is a fixed cost because it will not change no matter how many packages Mary sells. The cost of the package itself is a variable cost because it increases in proportion to the number of packages sold. Mary will incur a cost of $120 for each package that she sells. To get an idea of how operating income will change as a result of selling different quantities of packages, Mary calculates operating income if sales are 5 packages and if sales are 40 packages.
Revenues Variable purchase costs Fixed costs Operating income
5 packages sold 40 packages sold $1,000 ($200 per package X 5 packages) $8,000 ($200 per package x 40 packages)
600 ($120 per package X 5 packages) 2,000 $(1,600) 4,800 ($120 per package X 40 packages) 2,000
The only numbers that change from selling different quantities of packages are total revenues and total variable costs. The difference between total revenues and total variable costs is called contribution margin. Contribution margin indicates why operating income changes as the number of units sold changes. The contribution margin when Mary sells 5 packages is $400 ($1,000 in total revenues minus $600 in total variable costs); the contribution margin when Mary sells 40 packages is $3,200 ($8,000 in total revenues minus $4,800 in total variable costs). When calculating the contribution margin, be sure to subtract all variable costs. For example, if Mary had variable selling costs
ESSENTIALS OF CVP ANALYSIS H 63
because she paid a commission to salespeople for each package they sold at the convention, variable costs would include the cost of each package plus the sales commission. Contribution margin per unit is a useful tool for calculating contribution margin and operating income. Contribution margin per unit is the difference between selling price and variable cost per unit. In the Do-All Software example, contribution margin per package, or per unit, is $200 - $120 = $80. Contribution margin per unit recognizes the tight coupling of selling price and variable cost per unit. Unlike fixed costs, Mary will only incur the variable cost per unit of $120 when she sells a unit of Do-All Software for $200. Consequently, a second way to calculate contribution margin is: Contribution margin
Contribution margin per unit x Number o units sold f
For example, when 40 packages are sold, contribution margin = $80 per unit x 40 units = $3,200. Even before she gets to the convention, Mary incurs $2,000 in fixed costs. For each package that Mary sells at the convention, she recovers $80 of the $2,000. Mary hopes to sell enough packages to fully recover the $2,000 she spent for renting the booth and to then make a profit. Exhibit 3-1 presents contribution margins for different quantities of packages sold. The income statement in Exhibit 3-1 is called a contribution income statement because it groups costs into variable costs and fixed costs to highlight contribution margin. See how each additional package sold from 0 to 1to 5 increases contribution margin by $80 per package, recovering more of the fixed costs and reducing the operating loss. If Mary sells 25 packages, contribution margin equals $2,000 ($80 per package x 25 packages), exactly recovering fixed costs and resulting in $0 operating income. If Mary sells 40 packages, contribution margin increases by another $1,200 ($3,200 - $2,000), all of which becomes operating income. As you look across Exhibit 3-1 from left to right, you see that the increase in contribution margin exactly equals the increase in operating income (or the decrease in operating loss). Instead of expressing contribution margin as a dollar amount per unit, we can express it as a percentage. Contribution margin percentage (also called contribution margin ratio) equals contribution margin per unit divided by selling price. In our example, Contribution margin percentage
0.40, or 40%
Contribution margin percentage is the contribution margin per dollar of revenue. In this example, contribution margin percentage is 40% of each dollar of revenue (equal to 40 cents). Mary can calculate total contribution margin for different output levels by multiplying the contribution margin percentage by the total revenues shown in Exhibit 3-1. For example, if Mary sells 40 packages, revenues will be $8,000 and contribution margin will equal 40% of $8,000, or 0.40 x $8,000 = $3,200. Mary earns operating income of $1,200 ($3,200 - $2,000) by selling 40 packages for $8,000. How was the Excel spreadsheet in Exhibit 3-1 constructed? Underlying the Exhibit are some equations that express the CVP relationships. To make good decisions using CVP analysis, we must understand these relationships and the structure of the
Revenues Variable costs Contribution margin Fixed costs Operating income
$ 200 per package $ 120 per package $ 80 per package $2,000
Number of Packages Sold 0 25 40 5 $ 200 $1,000 $5,000 $8,000 $ 0 01 600 3,000 4,800 120 - - 80 0 400 2,000 3,200 2,000 2,000 ----2,000 2,000 2,000
Contribution Income Statement for Different Quantities of Do-All Software Packages Sold
contribution income statement in Exhibit 3-1. There are three related ways (we will call them methods) to think more deeply about and model CVP relationships: the equation method, the contribution margin method, and the graph method. The equation method and the contribution margin method are most useful when managers want to determine operating income at few specific levels of sales (for example 5, 15, 25, and 40 units sold). The graph method helps managers visualize the relationship between units sold and operating income over a wide range of quantities of units sold. As we shall see later in the chapter, different methods are useful for different decisions.
Each column in Exhibit 3-1 is expressed as an equation.
Revenues - Variable costs
Fixed costs = Operating income
H o w are revenues in each column calculated?
Revenues = Selling price (SP) x Quantity of units sold (a)
How are variable costs In each column calculated?
Variable costs = Var~able cost per u n ~ (VCU) x Quant~ty units sold ( 0 ) t of
Quantityof units sold
Var~ablecost Q u a n t l t y ~ f ) ] X units sold per unit
Fixed - Operating costs income
Equation 1 becomes the basis for calculating operating income for different quantities of units sold. For example, if you go to cell F7 in Exhibit 3-1, the calculation of operating income when Mary sells 5 packages is
Contribution Margin Method
Rearranging equation 1,
Selling - Variable cost) price per unit Contribution margin per unit
(Quantity ~ f ) ] - Fixed - Operating units sold costs income
In our DO-All Software example, contribution margin per unit is $80 ($200 - $120), so when Mary sells 5 packages,
Operating income = ($80 X
5) - $2,000
Equation 2 expresses the basic idea we described earlier-each unit sold helps Mary recover $80 (in contribution margin) of the $2,000 in fixed costs.
In the graph method, we represent total costs and total revenues graphically. Each is shown as a line on a graph. Exhibit 3-2 illustrates the graph method for Do-A11 Software. Because we have assumed that total costs and total revenues behave in a linear fashion, we need only two points t o plot the line representing each of them.
1. Total costs line. The total costs line is the sum of fixed costs and variable costs. Fixed costs are $2,000 at all quantities of units sold within the relevant range. To plot the total costs line, use as one point the $2,000 fixed costs at zero units sold (point A), because variable costs are $0 when no units are sold. Select a second point by choosing any other convenient output level (say, 40 unlts sold) and determine the corresponding total costs. Total variable costs at this output level are $4,800 (40 units x $120 per unit).
Total & -
Cost-Volume Graph for Do-All Software
= 25 units
**slope of the total costs line is the variable cost per unit = $120 * Slope of the total revenues line is the selling price = $200
Remember, fixed costs are $2,000 at all quantities of units sold within the relevant range, so total costs at 40 units sold equal $6,800 ($2,000 + $4,800), which is point B in Exhibit 3-2. The total costs line is the straight line from point A through point B. 2. Total revenues line. One convenient starting point is $0 revenues at 0 units sold, which is point C in Exhibit 3-2. Select a second point by choosing any other convenient output level and determining the corresponding total revenues. At 40 units sold, total revenues are $8,000 ($200 per unit X 40 units), which is point D in Exhibit 3-2. The total revenues line is the straight line from point C through point D. Profit or loss at any sales level can be determined by the vertical distance between the two lines at that level in Exhibit 3-2. For quantities fewer than 25 units sold, total costs exceed total revenues, and the purple area indicates operating losses. For quantities greater than 25 units sold, total revenues exceed total costs, and the blue-green area indicates operating incomes. At 25 units sold, total revenues equal total costs. Mary will break even by selling 25 packages.
Now that you have seen how CVP analysis works, think about the following assumptions we made during the analysis: 1. Changes in the levels of revenues and costs arise only because of changes in the number of product (or service) units sold. The number of units sold is the only revenue driver and the only cost driver. Just as a cost driver is any factor that affects costs, a revenue driver is a variable, such as volume, that causally affects revenues, 2. Total costs can be separated into two components: a fixed component that does not vary with units sold and a variable component that changes with respect to units sold. Furthermore, you know from Chapter 2 (Exhibit 2-5, p. 34) that variable costs include both direct variable costs and indirect variable costs of a product. Similarly, fixed costs include both direct fixed costs and indirect fixed costs of a product. 3. When represented graphically, the behaviors of total revenues and total costs are [inear (meaning they can be represented as a straight line) in relation to units sold within a relevant range (and time period). 4. Selling price, variable cost per unit, and total fixed costs (within a relevant range and time period) are known and constant.
66 1 CHAPTER 3
As the CVP assumptions make clear, an important feature of CVP analysis is distinguishing fixed from variable costs. Always keep in mind, however, that whether a cost is variable or fixed depends on the time period for a decision. The shorter the time horizon, the higher the percentage of total costs considered fixed. Suppose an American Airlines plane will depart from its gate in the next hour and currently has 20 seats unsold. A potential passenger arrives with a transferable ticket from a competing airline. What are the variable costs to American of placing one more passenger in an otherwise empty seat? Variable costs (such as one more meal) would be negligible. Virtually all the costs in this decision situation (such as crew costs and baggage-handling costs) are fixed. Alternatively, suppose American must decide whether to include another city in its routes. This decision may have a one-year planning horizon. Many more costs, including crew costs, baggage-handling costs, and airport fees, would be considered variable. Always consider the relevant range, the length of the time horizon, and the specific decision situation when classifying costs as variable or fixed.
Breakeven Point and Target Income
Determine the breakeven point and output level needed to achieve a target operating income
. .compare contribution margin and fixed costs
The breakeven point (BEP) is that quantity of output sold at which total revenues equal total costs-that is, the quantity of output sold that results in $0 of operating income. Managers are interested in the breakeven point because they want to avoid operating losses. The breakeven point tells them how much output they must sell to avoid a loss. We have already seen how to use the graph method to calculate the breakeven point. Recall from ~ x h i b i t3-1 that operating income was $0 when Mary sold 2 5 units, the breakeven point. But by understanding the equations underlying the calculations in . Exhibit 3-1, we can calculate the breakeven point directly for Do-A11 Software rather than trvine out different auantities and checking when o ~ e r a t i n ~ income eauals $0. , u " Recall the equation method (equation 1):
Setting operating income equal to $0 and denoting quantity of output units that must be sold by Q,
- $2,000 = $O
$80 X 0 = $2,000
0 = $2,000 + $80 per unit = 25 units
If Mary sells fewer than 25 units, she will have a loss; if she sells 25 units, she will break even; and if she sells more than 25 units, she will make a profit. While this breakeven point is expressed in units, it can also be expressed in terms of revenues: 25 units x $200 selling price = $5,000. Recall the contribution margin method (equation 2):
Contribution margin per unit
Quantity of units sold
- Fixed costs = Operating income
At the breakeven point, operating income is by definition $0 and so:
Contribution margin per unit
x Breakeven number of units
= Fixed cost
(Equation 3 )
Rearranging equation 3 and entering the data,
Brea keven Fixed costs - $2,000 = 25 units number of units Contribution margin per unit $80 per unit
To calculate the breakeven point in terms of revenues, recall that in the Do-All Software exampl e,
Contribution margin - Contribution margin per unit - $80 percentage Selling price $200
0.40, or 40%
BREAKEVEN POINT AND TARGET INCOME E 67
That is, 40% of each dollar of revenue, or 40 cents, is contribution margin. To break even, contribution margin must equal fixed costs of $2,000. To earn $2,000 of contribution margin, revenues must equal $2,000 + 0.40 = $5,000.
Brea keven revenues
Fixed costs - $2,000 - -- $5,000 Contribution margin % 0.40
The breakeven point tells managers how much they must sell to avoid a loss. But managers are equally interested in how they will achieve the operating income targets underlying their strategies and plans. For example, selling 25 units at a price of $200 assures Mary that she will not lose money if she rents the booth. This news is comforting, but Mary is equally interested in learning how much she needs to sell to achieve a targeted amount of operating income.
Target Operating Income
We illustrate target operating income calculations by asking: How many units must Mary sell to earn an operating income of $1,200? Exhibit 3-1 shows that operating income is $1,200 when 40 packages are sold. Equation 1 helps us to find Q directly without plugging in different quantities into Exhibit 3-1 and checking when operating income equals $1,200.
- $2,000 = $1,200
$3,200 + $80 per unit = 40 units
Alternatively, we could modify the contribution margin method and equation 2,
required to be sold Quantity of units - Fixed costs + Target operating income Contribution margin per unit
Quantity of units - $2,000 + $1,200 = 40 units required to be sold $80 per unit
Revenues, $200 per unit x 40 units Variable costs, $120 per unit X 40 units Contribution margin, $80 per unit x 40 units Fixed costs Operating income
The revenues needed to earn an operating income of $1,200 can also be calculated directly by recognizing (1)that $3,200 of contribution margin must be earned (fixed costs of $2,000 plus operating income of $1,200) and (2) that each dollar of revenue earns 40 cents of contribution margin. To earn $3,200 of contribution margin, revenues must equal $3,200 t 0.40 = $8,000.
Revenues needed to earn $1,200 =
$2 000 + $1,200 - - = $8,000 - $3,200 0.40 0.40
The graph in Exhibit 3-2 is very difficult to use if the question is: How many units must Mary sell to earn an operating income of $1,200. Why? Because it is not easy to determine from the graph the precise point at which the difference between the total revenues line and the total costs line equals $1,200. However, recasting Exhibit 3-2 in the form of a profitvolume (PV) graph makes it easier to answer this question. A PV graph shows how changes in the quantity of units sold affect operating income. Exhibit 3-3 is the PV graph for Do-All Software (fixed costs, $2,000; selling price, $200; and variable cost per unit, $120). The PV line can be drawn using two points. One convenient point (M) is the operating loss at 0 units sold, which is equal to the fixed costs of $2,000, shown at -$2,OOO on the vertical axis. A second convenient point (N) is the breakeven point, which is 25 units in our example (see p. 66). The PV line is the straight line from point M through point N. To find the number of units Mary must sell to earn an operating income of $1,200, draw a horizontal line parallel to the x-axis corresponding to
68 W CHAPTER 3 COST-VOLUME-PROFIT ANALYSIS
$1,200 on the vertical axis (that's the y-axis). At the point where this line intersects the PV line, draw a vertical line down t o the horizontal axis (that's the x-axis). The vertical line intersects the x-axis at 4 0 units, indicating that by selling 4 0 units Mary will earn a n operating income of $1,200.
Target Net Income and Income Taxes
Net income is operating income plus nonoperating revenues (such as interest revenue) minus nonoperating costs (such as interest cost) minus income taxes. For simplicity, throughout this chapter we assume nonoperating revenues and nonoperating costs are zero. Thus, net income is computed as operating income minus income taxes. Thus far, we have ignored the effect of income taxes in our CVP analysis. In many companies, the income targets for managers in their strategic plans are expressed in terms of net income. That's because top management wants subordinate managers t o take into account the effects their decisions have on operating income after income taxes are paid. Some decisions may not result in large operating incomes. But they may have favorable tax consequences and s o may be attractive on a net income basis-the measure that drives shareholders' dividends and returns. To make net income evaluations, CVP calculations for target income must be stated in terms of target net income instead of target operating income. For example, Mary may be interested in knowing the quantity of units she must sell t o earn a net income of $960, assuming a n income tax rate of 40%. Using the equation method,
Understand how income taxes affect CVP analysis
. . . focus on net income
Variable costs - Fixed costs = Target operating income
Target net income = Target operating income
Target operating income
x Tax rate
Target net income = (Target operating income) x (1 - Tax rate) Target operating income = Target net income
1 - Tax rate
Substituting for target operating income:
Fixed costs =
Target net income
Profit-Volume G r a p h for Do-All Software
BEP = Breakeven point
U S I N G CVF' ANALYSIS FOR DECISION M A K I N G
Substituting numbers from our Do-All Software example:
$960 $2,000 = 1 - 0.40 $2,000 = $1,600
($200 x Q)
($120 x 0 )
$80 x Q = $3,600 Q = $3,600 + $80 per unit = 45 units
Alternatively, we can use the contribution margin method and equation 4 and substitute:
Target operating income = Target net income
Quantity of units required to be sold
+ Target net income 1 Tax rate
Contribution margin per unit $2,000 $960 + -- $2,000 + $1,600 1 - 0.40
Quantity of units required to be sold
= 45 units
$80 per unit $9,000 5,400 3,600 2,000 1,600 640
Revenues, $200 per unit X 45 units Variable costs, $120 per unit X 45 units Contribution margin Fixed costs Operating income Income taxes, $1,600 X 0.40 Net income
Mary can also use the PV graph in Exhibit 3-3. For a target net income of $960,
Target operating income = Target net income
1 - Tax rate
$960 - $1,600 1 - 0.40
From Exhibit 3-3, to earn target operating income of $1,600, Mary needs to sell 4 5 units. Focusing the analysis on target net income instead of target operating income will not change the breakeven point. That's because, by definition, operating income a t the breakeven point is $0, and no income taxes are paid when there is no operating income.
Using CVP Analysis for Decision Making
We have seen how CVP analysis is useful for calculating the units that need to be sold to break even, or to achieve a target operating income or target net income. Managers also use CVP analysis to guide other decisions, many of them strategic decisions. Consider a decision about choosing additional features for an existing product. Different choices can affect selling prices, variable cost per unit, fixed costs, units sold, and operating income. CVP analysis helps managers make product decisions by estimating the expected profitability of these choices. Strategic decisions invariably entail risk. CVP analysis can be used t o evaluate how operating incmne will be affected if the original predicted data are not achieved-say, if sales are 1 0 % lower than estimated. Evaluating this risk affects other strategic decisions a company might make. For example, if the probability of a decline in sales seems high, a manager may take actions to change the cost structure to have more variable costs and fewer fixed costs. We return to our Do-All Software example to illustrate using CVP analysis for strategic decisions concerning advertising and selling price.
Explain CVP analysis in decision making and how sensitivity analysis helps managers cope with uncertainty
Decision to Advertise
Returning to Do-All Software, suppose Mary anticipates selling 40 units at the convention. Exhibit 3-3 indicates that Mary's operating income will be $1,200. Mary is considering
. . . determine the effect on operating income of different assumptions
CHAPTER 3 COST-VOLUME-PROFIT ANALYSIS
placing an advertisement describing the product and its features in the convention brochure. The advertisement will cost $500. This cost is a fixed cost because it will not change regardless of the number of units Mary sells. She thinks that advertising will increase sales by 10% to 44 packages. Should Mary advertise? The following table presents the CVP analysis.
40 Packages Sold with N o Advertising (1 $8,000 4,800 3,200 2,000 $1,200 -
Revenues ($200 x 40; $200 x 44) Variable costs ($120 x 40; $120 x 44) Contribution margin ($80 x 40; $80 X 44) Fixed costs Operating income
44 Packages Sold with Advertising (2) $8,800 5,280 3,520 2,500 $1,020 -
(3) = (2) - (1) $800 480 320 500 $(180) -
Operating income decreases from $1,200 to $1,020, so Mary should not advertise. Note that Mary could focus only on the difference column and come to the same conclusion: If Mary advertises, contribution margin will increase by $320 (revenues, $800-variable costs, $480), and fixed costs will increase by $500, resulting in a $180 decrease in operating income. As you become more familiar with CVP analysis, try evaluating decisions based on differences rather than mechanically working through the contribution income statement. Analyzing differences gets to the heart of CVP analysis and sharpens intuition by focusing only on the revenues and costs that will change by implementing new decisions.
Decision to Reduce Selling Price
Having decided not to advertise, Mary is contemplating whether to reduce the selling price to $175. At this price, she thinks she kill sell 50 units. At this quantity, the software wholesaler who supplies Do-All Software will sell the packages to Mary for $115 per unit instead of $120. Should Mary reduce the selling price? No, as the following CVP analysis shows.
Contribution margin from lowering price t o $175: ($175 - $115) per unit x 50 units Contribution margin from maintaining price at $200: ($200 - $120) per unit X 40 units Change in contribution margin from lowering price
Decreasing the price will reduce contribution margin by $200 and, because the fixed costs of $2,000 will not change, it will also reduce operating income by $200. Mary could also ask "At what price can I sell 50 units (purchased at $115 per unit) and continue to earn an operating income of $l,200?" The answer is $179, as the following calculations show.
Target operating income Add fixed costs Target contribution margin Divided by number of units sold Target contribution margin per unit Add variable cost per unit Target selling price Proof: Revenues, $179 per unit X 50 units Variable costs, $1 15 per unit x 50 units Contribution margin Fixed costs Operating income
$1,200 2,000 $3,200 +50 units $ 64
Mary should also examine the effects of other decisions, such as simultaneously increasing advertising costs and lowering prices. In each case, Mary will compare the changes in contribution margin (through the effects on selling prices, variable costs, and quantities of units sold) to the changes in fixed costs, and she will choose the alternative that provides the highest operating income.
SENSITIVITY ANALYSIS AND UNCERTAINlY W 71
Sensitivity Analysis and Uncertainty
Before choosing strategies and plans about how t o implement strategies, managers frequently analyze the sensitivity of their decisions to changes in underlying assumptions. Sensitivity analysis is a "what-if" technique that managers use to examine how an outcome will change if the original predicted data are not achieved or if an underlying assumption changes. In the context of CVP analysis, sensitivity analysis answers questions such as, What will operating income be if the quantity of units sold decreases by 5 % from the original prediction? And, What will operating income be if variable cost per unit increases by l o % ? The sensitivity of operating income to various possible outcomes broadens managers' perspectives about what might actually occur before they commit costs. Electronic spreadsheets, such as Excel, enable managers to conduct CVP-based sensitivity analyses in a systematic and efficient way. Using spreadsheets, managers can conduct sensitivity analysis to examine the effect and interaction of changes in selling price, variable cost per unit, fixed costs, and target operating income. Exhibit 3-4 displays a spreadsheet for the Do-A11 Software example. Mary can immediately see how many units she needs to sell to achieve particular operating-income levels, given alternative levels of fixed costs and variable cost per unit that she may face. For example, 32 units must be sold to earn a n operating income of $1,200 if fixed costs are $2,000 and variable cost per unit is $100. Mary can also use Exhibit 3-4 to determine that she needs to sell 56 units to break even (earn operating income of $0) if the booth rental at the Chicago convention is raised to $2,800 (increasing fixed costs to $2,800) and if the software supplier raises its price to $150 (increasing variable cost t o $150 per unit). Mary can use information about costs and sensitivity analysis, together with realistic predictions about how much she can sell to decide if she should rent a booth at the convention. Another aspect of sensitivity analysis is margin of safety, the amount by which budgeted (or actual) revenues exceed breakeven revenues. Expressed in units, margin of safety is the sales quantity minus the breakeven quantity. The margin of safety answers the "what-if" question: If budgeted revenues are above breakeven and drop, how far can they fall below budget before the breakeven point is reached? Such a fall could be a result of a competitor introducing a better product, or poorly executed marketing programs, and so on. Assume that Mary has fixed costs of $2,000, a selling price of $200, and variable cost per unit of $120. For 40 units sold, the budgeted revenues are $8,000 and the budgeted operating income is $1,200. The breakeven point for this set of assumptions is 25 units
Exhibit 3-4 Spreadsheet Analysis of CVP Relationships for Do-All Software
of units required to be sold at $ to Earn Taraet Ooeratina
Fixed Costs $2,000 $2,000
per Unit $100
(Breakeven point) 20 25 4
CHAPTER 3 COST-VOLUME-PROFIT ANALYSIS
($2,000 + $80 per unit), or $5,000 ($200 per unit margin of safety by using the following equation:
Margin of safety = Margin of safety (in units)
25 units). Mary can determine the
Breakeven = $8,000 revenues
$5,000 = $3,000 25 = 15 units
Budgeted - Breakeven = 40 sales (units) sales (units)
Sometimes margin of safety is expressed as a percentage:
Margin of safety percentage = Margin of safety in dollars
Budgeted (or actual) revenues
= ----- =
In our example, margin of safety percentage
This result means that revenues would have to decrease substantially, by 37.5%, to reach breakeven revenues. The high margin of safety gives Mary confidence that she is unlikely to suffer a loss. If, however, Mary expected to sell only 30 units, budgeted revenues would be $6,000 ($200 per unit x 30 units) and the margin of safety would equal:
Budgeted revenues - Breakeven revenues = $6,000
$5,000 = $1,000
Margin of - Margin of safety in dollars - $1,000 safety percentage Budgeted (or actual) revenues $6,000
This result means that if revenues decrease by more than 16.67%, Mary would suffer a loss. A low margin of safety increases the risk of a loss. If Mary does not have the tolerance for this level of risk, she will prefer not to rent a booth at the convention. Sensitivity analysis is a simple approach to recognizing uncertainty, which is the possibility that an actual amount will deviate from an expected amount. Sensitivity analysis gives managers a good feel for the risks involved. A more comprehensive approach to recognizing uncertainty is to compute expected values using probability distributions. This approach is illustrated in the appendix to this chapter.
Cost Planning and CVP
Use CVP analysis to plan variable and fixed costs
Managers have the ability to choose the levels of fixed and variable costs in their cost structures. This is a strategic decision. In this section, we describe various factors that managers and management accountants consider as they make this decision.
. . . compare risk of
Alternative Fixed-CostNariable-Cost Structures
CVP-based sensitivity analysis highlights the risks and returns as fixed costs are substituted for variable costs in a company's cost structure. In Exhibit 3-4, compare line 6 and line 11.
Number of units required to be sold at $200 selling price to earn target operating income of $0 (Breakeven point) $2.000 25 50 28 48
losses versus higher returns
Line 6 Line 11
Fixed Cost $2,000 $2.800
Variable Cost $1 20 $1 00
Compared to Line 6, Line 11, with higher fixed costs, has more risk of loss (has a higher breakeven point) but requires fewer units to be sold (48 versus 50) to earn operating income of $2,000. CVP analysis can help managers evaluate various fixed-cost/variablecost structures. We next consider the effects of these choices in more detail. Suppose Computer Conventions, Inc. offers Mary three rental alternatives: Option 1: $2,000 fixed fee Option 2: $800 fixed fee plus 1 5 % of convention revenues Option 3: 25% of convention revenues with no fixed fee
COST PLANNING AND CVP
Mary's variable cost per unit is $120. Mary is interested in how her choice of a rental agreement will affect the income she earns and the risks she faces. Exhibit 3-5 graphically depicts the profit-volume relationship for each option. The line representing the relationship between units sold and operating income for Option 1 is the same as the line in the PV graph shown in Exhibit 3-3 (fixed costs of $2,000 and contribution margin per unit of $80). The line representing Option 2 shows fixed costs of $800 and a contribution margin per unit of $50 [selling price, $200, minus variable cost per unit, $120, minus variable rental fees per unit, $30, (0.15 x $200)]. The line representing Option 3 has fixed costs of $0 and a contribution margin per unit of $30 [$200 $120 - $50 (0.25 X $200)1. Option 3 has the lowest breakeven point (0 units), and Option 1 has the highest breakeven point ( 2 5 units). Option 1 has the highest risk of loss if sales are low, but it also has the highest contribution margin per unit ($80) and hence the highest operating income when sales are high (greater than 40 units). The choice among Options 1, 2, and 3 is a strategic decision that Mary faces. As in most strategic decisions, what she decides now will significantly affect her operating income (or loss), depending on the demand for Do-All Software. Faced with this uncertainty, Mary's choice will be influenced by her confidence in the level of demand for the software package and her willingness to risk losses if demand is low. For example, if Mary's tolerance for risk is high, she will choose Option 1 with its high potential rewards. If, however, Mary is averse to taking risk, she will prefer Option 3, where the rewards are smaller if sales a r e high but where she never suffers a loss if sales are low.
The risk-return trade-off across alternative cost structures can be measured as operating leverage. Operating leverage describes the effects that fixed costs have on changes in operating income as changes occur in units sold and contribution margin. Organizations with a high proportion of fixed costs in their cost structures, as is the case under Option 1, have high operating leverage. The line representing Option 1 in Exhibit 3-5 is the steepest of t h e three lines. Small increases in sales lead to large increases in operating income. Small decreases in sales result in relatively large decreases in operating income, leading to a greater risk of operating losses. At any given level of sales,
Degree of - Contribution margin operating leverage Operating income
The following table shows the degree of operating leverage at sales of 40 units for the three rental options.
Option 1 80 Option 2 50 Option 3 30
1. Contribution margin per unit (p. 73) 2. Contribution margin (Row 1 X 40 units] 3. Operating income (from Exhibit 3-51
4. Degree of operating leverage (Row 2 + Row 3)
These results indicate that, when sales are 40 units, a percentage change in sales and contribution margin will resilt in 2.67 times that percentage change in operating income for Option 1, but t h e same percentage change (1.00) In operating income for Option 3. Consider, for example, a sales increase of 50% from 40 to 6 0 units. Contribution margin will increase by 5 0 % under each option. Operating income, however, will increase by 2.67 x 50% = 133% from $1,200 to $2,800 in Option 1, but it will increase by only 1.00 x 50% = 5 0 % from $1,200 to $1,800 in Option 3 (see Exhibit 3-5). The degree of operating leverage at a given level of sales helps managers calculate the effect of fluctuations in sales on operating income. Keep in mind that, in the presence of fixed costs, the degree of operating leverage is different at different levels of sales. For example, at sales of 60 units, the degree of operating leverage under each of the three options is as follows:
Profit-Volume Graph for Alternative Rental Options for Do-All Software
Operating loss area BEP = Breakeven point
$ 50 $3,000 $2,200
1. Contribution margin per unit (p. 73) 2. Contribution margin (Row 1 X 60 units) 3. Operating income (from Exhibit 3-5) 4. Degree of operating leverage (Row 2 + Row 3)
80 $4,800 $2,800
$ 30 $1,800 $1,800
The degree of operating leverage decreases from 2.67 (at sales of 40 units) to 1.71 (at sales of 60 units) under Option 1 and from 1.67 to 1.36 under Option 2. In general, whenever there are fixed costs, the degree of operating leverage decreases as the level of sales increases beyond the breakeven point. If fixed costs are $0 as in Option 3, contribution margin equals operating income, and the degree of operating leverage equals 1.00 at all sales levels. But why must managers monitor operating leverage carefully? Again, consider companies such as US Airways, United Airlines, Worldcorn, and Global Crossing. Their high operating leverage was a major reason for their financial problems. Anticipating high demand for their services, these companies borrowed money to acquire assets, resulting in high fixed costs. As sales declined in 2001 and 2002, these companies suffered losses and could not generate sufficient cash to service their interest and debt, causing them to seek bankruptcy protection. Could these problems have been avoided? Perhaps, if managers had not built up assets and fixed costs too quickly to take advantage of the opportunities they saw in the marketplace. However, by doing so they simultaneously increased the risk of losses if demand for their products proved to be weak. Managers could also have reduced the magnitude of these problems by using equity rather than debt to finance the purchase of assets. Unlike debt, equity does not have a predetermined schedule of repayments. Equity financing w o d d have given these companies more time to ride out the periods of weak demand for their services. So why didn't these companies use equity? Because relative to debt, equity financing is more costly. Managers and management accountants should always evaluate how the level of fixed costs and variable costs they choose will affect the risk-return trade-off. See Concepts in Action, p. 77, for another example of the risks of high fixed costs. What actions are managers taking to reduce their fixed costs? Many companies are moving their manufacturing facilities from the United States to lower-cost countries, such as Mexico and China. To substitute high fixed costs with lower variable costs, companies are purchasing products from lower-cost suppliers instead of manufacturing products themselves. These actions reduce both costs and operating leverage. More recently,
EFFECTS O F SALES MIX O N I N C O M E
General Electric and Hewlett-Packard began outsourcing service functions, such as postsales customer service, by shifting their customer call centers to countries, such as India, where costs are lower. These decisions by companies are not without controversy. Some economists argue that outsourcing helps to keep costs, and therefore prices, low and enables U.S. companies to remain globally competitive. Others argue that outsourcing reduces job opportunities in the United States and hurts working-class families.
Effects of Sa.les Mix on Income
Sales mix is the quantities (or proportion] of various products (or services) that constitute total unit sales of a company. Suppose Mary is now budgeting for a subsequent computer convention in Boston. She plans t o sell two different software products-Do-All and Superword-and budgets the following:
Expected sales Revenues, $200 and $100 per unit Variable costs, $120 and $70 per unit Contribution margin, $80 and $30 per unit Fixed costs Operating income Apply CVP analysis t o a company producing multiple products
Do-All 60 $12,000 7,200 $4,800
Suoerword 40 $4,000 2,800 $1,200
Total 100 $16,000 10,000 6,000 4,500 $1,500
. . . assume sales mix of
products remains constant as total units sold changes
What is the breakeven point? In contrast to the single-product (or service) situation, the number of total units that must be sold to break even in a multiproduct company depends on the sales mix-the combination of the number of units of Do-All sold and the number of units of Superword sold. We assume that the budgeted sales mix (60 units of Do-A11 sold for every 40 units o Superword sold, that is, 3 units of Do-A11 sold for every 2 units of f Superword sold) will not change at different levels of total unit sales. That is, we think of Mary selling a bundle of 3 units of Do-A11 and 2 units of Superword. Note that this does not mean that Mary physically bundles the two products together into one big package. Instead, we think in terms of bundling to assist in budgeting. Each bundle yields a contribution margin of $300 calculated as follows:
Number of Units of Do-All and Superword in Each Bundle 3 2 Contribution Margin per Unit for Do-All and Superword $80 30 Contribution Margin of the Bundle $240 60
DO-All Superword Total
$300 Brea keven Fixed costs $4.500 = 15 bundles point in = Contribution margin per bundle $300 per bundle bundles
To compute the breakeven point, we calculate the number of bundles Mary needs to sell.
Breakeven point in units of Do-All and Superword is:
DO-Alf: 15 bundles x 3 units of Do-All per bwldle Superword: 15 bundles X 2 units of Superword per bundle Total number of units to breakeven
- units 75 -
Breakeven point in dollars for Do-All and Superword is:
Do-All: 45 units X $200 per unit Superword: 30 units x $100 per unit Breakeven revenues
We can also calculate the breakeven point in revenues for the multiple-products situation as follows:
76 W CHAPTER 3 COST-VOLUME-PROFITANALYSIS Number of Units of Do-All and Superword in Each Bundle 3 2 Selling Price for Do-All and Superword $200 100
DO-All Superword Total
Revenue of the Bundle $600 200 -
Contribution percentage for the bundle
Contribution margin o the bundle f Revenue o the bundle f
$300 = 0.375 or 37.5%
Fixed costs Breakeven -- $4f500 - $12,000 revenues Contribution margin % for the bundle 0.375 Number o bundles f required to be sold to break even
Breakeven revenues Revenue per bundle
$1 2,000 $800 per bundle
= 15 bundles
That is, breakeven point in units and dollars for Do-All and Superword are: Do-All: 15 bundles X 3 units of Do-All per bundle = 45 units X $200 per unit = $9,000 Superword: 15 bundles X 2 units o Superword per bundle = 30 units X $100 per unit = $3,000 f Recall that in all our calculations, we have assumed that the budgeted sales mix ( 3 units of Do-All for every 2 units of Superword) will not change at different levels of total unit sales. Of course, there are many different sales mixes (in units) that result in a contribution margin of $4,500 and cause Mary to break even, as the following table shows:
Sales Mix (Units) Do-All Superword Contribution Margin from Do-All Superword Total Contribution Margin
If for example, the sales mix changes to 3 units of Do-A11 for every 7 units of Superword, you can see in the preceding table that the breakeven point increases from 75 units to 100 units, comprising 30 units of Do-A11 and 70 units of Superword. The breakeven quantity increases because the sales mix has shifted toward the lower-contributionmargin product, Superword ($30 per unit compared to Do-All's $80 per unit). In general, for any given total quantity of units sold, as the sales mix shifts toward units with lower contribution margins (more units of Superword compared t o Do-All), operating income will be lower. How do companies choose their sales mix? They adjust their mix to respond to demand changes. For example, as gasoline prices increase and customers want smaller cars, auto companies shift their production mix to produce additional smaller cars.
Multiple Cost Drivers
Adapt CVP analysis to situations in which a product has more than one cost driver Throughout this chapter, we have assumed that the number of output units is the only revenue driver and the only cost driver. Now we describe how some aspects of CVP analysis can be adapted to the general case of multiple cost drivers. Consider again the single-product Do-A11 Software example. Suppose Mary will incur a variable cost of $10 for preparing documents (including an invoice) for each customer who buys Do-All Software. That is, the cost driver of document-preparation costs is the number of customers who buy Do-All Software. Mary's operating income can then be expressed in terms of revenues and these costs:
. . . basic concepts apply but simple formulas do not
MULTIPLE COST DRIVERS W 77
Sky-High Fixed Costs Trouble XM Satellite Radio
Building up too much fixed costs can be hazardous to a company's health. Because fixed costs, unlike variable costs, do not automatically decrease as volume declines, companies with too much fixed costs can lose a considerable amount of money during lean times. XM Satellite Radio, once the market leader in satellite radio broadcasting, learned this lesson the hard way. To begin broadcasting in 2001, XM had to spend over $1 billion on a broadcasting license, two space satellites, and other technology infrastructure. Once operational, the company also spent billions on other fixed items such as programming and content, satellite transmission, and R&D. In contrast, XM's variable costs were minimal, consisting mainly of artist-royalty fees and customer service and billing. In effect, this created a business model with a high operating leverage-that is, XM's cost structure had a very significant proportion of fixed costs. As such, the only way XM could be profitable was by amassing millions of paid subscribers and selling advertising. The competitive disadvantage of this highly-leveraged business model became apparent almost immediately. In 2002, Sirius Satellite Radio entered the market with basically the same offering as its competitor, XM: loo+ channels of music and talk radio available nationwide for a monthly subscription fee. Using thk samehighly leveraged business model as XM, Sirius pursued a nearly identical growth strategy of selling radio advertisements while growing a huge subscriber base. Other competitors lurked, as well. Traditional radio still held a huge share of the market, and around the same time as the launch of XM and Sirius, Apple released its first iPod portable digital-music player. Notably, Apple's iPod had a much lower operating leverage than satellite radio: R&D costs were much smaller, and its marginal costs were primarily tied to manufacturing and distribution. The iPod was profitable even at low sales volumes because of its low fixed costs. In response to Sirius and other competitors, XM began spending extravagantly for exclusive programming content. XM spent $650 million on the exclusive satellite broadcasting rights for Major League Baseball and gave Oprah Winfrey $55 million to start her XM show. Sirius responded by inking an exclusive deal with the National Football League and paying "shock-jock" Howard Stern nearly $500 million to move to Sirius. This added to the highly leveraged operating position of both companies. By 2006, despite its nearly 8 million subscribers, XM never turned a profit and most analysts and observers felt that neither XM nor Sirius (with 6 million subscribers) would ever be able to recover its high fixed costs. In 2007, XM bowed to cost and marketplace pressure and agreed to merge with Sirius. One observer called it the "stop us before we spend again" merger. Sirius CEO Me1 Karmazin-who will head up the combined entity-noted that operating leverage drove the merger. He vowed to look for "synergies on every line of the income statement."
Sources: =XM Satellite Radio (A)," Harvard Business School Case No. 9-504-009; "Satellite Radio: An Industry Case Study," Kellogg School of Management (Northwestern University) Case N o . 5-206-255; Testimony of Sean Buston, CFA, before the Copyright Royalty Board of the Library of Justin Fox, "The 'stop us before we spend again' merger," Time.com, February 20,2007. time-blog.com~curious~capitalist~ Congress (October 2006); 2007/021the~stop~us~before~we~spend~ag.html; analysts reports. Various
Cost of each ~ u r n b e of) r Do-All software X packages package sold
Cost of preparing Number of documents for x customers each customer
If Mary sells 40 packages t o 15 customers, then
Operating income = ($200 per package X 40 packages) - ($120 per package x 40 packages) ($10 per customer x 15 customers) - $2,000 = $8,000 - $4.800 - $150 - $2,000 = $1,050
If instead Mary sells 40 packages t o 40 customers, then
Operating income = ($200 X 40) - ($120 x 40) - ($10 x 40) - $2,000 = $8,000 - $4,800 - $400 - $2,000 = $800
78 W CHAPTER 3
The number of packages sold is not the only determinant of Mary's operating income. For a given number of packages sold, Mary's operating income will be lower if she sells Do-All Software to more customers. Mary's costs depend on two cost drivers: the number of packages sold and the number of customers. Just as in the case of multiple products, there is no unique breakeven point when there are multiple cost drivers. For example, Mary will break even if she sells 26 packages to 8 customers or 2 7 packages to 16 customers:
CVP Analysis in Service and Nonprofit Organizations
Thus far, our CVP analysis has focused on a merchandising company. CVP can also be applied to decisions by manufacturing, service, and nonprofit organizations. To apply CVP analysis in service and nonprofit organizations, we need to focus on measuring their output, which is different from the tangible units sold by manufacturing and merchandising companies. Examples of output measures in various service and nonprofit industries are:
Industry Airlines Hotels/motels Hospitals Universities Measure of Output Passenger miles Room-nights occupied Patient days Student credit-hours
Consider a n agency of the Massachusetts Department of Social Welfare with a $900,000 budget appropriation (its revenues) for 2008. This nonprofit agency's purpose is to assist handicapped people seeking employment. O n average, the agency supplements each person's income by $5,000 annually. The agency's only other costs are fixed costs of rent and administrative salaries equal to $270,000. The agency manager wants to know how many people could be assisted in 2008. We can use CVP analysis here by setting operating income to $0. Let Q be the number of handicapped people to be assisted:
Revenues - Variable costs - Fixed costs = 0 $900,000 - $5,000 0 - $270,000 = 0 $5,000 0 = $900,000 - $270,000 = $630,000 a = $630,000 + $5,000 per person = 126 people
Suppose the manager is concerned that the total budget appropriation for 2009 will be reduced by 1 5 % to $900,000 x (1 - 0.15) = $765,000. The manager wants to know how many handicapped people could be assisted with this reduced budget. Assume the same amount of monetary assistance per person:
$765,000 - $5,000 a - $270,ooo = o $5,OOOQ = $765,000 - $270,000 = $495,000 a = $495,000 + $5,000 per person = 99 people
Note the following two characteristics of the CVP relationships in this nonprofit situation: 1. The percentage drop in the number of people assisted, (126 - 99) + 126, or 21.4%, is greater than the 15% reduction in the budget That's appropriation. because the $270,000 in fixed costs still must be paid, leaving a proportionately lower budget to assist people. The percentage drop in service exceeds the percentage drop in budget appropriation. 2. Given the reduced budget appropriation (revenues) of $765,000, the manager can adjust operations to stay within this appropriation in one or more of three basic ways: (a) reduce the number of people assisted from the current 126, (b) reduce the
PROBLEM FOR SELF-STUDY
variable cost (the extent of assistance per person) from the current $5,000 per person, or (c) reduce the total fixed costs from the current $270,000.
Contribution Margin versus Gross Margin
Clearly distinguish contribution margin, which provides information for CVP analysis, from gross margin discussed in Chapter 2.
Gross margin = Revenues Contribution margin = Revenues
Cost of goods sold All variable costs
Gross margin is a measure of competitiveness-how much a company can charge for its products over and above the cost of acquiring or producing them. Companies, such as branded pharmaceuticals, have high gross margins because their products provide unique and distinctive benefits to consumers. Products such as televisions that operate in competitive markets, have low gross margins. Contribution margin indicates how much of a company's revenues are available t o cover fixed costs. It helps in assessing risk of loss. Risk of loss is low (high) if, when sales are low, contribution margin exceeds (is less than) fixed costs. Gross margins and contribution margin are related but give different insights. For example, a company operating in a competitive market with a low gross margin will have a low risk of loss if its fixed costs are small. Consider the distinction between gross margin and contribution margin in the context of manufacturing companies. In the manufacturing sector, contribution margin and gross margin differ in two respects: fixed manufacturing costs and variable nonmanufacturing costs. The following example (figures assumed) illustrates this difference:
Contribution Income Statement Emphasizing Contribution Margin (in 000s)
Revenues Variable manufacturing costs Variable nonmanufacturing costs Contribution margin Fixed manufacturing costs Fixed nonmanufacturing costs Operating income $1,000 $250 270 160 138 520 480
Financial Accounting Income Statement Emphasizing Gross Margin (in 000s) Revenues $1,000 Cost of goods sold ($250 + $160) 410
I Gross margin 1 Nonmanufacturing costs ($270 $138) 298 I Operating income $182 -
Fixed manufacturing costs of $160,000 are not deducted from revenues when computing contribution margin but are deducted when computing gross margin. Cost of goods sold in a manufacturing company includes all variable manufacturing costs and all fixed manufacturing costs ($250,000 + $160,000). Variable nonmanufacturing costs (such as commissions paid to salespersons) of $270,000 are deducted from revenues when computing contribution margin but are not deducted when computing gross margin. Like contribution margin, gross margin can be expressed as a total, as an amount per unit, or as a percentage. For example, the gross margin percentage is the gross margin divided by revenues-59% ($590 + $1,000) in our manufacturing-sector example.
Problem for Self-study
Wembley Travel Agency specializes in flights between Los Angeles and London. It books passengers on United Airlines at $900 per round-trip ticket. Until last month, United paid Wembley a commission of 1 0 % of the ticket price paid by each passenger. This commission was Wembley's only source of revenues. Wembley's fixed costs are $14,000 per month (for salaries, rent, and so on), and its variable costs are $20 per ticket purchased for a passenger. This $20 includes a $15 per ticket delivery fee paid to Federal Express. (To keep the analysis simple, we assume each round-trip ticket purchased is delivered in a separate package. Thus, the $15 delivery fee applies t o each ticket.)
CHAPTER 3 COST-VOLUME-PROFIT ANALYSIS
United Airlines has just announced a revised payment schedule for all travel agents. It will now pay travel agents a 10% commission per ticket up to a maximum of $50. Any ticket costing more than $500 generates only a $50 commission, regardless of the ticket price.
1. Under the old 10% commission structure, how many round-trip tickets must Wembley sell each month (a) to break even and (b) to earn an operating income of $7,000? 2. How does United's revised payment schedule affect your answers to (a) and (b) in requirement 1?
1. Wembley receives a 10% commission on each ticket: 1 0 % x $900
Selling price Variable cost per unit Contribution margin per unit Fixed costs
= $90 per ticket
= $20 per ticket
= $90 - $20 = $70 per ticket
= $14,000 per month
Breakeven number Fixed costs $14,000 -= 200tickets of tickets Contribution margin per unit $70 per ticket
b. When target operating income
Quantity of tickets required to be sold
$7,000 per month:
+ Target operating income
Contribution margin per unit
$21,000 - $14,000 + $7,000 = 300 tickets $70 per ticket $70 per ticket
2. Under the new system, Wembley would receive only $50 o n the $900 ticket. Thus,
Selling price Variable cost per unit Contribution margin per unit Fixed costs
= $50 per ticket = $20 per ticket
= $50 - $20 = $30 per ticket = $14,000 per month
$14,000 Breakeven number = 467 tickets (rounded up) of tickets $30 per ticket Quantity of tickets required to be sold $21,000 $30 per ticket
= 700 tickets
The $50 cap on the commission paid per ticket causes the breakeven point to more than double (from 200 to 467 tickets) and the tickets required to be sold to earn $7,000 per month to also more than double (from 300 to 700 tickets). As would be expected, travel agents reacted very negatively to the United Airlines announcement to change commission payments. Unfortunately for travel agents, other airlines also changed their commission structure in similar ways.
The following question-and-answer format summarizes the chapter's learning objectives. Each decision presents a key question related t o a learning objective. The guidelines are the answer t o that question.
Decision Guidelines CVP analysis assists managers in understanding the behavior of a product's or service's total costs, total revenues, and operating income as changes occur in the output level, selling price, variable costs, or fixed costs.
1. H o w can CVP analysis assist managers?
APPENDIX: DECISION MODELS AND LJNCERTAINN J 81
2. H o w do co~npanics
deter~nine hre~tkeven the point or the o ~ ~ t p~~~ t d c d le t o achieve 3 target o p e r ~ t i n g income?
3 . H o w should companies incorporate income taxes into CVP analysis?
The 111-cakevenpoint is thc cl~~antity o i ~ t p ~ ltt which total r e v e n ~ ~ ccl~ral of a es total costs. 'The three methods for coniputirlg the hl-eakeven point ;ind the quantity o f oiltpllt t o ;icliieve target operating income arc the equation ~nethocl,the contribution margirl net hod, and the graph method. F,acli method is merely a restatement of the others. Managers ofter~ select the method they find easiest to use in the specific decision s i t ~ ~ a t i o n . Income taxes can be incorporated into C V P analysis hy using target net income rather than target operating income. The breakeven point is ilnaffected by income taxes because no income taxes are paid when operliting incorne eq~inls zero. Sensitivity analysis, a "what-if" technique, exarnines how a n oLrtcome will change if the original predicted data are not achieved o r if an underlying assumption changes. When making decisions, managers use CVP ~inalysisto cornpdre c o n t r i b u t i o ~margins and fixed costs under different a s s ~ ~ m p t i o n s . ~ Choosing the variable-cost/fixed-cost structure is a strategic decision tor cornpanies. CVP analysis highlights the risk of losses when revenues are low and the upside profits when revenues are high for different proportions of variable and fixed costs in a company's cost structure. CVP a n a l y s ~ s can be applied to a company producing m ~ ~ l t i p products by le assuming the sales mix of products sold remains constant as the total quantity of units sold changes. The basic concepts of CVP analysis can be applied t o multiple-cost-driver situations, but there is n o unique breakeven point.
4. H o w should companies cope with uncertainty o r changes in underlying assumptions?
5. H o w should companies
choose between different varia ble-cost/fixed-cost structures? 6. Can CVP analysis be applied t o a company producing multiple products?
7. Can CVP analysis be applied t o a product that has multiple cost drivers?
APPENDllX: DEC!SBON MODELS AND UNGEWTABNW
This appendix explores the characteristics of uncertainty and describes an approach managers can use t o make decisions in a world of uncertainty. We will also illustrate the insights gained when uncertainty is recognized in CVP analysis.
Coping with Uncertainty2
In the face of uncertainty, managers rely o n decision models t o help them make the right choices.
Role of a Decision Mode8
Uncertainty is the possibility that an actual amount will deviate from an expected amount. In the Do-A11 example, Mary might forecast sales a t 40 units, but actual sales might turn out t o be 3 0 units o r 60 units. , decision model helps managers deal with such uncertainty. 4 It is a formal method for making a choice, commonly involving both quantitative and qualitative analyses. The quantitative analysis usually includes the following steps: Step 1: ldentify a choice criterion. A choice criterion is an objective that can be quantified. This objective can take many forms. Most often the choice criterion is t o maxlmlze income or t o minimlze costs. The choice criterion provides a basis for choosing the best alternative action. Mary's choice criterion is t o maximize expected operating income a t the Chicago computer convention. Step 2: Identify the set of alternative actions t o be considered. We use the letter a with subscripts ,, a n d ;to distinguish each of Mary's three ~ o s s i b l e actions:
' T h e presentation here draws (in part) from teaching notes prepared hv R. Williamson.
2OST-VOLUME-PROFITANALYSIS a, = Pay $2,000 fixed fee a, = Pay $800 fixed a, =
fee plus 15% o convention revenues f Pay 25% of convention revenues with no fixed fee
Step 3: Identify the set of events that can occur. An event is a possible relevant occurrence, such as the actual number of software packages Mary may sell at the convention. The set of events should be mutually exclusive and collectively exhaustive. Events are mutually exclusive if they cannot occur at the same time. Events are collectively exhaustive if, taken together, they make up the entire set of possible relevant occurrences (no other event can occur). Examples of mutually exclusive and collectively exhaustive events are growth, decline, or no change in industry demand, and increase, decrease, or no change in interest rates. Only one event out of the entire set of mutually exclusive and collectively exhaustive events will actually occur. Suppose Mary's only uncertainty is the number of units of Do-A11 Software that she can sell. For simplicity, suppose Mary estimates that sales will be either 30 or 6 0 units. We use the letter x with subscripts and to distinguish the set of mutually exclusive and collectively exhaustive events:
x, = X, =
30 units 60 units
Step 4: Assign a probability to each event that can occur. A probability is the likelihood or chance that an event will occur. The decision model approach t o coping with uncertainty assigns probabilities to events. A probability distribution describes the likelihood, or the probability, that each of the mutually exclusive and collectively exhaustive set of events will occur. In some cases, there will be much evidence to guide the assignment of probabilities. For example, the probability of obtaining heads in the toss of a coin is 112 and that of drawing a particular playing card from a standard, well-shuffled deck is 1/52. In business, the probability of having a specified percentage of defective units may be assigned with great confidence on the basis of production experience with thousands of units. In other cases, there will be little evidence supporting estimated probabilities-for example, expected sales of a new pharmaceutical product next year. Suppose that Mary, on the basis of past experience, assesses a 60% chance, or a 6/10 probability, that she will sell 30 units and a 40% chance, or a 4/10 probability, that she will sell 60 units. Using P(x) as the notation for the probability of an event, the probabilities are:
The probabilities of these events add to 1.00 because they are mutually exclusive and collectively exhaustive. Step 5: Identify the set of possible outcomes. Outcomes specify, in terms of the choice criterion, the predicted economic results of the various possible combinations of actions and events. The outcomes in the Do-A11 Software example take the form of six possible operating incomes that are displayed in a decision table in Exhibit 3-6. A decision table is a summary of the alternative actions, events, outcomes, and probabilities of events. Distinguish actions from events. Actions are decision choices available to managersfor example, the particular rental alternatives that Mary can choose. Evenjs are the set of all relevant occurrences that can happen-for example, the different quantities of software packages that may be sold at the convention. The outcome is operating income, which depends both o n the action the manager selects (rental alternative chosen) and the event that occurs (the quantity of packages sold). Exhibit 3-7 presents an overview of relationships among a decision model, the implementation of a chosen action, its outcome, and a subsequent performance evaluation. Thoughtful managers step back and evaluate what happened and learn from their experiences. This learning serves as feedback for adapting the decision model for future actions.
APPENDIX: DECISION PylODELS AND UNCERTPINW 183
Decision Table for Do-All Software
I B I
~ , ~ ~ ,
Package cost zi$l2O I ~
I F I G I O~ti?g!nco~ - (GdG~ach Possible Event ;
1 .L .
. .--. ~
~ L . i Percentage I Fixed 4 of Convention Event x : .. .
!~ c eI
Units Sold = 3 0 _-+-
1~-~. ' Event x,: Units Sold = --.-60 .
Probability(~,) = i 0.40
1 15 1 'Operating Income = ($200 - $120 - 25% x $200)(60)
14 qOperat~ng -- = ($200 - $120 - - -x---- . Income 25% $200)(30)
An expected value is the weighted average of the outcomes, with the probability of each outcome serving as the weight. When the outcomes are measured in monetary terms, expected value is often called expected monetary value. Using information in Exhibit 3-6, the expected monetary value of each booth-rental alternative denoted by E(a,), E(a,), and E(a3)is:
Pay $2,000 fixed fee: Pay $800 fixed fee plus 15%o revenues: f Pay 25% of revenues with no fixed fee:
E(a,) = 0.60($400) Ra,) = 0.60($700) E(a,)
+ 0.40($2,800) = + 0.40($2,200) = = 0.60($900) + 0.40($1,800) =
$1,360 $1,300 $1,260
To maximize expected operating income, Mary should select action a,-pay Computer Conventions, Inc. a $2,000 fixed fee. To interpret the expected value of selecting action a,, imagine that Mary attends many conventions, each with the probability distribution of operating incomes given in Exhibit 3-6. For a specific convention, Mary will earn operating income of either $400, if she sells 30 units, or $2,800, if she sells 60 units. But if Mary attends 100 conventions, she will expect t o earn $400 operating income 60% of the time (at 60 conventions), and $2,800 operating income 40% of the time (at 40 conventions), for a total operating income of $136,000 ($400 x 60 + $2,800 x 40). The expected value of $1,360 is the
.-. ..:-.pii .\i: q.,.I ...... ,. ": .;
- ~-,:: : . b
A Decision Made and Its Link to Performance Evaluation
1. Choice criter~on 2. Set of altemat~ve actions 3. Set of relevant events 4 Set of probabilities 5. Set of possible outcomes
Implementafion of Chosen Action
Uncertainty Resolved *
*uncertainty resolved means the event becomes known
operating income per convention that Mary will earn when averaged across all conventions ($136,000 + 100). Of course, in many real-world situations, managers must make one-time decisions under uncertainty. Even in these cases, expected value is a useful tool for choosing among alternatives. Consider the effect of uncertainty on the preferred action choice. I t Mary were certain she would sell only 30 units (that is, P(x,)= I), she would prefer alternative a,-pay 25% of convention revenues with no fixed fee. To follow this reasoning, examine Exhibit 3-6. When 30 units are sold, alternative a; yields the maximum operating income of $900. Because fixed costs are $0, booth-rental costs are lower, equal to $1,500 ( 2 5 % of revenues = 0.25 x $200 per unit X 30 units), when sales are low. However, if Mary were certain she would sell 60 software packages (that is, P(x,) = 1 , 1 she would prefer alternative a,-pay a $2,000 fixed fee. Exhibit 3-6 indicates that when 60 units are sold, alternative a , yields the maximum operating income of $2,800. Rental payments under a2 and a , increase with units sold but are fixed under a , . Despite the high probability of selling only 30 units, Mary still prefers to take action a,, which is to pay a fixed fee of $2,000. That's because the high risk of low operating income (the 60% probability of selling only 30 units) is more than offset by the high return from selling 60 units, which has a 40% probability. If Mary were rnore averse to risk (measured in our example by the difference benveen operating incomes when 30 versus 60 units are sold), she might have preferred action a 2 or a3. For example, action az ensures an operating income of a t least $700, greater than the operating income of $400 that she would earn under action a l if only 30 units were sold. Of course, choosing a 2 limits the upside potential to $2,200 relative to $2,800 under al, if 60 units are sold. If Mary is very concerned about downside risk, however, she may be willing t o forgo some upside benefits to protect against a $400 outcome by choosing a2.3
Good Decisions and Good Outcomes
Always distinguish between a good decision and a good outcome. One can exist without the other. Suppose you are offered a one-time-only gamble tossing a coin. You will win $20 if the event is heads, but you will lose $1 if the event is tails. As a decision maker, you proceed through the logical phases: gathering information, assessing outcomes, and making a choice. You accept the bet. Why? Because the expected value is $9.50 [0.5($20) + 0.5( - $ I ) ] .The coin is tossed and the event is tails. You lose. From your viewpoint, this was a good decision but a bad outcome. A decision can he made only on the basis of information that is available at the time of evaluating and making the decision. By definition, uncertainty rules out guaranteeing that the best outcome will always be obtained. As in our example, it is possible that bad luck will produce bad outcomes even when good decisions have been made. A bad outcome does not mean a bad decision was made. The best protection against a bad outcome is a good decision.
TERMS TO LEARN
This chapter and the Glossary at the end of the book contain definitions of the following important terms:
breakeven point (BEP)(p. 66) choice criterion (p. 81) contribution income statement (p. 63) contribution margin (p. 62) contribution margin per u n i t (p. 63) contribution margin percentage (p. 63) contribution margin ratio (p. 63) cost-volume-profit (CVP) analysis decision table (p. 82) degree of operating leverage (p. 73) event (p. 82) expected monetary value (p. 83) expected value (p. 83) gross margin percentage (p. 79) margin of safety (p. 71) net income (p. 68) operating leverage (p. 73) outcomes (p. 82) probability (p. 82) probability diitribution (p. 82) P graph (p. 67) V revenue driver (p. 65) sales mix (p. 75) sensitivity analysis (p. 71) uncertainty (p. 72)
For more formal approaches, refer to J. Moorc and L. Weatherford, Decision Modeling with Microsoft Excel, 6th ed. (Upper Saddle River, NJ: Prentice Hall, 2001).
Notc.: To rr?ltlcrsc.orc the hrrsic CVI' rclotionshi/>s,tl7c assi,qllllzclrt ~lratcr~irl ignorcs income luxes urilcss statcti otherwise.
Define cost-volume-profit analysis Descr~beh e assumptions underlying CVP analysis t
2-:3 Dist~nguishbetween operating income and net income.
3-4 Define contribution margin, contribution margin per unit, and contribution margin percentage. ?-5 Descr~be three methods that can be used to express CVP relationships.
3-6 Why is i t m o r e accurate to describe the subject matter of this chapter as CVP analysis rather than
z-, "CVP analysis is both slmple and simplistic. If you want realistic analysis to underpin your decisions, look beyond CVP analysis." Do you agree? Explain. --, -".;, How does an increase in the income tax rate affectthe breakeven point?
- as breakeven analysis?
of sensitivity analysis?
3-3 Describe sensitivity analysis. How has the advent of the electronic spreadsheet affected the use
3-10 Give an example of h o w a manager can decrease variable costs while increasing fixed costs. ...+ G- . 1 Give an example of h o w a manager can increase variable costs while decreasing fixed costs. i
3' What is operating leverage? How is knowing the degree of operating leverage helpful to managers? -2 3 ' 1 3 "There is no such thing as a fixed cost. All costs can be 'unfixed' given sufficient time." Do you
agree? W h a t is the implication of your answer for CVP analysis?
3-14 How can a company with multiple products compute its breakeven point? 3-15 "In CVP analysis, gross margin is a less-useful concept than contribution margin." Do you agree?
3-16 CVP computations. Fill i n the blanks for each of the following independent cases
Case a. Revenues Variable Costs $500 Fixed Costs Total Costs $ 800 Contribution Operating Income Margin Percentage $1,200
3-15 CVP computations. Patel Manufacturing sold 200,000 units of its product for $30 per unit in 2008. Variable cost per u n i t is $25 and total fixed costs are$800,000.
1. Calculate (a) contribution margin and (b) operating income. 2. Patel's current manufacturing process is labor intensive. Kate Schoenen, Patel's production manager,
has proposed investing in state-of-the-art manufacturing equipment, which will increase the annual fixed costs to $2,400,000. The variable costs are expected to decrease to $16 per unit. Patel expects to maintain the same sales volume and selling price next year. H o w would acceptance of Schoenen's proposal affect your answers to (a) and (b) i n requirement I ? 3. Should Patel accept Schoenen's proposal? Explain.
3-18 CYP analysis, changing revenues and costs. Sunshine Travel Agency specializes in flights between Toronto and Jamaica. It books passengers on Canadian Air. Sunshine's fixed costs are $22,000 per month. Canadian Air charges passengers $1,000 per round-trip ticket. Calculate the number of tickets Sunshine must sell each month to (a) break even and (b) make a target operating income o f $10,000 per month in each of the following independent cases.
1. Sunshine's variable costs are $35 per ticket. Canadian Air pays Sunshine 8% commission on ticket price.
2. Sunshine'svariable costs are $29 perticket. Canadian Air pays Sunshine 8% commission on t ~ c k eprice. t 3. Sunshine's variable costs are $29 per ticket. Canadian Air pays $48 fixed commission per ticket to
Sunshine. Comment on the results. 4. Sunshine's variable costs are $29 per ticket. It receives $48 commission per ticket from Canadian Air. It charges its customers a delivery fee of $5 perticket. Comment on the results.
2HAPTER 3 COST-VOLUME-PROFIT ANALYSIS
3-19 CVP exercises. The Super Donut owns and operates six doughnut outlets in and around Kansas City. You are given the following corporate budget data for next year:
Revenues Fixed costs Variable costs Variable costs change with respect to the number of doughnuts sold. Compute the budgeted operating income for each of the following deviations from the original budget data. (Consider each case independently.) 1. A 10% increase in contribution margin, holding revenues constant 2. A 10% decrease in contribution margin, holding revenues constant 3. A 5% increase in fixed costs 4. A 5% decrease in fixed costs 5. An 8% increase in units sold 6. An 8% decrease in units sold 7. A 10% increase in fixed costs and a 10% increase in units sold 8. A 5% increase in fixed costs and a 5% decrease in variable costs
3-20 CVP exercises. The Doral Company manufactures and sells pens. Currently, 5,000,000 units are sold per year at $0.50 per unit. Fixed costs are $900,000 per year. Variable costs are $0.30 per unit. Consider each case separately:
1. a. What is the current annual operating income? b. What is the present breakeven point in revenues? Compute the new operating income for each of the following changes:
2. A$0.04 per unit increase in variable costs 3. A 10% increase in fixed costs and a 10% increase in units sold 4. A 20% decrease in fixed costs, a 20% decrease in selling price, a 10% decrease in variable cost per unit, and a 40% increase in units sold
Compute the new breakeven point in units for each of the following changes: 5. A 10% increase in fixed costs 6. A 10% increase in selling price and a $20,000 increase in fixed costs
3-21 CVP analysis, income taxes. Diego Motors is a small car dealership. On average, it sells a car for $26,000, which it purchases from the manufacturer for $22,000. Each month, Diego Motors pays $60,000 in rent and utilities and $70,00Ofor salespeople's salaries. In addition to their salaries, salespeople are paid a commission of $500for each car they sell. Diego Motors also spends $10,000 each month for local advertisements. Its tax rate is 40%.
1. How many cars must Diego Motors sell each month to break even? 2. Diego Motors has a target monthly net income of $63,000. What is its target monthly operating income? How many cars must be sold each month to reach the target monthly net income of $63,000?
3-22 CVP analysis, income taxes. The Rapid Meal has two restaurants that are open 24 hours a day. Fixed costs for the two restaurants together total $450,000 per year. Service varies from a cup of coffee to full meals. The average sales check per customer is $8.00. The average cost of food and other variable costs for each customer is $3.20. 'The income tax rate is 30%. Target net income is $105,000.
1. Compute the revenues needed to earn the target net income. 2. How many customers are needed to break even? To earn net income of $105,000? 3. Compute net income if the number of customers is 150,000.
3-23 CVP analysis, sensitivity analysis. Hoot Washington is the newly elected leader of the Republican Party. Media Publishers is negotiating to publish Hoot's Manifesto, a new book that promises to be an instant best-seller. The fixed costs of producing and marketing the book will be $500,000. The variable costs of producing and marketing will be $4.00 per copy sold. These costs are before any payments to Hoot. Hoot negotiates an up-front payment of $3 million, plus a 15% royalty rate on the net sales price of each book. The net sales price is the listed bookstore price of $30, minus the margin paid to the bookstore to sell the book. The normal bookstore margin of 30% of the listed bookstore price is expected to apply.
1. Prepare a PV graph for Media Publishers. 2. How many copies must Media Publishers sell to (a) break even and (bl earn a target operating income of $2 million? 3. Examine the sensitivity of the breakeven point to the following changes: a. Decreasing the normal bookstore margin to 20% of the listed bookstore price of $30.
ASSIGNMENT MATERIAL 1 87
b. Increasing the listed bookstore price to $40 while keeping the bookstore margin at30%.
c. Comment on the results.
13-24 CVP analysis, margin of safety. Suppose Lattin Corp.'s breakeven point is revenues of $1,500,000. Fixed costs are $600,000.
1. Compute the contribution margin percentage. 2. Compute the selling price if variable costs are $15 per unit. 3. Suppose 80,000 units are sold. Compute the margin of safety in units and dollars.
3-25 Operating leverage. Color Rugs is holding a two-week carpet sale at Jerry's Club, a local warehouse store. Color Rugs plans to sell carpets for $500 each. The company will purchase the carpets from a local distributor for $350 each, with the privilege of returning any unsold units for a full refund. Jerry's Club has offered Color Rugs two payment alternatives for the use of space.
Option 1: A fixed payment of $5,000 forthe sale period Option 2: 10% of total revenues earned during the sale period Assume Color Rugs will incur no other costs. 1. Calculate the breakeven point in units for (a) option 1 and (b) option 2. 2. At what level of revenues will Color Rugs earn the same operating income under either option? a. For what range of unit sales will Color Rugs prefer option I ? b. For what range of unit sales will Color Rugs prefer option 2? 3. Calculate the degree of operating leverage at sales of 100 units for the two rental options. 4. Briefly explain and interpret your answer to requirement 4.
3-26 CVP analysis, international cost structure differences. Knitwear, Inc., is considering three countries for the sole manufacturing site of its new sweater: Singapore, Thailand, or the United States. All sweaters are to be sold to retail outlets in the United States at$32 per unit. These retail outlets add their o w n markup when selling to final customers. Fixed costs and variable cost per unit (sweater) differ in the three countries.
- e - 4
VariableMarketing & Distribution Cost ~ w e ~ h a ~
$1 1.00 $11.50 $ 9.00
1 $ 4 5- 1
$ 5.50 _i $13.00 i
If you want to use Excel to solve this exercise, go to the Excel Lab at www.prenhalI.com/horngren/costl3e and download the template for Exercise 3-26.
1. Compute the breakeven point for Knitwear, Inc., in each country in (a) units sold (b) revenues. 2. If Knitwear, Inc., plans to produce and sell 800,000 sweaters in 2009, what is the budgeted operating income for each of the three manufacturing locations? Comment on the results.
3-27 Sales mix, new and upgrade customers. Zapo 1-2-3 is a top-selling electronic spreadsheet product. Zapo is about to release version 5.0. It divides its customers into t w o groups: n e w customers and upgrade customers (those who previously purchased Zapo 1-2-3, 4.0 or earlier versions). Although the same physical product is provided to each customer group, sizable differences exist in selling prices and variable marketing costs:
$210 $25 65
$120 $25 15
Selling price Variable costs Manufacturing Marketing Contribution margin
90 $120 -
The fixed costs of Zapo 1-2-3 5.0 are $14,000,000. The planned sales mix in units is 60% new customers and 40% upgrade customers.
88 E CHAPTER 3 COST-VOLUME-PROFITANALYSIS
1. What is the Zapo 1-2-3 5.0 breakeven point in units, assuming that the planned 60%/40% sales mix is attained? 2. If the sales mix is attained, what is the operating income when 200,000 units are sold? 3. Show how the breakeven point in units changes with the following customer mixes: a. N e w 50%/Upgrade 50% b. N e w 9O%/Upgrade 10% c. Comment on the results.
3-28 CVP analysis. multiple cost drivers. Susan Wong is a distributor of brass picture frames. For 2008, she plans to purchase frames for $30 each and sell them for $45 each. Susan's fixed costs are expected to be $240,000. Susan's only other costs will be variable costs of $60 per shipmentfor preparing the invoice and delivery documents, organizing the delivery, and following up for collecting accounts receivable. The $60 cost will be incurred each time Susan ships an order of picture frames, regardless of the number of frames in the order.
1. a. Suppose Susan sells 40,000 picture frames in 1,000 shipments in 2008. Calculate Susan's 2008 operating income. b. Suppose Susan sells 40,000 picture frames i n 800 shipments in 2008. Calculate Susan's 2008 operating income. 2. Suppose Susan anticipates making 500 shipments in 2008. How many picture frames must Susan sell to break even in 2008? 3. Calculate another breakeven point for 2008, different from the one described in requirement 2. Explain briefly why Susan has multiple breakeven points.
3-29 CVP, Not for profit. The Sunrise Group (SG) is an environmentally conscious organization that buys land with the objective of preserving the natural environment. SG receives private contributions and takes no assistance from the government. Fixed costs of operating the organization are $1,000,000 per year. Variable costs (including purchase of land, environmental impact reports and title search) average $3,000 per acre. In 2009, SG expects to receive contributions of $19,000,000. All contributions in excess of operating costs will be used to purchase land.
1. How many acres will SG be able to purchase in 2009? 2. SG is considering participating in a new government program thatwill provide $1,000 per acre to subsidize the purchase of environmentally sensitive land. If SG participates in this program they estimate they will lose $5,000,000 in contributions from supporters who believe that accepting money from the government is not consistentwith SG's mission. If SG participates in the program, how many acres of land will SG be able to buy in 2009? On financial considerations alone, should SG take the $1,000 per acre of subsidy? 3. SG is worried that contributions may drop by more than $5,000,000 if it takes the government subsidy. By how much can contributions decrease for SG t o be able t o buy the same amount of land if it takes the government subsidy or rejects it?
3-30 Contribution margin, decision making. Schmidt Men's Clothing's revenues and cost data for 2009 are:
Revenues Cost of goods sold 140% of sales) Gross margin Operating costs: Salaries fixed Sales commissions (10% of sales) Depreciation of equipment and fixtures Store rent ($4,000 per month) Other operating costs Operating income (loss)
Mr. Schmidt, the owner of the store, is unhappy with the operating results. An analysis of other operating costs reveals that i t includes $40,000 variable costs, which vary with sales volume, and $10,000 (fixed) costs.
1. Compute the contribution margin of Schmidt Men's Clothing. 2. Compute the contribution margin percentage. 3. Mr. Schmidt estimates that he can increase revenues by 20% by incurring additional advertising costs of $10,000. Calculate the impact of the additional advertising costs on operating income.
3-31 Contribution margin, gross margin, and margin of safety. Mirabella Cosmetics manufactures and sells a face cream to small ethnic stores in the greater N e w York area. It presents the monthly operating income statement shown here to George Lopez, a potential investor in the business. Help Mr. Lopez understand Mirabella's cost structure.
ASSlGhlMENT MATERIAL P 89
g e ~ l insert
Operating Income Statement, June 2008
. .~ .-
5 -Cost of goods sold
Variable manufacturing costs .~~
~~ ~ ~
Fixed manufacturing costs i- -~ Total - - - ~~~ ~ ~~ ~~
i $55,000 20,000 1 ~~ ~~~
Gross margin .
10 Operating costs 11 Variable marketing costs 12 13
Fixed marketing 8 administration costs
Total operating costs ~.
5!000 '' 10,000 l-~
14 Operating income
15,000 $ 10,000
If you want to use Excel t o solve this exercise, go to the Excel Lab at www.prenhall.com/horngrenlcostl3e and download the template for Exercise 3-31.
1. Recast the income statement to emphasize contribution margin. 2. Calculate the contribution margin percentage and breakeven point in units and revenuesfor June 2008. 3. What is the margin of safety lin units) for June 2008? 4. If sales in June were only 8,000 units and Mirabella's tax rate is 30%, calculate its net income.
3-32 Uncertainty and expected costs. Dawmart Corp, an international retail giant, is considering imple menting a new business to business ( 0 2 0 ) information system for processing purchase orders. The current system costs Dawmart $1,000,000 per month and $40 per order. Dawmart has t w o options, a partially automated B2B and a fully automated 0 2 0 system. The partially automated B2B system will have a fixed cost of $5,000,000 per month and a variable cost of $30 per order. The fully automated 0 2 0 system has a fixed cost of $10,000,000 per month and $20 per order. Based on data from the last two years, Dawmart has determined the following distribution on monthly orders:
Monthlv Number of Orders Probabilitv
1. Prepare a table showing the cost of each plan for each quantity of monthly orders.
2. What is the expected cost of each plan? 3. In addition to the information systems costs, what other factors should Dawmart consider before
deciding to implement a new 020 system?
3-33 CVP analysis, service firm. Wildlife Escapes generates average revenue of $4,000 per person on its
five-day package tours to wildlife parks in Kenya. The variable costs per person are: Airfare Hotel accommodations Meals Ground transportation Park tickets and other costs Total
CHAPTER 3 COST-VOLUME-PROFIT ANALYSIS
Annual fixed costs total $480,000. 1. Calculate the number of package tours that must be sold to break even. 2. Calculate the revenue needed to earn a target operating income of $100,000. 3. If fixed costs increase by $24,000, what decrease in variable cost per person must be achieved to maintain the breakeven point calculated in requirement I?
3-34 CVP, target operating income, service firm. Teddy Bear Daycare provides daycare for children Mondays through Fridays. Its monthly variable costs per child are:
Lunch and snacks Educational supplies Other supplies (paper products, toiletries, etc.) Total Monthly fixed costs consist of: Rent Utilities Insurance Salaries Miscellaneous Total
Teddy Bear charges each parent $600 per child. 1. Calculate the breakeven point. 2. Teddy Bear's target operating income is $10,400per month. Compute the number of children who must be enrolled t o achieve thetarget operating income. 3. Teddy Bear lost its lease and had to move to another building. Monthly rent for the new building is $3,000. the suggestion of parents, Teddy Bear plans to take children on field trips. Monthly costs of At the field trips are $1,000.By how much should Teddy Bear increase fees per child to meet the target operating income of $10,400per month, assuming the same number of children as in requirement 2?
3-35 CVP analysis. (CMA, adapted) Galaxy Disk's projected operating income for 2008 is $200,000,based on a salesvolume of 200,000 units. Galaxy sells disks for $16 each. Variable costs consist of the $10 purchase price and a $2 shipping and handling cost. Galaxy's annual fixed costs are $600,000. 1. Calculate Galaxy's breakeven point and margin of safety in units. 2. Calculate the company's operating income for 2008 if there is a 10% increase in projected unit sales. 3. For 2009,management expects that the unit purchase price of the disks will increase by 30%. Calculate the sales revenue Galaxy must generate for 2009 t o maintain the current year's operating income if the selling price remains unchanged. 3-36 CVP analysis, income taxes. (CMA, adapted) R. A. Ro and Company, a manufacturer of quality handmade walnut bowls, has had a steady growth in sales for the past five years. However, increased competition has led Mr. Ro, the president, to believe that an aggressive marketing campaign will be necessary next year to maintain the company's present growth. To prepare for next year's marketing campaign, the company's controller has prepared and presented Mr. Ro with the following data for the current year, 2008:
Variable cost (per bowl) Direct materials Direct manufacturing labor Variable overhead (manufacturing, marketing, distribution and customer service) Total variable cost per bowl Fixed costs Manufacturing Marketing, distribution, and customer service Total fixed costs Selling price Expected sales, 20,000 units Income tax rate
3.25 8.00 2.50
1. What is the projected net income for 2008? 2 What is the breakeven point in units for 2008? .
ASSIGNMENT MATERIAL ; 91 1
3. Mr. Ro has set the revenue target for 2009 at a level of $550,000 (or 22,000 bowls). He believes an additional marketing cost of $11,250 for advertising in 2009, with all other costs remaining constant, will be necessary to attain the revenue target. What is the net income for 2009 if the additional $1 1,250 is spent and the revenue target is met? 4. What is the breakeven point in revenues for 2009 if the additional $11,250 is spent for advertising? 5. If the additional $1 1,250 is spent, what are the required 2009 revenues for 2009 net income to equal 2008 net income? 6. At a sales level of 22,000 units, what maximum amount can be spent on advertising if a 2009 net income of $60,000 is desired?
3-37 CVP, sensitivity analysis. Technology of the Past (TOP) produces old-fashioned simple corkscrews. Last year was not a good year for sales but TOP expects the market to pick up this year. Last year's income statement was:
Sales revenue ($4 per corkscrew) Variable cost ($3 per corkscrewi Contribution margin Fixed cost Operating income To take advantage of the anticipated growth in the market, TOP is considering the following courses of action. 1. 2. 3. 4. Do nothing. If TOP does nothing, it expects sales to increase by 10%. Spend $2,000 on a n e w advertising campaign that is expected to increase sales by 50%. Raise the price of the corkscrewto $5. This is expected to decrease sales quantities by 20%. Redesign the classic corkscrew and increase the selling price to $6 while increasing the variable cost by $1 per corkscrew. The sales level is not expected to change from last year.
Evaluate each of the alternatives considered by TOP. What should TOP do?
3-38 CVP analysis, shoe stores. The WalkRite Shoe Company operates a chain of shoe stores that sell 10 different styles of inexpensive men's shoes with identical unit costs and selling prices. A unit is defined as a pair of shoes. Each store has a store manager who is paid a fixed salary. Individual salespeople receive a fixed salary and a sales commission. WalkRite is considering opening another store that is expected to have the revenue and cost relationships shown here:
D Annual Fixed Costs
A B Unit Variable Data (per pair of shoes)
I c I 1 1
Selling price Cost of shoes Sales commission Variable cost per unit
p p p p
$30.00 ~ = $19.50 200,000
p p p p p -
If you w a n t to use Excel to solve this problem, go to the Excel Lab at www,prenhaII.com/horngren/costl3e and download the template for Problem 3-38. Consider each question independently: 1. What is the annual breakeven point in (a) units sold and Ib) revenues? 2. If 35,000 units are sold, what will be the store's operating income (loss)? 3. If sales commissicxls are discontinued and fixed salaries rare raised by a total of $81,000, what would be the annual breakeven point in (a) units sold and (b) revenues? 4. Refer to the original data. If, in addition to his fixed salary, the store manager is paid a commission of $0.30 per unit sold, whatwould be the annual breakeven point in (a) units sold and (b) revenues? 5. Refer to the original data. If, in addition to his fixed salary, the store manager is paid a commission of $0.30 per unit in excess of the breakeven point, what would be the store's operating income if 50,000 units were sold?
3-39 CVP analysis, shoe stores (continuation of 3-38). Refer to requirement 3 of Problem 3-38. In this problem, assume the role of the owner of WalkRite. If you want to use Excel to solve this problem, go to the Excel Lab at www.prenhall.com/horngren/costl3e and download the template for Problem 3-38.
1. Calculate the number of units sold at which the owner of WalkRite would be indifferent between the original salary-plus-commissions plan for salespeople and the higher fixed-salaries-only plan. 2. As owner, which sales compensation plan would you choose if forecasted annual sales of the new store were at least 55,000 units? What do you think of the motivational aspect of your chosen compensation plan? 3. Suppose the target operating income is $168,000. How many units must be sold to reach the target operating income under (a) the original salary-plus-commissions plan and (b) the higher-fixed-salaries-only plan? 4. You open the new store o n January 1, 2008, with the original salary-plus-commission compensation plan in place. Because you expect the cost of the shoes to rise due to inflation, you place a firm bulk order for 50,000 shoes and lock in the $19.50 price per unit. But, toward the end of the year, only 48,000 shoes are sold, and you authorize a markdown of the remaining inventory t o $18 per unit. Finally, all units are sold. Salespeople, as usual, get paid a commission of 5% of revenues. What is the annual operating income for the store?
3-40 Alternate cost structures, uncertainty, and sensitivity analysis. Edible Bouquets (EBI makes and sells flower bouquets. EB is considering opening a new store in the local mall. The mall has several empty shops and EB is unsure of the demand for its product. The mall has offered EB t w o alternative rental agreements. The first is a standard fixed rent agreement where EB will pay the mall $5,000 per month. The second is a royalty agreement where the mall receives $10 for each bouquet sold. EB estimates that a bouquet will sell for $50 and have a variable cost of $30 t o make (including the cost of flowers, and commission for the salesperson).
1. What is the breakeven point in units under each rental agreement? 2. For what range of sales levels will EB prefer (a1 the fixed rent agreement (b) the royalty agreement? 3. If EB signs a sales agreementwith a local flower stand, it will save$5 in variable costs per bouquet. How would this affect your answer in requirement 2? 4. Do this question only if you have covered the chapter appendix in your class. EB estimatesthatthe store is equally likely to sell 200,400,600,800 or 1,000 arrangements. Using information from the original problem, prepare a table that shows the expected profit at each sales level under each rental agreement. What is the expected value of each rental agreement? Which rental agreement should EB choose?
3-41 CVP, alternative cost structures. Kids Lemonade Stand (KLS) is run by Sarah, who sells lemonade for $0.50 per glass. Lemons, sugar and water cost $0.15 per glass. Sarah's friend, Jessica, helps out by squeezing the lemons for $0.10 each. (Each lemon will provide enough juice for 2 glasses of lemonade.) Sarah uses tables, chairs and pitchers that belong to David who gathered the furniture when he had the stand last summer. David charges $6 per day for use of the furniture.
1. How many glasses of lemonade does Sarah have to sell each day t o breakeven? 2. Sarah wants t o earn $3 per day after expenses. How many glasses does she have to sell to earn $3. 3. David wants more money, so he has offered to squeeze all the lemons Sarah needsfor $1.70 per day. If Sarah hires David instead of Jessica, h o w many glasses will Sarah have to sell each day to breakeven? 4. A t w h a t sales level will Sarah be indifferent between hiring Jessica or David to squeeze the lemons? At what sales levels would she prefer to (a) hire Jessica (b) hire David?
3-42 CVP analysis, income taxes, sensitivity. (CMA, adapted) Almo Company manufactures and sells
adjustable canopies that attach to motor homes and trailers. For its 2009 budget, Almo estimates the following: Selling price Variable cost per canopy Annual fixed costs Net income Income tax rate The M a y income statement reported that sales were not meeting expectations. For the first five months of the year;-only 350 units had been sold a t the established price, with variable costs as planned, and it was clear thatthe net income projection for 2009 would not be reached unless some actions were taken. A management committee presented the following mutually exclusive alternatives to the president: a. Reduce the selling price by $40. The sales organization forecasts that at this significantly reduced price, 2,700 units can be sold during the remainder of the year. Total fixed costs and variable cost per unit will stay as budgeted. b. Lower variable cost per unit by $10 through the use of less-expensive direct materials and slightly modified manufacturing techniques. The selling price will also be reduced by $30, and sales of 2,200 units are expected for the remainder of the year. c. Reduce fixed costs by $10,000 and lower the selling price by 5%. Variable cost per unit will be unchanged. Sales of 2,000 units are expected for the remainder of the year.
ASSIGNMCNT MATERIAL 1 93
1. If no changes are made to the selling price or cost structure, determine the number of units that Almo Company must sell (a) to break even and (bl to achieve its net income objective. 2. Determine which alternative Almo should select to achieve ~ t snet income objective. Show your calculations. .. * . ; - + Choosing between compensation plans, operating leverage. (CMA, adapted) Marston Corporation manufactures pharmaceutical products that are sold through a network of external sales agents. The agents are paid a commission of 18% of revenues. Marston is considering replacing the sales agents with its own salespeople, who would be paid a commission of 10% of revenues and total salaries of $2,080,000. The income statement for the year ending December 31,2008, under the t w o scenarios is shown here.
Marston Corporation Income s t a t e m e n t . For theyear Ended December 31,2008 Using Sales Agents Using Own Sales Force
1 1 1
6 Cost of aoods sold 7 Variable a Fixed 9 ( ~ r o s margin s
1 $11,700,000 1
$ 1,700,000 1 1 2,870,000 14,570.000 2,870,000 14.570,OOO ( 11,430,000 ( 11,430,000
1 1 Commiss~ons 12 Fixed costs 13 Operating income
3,420,000 8,100,000 $ 3.330.000
If you want to use Excel to solve this problem, go to the Excel Lab at www.prenhaIl.com/horngren/costl3e and download the template for Problem 3-43. 1. Calculate Marston's 2008 contribution margin percentage, breakeven revenues, and degree of operating leverage under the two scenarios. 2. Describe the advantages and disadvantages of each type of sales alternative. 3. In 2009, Marston uses its o w n salespeople, who demand a 15% commiss~on.If all other cost behavior patterns are unchanged, h o w much revenue must the salespeople generate in order to earn the same operating income as in 2008?
3-44 Sales mix, three products.The Ronowski Company has three product lines of b e l t s A, B, and Cwith contribution margins of $3, $2, and $1, respectively. The president foresees sales of 200,000 units in the coming period, consisting of 20,000 units of A, 100,000 units of B, and 80,000 units of C. The company's fixed costs for the period are $255,000.
1. What is the company's breakeven point in units, assuming that the given sales mix is maintained? 2. If the sales mix is maintained, what is the total contribution margin when 200,000 units are sold? What is the operating income? 3. What would operating income be if 20,000 units of A, 80,000 units of B, and 100,000 units of C were sold? What is the n e w breakeven point in units if these relationships persist in the next period?
3-45 Multi-product CVP and decision making. Pure Water Products produces 2 types of water filters. One attaches t o the faucet and cleans all waterthat passes through the faucet. The other is a pitcher-cumfilter that only purifies water meant for drinking. costs of $20. The unit that attaches to the faucet is sold for $80 and has va~iable The pitcher-cum-filter sells for $90 and has variable costs of $25. Pure Water sells 2 faucet models for every 3 pitchers sold. Fixed costs equal $945,000.
1. What is the breakeven point in unit sales and dollars for each type of filter at the current sales mix? 2. Pure Water is considering buying new production equipment. The new equipment will increase fixed
cost by $181,400 per year and will decrease the variable cost of the faucet and the pitcher units by $5 and $9 respectively. Assuming the same sales mix, h o w many of each type of filter does Pure Water need to sell to breakeven? 3. Assuming the same sales mix, at what total sales level would Pure Water be indifferent between using the old equipment and buying the new production equipment? If total sales are expected to be 30,000 units, should Pure Water buy the new production equipment?
94 W CHAPTER 3
3-46 Sales mix, two products. The Goldman Company retails two products: a standard and a deluxe version of a luggage carrier. The budgeted income statement for next period is as follows:
Units sold Revenues at $20 and $30 per unit Variable costs at $14 and$18 per unit
Standard Carrier 150,000 $3,000,000 Deluxe Carrier 50,000 $1,500,000 Total 200,000 $4,500,000
1. Compute the breakeven point in units, assuming that the planned sales mix is attained. 2. Compute the breakeven point in units (a) if only standard carriers are sold and (b) if only deluxe carriers are sold. 3. Suppose 200,000 units are sold but only 20,000 of them are deluxe. Compute the operating income. Compute the breakeven point in units. Compare your answer with the answer to requirement 1. What is the major lesson of this problem?
3-47 Gross margin and contribution margin. The Museum of Art is preparing for its annual appreciation dinner for contributing members. Last year, 500 members attended the dinner. Tckets for the dinner were $20 per attendee. The profit report for last year's dinner follows.
Xcket sales Cost of dinner Gross margin Invitations and paperwork Profit (loss) $10,000 11,000 (1,000) 3,000 $(4.000)
This yearthe dinner committee does notwantto lose money on the dinner. To help achieve its goal, the committee analyzed last year's costs. Of the $11,000 cost of the dinner, $6,000 were fixed costs and $5,000 were variable costs. Of the $3,000 cost of invitation and paperwork, $2,500 were fixed and $500 were variable.
1. Prepare last year's profit report using the contribution margin format. 2. The committee is considering expanding this year's dinner invitation list to include volunteer members (in addition to contributing members). If they expand the dinner invitation list, they expect attendance to double. Calculate the effect this will have on the profitability of the dinner.
3-48 Ethics, CVP analysis. Allen Corporation produces a molded plastic casing, LX201, for desktop computers. Summary data from its 2008 income statement are as follows:
Revenues Variable costs Fixed costs Operating income $5,000,000 3,000,000 2,160,000
Jane Woodall, Allen's president, is very concerned about Allen Corporation's poor profitability. She asks Max Lemond, production manager, and Lester Bush, controller, to see if there are ways to reduce costs. Aftertwo weeks, Max returns with a proposal to reduce variable costs to 52% of revenues by reducing the costs Allen currently incurs for safe disposal of wasted plastic. Lester is concerned that this would expose the company to potential environmental liabilities. He tells Max, "We would need to estimate some of these potential environmental costs and include them in our analysis." "You can't do that," Max replies. "We are not violating any laws. There is some possibility that we may have to incur environmental costs in the future, but if we bring it up now, this proposal will not go through because our senior management always assumes thesBcosts to be larger thgn they turn out to be. The market is very tough, and we are in danger of shutting down the company. We don't want all our colleagues t o lose their jobs. The only reason our competitors are making money is because they are doing exactly what I am proposing."
1. 2. 3. 4.
Calculate Allen Corporation's breakeven revenues for 2008. Calculate Allen Corporation's breakeven revenues if variable costs are 52% of revenues. Calculate Allen Corporation's operating income for 2008 if variable costs had been 52% of revenues. Given M a x Lemond's comments, what should Lester Bush do?
ASSIGNMENT MATERIAL 1 95
Collaborative Learning Problem
.3-42 Deciding where to produce. (CMA, adapted) The Domestic Engines Co. produces the same power generators in two Illinois plants, a new plant in Peoria and an older plant in Moline. The following data are available for the t w o plants:
i 9 F i l e Ed~t gew
2 Iselling price
Fixed marketing and distribution cost per unit
7 Total cost per unit
10 Normal annual capacity usage 1 1 Maximum annual capacity
$ 15.00 400 units 240 days 300 days
131.50 320 units 240 days 300 days
All fixed costs per unit are calculated based on a normal capacity usage consisting of 240 working days. When the number o f working days exceeds 240, overtime charges raise the variable manufacturing costs of additional units by $3.00 per unit in Peoria and $8.00 per unit in Moline. Domestic Engines Co. is expected to produce and sell 192,000 power generators during the coming year. Wanting to take advantage of the higher operating income per unit at Moline, the company's production manager has decided to manufacture 96,000 units at each plant, resulting in a plan in which Moline operates at capacity (320 units per day X 300 days) and Peoria operates at its normal volume (400 units per day X 240 days). If you want t o use Excel to solve this problem, go to the Excel Lab at www.prenhall.com/ horngren/costl3e and download the template for Problem 3-49.
1. Calculate the breakeven point in units for the Peoria plant and for the Moline plant. 2. Calculate the operating income that would result from the production manager's plan to produce 96,000 units at each plant. 3. Determine h o w the production of 192,000 units should be allocated between the Peoria and Moline plants to maximize operating income for Domestic Engines. Show your calculations.
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