Final Paper Accounting 206
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chapter 5
Cost–Volume–Profit Analysis
Learning Objectives
• Extend your knowledge of fixed and variable costs, and be able to perform cost behavior analysis.
• Understand the contribution margin, contribution margin ratio, and how knowledge of these concepts can be used to calculate breakeven and other performance measures.
• Know the critical assumptions of cost–volume–profit analysis.
• Understand variable versus absorption costing.
• Be able to calculate residual income.
istockphoto
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CHAPTER 5Section 5.1 Mixed Costs
Chapter Outline
5.1 Mixed Costs
5.2 Cost–Volume–Profit Analysis The Algebra of Break-Even and Targeted Income Analysis Influence of Taxes Changing Costs Changing Revenues Multiple Products
5.3 CVP Assumptions Direct Costing Comprehensive Income Statements Under Variable and Absorption Costing Fluctuating Inventory
5.4 Evaluating Residual Income
You have previously learned about fixed and variable costs. Fixed costs are the same over the relevant range of expected production. Variable costs fluctuate in direct pro- portion to volume. You have seen how cost behavior influences measures of income, flex- ible budgeting, standard costing models, and so forth. Management must understand cost behavior to operate a successful business organization effectively. In this chapter, your knowledge of cost behavior will be extended to encompass techniques useful in studying a business’s break-even point and similar concepts. These techniques are com- monly referred to as cost–volume–profit analysis or just CVP. You will also apply your knowledge of cost behavior to understand alternative costing methods that are useful in managing business decisions.
5.1 Mixed Costs
Before diving into CVP and alternative costing models, one must give consideration to the prospect of a mixed cost. Mixed costs entail a fixed component and a variable component. They are actually quite common. If you have ever committed to a cell phone contract, it is very possible that you have some hands-on experience with mixed costs. Your monthly cellular bill may include both fixed and variable amounts. Perhaps there is a fixed charge for basic monthly service and variable charges related to Internet access, texting, and so forth. Mixed costs change in response to fluctuations in volume, but not in a way that is immediately apparent. Before a manager can study the effects of volume fluctuation on a business, it is first necessary to develop a model that separates mixed costs into their fixed and variable components.
Assume that Charlie’s Restaurant receives a monthly electric bill. Charlie’s electricity use fluctuates significantly each month. The cause of the fluctuation relates mostly to seasonal differences in utility consumption, based on heating and air-conditioning needs. Charlie’s provides data about its monthly electric bill in Table 5.1.
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CHAPTER 5Section 5.1 Mixed Costs
Table 5.1: Charlie’s electric bill data
Total cost Kilowatts used
January $1,950 15,000
February 1,750 13,000
March 1,650 12,000
April 1,350 9,000
May 1,450 10,000
June 1,750 13,000
July 2,150 17,000
August 2,050 16,000
September 1,850 14,000
October 1,350 9,000
November 1,550 11,000
December 1,750 13,000
At first glance, it may not be at all apparent how the total cost relates to the total usage. However, a graphical representation of this cost is quite revealing. Exhibit 5.1 is a chart with the total cost indicated along the vertical axis and the total usage along the horizontal axis. From this chart, you are able to see that fixed cost is the same, at $450, no matter the electricity consumed. Variable cost is rising at $0.10 per kilowatt hour.
Exhibit 5.1
KILOWATTS USED
TOTAL ELECTRICITY COST
Variable cost area
Fixed cost area
18,00016,00014,00012,00010,0008,0006,0004,0002,0000
$2,500
$2,000
$1,500
$1,000
$500
$0
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CHAPTER 5Section 5.1 Mixed Costs
Perhaps you are able to “eyeball” the data in the table and make a determination of the fixed and variable portions in the electric bill. However, what if the data set is much larger and more cryptic? How can you estimate the fixed and variable amounts? This problem is frequently encountered because many expenses contain both fixed and variable compo- nents. A simple (and sometimes imprecise) approach is the high–low method. With this technique, the highest and lowest levels of activity are identified and the difference in cost is deemed to be representative of the variable portion. The variable portion is divided by the difference in activity/consumption between the high and low activity levels to find the variable cost per unit. The fixed cost can be calculated by subtracting variable cost from total cost. In Table 5.2 are calculations of the fixed and variable costs for Exhibit 5.1, determined by using the high–low method.
Table 5.2: Fixed and variable costs for Charlie’s Restaurant
Kilowatts Cost
Highest level 17,000 $2,150
Lowest level 9,000 1,350
Difference 8,000 $800
Variable cost per unit $800/8,000 5 $0.10
High Low
Total cost $2,150 $1,350
Less: Variable cost (kilowatts 3 $0.10)
1,700 900
Fixed cost $450 $450
Certainly, the high–low method is not the only technique that can be used to estimate fixed and variable components. Also, if there are outlying data points (on the high or low end), the resulting estimates of fixed and variable components can be quite misleading. When data are not as linear as presented in the illustration, more precise tools are needed to separate costs into fixed and variable components.
One such tool is regression analysis (also known as the method of least squares regression analysis), which defines a line that has a best fit to a set of data. The line is defined in terms of its intercept with the vertical axis and its slope. To better understand regression analy- sis, consider Exhibit 5.2 showing a line that intercepts the y axis at 2 and has a slope of 0.8.
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CHAPTER 5Section 5.1 Mixed Costs
Exhibit 5.2
In the diagram, note that the line is rising consistently upward to the right as it moves out along the x axis. The rate of rise is called the slope of the line, and it is occurring at the rate of 0.8 along the y axis for every 1 unit increase along the x axis. It is said that one picture is worth a thousand words, and the same can be true of some mathematical equations. You should be able to close your eyes and imagine the same line based on knowledge of its mathematical formula:
Y 5 2 1 0.8X
where a is the intercept on the y axis, b is the slope of the line, and X is the position on the x axis.
This conventional mathematical formulation of a line can be translated to a discussion of fixed and variable costs in an accounting context. In other words, the formula can also be used to describe a mixed cost that consists of $2 of fixed cost and an additional variable component of $0.80 per unit. For example, if five units were produced, total costs would be $6 (see the circle in Exhibit 5.2), consisting of $2 fixed and $4 variable (5 units 3 $0.80).
Given a large historical data set about a mixed cost over time, how can regression analysis be used to analyze the data and find the formula for the line that best passes through the data? In a precise context, regression provides a mathematical model that processes the data set to find a line where the cumulative sum of the squared distances between the points and the line is minimized (hence the name “least squares”). You might actually learn to do these calculations in an advanced statistics class. Fortunately, however, elec- tronic spreadsheets include built-in functions that do these calculations for you. Exhibit 5.3 is an example of a spreadsheet plotting hypothetical cost data against hypothetical production data for a series of years:
20
2
0
4
6
8
10
12
4 6 8 10 12
X
Run = 10
Rise = 8Y
SLOPE = 0.8
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CHAPTER 5Section 5.2 Cost–Volume–Profit Analysis
Exhibit 5.3
In the spreadsheet, column C includes annual production data, whereas column D identi- fies total cost. The formula included in cell C16 (=INTERCEPT(D5:D13,C5:C13)) serves to calculate the intercept for the cost plotted against the volume. The indicated value of approximately $250,000 suggests fixed costs of approximately that level for each year. The slope reported in cell C17 (5SLOPE(D5:D13,C5:C13)) can be interpreted to mean that variable cost is $2.63 per unit of production. The accompanying graph shows the indi- vidual points and the resulting line defined by this formula:
Y 5 $250,044 1 $2.63X
This line resulting under regression analysis produces the best fit line, such that the verti- cal distance, squared, between each point and the resulting line is minimized. This line is deemed to be the best fit line, and it gives the best indication of the fixed and variable costs over time. A simple approach to regression is to simply “eyeball the points” and draw a line through them. You would then estimate the slope and intercept of this estimated line. This approach is not as precise as regression analysis, but it can get you in the right ball- park for a quick estimate.
5.2 Cost–Volume–Profit Analysis
A good manager must understand an organization’s variable and fixed cost components. That is why it is essential to perform analysis such as that just illustrated to discern the precise nature of a company’s cost behavior. Knowledge about the cost structure is essen- tial for cost–volume–profit (CVP) analysis. CVP is helpful in assessing the relationships between costs, business volume, and profitability. These relationships take into account variables pertaining to pricing, volume, variable and fixed costs, and product mix.
$0
$600,000
$500,000
$400,000
$300,000
$200,000
$100,000
20,000 40,000 60,000 80,000
TOTAL
COST
100,000 120,000
Year Production Total cost
20X1
20X2
20X3
20X4
20X5
20X6
20X7
20X8
20X9
100,000
90,000
75,000
110,000
70,000
105,000
95,000
60,000
85,000
$500,000
$480,000
$465,000
$550,000
$440,000
$535,000
$485,000
$399,500
$475,000
Intercept = 250044.335 Slope = 2.631773399
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CHAPTER 5Section 5.2 Cost–Volume–Profit Analysis
The goal of CVP is to provide a foundation for pricing decisions, product offerings, and management of an organization’s cost structure. In the following discussion, you will learn how to calculate a company’s break-even point as well as the volume level neces- sary to achieve a targeted amount of income.
The core of CVP analysis is the contribution margin or revenues minus all variable expenses:
Contribution Margin 5 Revenues 2 Variable Expenses
Some of these variable costs are product costs and some relate to selling and administra- tive activities. The contribution margin should not be confused with gross profit (revenues minus cost of sales). Gross profit would be calculated after deducting all manufacturing costs associated with sold units, whether fixed or variable. Furthermore, gross profit is calculated before considering selling, general, and administrative costs. Thus, the contribu- tion margin and gross profit are two entirely different concepts. The contribution margin is a calculated value for internal analysis, but it is ordinarily not reported to parties external to the firm.
Assume that Mustang Corporation manufactures and sells fishing boats. Each boat sells for $10,000, and variable manufacturing costs are $6,000 per boat. In addition, the boats are only sold through commissioned agents who receive $1,500 for each boat sold. Mus- tang’s per-unit contribution margin is $2,500 ($10,000 2 ($6,000 1 $1,500)). Mustang incurs $2,500,000 of fixed costs, no matter how many boats are produced and sold. The company must sell 1,000 units to break even, as shown in Table 5.3.
Table 5.3: Breaking even
Total Per boat Ratio
Sales (1,000 3 $10,000) $10,000,000 $10,000 100% (or 1.00)
Variable costs (1,000 3 $7,500) 7,500,000 7,500 75% (or 0.75)
Contribution margin $ 2,500,000 $ 2,500 25% (or 0.25)
Fixed costs 2,500,000
Net income $ 0
In reviewing Table 5.3, you likely noticed that the contribution margin can be reflected in the aggregate, on a per-unit basis, or on a ratio basis. The ratios may be expressed as percentages or fractional amounts (e.g., 50% or 0.50). These data were designed to reflect a break-even outcome of 1,000 units. In the following paragraphs, you will learn how to determine, in advance, the sales that are necessary to break even. Before looking at those formulations, let’s first consider what would happen to Mustang if sales were 1,500 units. Logic suggests that the company will be profitable. If 1,000 units are first needed to break even, then selling an additional 500 units should produce profits equivalent to the added contribution on those 500 units (500 3 $2,500 5 $1,250,000). The calculations in Table 5.4 prove this logic:
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CHAPTER 5Section 5.2 Cost–Volume–Profit Analysis
Table 5.4: Logic of being profitable
Total Per boat Ratio
Sales (1,500 3 $10,000) $15,000,000 $10,000 100% (or 1.00)
Variable costs (1,500 3 $7,500)
11,250,000 7,500 75% (or 0.75)
Contribution margin $ 3,750,000 $ 2,500 25% (or 0.25)
Fixed costs 2,500,000
Net income $ 1,250,000
The changes in volume only impacted the total column in Table 5.4. Volume changes do not change the per-unit or ratio effects. This will be important to remember in the ensuing formulas that you will learn for break-even calculations. Break-even analysis can also be presented in a graphical manner as in Exhibit 5.4.
Exhibit 5.4
A break-even chart, such as the one shown for Mustang, is intended to allow the user to observe the unit sales volume (as revealed along the horizontal axis in Exhibit 5.4) that is necessary for a company to break even. In other words, it is the point where the amount of sales in dollars equals the total cost in dollars. Total sales are portrayed by the line starting at zero and sloping upward at $10,000 per unit. In contrast, total costs start at $2,500,000 (the amount of fixed costs) and rise more slowly at $7,500 per unit (the amount of variable cost per unit).
TOTAL UNITS
CVP ANALYSIS
Variable cost area
Profit area
Loss area
Total cost line
Break-even point
Total sales line
Fixed cost area
2,0001,5001,0005000
0
20,000,000
10,000,000
2,500,000
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CHAPTER 5Section 5.2 Cost–Volume–Profit Analysis
Some companies utilize graphs such as that shown in Exhibit 5.4 to keep an eye on their margin of safety. The margin of safety is simply the amount by which sales exceed the break-even sales level. If Mustang’s actual sales were $15,000,000, their margin of safety would be $5,000,000 ($15,000,000 2 $10,000,000 break-even sales). Operating leverage is a related CVP term that is often used. It refers to the amount of increase in income associ- ated with an increase in sales. This concept is based on the differences in slope between the total revenue line and the variable cost line; in essence, it reflects the contribution mar- gin rate. Some businesses refer to the process of evaluating margin of safety and operating leverage as tools in “sensitivity” or “scalability” analysis. Basically, it is perspective on how changes in volume impact changes in income.
The Algebra of Break-Even and Targeted Income Analysis
The preceding graphical representation can be converted to algebraic formulas. Consider the following relationships:
Break-Even Sales 5 Total Variable Costs 1 Total Fixed Costs
Mustang’s 10,000 units in sales to break even is confirmed via the following:
(Units 3 $10,000) 5 (Units 3 $7,500) 1 $2,500,000
Solving:
(Units 3 $10,000) 2 (Units 3 $7,500) 5 $2,500,000
(Units 3 $2,500) 5 $2,500,000
Units 5 1,000
The 1,000 units, at $10,000 each, translate into total sales of $10,000,000. The preceding relationships can be algebraically modified to formulate a calculation of breakeven by reference to the contribution margin ratio:
Break-Even Sales = Total Fixed Costs / Contribution Margin Ratio
$10,000,000 5 $2,500,000/0.25
Utilization of this ratio-based approach is helpful for multiproduct companies as long as all products have a consistent contribution margin.
As yet another modification to the algebra, consider that total fixed costs can simply be divided by the contribution margin per unit:
Break-Even Point in Units = Total Fixed Costs / Contribution Margin Per Unit
1,000 Units 5 $2,500,000/$2,500
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Of course, businesses are not in business just to break even. They likely have targeted income levels and desire to know the amount of sales that will be needed to reach those goals. The determination of sales necessary to achieve a targeted amount of income is a very easy modification of the break-even calculations. All that is required is to treat the desired income in a manner similar to the amount of fixed costs that must be covered by the margin:
Sales to Achieve Targeted Income 5 Total Variable Costs 1 Total Fixed Costs 1 Target Income
If Mustang desired to earn $1,000,000 of income, the following calculations would be appropriate:
(Units 3 $10,000) 5 (Units 3 $7,500) 1 $2,500,000 1 $1,000,000
Units 3 $2,500 5 $3,500,000
Units 5 1,400
If you want to know the dollar level of sales to achieve this targeted income, you could multiply the 1,400 units by the $10,000 selling price per unit, or
$14,000,000 5 (Total Fixed Costs 1 Target Income) / Contribution Margin Ratio
$14,000,000 5 $3,500,000/0.25
Influence of Taxes
Taxes are a significant cost of doing business. Some taxes are fixed in amount, such as property taxes. They are easily factored into CVP by increasing the total fixed cost pool. However, taxes based on income present a slight complication to CVP. Income taxes are nonexistent up to the break-even point (i.e., you do not pay income taxes until you turn profitable) and then kick in based on a predetermined rate. The effect of an income tax essentially means that you have two different contribution margin rates—one based on sales minus variable expenses (without taxes) up to the break-even point and another based on sales minus variable expense and income taxes once the break-even point is exceeded.
The preceding discussion points to the rather obvious need to modify the algebra associ- ated with profitability analysis. First, income taxes will not modify the break-even cal- culations. However, sales necessary to achieve target income level calculations must be amended. One simple way to perform this analysis is in two stages. The first stage is to calculate the break-even point. The second stage is to calculate the additional sales needed to reach the target income. In the second stage, it is important to remember that fixed costs have already been covered at the break-even point, but the contribution margin is reduced because of the income taxes.
To illustrate, assume the Go for Gold Mining faces the following facts:
Fixed costs $2,000,000
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CHAPTER 5Section 5.2 Cost–Volume–Profit Analysis
Variable mining costs $ 750 per ounce
Income tax rate 50%
If gold is selling for $1,500 per ounce (giving rise to a pretax contribution margin of 50%), and Go for Gold desires to reach an after-tax income level of $1,000,000, how much gold must be sold?
The first step is to calculate break-even sales:
$2,000,000 (fixed costs)/0.50 contribution margin ratio 5 $4,000,000 in sales
The second step is to calculate the additional sales to earn a $1,000,000 profit:
$1,000,000 (target income)/0.25 revised contribution margin ratio 5 $4,000,000 in sales
Combining the sales to reach breakeven plus the additional sales to reach the target income level reveals that Go for Gold must sell $8,000,000 to achieve the desired income level. You likely noticed that the contribution margin in the second step was only 25% instead of 50%. The reason is that any profits had to be shared 50:50 with the government (given the assumed 50% income tax rate). This means that the company’s contribution was reduced in half for all sales above the break-even point!
Changing Costs
Costs can naturally be expected to shift over time. These changes will impact the struc- tural relationships between fixed and variable components. Management must be able to contemplate how cost shifts will impact the business. For instance, an increase in fixed costs, without a change in per-unit variable costs and revenues, will obviously increase the break-even point. The proper analysis for an increase in fixed cost requires that the new total fixed cost be divided by the contribution margin. Suppose Mustang’s total fixed costs increased from $2,500,000 to $3,000,000. What sales level is now necessary to break even? Recall that the break-even point in sales can be derived by dividing total fixed costs by the contribution margin ratio. Thus, the new calculation of breakeven is as follows:
$12,000,000 5 $3,000,000/0.25
The $500,000 additional fixed cost requires an additional $2,000,000 in sales. As you can see, the revisions in fixed costs are relatively simple to incorporate into the break-even framework with which you are already familiar. However, what about changes in variable costs? What if a new environmental regulation required that an additional $500 be spent on each boat to use a safer fiberglass handling process? Now, the contribution margin is only $2,000 per unit ($10,000 2 ($7,500 1 $500)). Assuming the added cost cannot be passed through, how will this impact the break-even point? The revised break-even point (let’s assume fixed costs are still $2,500,000 for this illustration) is now calculated as follows:
$12,500,000 5 $2,500,000/0.20
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CHAPTER 5Section 5.2 Cost–Volume–Profit Analysis
Of course, a business sometimes must choose between adding either a fixed or a vari- able cost. Suppose the per-unit increase in variable cost associated with a safer fiberglass handling process could be avoided by instead incurring a $500,000 increase in fixed cost. If you review the two preceding examples, you can see that breakeven is lower with the added fixed cost, and you might jump to the conclusion that it would be the preferred option. However, if the business’s sales fail to reach even the break-even level, there is a point at which the added fixed cost would become disadvantageous. For example, if sales reached only $8,000,000, Table 5.5 reveals that the loss is less for the case in which the increased fixed cost was avoided.
Table 5.5: Loss is less
With increased fixed cost Without increased fixed cost
Sales $8,000,000 $8,000,000
Less: Fixed costs ($3,000,000) ($2,500,000)
Less: Variable costs (800 , $7,500)
($6,000,000)
Less: Variable costs (800 , $8,000)
($ 6,400,000)
Net loss ($1,000,000) ($ 900,000)
Changing Revenues
Changes in per-unit revenue, without changes in total fixed costs or per-unit variable cost, can sometimes cause dramatic impacts on firm profits. This is especially true for busi- nesses with a low variable cost structure. Consider the example in Table 5.6, in which firm profits are calculated before and after a $10 per-unit increase in selling price.
Table 5.6: Calculating profits
Before price increase After price increase
Sales (5,000 units) $500,000 $550,000
Variable costs ($40 per unit) 200,000 200,000
Contribution margin $300,000 $350,000
Fixed costs 275,000 275,000
Net income $25,000 $75,000
Notice that the $10 (10%) increase in selling price caused a tripling of profits from $25,000 to $75,000. This simple illustration shows the importance of small adjustments in selling prices. Of course, markets are at times very sensitive to pricing. Customers may not be willing to pay the added $10, which can cause a reduction in per-unit sales. Management must be very careful in setting its pricing policies.
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Multiple Products
Most businesses offer more than one product. Each product may have a different selling price, contribution margin, and contribution margin ratio. This has the potential to com- plicate CVP analysis. Now, knowledge is also required about the proportion of total sales attributable to each product.
To illustrate, assume that Infusion Technology sells hospital medication pumps and dis- posable cassettes that hold various medications. The pumps sell for $5,000 and have vari- able costs of $4,000. The contribution margin is therefore $1,000 per pump. The cassettes sell for $20 and have variable costs of $10, giving rise to a $10 per-unit contribution mar- gin. Infusion Technology sells 1,000 cassettes for each pump sold. How many pumps and cassettes must be sold to cover the business’s $1,100,000 of total fixed costs? Consider that a product “unit” typically consists of one pump and 1,000 cassettes. Thus, the “unit” would have a contribution margin of $11,000, as shown in Table 5.7.
Table 5.7: Contribution margin
Contribution margin
Pump 1 item at $1,000
Cassette 1,000 items at $10 5 $10,000
“Unit contribution” $11,000
To recover $1,100,000 of fixed cost requires sales of 100 “units” ($1,100,000/$11,000). This is equivalent to selling 100 pumps and 100,000 cassettes. Total break-even sales equal $2,500,000 (($5,000 3 100 pumps) 1 ($20 3 100,000 cassettes)). This break-even sales level would shift dramatically if the product mix is not as projected. Pumps have a much lower contribution margin than cassettes, and increasing their sales (without a corresponding increase in the high-margin cassettes) would cause a dramatic shift in the break-even level of sales.
5.3 CVP Assumptions
The CVP techniques illustrated in this chapter are simply models of cost behavior. Financial models are typically based on various assumptions. Violating an assump- tion can cause a model to produce misleading results. Therefore, it is very important for you to consider the assumptions of CVP in Table 5.8.
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Table 5.8: Assumptions of CVP
Inventory levels Constant, with the number of units sold equaling the number of units produced. Fluctuations in inventory would result in a portion of the variable and fixed costs being transferred in and out of inventory rather than income.
Identification of costs Costs can be clearly and reliably identified as fixed and variable in nature.
Preservation of linearity Variable costs are constant per unit, and total fixed costs are stable and constant over the relevant range of activity. Revenues are constant per unit.
Product mix ratios meet expectations
Revenues are constant per unit, and multiple-product firms meet the expected product mix ratios.
Direct Costing
Now that you have examined the contribution margin and how it can be useful in corpo- rate analysis, it is time to expand upon the concept to see how it dovetails with report- ing. Two general models can be used to measure and report income for a manufacturer. One is absorption (or full) costing. It is the model with which you are currently familiar, and it is required for external reporting purposes. There is an alternative model, accept- able only for internal use, called direct (or variable) costing. Each has its advantages and disadvantages.
Absorption costing provided the basis for prior chapter illustrations. Under this tech- nique, all manufacturing costs are deemed to be product costs and are therefore included in inventory. When sold, the full cost of inventory is transferred to cost of goods sold. The result is that gross profit is reduced by all costs of manufacturing, including direct mate- rials, direct labor, and variable and fixed manufacturing overhead. Also recall that sell- ing, general, and administrative costs (SG&A) are classified as period expenses, whether fixed or variable in nature. Generally accepted accounting principles (GAAP) require this approach based on the premise that inventory should be measured and reported at its complete cost. There is obvious merit to this conclusion. A product could likely not be produced without a certain amount of fixed manufacturing overhead, and it seems inap- propriate to exclude such costs as one attempts to report on their manufacturing profits.
Variable (direct) costing only assigns variable product costs to inventory and cost of goods sold. Thus, product costs are deemed to include direct materials, direct labor, and variable manufacturing overhead. The fixed manufacturing overhead is regarded as a period cost. Table 5.9 highlights the difference in perspective between absorption and variable costing.
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Table 5.9: Absorption versus variable costing
Absorption costing Variable costing
Product cost Period cost Product cost Period cost
Direct material ✔ ✔
Direct labor ✔ ✔
Variable manufacturing overhead ✔ ✔
Fixed manufacturing overhead ✔ ✔
Variable SG&A ✔ ✔
Fixed SG&A ✔ ✔
In light of GAAP’s requirement for absorption costing, and the associated arguments in support of this view, why might a company opt for variable costing for internal use? Regardless of the claims in support of absorption costing, it does suffer from some limita- tions that can impede appropriate management decisions. Absorption costing does not necessarily provide the best signals about product pricing, whether to continue to produce a product, whether to accept a special order, and similar decisions. With variable costing, fixed manufacturing costs are shifted from product costs to period costs because they will be incurred no matter the level of production. Simply stated, in many cases, a company should continue to produce a product that has a positive contribution margin, even if the overall results still appear to be producing a loss; the loss would be larger if the fixed costs were incurred and nothing was produced. Absorption costing does not illuminate this reality in a way that enables good decisions. Numerous similar situations can arise. This is a very important concept and bears much deeper analysis via a series of examples.
Assume that Home Pride produces 500,000 loaves of bread per month, and per-unit costs are $0.45 for direct material, $0.30 for direct labor, and $0.25 for variable factory over- head. Total fixed factory overhead amounts to $250,000. Under absorption costing, a loaf of bread costs $1.50 to produce. This consists of variable costs ($0.45 1 $0.30 1 $0.25 5 $1) and fixed costs ($250,000/500,000 loaves 5 $0.50). Under variable costing, the prod- uct cost includes just the $1.00 of variable manufacturing components. If Home Pride is approached by Super Grocery to produce a private-label bread product, and Super Gro- cery is willing to pay $1.25 per loaf, should Home Pride accept the deal? Home Pride has evaluated the transaction and concluded that it will not result in any added variable or fixed SG&A costs, and it will not cause a reduction in sales of its own bread products. With absorption costing, it appears that the offer should be rejected. Why sell something for $1.25 when it costs $1.50 to produce? This seems obviously irrational. Conversely, vari- able costing suggests that a profit of $0.25 per loaf will result by accepting Super Grocery’s offer. Which decision is right? Management may well decide to accept the offer to enhance profits. It is important to recall that no other costs will be incurred. Reliance on absorption costing for decision making could have resulted in this opportunity having been missed. Very likely, you are now beginning to understand why some companies prefer a variable costing structure for internal measurement and decision-making purposes.
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CHAPTER 5Section 5.3 CVP Assumptions
Comprehensive Income Statements Under Variable and Absorption Costing
The preceding discussion focused on the general structure of income measurement under absorption and variable costing. The Home Pride example further assumed that SG&A was unaffected by the decision to sell to Super Grocery. That assumption would often not be valid. Variable SG&A typically increases along with rising sales, and this factor will be reflected in a variable costing income statement. Consider the following income statements for Garcia Company. Garcia does not maintain inventory, and it sells all that is produced each period. As a result, total income is the same, whether measured under absorption or variable costing. The difference, therefore, is only in how the data are pre- sented. Absorption costing will focus on an intermediate subtotal relating to gross profit. This is a different focus than with variable costing, in which the emphasis is on contribu- tion margins. Begin by closely examining the absorption costing income statement shown in Exhibit 5.5, and then review the additional commentary that follows.
Exhibit 5.5
Under absorption costing, assume the $500,000 cost of goods sold consists of direct mate- rials ($150,000), direct labor ($200,000), and variable ($50,000) and fixed manufacturing overhead ($100,000). Gross profit is reduced by SG&A, which is assumed to be $125,000 variable and $75,000 fixed. When these same factors are rearranged and presented as in a variable costing income statement format, you will first notice that all variable costs are subtracted from sales to arrive at the contribution margin. Garcia Company further divides the contribution margin between the manufacturing margin and the overall mar- gin, after subtracting variable SG&A (Exhibit 5.6).
Sales
Cost of goods sold
Gross profit
Less: Variable SG&A
Fixed SG&A
Net income
$ 125,000
75,000
$1,000,000
500,000
$ 500,000
200,000
$ 300,000
GARCIA COMPANY Absorption Costing Income Statement For the Year Ending December 31, 20XX
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CHAPTER 5Section 5.3 CVP Assumptions
Exhibit 5.6
Fluctuating Inventory
You may be wondering what happens if inventory levels fluctuate. With absorption cost- ing, inventory will carry all manufacturing costs, whereas only variable manufacturing costs are assigned to inventory with variable costing. Generalizing, therefore, inventory is measured at a higher value with absorption costing; in other words, certain costs (a por- tion of the fixed manufacturing overhead) are placed in inventory that would otherwise be expensed immediately under variable costing. This means that income is higher with absorption costing in those periods during which inventory levels are increasing. Let’s revisit Garcia Company, this time assuming that sales are 10% less, and the unsold units become part of ending inventory. The income statements (Exhibits 5.7 and 5.8) show how income is higher under absorption costing by $10,000. This is exactly as expected. In other words, 10% of the $100,000 of fixed manufacturing overhead is assigned to inventory under absorption costing versus what is expensed under variable costing.
Sales
Less: Variable product costs
Manufacturing margin
Less: Variable SG&A
Contribution margin
Less: Fixed factory cost
Fixed SG&A
Net income
$ 100,000
75,000
$1,000,000
400,000
$ 600,000
125,000
$ 475,000
175,000
$ 300,000
GARCIA COMPANY Variable Costing Income Statement
For the Year Ending December 31, 20XX
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CHAPTER 5Section 5.4 Evaluating Residual Income
Exhibit 5.7
Exhibit 5.8
5.4 Evaluating Residual Income
Comparing income measures under absorption and variable costing provides helpful clues to guide correct managerial decisions. However, these measures are not a pana- cea for management. Additional economic facets must be considered. For instance, neither measure adjusts income for the embedded amount of capital that must be deployed to gen- erate the reported income numbers. In other words, the level of stockholder investments is not factored into the basic income calculations. If two businesses each generate income of $1,000,000 but one of the businesses has stockholder investments of $5,000,000 and the other has stockholder investments of $10,000,000, it is apparent that the former business
Sales
Less: Variable product costs
Manufacturing margin
Less: Variable SG&A
Contribution margin
Less: Fixed factory cost
Fixed SG&A
Net income
$ 100,000
75,000
$ 900,000
360,000
$ 540,000
112,500
$ 427,500
175,000
$ 252,500
GARCIA COMPANY Variable Costing Income Statement
For the Year Ending December 31, 20XX
Sales
Cost of goods sold
Gross profit
Less: Variable SG&A
Fixed SG&A
Net income
$ 112,500
75,000
$ 900,000
450,000
$ 450,000
187,500
$ 262,500
GARCIA COMPANY Absorption Costing Income Statement For the Year Ending December 31, 20XX
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CHAPTER 5Section 5.4 Evaluating Residual Income
is generating a better rate of return on the amount of invested capital. Thus, not only is it important that a business have profitable operations to maintain long-run economic viabil- ity but also it must generate returns that are sufficient to justify the investment. In a later chapter, you will study many capital budgeting tools that aid in these evaluations.
However, you are already in a position to consider the concept of residual income. Like vari- able costing, residual income is not a GAAP-based measure. Instead, it is another internal financial assessment technique. Residual income provides a scale of business success or fail- ure after adjusting for the presumed cost of capital. The cost of capital is the theoretical rate that funds could earn if invested in alternative use. The cost of capital varies by firm and is based on general economic conditions. Although there are variations in the way in which residual income could be measured, one general approach is based on this formulation:
Residual Income 5 Operating Income 2 (Operating Assets 3 Cost of Capital)
To see how residual income can be used for business assessments, begin by looking at the data for two separate business segments in Table 5.10.
Table 5.10: Data for two business segments
Segment A Segment B
Operating income $ 250,000 $500,000
Less: Cost of capital
Segment A capital $3,000,000 3 5% cost of capital (150,000)
Segment B capital $9,000,000 3 5% cost of capital (450,000)
Residual income $ 100,000 $ 50,000
At first glance, it appears that Segment B is more successful because its operating income is twice that of Segment A. However, Segment B has much more capital invested in opera- tions ($9,000,000 for B vs. $3,000,000 for A). Assuming a 5% cost of capital, Segment A’s residual income is twice that of Segment B. This information casts the relative success of the two divisions in a completely different light. Thus, residual income can be a powerful tool for identifying and ranking the performance of segments, products, and other com- ponents of business activity.
As with most analysis techniques, great care must be taken in interpreting residual income. Conclusions can be impacted by the assumption about the cost of capital and different rank- ings achieved by revisions in interest rates. In addition, management needs to understand the accounting principles that were used to measure operating income. For example, a unit may be spending heavily on developmental costs. Were these costs expensed? If so, then near-term income could be negatively impacted. In the long term, those same costs (having already been expensed) would be excluded from the calculation of invested capital and per- haps inflate the residual income in the latter stages of a project. Thus, management needs to be very careful in interpreting residual income. Nevertheless, when used appropriately, the technique is highly valuable in helping a business identify and rank products, segments, and business activities. It is crucial that business decisions about which products and ser- vices to offer, or cease to offer, be made with deliberate care and attention to detail.
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CHAPTER 5Concept Check
Concept Check
The five questions that follow relate to several issues raised in the chapter. Test your knowledge of the issues by selecting the best answer. (The correct answers can be found at the end of your text.)
1. Variable costs (from the accountant’s viewpoint) a. are graphed by means of a curvilinear line. b. remain constant in total through the relevant range. c. are constant on a per-unit basis through the relevant range. d. are commonly divided into committed and discretionary classifications.
2. The high–low method of analyzing cost behavior a. can be used to determine the variable and fixed components of a mixed cost
function. b. uses the same number of data observations as a scattergraph. c. relies on the following computation to figure the variable cost per unit (or hour):
Change in activity between the high and low points / change in cost between the high and low points.
d. results in different amounts of fixed cost at the high and low data points.
3. Foster Company has sales of $800,000, variable costs that total 60% of sales, and fixed costs of $180,000. The firm’s break-even point is
a. $140,000. b. $300,000. c. $450,000. d. $560,000.
4. The contribution margin a. is the amount that each unit contributes toward covering variable costs and
producing income. b. is the result of subtracting both the variable and fixed costs per unit from the
selling price. c. may, in select cases, be less than net income. d. is the difference between a unit’s selling price and variable cost and, when
divided into fixed costs, will produce the unit sales required to break even.
5. The cost–volume–profit model a. can be used only by single-product companies. b. assumes that the sales mix will remain as predicted. c. assumes that technology, efficiency, and costs can change. d. cannot be used to study operating changes of the firm.
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CHAPTER 5Critical Thinking Questions
Critical Thinking Questions
1. Define the break-even point. 2. Define the contribution margin. What does the contribution margin represent, and
how is it used in finding the break-even point? 3. Product A has a negative contribution margin. Explain how a negative contribution
margin can arise, and determine whether product A should continue to be sold. 4. Discuss the benefits associated with using a break-even chart. 5. Determine the effect, if any, on the break-even point that each of the following
events would have: a. An increase in sales price b. A decrease in fixed cost c. An increase in the number of units sold 6. Will a change in a company’s sales mix likely affect the break-even point? Briefly
explain. 7. What are the limiting assumptions of CVP analysis?
absorption costing A technique by which all manufacturing costs are deemed to be product costs and are therefore included in inventory.
break-even chart Used to allow the user to observe the unit sales volume that is necessary for a company to break even.
contribution margin At the core of a CVP analysis, and it represents revenues minus all variable expenses.
cost–volume–profit (CVP) analysis The process of providing a foundation for pricing decisions, product offerings, and management of an organization’s cost structure.
high–low method A method of identify- ing the highest and lowest levels of activity and where the difference in cost is deemed to be representative of the variable portion.
margin of safety The amount by which sales exceed the break-even sales level.
mixed costs A type of cost that entails a fixed component and a variable component.
operating leverage Refers to the amount of increase in income associated with an increase in sales, based on the differences in slope between the total revenue line and the variable cost line.
residual income An internal financial assessment technique that provides a scale of business success or failure after adjust- ing for the presumed cost of capital.
targeted income A measuring point for a company to pinpoint the amount of sales that will be required to reach financial goals.
variable (direct) costing A method in which variable product costs are assigned to inventory and cost of goods sold. Prod- uct costs are deemed to include direct materials, direct labor, and variable manu- facturing overhead.
Key Terms
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CHAPTER 5Exercises
Exercises
1. High–low method The following cost data pertain to 20X6 operations of Heritage Products:
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Shipping costs $58,200 $58,620 $60,125 $59,400
Orders shipped 120 140 175 150
The company uses the high–low method to analyze costs.
a. Determine the variable cost per order shipped. b. Determine the fixed shipping costs per quarter. c. If present cost behavior patterns continue, determine total shipping costs for
20X7 if activity amounts to 570 orders.
2. Break-even and other CVP relationships Delta Gamma Upsilon sorority is in the process of planning its annual homecoming dinner and dance. The treasurer anticipates the following costs for the event, which will be held at the Regency Hotel:
Room rental $300
Dinner cost (per person) 25
Chartered buses 500
Favors and souvenirs (per person) 5
Band 900
Each person would pay $40 to attend; 200 attendees are expected.
a. Will the event be profitable for the sorority? Show computations. b. How many people must attend for the sorority to break even? c. Suppose the sorority encouraged its members to drive to the hotel and did not
charter the buses. Furthermore, a planned menu change will reduce the cost per meal by $2. If each member will still be charged $40, compute the contribution margin per person.
3. Break-even and other CVP relationships Cedars Hospital has average revenue of $180 per patient day. Variable costs are $45 per patient day; fixed costs total $4,320,000 per year.
a. How many patient days does the hospital need to break even? b. What level of revenue is needed to earn a target income of $540,000? c. If variable costs drop to $36 per patient day, what increase in fixed costs can be
tolerated without changing the break-even point as determined in part (a)?
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CHAPTER 5Exercises
4. CVP relationships: Working backward Determine the missing amounts in each of the independent cases that follow:
Case Units sold
Sales Variable costs
Contribution margin per unit
Fixed costs
Net income
A ? $70,000 $ ? $6 $14,000 $10,000
B 7,000 ? 42,000 5 ? 8,000
C 4,000 53,000 ? ? 21,000 (2,000)
D 8,000 92,000 40,000 ? 24,000 ?
5. Direct and absorption inventory costing Milsap Industries began business on January 1 of the current year, manufacturing and selling a single product. Consider the data that follow:
Units Variable cost per unit Fixed costs
Production volume 80,000
Sales volume 72,000
Direct materials $1.30
Direct labor 2.80
Factory overhead 4.40 $540,000
Selling expenses 0.20 180,000
a. Compute the cost of the company’s ending inventory by using direct costing. b. Compute the cost of the company’s ending inventory by using absorption costing. c. Suppose that Milsap’s accountant had accidentally excluded straight-line depre-
ciation on machinery from the data presented. Determine the effect of this error (overstate, understate, or no impact) on the company’s
1) direct costing ending inventory. 2) absorption costing ending inventory.
6. Direct and absorption income computations Crawford Company began operations on January 1 of the current year. The follow- ing information has been gathered from the accounting records:
Variable costs per unit Manufacturing: $12.50 Selling & administrative: $1.10
Fixed costs Manufacturing: $120,000 Selling & administrative: $60,000
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CHAPTER 5Problems
Production and sales amounted to 80,000 units and 75,000 units, respectively. The selling price is $17.
a. Compute net income for the year just ended by using the direct costing method. b. Compute net income for the year just ended by using the absorption costing
method.
Problems
1. Cost behavior and analysis The chief accountant of Stevenson Corporation is studying certain costs (direct labor, plant security, utilities, and maintenance) in an effort to better control opera- tions. Normal production activity ranges from 7,500 to 8,000 units per month. In the past 3 months, the following cost behavior has been observed:
Month 1 Month 2 Month 3
Production (units) 7,540 7,950 7,680
Direct labor $18,850 $19,875 $19,200
Plant security 14,600 14,600 14,600
Utilities 28,044 29,520 28,548
In addition, maintenance costs have displayed the following step behavior:
Activity range (units) Cost
Up to 7,600 $ 8,000
7,601–7,800 9,500
7,801–8,000 11,000
Stevenson uses the high–low method to analyze cost behavior.
Instructions a. Production for next month is expected to total 7,850 units. Calculate the cost of
direct labor, plant security, utilities, and maintenance for this level of activity. b. Comment on the cost-effectiveness of producing at a 7,850-unit level of activity
with respect to maintenance costs. If you believe this is an ineffective production level, describe how effectiveness could be improved.
c. There is a high probability that Stevenson’s production volume will nearly double in forthcoming months because of a new customer. Can the data and methods used in part (a) for predicting the cost of 7,850 units be employed to estimate total costs for, say, 17,500 units? Why?
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CHAPTER 5Problems
2. Break-even and other CVP analysis Hodge and Best manufactures a single product. The information that follows relates to current operations:
Sales (80,000 units , $15) $1,200,000
Less: Variable cost $720,000
Fixed cost 360,000 1,080,000
Net income $ 120,000
Instructions a. The sales outlook for next year is bleak. Calculate the number of units that must
be sold to break even if current revenue and cost behavior patterns continue. b. If Hodge and Best wishes to earn a target income of $90,000 during the next
accounting period, what level of dollar sales must be generated? c. Management is studying an increase in the selling price to $18 per unit. If con-
sumers balk and volume drops, calculate the number of units that must be sold to earn the target income of $90,000. Should the change be implemented? Why?
d. Hodge and Best’s projected break-even point and target income are the result of interactions of numerous financial events and transactions. Determine the impact of the following operating changes by filling in the blanks below with “increase,” “decrease,” or “not affect.”
1) An increase in direct labor cost will _______________________ total variable costs, _______________________ the contribution margin, and _______________________ the break-even point.
2) An increase in plant insurance will _______________________ the break-even point and _______________________ the dollar sales level calculated in part (b).
3. Straightforward CVP analysis FRB Inc. sells a single product for $40. The following costs and expenses were incurred at store No. 504:
Variable costs per unit Annual fixed costs
Invoice cost $24 Salaries $60,000
Sales commission 4 Advertising 14,000
Other 16,000
The company sold 8,200 units during 20X4.
Instructions a. Compute the 20X4 break-even point in both dollar and unit sales. b. By how much will sales have to increase in 20X5 over 20X4 levels if management
wishes to earn a target income of $14,400?
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CHAPTER 5Problems
c. At present, how much does each unit provide toward covering FRB’s fixed costs and generating income? Assume that management believes this amount is too low. What alternatives are available to FRB?
d. What would be the effect on the break-even point if management reduced salary costs by $11,600 and increased the $4 sales commission by 20%?
4. Break-even and other CVP analysis Quebec Inc. manufactures and sells a single product. The information that follows relates to the year just ended, when 230,000 units were sold:
Sales price per unit $ 10
Variable cost per unit 4
Fixed costs 930,000
Instructions a. Determine the number of units that Quebec sold in excess of its break-even point. b. If current revenue and cost patterns continue, compute the dollar sales needed
next year to produce a target income of $492,000. c. Assume that a different compensation plan was in effect during the current year.
Rather than pay six salespeople an average salary of $36,000 each, management has proposed that the salespeople receive a $10,000 base salary and a 6% commis- sion based on gross sales.
1) Would the company have been better off financially if the new plan had been adopted for the year just ended? By how much?
2) What effect might paying a commission have on gross sales? Briefly explain.
d. In addition to the compensation plan described in part (c), Quebec is studying the impact of other operating changes as well. State whether you agree or dis- agree with the following findings of a newly hired staff accountant:
1) A rise in property taxes will increase the break-even point. 2) A decrease in raw material cost will increase the contribution margin and
decrease total fixed costs.
5. Direct and absorption costing The following information pertains to Turbo Enterprises for the year ended December 31, 20X8:
Variable cost per unit:
Direct materials $ 6
Direct labor 4
Factory overhead 9
Selling & administrative expense 3
Total $ 22
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CHAPTER 5Problems
Annual fixed costs:
Factory overhead $600,000
Selling &. administrative expense 115,000
Total $715,000
Other data (units):
Sales 21,000
Production 25,000
Inventory, 12/31/X8 11,000
The unit selling price is $62. Assume that costs have been stable in recent years.
Instructions a. Compute the number of units in the beginning inventory on January 1, 20X8. b. Calculate the cost of the December 31 inventory assuming use of
1) direct costing. 2) absorption costing.
c. Prepare an income statement for the year ended December 31, 20X8, by using direct costing.
d. Prepare an income statement for the year ended December 31, 20X8, by using absorption costing.
6. Direct and absorption costing The information that follows pertains to Consumer Products for the year ended December 31, 20X6:
Inventory, 1/1/X6 24,000 units
Units manufactured 80,000
Units sold 82,000
Inventory, 12/31/X6 ? units
Manufacturing costs:
Direct materials $3 per unit
Direct labor $5 per unit
Variable factory overhead $9 per unit
Fixed factory overhead $280,000
Selling & administrative expenses:
Variable $2 per unit
Fixed $136,000
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CHAPTER 5Problems
The unit selling price is $26. Assume that costs have been stable in recent years.
Instructions a. Compute the number of units in the ending inventory. b. Calculate the cost of a unit assuming use of
1) direct costing. 2) absorption costing.
c. Prepare an income statement for the year ended December 31, 20X6, by using direct costing.
d. Prepare an income statement for the year ended December 31, 20X6, by using absorption costing.
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