Cost‐Volume‐Profit Analysis: Additional Issues
As the Feature Story about Whole Foods Market suggests, the relationship between a company’s fixed and variable costs can have a huge impact on its profitability. In particular, the trend toward cost structures dominated by fixed costs has significantly increased the volatility of many companies’ net income. The purpose of this chapter is to demonstrate additional uses of cost‐volume‐profit analysis in making sound business decisions.
Not Even a Flood Could Stop It
America has a reputation as a country populated with people who won’t buy a restaurant meal unless it can be ordered from the driver’s seat of a car. Customers want to receive said “meal” 30 seconds later from a drive‐up window and then consume the bagged product while driving one‐handed down an 8‐lane freeway. This is actually a fairly accurate depiction of the restaurant preferences (and eating habits) of one of the authors of this textbook. However, given the success of Whole Foods Market, this certainly cannot be true of all Americans.
Whole Foods Market began humbly in 1978 as a natural‐foods store called SaferWay. (Get it? A play on SafeWay grocery stores.) It was founded in Austin, Texas, by 25 year‐old John Mackey (a self‐described college dropout) and 21 year‐old Renee Lawson Hardy. They financed the first store by borrowing $45,000 from family and friends. The early days were “interesting.” First, John and Renee got kicked out of their apartment for storing grocery products there. No problem—they just moved into the store. They bathed in the store’s dishwasher with an attached hose. They did whatever it took to keep their costs down and the store going.
Two years later, John and Renee merged SaferWay with another store to form the first Whole Foods Market. The store’s first year was very successful. Well, that is until everything in the store was completely destroyed by Austin’s biggest flood in more than 70 years. They lost $400,000 in goods—and they had no insurance. But within 28 days, with tons of volunteer work and understanding creditors and vendors, the store reopened.
Today, Whole Foods operates approximately 270 stores. The size of the average store has actually declined in recent years. While huge stores (up to 80,000 square feet) were successful in a few cities, in most locations the fixed costs of such a large facility made it hard to achieve profit targets. Then, when sales became sluggish during the recession, the company determined that it could reduce its fixed costs, such as rent and utility costs, by reducing its average store size by about 20%. However, with fewer square feet, managers must keep a close eye on the sales mix. They need to be aware of the relative contribution margins of each product line to maximize the profit per square foot while still providing the products its customers want.
Why is a company as successful as Whole Foods so concerned about controlling costs? The answer is that the grocery business runs on very thin margins. So while we doubt that anybody is bathing in the store’s dishwashers anymore, Whole Foods is as vigilant about its costs today as it was during its first year of operations.
LEARNING OBJECTIVE 1
Apply basic CVP concepts.
As indicated in Chapter 18 , cost‐volume‐profit (CVP) analysis is the study of the effects of changes in costs and volume on a company’s profit. CVP analysis is important to profit planning. It is also a critical factor in determining product mix, maximizing use of production facilities, and setting selling prices.
Because CVP is so important for decision‐making, management often wants this information reported in a CVP income statement format for internal use. The CVP income statement classifies costs as variable or fixed, and computes a contribution margin. Contribution margin is the amount of revenue remaining after deducting variable costs. It is often stated both as a total amount and on a per unit basis.
|VARGO VIDEO COMPANY CVP Income Statement For the Month Ended June 30, 2017|
|Sales (1,600 camcorders)||$ 800,000||$ 500|
ILLUSTRATION 19-1 Basic CVP income statement
Companies often prepare detailed CVP income statements. The CVP income statement in Illustration 19-2 uses the same base information as that presented in Illustration 19-1 but provides more detailed information (using assumed data) about the composition of expenses.
|VARGO VIDEO COMPANY CVP Income Statement For the Month Ended June 30, 2017|
|Cost of goods sold||$400,000|
|Total variable expenses||480,000||300|
|Cost of goods sold||120,000|
|Total fixed expenses||200,000|
ILLUSTRATION 19-2 Detailed CVP income statement
▼ HELPFUL HINT
The appendix to this chapter provides additional discussion of income statements used for decision‐making.
In the applications of CVP analysis that follow, we assume that the term “cost” includes all costs and expenses related to production and sale of the product. That is, cost includes manufacturing costs plus selling and administrative expenses.
Before we introduce additional issues of CVP analysis, let’s review some of the basic concepts that you learned in Chapter 18 , specifically break‐even analysis, target net income, and margin of safety.
Vargo Video’s CVP income statement ( Illustration 19-2 ) shows that total contribution margin (sales minus variable expenses) is $320,000, and the company’s unit contribution margin is $200. Recall that contribution margin can also be expressed in the form of the contribution margin ratio(contribution margin divided by sales), which in the case of Vargo is 40% ($200÷$500)40% ($200÷$500).
Illustration 19-3 demonstrates how to compute Vargo’s break‐even point in units (using unit contribution margin).
Fixed Costs÷Unit Contribution Margin=Break-Even Point in Units$200,000÷$200=1,000 unitsFixed Costs÷Unit Contribution Margin=Break-Even Point in Units$200,000÷$200=1,000 units ILLUSTRATION 19-3 Break‐even point in units
Illustration 19-4 shows the computation for the break‐even point in dollars (using contribution margin ratio).
Fixed Costs÷Contribution Margin Ratio=Break-Even Point in Dollars$200,000÷.40=$500,000Fixed Costs÷Contribution Margin Ratio=Break-Even Point in Dollars$200,000÷.40=$500,000 ILLUSTRATION 19-4 Break‐even point in dollars
When a company is in its early stages of operation, its primary goal is to break even. Failure to break even will lead eventually to financial failure.
Target Net Income
Once a company achieves break‐even, it then sets a sales goal that will generate a target net income. For example, assume that Vargo’s management has a target net income of $250,000. Illustration 19-5 shows the required sales in units to achieve its target net income.
(Fixed Costs+Target Net Income)÷Unit Contribution Margin=Required Sales in Units($200,000+$250,000)÷$200=2,250 units(Fixed Costs+Target Net Income)÷Unit Contribution Margin=Required Sales in Units($200,000+$250,000)÷$200=2,250 units ILLUSTRATION 19-5 Target net income in units
Illustration 19-6 uses the contribution margin ratio to compute the required sales in dollars.
(Fixed Costs+Target Net Income)÷Contribution Margin Ratio=Required Sales in Dollars($200,000+$250,000)÷.40=$1,125,000(Fixed Costs+Target Net Income)÷Contribution Margin Ratio=Required Sales in Dollars($200,000+$250,000)÷.40=$1,125,000 ILLUSTRATION 19-6 Target net income in dollars
In order to achieve net income of $250,000, Vargo has to sell 2,250 camcorders, for a total price of $1,125,000.
Margin of Safety
Another measure managers use to assess profitability is the margin of safety. The margin of safety tells us how far sales can drop before the company will be operating at a loss. Managers like to have a sense of how much cushion they have between their current situation and operating at a loss. This can be expressed in dollars or as a ratio. In Illustration 19-2 (page 924), for example, Vargo reported sales of $800,000. At that sales level, its margin of safety in dollars and as a ratio are as follows.
Actual (Expected) Sales−Break-Even Sales=Margin of Safety in Dollars$800,000−$500,000=$300,000Actual (Expected) Sales−Break-Even Sales=Margin of Safety in Dollars$800,000−$500,000=$300,000 ILLUSTRATION 19-7 Margin of safety in dollars
As shown in Illustration 19-8 , Vargo’s sales could drop by $300,000, or 37.5%, before the company would operate at a loss.
Margin of Safety in Dollars÷Actual (Expected) Sales=Margin of Safety Ratio$300,000÷$800,000=37.5%Margin of Safety in Dollars÷Actual (Expected) Sales=Margin of Safety Ratio$300,000÷$800,000=37.5% ILLUSTRATION 19-8 Margin of safety ratio
CVP AND CHANGES IN THE BUSINESS ENVIRONMENT
To better understand how CVP analysis works, let’s look at three independent situations that might occur at Vargo Video. Each case uses the original camcorder sales and cost data, which were as follows.
|Unit selling price||$500|
|Unit variable cost||$300|
|Total fixed costs||$200,000|
|Break-even sales||$500,000 or 1,000 units|
ILLUSTRATION 19-9 Original camcorder sales and cost data
A competitor is offering a 10% discount on the selling price of its camcorders. Management must decide whether to offer a similar discount.
Question: What effect will a 10% discount on selling price have on the break‐even point for camcorders?
Answer: A 10% discount on selling price reduces the selling price per unit to $450 [$500 − ($500 × 10%)]. Variable costs per unit remain unchanged at $300. Thus, the unit contribution margin is $150. Assuming no change in fi xed costs, break-even sales are 1,333 units, computed as follows.
Fixed Costs÷Unit Contribution Margin=Break-Even Sales$200,000÷$150=1,333 units (rounded)Fixed Costs÷Unit Contribution Margin=Break-Even Sales$200,000÷$150=1,333 units (rounded) ILLUSTRATION 19-10 Computation of break‐even sales in units
For Vargo, this change requires monthly sales to increase by 333 units, or 33⅓%, in order to break even. In reaching a conclusion about offering a 10% discount to customers, management must determine how likely it is to achieve the increased sales. Also, management should estimate the possible loss of sales if the competitor’s discount price is not matched.
To meet the threat of foreign competition, management invests in new robotic equipment that will lower the amount of direct labor required to make camcorders. The company estimates that total fixed costs will increase 30% and that variable cost per unit will decrease 30%.
Question: What effect will the new equipment have on the sales volume required to break even?
Answer: Total fixed costs become $260,000 [$200,000 + (30% × $200,000)]. The variable cost per unit becomes $210 [$300 − (30% × $300)]. The new break-even point is approximately 897 units, computed as shown in Illustration 19-11 .
Fixed Costs÷Unit Contribution Margin=Break-Even Sales$260,000÷($500−$210)=897 units (rounded)Fixed Costs÷Unit Contribution Margin=Break-Even Sales$260,000÷($500−$210)=897 units (rounded) ILLUSTRATION 19-11 Computation of break‐even sales in units
These changes appear to be advantageous for Vargo. The break‐even point is reduced by approximately 10%, or 100 units.
Vargo’s principal supplier of raw materials has just announced a price increase. The higher cost is expected to increase the variable cost of camcorders by $25 per unit. Management decides to hold the line on the selling price of the camcorders. It plans a cost‐cutting program that will save $17,500 in fixed costs per month. Vargo is currently realizing monthly net income of $80,000 on sales of 1,400 camcorders.
Question: What increase in units sold will be needed to maintain the same level of net income?
Answer: The variable cost per unit increases to $325 ($300 + $25). Fixed costs are reduced to $182,500 ($200,000 − $17,500). Because of the change in variable cost, the unit contribution margin becomes $175 ($500 − $325). The required number of units sold to achieve the target net income is computed as follows.
(Fixed Costs+Target Net Income)÷Unit Contribution Margin=Required Sales in Units($182,500+$80,000)÷$175=1,500(Fixed Costs+Target Net Income)÷Unit Contribution Margin=Required Sales in Units($182,500+$80,000)÷$175=1,500 ILLUSTRATION 19-12 Computation of required sales
To achieve the required sales, Vargo Video will have to sell 1,500 camcorders, an increase of 100 units. If this does not seem to be a reasonable expectation, management will either have to make further cost reductions or accept less net income if the selling price remains unchanged.
We hope that the concepts reviewed in this section are now familiar to you. We are now ready to examine additional ways that companies use CVP analysis to assess profitability and to help in making effective business decisions.
Don’t Just Look—Buy Something
When analyzing an Internet business such as Amazon.com, analysts closely watch the so‐called “conversion rate.” This rate is calculated by dividing the number of people who actually take action at an Internet site (buy something) by the total number of people who visit the site. Average conversion rates are from 3% to 5%. A rate below 2% is poor, while a rate above 10% is great.
Conversion rates have an obvious effect on the break‐even point. Suppose you spend $10,000 on your site, which then attracts 5,000 visitors. If you get a 2% conversion rate (100 purchases), your site costs $100 per purchase ($10,000÷100)($10,000÷100). A 4% conversion rate lowers your cost to $50 per transaction, and an 8% conversion rate gets you down to $25. Studies show that conversion rates increase if the site has an easy‐to‐use interface, fast‐performing screens, a convenient ordering process, and advertising that is both clever and clear.
Sources: J. William Gurley, “The One Internet Metric That Really Counts,” Fortune (March 6, 2000), p. 392; and Milind Mody, “Chief Mentor: How Startups Can Win Customers Online,” Wall Street Journal Online (May 11, 2011).
Besides increasing their conversion rates, what steps can online merchants use to lower their break‐even points? (Go to WileyPLUS for this answer and additional questions.)
DO IT! 1
Krisanne Company reports the following operating results for the month of June.
|KRISANNE COMPANY CVP Income Statement For the Month Ended June 30, 2017|
|Sales (5,000 units)||$300,000||$60|
|Net income||$ 20,000|
To increase net income, management is considering reducing the selling price by 10%, with no changes to unit variable costs or fixed costs. Management is confident that this change will increase unit sales by 25%.
Using the contribution margin technique, compute the break‐even point in units and dollars and margin of safety in dollars (a) assuming no changes to sales price or costs, and (b) assuming changes to sales price and volume as described above. (c) Comment on your findings.
✓ Apply the formula for the break‐even point in units.
✓ Apply the formula for the break‐even point in dollars.
✓ Apply the formula for the margin of safety in dollars.
a. Assuming no changes to sales price or costs:
Break-even point in units = 4,167 units (rounded) ($100,000 ÷ $24)
Break-even point in sales dollars = $250,000 ($100,000 ÷ .40 a )
Margin of safety in dollars = $50,000 ($300,000 − $250,000)
a $24 ÷ $60
b. Assuming changes to sales price and volume:
Break-even point in units = 5,556 units (rounded) ($100,000 ÷ $18 b )
Break-even point in sales dollars = $300,000 ($100,000 ÷ ($18 ÷ $54 c ))
Margin of safety in dollars = $37,500 ($337,500 d − $300,000)
b $60 − (.10 × $60) − 36 = $18
c $60 − (.10 × $60)
d 5,000 + (.25 × 5,000) = 6,250 units; 6,250 units × $54 = $337,500
c. The increase in the break‐even point and the decrease in the margin of safety indicate that management should not implement the proposed change. The increase in sales volume will result in a contribution margin of $112,500 (6,250×$18)$112,500 (6,250×$18), which is $7,500 less than the current amount.
Related exercise material: BE19-3, BE19-4, BE19-5, BE19-6, E19-1, E19-2, E19-3, E19-4, E19-5, and DO IT! 19-1.
LEARNING OBJECTIVE 2
Explain the term sales mix and its effects on break‐even sales.
To this point, our discussion of CVP analysis has assumed that a company sells only one product. However, most companies sell multiple products. When a company sells many products, it is important that management understand its sales mix.
Sales mix is the relative percentage in which a company sells its multiple products. For example, if 80% of Hewlett Packard’s unit sales are printers and the other 20% are PCs, its sales mix is 80% printers to 20% PCs.
Sales mix is important to managers because different products often have substantially different contribution margins. For example, Ford’s SUVs and F150 pickup trucks have higher contribution margins compared to its economy cars. Similarly, first‐class tickets sold by United Airlines provide substantially higher contribution margins than coach‐class tickets. Intel’s sales of computer chips for netbook computers have increased, but the contribution margin on these chips is lower than for notebook and desktop PCs.
BREAK‐EVEN SALES IN UNITS
Companies can compute break‐even sales for a mix of two or more products by determining the weighted‐average unit contribution margin of all the products. To illustrate, assume that Vargo Video sells not only camcorders but high‐definition TVs as well. Vargo sells its two products in the following amounts: 1,500 camcorders and 500 TVs. The sales mix, expressed as a percentage of the 2,000 total units sold, is as follows.
|1,500 units ÷ 2,000 units = 75%||500 units ÷ 2,000 units = 25%|
ILLUSTRATION 19-13 Sales mix as a percentage of units sold
That is, 75% of the 2,000 units sold are camcorders, and 25% of the 2,000 units sold are TVs.
Illustration 19-14 shows additional information related to Vargo. The unit contribution margin for camcorders is $200, and for TVs it is $500. Vargo’s fixed costs total $275,000.
|Fixed costs = $275,000|
ILLUSTRATION 19-14 Per unit data—sales mix
To compute break‐even for Vargo, we must determine the weighted‐average unit contribution margin for the two products. We use the weighted‐average contribution margin because Vargo sells three times as many camcorders as TVs. As a result, in determining an average unit contribution margin, three times as much weight should be placed on the contribution margin of the camcorders as on the TVs. Therefore, the camcorders must be counted three times for every TV sold. The weighted‐average contribution margin for a sales mix of 75% camcorders and 25% TVs is $275, which is computed as follows.
|Camcorders¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯TVs¯¯¯¯¯¯¯¯⎛⎜⎝UnitContributionMargin×Sales MixPercentage⎞⎟⎠+⎛⎜⎝UnitContributionMargin×Sales MixPercentage⎞⎟⎠=Weighted-AverageUnit ContributionMargin($200×.75)+($500×.25)=$275Camcorders¯TVs¯(UnitContributionMargin×Sales MixPercentage)+(UnitContributionMargin×Sales MixPercentage)=Weighted-AverageUnit ContributionMargin($200×.75)+($500×.25)=$275|
ILLUSTRATION 19-15 Weighted‐average unit contribution margin
Similar to our calculation in the single‐product setting, we can compute the break‐even point in units by dividing the fixed costs by the weighted‐average unit contribution margin of $275. The computation of break‐even sales in units for Vargo Video, assuming $275,000 of fixed costs, is as follows.
The break‐even point in units helps managers determine how many units of each product need to be sold to avoid a loss.
Illustration 19-16 shows the break‐even point for Vargo is 1,000 units—camcorders and TVs combined. Management needs to know how many of the 1,000 units sold are camcorders and how many are TVs. Applying the sales mix percentages that we computed previously of 75% for camcorders and 25% for TVs, these 1,000 units would be comprised of 750 camcorders (.75×1,000 units)(.75×1,000 units) and 250 TVs (.25×1,000)(.25×1,000). This can be verified by the computations in Illustration 19-17 , which shows that the total contribution margin is $275,000 when 1,000 units are sold, which equals the fixed costs of $275,000.
Fixed Costs÷Weighted-Average Unit Contribution Margin=Break-Even Point in Units$275,000÷$275=1,000 unitsFixed Costs÷Weighted-Average Unit Contribution Margin=Break-Even Point in Units$275,000÷$275=1,000 units ILLUSTRATION 19-16 Break‐even point in units
|Product||Unit Sales||×||Unit Contribution Margin||=||Total Contribution Margin|
ILLUSTRATION 19-17 Break‐even proof—sales units
Management should continually review the company’s sales mix. At any level of units sold, net income will be greater if higher contribution margin units are sold rather than lower contribution margin units. For Vargo, the TVs produce the higher contribution margin. Consequently, if Vargo sells 300 TVs and 700 camcorders, net income would be higher than in the current sales mix even though total units sold are the same.
An analysis of these relationships shows that a shift from low‐margin sales to high‐margin sales may increase net income even though there is a decline in total units sold. Likewise, a shift from high‐ to low‐margin sales may result in a decrease in net income even though there is an increase in total units sold.
BREAK‐EVEN SALES IN DOLLARS
The calculation of the break‐even point presented for Vargo Video in the previous section works well if a company has only a small number of products. In contrast, consider 3M, the maker of Post‐it Notes, which has more than 30,000 products. In order to calculate the break‐even point for 3M using a weighted‐average unit contribution margin, we would need to calculate 30,000 different unit contribution margins. That is not realistic.
Therefore, for a company with many products, we calculate the break‐even point in terms of sales dollars (rather than units sold), using sales information for divisions or product lines (rather than individual products). This requires that we compute both sales mix as a percentage of total dollar sales (rather than units sold) and the contribution margin ratio (rather than unit contribution margin).
To illustrate, suppose that Kale Garden Supply Company has two divisions—Indoor Plants and Outdoor Plants. Each division has hundreds of different types of plants and plant‐care products. Illustration 19-18 provides information necessary for determining the sales mix percentages for the two divisions of Kale Garden Supply.
|Indoor Plant Division||Outdoor Plant Division||Company Total|
|Sales||$ 200,000||$ 800,000||$1,000,000|
|Contribution margin||$ 80,000||$ 240,000||$ 320,000|
|Sales mix percentage||$ 200,000||=.20||$ 800,000||=.80|
|(Division sales ÷ Total sales)||$1,000,000||$1,000,000|
ILLUSTRATION 19-18 Cost‐volume‐profit data for Kale Garden Supply
As shown in Illustration 19-19 , the contribution margin ratio for the combined company is 32%, which is computed by dividing the total contribution margin by total sales.
|Indoor Plant Division||Outdoor Plant Division||Company Total|
|Contribution margin ratio (Contribution margin ÷ Sales)||$ 80,000$200,000=.40$ 80,000$200,000=.40||$240,000$800,000=.30$240,000$800,000=.30||$ 320,000$1,000,000=.32$ 320,000$1,000,000=.32|
ILLUSTRATION 19-19 Contribution margin ratio for each division
It is useful to note that the contribution margin ratio of 32% for the total company is a weighted average of the individual contribution margin ratios of the two divisions (40% and 30%). To illustrate, in Illustration 19-20 we multiply each division’s contribution margin ratio by its sales mix percentage, based on dollar sales, and then total these amounts. The calculation in Illustration 19-20 is useful because it enables us to determine how the break‐even point changes when the sales mix changes.
|Indoor Plant Division||Outdoor Plant Division|
|(ContributionMargin Ratio(ContributionMargin Ratio||×||Sales MixPercentage)Sales MixPercentage)||+||(ContributionMargin Ratio(ContributionMargin Ratio||×||Sales MixPercentage)Sales MixPercentage)||=||Weighted-AverageContributionMargin RatioWeighted-AverageContributionMargin Ratio|
ILLUSTRATION 19-20 Calculation of weighted‐average contribution margin
Kale Garden Supply’s break‐even point in dollars is then computed by dividing its fixed costs of $300,000 by the weighted‐average contribution margin ratio of 32%, as shown in Illustration 19-21 (page 932).
Fixed Costs÷Weighted-Average Contribution Margin Ratio=Break-Even Point in Dollars$300,000÷.32=$937,500Fixed Costs÷Weighted-Average Contribution Margin Ratio=Break-Even Point in Dollars$300,000÷.32=$937,500 ILLUSTRATION 19-21 Calculation of break‐even point in dollars
The break‐even point is based on the sales mix of 20% to 80%. We can determine the amount of sales contributed by each division by multiplying the sales mix percentage of each division by the total sales figure. Of the company’s total break‐even sales of $937,500, a total of $187,500 (.20×$937,500)$187,500 (.20×$937,500) will come from the Indoor Plant Division, and $750,000 (.80×$937,500)$750,000 (.80×$937,500) will come from the Outdoor Plant Division.
The break‐even point in dollars helps managers determine the sales dollars required from each division to avoid a loss.
What would be the impact on the break‐even point if a higher percentage of Kale Garden Supply’s sales were to come from the Indoor Plant Division? Because the Indoor Plant Division enjoys a higher contribution margin ratio, this change in the sales mix would result in a higher weighted‐average contribution margin ratio and consequently a lower break‐even point in dollars. For example, if the sales mix changes to 50% for the Indoor Plant Division and 50% for the Outdoor Plant Division, the weighted‐average contribution margin ratio would be 35% [(.40×.50)+(.30×.50)]35% [(.40×.50)+(.30×.50)]. The new, lower, break‐even point is $857,143 ($300,000÷.35)$857,143 ($300,000÷.35). The opposite would occur if a higher percentage of sales were expected from the Outdoor Plant Division. As you can see, the information provided using CVP analysis can help managers better understand the impact of sales mix on profitability.
SERVICE COMPANY INSIGHT
Healthy for You, and Great for the Bottom Line
Zoom Kitchen, a chain of restaurants in the Chicago area, was known for serving sizable portions of meat and potatoes. But the company’s management was quite pleased when salad sales increased from 18% of its sales mix to 40%. Why were they pleased? Because the contribution margin on salads was much higher than on meat. The restaurant made a conscious effort to encourage people to buy more salads by offering an interesting assortment of salad ingredients including jicama, beets, marinated mushrooms, grilled tuna, and carved turkey. Management had to be very sensitive to contribution margin as opening up a new Zoom Kitchen restaurant was very costly.
Source: Amy Zuber, “Salad Sales ‘Zoom’ at Meat‐and‐Potatoes Specialist,” Nation’s Restaurant News (November 12, 2001), p. 26.
Why do you suppose restaurants are so eager to sell beverages and desserts? (Go to WileyPLUS for this answer and additional questions.)
DO IT! 2
Sales Mix Break‐Even
Manzeck Bicycles International produces and sells three different types of mountain bikes. Information regarding the three models is shown below.
The company’s total fixed costs to produce the bicycles are $7,500,000.
(a) Determine the sales mix as a function of units sold for the three products.
(b) Determine the weighted‐average unit contribution margin.
(c) Determine the total number of units that the company must sell to break even.
(d) Determine the number of units of each model that the company must sell to break even.
✓ The sales mix is the relative percentage of each product sold in units.
✓ The weighted‐average unit contribution margin is the sum of the unit contribution margins multiplied by the respective sales mix percentage.
✓ Determine the break‐even point in units by dividing the fixed costs by the weighted‐average unit contribution margin.
✓ Determine the number of units of each model to sell by multiplying the total break‐even units by the respective sales mix percentage for each product.
(a) The sales mix percentages as a function of units sold are:
|5,000/40,000 = 12.5%||10,000/40,000 = 25%||25,000/40,000 = 62.5%|
(b) The weighted‐average unit contribution margin is:
(c) The break‐even point in units is:
$7,500,000÷$150=50,000 units$7,500,000÷$150=50,000 units
(d) The break‐even units to sell for each product are:
|Pro:||50,000 units × 12.5%||=||6,250 units|
|Intermediate:||50,000 units × 25%||=||12,500 units|
|Standard:||50,000 units × 62.5%||=||31,250 units|
Related exercise material: BE19-7, BE19-8, BE19-9, BE19-10, E19-6, E19-7, E19-8, E19-9, E19-10, and DO IT! 19-2.
LEARNING OBJECTIVE 3
Determine sales mix when a company has limited resources.
In the previous discussion, we assumed a certain sales mix and then determined the break‐even point given that sales mix. We now discuss how limited resources influence the sales‐mix decision.
All companies have resource limitations. The limited resource may be floor space in a retail department store, or raw materials, direct labor hours, or machine capacity in a manufacturing company. When a company has limited resources, management must decide which products to make and sell in order to maximize net income.
Determining the contribution margin per unit of limited resource helps managers decide which product should receive any additional capacity of the limited resource.
To illustrate, recall that Vargo Video manufactures camcorders and TVs. The limiting resource is machine capacity, which is 3,600 hours per month. Relevant data consist of the following.
|Unit contribution margin||$200||$500|
|Machine hours required per unit||.2||.625|
ILLUSTRATION 19-22 Contribution margin and machine hours
The TVs may appear to be more profitable since they have a higher unit contribution margin ($500) than the camcorders ($200). However, the camcorders take fewer machine hours to produce than the TVs. Therefore, it is necessary to find the contribution margin per unit of limited resource—in this case, contribution margin per machine hour. This is obtained by dividing the unit contribution margin of each product by the number of units of the limited resource required for each product, as shown in Illustration 19-23 .
▼ HELPFUL HINT
CM alone is not enough to make this decision. The key factor is CM per unit of limited resource.
|Unit contribution margin (a)||$200||$500|
|Machine hours required (b)||0.2||0.625|
|Contribution margin per unit of limited resource [(a) ÷ (b)]||$1,000||$800|
ILLUSTRATION 19-23 Contribution margin per unit of limited resource
The computation shows that the camcorders have a higher contribution margin per unit of limited resource. This would suggest that, given sufficient demand for camcorders, Vargo should shift the sales mix to produce more camcorders or increase machine capacity.
As indicated in Illustration 19-23 , the constraint for the production of the TVs is the larger number of machine hours needed to produce them. In addressing this problem, we have taken the limited number of machine hours as a given and have attempted to maximize the contribution margin given the constraint. One question that Vargo should ask, however, is whether this constraint can be reduced or eliminated. If Vargo is able to increase machine capacity from 3,600 hours to 4,200 hours, the additional 600 hours could be used to produce either the camcorders or TVs. The total contribution margin under each alternative is found by multiplying the machine hours by the contribution margin per unit of limited resource, as shown below.
|Machine hours (a)||600||600|
|Contribution margin per unit of limited resource (b)||$ 1,000||$ 800|
|Contribution margin [(a) × (b)]||$600,000||$480,000|
ILLUSTRATION 19-24 Incremental analysis—computation of total contribution margin
From this analysis, we can see that to maximize net income, all of the increased capacity should be used to make and sell the camcorders.
Vargo’s manufacturing constraint might be due to a bottleneck in production or to poorly trained machine operators. In addition to finding ways to solve those problems, the company should consider other possible solutions, such as outsourcing part of the production, acquiring additional new equipment (discussed in Chapter 24 ), or striving to eliminate any non–value‐added activities (see Chapter 17 ). As discussed in Chapter 14 , this approach to evaluating constraints is referred to as the theory of constraints. The theory of constraints is a specific approach used to identify and manage constraints in order to achieve the company’s goals. According to this theory, a company must continually identify its constraints and find ways to reduce or eliminate them, where appropriate.
When fragrance sales went flat, retailers such as Macy’s turned up the heat on fragrance manufacturers. They reduced the amount of floor space devoted to fragrances, leaving fragrance manufacturers fighting each other for the smaller space. The retailer doesn’t just choose the fragrance with the highest contribution margin. Instead, it chooses the fragrance with the highest contribution margin per square foot for a given period of time. In this game, a product with a lower contribution margin, but a higher turnover, could well be the winner.
What is the limited resource for a retailer, and what implications does this have for sales mix? (Go to WileyPLUS for this answer and additional questions.)
DO IT! 3
Sales Mix with Limited Resources
Carolina Corporation manufactures and sells three different types of high‐quality sealed ball bearings for mountain bike wheels. The bearings vary in terms of their quality specifications—primarily with respect to their smoothness and roundness. They are referred to as Fine, Extra‐Fine, and Super‐Fine bearings. Machine time is limited. More machine time is required to manufacture the Extra‐Fine and Super‐Fine bearings. Additional information is provided below.
|Variable costs and expenses||4.00||6.50||11.00|
|Contribution margin||$2.00||$ 3.50||$ 5.00|
|Machine hours required||0.02||0.04||0.08|
(a) Ignoring the machine time constraint, what strategy would appear optimal?
(b) What is the contribution margin per unit of limited resource for each type of bearing?
(c) If additional machine time could be obtained, how should the additional capacity be used?
✓ Calculate the contribution margin per unit of limited resource for each product.
✓ Apply the formula for the contribution margin per unit of limited resource.
✓ To maximize net income, shift sales mix to the product with the highest contribution margin per unit of limited resource.
(a) The Super‐Fine bearings have the highest unit contribution margin. Thus, ignoring any manufacturing constraints, it would appear that the company should shift toward production of more Super‐Fine units.
(b) The contribution margin per unit of limited resource (machine hours) is calculated as:
|Unit contribution marginLimited resource consumed per unitUnit contribution marginLimited resource consumed per unit||$2.02=$100$2.02=$100||$3.5.04=$87.50$3.5.04=$87.50||$5.08=$62.50$5.08=$62.50|
(c) The Fine bearings have the highest contribution margin per unit of limited resource even though they have the lowest unit contribution margin. Given the resource constraint, any additional capacity should be used to make Fine bearings.
Related exercise material: BE19-11, BE19-12, E19-11, E19-12, E19-13, and DO IT! 19-3.
LEARNING OBJECTIVE 4
Indicate how operating leverage affects profitability.
Cost structure refers to the relative proportion of fixed versus variable costs that a company incurs. Cost structure can have a significant effect on profitability. For example, computer equipment manufacturer Cisco Systems has substantially reduced its fixed costs by choosing to outsource much of its production. By minimizing its fixed costs, Cisco is now less susceptible to economic swings. However, as the following discussion shows, its reduced reliance on fixed costs has also reduced its ability to experience the incredible profitability that it used to have during economic booms.
The choice of cost structure should be carefully considered. There are many ways that companies can influence their cost structure. For example, by acquiring sophisticated robotic equipment, many companies have reduced their use of manual labor. Similarly, some brokerage firms, such as E*Trade, have reduced their reliance on human brokers and have instead invested heavily in computers and online technology. In so doing, they have increased their reliance on fixed costs (through depreciation on the robotic equipment or computer equipment) and reduced their reliance on variable costs (the variable employee labor cost). Alternatively, some companies have reduced their fixed costs and increased their variable costs by outsourcing their production. Nike, for example, does very little manufacturing but instead outsources the manufacture of nearly all of its shoes. It has consequently converted many of its fixed costs into variable costs and therefore changed its cost structure.
Consider the following example of Vargo Video and one of its competitors, New Wave Company. Both make camcorders. Vargo uses a traditional, labor‐intensive manufacturing process. New Wave has invested in a completely automated system. The factory employees are involved only in setting up, adjusting, and maintaining the machinery. Illustration 19-25 shows CVP income statements for each company.
|Vargo Video||New Wave Company|
ILLUSTRATION 19-25 CVP income statements for two companies
Both companies have the same sales and the same net income. However, because of the differences in their cost structures, they differ greatly in the risks and rewards related to increasing or decreasing sales. Let’s evaluate the impact of cost structure on the profitability of the two companies.
EFFECT ON CONTRIBUTION MARGIN RATIO
First let’s look at the contribution margin ratio. Illustration 19-26 shows the computation of the contribution margin ratio for each company.
Contribution Margin÷Sales=Contribution Margin RatioVargo Video$320,000÷$800,000=.40New Wave$640,000÷$800,000=.80Contribution Margin÷Sales=Contribution Margin RatioVargo Video$320,000÷$800,000=.40New Wave$640,000÷$800,000=.80 ILLUSTRATION 19-26 Contribution margin ratio for two companies
Because of its lower variable costs, New Wave has a contribution margin ratio of 80% versus only 40% for Vargo Video. That means that with every dollar of sales, New Wave generates 80 cents of contribution margin (and thus an 80‐cent increase in net income), versus only 40 cents for Vargo. However, it also means that for every dollar that sales decline, New Wave loses 80 cents in net income, whereas Vargo will lose only 40 cents. New Wave’s cost structure, which relies more heavily on fixed costs, makes it more sensitive to changes in sales revenue.
EFFECT ON BREAK‐EVEN POINT
The difference in cost structure also affects the break‐even point. The break‐even point for each company is calculated in Illustration 19-27 .
Fixed Costs÷Contribution Margin Ratio=Break-Even Point in DollarsVargo Video$200,000÷.40=$500,000New Wave$520,000÷.80=$650,000Fixed Costs÷Contribution Margin Ratio=Break-Even Point in DollarsVargo Video$200,000÷.40=$500,000New Wave$520,000÷.80=$650,000 ILLUSTRATION 19-27 Computation of break‐even point for two companies
New Wave needs to generate $150,000 ($650,000−$500,000)$150,000 ($650,000−$500,000) more in sales than Vargo Video before it breaks even. This makes New Wave riskier than Vargo because a company cannot survive for very long unless it at least breaks even.
EFFECT ON MARGIN OF SAFETY RATIO
We can also evaluate the relative impact that changes in sales would have on the two companies by computing the margin of safety ratio. Illustration 19-28 shows the computation of the margin of safety ratio for the two companies.
(Actual Sales−Break-Even Sales)÷Actual Sales=Margin of Safety RatioVargo Video($800,000−$500,000)÷$800,000=.38New Wave($800,000−$650,000)÷$800,000=.19(Actual Sales−Break-Even Sales)÷Actual Sales=Margin of Safety RatioVargo Video($800,000−$500,000)÷$800,000=.38New Wave($800,000−$650,000)÷$800,000=.19 ILLUSTRATION 19-28 Computation of margin of safety ratio for two companies
The difference in the margin of safety ratio also reflects the difference in risk between the two companies. Vargo Video could sustain a 38% decline in sales before it would be operating at a loss. New Wave could sustain only a 19% decline in sales before it would be “in the red.”
Operating leverage refers to the extent to which a company’s net income reacts to a given change in sales. Companies that have higher fixed costs relative to variable costs have higher operating leverage. When a company’s sales revenue is increasing, high operating leverage is a good thing because it means that profits will increase rapidly. But when sales are declining, too much operating leverage can have devastating consequences.
Calculating the degree of operating leverage helps managers determine how sensitive the company’s net income is to changes in sales.
Degree of Operating Leverage
How can we compare operating leverage between two companies? The degree of operating leverage provides a measure of a company’s earnings volatility and can be used to compare companies. Degree of operating leverage is computed by dividing contribution margin by net income. This formula is presented in Illustration 19-29 and applied to our two manufacturers of camcorders.
Contribution Margin÷Net Income=Degree of Operating LeverageVargo Video$320,000÷$120,000=2.67New Wave$640,000÷$120,000=5.33Contribution Margin÷Net Income=Degree of Operating LeverageVargo Video$320,000÷$120,000=2.67New Wave$640,000÷$120,000=5.33 ILLUSTRATION 19-29 Computation of degree of operating leverage
New Wave’s earnings would go up (or down) by about two times (5.33÷2.67=2.00)(5.33÷2.67=2.00) as much as Vargo Video’s with an equal increase (or decrease) in sales. For example, suppose both companies experience a 10% decrease in sales. Vargo’s net income will decrease by 26.7% (2.67×10%)26.7% (2.67×10%), while New Wave’s will decrease by 53.3% (5.33×10%)53.3% (5.33×10%). Thus, New Wave’s higher operating leverage exposes it to greater earnings volatility risk.
You should be careful not to conclude from this analysis that a cost structure that relies on higher fixed costs, and consequently has higher operating leverage, is necessarily bad. Some have suggested that Internet radio company Pandora has limited potential for growth in its profitability because it has very little operating leverage. When its revenues grow, its variable costs (fees it pays for the right to use music) grow proportionally. When used carefully, operating leverage can add considerably to a company’s profitability. For example, computer equipment manufacturer Komag enjoyed a 66% increase in net income when its sales increased by only 8%. As one commentator noted, “Komag’s fourth quarter illustrates the company’s significant operating leverage; a small increase in sales leads to a big profit rise.” However, as our illustration demonstrates, increased reliance on fixed costs increases a company’s risk.
SERVICE COMPANY INSIGHT
Burlington Northern Railroad
There Is Something About a Train
A few years ago, Warren Buffett, arguably the most successful investor in history, bought a new train set—for $44 billion. The sage from Omaha bought Burlington Northern Railroad for a price that exceeded its fair value by 31%. At a time when the rest of the investing public was obsessed with technology companies like Facebook and Twitter, what could Buffett possibly see in a railroad? What he sees is a business whose costs are between 50–60% fixed. With such high fixed costs, railways have huge operating leverage. And because he bought the railroad at the bottom of a recession, when the economy turns around, Burlington could take off as well. Add to that the fact that railroad transport is very energy‐efficient, and it has high barriers to entry. So, as energy prices increase, more people will turn to the rails, but there are a limited number of railways. Makes sense to me.
Source: Liam Denning, “Buffett’s Unusual Train of Thought,” Wall Street Journal (November 4, 2009).
Why did Warren Buffett think that this was a good time to invest in railroad stocks? (Go to WileyPLUS for this answer and additional questions.)
DO IT! 4
Rexfield Corp., a company specializing in crime scene investigations, is contemplating an investment in automated mass‐spectrometers. Its current process relies on a high number of lab technicians. The new equipment would employ a computerized expert system. The company’s CEO has requested a comparison of the old technology versus the new technology. The accounting department has prepared the following CVP income statements for use in your analysis.
|Net income||$ 200,000||$ 200,000|
Use the information provided above to do the following.
(a) Compute the degree of operating leverage for the company under each scenario.
(b) Discuss your results.
✓ Divide contribution margin by net income to determine degree of operating leverage.
✓ A higher degree of operating leverage will result in a higher change in net income with a given change in sales.
|Contribution Margin||÷||Net Income||=||Degree of Operating Leverage|
(b) The degree of operating leverage measures the company’s sensitivity to changes in sales. By switching to a cost structure dominated by fixed costs, the company would significantly increase its operating leverage. As a result, with a percentage change in sales, its percentage change in net income would be 2.33 (7÷3)2.33 (7÷3) times as much with the new technology as it would under the old.
Related exercise material: BE19-13, BE19-14, BE19-15, E19-14, E19-15, E19-16, and DO IT! 19-4.