The marketing manager believes that an $8 000 increase

Chapter 5 Cost-Volume-Profit Relationships

LEARNING OBJECTIVES

After studying Chapter 5 , you should be able to:

· LO1 Explain how changes in activity affect contribution margin and net operating income.

· LO2 Prepare and interpret a cost-volume-profit (CVP) graph and a profit graph.

· LO3 Use the contribution margin ratio (CM ratio) to compute changes in contribution margin and net operating income resulting from changes in sales volume.

· LO4 Show the effects on net operating income of changes in variable costs, fixed costs, selling price, and volume.

· LO5 Determine the level of sales needed to achieve a desired target profit.

· LO6 Determine the break-even point.

· LO7 Compute the margin of safety and explain its significance.

· LO8 Compute the degree of operating leverage at a particular level of sales and explain how it can be used to predict changes in net operating income.

· LO9 Compute the break-even point for a multiproduct company and explain the effects of shifts in the sales mix on contribution margin and the break-even point.

BUSINESS FOCUS: Moreno Turns Around the Los Angeles Angels

When Arturo Moreno bought Major League Baseball's Los Angeles Angels in 2003, the team was drawing 2.3 million fans and losing $5.5 million per year. Moreno immediately cut prices to attract more fans and increase profits. In his first spring training game, he reduced the price of selected tickets from $12 to $6. By increasing attendance, Moreno understood that he would sell more food and souvenirs. He dropped the price of draft beer by $2 and cut the price of baseball caps from $20 to $7.

The Angels now consistently draw about 3.4 million fans per year. This growth in attendance helped double stadium sponsorship revenue to $26 million, and it motivated the Fox Sports Network to pay the Angels $500 million to broadcast all of its games for the next ten years. Since Moreno bought the Angels, annual revenues have jumped from $127 million to $212 million, and the team's operating loss of $5.5 million has been transformed to a profit of $10.3 million. ▪

Source: Matthew Craft, “Moreno's Math,” Forbes, May 11, 2009, pp. 84–87.

Cost-volume-profit (CVP) analysis is a powerful tool that helps managers understand the relationships among cost, volume, and profit. CVP analysis focuses on how profits are affected by the following five factors:

· 1. Selling prices.

· 2. Sales volume.

· 3. Unit variable costs.

· 4. Total fixed costs.

· 5. Mix of products sold.

Because CVP analysis helps managers understand how profits are affected by these key factors, it is a vital tool in many business decisions. These decisions include what products and services to offer, what prices to charge, what marketing strategy to use, and what cost structure to maintain. To help understand the role of CVP analysis in business decisions, consider the case of Acoustic Concepts, Inc., a company founded by Prem Narayan.

Prem, who was a graduate student in engineering at the time, started Acoustic Concepts to market a radical new speaker he had designed for automobile sound systems. The speaker, called the Sonic Blaster, uses an advanced microprocessor and proprietary software to boost amplification to awesome levels. Prem contracted with a Taiwanese electronics manufacturer to produce the speaker. With seed money provided by his family, Prem placed an order with the manufacturer and ran advertisements in auto magazines.

MANAGERIAL ACCOUNTING IN ACTION

The Issue

The Sonic Blaster was an almost immediate success, and sales grew to the point that Prem moved the company's headquarters out of his apartment and into rented quarters in a nearby industrial park. He also hired a receptionist, an accountant, a sales manager, and a small sales staff to sell the speakers to retail stores. The accountant, Bob Luchinni, had worked for several small companies where he had acted as a business advisor as well as accountant and bookkeeper. The following discussion occurred soon after Bob was hired:

Prem: Bob, I've got a lot of questions about the company's finances that I hope you can help answer.

Bob: We're in great shape. The loan from your family will be paid off within a few months.

Prem: I know, but I am worried about the risks I've taken on by expanding operations. What would happen if a competitor entered the market and our sales slipped? How far could sales drop without putting us into the red? Another question I've been trying to resolve is how much our sales would have to increase to justify the big marketing campaign the sales staff is pushing for.

Bob: Marketing always wants more money for advertising.

Prem: And they are always pushing me to drop the selling price on the speaker. I agree with them that a lower price will boost our sales volume, but I'm not sure the increased volume will offset the loss in revenue from the lower price.

Bob: It sounds like these questions are all related in some way to the relationships among our selling prices, our costs, and our volume. I shouldn't have a problem coming up with some answers.

Prem: Can we meet again in a couple of days to see what you have come up with?

Bob: Sounds good. By then I'll have some preliminary answers for you as well as a model you can use for answering similar questions in the future.

The Basics of Cost-Volume-Profit (CVP) Analysis

Bob Luchinni's preparation for his forthcoming meeting with Prem begins with the contribution income statement. The contribution income statement emphasizes the behavior of costs and therefore is extremely helpful to managers in judging the impact on profits of changes in selling price, cost, or volume. Bob will base his analysis on the following contribution income statement he prepared last month:

Notice that sales, variable expenses, and contribution margin are expressed on a per unit basis as well as in total on this contribution income statement. The per unit figures will be very helpful to Bob in some of his calculations. Note that this contribution income statement has been prepared for management's use inside the company and would not ordinarily be made available to those outside the company.

LEARNING OBJECTIVE 1

Explain how changes in activity affect contribution margin and net operating income.

Contribution Margin

Contribution margin is the amount remaining from sales revenue after variable expenses have been deducted. Thus, it is the amount available to cover fixed expenses and then to provide profits for the period. Notice the sequence here—contribution margin is used first to cover the fixed expenses, and then whatever remains goes toward profits. If the contribution margin is not sufficient to cover the fixed expenses, then a loss occurs for the period. To illustrate with an extreme example, assume that Acoustic Concepts sells only one speaker during a particular month. The company's income statement would appear as follows:

For each additional speaker the company sells during the month, $100 more in contribution margin becomes available to help cover the fixed expenses. If a second speaker is sold, for example, then the total contribution margin will increase by $100 (to a total of $200) and the company's loss will decrease by $100, to $34,800:

If enough speakers can be sold to generate $35,000 in contribution margin, then all of the fixed expenses will be covered and the company will break even for the month—that is, it will show neither profit nor loss but just cover all of its costs. To reach the break-even point, the company will have to sell 350 speakers in a month because each speaker sold yields $100 in contribution margin:

Computation of the break-even point is discussed in detail later in the chapter; for the moment, note that the break-even point is the level of sales at which profit is zero.

Once the break-even point has been reached, net operating income will increase by the amount of the unit contribution margin for each additional unit sold. For example, if 351 speakers are sold in a month, then the net operating income for the month will be $100 because the company will have sold 1 speaker more than the number needed to break even:

If 352 speakers are sold (2 speakers above the break-even point), the net operating income for the month will be $200. If 353 speakers are sold (3 speakers above the break-even point), the net operating income for the month will be $300, and so forth. To estimate the profit at any sales volume above the break-even point, multiply the number of units sold in excess of the break-even point by the unit contribution margin. The result represents the anticipated profits for the period. Or, to estimate the effect of a planned increase in sales on profits, simply multiply the increase in units sold by the unit contribution margin. The result will be the expected increase in profits. To illustrate, if Acoustic Concepts is currently selling 400 speakers per month and plans to increase sales to 425 speakers per month, the anticipated impact on profits can be computed as follows:

These calculations can be verified as follows:

To summarize, if sales are zero, the company's loss would equal its fixed expenses. Each unit that is sold reduces the loss by the amount of the unit contribution margin. Once the break-even point has been reached, each additional unit sold increases the company's profit by the amount of the unit contribution margin.

CVP Relationships in Equation Form

The contribution format income statement can be expressed in equation form as follows:

For brevity, we use the term profit to stand for net operating income in equations.

When a company has only a single product, as at Acoustic Concepts, we can further refine the equation as follows:

We can do all of the calculations of the previous section using this simple equation. For example, on the previous page we computed that the net operating income (profit) at sales of 351 speakers would be $100. We can arrive at the same conclusion using the above equation as follows:

It is often useful to express the simple profit equation in terms of the unit contribution margin (Unit CM) as follows:

We could also have used this equation to determine the profit at sales of 351 speakers as follows:

For those who are comfortable with algebra, the quickest and easiest approach to solving the problems in this chapter may be to use the simple profit equation in one of its forms.

LEARNING OBJECTIVE 2

Prepare and interpret a cost-volume-profit (CVP) graph and a profit graph.

CVP Relationships in Graphic Form

The relationships among revenue, cost, profit, and volume are illustrated on a cost-volume-profit (CVP) graph . A CVP graph highlights CVP relationships over wide ranges of activity. To help explain his analysis to Prem Narayan, Bob Luchinni prepared a CVP graph for Acoustic Concepts.

Preparing the CVP Graph

In a CVP graph (sometimes called a break-even chart), unit volume is represented on the horizontal (X) axis and dollars on the vertical (Y) axis. Preparing a CVP graph involves the three steps depicted in Exhibit 5–1 :

EXHIBIT 5–1 Preparing the CVP Graph

· 1. Draw a line parallel to the volume axis to represent total fixed expense. For Acoustic Concepts, total fixed expenses are $35,000.

· 2. Choose some volume of unit sales and plot the point representing total expense (fixed and variable) at the sales volume you have selected. In Exhibit 5–1 , Bob Luchinni chose a volume of 600 speakers. Total expense at that sales volume is:

After the point has been plotted, draw a line through it back to the point where the fixed expense line intersects the dollars axis.

· 3. Again choose some sales volume and plot the point representing total sales dollars at the activity level you have selected. In Exhibit 5–1 , Bob Luchinni again chose a volume of 600 speakers. Sales at that volume total $150,000 (600 speakers × $250 per speaker). Draw a line through this point back to the origin.

The interpretation of the completed CVP graph is given in Exhibit 5–2 . The anticipated profit or loss at any given level of sales is measured by the vertical distance between the total revenue line (sales) and the total expense line (variable expense plus fixed expense).

EXHIBIT 5–2 The Completed CVP Graph

The break-even point is where the total revenue and total expense lines cross. The break-even point of 350 speakers in Exhibit 5–2 agrees with the break-even point computed earlier.

As discussed earlier, when sales are below the break-even point—in this case, 350 units—the company suffers a loss. Note that the loss (represented by the vertical distance between the total expense and total revenue lines) gets bigger as sales decline. When sales are above the break-even point, the company earns a profit and the size of the profit (represented by the vertical distance between the total revenue and total expense lines) increases as sales increase.

An even simpler form of the CVP graph, which we call a profit graph, is presented in Exhibit 5–3 . That graph is based on the following equation:

EXHIBIT 5–3 The Profit Graph

In the case of Acoustic Concepts, the equation can be expressed as:

Because this is a linear equation, it plots as a single straight line. To plot the line, compute the profit at two different sales volumes, plot the points, and then connect them with a straight line. For example, when the sales volume is zero (i.e., Q = 0), the profit is −$35,000 (= $100 × 0 − $35,000). When Q is 600, the profit is $25,000 (= $100 × 600 −$35,000). These two points are plotted in Exhibit 5–3 and a straight line has been drawn through them.

The break-even point on the profit graph is the volume of sales at which profit is zero and is indicated by the dashed line on the graph. Note that the profit steadily increases to the right of the break-even point as the sales volume increases and that the loss becomes steadily worse to the left of the break-even point as the sales volume decreases.

LEARNING OBJECTIVE 3

Use the contribution margin ratio (CM ratio) to compute changes in contribution margin and net operating income resulting from changes in sales volume.

Contribution Margin Ratio (CM Ratio)

In the previous section, we explored how cost-volume-profit relationships can be visualized. In this section, we show how the contribution margin ratio can be used in cost-volume-profit calculations. As the first step, we have added a column to Acoustic Concepts’ contribution format income statement in which sales revenues, variable expenses, and contribution margin are expressed as a percentage of sales:

The contribution margin as a percentage of sales is referred to as the contribution margin ratio (CM ratio) . This ratio is computed as follows:

For Acoustic Concepts, the computations are:

In a company such as Acoustic Concepts that has only one product, the CM ratio can also be computed on a per unit basis as follows:

The CM ratio shows how the contribution margin will be affected by a change in total sales. Acoustic Concepts’ CM ratio of 40% means that for each dollar increase in sales, total contribution margin will increase by 40 cents ($1 sales × CM ratio of 40%). Net operating income will also increase by 40 cents, assuming that fixed costs are not affected by the increase in sales. Generally, the effect of a change in sales on the contribution margin is expressed in equation form as:

As this illustration suggests, the impact on net operating income of any given dollar change in total sales can be computed by applying the CM ratio to the dollar change. For example, if Acoustic Concepts plans a $30,000 increase in sales during the coming month, the contribution margin should increase by $12,000 ($30,000 increase in sales × CM ratio of 40%). As we noted above, net operating income will also increase by $12,000 if fixed costs do not change. This is verified by the following table:

The relation between profit and the CM ratio can also be expressed using the following equation:

Profit = CM ratio × Sales − Fixed expenses 1

For example, at sales of $130,000, the profit is expected to be $17,000 as shown below:

Again, if you are comfortable with algebra, this approach will often be quicker and easier than constructing contribution format income statements.

The CM ratio is particularly valuable in situations where the dollar sales of one product must be traded off against the dollar sales of another product. In this situation, products that yield the greatest amount of contribution margin per dollar of sales should be emphasized.

LEARNING OBJECTIVE 4

Show the effects on net operating income of changes in variable costs, fixed costs, selling price, and volume.

1

This equation can be derived using the basic profit equation and the definition of the CM ratio as follows:

Profit = (Sales − Variable expenses) − Fixed expenses

Profit = Contribution margin − Fixed expenses

Profit = CM ratio × Sales − Fixed expenses

Some Applications of CVP Concepts

Bob Luchinni, the accountant at Acoustic Concepts, wanted to demonstrate to the company's president Prem Narayan how the concepts developed on the preceding pages can be used in planning and decision making. Bob gathered the following basic data:

Recall that fixed expenses are $35,000 per month. Bob Luchinni will use these data to show the effects of changes in variable costs, fixed costs, sales price, and sales volume on the company's profitability in a variety of situations.

Before proceeding further, however, we need to introduce another concept—the variable expense ratio. The variable expense ratio is the ratio of variable expenses to sales. It can be computed by dividing the total variable expenses by the total sales, or in a single product analysis, it can be computed by dividing the variable expenses per unit by the unit selling price. In the case of Acoustic Concepts, the variable expense ratio is 0.60; that is, variable expense is 60% of sales. Expressed as an equation, the definition of the variable expense ratio is:

This leads to a useful equation that relates the CM ratio to the variable expense ratio as follows:

Change in Fixed Cost and Sales Volume

Acoustic Concepts is currently selling 400 speakers per month at $250 per speaker for total monthly sales of $100,000. The sales manager feels that a $10,000 increase in the monthly advertising budget would increase monthly sales by $30,000 to a total of 520 units. Should the advertising budget be increased? The table on the next page shows the financial impact of the proposed change in the monthly advertising budget.

Assuming no other factors need to be considered, the increase in the advertising budget should be approved because it would increase net operating income by $2,000. There are two shorter ways to arrive at this solution. The first alternative solution follows:

Alternative Solution 1

Because in this case only the fixed costs and the sales volume change, the solution can also be quickly derived as follows:

Alternative Solution 2

Notice that this approach does not depend on knowledge of previous sales. Also note that it is unnecessary under either shorter approach to prepare an income statement. Both of the alternative solutions involve incremental analysis —they consider only the revenue, cost, and volume that will change if the new program is implemented. Although in each case a new income statement could have been prepared, the incremental approach is simpler and more direct and focuses attention on the specific changes that would occur as a result of the decision.

Change in Variable Costs and Sales Volume

Refer to the original data. Recall that Acoustic Concepts is currently selling 400 speakers per month. Prem is considering the use of higher-quality components, which would increase variable costs (and thereby reduce the contribution margin) by $10 per speaker. However, the sales manager predicts that using higher-quality components would increase sales to 480 speakers per month. Should the higher-quality components be used?

The $10 increase in variable costs would decrease the unit contribution margin by $10—from $100 down to $90.

Solution

According to this analysis, the higher-quality components should be used. Because fixed costs would not change, the $3,200 increase in contribution margin shown above should result in a $3,200 increase in net operating income.

IN BUSINESS: GROWING SALES AT AMAZON.COM

Amazon.com was deciding between two tactics for growing sales and profits. The first approach was to invest in television advertising. The second approach was to offer free shipping on larger orders. To evaluate the first option, Amazon.com invested in television ads in two markets—Minneapolis, Minnesota, and Portland, Oregon. The company quantified the profit impact of this choice by subtracting the increase in fixed advertising costs from the increase in contribution margin. The profit impact of television advertising paled in comparison to the free “super saver shipping” program, which the company introduced on orders over $99. In fact, the free shipping option proved to be so popular and profitable that within two years Amazon.com dropped its qualifying threshold to $49 and then again to a mere $25. At each stage of this progression,Amazon.com used cost-volume-profit analysis to determine whether the extra volume from liberalizing the free shipping offer more than offset the associated increase in shipping costs.

Source: Rob Walker, “Because ‘Optimism is Essential,’” Inc. magazine, April 2004 pp. 149–150.

Change in Fixed Cost, Sales Price, and Sales Volume

Refer to the original data and recall again that Acoustic Concepts is currently selling 400 speakers per month. To increase sales, the sales manager would like to cut the selling price by $20 per speaker and increase the advertising budget by $15,000 per month. The sales manager believes that if these two steps are taken, unit sales will increase by 50% to 600 speakers per month. Should the changes be made?

A decrease in the selling price of $20 per speaker would decrease the unit contribution margin by $20 down to $80.

Solution

According to this analysis, the changes should not be made. The $7,000 reduction in net operating income that is shown above can be verified by preparing comparative income statements as shown on the next page.

Change in Variable Cost, Fixed Cost, and Sales Volume

Refer to Acoustic Concepts’ original data. As before, the company is currently selling 400 speakers per month. The sales manager would like to pay salespersons a sales commission of $15 per speaker sold, rather than the flat salaries that now total $6,000 per month. The sales manager is confident that the change would increase monthly sales by 15% to 460 speakers per month. Should the change be made?

Solution

Changing the sales staff's compensation from salaries to commissions would affect both fixed and variable expenses. Fixed expenses would decrease by $6,000, from $35,000 to $29,000. Variable expenses per unit would increase by $15, from $150 to $165, and the unit contribution margin would decrease from $100 to $85.

According to this analysis, the changes should be made. Again, the same answer can be obtained by preparing comparative income statements:

Change in Selling Price

Refer to the original data where Acoustic Concepts is currently selling 400 speakers per month. The company has an opportunity to make a bulk sale of 150 speakers to a wholesaler if an acceptable price can be negotiated. This sale would not disturb the company's regular sales and would not affect the company's total fixed expenses. What price per speaker should be quoted to the wholesaler if Acoustic Concepts is seeking a profit of $3,000 on the bulk sale?

Solution

Notice that fixed expenses are not included in the computation. This is because fixed expenses are not affected by the bulk sale, so all of the additional contribution margin increases the company's profits.