Absorption versus Variable Costing

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.

IN BUSINESS: MANAGING RISK IN THE BOOK PUBLISHING INDUSTRY

Greenleaf Book Group is a book publishing company in Austin, Texas, that attracts authors who are willing to pay publishing costs and forgo up-front advances in exchange for a larger royalty rate on each book sold. For example, assume a typical publisher prints 10,000 copies of a new book that it sells for $12.50 per unit. The publisher pays the author an advance of $20,000 to write the book and then incurs $60,000 of expenses to market, print, and edit the book. The publisher also pays the author a 20% royalty (or $2.50 per unit) on each book sold above 8,000 units. In this scenario, the publisher must sell 6,400 books to break even (= $80,000 in fixed costs ÷ $12.50 per unit). If all 10,000 copies are sold, the author earns $25,000 (= $20,000 advance + 2,000 copies × $2.50) and the publisher earns $40,000 (= $125,000 − $60,000 − $20,000 − $5,000).

Greenleaf alters the financial arrangement described above by requiring the author to assume the risk of poor sales. It pays the author a 70% royalty on all units sold (or $8.75 per unit), but the author forgoes the $20,000 advance and pays Greenleaf $60,000 to market, print, and edit the book. If the book flops, the author fails to recover her production costs. If all 10,000 units are sold, the author earns $27,500 (= $10,000 units × $8.75 − $60,000) and Greenleaf earns $37,500 (= 10,000 units × ($12.50 − $8.75)).

 

Source: Christopher Steiner, “Book It,” Forbes, September 7, 2009, p. 58.

Target Profit Analysis

LEARNING OBJECTIVE 5

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

Target profit analysis is one of the key uses of CVP analysis. In  target profit analysis , we estimate what sales volume is needed to achieve a specific target profit. For example, suppose that Prem Narayan of Acoustic Concepts would like to know what sales would have to be to attain a target profit of $40,000 per month. To answer this question, we can proceed using the equation method or the formula method.

The Equation Method

We can use a basic profit equation to find the sales volume required to attain a target profit. In the case of Acoustic Concepts, the company has only one product so we can use the contribution margin form of the equation. Remembering that the target profit is $40,000, the unit contribution margin is $100, and the fixed expense is $35,000, we can solve as follows:

Thus, the target profit can be achieved by selling 750 speakers per month.

The Formula Method

The formula method is a short-cut version of the equation method. Note that in the next to the last line of the above solution, the sum of the target profit of $40,000 and the fixed expense of $35,000 is divided by the unit contribution margin of $100. In general, in a single-product situation, we can compute the sales volume required to attain a specific target profit using the following formula:

In the case of Acoustic Concepts, the formula yields the following answer:

Note that this is the same answer we got when we used the equation method—and it always will be. The formula method simply skips a few steps in the equation method.

Target Profit Analysis in Terms of Sales Dollars

Instead of unit sales, we may want to know what dollar sales are needed to attain the target profit. We can get this answer using several methods. First, we could solve for the unit sales to attain the target profit using the equation method or the formula method and then multiply the result by the selling price. In the case of Acoustic Concepts, the required sales volume using this approach would be computed as 750 speakers × $250 per speaker or $187,500 in total sales.

We can also solve for the required sales volume to attain the target profit of $40,000 at Acoustic Concepts using the basic equation stated in terms of the contribution margin ratio:

Note that in the next to the last line of the previous solution, the sum of the target profit of $40,000 and the fixed expense of $35,000 is divided by the contribution margin ratio of 0.40. In general, we can compute dollar sales to attain a target profit as follows:

At Acoustic Concepts, the formula yields the following answer:

Again, you get exactly the same answer whether you use the equation method or just use the formula.

In companies with multiple products, sales volume is more conveniently expressed in terms of total sales dollars than in terms of unit sales. The contribution margin ratio approach to target profit analysis is particularly useful for such companies.

2

This equation can be derived as follows:

Break-Even Analysis

LEARNING OBJECTIVE 6

Determine the break-even point.

Earlier in the chapter we defined the break-even point as the level of sales at which the company's profit is zero. What we call break-even analysis is really just a special case of target profit analysis in which the target profit is zero. We can use either the equation method or the formula method to solve for the break-even point, but for brevity we will illustrate just the formula method. The equation method works exactly like it did in target profit analysis. The only difference is that the target profit is zero in break-even analysis.

Break-Even in Unit Sales

In a single product situation, recall that the formula for the unit sales to attain a specific target profit is:

To compute the unit sales to break even, all we have to do is to set the target profit to zero in the above equation as follows:

In the case of Acoustic Concepts, the break-even point can be computed as follows:

Thus, as we determined earlier in the chapter, Acoustic Concepts breaks even at sales of 350 speakers per month.

3

This equation can be derived as follows:

Break-Even in Sales Dollars

We can find the break-even point in sales dollars using several methods. First, we could solve for the break-even point in unit sales using the equation method or the formula method and then multiply the result by the selling price. In the case of Acoustic Concepts, the break-even point in sales dollars using this approach would be computed as 350 speakers × $250 per speaker or $87,500 in total sales.

We can also solve for the break-even point in sales dollars at Acoustic Concepts using the basic profit equation stated in terms of the contribution margin ratio or we can use the formula for the target profit. Again, for brevity, we will use the formula.

The break-even point at Acoustic Concepts would be computed as follows:

IN BUSINESS: COST OVERRUNS INCREASE THE BREAK-EVEN POINT

When Airbus launched the A380 555-seat jetliner in 2000, the company said it would need to sell 250 units to break even on the project. By 2006, Airbus was admitting that more than $3 billion of cost overruns had raised the project's break-even point to 420 airplanes. Although Airbus has less than 170 orders for the A380, the company remains optimistic that it will sell 751 units over the next 20 years. Given that Airbus rival Boeing predicts the total market size for all airplanes with more than 400 seats will not exceed 990 units, it remains unclear if Airbus will ever break even on its investment in the A380 aircraft.

 

Source: Daniel Michaels, “Embattled Airbus Lifts Sales Target for A380 to Profit,” The Wall Street Journal, October 20, 2006, p. A6.

The Margin of Safety

LEARNING OBJECTIVE 7

Compute the margin of safety and explain its significance.

The  margin of safety  is the excess of budgeted or actual sales dollars over the break-even volume of sales dollars. It is the amount by which sales can drop before losses are incurred. The higher the margin of safety, the lower the risk of not breaking even and incurring a loss. The formula for the margin of safety is:

The margin of safety can also be expressed in percentage form by dividing the margin of safety in dollars by total dollar sales:

The calculation of the margin of safety for Acoustic Concepts is:

This margin of safety means that at the current level of sales and with the company's current prices and cost structure, a reduction in sales of $12,500, or 12.5%, would result in just breaking even.

In a single-product company like Acoustic Concepts, the margin of safety can also be expressed in terms of the number of units sold by dividing the margin of safety in dollars by the selling price per unit. In this case, the margin of safety is 50 speakers ($12,500 ÷ $250 per speaker = 50 speakers).

IN BUSINESS: COMPUTING MARGIN OF SAFETY FOR A SMALL BUSINESS

Sam Calagione owns Dogfish Head Craft Brewery, a microbrewery in Rehobeth Beach, Delaware. He charges distributors as much as $100 per case for his premium beers such as World Wide Stout. The high-priced microbrews bring in $800,000 in operating income on revenue of $7 million. Calagione reports that his raw ingredients and labor costs for one case of World Wide Stout are $30 and $16, respectively. Bottling and packaging costs are $6 per case. Gas and electric costs are about $10 per case.

If we assume that World Wide Stout is representative of all Dogfish microbrews, then we can compute the company's margin of safety in five steps. First, variable cost as a percentage of sales is 62% [($30 + $16 + $6 + $10)/$100]. Second, the contribution margin ratio is 38% (1 − 0.62). Third, Dogfish's total fixed cost is $1,860,000 [($7,000,000 × 0.38) − $800,000]. Fourth, the break-even point in sales dollars is $4,894,737 ($1,860,000/0.38). Fifth, the margin of safety is $2,105,263 ($7,000,000 − $4,894,737).

 

Source: Patricia Huang, “Château Dogfish,” Forbes, February 28, 2005, pp. 57–59.

MANAGERIAL ACCOUNTING IN ACTION

The Wrap-up

Prem Narayan and Bob Luchinni met to discuss the results of Bob's analysis.

· Prem: Bob, everything you have shown me is pretty clear. I can see what impact the sales manager's suggestions would have on our profits. Some of those suggestions are quite good and others are not so good. I am concerned that our margin of safety is only 50 speakers. What can we do to increase this number?

· Bob: Well, we have to increase total sales or decrease the break-even point or both.

· Prem: And to decrease the break-even point, we have to either decrease our fixed expenses or increase our unit contribution margin?

· Bob: Exactly. 

· Prem: And to increase our unit contribution margin, we must either increase our selling price or decrease the variable cost per unit?

· Bob: Correct.

· Prem: So what do you suggest?

· Bob: Well, the analysis doesn't tell us which of these to do, but it does indicate we have a potential problem here.

· Prem: If you don't have any immediate suggestions, I would like to call a general meeting next week to discuss ways we can work on increasing the margin of safety. I think everyone will be concerned about how vulnerable we are to even small downturns in sales.

CVP Considerations in Choosing a Cost Structure

Cost structure refers to the relative proportion of fixed and variable costs in an organization. Managers often have some latitude in trading off between these two types of costs. For example, fixed investments in automated equipment can reduce variable labor costs. In this section, we discuss the choice of a cost structure. We also introduce the concept of operating leverage.

Cost Structure and Profit Stability

Which cost structure is better—high variable costs and low fixed costs, or the opposite? No single answer to this question is possible; each approach has its advantages. To show what we mean, refer to the contribution format income statements given below for two blueberry farms. Bogside Farm depends on migrant workers to pick its berries by hand, whereas Sterling Farm has invested in expensive berry-picking machines. Consequently, Bogside Farm has higher variable costs, but Sterling Farm has higher fixed costs:

Which farm has the better cost structure? The answer depends on many factors, including the long-run trend in sales, year-to-year fluctuations in the level of sales, and the attitude of the owners toward risk. If sales are expected to exceed $100,000 in the future, then Sterling Farm probably has the better cost structure. The reason is that its CM ratio is higher, and its profits will therefore increase more rapidly as sales increase. To illustrate, assume that each farm experiences a 10% increase in sales without any increase in fixed costs. The new income statements would be as follows:

Sterling Farm has experienced a greater increase in net operating income due to its higher CM ratio even though the increase in sales was the same for both farms.

What if sales drop below $100,000? What are the farms’ break-even points? What are their margins of safety? The computations needed to answer these questions are shown below using the formula method:

Bogside Farm's margin of safety is greater and its contribution margin ratio is lower than Sterling Farm. Therefore, Bogside Farm is less vulnerable to downturns than Sterling Farm. Due to its lower contribution margin ratio, Bogside Farm will not lose contribution margin as rapidly as Sterling Farm when sales decline. Thus, Bogside Farm's profit will be less volatile. We saw earlier that this is a drawback when sales increase, but it provides more protection when sales drop. And because its break-even point is lower, Bogside Farm can suffer a larger sales decline before losses emerge.

To summarize, without knowing the future, it is not obvious which cost structure is better. Both have advantages and disadvantages. Sterling Farm, with its higher fixed costs and lower variable costs, will experience wider swings in net operating income as sales fluctuate, with greater profits in good years and greater losses in bad years. Bogside Farm, with its lower fixed costs and higher variable costs, will enjoy greater profit stability and will be more protected from losses during bad years, but at the cost of lower net operating income in good years.

Operating Leverage

LEARNING OBJECTIVE 8

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.

A lever is a tool for multiplying force. Using a lever, a massive object can be moved with only a modest amount of force. In business, operating leverage serves a similar purpose.  Operating leverage  is a measure of how sensitive net operating income is to a given percentage change in dollar sales. Operating leverage acts as a multiplier. If operating leverage is high, a small percentage increase in sales can produce a much larger percentage increase in net operating income.

Operating leverage can be illustrated by returning to the data for the two blueberry farms. We previously showed that a 10% increase in sales (from $100,000 to $110,000 in each farm) results in a 70% increase in the net operating income of Sterling Farm (from $10,000 to $17,000) and only a 40% increase in the net operating income of Bogside Farm (from $10,000 to $14,000). Thus, for a 10% increase in sales, Sterling Farm experiences a much greater percentage increase in profits than does Bogside Farm. Therefore, Sterling Farm has greater operating leverage than Bogside Farm.

The  degree of operating leverage  at a given level of sales is computed by the following formula:

The degree of operating leverage is a measure, at a given level of sales, of how a percentage change in sales volume will affect profits. To illustrate, the degree of operating leverage for the two farms at $100,000 sales would be computed as follows:

Because the degree of operating leverage for Bogside Farm is 4, the farm's net operating income grows four times as fast as its sales. In contrast, Sterling Farm's net operating income grows seven times as fast as its sales. Thus, if sales increase by 10%, then we can expect the net operating income of Bogside Farm to increase by four times this amount, or by 40%, and the net operating income of Sterling Farm to increase by seven times this amount, or by 70%. In general, this relation between the percentage change in sales and the percentage change in net operating income is given by the following formula:

Bogside Farm: Percentage change in net operating income = 4 × 10% = 40%

Sterling Farm: Percentage change in net operating income = 7 ×10% = 70%

What is responsible for the higher operating leverage at Sterling Farm? The only difference between the two farms is their cost structure. If two companies have the same total revenue and same total expense but different cost structures, then the company with the higher proportion of fixed costs in its cost structure will have higher operating leverage. Referring back to the original example on page 201, when both farms have sales of $100,000 and total expenses of $90,000, one-third of Bogside Farm's costs are fixed but two-thirds of Sterling Farm's costs are fixed. As a consequence, Sterling's degree of operating leverage is higher than Bogside's.

The degree of operating leverage is not a constant; it is greatest at sales levels near the break-even point and decreases as sales and profits rise. The following table shows the degree of operating leverage for Bogside Farm at various sales levels. (Data used earlier for Bogside Farm are shown in color.)

Thus, a 10% increase in sales would increase profits by only 15% (10% × 1.5) if sales were previously $225,000, as compared to the 40% increase we computed earlier at the $100,000 sales level. The degree of operating leverage will continue to decrease the farther the company moves from its break-even point. At the break-even point, the degree of operating leverage is infinitely large ($30,000 contribution margin ÷ $0 net operating income = ∞).

IN BUSINESS: THE DANGERS OF A HIGH DEGREE OF OPERATING LEVERAGE

In recent years, computer chip manufacturers have poured more than $75 billion into constructing new manufacturing facilities to meet the growing demand for digital devices such as iPhones and Blackberrys. Because 70% of the costs of running these facilities are fixed, a sharp drop in customer demand forces these companies to choose between two undesirable options. They can slash production levels and absorb large amounts of unused capacity costs, or they can continue producing large volumes of output in spite of shrinking demand, thereby flooding the market with excess supply and lowering prices. Either choice distresses investors who tend to shy away from computer chip makers in economic downturns.

 

Source: Bruce Einhorn, “Chipmakers on the Edge,” BusinessWeek, January 5, 2009, pp. 30–31.

The degree of operating leverage can be used to quickly estimate what impact various percentage changes in sales will have on profits, without the necessity of preparing detailed income statements. As shown by our examples, the effects of operating leverage can be dramatic. If a company is near its break-even point, then even small percentage increases in sales can yield large percentage increases in profits. This explains why management will often work very hard for only a small increase in sales volume. If the degree of operating leverage is 5, then a 6% increase in sales would translate into a 30% increase in profits.

Structuring Sales Commissions

Companies usually compensate salespeople by paying them a commission based on sales, a salary, or a combination of the two. Commissions based on sales dollars can lead to lower profits. To illustrate, consider Pipeline Unlimited, a producer of surfing equipment. Salespersons sell the company's products to retail sporting goods stores throughout North America and the Pacific Basin. Data for two of the company's surfboards, the XR7 and Turbo models, appear below:

Which model will salespeople push hardest if they are paid a commission of 10% of sales revenue? The answer is the Turbo because it has the higher selling price and hence the larger commission. On the other hand, from the standpoint of the company, profits will be greater if salespeople steer customers toward the XR7 model because it has the higher contribution margin.

To eliminate such conflicts, commissions can be based on contribution margin rather than on selling price. If this is done, the salespersons will want to sell the mix of products that maximizes contribution margin. Providing that fixed costs are not affected by the sales mix, maximizing the contribution margin will also maximize the company's profit. 4  In effect, by maximizing their own compensation, salespersons will also maximize the company's profit.

IN BUSINESS: AN ALTERNATIVE APPROACH TO SALES COMMISSIONS

Thrive Networks, located in Concord, Massachusetts, used to pay its three salesmen based on individually earned commissions. This system seemed to be working fine as indicated by the company's sales growth from $2.7 million in 2002 to $3.6 million in 2003. However, the company felt there was a better way to motivate and compensate its salesmen. It pooled commissions across the three salesmen and compensated them collectively. The new approach was designed to build teamwork and leverage each salesman's individual strengths. Jim Lippie, the director of business development, was highly skilled at networking and generating sales leads. John Barrows, the sales director, excelled at meeting with prospective clients and producing compelling proposals. Nate Wolfson, the CEO and final member of the sales team, was the master at closing the deal. The new approach has worked so well that Wolfson plans to use three-person sales teams in his offices nationwide.

 

Source: Cara Cannella, “Kill the Commissions,” Inc. Magazine, August 2004, p. 38.

Sales Mix

Before concluding our discussion of CVP concepts, we need to consider the impact of changes insales mix on a company's profit.

LEARNING OBJECTIVE 9

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.

The Definition of Sales Mix

The term  sales mix  refers to the relative proportions in which a company's products are sold. The idea is to achieve the combination, or mix, that will yield the greatest profits. Most companies have many products, and often these products are not equally profitable. Hence, profits will depend to some extent on the company's sales mix. Profits will be greater if high-margin rather than low-margin items make up a relatively large proportion of total sales.

Changes in the sales mix can cause perplexing variations in a company's profits. A shift in the sales mix from high-margin items to low-margin items can cause total profits to decrease even though total sales may increase. Conversely, a shift in the sales mix from low-margin items to high-margin items can cause the reverse effect—total profits may increase even though total sales decrease. It is one thing to achieve a particular sales volume; it is quite another to sell the most profitable mix of products.

IN BUSINESS: WALMART ATTEMPTS TO SHIFT ITS SALES MIX

Almost 130 million customers shop at Walmart's 3,200 U.S. stores each week. However, less than half of them shop the whole store—choosing to buy only low-margin basics while skipping higher-margin departments such as apparel. In an effort to shift its sales mix toward higher-margin merchandise, Walmart has reduced spending on advertising and plowed the money into remodeling the clothing departments within its stores. The company hopes this remodeling effort will entice its customers to add clothing to their shopping lists while bypassing the apparel offerings of competitors such as Kohl's and Target.

 

Source: Robert Berner, “Fashion Emergency at Walmart,” BusinessWeek, July 31, 2006, p. 67.

4

This also assumes the company has no production constraint. If it does, the sales commissions should be modified. See the Profitability Appendix at the end of the book.

Sales Mix and Break-Even Analysis

If a company sells more than one product, break-even analysis is more complex than discussed to this point. The reason is that different products will have different selling prices, different costs, and different contribution margins. Consequently, the break-even point depends on the mix in which the various products are sold. To illustrate, consider Virtual Journeys Unlimited, a small company that imports DVDs from France. At present, the company sells two DVDs: the Le Louvre DVD, a tour of the famous art museum in Paris; and the Le Vin DVD, which features the wines and wine-growing regions of France. The company's September sales, expenses, and break-even point are shown in  Exhibit 5–4 .

EXHIBIT 5–4 Multiproduct Break-Even Analysis

As shown in the exhibit, the break-even point is $60,000 in sales, which was computed by dividing the company's fixed expenses of $27,000 by its overall CM ratio of 45%. However, this is the break-even only if the company's sales mix does not change. Currently, the Le Louvre DVD is responsible for 20% and the Le Vin DVD for 80% of the company's dollar sales. Assuming this sales mix does not change, if total sales are $60,000, the sales of the Le Louvre DVD would be $12,000 (20% of $60,000) and the sales of the Le Vin DVD would be $48,000 (80% of $60,000). As shown in  Exhibit 5–4 , at these levels of sales, the company would indeed break even. But $60,000 in sales represents the break-even point for the company only if the sales mix does not change. If the sales mix changes, then the break-even point will also usually change. This is illustrated by the results for October in which the sales mix shifted away from the more profitable Le Vin DVD (which has a 50% CM ratio) toward the less profitable Le Louvre CD (which has a 25% CM ratio). These results appear in  Exhibit 5–5 .

EXHIBIT 5–5 Multiproduct Break-Even Analysis: A Shift in Sales Mix (see  Exhibit 5–4 )

Although sales have remained unchanged at $100,000, the sales mix is exactly the reverse of what it was in  Exhibit 5–4 , with the bulk of the sales now coming from the less profitable Le Louvre DVD. Notice that this shift in the sales mix has caused both the overall CM ratio and total profits to drop sharply from the prior month even though total sales are the same. The overall CM ratio has dropped from 45% in September to only 30% in October, and net operating income has dropped from $18,000 to only $3,000. In addition, with the drop in the overall CM ratio, the company's break-even point is no longer $60,000 in sales. Because the company is now realizing less average contribution margin per dollar of sales, it takes more sales to cover the same amount of fixed costs. Thus, the break-even point has increased from $60,000 to $90,000 in sales per year.

In preparing a break-even analysis, an assumption must be made concerning the sales mix. Usually the assumption is that it will not change. However, if the sales mix is expected to change, then this must be explicitly considered in any CVP computations.

Assumptions of CVP Analysis

A number of assumptions commonly underlie CVP analysis:

· 1. Selling price is constant. The price of a product or service will not change as volume changes.

· 2. Costs are linear and can be accurately divided into variable and fixed elements. The variable element is constant per unit, and the fixed element is constant in total over the entire relevant range.

· 3. In multiproduct companies, the sales mix is constant.

· 4. In manufacturing companies, inventories do not change. The number of units produced equals the number of units sold.

While these assumptions may be violated in practice, the results of CVP analysis are often “good enough” to be quite useful. Perhaps the greatest danger lies in relying on simple CVP analysis when a manager is contemplating a large change in volume that lies outside of the relevant range. For example, a manager might contemplate increasing the level of sales far beyond what the company has ever experienced before. However, even in these situations the model can be adjusted as we have done in this chapter to take into account anticipated changes in selling prices, fixed costs, and the sales mix that would otherwise violate the assumptions mentioned above. For example, in a decision that would affect fixed costs, the change in fixed costs can be explicitly taken into account as illustrated earlier in the chapter in the Acoustic Concepts example on pages 192–195.

Summary

CVP analysis is based on a simple model of how profits respond to prices, costs, and volume. This model can be used to answer a variety of critical questions such as what is the company's break-even volume, what is its margin of safety, and what is likely to happen if specific changes are made in prices, costs, and volume.

A CVP graph depicts the relationships between unit sales on the one hand and fixed expenses, variable expenses, total expenses, total sales, and profits on the other hand. The profit graph is simpler than the CVP graph and shows how profits depend on sales. The CVP and profit graphs are useful for developing intuition about how costs and profits respond to changes in sales.

The contribution margin ratio is the ratio of the total contribution margin to total sales. This ratio can be used to quickly estimate what impact a change in total sales would have on net operating income. The ratio is also useful in break-even analysis.

Target profit analysis is used to estimate how much sales would have to be to attain a specified target profit. The unit sales required to attain the target profit can be estimated by dividing the sum of the target profit and fixed expense by the unit contribution margin. Break-even analysis is a special case of target profit analysis that is used to estimate how much sales would have to be to just break even. The unit sales required to break even can be estimated by dividing the fixed expense by the unit contribution margin.

The margin of safety is the amount by which the company's current sales exceeds break-even sales.

The degree of operating leverage allows quick estimation of what impact a given percentage change in sales would have on the company's net operating income. The higher the degree of operating leverage, the greater is the impact on the company's profits. The degree of operating leverage is not constant—it depends on the company's current level of sales.

The profits of a multiproduct company are affected by its sales mix. Changes in the sales mix can affect the break-even point, margin of safety, and other critical factors.

Review Problem: CVP Relationships

Voltar Company manufactures and sells a specialized cordless telephone for high electromagnetic radiation environments. The company's contribution format income statement for the most recent year is given below:

Management is anxious to increase the company's profit and has asked for an analysis of a number of items.

Required:

· 1. Compute the company's CM ratio and variable expense ratio.

· 2. Compute the company's break-even point in both units and sales dollars. Use the equation method.

· 3. Assume that sales increase by $400,000 next year. If cost behavior patterns remain unchanged, by how much will the company's net operating income increase? Use the CM ratio to compute your answer.

· 4. Refer to the original data. Assume that next year management wants the company to earn a profit of at least $90,000. How many units will have to be sold to meet this target profit?

· 5. Refer to the original data. Compute the company's margin of safety in both dollar and percentage form.

· 6.

· a. Compute the company's degree of operating leverage at the present level of sales.

· b. Assume that through a more intense effort by the sales staff, the company's sales increase by 8% next year. By what percentage would you expect net operating income to increase? Use the degree of operating leverage to obtain your answer.

· c. Verify your answer to (b) by preparing a new contribution format income statement showing an 8% increase in sales.

· 7. In an effort to increase sales and profits, management is considering the use of a higher-quality speaker. The higher-quality speaker would increase variable costs by $3 per unit, but management could eliminate one quality inspector who is paid a salary of $30,000 per year. The sales manager estimates that the higher-quality speaker would increase annual sales by at least 20%.

· a. Assuming that changes are made as described above, prepare a projected contribution format income statement for next year. Show data on a total, per unit, and percentage basis.

· b. Compute the company's new break-even point in both units and dollars of sales. Use the formula method.

· c. Would you recommend that the changes be made?

Solution to Review Problem

· 1. 

· 2. 

· 3.

Because the fixed expenses are not expected to change, net operating income will increase by the entire $100,000 increase in contribution margin computed above.

· 4. Equation method:  Formula method:

· 5. 

· 6.

· a. 

· b.

· c. If sales increase by 8%, then 21,600 units (20,000 × 1.08 = 21,600) will be sold next year. The new contribution format income statement would be as follows:

Thus, the $84,000 expected net operating income for next year represents a 40% increase over the $60,000 net operating income earned during the current year: Note from the income statement on the prior page that the increase in sales from 20,000 to 21,600 units has increased both total sales and total variable expenses.

· 7.

· a. A 20% increase in sales would result in 24,000 units being sold next year: 20,000 units × 1.20 = 24,000 units.

Note that the change in per unit variable expenses results in a change in both the per unit contribution margin and the CM ratio.

· b. 

· c. Yes, based on these data, the changes should be made. The changes increase the company's net operating income from the present $60,000 to $78,000 per year. Although the changes also result in a higher break-even point (17,500 units as compared to the present 16,000 units), the company's margin of safety actually becomes greater than before:  As shown in (5) on the prior page, the company's present margin of safety is only $240,000. Thus, several benefits will result from the proposed changes.

Glossary

Break-even point

The level of sales at which profit is zero. (p. 186)

Contribution margin ratio (CM ratio)

A ratio computed by dividing contribution margin by dollar sales. (p. 191)

Cost-volume-profit (CVP) graph

A graphical representation of the relationships between an organization's revenues, costs, and profits on the one hand and its sales volume on the other hand. (p. 188)

Degree of operating leverage

A measure, at a given level of sales, of how a percentage change in sales will affect profits. The degree of operating leverage is computed by dividing contribution margin by net operating income. (p. 202)

Incremental analysis

An analytical approach that focuses only on those costs and revenues that change as a result of a decision. (p. 193)

Margin of safety

The excess of budgeted or actual dollar sales over the break-even dollar sales. (p. 199)

Operating leverage

A measure of how sensitive net operating income is to a given percentage change in dollar sales. (p. 202)

Sales mix

The relative proportions in which a company's products are sold. Sales mix is computed by expressing the sales of each product as a percentage of total sales. (p. 205)

Target profit analysis

Estimating what sales volume is needed to achieve a specific target profit. (p. 196)

Variable expense ratio

A ratio computed by dividing variable expenses by dollar sales (p. 192)

Questions

· 5–1 What is meant by a product's contribution margin ratio? How is this ratio useful in planning business operations?

· 5–2 Often the most direct route to a business decision is an incremental analysis. What is meant by an incremental analysis?

· 5–3 In all respects, Company A and Company B are identical except that Company A's costs are mostly variable, whereas Company B's costs are mostly fixed. When sales increase, which company will tend to realize the greatest increase in profits? Explain.

· 5–4 What is meant by the term operating leverage?

· 5–5 What is meant by the term break-even point?

· 5–6 In response to a request from your immediate supervisor, you have prepared a CVP graph portraying the cost and revenue characteristics of your company's product and operations. Explain how the lines on the graph and the break-even point would change if (a) the selling price per unit decreased, (b) fixed cost increased throughout the entire range of activity portrayed on the graph, and (c) variable cost per unit increased.

· 5–7 What is meant by the margin of safety?

· 5–8 What is meant by the term sales mix? What assumption is usually made concerning sales mix in CVP analysis?

· 5–9 Explain how a shift in the sales mix could result in both a higher break-even point and a lower net income.

Multiple-choice questions are provided on the text website at  www.mhhe.com/garrison14e .

Applying Excel 

LEARNING OBJECTIVES 6, 7, 8

Available with McGraw-Hill's Connect™ Accounting.

The Excel worksheet form that appears on the next page is to be used to recreate portions of the Review Problem on pages 208–210. Download the workbook containing this form from the Online Learning Center at  www.mhhe.com/garrison14e . On the website you will also receive instructions about how to use this worksheet form.

You should proceed to the requirements below only after completing your worksheet.

Required:

· 1. Check your worksheet by changing the fixed expenses to $270,000. If your worksheet is operating properly, the degree of operating leverage should be 10. If you do not get this answer, find the errors in your worksheet and correct them. How much is the margin of safety percentage? Did it change? Why or why not?

· 2. Enter the following data from a different company into your worksheet:

Unit sales	10,000 units
Selling price per unit	$120 per unit
Variable expenses per unit	$72 per unit
Fixed expenses	$420,000

· What is the margin of safety percentage? What is the degree of operating leverage?

· 3. Using the degree of operating leverage and without changing anything in your worksheet, calculate the percentage change in net operating income if unit sales increase by 15%.

· 4. Confirm the calculations you made in part (3) above by increasing the unit sales in your worksheet by 15%. What is the new net operating income and by what percentage did it increase?

· 5. Thad Morgan, a motorcycle enthusiast, has been exploring the possibility of relaunching the Western Hombre brand of cycle that was popular in the 1930s. The retro-look cycle would be sold for $10,000 and at that price, Thad estimates 600 units would be sold each year. The variable cost to produce and sell the cycles would be $7,500 per unit. The annual fixed cost would be $1,200,000.

· a. What would be the break-even unit sales, the margin of safety in dollars, and the degree of operating leverage?

· b. Thad is worried about the selling price. Rumors are circulating that other retro brands of cycles may be revived. If so, the selling price for the Western Hombre would have to be reduced to $9,000 to compete effectively. In that event, Thad would also reduce fixed expenses by $300,000 by reducing advertising expenses, but he still hopes to sell 600 units per year. Do you think this is a good plan? Explain. Also, explain the degree of operating leverage that appears on your worksheet.

Exercises 

All applicable exercises are available with McGraw-Hill's Connect™ Accounting.

Exercise 5–1 Preparing a Contribution Format Income Statement [LO1]

Wheeler Corporation's most recent income statement follows:

Required:

Prepare a new contribution format income statement under each of the following conditions (consider each case independently):

· 1. The sales volume increases by 50 units.

· 2. The sales volume declines by 50 units.

· 3. The sales volume is 7,000 units.

EXERCISE 5–2 Prepare a Cost-Volume-Profit (CVP) Graph [LO2]

Katara Enterprises distributes a single product whose selling price is $36 and whose variable expense is $24 per unit. The company's monthly fixed expense is $12,000.

Required:

· 1. Prepare a cost-volume-profit graph for the company up to a sales level of 2,000 units.

· 2. Estimate the company's break-even point in unit sales using your cost-volume-profit graph.

EXERCISE 5–3 Prepare a Profit Graph [LO2]

Capricio Enterprises distributes a single product whose selling price is $19 and whose variable expense is $15 per unit. The company's fixed expense is $12,000 per month.

Required:

· 1. Prepare a profit graph for the company up to a sales level of 4,000 units.

· 2. Estimate the company's break-even point in unit sales using your profit graph.

EXERCISE 5–4 Computing and Using the CM Ratio [LO3]

Last month when Harrison Creations, Inc., sold 40,000 units, total sales were $300,000, total variable expenses were $240,000, and fixed expenses were $45,000.

Required:

· 1. What is the company's contribution margin (CM) ratio?

· 2. Estimate the change in the company's net operating income if it were to increase its total sales by $1,500.

EXERCISE 5–5 Changes in Variable Costs, Fixed Costs, Selling Price, and Volume [LO4]

Data for Herron Corporation are shown below:

Fixed expenses are $75,000 per month and the company is selling 3,000 units per month.

Required:

· 1. The marketing manager believes that an $8,000 increase in the monthly advertising budget would increase monthly sales by $15,000. Should the advertising budget be increased?

· 2. Refer to the original data. Management is considering using higher-quality components that would increase the variable cost by $3 per unit. The marketing manager believes that the higher-quality product would increase sales by 15% per month. Should the higher-quality components be used?

EXERCISE 5–6 Compute the Level of Sales Required to Attain a Target Profit [LO5]

Liman Corporation has a single product whose selling price is $140 and whose variable expense is $60 per unit. The company's monthly fixed expense is $40,000.

Required:

· 1. Using the equation method, solve for the unit sales that are required to earn a target profit of $6,000.

· 2. Using the formula method, solve for the dollar sales that are required to earn a target profit of $8,000.

EXERCISE 5–7 Compute the Break-Even Point [LO6]

Maxson Products distributes a single product, a woven basket whose selling price is $8 and whose variable cost is $6 per unit. The company's monthly fixed expense is $5,500.

Required:

· 1. Solve for the company's break-even point in unit sales using the equation method.

· 2. Solve for the company's break-even point in sales dollars using the equation method and the CM ratio.

· 3. Solve for the company's break-even point in unit sales using the formula method.

· 4. Solve for the company's break-even point in sales dollars using formula method and the CM ratio.

EXERCISE 5–8 Compute the Margin of Safety [LO7]

Mohan Corporation is a distributor of a sun umbrella used at resort hotels. Data concerning next month's budget appear below:

Selling price	$25 per unit
Variable expenses	$15 per unit
Fixed expenses	$8,500 per month
Unit sales	1,000 units per month

Required:

· 1. Compute the company's margin of safety.

· 2. Compute the company's margin of safety as a percentage of its sales.

EXERCISE 5–9 Compute and Use the Degree of Operating Leverage [LO8]

Eneliko Company installs home theater systems. The company's most recent monthly contribution format income statement appears below:

Required:

· 1. Compute the company's degree of operating leverage.

· 2. Using the degree of operating leverage, estimate the impact on net operating income of a 10% increase in sales.

· 3. Verify your estimate from part (2) above by constructing a new contribution format income statement for the company assuming a 10% increase in sales.

EXERCISE 5–10 Compute the Break-Even Point for a Multiproduct Company [LO9]

Lucky Products markets two computer games: Predator and Runway. A contribution format income statement for a recent month for the two games appears below:

Required:

· 1. Compute the overall contribution margin (CM) ratio for the company.

· 2. Compute the overall break-even point for the company in sales dollars.

· 3. Verify the overall break-even point for the company by constructing a contribution format income statement showing the appropriate levels of sales for the two products.

EXERCISE 5–11 Break-Even Analysis; Target Profit; Margin of Safety; CM Ratio [LO1, LO3, LO5, LO6, LO7]

Pringle Company distributes a single product. The company's sales and expenses for a recent month follow:

Required:

· 1. What is the monthly break-even point in units sold and in sales dollars?

· 2. Without resorting to computations, what is the total contribution margin at the break-even point?

· 3. How many units would have to be sold each month to earn a target profit of $18,000? Use the formula method. Verify your answer by preparing a contribution format income statement at the target level of sales.

· 4. Refer to the original data. Compute the company's margin of safety in both dollar and percentage terms.

· 5. What is the company's CM ratio? If monthly sales increase by $80,000 and there is no change in fixed expenses, by how much would you expect monthly net operating income to increase?

EXERCISE 5–12 Break-Even and Target Profit Analysis [LO4, LO5, LO6]

Reveen Products sells camping equipment. One of the company's products, a camp lantern, sells for $90 per unit. Variable expenses are $63 per lantern, and fixed expenses associated with the lantern total $135,000 per month.

Required:

· 1. Compute the company's break-even point in number of lanterns and in total sales dollars.

· 2. If the variable expenses per lantern increase as a percentage of the selling price, will it result in a higher or a lower break-even point? Why? (Assume that the fixed expenses remain unchanged.)

· 3. At present, the company is selling 8,000 lanterns per month. The sales manager is convinced that a 10% reduction in the selling price will result in a 25% increase in the number of lanterns sold each month. Prepare two contribution format income statements, one under present operating conditions, and one as operations would appear after the proposed changes. Show both total and per unit data on your statements.

· 4. Refer to the data in (3) above. How many lanterns would have to be sold at the new selling price to yield a minimum net operating income of $72,000 per month?

EXERCISE 5–13 Break-Even Analysis and CVP Graphing [LO2, LO4, LO6]

Chi Omega Sorority is planning its annual Riverboat Extravaganza. The Extravaganza committee has assembled the following expected costs for the event:

Dinner (per person)	$7
Favors and program (per person)	$3
Band	$1,500
Tickets and advertising	$700
Riverboat rental	$4,800
Floorshow and strolling entertainers	$1,000

The committee members would like to charge $30 per person for the evening's activities.

Required:

· 1. Compute the break-even point for the Extravaganza (in terms of the number of persons that must attend).

· 2. Assume that only 250 persons attended the Extravaganza last year. If the same number attend this year, what price per ticket must be charged to break even?

· 3. Refer to the original data ($30 ticket price per person). Prepare a CVP graph for the Extravaganza from zero tickets up to 600 tickets sold.

EXERCISE 5–14 Multiproduct Break-Even Analysis [LO9]

Okabee Enterprises is the distributor for two products, Model A100 and Model B900. Monthly sales and the contribution margin ratios for the two products follow:

The company's fixed expenses total $598,500 per month.

Required:

· 1. Prepare a contribution format income statement for the company as a whole.

· 2. Compute the break-even point for the company based on the current sales mix.

· 3. If sales increase by $50,000 per month, by how much would you expect net operating income to increase? What are your assumptions?

EXERCISE 5–15 Operating Leverage [LO4, LO8]

Superior Door Company sells prehung doors to home builders. The doors are sold for $60 each. Variable costs are $42 per door, and fixed costs total $450,000 per year. The company is currently selling 30,000 doors per year.

Required:

· 1. Prepare a contribution format income statement for the company at the present level of sales and compute the degree of operating leverage.

· 2. Management is confident that the company can sell 37,500 doors next year (an increase of 7,500 doors, or 25%, over current sales). Compute the following:

· a. The expected percentage increase in net operating income for next year.

· b. The expected net operating income for next year. (Do not prepare an income statement; use the degree of operating leverage to compute your answer.)

EXERCISE 5–16 Break-Even and Target Profit Analysis [LO3, LO4, LO5, LO6]

Super Sales Company is the exclusive distributor for a revolutionary bookbag. The product sells for $60 per unit and has a CM ratio of 40%. The company's fixed expenses are $360,000 per year. The company plans to sell 17,000 bookbags this year.

Required:

· 1. What are the variable expenses per unit?

· 2. Using the equation method:

· a. What is the break-even point in units and in sales dollars?

· b. What sales level in units and in sales dollars is required to earn an annual profit of $90,000?

· c. Assume that through negotiation with the manufacturer the Super Sales Company is able to reduce its variable expenses by $3 per unit. What is the company's new break-even point in units and in sales dollars?

· 3. Repeat (2) above using the formula method.

EXERCISE 5–17 Using a Contribution Format Income Statement [LO1, LO4]

Porter Company's most recent contribution format income statement is shown below:

Required:

Prepare a new contribution format income statement under each of the following conditions (consider each case independently):

· 1. The number of units sold increases by 15%.

· 2. The selling price decreases by 50 cents per unit, and the number of units sold increases by 20%.

· 3. The selling price increases by 50 cents per unit, fixed expenses increase by $10,000, and the number of units sold decreases by 5%.

· 4. Variable expenses increase by 20 cents per unit, the selling price increases by 12%, and the number of units sold decreases by 10%.

EXERCISE 5–18 Missing Data; Basic CVP Concepts [LO1, LO9]

Fill in the missing amounts in each of the eight case situations below. Each case is independent of the others. (Hint: One way to find the missing amounts would be to prepare a contribution format income statement for each case, enter the known data, and then compute the missing items.)

· a. Assume that only one product is being sold in each of the four following case situations:

· b. Assume that more than one product is being sold in each of the four following case situations:

Problems 

All applicable problems are available with McGraw-Hill's Connect™ Accounting.

PROBLEM 5–19 Basic CVP Analysis; Graphing [LO1, LO2, LO4, LO6]

Shirts Unlimited operates a chain of shirt stores that carry many styles of shirts that are all sold at the same price. To encourage sales personnel to be aggressive in their sales efforts, the company pays a substantial sales commission on each shirt sold. Sales personnel also receive a small basic salary.

The following worksheet contains cost and revenue data for Store 36. These data are typical of the company's many outlets:

The company has asked you, as a member of its planning group, to assist in some basic analysis of its stores and company policies.

Required:

· 1. Calculate the annual break-even point in dollar sales and in unit sales for Store 36.

· 2. Prepare a CVP graph showing cost and revenue data for Store 36 from zero shirts up to 30,000 shirts sold each year. Clearly indicate the break-even point on the graph.

· 3. If 19,000 shirts are sold in a year, what would be Store 36's net operating income or loss?

· 4. The company is considering paying the store manager of Store 36 an incentive commission of $3 per shirt (in addition to the salespersons’ commissions). If this change is made, what will be the new break-even point in dollar sales and in unit sales?

· 5. Refer to the original data. As an alternative to (4) above, the company is considering paying the store manager a $3 commission on each shirt sold in excess of the break-even point. If this change is made, what will be the store's net operating income or loss if 23,500 shirts are sold in a year?

· 6. Refer to the original data. The company is considering eliminating sales commissions entirely in its stores and increasing fixed salaries by $107,000 annually.

· a. If this change is made, what will be the new break-even point in dollar sales and in unit sales in Store 36?

· b. Would you recommend that the change be made? Explain.

PROBLEM 5–20 Basics of CVP Analysis; Cost Structure [LO1, LO3, LO4, LO5, LO6]

Memofax, Inc., produces memory enhancement kits for fax machines. Sales have been very erratic, with some months showing a profit and some months showing a loss. The company's contribution format income statement for the most recent month is given below:

Required:

· 1. Compute the company's CM ratio and its break-even point in both units and dollars.

· 2. The sales manager feels that an $8,000 increase in the monthly advertising budget, combined with an intensified effort by the sales staff, will result in a $70,000 increase in monthly sales. If the sales manager is right, what will be the effect on the company's monthly net operating income or loss? (Use the incremental approach in preparing your answer.)

· 3. Refer to the original data. The president is convinced that a 10% reduction in the selling price, combined with an increase of $35,000 in the monthly advertising budget, will double unit sales. What will the new contribution format income statement look like if these changes are adopted?

· 4. Refer to the original data. The company's advertising agency thinks that a new package would help sales. The new package being proposed would increase packaging costs by $0.60 per unit. Assuming no other changes, how many units would have to be sold each month to earn a profit of $4,500?

· 5. Refer to the original data. By automating, the company could slash its variable expenses in half. However, fixed costs would increase by $118,000 per month.

· a. Compute the new CM ratio and the new break-even point in both units and dollars.

· b. Assume that the company expects to sell 20,000 units next month. Prepare two contribution format income statements, one assuming that operations are not automated and one assuming that they are.

· c. Would you recommend that the company automate its operations? Explain.

PROBLEM 5–21 Basic CVP Analysis [LO1, LO3, LO4, LO6, LO8]

Stratford Company distributes a lightweight lawn chair that sells for $15 per unit. Variable expenses are $6 per unit, and fixed expenses total $180,000 annually.

Required:

Answer the following independent questions:

· 1. What is the product's CM ratio?

· 2. Use the CM ratio to determine the break-even point in sales dollars.

· 3. The company estimates that sales will increase by $45,000 during the coming year due to increased demand. By how much should net operating income increase?

· 4. Assume that the operating results for last year were as follows:

· a. Compute the degree of operating leverage at the current level of sales.

· b. The president expects sales to increase by 15% next year. By how much should net operating income increase?

· 5. Refer to the original data. Assume that the company sold 28,000 units last year. The sales manager is convinced that a 10% reduction in the selling price, combined with a $70,000 increase in advertising expenditures, would increase annual unit sales by 50%. Prepare two contribution format income statements, one showing the results of last year's operations and one showing what the results of operations would be if these changes were made. Would you recommend that the company do as the sales manager suggests?

· 6. Refer to the original data. Assume again that the company sold 28,000 units last year. The president feels that it would be unwise to change the selling price. Instead, he wants to increase the sales commission by $2 per unit. He thinks that this move, combined with some increase in advertising, would double annual unit sales. By how much could advertising be increased with profits remaining unchanged? Do not prepare an income statement; use the incremental analysis approach.

PROBLEM 5–22 Sales Mix; Multiproduct Break-Even Analysis [LO9]

Marlin Company, a wholesale distributor, has been operating for only a few months. The company sells three products—sinks, mirrors, and vanities. Budgeted sales by product and in total for the coming month are shown below:

As shown by these data, net operating income is budgeted at $36,400 for the month, and break-even sales at $430,000.

Assume that actual sales for the month total $500,000 as planned. Actual sales by product are: sinks, $160,000; mirrors, $200,000; and vanities, $140,000.

Required:

· 1. Prepare a contribution format income statement for the month based on actual sales data. Present the income statement in the format shown above.

· 2. Compute the break-even point in sales dollars for the month, based on your actual data.

· 3. Considering the fact that the company met its $500,000 sales budget for the month, the president is shocked at the results shown on your income statement in (1) above. Prepare a brief memo for the president explaining why both the operating results and the break-even point in sales dollars are different from what was budgeted.

PROBLEM 5–23 Sales Mix; Break-Even Analysis; Margin of Safety [LO7, LO9]

Puleva Milenario SA, a company located in Toledo, Spain, manufactures and sells two models of luxuriously finished cutlery—Alvaro and Bazan. Present revenue, cost, and unit sales data for the two products appear below. All currency amounts are stated in terms of euros, which are indicated by the symbol €.

	Alvaro	Bazan
Selling price per unit	€4.00	€6.00
Variable expenses per unit	€2.40	€1.20
Number of units sold monthly	200 units	80 units

Fixed expenses are €660 per month.

Required:

· 1. Assuming the sales mix above, do the following:

· a. Prepare a contribution format income statement showing both euro and percent columns for each product and for the company as a whole.

· b. Compute the break-even point in euros for the company as a whole and the margin of safety in both euros and percent of sales.

· 2. The company has developed another product, Cano, that the company plans to sell for €8 each. At this price, the company expects to sell 40 units per month of the product. The variable expense would be €6 per unit. The company's fixed expenses would not change.

· a. Prepare another contribution format income statement, including sales of Cano (sales of the other two products would not change).

· b. Compute the company's new break-even point in euros for the company as a whole and the new margin of safety in both euros and percent of sales.

· 3. The president of the company was puzzled by your analysis. He did not understand why the break-even point has gone up even though there has been no increase in fixed expenses and the addition of the new product has increased the total contribution margin. Explain to the president what has happened.

PROBLEM 5–24 Sales Mix; Multiproduct Break-Even Analysis [LO9]

Topper Sports, Inc., produces high-quality sports equipment. The company's Racket Division manufactures three tennis rackets—the Standard, the Deluxe, and the Pro—that are widely used in amateur play. Selected information on the rackets is given below:

All sales are made through the company's own retail outlets. The Racket Division has the following fixed costs:

Sales, in units, over the past two months have been as follows:

	Standard	Deluxe	Pro	Total
April	2,000	1,000	5,000	8,000
May	8,000	1,000	3,000	12,000

Required:

· 1. Prepare contribution format income statements for April and May. Use the following headings:

Place the fixed expenses only in the Total column. Do not show percentages for the fixed expenses.

· 2. Upon seeing the income statements in (1) above, the president stated, “I can't believe this! We sold 50% more rackets in May than in April, yet profits went down. It's obvious that costs are out of control in that division.” What other explanation can you give for the drop in net operating income?

· 3. Compute the Racket Division's break-even point in dollar sales for April.

· 4. Without doing any calculations, explain whether the break-even point would be higher or lower with May's sales mix than with April's sales mix.

· 5. Assume that sales of the Standard racket increase by $20,000. What would be the effect on net operating income? What would be the effect if Pro racket sales increased by $20,000? Do not prepare income statements; use the incremental analysis approach in determining your answer.

PROBLEM 5–25 Break-Even Analysis; Pricing [LO1, LO4, LO6]

Detmer Holdings AG of Zurich, Switzerland, has just introduced a new fashion watch for which the company is trying to find an optimal selling price. Marketing studies suggest that the company can increase sales by 5,000 units for each SFr2 per unit reduction in the selling price. (SFr2 denotes 2 Swiss francs.) The company's present selling price is SFr90 per unit, and variable expenses are SFr60 per unit. Fixed expenses are SFr840,000 per year. The present annual sales volume (at the SFr90 selling price) is 25,000 units.

Required:

· 1. What is the present yearly net operating income or loss?

· 2. What is the present break-even point in units and in Swiss franc sales?

· 3. Assuming that the marketing studies are correct, what is the maximum profit that the company can earn yearly? At how many units and at what selling price per unit would the company generate this profit?

· 4. What would be the break-even point in units and in Swiss franc sales using the selling price you determined in (3) above (i.e., the selling price at the level of maximum profits)? Why is this break-even point different from the break-even point you computed in (2) above?

PROBLEM 5–26 Changes in Cost Structure; Break-Even Analysis; Operating Leverage; Margin of Safety [LO4, LO6, LO7, LO8]

Frieden Company's contribution format income statement for the most recent month is given below:

The industry in which Frieden Company operates is quite sensitive to cyclical movements in the economy. Thus, profits vary considerably from year to year according to general economic conditions. The company has a large amount of unused capacity and is studying ways of improving profits.

Required:

· 1. New equipment has come on the market that would allow Frieden Company to automate a portion of its operations. Variable expenses would be reduced by $6 per unit. However, fixed expenses would increase to a total of $432,000 each month. Prepare two contribution format income statements, one showing present operations and one showing how operations would appear if the new equipment is purchased. Show an Amount column, a Per Unit column, and a Percent column on each statement. Do not show percentages for the fixed expenses.

· 2. Refer to the income statements in (1) above. For both present operations and the proposed new operations, compute (a) the degree of operating leverage, (b) the break-even point in dollars, and (c) the margin of safety in both dollar and percentage terms.

· 3. Refer again to the data in (1) above. As a manager, what factor would be paramount in your mind in deciding whether to purchase the new equipment? (Assume that ample funds are available to make the purchase.)

· 4. Refer to the original data. Rather than purchase new equipment, the marketing manager argues that the company's marketing strategy should be changed. Instead of paying sales commissions, which are included in variable expenses, the marketing manager suggests that salespersons be paid fixed salaries and that the company invest heavily in advertising. The marketing manager claims that this new approach would increase unit sales by 50% without any change in selling price; the company's new monthly fixed expenses would be $240,000; and its net operating income would increase by 25%. Compute the break-even point in dollar sales for the company under the new marketing strategy. Do you agree with the marketing manager's proposal?

PROBLEM 5–27 Interpretive Questions on the CVP Graph [LO2, LO6]

A CVP graph, as illustrated on the next page, is a useful technique for showing relationships among an organization's costs, volume, and profits.

Required:

· 1. Identify the numbered components in the CVP graph.

· 2. State the effect of each of the following actions on line 3, line 9, and the break-even point. For line 3 and line 9, state whether the action will cause the line to:

· Remain unchanged.

· Shift upward.

· Shift downward.

· Have a steeper slope (i.e., rotate upward).

· Have a flatter slope (i.e., rotate downward).

· Shift upward and have a steeper slope.

· Shift upward and have a flatter slope.

· Shift downward and have a steeper slope.

· Shift downward and have a flatter slope.

In the case of the break-even point, state whether the action will cause the break-even point to:

· Remain unchanged.

· Increase.

· Decrease.

· Probably change, but the direction is uncertain.

Treat each case independently.

· x. Example. Fixed costs are increased by $20,000 each period.

Answer (see choices above):	Line 3: Shift upward.
	Line 9: Remain unchanged.
	Break-even point: Increase.

· a. The unit selling price is decreased from $30 to $27.

· b. The per unit variable costs are increased from $12 to $15.

· c. The total fixed costs are reduced by $40,000.

· d. Five thousand fewer units are sold during the period than were budgeted.

· e. Due to purchasing a robot to perform a task that was previously done by workers, fixed costs are increased by $25,000 per period, and variable costs are reduced by $8 per unit.

· f. As a result of a decrease in the cost of materials, both unit variable costs and the selling price are decreased by $3.

· g. Advertising costs are increased by $50,000 per period, resulting in a 10% increase in the number of units sold.

· h. Due to paying salespersons a commission rather than a flat salary, fixed costs are reduced by $21,000 per period, and unit variable costs are increased by $6.

PROBLEM 5–28 Graphing; Incremental Analysis; Operating Leverage [LO2, LO4, LO5, LO6, LO8]

Teri Hall has recently opened Sheer Elegance, Inc., a store specializing in fashionable stockings. Ms. Hall has just completed a course in managerial accounting, and she believes that she can apply certain aspects of the course to her business. She is particularly interested in adopting the cost-volume-profit (CVP) approach to decision making. Thus, she has prepared the following analysis:

Required:

· 1. How many pairs of stockings must be sold to break even? What does this represent in total dollar sales?

· 2. Prepare a CVP graph or a profit graph for the store from zero pairs up to 70,000 pairs of stockings sold each year. Indicate the break-even point on the graph.

· 3. How many pairs of stockings must be sold to earn a $9,000 target profit for the first year?

· 4. Ms. Hall now has one full-time and one part-time salesperson working in the store. It will cost her an additional $8,000 per year to convert the part-time position to a full-time position. Ms. Hall believes that the change would bring in an additional $20,000 in sales each year. Should she convert the position? Use the incremental approach. (Do not prepare an income statement.)

· 5. Refer to the original data. Actual operating results for the first year are as follows:

· a. What is the store's degree of operating leverage?

· b. Ms. Hall is confident that with some effort she can increase sales by 20% next year. What would be the expected percentage increase in net operating income? Use the degree of operating leverage concept to compute your answer.

PROBLEM 5–29 Various CVP Questions: Break-Even Point; Cost Structure; Target Sales [LO1, LO3, LO4, LO5, LO6, LO8]

Tyrene Products manufactures recreational equipment. One of the company's products, a skateboard, sells for $37.50. The skateboards are manufactured in an antiquated plant that relies heavily on direct labor workers. Thus, variable costs are high, totaling $22.50 per skateboard of which 60% is direct labor cost.

Over the past year the company sold 40,000 skateboards, with the following operating results:

Management is anxious to maintain and perhaps even improve its present level of income from the skateboards.

Required:

· 1. Compute (a) the CM ratio and the break-even point in skateboards, and (b) the degree of operating leverage at last year's level of sales.

· 2. Due to an increase in labor rates, the company estimates that variable costs will increase by $3 per skateboard next year. If this change takes place and the selling price per skateboard remains constant at $37.50, what will be the new CM ratio and the new break-even point in skateboards?

· 3. Refer to the data in (2) above. If the expected change in variable costs takes place, how many skateboards will have to be sold next year to earn the same net operating income, $120,000, as last year?

· 4. Refer again to the data in (2) above. The president has decided that the company may have to raise the selling price of its skateboards. If Tyrene Products wants to maintain the same CM ratio as last year, what selling price per skateboard must it charge next year to cover the increased labor costs?

· 5. Refer to the original data. The company is considering the construction of a new, automated plant. The new plant would slash variable costs by 40%, but it would cause fixed costs to increase by 90%. If the new plant is built, what would be the company's new CM ratio and new break-even point in skateboards?

· 6. Refer to the data in (5) above.

· a. If the new plant is built, how many skateboards will have to be sold next year to earn the same net operating income, $120,000, as last year?

· b. Assume that the new plant is constructed and that next year the company manufactures and sells 40,000 skateboards (the same number as sold last year). Prepare a contribution format income statement, and compute the degree of operating leverage.

· c. If you were a member of top management, would you have been in favor of constructing the new plant? Explain.

PROBLEM 5–30 Break-Even and Target Profit Analysis [LO5, LO6]

The Marbury Stein Shop sells steins from all parts of the world. The owner of the shop, Clint Marbury, is thinking of expanding his operations by hiring college students, on a commission basis, to sell steins at the local college. The steins will bear the school emblem.

These steins must be ordered from the manufacturer three months in advance, and because of the unique emblem of each college, they cannot be returned. The steins would cost Marbury $15 each with a minimum order of 200 steins. Any additional steins would have to be ordered in increments of 50.

Because Marbury's plan would not require any additional facilities, the only costs associated with the project would be the cost of the steins and the cost of sales commissions. The selling price of the steins would be $30 each. Marbury would pay the students a commission of $6 for each stein sold.

Required:

· 1. To make the project worthwhile in terms of his own time, Marbury would require a $7,200 profit for the first six months of the venture. What level of sales in units and dollars would be required to attain this target net operating income? Show all computations.

· 2. Assume that the venture is undertaken and an order is placed for 200 steins. What would be Marbury's break-even point in units and in sales dollars? Show computations, and explain the reasoning behind your answer.

PROBLEM 5–31 Changes in Fixed and Variable Costs; Break-Even and Target Profit Analysis [LO4, LO5, LO6]

Novelties, Inc., produces and sells highly faddish products directed toward the preteen market. A new product has come onto the market that the company is anxious to produce and sell. Enough capacity exists in the company's plant to produce 30,000 units each month. Variable expenses to manufacture and sell one unit would be $1.60, and fixed expenses would total $40,000 per month.

The Marketing Department predicts that demand for the product will exceed the 30,000 units that the company is able to produce. Additional production capacity can be rented from another company at a fixed expense of $2,000 per month. Variable expenses in the rented facility would total $1.75 per unit, due to somewhat less efficient operations than in the main plant. The product would sell for $2.50 per unit.

Required:

· 1. Compute the monthly break-even point for the new product in units and in total dollar sales.

· 2. How many units must be sold each month to make a monthly profit of $9,000?

· 3. If the sales manager receives a bonus of 15 cents for each unit sold in excess of the break-even point, how many units must be sold each month to earn a return of 25% on the monthly investment in fixed expenses?

Cases 

All applicable cases are available with McGraw-Hill's Connect™ Accounting.

CASE 5–32 Cost Structure; Break-Even Point; Target Profits [LO4, LO5, LO6]

Marston Corporation manufactures disposable thermometers that are sold to hospitals through a network of independent sales agents located in the United States and Canada. These sales agents sell a variety of products to hospitals in addition to Marston's disposable thermometer. The sales agents are currently paid an 18% commission on sales, and this commission rate was used when Marston's management prepared the following budgeted absorption income statement for the upcoming year.

Since the completion of the above statement, Marston's management has learned that the independent sales agents are demanding an increase in the commission rate to 20% of sales for the upcoming year. This would be the third increase in commissions demanded by the independent sales agents in five years. As a result, Marston's management has decided to investigate the possibility of hiring its own sales staff to replace the independent sales agents.

Marston's controller estimates that the company will have to hire eight salespeople to cover the current market area, and the total annual payroll cost of these employees will be about $700,000, including fringe benefits. The salespeople will also be paid commissions of 10% of sales. Travel and entertainment expenses are expected to total about $400,000 for the year. The company will also have to hire a sales manager and support staff whose salaries and fringe benefits will come to $200,000 per year. To make up for the promotions that the independent sales agents had been running on behalf of Marston, management believes that the company's budget for fixed advertising expenses should be increased by $500,000.

Required:

· 1. Assuming sales of $30,000,000, construct a budgeted contribution format income statement for the upcoming year for each of the following alternatives:

· a. The independent sales agents’ commission rate remains unchanged at 18%.

· b. The independent sales agents’ commission rate increases to 20%.

· c. The company employs its own sales force.

· 2. Calculate Marston Corporation's break-even point in sales dollars for the upcoming year assuming the following:

· a. The independent sales agents’ commission rate remains unchanged at 18%.

· b. The independent sales agents’ commission rate increases to 20%.

· c. The company employs its own sales force.

· 3. Refer to your answer to (1)(b) above. If the company employs its own sales force, what volume of sales would be necessary to generate the net operating income the company would realize if sales are $30,000,000 and the company continues to sell through agents (at a 20% commission rate)?

· 4. Determine the volume of sales at which net operating income would be equal regardless of whether Marston Corporation sells through agents (at a 20% commission rate) or employs its own sales force.

· 5. Prepare a graph on which you plot the profits for both of the following alternatives.

· a. The independent sales agents’ commission rate increases to 20%.

· b. The company employs its own sales force.

On the graph, use total sales revenue as the measure of activity.

· 6. Write a memo to the president of Marston Corporation in which you make a recommendation as to whether the company should continue to use independent sales agents (at a 20% commission rate) or employ its own sales force. Fully explain the reasons for your recommendation in the memo.

(CMA, adapted)

CASE 5–33 Break-Evens for Individual Products in a Multiproduct Company [LO6, LO9]

Jasmine Park encountered her boss, Rick Gompers, at the pop machine in the lobby. Rick is the vice president of marketing at Down South Lures Corporation. Jasmine was puzzled by some calculations she had been doing, so she asked him:

· Jasmine: “Rick, I'm not sure how to go about answering the questions that came up at the meeting with the president yesterday.”

· Rick: “What's the problem?”

· Jasmine: “The president wanted to know the break even for each of the company's products, but I am having trouble figuring them out.”

· Rick: “I'm sure you can handle it, Jasmine. And, by the way, I need your analysis on my desk tomorrow morning at 8:00 a.m. sharp so I can look at it before the follow-up meeting at 9:00.”

Down South Lures makes three fishing lures in its manufacturing facility in Alabama. Data concerning these products appear below.

	Frog	Minnow	Worm
Normal annual sales volume	100,000	200,000	300,000
Unit selling price	$2.00	$1.40	$0.80
Variable cost per unit	$1.20	$0.80	$0.50

Total fixed expenses for the entire company are $282,000 per year. All three products are sold in highly competitive markets, so the company is unable to raise its prices without losing unacceptable numbers of customers. The company has no work in process or finished goods inventories due to an extremely effective lean manufacturing system.

Required:

· 1. What is the company's overall break-even point in total sales dollars?

· 2. Of the total fixed costs of $282,000, $18,000 could be avoided if the Frog lure product were dropped, $96,000 if the Minnow lure product were dropped, and $60,000 if the Worm lure product were dropped. The remaining fixed expenses of $108,000 consist of common fixed costs such as administrative salaries and rent on the factory building that could be avoided only by going out of business entirely.

· a. What is the break-even point in units for each product?

· b. If the company sells exactly the break-even quantity of each product, what will be the overall profit of the company? Explain this result.