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− 421,242 breakeven volume

= 157,258 units sold in excess of breakeven

× $15.51 contribution margin per unit

= $2,439,365 profit

Technical note:
Contribution margin per unit shown here is a rounded figure; the precise contribution margin per unit is used in calculating profit.

This method assigns the first 421,242 units sold during the year to covering fixed expenses. In other words, the contribution margin from the first 421,242 units sold during the year is viewed as consumed by fixed expenses. The 157,258 units sold in excess of the breakeven volume are viewed as the source of profit. In other words, annual sales volume is divided into two piles: (1) the breakeven group and (2) the profit group.

Profit is the same amount as calculated by the first method, although the method of getting there is different. The difference is a little more complex than meets the eye. It’s not just an exercise with numbers; it concerns how managers think about making profit in the first place. The first method of computing profit stresses the multiplication of unit contribution margin by sales volume to get total contribution margin for the period. Fixed expenses are not ignored, but are deducted from total contribution margin to work down to profit. In contrast, the excess over breakeven method puts fixed expenses first and profit second—the business first has to exceed its fixed expenses before it gets into the black.

Pathway to Profit #3: Average Profit Per Unit

The excess over breakeven profit method divides sales volume into two piles: (1) the breakeven quantity necessary to cover total fixed expenses and (2) the surplus over breakeven volume that provides profit. A third pathway to profit divides every unit sold into two parts: fixed expenses and profit.

The basic concept of the third method is that profit derives from spreading fixed expenses over a sufficiently large sales
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volume to ensure that the average fixed cost per unit is less than the contribution margin per unit. The fundamental thinking is that every unit sold has to do two things: (1) contribute its share to cover fixed expenses and (2) provide a profit residual. The computation of profit by this method is as follows: $6,534,250 total fixed costs

÷ 578,500 units sales volume for year

=

$11.29 average fixed cost per unit sold

versus $15.51 contribution margin per unit

=

$ 4.22 average profit per unit

× 578,500 total units sold (sales volume)

= $2,439,365 profit

Technical note:
The contribution margin per unit, average fixed cost per unit, and average profit per unit are rounded figures; the precise figures for each are used in calculating profit.

This method spreads fixed expenses for the year over the total number of units sold, which gives $11.29 as the average fixed cost per unit. Profit according to this method is viewed as the spread between the $11.29 average fixed cost per unit and the $15.51 contribution margin per unit, which is $4.22

average profit per unit. Of course, the amount of profit for the year (earnings before income tax) is the same as for the two computation methods explained previously.

Suppose the business had sold only 421,242 units (its breakeven volume). The average fixed expenses per unit sold would have been much higher. In fact, it would have been $15.51 per unit ($6,534,250 total fixed expenses ÷ 421,242

units breakeven volume = $15.51 average fixed cost per unit).

In this hypothetical situation the average fixed cost per unit would equal the average contribution margin per unit. So the business would have made precisely zero profit per unit. In other words, profit would be zero.

s

END POINT

Because a business has fixed expenses, it has to worry about its breakeven point—which is determined by dividing its total
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fixed expenses for the period by its contribution profit margin per unit. The breakeven point is that precise sales volume at which the business’s sales revenue would equal its total expenses and thus would experience exactly zero profit. The only advantage of breaking even is that the business would have no income tax to pay. At breakeven, the company’s bottom-line net income is zero. Of course, a business does not deliberately try to earn zero profit.

This chapter examines the nature of fixed expenses, especially the depreciation expense component of fixed expenses, noting that fixed expenses are not really 100 percent fixed and unchangeable, but are treated as if they were over the short run for breakeven analysis and for examining the pathways to profit. The chapter demonstrates the three different ways to compute profit, each of which has unique advantages for management analysis. The manager may find one more useful than the others in a given situation or for explaining the profit strategy of his or her business to others.

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TEAMFLY

Team-Fly®

C H A P T E R 9

Sales Volume Changes

BBusiness managers face constant change in the pursuit of profit. All profit factors are subject to change—due to both external changes beyond the control of the business and changes initiated by the managers themselves. Many management decisions are triggered by change. Indeed, managers are often characterized as
change agents.

Its suppliers may increase the purchase costs of the products sold by the business. Or the cost of manufacturing products may change, as may the productivity performance of its manufacturing operations. The company may raise wages for some or all of its employees, or wage rates might actually be reduced by employee givebacks or downsizing. The landlord may raise the rent; competitors may drop their sales prices and the business may have to follow suit. Managers may decide to raise sales prices. And so on.

One basic function of managers is to keep a close watch on all relevant changes and know how to deal with those changes. Changes set in motion a new round of profit-making decisions. This chapter is the first of four that analyze the impact of changes in the factors that drive profit. The basic factors are changed to determine the resulting change in profit. For example, if you sold 10 percent more units, would your profit be 10 percent higher? Nope, it’s not as simple as this, and managers should know why.

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THREE WAYS OF MAKING

A $1 MILLION PROFIT

By and large, previous chapters take a macro, or business-as-a-whole, approach to profit analysis techniques that business managers need to understand. This chapter shifts gears and takes more of a micro and focused point of view. The typical business consists of many different profit pieces, or
profit
modules,
as I prefer to call them. A profit module is a separate identifiable source of sales and profit of a business. A product line is a typical example of a profit module.

One product by itself could be a profit module if the product stands alone and generates a significant amount of sales revenue and profit. A separate store location or each branch of a business could be operated as a separate segment of the business and, accordingly, be accounted for as a profit module.

Organizational units that have profit responsibility are also called
profit centers.

A profit center may consist of two or more profit modules.

A brand generally covers too broad a range of different products to be just one profit module, although in some cases a brand might be a profit module. Managers have to figure out the best way to organize their sales activities into separate and distinguishable profit modules, which are the constituent profit members of the whole business. For each one of these organizational slices of the total business, a meaningful measure of profit is adopted that is appropriate for that particular management unit of the organization. Certain designated managers plan and control each profit module, which is necessary to achieve the overall profit goals of the business.

Figure 9.1 presents management profit reports for three contrasting profit modules of a business. Each is a basic product line of the business. The generic product line is an example of high volume and low unit margin. The business’s premier product line is at the opposite end of the how-to-make-profit spectrum—low volume and high unit margin. Its standard product line falls in the middle—moderate volume and moderate unit margin. Each product line generated a $1

million profit for the year just ended.

I designed these three examples so that profit is $1 million for each module. This makes it easier to compare the impacts caused by changes in profit factors between the three product
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S A L E S V O L U M E C H A N G E S

Standard Product Line

100,000 units sold

Per Unit

Totals

Sales revenue

$100.00

$10,000,000

Cost of goods sold

$ 65.00

$ 6,500,000

Gross margin

$ 35.00

$ 3,500,000

Revenue-driven expenses @ 8.5%

$ 8.50

$

850,000

Unit-driven expenses

$ 6.50

$

650,000

Contribution margin

$ 20.00

$ 2,000,000

Fixed operating expenses

$ 10.00

$ 1,000,000

Profit

$ 10.00

$ 1,000,000

Generic Product Line

150,000 units sold

Per Unit

Totals

Sales revenue

$ 75.00

$11,250,000

Cost of goods sold

$ 57.00

$ 8,550,000

Gross margin

$ 18.00

$ 2,700,000

Revenue-driven expenses @ 4.0%

$ 3.00

$

450,000

Unit-driven expenses

$ 5.00

$

750,000

Contribution margin

$ 10.00

$ 1,500,000

Fixed operating expenses

$ 3.33

$

500,000

Profit

$ 6.67

$ 1,000,000

Premier Product Line

50,000 units sold

Per Unit

Totals

Sales revenue

$150.00

$ 7,500,000

Cost of goods sold

$ 80.00

$ 4,000,000

Gross margin

$ 70.00

$ 3,500,000

Revenue-driven expenses @ 7.5%

$ 11.25

$

562,500

Unit-driven expenses

$ 8.75

$

437,500

Contribution margin

$ 50.00

$ 2,500,000

Fixed operating expenses

$ 30.00

$ 1,500,000

Profit

$ 20.00

$ 1,000,000

FIGURE 9.1
Three contrasting profit modules of a business.

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lines. Profit is the same for all three modules, but the sales prices, unit margins, and fixed operating expenses are quite different for the three product lines. Note that the business had to sell three times as many units of its generic products (150,000 units) as its premier products (50,000 units) to earn the same profit.

Chapter 8 explains the different ways of analyzing profit, which I call
pathways to profit.
The three management profit reports presented in Figure 9.1 for the three profit modules follow the layout of the #1 pathway to profit, as follows: Unit margin × sales volume = contribution margin

− fixed costs

= profit

The management profit reports in Figure 9.1 also include data for the #3 pathway to profit. For instance, for the pre-miere product line the business spread its $1.5 million fixed costs over 50,000 units, which gives a $30.00 average fixed cost per unit sold. On this product line, the business makes a $50.00 unit margin, so its profit is $20.00 per unit, which multiplied times the 50,000 units sales volume gives $1 million profit for the year. The #2 pathway to profit is brought into play later to explain why the percent change in profit is greater than the percent change in sales volume.

The three variable expenses per unit reported in Figure 9.1

for each profit module (i.e., product cost, revenue-driven, and unit-driven) are
incremental costs.
That is to say, if the business sells one more unit, then total cost increases by the per unit amounts shown in Figure 9.1. The total amount of each of these expenses for the period depends on the number of units sold (or sales volume). In contrast, the per-unit amount of fixed operating expenses for each product line is determined by dividing the total fixed costs for the period by the number of units sold. If the business had sold one unit more or one unit less than it did, the total amount of fixed costs for the period would be the same, but the
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average fixed cost per unit would be slightly different because this is a calculated amount that depends on the number of units sold.

Defining Profit and the Matter of Fixed Costs

Each profit module (product line) shown in Figure 9.1 is charged with its
direct
fixed operating expenses for the year.

These include such costs as the salaries of the managers and other employees who work exclusively in this area of the business, advertising expenditures for the products (except for the generic product, which is not advertised), depreciation of various fixed assets used by each of these profit segments of the business, and so on. Several fixed costs of the business cannot be allocated directly to any of its profit modules (the general legal costs of the business, the compensation of companywide top-level executives, the cost of its annual independent audit, charitable contributions made by the business, the cost of institutional advertising in which the name of the company but no specific products are promoted, etc.). Every profit module is expected to earn a sufficient profit after deducting its direct fixed costs from its contribution margin.