Principles of Corporate Finance_ 12th Edition

Chapter 10 Project Analysis 257

bre44380_ch10_249-278.indd 257 09/30/15 12:45 PM

is the point at which the project has zero NPV. As long as sales are greater than 85,000, the
project has a positive NPV.^6
Managers frequently calculate break-even points in terms of accounting profits rather than
present values. Table  10.5 shows Otobai’s after-tax profits at three levels of scooter sales.
Figure 10.3 once again plots revenues and costs against sales. But the story this time is dif-
ferent. Figure  10.3, which is based on accounting profits, suggests a break-even of 60,000
scooters. Figure 10.2, which is based on present values, shows a break-even at 85,000 scoot-
ers. Why the difference?
When we work in terms of accounting profit, we deduct depreciation of ¥1.5 billion each
year to cover the cost of the initial investment. If Otobai sells 60,000 scooters a year, revenues
will be sufficient both to pay operating costs and to recover the initial outlay of ¥15 billion.
But they will not be sufficient to repay the opportunity cost of capital on that ¥15 billion. A
project that breaks even in accounting terms will surely have a negative NPV.

Operating Leverage and the Break-Even Point

A project’s break-even point depends on the extent to which its costs vary with the level of
sales. Suppose that electric scooters fall out of favor. The bad news is that Otobai’s sales

(^6) We could also calculate break-even sales by plotting equivalent annual costs and revenues. Of course, the break-even point would be
identical at 85,000 scooters.
❱ TABLE 10.5 The electric scooter project’s accounting profit under different assumptions about unit sales
(figures in ¥ billions except as noted).
Unit Sales
0
100
200
0
37.5
75.0
0
30
60
3
3
3
1.5
1.5
1.5

• 2.25
  1.5
  5.25

2.25

36.0

69.75

• 2.25
  1.5
  5.25

(thousands)

Revenues

(years 1–10)

Variable

Costs

Fixed

Costs Taxes

Total

Costs

Profit

Depreciation after Tax

◗ FIGURE 10.3

Sometimes break-even charts are con-

structed in terms of accounting numbers.

After-tax profit is zero when sales are

60,000.

Scooter sales, thousands

Break-even point:

Profit = 0

Costs

(including depreciation

and taxes)

Revenues

60 200

Accounting revenues and costs,

billions of yen

20

60

40