Introduction to Corporate Finance

PArT 3: CAPITAL BUDGETING

10- 4b EQUIPMENT rEPLACEMENT AND EQUIVALENT

ANNUAL COST

Assume that a company must purchase an electronic control device to monitor its assembly line. Two types

of devices are available. Both meet the company’s minimum quality standards, but they differ in three

dimensions. First, one device is less costly than the other. Second, the cheaper device requires higher

maintenance expenditures. Third, the less expensive device (three-year life) does not last as long as the

more expensive one (four-year life), so it will have to be replaced sooner. The sequence of expected cash

outflows (we have omitted the negative signs for convenience) for each device are shown in Table 10.5.

TABLE 10.5 CAPITAL RATIONING AND THE PROFITABILITY INDEX (12% REQUIRED RETURN)

Projects

Year 1 2 3 4 5

0 –$ 70 –$ 80 –$ 100 –$ 150 –$ 200

1 30 30 40 50 90

2 40 35 50 55 80

3 50 55 60 60 80

4 55 60 65 90 110

NPV $ 59.2 $ 52.0 $ 59.6 $ 38.4 $ 71.0

IRR 44% 36% 36% 23% 28%

PI 1.8 1.6 1.6 1.3 1.4

End of year (all values are outflows)

Device 0 1 2 3 4

A $12,000 $ 1,500 $ 1,500 $ 1,500

B 14,000 1,200 1,200 1,200 $ 1,200

Notice that, to keep the example simple, the maintenance costs do not rise over time. Suppose this

company uses a discount rate of 7%. Following is the NPV cost of each stream of cash outflows:

Device NPV cost of cash outflows

A $15,936

B 18,065

Purchasing and operating device A seems to be much cheaper than using device B (remember that

we are looking for a lower NPV, because these are cash outflows). But this calculation ignores the fact

that using device A will necessitate a large replacement expenditure in year 4, one year earlier than

device B must be replaced. We need a way to capture the value of replacing device B less frequently

than device A.

One way to do this is to look at both machines over a 12-year time horizon. Over the next 12 years,

the company will replace device A four times (4 × 3 years = 12 years) and device B three times (3 × 4

years = 12 years). At the end of the twelfth year, both machines have to be replaced, and thus begins

another 12-year cycle. Table 10.6 shows the streams of cash flows over the cycle, assuming that when

either control device wears out it can be replaced and maintained at the same costs that initially applied

(all future costs remain the same). Notice that in the replacement years, the company must pay both the

How would you decide between

two machines, one that costs

more and last longer versus

another one that is less

expensive but must be replaced

more often?

thinking cap
question