Principles of Corporate Finance_ 12th Edition

bre44380_ch06_132-161.indd 148 09/30/15 12:46 PM

148 Part One Value

Because the two machines produce exactly the same product, the only way to choose

between them is on the basis of cost. The present value of each machine’s cost is as follows:

Costs ($ thousands)

Year: 0 1 2 3

PV at 6%

($ thousands)

Machine A 15 5 5 5 $28.37

Machine B 10 6 6 — 21.00

Should we take machine B, the one with the lower present value of costs? Not necessarily. All

we have shown is that machine B offers two years of service for a lower total cost than three

years of service from machine A. But is the annual cost of using B lower than that of A?

Suppose the financial manager agrees to buy machine A and pay for its operating costs out

of her budget. She then charges the plant manager an annual amount for use of the machine.

There will be three equal payments starting in year 1. The financial manager has to make sure

that the present value of these payments equals the present value of the costs of each machine.

When the discount rate is 6%, the payment stream with such a present value turns out to be

$10,610 a year. In other words, the cost of buying and operating machine A over its three-year

life is equivalent to an annual charge of $10,610 a year for three years.

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Equivalent annual

costs

Costs ($ thousands)

Year: 0 1 2 3

PV at 6%

($ thousands)

Machine A 15 5 5 5 28.37

Equivalent annual cost 10.61 10.61 10.61 28.37

We calculated the equivalent annual cost by finding the three-year annuity with the same

present value as A’s lifetime costs.

PV of annuity = PV of A’s costs = 28.37

= annuity payment × 3-year annuity factor

At a 6% cost of capital, the annuity factor is 2.673 for three years, so

Annuity payment = _____28.37

2.673

= 10.61

A similar calculation for machine B gives an equivalent annual cost of $11,450:

Costs ($ thousands)

Year: 0 1 2

PV at 6%

($ thousands)

Machine B 10 6 6 21.00

Equivalent annual cost 11.45 11.45 21.00

Machine A is better, because its equivalent annual cost is less ($10,610 versus $11,450 for

machine B).