Introduction to Corporate Finance

Ross et al.: Fundamentals

of Corporate Finance, Sixth

Edition, Alternate Edition

IV. Capital Budgeting 10. Making Capital

Investment Decisions

© The McGraw−Hill^367

Companies, 2002

Machine A: PV
$100 
10/1.1 
10/1.1^2 
$117.36

Machine B: PV
$140 
8/1.1 
8/1.1^2 
8/1.1^3


$159.89

Notice that allthe numbers here are costs, so they all have negative signs. If we stopped

here, it might appear that A is the more attractive because the PV of the costs is less.

However, all we have really discovered so far is that A effectively provides two years’

worth of stamping service for $117.36, whereas B effectively provides three years’

worth for $159.89. These costs are not directly comparable because of the difference in

service periods.

We need to somehow work out a cost per year for these two alternatives. To do this,

we ask the question, What amount, paid each year over the life of the machine, has the

same PV of costs? This amount is called the equivalent annual cost (EAC).

Calculating the EAC involves finding an unknown payment amount. For example,

for Machine A, we need to find a two-year ordinary annuity with a PV of 
$117.36 at

10 percent. Going back to Chapter 6, we know that the two-year annuity factor is:

Annuity factor (1 
1/1.10^2 )/.10 1.7355

For Machine A, then, we have:

PV of costs 
$117.36 EAC 1.7355

EAC 
$117.36/1.7355


$67.62

For Machine B, the life is three years, so we first need the three-year annuity factor:

Annuity factor (1 
1/1.10^3 )/.10 2.4869

We calculate the EAC for B just as we did for A:

PV of costs 
$159.89 EAC 2.4869

EAC 
$159.89/2.4869


$64.29

Based on this analysis, we should purchase B because it effectively costs $64.29 per

year versus $67.62 for A. In other words, all things considered, B is cheaper. In this

case, the longer life and lower operating cost are more than enough to offset the higher

initial purchase price.

338 PART FOUR Capital Budgeting

equivalent annual cost
(EAC)
The present value of a
project’s costs
calculated on an annual
basis.

Equivalent Annual Costs

This extended example illustrates what happens to the EAC when we consider taxes. You are

evaluating two different pollution control options. A filtration system will cost $1.1 million to

install and $60,000 annually, before taxes, to operate. It will have to be completely replaced

every five years. A precipitation system will cost $1.9 million to install, but only $10,000 per

year to operate. The precipitation equipment has an effective operating life of eight years.

Straight-line depreciation is used throughout, and neither system has any salvage value.

Which option should we select if we use a 12 percent discount rate? The tax rate is

34 percent.

We need to consider the EACs for the two systems because they have different service

lives and they will be replaced as they wear out. The relevant information can be summarized

as follows:

EXAMPLE 10.4