10: Cash Flow and Capital Budgetingmaintenance cost on the old device (to keep it running through the year) and the purchase price of the
new device. The present value cost (using a 7% discount rate) of the cash outflows for the devices over
the entire 12-year period follows:
Device NPV
A $48,233
B 42,360Taking into account the greater longevity of device B, it is the better choice. Remember, our objective
is to find the minimum-cost alternative, which, in this case, is device B.
An alternative approach to this problem is called
the equivalent annual cost (EAC) method. The EAC method
begins by calculating the present value of cash flows
for each device over its lifetime. We have already seen
that the NPV for operating device A for three years is
$15,936, and the NPV for operating device B for four
years is $18,065. Next, the EAC method asks, what
annual expenditure over the life of each machine would
have the same present value? That is, the EAC solves
each expression as follows:=++
XXX
$15,936
1.07 1.07 1.07
123 X = $6,072YYYY
$18,065
1.07 1.07 1.07 1.07=+ 12 ++ 34 Y = $5,333
In the first equation, the variable X represents the
annual cash flow from a three-year annuity that has the
same present value as the actual purchase and operating
costs of device A. If the company purchases device A
and keeps replacing it every three years for the indefinite
future, the company will incur a sequence of cash flows
over time with the same present value as a perpetuity
of $6,072. In other words, $6,072 is the equivalent
annual cost (EAC) of device A. Likewise, in the secondequation, Y represents the annual cash flow from a four-year annuity with the same present value as the
purchase and operating costs of device B. If the company buys device B and replaces it every four years,
then it will incur a sequence of cash flows having the same present value as a perpetuity of $5,333. The
company should choose the alternative with the lower EAC, which is device B.
Our approaches for solving the problem of choosing between equipment with unequal lives both
assume that the company will continue to replace worn-out equipment with similar machines for a long
period of time. That may not be a bad assumption in some cases, but new technology often makes old
equipment obsolete. For example, suppose that the company in our example believes that in three years
a new electronic device will be available that is more reliable, less costly to operate and longer-lived. If
this new device becomes available in three years, the company will replace whatever device it is using
at the time with the newer model. Furthermore, the superior attributes of the new model imply that the
salvage value for the old device will be zero. How should the company proceed?
equivalent annual cost
(EAC) method
Represents the annual
expenditure over the life of
each asset that has a present
value equal to the present
value of the asset’s annual
cash flows over its lifetimeTABLE 10.6 OPERATING AND REPLACEMENT
CASH FLOWS FOR TWO DEVICES
(ALL VALUES ARE OUTFLOWS)
Device
Year A B
0 $12,000 $14,000
1 1,500 1,200
2 1,500 1,200
3 13,500 1,200
4 1,500 15,200
5 1,500 1,200
6 13,500 1,200
7 1,500 1,200
8 1,500 15,200
9 13,500 1,200
10 1,500 1,200
11 1,500 1,200
12 1,500 1,200
NPV (@7%) $48,233 $42,360
Note: At the end of 12 years, the company has to replace
equipment, regardless of whether it chooses device A or B;
thus, a new 12-year cycle begins.