442 PART 3 Long-Term Investment Decisions
The Problem
A simple example will demonstrate the basic problem of noncomparability
caused by the need to select the best of a group of mutually exclusive projects
with differing usable lives.
EXAMPLE The AT Company, a regional cable television company, is evaluating two proj-
ects, X and Y. The relevant cash flows for each project are given in the following
table. The applicable cost of capital for use in evaluating these equally risky proj-
ects is 10%.
Table Use The net present value of each project at the 10% cost of capital is
calculated by finding the present value of each cash inflow, summing them, and
subtracting the initial investment from the sum of the present values.
NPVX[$28,000(0.909)][$33,000(0.826)][$38,000(0.751)]$70,000
($25,452$27,258$28,538)$70,000
$81,248$70,000
$
1
1
,
2
4
8
NPVY [$35,000(0.909)][$30,000(0.826)][$25,000(0.751)]
[$20,000 (0.683)][$15,000(0.621)][$10,000(0.564)]$85,000
($31,815$24,780$18,775$13,660$9,315$5,640)$85,000
$103,985$85,000
$
1
8
,
9
8
5
The NPV for project X is $11,248; that for project Y is $18,985.
Calculator Use Employing the preprogrammed NPV function in a financial
calculator, we use the keystrokes shown at the left for project X and for project
Y to find their respective NPVs of $11,277.24 and $19,013.27.
Spreadsheet Use Comparison of the net present values of two projects with
unequal lives also can be calculated as shown on the following Excel spreadsheet.
Project X Project Y
Initial investment $70,000 $85,000
Year Annual cash inflows
1 $28,000 $35,000
2 33,000 30,000
3 38,000 25,000
4 — 20,000
5 — 15,000
6 — 10,000
11277.24
70000 CF 0
CF 1
CF 3
I
NPV
CF 2
28000
33000
38000
10
Solution
Input Function
Project X
19013.27
85000 CF 0
CF 1
CF 3
CF 4
CF 5
CF 6
I
NPV
CF 2
35000
30000
25000
20000
15000
10000
10
Solution
Input Function
Project Y