Principles of Managerial Finance

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