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alternative approach, the equivalent annual annuity method.

This procedure involves three steps:

Determine each projectвЂ™s NPV over its original life.

Find the constant annuity cash flow or EAA, using

NPV of each project

PVIFA,,,

Assuming infinite replacement, find the infinite horizon (or perpetuity) NPV of each project,

using

EAA of each

cost of capital

EXAMPLE 8.15 From Example 8.14, NPVA = $537.28 and NPVB = $598.60.

To obtain the constant annuity cash f o or EAA, we do the following:

lw

EAAA = $537.28/PVIFAlo,l4= $537.28/5.2161 = $103.00

EAAB = $598.6O/PVIFAs,14= $598.60/3.4331 = $174.36

Thus, the infinite horizon NPVs are as follows:

Infinite horizon NPVA = $103.00/0.14 = $735.71

Infinite horizon NPVB= $174.36/0.14 = $1,245.43

8.7 THE CONCEPT OF ABANDONMENT VALUE

The notion of abandonment value recognizes that abandonment of a project before the end of its

physical life can have a significant impact on the projectвЂ™s return and risk. This distinguishes between

the projectвЂ™s economic life and physical life. Two types of abandonment can occur:

1. Abandonment of an asset since it is being unprofitable.

2. Sale of the asset to some other party who can extract more value than the original owner.

EXAMPLE 8.16 ABC Company is considering a project with an initial cost of $5,000 and net cash flows of $2,000

for next three years. The expected abandonment cash flows for years 0,1,2, and 3 are $5,000, $3,000, $2,500, and

$0. The firmвЂ™s cost of capital is 10 percent. We will compute NPVs in three cases.

Case 1. NPV of the project if kept for 3 years

NPV = PV - I = $2,000 PVIFAI03 = $2,000(2.4869) - $5,OOO

= $26.20

NPV of the project if abandoned after Year 1

Case 2.

PV - I = $2,000 PVIFlo,l + $3,500 PVIFlo.2 - $5,000

NPV =

= $2,000(0.9091) + $3,000(0.9091)- $5,000

= $1,818.20 + $2,717,30 - $S,OOO = -$454,50

211

CAPITAL BUDGETING (INCLUDING LEASING)

CHAP. 81

Case 3. NPV of the project if abandoned after Year 2

PV - I = $2,000 PVIFl0,l + $2,000 PVIFlo.2 + $1,500 PVIFIoJ - $5,000

NPV =

= $2,000(0.9091) + $2,000(0.8264) + $2,500(0.8264) - $5,000

= $1,818.20 + $1,652.80 + $2,066.00 - $5,Q00= $537

The company should abandon the project after Year 2.

8.8 CAPITAL RATIONING

Many firms specify a limit on the overall budget for capital spending. Capital rationing is concerned

with the problem of selecting the mix of acceptable projects that provides the highest overall NPV. The

profitability index is used widely in ranking projects competing for limited funds.

EXAMPLE 8.17 A company with a fixed budget of $250,000 needs to select a mix of acceptable projects from the

following:

Ranking

Profitability Index

NPV ($)

I ($)

Projects PV ($)

1.6 1

112,000 42,000

70,000

A

2

45,000 1.45

145,000

100,000

B

5

16,500 1.15

126,500

110,000

C

3

19,000 1.32

79,000

60,000

D

6

0.95

-2,000

40,000 38,000

E

4

15,000 1.19

95,000

80,000

F

The ranking resulting from the profitability index shows that the company should select projects A, B,

and D:

PV

I

$112,000

A $ 70,000

145,000

100,000

B

79,000

D 60,000

$336,000

$230,000

Therefore,

NPV = $336,000 - $230,000 = $106,000

Unfortunately, the profitability index method has some limitations. One of the more serious is that

it breaks down whenever more than one resource is rationed.

A more general approach to solving capital rationing problems is the use of mathematical (or zero-

one) programming.вЂ™ Here the objective is to select the mix of projects that maximizes the NPV subject

to a budget constraint.

EXAMPLE 8.18 Using the data given in Example 8.13 set up the problem as a mathematical programming

problem. First label project A as X I ,B as X2,and so on;the problem can be stated as follows: Maximize

+ $16,500X3 + $19,OOOX4- $2,OOOX5+ $l5,000X6

= $42,OOOX1 + $45,OOOX2

NPV

A comprehensive treatment of the problem appears in H. Martin Weingartner, вЂњCapital Budgeting of Interrelated

Projects-Survey and Synthesis,вЂќ Management Science, vol. 12,March 1966,pp. 485-516.

212 CAPITAL BUDGETING (INCLUDING LEASING) [CHAP. 8

subject to

+

+ +

$70,0OOX1 $lOO,OOX˜ $llO,OOOX˜ $6O,OOOX4+ $40,0OOX5+ $80,0OOX6 S $250,000

X , = O , l - ( i = 1 , 2,..., 6)

Using the mathematical program solution routine, the solution to this problem is:

x,= 1, x = 1

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