135
Chapter 9
Mutually
Exclusive
Alternatives
9-1
Using an 8-year analysis and a 10% interest rate, determine which alternative should be selected,
based on net present worth.
Alternative
A
B
First Cost
$5,300
$10,700
Uniform Annual Benefit
1,800
2,100
Useful life
4 years
8 years
Solution
NPW = PW(benefits) - PW(costs)
Alternative A:
NPW = 1,800(P/A, 10%, 8) - 5,300 - 5,300(P/F, 10%, 4)
= $683.10
Alternative B:
NPW = 2,100(P/A, 10%, 8) - 10,700 = $503.50
Select alternative A
9-2
Three purchase plans are available for a new car.
Plan A:
$5,000 cash immediately
Plan B:
$1,500 down and 36 monthly payments of $116.25
Plan C:
$1,000 down and 48 monthly payments of $120.50
If a customer expects to keep the car five years and her minimum attractive rate of return (MARR)
is 18% compounded monthly, which payment plan should she choose?

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136
Chapter 9
Mutually Exclusive Alternatives
Solution
Note that in all cases the car is kept 5 years that is the common analysis period.
Therefore
PWC is the easiest method.
i = 18%/12 = 1½%
PWC
A
= $5,000
PWC
B
= 1,500 + 116.25(P/A, 1½%, 36) = $4,715,59
PWC
C
= 1,000 + 120.50(P/A, 1½%, 48) =
$5,102.18
Therefore Plan B is best
9-3
Given the following three mutually exclusive alternatives.
Alternative
A
B
C
Initial Cost
$50
$30
$40
Annual Benefits
15
10
12
Useful Life(years)
5
5
5
What alternative is preferable if i = 10%?
Solution
Using simplest method (NPW):
A
B
C
Initial Cost
50.00
30.00
40.00
Annual Benefits
15.00
10.00
12.00
Useful Life(years)
5
5
5
Present Worth Benefits
56.87
37.91
45.49
Present Worth Costs
50.00
30.00
40.00
Net Present Worth = PWB - PWC
6.87
7.91
5.49
Choose C