Chapter 9
Mutually Exclusive Alternatives
137
9-4
Consider two investments:
(1) Invest $1000 and receive $110 at the end of each month for the next 10 months.
(2) Invest $1200 and receive $130 at the end of each month for the next 10 months.
If this were your money, and you want to earn at least 12% interest on your money, which
investment would you make, if any?
What nominal interest rate do you earn on the investment
you choose?
Solve by present worth analysis.
Solution
PW Analysis
i = 12%/12 = 1% per month
Alternative 1:
NPW = 110(P/A, 1%, 10) - 1,000 = $41.81
Alternative 2:
NPW = 130(P/A, 1%, 10) - 1,200 = $31.23
Choose Alternative 1
→
Maximum NPW
Nominal Interest: NPW = 0 = -1,000 + 110(P/A, i%, 10)
(P/A, i%, 10) = 9.1
From tables:
i
≅
1.75%
Nominal interest = 1.75% x 12 mo. = 21%
9-5
A farmer has just purchased a tractor for which he had to borrow $20,000.
The bank has offered
the following choice of payment plans determined using an interest rate of 8%.
If the farmer's
minimum attractive rate of return (MARR) is 15%, which plan should he choose?
Plan A: $5,010 per year for 5 years
Plan B: $2,956 per year for 4 years plus $15,000 at end of 5 years
Plan C: Nothing for 2 years, then $9048 per year for 3 years
Solution
PWC
A
= 5,010(P/A, 15%, 5) = $16,794
PWC
B
= 2,956(P/A, 15%, 4) + 15,000(P/F, 15%, 5) = $15,897.
PWC
C
= 9,048(P/A, 15%, 3)(P/F, 15%, 2) = $15,618
Plan C is lowest cost plan