Three mutually exclusive alternatives are being evaluated. The economic data is
ID: 1216419 • Letter: T
Question
Three mutually exclusive alternatives are being evaluated. The economic data is shown below:
Alternatives
A B C
Initial cost $100,000 $160,000 $200,000
Annual Revenues $25,000 $40,000 $65,000
Annual expenses $10,000 $10,000 $10,000
Market value at 10 Years $10,000 $15,000 $20,000
If the study period is 10 years and the MARR is 18% per year, which alternative, if any, should be selected based on Present Worth analysis?
Explanation / Answer
Alternative A:
Intial cost (P) = $100,000
Net Annual Revenue(A) = $25000 - $10000 = $15000
Salvage Value(F) = $10000
N = 10
i = 18%
PW(18%) = -P + A(P/A, i, N) + F(P/F.i.N)
= -100,000 + 15000(P/A, 18%, 10) + 10000(P/F, 18%, 10)
= -100,000 + 15000(4.4941) + 10000(0.1911)
= -100,000 + 67411.5 + 1911 = -$30677.5
Alternative B:
Intial cost (P) = $160,000
Net Annual Revenue(A) = $40000 - $10000 = $30000
Salvage Value(F) = $15000
N = 10
i = 18%
PW(18%) = -P + A(P/A, i, N) + F(P/F.i.N)
= -160,000 + 30000(P/A, 18%, 10) + 15000(P/F, 18%, 10)
= -160,000 + 30000(4.4941) + 15000(0.1911)
= -160,000 + 134823 + 2866.5 = -$22310.5
Alternative C:
Intial cost (P) = $200,000
Net Annual Revenue(A) = $65000 - $10000 = $55000
Salvage Value(F) = $20000
N = 10
i = 18%
PW(18%) = -P + A(P/A, i, N) + F(P/F.i.N)
= -200,000 + 55000(P/A, 18%, 10) + 20000(P/F, 18%, 10)
= -200,000 + 55000(4.4941) + 20000(0.1911)
= -200,000 + 247175.5 + 3822 = $50997.5
Since, only Alternative C gives positive PW, so Anternative C should be selected.
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