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Lecture6

# Select b conclusion is consistent with pw method as

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Unformatted text preview: 8(A/P,10%,12)=151 AW(10%)B =2262(A/P,10%,12)=332. Select B. Conclusion is consistent with PW method as it should be. SEEM5740/ECLT5930 24 What is the AW(MARR) of each alternative over its single useful life? AW(10%)A =-3500(A/P,10%,4)+1255=151 AW(10%)B =-5000(A/P,10%,6)+1480=332 Observation: The AW of each alternative over its single life cycle is equal to its AW over the entire study period. Conclusion: When repeatability assumption holds, it is sufﬁcient to compare the AW values of the alternatives over their own useful life and select the alternative that maximizes AW. SEEM5740/ECLT5930 25 Proof for AW observation PW be the present worth of a project in a single life cycle. N : the number of periods in a single life cycle k: number of times the project repeats i: the effective interest rate per period AW for the entire study period: PW PW + ··· + (1 + i)N (1 + i)N (k−1) i 1 − (1 + i)−kN = PW 1 − (1 + i)−N 1 − (1 + i)−kN i = PW . 1 − (1 + i)−N PW + (A/P, i, kN ) AW for one life cycle: PW (A/P, i, N ) = PW SEEM5740/ECLT5930 i . 1 − (1 + i)−N 26 N-period project repeated k times PW PW PW 0 SEEM5740/ECLT5930 PW N 2N 3N PW PW (k-1)N kN 27 Cotermination: study period > useful life Example 6.5: Suppose the study period is 6 years. (Study period > Useful life of A) We need to adjust the cash ﬂow of Alternative A to terminate at the end of 6 years. Let’s assume that all cash ﬂows of Alternative A can be reinvested at the MARR from year 4 to year 6. Let’s use the FW method: FW (10%)A = [−3500(F /P, 10%, 4) + 1255(F /A, 10%, 4)](F /P, 10%, 2) = 847. FW (10%)B = −5000(F /P, 10%, 6) + 1480(F /A, 10%, 6) = 2561 Alternative B is still preferred. Remark: For investment alternatives, the cash ﬂows are assumed to reinvested until the end of study period. For cost alternatives, lease the equipment until the end of the study period. SEEM5740/ECLT5930 28 Cotermination: study period < useful life The strategy is to truncate the alternative at the end of the study period. We need the following additional information: market value of the ass...
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