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 Nperiod project repeated k times PW PW PW 0 SEEM5740/ECLT5930 PW N 2N 3N PW PW (k1)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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 Fall '12
 ZHOU,Xiang
 PW, study period, PWA

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