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Unformatted text preview: ets at the end of the study period
We can use
the market value information if it is available.
otherwise the imputed market value.
Once we obtain this information, we adjust the cash ﬂow
stream for this alternative and apply the analysis techniques we
have learned for equal useful lives to the study period. SEEM5740/ECLT5930 29 Imputed market value Let T denote the study period (T< useful life), and let MVT
denote the market value at time T. Then,
MVT =PW at the end of year T of remaining capital recovery
amount + PW at the end of year T of original market (salvage)
value at end of useful life.
Formally, let I be the initial investment and S be the salvage
value of a project with a useful life of U time periods where U>T.
MVT = [I (A/P, MARR, U ) − S(A/F , MARR, U )](P/A, MARR, U − T )
+ S(P/F , MARR, U − T ). SEEM5740/ECLT5930 30 S
MVT CR CR CR U–1 U …
0 T T+1 CR = I(A/P, i%, U) – S(A/F, i%, U) SEEM5740/ECLT5930 31 CR as the lease fee Let’s consider the following situation: a company buys a
machine (initial cost I ) not for production, but will lease it out.
The machine is supposed to last U years with salvage value S.
What should be the annual lease fee? The company looks for a
rate of return equal to MARR.
Suppose the annual lease fee is X . Then X should satisfy
I = X (P/A, MARR, U ) + S(P/F , MARR, U )
⇒ X = I (A/P, MARR, U ) − S(A/F , MARR, U ) = CR.
Hence CR can interpreted as the annual lease fee. SEEM5740/ECLT5930 32 Interpretation of the imputed market value
How to determine the market value of the machine at the end of
year T ?
If you have the machine, you can lease it out for U − T years,
charging CR every year, and recover S in the end. Now if you
want to sell the machine at the end of year T , you should
charge the buyer
CR(P/A, MARR, U − T ) + S(P/F , MARR, U − T )
as this is the PW of future cash ﬂows you will receive if you
have the machine. Therefore
MVT = CR(P/A, MARR, U − T ) + S(P/F , MARR, U − T ). SEEM5740/ECLT5930 33 Example 6.6: Consider a project with a capital investment of
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- Fall '12