The following data is available for three different alternatives. Alternatives B

Question

The following data is available for three different alternatives. Alternatives B and C are replaced at the end of their useful lives with identical replacements. Using present worth analysis, find the best alternative.

9. The following data is available for three different alternatives. Data Alternative 2,000 1,500 276.20 S654.80 nitial Cost niform Annual Benefits seful Life in years nterest Rate S1,000 S200 10 12% Alternatives B and C are replaced at the end of their useful lives with identical replacements. Using present worth analysis, find the best alternative.

Explanation / Answer

Consider the given problem here there are 3 alternatives, “A”, “B” and “C” and all the given detail is mentioned in the table.

So, for the 1st alternative “A”, the PW is mentioned below,

PW(A) = (-$1,000) + ($200/0.12) = (-$1,000) + $1,666.67 = $666.67 > 0.

Now, for the 2nd alternative “B”, the PW is mentioned below,

PW(B) = (-$1,500) + $276.2*[(1+0.12)^10 - 1] / [0.12*(1+0.12)^10].

=> (-$1,500) + $276.2*[(1.12)^10 - 1] / [0.12*(1.12)^10].

=> (-$1,500) + $276.2*[2.1058] / [0.12*(3.1058)].

=> (-$1,500) + $276.2*(2.1058 / 0.3727), => (-$1,500) + $276.2*5.65.

=> (-$1,500) + $276.2*5.65, => (-$1,500) + $1,560.53, => $60.53 > 0.

So, the PW(B) = $60.53 > 0.

Now, for the 3rd alternative “C”, the PW is mentioned below,

PW(C) = (-$2,000) + $654.8*[(1+0.12)^5 - 1] / [0.12*(1+0.12)^5].

=> (-$2,000) + $654.8*[(1.12)^5 - 1] / [0.12*(1.12)^5].

=> (-$2,000) + $654.8*(0.7623 / 0.2115), => (-$2,000) + $654.8*(3.6043).

=> (-$2,000) + $2,360.09, => $360 > 0.

So, the PW(C) = $360 > $60.53, $666.67 > 0.

So, as we can see that if we compare all these alternatives then “C” be the best possible alternative, having highest possible PW.

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