A firm is considering three mutually exclusive alternatives as part of a product

Question

A firm is considering three mutually exclusive alternatives as part of a production improvement program. The alternatives are as follows:

For each alternative, the salvage value at the end of useful life is zero. At the end of 10 years, Alt. A could be replaced by another A with identical cost and benefits. The MARR is 6%. If the analysis period is 20 years, which alternative should be selected?

A B C Installed cost, $ 10,000 15,000 20,000 Uniform Annual Benefit, $ 1,625 1,625 1,890 Useful Life, in years 10 20 20

Explanation / Answer

PVA = PMT [(1+r)^n - 1] / [r*(1+r)^n]

PV = FV / (1+R)^n

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Altternate A.

NPV = -10,000 + 1,625 [(1+0.06)^10 - 1] / [0.06*(1+0.06)^10]

NPV = 1,960.14

That's for first 10 years, for years 11-20 it will be same. But catch is that you have to find 10 present value of that.

NPV for 11-20: 1,960.14 / (1+0.06)^10 = 1,094.52

Now add both NPV's and that will be NPV of Alternate A

NPV Alternate A = $3,054.67

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Altternate B.

NPV = -15,000 + 1,625 [(1+0.06)^20 - 1] / [0.06*(1+0.06)^20]

NPV = -15,000 + 18,638.62

NPV Alternate B = $3,638.62

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Altternate C.

NPV = -20,000 + 1,890 [(1+0.06)^20 - 1] / [0.06*(1+0.06)^20]

NPV = -20,000 + 21,678.15

NPV Alternate B = $1,678.15

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Alternate B is best becasue it has highest Net Present Value (NPV).

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