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Two investment opportunities are as follows: For A: First cost 150, Uniform annual benefit 25,...

Question:

Two investment opportunities are as follows:

For A: First cost = $150, Uniform annual benefit = 25, End-of-useful-life salvage value = 20, Useful life = 15 years

For B: First cost = $100, Uniform annual benefit = 22.25, End-of-useful-life salvage value = 0, Useful life = 10 years

At the end of 10 years, Alt. B is not replaced. Thus, the comparison is 15 years of A versus 10 years of B. If the MARR is 10%, which alternative should be selected?

Investment:

The buying of products and services for creating wealth in the future is known as investment. The product and services bought for investment are not consumed by an individual initially. The product and services are in the form of monetary and sold for earning profit.

Answer and Explanation:

For A

First cost = $150

Uniform annual benefit = $25

Salvage value = $20

Useful life = 15 years

Calculating the annual worth of alternative A =

{eq}AW = -$150(A/P, 10\%, 15) + $25 + $20(A/F, 10\%, 15)\\ = (-$150 * 0.13147) + $25 + ($20 * 0.03147)\\ = -$19.72 + $25 + $0.63\\ = $5.91\\ {/eq}

Alternative A Annual worth = $5.91

For B

First cost = $100

Uniform annual benefit = $22.25

Salvage value = $ 0

Useful life = 10 years

Calculating the annual worth of alternative B -

{eq}AW = -$100(A/P, 10\%, 10) + $22.25 = (-$100 * 0.16275) + $22.25 = -$16.28 + $22.25 = $5.97 = $5.97 {/eq}

Alternative B annual worth is = $5.97

Hence, the annual work of Alternative B is higher than Alternative A

.

Thus, Alternative B will be selected because the useful life of both the alternative is different.


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