Question

In: Economics

Consider two equally selected alternatives that have ten years live. Alternative A has a cost of...

Consider two equally selected alternatives that have ten years live. Alternative A has a cost of $3,500 with annual benefits of $846. Alternative B has $7,000 with annual benefits of $2,664. MARR is 8%, provide each alternative is the best.

Solve using

a) Present worth analysis

b) Annual cash flow analysis

c) Rate of return analysis

Expert Solution

Consider two equally selected alternatives that have ten years live.

Alternative A has a cost of $3,500 with annual benefits of $846.

Alternative B has $7,000 with annual benefits of $2,664.

MARR is 8%, provide each alternative is the best.

Solve using

a) Present worth analysis

Alternative A has a cost of $3,500 with annual benefits of $846.

NPV = -3,500 + 846 (P/A, 8%, 10)

NPV = -3,500 + 846 (6.7101) = 2,177.5

Alternative B has $7,000 with annual benefits of $2,664

NPV = -7000 + 2,664 (P/A, 8%, 10)

NPV = -7000 + 2,664 (6.7101) = 10,875.7

b) Annual cash flow analysis (AW Analysis)

AW or AEC = NPV (A/P, 8%, 10)

Alternative A

AEC = 2,177.5 (0.1490) = 324.4

Alternative B

AEC = 10,875.7 (0.1490) = 1,620.4

c) Rate of return analysis

Alternative A

NPV = -3,500 + 846 (6.7101) = 2,177.5

Increasing rate of return to get negative NPW

NPW at 25%

NPV = -3,500 + 846 (P/A, 25%, 10)

NPV = -3,500 + 846 (3.5705) = -479

Using interpolation IRR = 8 % + 2177.5 / (2177.5 – (-479) * 17% = 22 % (Approx)

Alternative B

NPV = -7000 + 2,664 (6.7101) = 10,875.7

Increasing rate of return to get negative NPW

NPW at 40%

NPV = -7000 + 2,664 (P/A, 40%, 10)

NPV = -7000 + 2,664 (2.4136) = -570

Using interpolation IRR = 8 % + 10,875.7 / (10,875.7 – (-570) * 32% = 37 % (Approx)

On the basis of the above calculations, the alternative B is the best alternative.

Rahul Sunny answered 2 years ago

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