Question

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

Answer 1

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.