Question

Project A costs -$1500 amount of money to begin and -$95 amount to operate every year starting from end of year 5 and will last forever; also $1,000,000 of salvage value at year 100. Project B costs $-186 amount to begin and $-130 to operate every year starting from the end of year 1 to the end of year 5 and $70 of salvage value at the end of year 5. Use an annual rate of 6% to conduct a present worth analysis to determine the PW of both A and B.

Answer 1

We have the following information

	Project A	Project B
First Cost ($)	– 1500	– 186
Annual Operating Cost ($)	– 95 starting from the end of Year 5	– 130
Salvage Value ($)	1,000,000	70

Project A

Present Worth = – 1,500 – 95(A/F, 6%, 5)(P/A, 6%, n=infinite) + 1,000,000(P/F, 6%, 100)

Present Worth = – 1,500 – {95 × [0.06/((1 + 0.06)⁵ – 1)] × (1/0.06)} + 1,000,000/(1 + 0.06)¹⁰⁰

Present Worth = – 1,500 – {95 × 0.1774 × 16.67} + (1,000,000 × 0.0029)

Present Worth of Project A = $1,166.29

Project B

Present Worth = – 186 – 130(P/A, 6%, 5) + 70(P/F, 6%, 5)

Present Worth = – 186 – 130[((1+0.06)⁵ – 1)/0.06(1+0.06)⁵] + 70/(1 + 0.06)⁵

Present Worth = – 186 – (130 × 4.212) + (70 × 0.7473)

Present Worth of Project B = – ($675.25)

Since, the present worth of Project A is higher, so Project A should be selected.