Question

The data below are estimated for the project study of a certain business investment. If money is worth 12%, what is the difference in Present Worth between the alternatives?

Alternative A: The initial investment is $3,500, with an annual revenue of $1,900. Annual disbursement amounts to $645 with no salvage value at the end of its life, which is 4 years.

Alternative B: The initial investment is $5,000 with an annual revenue of $2,500. Annual disbursements is $1,383 with no salvage value at the end of its useful life, which is 8 years.

CHOICES:

A. $154

B. 238

C. $39

D. $481

Answer 1

We have the following information

Alternative A

Initial investment = $3500

Annual revenue = $1900

Annual disbursement = $645

Life (n) = 4 years

Interest rate (i) = 12% or 0.12

Net present worth (NPW) = – Initial investment + Annual revenue(P/A, i, n) – Annual disbursement(P/A, i, n)

NPW = – 3500 + 1900(P/A, 12%, 4) – 645(P/A, 12%, 4)

NPW = – 3500 + 1900[((1+0.12)⁴ – 1)/0.12 (1+0.12)⁴] – 645[((1+0.12)⁴ – 1)/0.12 (1+0.12)⁴]

NPW = – 3500 + 5770.96 – 1959.09

NPW of Alternative A = $312

Alternative B

Initial investment = $5000

Annual revenue = $2500

Annual disbursement = $1383

Life (n) = 8 years

Interest rate (i) = 12% or 0.12

Net present worth (NPW) = – Initial investment + Annual revenue(P/A, i, n) – Annual disbursement(P/A, i, n)

NPW = – 5000 + 2500(P/A, 12%, 8) – 1383(P/A, 12%, 8)

NPW = – 5000 + 2500[((1+0.12)⁸ – 1)/0.12 (1+0.12)⁸] – 1383[((1+0.12)⁸ – 1)/0.12 (1+0.12)⁸]

NPW = – 5000 + 12419.10 – 6870.25

NPW of Alternative B = $550

Difference between the NPW of Alternative A and Alternative B

Difference = 550 – 312

Difference = $238