Question

Answer 1

Answer: Select Alternative B

Annual Worth of Alternative A is -2109.90

Annual Worth of Alternative B is -1237.66

Explanation:

Compute Annual Worth

Alternative A

AW(A) = -35000 * (A/P, 8%, 8) + 3500 * (P/F, 8%, 2) * (A/P, 8%, 8) + 2800 + 7000 * (A/F, 8%, 8)

Compute (A/P, i%, n) using [i * (1 + i)ⁿ] / [(1 + i)ⁿ - 1]

(A/P, 8%, 8) = [0.08 * (1 + 0.08)⁸] / [(1 + 0.08)⁸ - 1] = [0.08 * (1.08)⁸] / [(1.08)⁸ - 1]

                    = [0.08 * 1.8509] / [1.8509 - 1] = 0.1740

Compute (P/F, i%, n) using (1 + i)^(-n)

(P/F, 8%, 2) = (1 + 0.08)^(-2) = (1.08)^(-2)= 0.8573

Compute (A/F, i%, n) using i / [(1 + i)ⁿ - 1]

(A/F, 8%, 8) = 0.08 / [(1 + 0.08)⁸ - 1] = 0.08 / [(1.08)⁸ - 1] = 0.08 / [1.8509 - 1] =0.0940

AW(A) = (-35000 * 0.1740) + (3500 * 0.8573 * 0.1740) + 2800 + (7000 * 0.0940) = -2109.90

Annual Worth of Alternative A is -2109.90

Alternative B

AW(B) = [-32000 + 4700 * (P/F, 8%, 2)] * 0.08 - 1500 + 2500

           = [-32000 + (4700 * 0.8573)] * 0.08 - 1500 + 2500

           = -27970.69 * 0.08 - 1500 + 2500 = -1237.66

Annual Worth of Alternative B is -1237.66

Annual Worth of Alternative B is higher.

Select Alternative B