Alien Corp. is considering the purchase of a new truck which costs $14,340. The truck is expected to save $3,600 in operating costs annually for the next 7 years. How low can the annual cost savings be and still provide a 15% return? Ignore income taxes.
A) $5,967
B) $475
C) $7,458
D) $3,441

Question

Quizplus · Accepted Answer

To find the minimum annual cost savings that provide a 15% return, we use the formula for the present value of an annuity: PV = PMT * [(1 - (1 + r)^-n) / r], where PV is the present value (cost of the truck), PMT is the annual payment (annual cost savings), r is the annual interest rate (15% or 0.15), and n is the number of periods (7 years). Rearranging the formula to solve for PMT gives us PMT = PV / [(1 - (1 + r)^-n) / r]. Substituting the given values: PMT = $14,340 / [(1 - (1 + 0.15)^-7) / 0.15] = $14,340 / 4.1603 ≈ $3,441.