Hay Ltd 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.

Question

Quizplus · Accepted Answer

To find the minimum annual cost savings that still provide a 15% return, we use the formula for the present value of an annuity: $PV = PMT \times \left[\frac{1 - (1 + r)^{-n}}{r}\right]$, where PV is the present value (cost of the truck, $14,340), PMT is the annual payment (cost savings, which we are solving for), 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 $PMT = \frac{PV}{\left[\frac{1 - (1 + r)^{-n}}{r}\right]}$. Plugging in the numbers: $PMT = \frac{14340}{\left[\frac{1 - (1 + 0.15)^{-7}}{0.15}\right]}$, which calculates to approximately $3,441. This is the minimum annual cost savings needed to achieve a 15% return.

Hay Ltd Is Considering the Purchase of a New Truck