Grant Ltd invested in a machine that has a 3-year useful life. The company's discount rate is 12%, and the net present value of the investment is $(573). Annual cost savings are: year 1 $3,000; year 2 $4,000; and year 3 $5,000. Determine the original cost of the machine. Ignore income taxes.

Question

Quizplus · Accepted Answer

The original cost of the machine can be determined by adding the net present value (NPV) of the investment to the present value (PV) of the cost savings. The PV of cost savings is calculated using the discount rate of 12%. For year 1, PV = $3,000 / (1 + 0.12)^1 = $2,678.57; for year 2, PV = $4,000 / (1 + 0.12)^2 = $3,191.44; and for year 3, PV = $5,000 / (1 + 0.12)^3 = $3,703.99. The total PV of cost savings = $2,678.57 + $3,191.44 + $3,703.99 = $9,574. Therefore, the original cost of the machine = $9,574 (total PV of cost savings) - $573 (NPV) = $10,000.

Grant Ltd Invested in a Machine That Has a 3-Year