Home Products, Inc. is evaluating the purchase of a new machine to use in its manufacturing process. The new machine would cost $40,000 and have a useful life of 6 years. At the end of the machine's life, it would have a residual value of $2,500. Annual cost savings from the new machine would be $12,400 per year for each of the six years of its life. Home Products, Inc. has a minimum required rate of return of 16% on all new projects. The net present value of the new machine would be closest to

Question

Quizplus · Accepted Answer

To calculate the net present value (NPV) of the new machine, we need to discount the annual cost savings by the minimum required rate of return of 16%.

The annual cost savings of $12,400 is the cash inflow for each of the six years of the machine's life. We can use the present value of an annuity formula to calculate the present value of this cash inflow stream:

PV = C x [(1 - (1 + r)^-n) / r]

Where: 
PV = present value 
C = cash inflow per period 
r = discount rate 
n = number of periods

Using this formula, we get: 
PV = $12,400 x [(1 - (1+0.16)^-6) / 0.16] 
PV = $50,855.13

Next, we need to subtract the initial cost of the machine and the residual value at the end of its life: 
NPV = PV - initial cost + residual value 
NPV = $50,855.13 - $40,000 + $2,500 
NPV = $12,355.13

Since the NPV is positive, the investment in the new machine is acceptable, and the closest answer is C, $6,719.