Martin's Auto Repair Service is considering the purchase of a new piece of equipment that costs $5,000. The equipment would allow Martin's to generate additional revenue of $1,400 per year for four years. If the interest rate is 5%, what is the net present value of this investment?

Question

Quizplus · Accepted Answer

The net present value (NPV) of an investment is calculated by discounting the future cash flows back to their present value and then subtracting the initial investment. Here, the future cash flows are $1,400 per year for four years, and the discount rate is 5%. The formula for NPV is:$$ NPV = \frac{CF_1}{(1+r)^1} + \frac{CF_2}{(1+r)^2} + \frac{CF_3}{(1+r)^3} + \frac{CF_4}{(1+r)^4} - Initial\ Investment $$Where $ CF $ is the cash flow in each period, and $ r $ is the discount rate.Plugging in the numbers:$$ NPV = \frac{1400}{(1+0.05)^1} + \frac{1400}{(1+0.05)^2} + \frac{1400}{(1+0.05)^3} + \frac{1400}{(1+0.05)^4} - 5000 $$$$ NPV = \frac{1400}{1.05} + \frac{1400}{1.1025} + \frac{1400}{1.157625} + \frac{1400}{1.21550625} - 5000 $$$$ NPV = 1333.33 + 1269.84 + 1208.16 + 1153.00 - 5000 $$$$ NPV = 4964.33 $$Therefore, the net present value of the investment is $4,964.33.

Martin's Auto Repair Service Is Considering the Purchase of a New