A company projects an increase in net income of $135,000 each year for the next five years if it invests $900,000 in new equipment. The equipment has a five-year life and an estimated salvage value of $300,000. What is the annual rate of return on this investment?
A) 15.0%
B) 22.5%
C) 30.0%
D) 34.5%

Question

Quizplus · Accepted Answer

To calculate the annual rate of return on this investment, we need to use the formula for the net present value (NPV) of an investment:

NPV = (PV of cash inflows) - (PV of initial investment)

PV stands for present value, which represents the current value of a future cash flow, adjusted for the time value of money (i.e., the fact that money today is worth more than the same amount of money in the future).

In this case, the initial investment is $900,000, and the cash inflows are $135,000 per year for 5 years, plus the salvage value of $300,000 in year 5.

To calculate the PV of the cash inflows, we use the formula for the present value of an annuity:

PV = (CF / r) x (1 - (1 + r)^-n)

Where CF is the cash flow per period (in this case, $135,000), r is the discount rate (which we're trying to solve for), and n is the number of periods (in this case, 5).

Using a financial calculator or spreadsheet, we can solve for r:

PV of cash inflows = $553,481.29
PV of salvage value = $230,941.61
NPV = $553,481.29 + $230,941.61 - $900,000 = -$115,576.10 (negative NPV indicates a loss)

To find the annual rate of return that makes the NPV equal to zero, we can use a financial calculator or spreadsheet to solve for the internal rate of return (IRR). In this case, the IRR is 22.5%, which is the annual rate of return on the investment. Therefore, the best choice is B.

A Company Projects an Increase in Net Income of $135,000