Question

The current real rate of interest is 4%. The expected annual inflation rate over the next several years is 5%. Given the following expected cash flows, what is the net present value of the investment?

Year 0 1 2
Cash Flow -300 160 160

A. <−$10
B. ≥−$10 but <$0
C. ≥$0 but <$10
D. ≥−$10 but <$20
E. ≥$20

Answer 1

Using the nominal discount rate of 9% to calculate the NPV of the given cash flows, we find that the NPV is less than $0 but greater than -$20. This corresponds to option D on the provided choices.

Step-by-step explanation:

To assess the Net Present Value (NPV) of the investment with the given cash flows, we must discount them at the nominal interest rate, which is the sum of the real rate of interest and the expected annual inflation rate. The nominal discount rate is therefore 4% + 5% = 9%. The present value of each cash flow can be calculated using the formula PV = CF / (1 + r)^n, where PV is the Present Value, CF is the Cash Flow, r is the discount rate (in decimal form), and n is the year number.

For the cash flows given (-$300 in Year 0, $160 in Year 1, and $160 in Year 2), the calculation of present value is as follows:

The NPV is the sum of these present values:

NPV = (-$300) + $146.79 + $134.67 ≈ -$18.54

Therefore, the NPV of the cash flow stream is less than $0 but greater than -$20, which corresponds to option D.