Question

A firm has 500,000 shares outstanding at a price of $100/share so that its market value is (500k)($100) = $50M. The firm’s investment projects are financed by debt only. Currently the firm is considering an investment project that will cost $1,000,000 and generate cash flows of $500,000, $400,000, $400,000, and $150,000 in years 1 through 4. (worked out by hand please)

(i) If the current required rate of return is 20%, find the present value of the cash flows. Note: This is actually a net present value.
(ii) Based on your answer in part (i), should the firm invest in this project?

Answer 1

The present value of the project's cash flows, discounted at a 20% required rate of return, is equal to the project cost, resulting in a net present value of zero. This indicates that the firm breaks even on the investment, making it neutral in financial terms to take on the project.

Step-by-step explanation:

To determine whether the firm should invest in the project, we will calculate the present value of the cash flows discounted at the required rate of return of 20%. The present value (PV) of each cash flow is calculated as follows:

1. PV Year 1 = $500,000 / (1 + 0.2)1 = $416,667
2. PV Year 2 = $400,000 / (1 + 0.2)2 = $277,778
3. PV Year 3 = $400,000 / (1 + 0.2)3 = $231,481
4. PV Year 4 = $150,000 / (1 + 0.2)4 = $74,074

The sum of these present values is the total present value of the project's cash flows:

Total PV of cash flows = $416,667 + $277,778 + $231,481 + $74,074 = $1,000,000

Since the total present value of the cash flows ($1,000,000) is equal to the project cost, the net present value (NPV) is zero. Given that the NPV of this investment is zero, it indicates that the investment breaks even at the required rate of return. Considering that an NPV of zero means the firm is indifferent on the decision to invest (neither gaining nor losing value), a firm might choose to invest if it expects that the actual return could be higher than the required rate, or it has strategic reasons. However, strictly from a financial standpoint, the firm would typically look for positive NPV opportunities.