Question

A firm has 500,000 shares outstanding at a price of $100/share so 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

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

Answer 1

The present value of the cash flows can be calculated using the NPV formula. The present value of the cash flows is $1,014,467.60. The firm should invest in this project.

Step-by-step explanation:

The present value of the cash flows can be calculated using the formula for Net Present Value (NPV). NPV is calculated by discounting the future cash flows at the required rate of return (i.e., interest rate). In this case, the required rate of return is 20%. The present value of the cash flows can be calculated as follows:

1. The cash flow in year 1: $500,000/(1+0.20)^1 = $416,666.67
2. The cash flow in year 2: $400,000/(1+0.20)^2 = $277,777.78
3. The cash flow in year 3: $400,000/(1+0.20)^3 = $231,481.48
4. The cash flow in year 4: $150,000/(1+0.20)^4 = $88,541.67

The sum of these present values is $416,666.67 + $277,777.78 + $231,481.48 + $88,541.67 = $1,014,467.60. Therefore, the present value of the cash flows is $1,014,467.60.

Since the present value of the cash flows ($1,014,467.60) is greater than the cost of the investment project ($1,000,000), the firm should invest in this project. This indicates that the project is expected to generate a positive net present value, which is a good indicator of profitability.