Question

Type 2D: You are a consultant to a firm evaluating an expansion of its current business. The cash-flow forecasts (in millions of dollars) for the project are as follows. Year 0: initial outlay of 100, Years 1 to 8: 18 each year. On the basis of the behavior of the firm’s stock, you believe that the beta of the firm is 1.0. Assuming that the rate of return available on risk-free investment is 4% and that the expected rate of return on the market portfolio is 10%, what is the (risk-adjusted) net present value of the project?

Answer 1

Step 1: Find the cost of capital.

From the given information, we can use Capital Asset Pricing Method(CAPM) to find the cost of capital.

Where.
ke = Cost of capital
Rf = Risk free rate
Rm = Market rate of return
= Beta

Step 2: Find the present value of cash inflows using 10% as discount rate. Since the cash flow is uniform we can use present value of annuity formula:

Where,
PVA = Present value of annuity
A = Cash flows
i = Cost of capital
n = Number of years

Substituting the values, we get:

Step 3: Net present value (NPV):

OR