Question

You are considering undertaking a project that has beta of 1.2, an initial cost of $100 million and annual after-tax inflows of $10 million for 20 years starting at the beginning of next year. The risk-free rate is 2% and the market is expected to yield 5% over the next year.

1. a) Assuming that the CAPM holds, what is the appropriate discount rate for this project?

2. b) What is the NPV of the project?

3. c) What is the IRR of the project?

4. d) What is the alpha of this project? Does a positive alpha correspond to a positive NPV? Why?

5. e) How high can the beta of the project be before the NPV turns negative?

Answer 1

a) Discount rate in this case would be cost of equity which will be calculated as: risk free rate + beta * (expected market yield - risk free rate). Hence discount rate is 5.6%

b) NPV = -100+(10/(1+5.6%)^1)+(10/(1+5.6%)^2)+(10/(1+5.6%)^3)+...+(10/(1+5.6%)^20)= 18.52. Hence NPV of the project over the next 20 years is $18.52mn

c) IRR is the rate at which NPV is 0. Since discount rate of 5.6% yields a positive NPV, IRR has to be more than 5.6%.  A discount rate of 8% yields a negative NPV of ($1.8mn), hence IRR has to be slightly lesser than 8.0%. The correct IRR is 7.8%. In case you are using MS Excel, you can jot down the numbers in a row starting with cash outflow in negative value (i.e. -100) followed by cash inflow of 10 for the next 20 years and apply IRR function.

d) Alpha = Actual rate of return - Expected rate of return i.e. 7.8%-5.6% = 2.2%. Since the alpha measures the excess of actual returns over the expected returns, the NPV will be positive as long as alpha is positive.     

e) Beta can be 1.9. A beta more than that will turn NPV negative.