Question

Assume CAPM holds and you have the following information regarding three investment opportunities:

Project 1 has a project beta of 2.0 and you have estimated that the project’s NPV using a cost of capital of 20% equals zero. Project 2 has a project beta of 1.5 and its NPV using a cost of capital of 10% equals zero. Lastly, project 3 has a project beta of 1.0 and its NPV equals zero using a cost of capital of 6%. None of these projects are ‘scale-enhancing’ for the firm, i.e. they are different than the regular operations the firm currently maintains. As the head of the capital budgeting department you are trying to decide which projects should be accepted. The company has a levered equity beta of 0.8 and a debt-to-equity ratio of 0.5, which the company is planning to maintain for the foreseeable future. The company currently faces a 40% tax rate. Given that the expected return on the market portfolio is 8% and the risk-free rate is 3%, which projects would you accept and why? (Assume there is no capital rationing and the projects are going to be financed with 100% equity.)

I am not sure how to use Company Beta and D/E ratio in solving this question

Answer 1

We have been given the levered beta, we have to calculate the unlevered beta using Hamada equation since its 100% equity

BL = BU [1 + (1-T)*D/E]

0.8 = BU * [ 1+(1-0.4)*0.5]

BU = 0.8/1.3

BU = 0.6153

Unlevered beta = 0.6153

Now, using the CAPM , Expected retun = Rf + unlevered beta*(Rm - Rf) = 3% + 0.6153*(8-3) = 6.0765%

The expceted rate of return for the company is 6.0765% and unlevered beta is 0.6153

All the three projects have a beta greater than the unlevered beta, hence they are all risky. Now, we have to accept projects which have an IRR greater than 6.0765%. Hence it would be best to choose Projects 1 and 2 since IRR for project 1 is 20% and that of project 2 is 10% (both hgiher than the return expected of 6.07%).

We cannot select project C since its return is lower than the expected return