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.
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.)

Answer 1

Cost of projects using CAPM: risk-free rate + beta*(market return - risk-free rate)

Project 1 = 3% + 2*(8%-3%) = 13%

Project 2 = 3% + 1.5*(8%-3%) = 10.5%

Project 3 = 3% + 1.0*(8%-3%) = 8%

Company cost of equity = 3% + 0.8*(8%-3%) = 7%

The cost of capital at which the project NPV's become zero is the IRR or the internal rate of return.

Project	Cost of capital	IRR
1	13%	20%
2	10.5%	10%
3	8%	6%

Projects which have a cost of capital higher than the IRR will anyway be rejected because the respective NPV will be negative. So, projects 2 and 3 will not be chosen. Project 1 should be taken up.

(Note: Since no information is provided about the cost of debt, WACC for the company cannot be computed for comparison purpose.)