Question

SML and WACC. An all-equity firm is considering the following projects:

The T-bill rate is 4 percent, and the expected return on the market is 12 percent.

a. Which projects have a higher expected return than the firm’s 12 percent cost of capital?

b. Which projects should be accepted?

c. Which projects will be incorrectly accepted or rejected if the firm’s overall cost of capital were used as a hurdle rate?

Answer 1

In evaluating multiple individual projects each projects has to be individually evaluated. Projects have to be evaluated based on the internal rate of return (IRR) of the project and market returns.

(a)

Consider the following information about the firm:

Project	Beta	IRR
W	0.80	10.2%
X	0.90	11.4%
Y	1.10	12.6%
Z	1.35	15.1%

The risk-free rate is 4%.

The Expected return on market is 12%.

The cost of capital is 12%.

Project Y and Project Z have a higher expected return than the firm’s 12 percent cost of capital. Project Y has an expected return of 12.6%, while Project Z has an expected return of 15.1%.

(b) Calculate the firm’s expected return:

In order to evaluate which project should be accepted, calculate the expected return on equity for each of the four projects.

Expected return on project can be calculated as follows:

Where,

Substitute values and calculate expected return for each project as shown below:

For the project W:

Hence, expected return on Project W is 10.4%.

For the Project X:

Hence, expected return on Project X is 11.2%.

For the Project Y:

Hence, expected return on Project Y is 12.8%

For the Project Z:

Hence, expected return on Project Z is 14.8%

Therefore, project Y and project Z give higher expected return than the market expectation rate.

(c)

Each project has its own risk as reflected by the value of beta. The firm’s overall cost of capital can be used as a hurdle rate only when the risk associated with the firm as a whole is equal to the risk associated with these projects.

Calculate the value of beta for the firm as a whole. Cost of capital is 12 %, market risk premium is 8 % and risk free rate is 4 %, then beta for company can be calculated as given below:

So, for the projects having beta less than 1.0 (project W and project X), firm’s cost of capital used as a hurdle rate will be incorrectly rejected though their risk is less than the firm. So the firm’s overall cost of capital is not appropriate to use as a hurdle rate.

Similarly, for the projects having beta more than 1.0 (project Y and project Z), firm’s cost of capital used as a hurdle rate will be incorrectly accepted though their risk is more than the firm. So the firm’s overall cost of capital is not appropriate to use as a hurdle rate.