Question

An all-equity firm is considering the following projects:

Project	Beta	IRR
W	.80	9.3%
X	.90	10.6
Y	1.10	11.4
Z	1.35	14.1

The T-bill rate is 4 percent, and the expected return on the market is 11 percent.

1. Which projects have a higher expected return than the firm’s 11 percent cost of capital?

2. Which projects should be accepted?

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

Answer 1

Answer :

The formula for expected return is as follows:

Expected return = Risk-free rate + Beta * ( Market return - Risk-free rate )

The risk-free rate is 4% and market return is 11%. Calculate the expected return for each project as follows:

Project	Beta	IRR	Expected Return
W	0.80	9.30%	9.60%
X	0.90	10.60%	10.30%
Y	1.10	11.40%	11.70%
Z	1.35	14.10%	13.45%

Expected return for the above table is calculated below as follows:

W = 4% + 0.80 * ( 11% - 4% ) = 4% + 5.6% = 9.60%

X = 4% + 0.90 * ( 11% - 4% ) = 4% + 6.30% = 10.30%

Y = 4% + 1.10 * ( 11% - 4% ) = 4% + 7.70% = 11.70%

Z = 4% + 1.35 * ( 11% - 4% ) = 4% + 9.45% = 13.45%

1) Projects having expected return higher than the cost of capital of 11% are Project Y with 11.70% expected return and Project Z with 13.45% expected return.

2) Project which has expected return higher than the IRR should be accepted. Project W with 9.60% expected return and Project Y with 11.70% expected return should be accepted.

3) In case, the firm's overall cost of capital was used as a hurdle rate, then Project W would be accepted incorrectly as it has expected return of 9.60% which is lower than 11% cost of capital. And Project X would be accepted incorrectly as it has expected return of 10.30% which is lower than 11% cost of capital and Project Y would be incorrectly rejected as it has expected return of 11.70% which is greater than 11% cost of capital and Project Z would be incorrectly rejected as it has expected return of 13.45% which is greater than 11% cost of capital.