Question

An all-equity firm is considering the following projects:

Project	Beta			IRR
W		.70			9.9	%
X		.77			10.9
Y		1.43			14.4
Z		1.54			17.4

The T-bill rate is 5.4 percent, and the expected return on the market is 12.4 percent.

a. Compared with the firm's 12.4 percent cost of capital, Project W has a (Click to select)higherlower expected return, Project X has a (Click to select)lowerhigher expected return, Project Y has a (Click to select)higherlower expected return, and Project Z has a (Click to select)higherlower expected return.

b. Project W should be (Click to select)rejectedaccepted , Project X should be (Click to select)rejectedaccepted , Project Y should be (Click to select)rejectedaccepted , and Project Z should be (Click to select)rejectedaccepted .

c. If the firm's overall cost of capital were used as a hurdle rate, Project W would be (Click to select)incorrectly rejectedincorrectly acceptedcorrectly rejectedcorrectly accepted , Project X would be (Click to select)correctly acceptedincorrectly acceptedincorrectly rejectedcorrectly rejected , Project Y would be (Click to select)correctly acceptedcorrectly rejectedincorrectly acceptedincorrectly rejected , and Project Z would be (Click to select)correctly rejectedincorrectly rejectedcorrectly acceptedincorrectly accepted .

Answer 1

a). According to CAPM,

kE = rF + beta[E(rM) - rF]

kE_W = 5.4% + 0.70[12.4% - 5.4%] = 5.4% + 4.9% = 10.30%

Compared with the firm's 12.4 percent cost of capital, Project W has a lower expected return.

kE_X = 5.4% + 0.77[12.4% - 5.4%] = 5.4% + 5.39% = 10.79%

Compared with the firm's 12.4 percent cost of capital, Project X has a lower expected return.

kE_Y = 5.4% + 1.43[12.4% - 5.4%] = 5.4% + 10.01% = 15.41%

Compared with the firm's 12.4 percent cost of capital, Project Y has a higher expected return.

kE_Z = 5.4% + 1.54[12.4% - 5.4%] = 5.4% + 10.78% = 16.18%

Compared with the firm's 12.4 percent cost of capital, Project Z has a higher expected return.

b). Project W should be accepted, Project X should be rejected, Project Y should be accepted, and Project Z should be rejected.

c). If the firm's overall cost of capital were used as a hurdle rate, Project W would be incorrectly rejected, Project X would be correctly rejected, Project Y would be correctly accepted, and Project Z would be incorrectly accepted.