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An all-equity firm is considering the following projects: Project Beta IRR W .63 9.4 % X .76 10.5 Y 1.29 14.0 Z 1.40 17.1 The T-bill rate is 5.1 percent, and the expected return on the market is 12.1 percent. a. Which projects have a higher/lower expected return than the firm’s 12.1 percent cost of capital? b. Which projects should be accepted? c. Which projects will be incorrectly accepted/rejected or correctly accepted/rejected if the firm's overall cost of capital were used as a hurdle rate?

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Answer:

Project Beta IRR project's cost of equity

W .63 9.4% = 5.1% + (0.63 x 7%) = 9.51%

X .76 10.5% = 5.1% + (0.76 x 7%) = 10.42%

Y 1.29 14.0% = 5.1% + (1.29 x 7%) = 14.13%

Z 1.40 17.1% = 5.1% + (1.40 x 7%) = 14.9%

the company's cost of capital = 12%

a. Which projects have a higher/lower expected return than the firm’s 12.1 percent cost

of capital?  

  • higher expected return ⇒ projects Y and Z
  • lower expected return ⇒ projects W and X

b. Which projects should be accepted?

  • accepted ⇒ projects X and Z (their IRR is higher than their Re)
  • rejected ⇒ projects W and Y (their IRR is lower than their Re)

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

  • if the company uses its cost of capital, then it would incorrectly reject project W  and incorrectly accept project Y  

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