Question

Your firm is planning to invest in an automated packaging plant. Harburtin Industries is an​ all-equity firm that specializes in this business. Suppose​ Harburtin's equity beta is 0.83​, the​ risk-free rate is 3%, and the market risk premium is 5%

a. If your​ firm's project is​ all-equity financed, estimate its cost of capital.

After computing the​ project's cost of capital you decided to look for other comparables to reduce estimation error in your cost of capital estimate. You find a second​ firm, Thurbinar​ Design, which is also engaged in a similar line of business. Thurbinar has a stock price of

$ 17 per​ share, with 15 million shares outstanding. It also has $109 million in outstanding​ debt, with a yield on the debt of 4.8 %.

​Thurbinar's equity beta is 1.00.

b. Assume​ Thurbinar's debt has a beta of zero. Estimate​ Thurbinar's unlevered beta. Use the unlevered beta and the CAPM to estimate​ Thurbinar's unlevered cost of capital.

c. Estimate​ Thurbinar's equity cost of capital using the CAPM. Then assume its debt cost of capital equals its yield and using these​ results, estimate​ Thurbinar's unlevered cost of capital.

d. Explain the difference between your estimate in part (b​) and part (c​).

e. You decide to average your results in part (b​) and part (c​), and then average this result with your estimate from part (a​).

What is your estimate for the cost of capital of your​ firm's project?

Answer 1

a.
=risk free rate+beta*market risk premium
=3%+0.83*5%
=7.15%

b.
Unlevered beta=levered beta/(1+(1-tax rate)*Debt/Equity)=1/(1+(1-tax rate)*Debt/Equity)
Assuming tax rate of 0:
Unlevered beta=1/(1+109/(17*15))=0.700549
Unlevered cost of capital=risk free rate+beta*market risk premium=3%+0.700549*5%=6.5027%

c.
leevred cost=3%+1*5%=8%
unlevered cost=(levered cost+D/E*cost of debt)/(1+D/E)=(8%+109/(17*15)*4.8%)/(1+109/(17*15))=7.04%

d.
In part b) we are not using cost of debt anywehere

e.
=(6.5027%+7.04%)/2
=6.7714%