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 0.85, the risk-free rate is 4%, and the market risk premium is 5%. 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 $20 per share, with 15 million shares outstanding. It also has $100 million in outstanding debt, with a yield on the debt of 4.5%. 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 (a) ,part (b) and part (c), and then average this result. What is your estimate for the cost of capital of your firm’s project?

Answer 1

a) Cost of Unlevered capital (from CAPM) =Risk free rate+ Unlevered beta* risk premium

= 4%+0.85*5% = 8.25%

b) Unlevered beta = levered beta/ (1+D/E)

Equity (E) = no. of shares * share price =  $20*15 million = $300 million

Debt (D) = $100 million

So, Unlevered Beta = 1/(1+100/300) = 0.75188

Unlevered cost of capital (from CAPM)= Risk free rate+ Unlevered beta* risk premium

= 4%+0.75188*5%

    =7.759398% or 7.76%

c) Cost of equity = Risk free rate+ levered beta* risk premium

=4%+1*5% = 9%

Cost of debt = 4.5%

So, Unlevered cost of capital= 100/(100+400)*4.5%+300/(100+300)*9% = 0.0765 = 7.65%

d) The estimate from part b) where cost of capital is derived from Unlevered beta is slightly higher as it does not take into account the cost of debt, whereas that derived in part c) is slightly less. However the difference is not significant

e) Average estimate for the cost of capital of your firm’s project = (8.25%+7.76%+7.65%)/3 = 7.89%