Question

(i) Mary has calculated the cost of capital (WACC) for WOW to be 7.1%, using an after-tax cost of debt of 2.8% and a cost of equity of 7.5% (there are no preferred shares in the company). What is the debt-to-capital ratio implied in Mary’s WACC calculation? .

(ii) Using the information from part (d), what is the levered beta used by Mary if the current risk-free rate is 2.7% and the risk premium is 5.6%? How do you interpret the value of this levered beta? What is the unlevered beta of WOW if the tax rate of the company is 30%?

Answer 1

1.
Let debt to capital ratio be x
Hence equity to capital ratio=1-x

WACC=Debt to capital*after tax cost of debt+Equity to capital*Cost of equity

Hence,
x*2.8%+(1-x)*7.5%=7.1%
=>x=(7.1%-7.5%)/(2.8%-7.5%)
=>x=0.0851064

2.
Levered beta=(cost of equity-risk free rate)/risk premium=(7.5%-2.7%)/5.6%=0.8571429

This is the sensitivity of cost of equity to the stock market in general i.e., market or systematic risk

3.
Unlevered beta=Levered Beta/(1+(1-tax rate)*Debt/Equity)=0.8571429/(1+(1-30%)*0.0851064/(1-0.0851064))=0.8047411