Question

1. Billick Brothers is estimating its WACC. The company has collected the following information:

• Its capital structure consists of 40 percent debt and 60 percent common equity.
• The company has 20-year bonds outstanding with a 9 percent annual coupon that are trading at par.
• The company’s tax rate is 40 percent.
• The risk-free rate is 5.5 percent.
• The market risk premium is 5 percent.
• The stock’s beta is 1.4.

What is the company’s WACC?

1. 5.88%
2. 8.94%
3. 9.66%
4. 10.26%
5. None of the above

The answer to this problem is 9.66%. I am confused on the formula for expected return. The formula is Re=Rf+B(Rm-Rf). But when I plug in all the numbers into this equation I get .048 = .055 + 1.4(.05 - .055) which gives the incorrect answer when solving for WACC. However, by not subtracting the Rf: .055 + 1.4(.05) I get .125. When I plug that into the WACC formula I get the correct answer of 9.66%. In summary, I don't know why the Rf is not subtracted when calculating Re for this problem. Please explain why and what bigger picture I'm missing here.

Answer 1

The thing that you are missing here is very easy as shown below:

The formula for computing return on equity as shown in the question also is

Re=Rf+B(Rm-Rf)

The formula of risk premium is follows:

= Return on market - Risk free rate or ( we can say Rm - Rf also as a short form)

Now in the question the risk premium is mentioned which is 5% or 0.05. This is the reason you have to put 0.05 in Rm - Rf instead of 0.05 - .055.

I hope you understand this

Feel free to ask in case of any query relating to this question