Q 1.) What would happen to the WACC if the firmd tax rate increases, and what would happen if the risk free rate were to increase?
If the tax rate increases, the fter tax cost of borrowing would ultimately decrease, decreasing WACC. However, the answer in the book states: “If the risk free rate increases, the costs of debt and equity will increase, causing the cost of capital to increase.”
When I went back into the book to check, you can use the CAPM model to find the cost of capital. Using the risk free rate: rF + β(rM - rF)
rF=10%: rF + β(rM - rF) ==> 10% + 2(20%-10%) ==> 30%
rF=15%: rF + β(rM - rF) ==> 15% + 2(20%-15%) ==> 25% So wouldn’t an increase in the rF rate decrease the cost of capital?
Try it with β = 0.5, or β = 1.
That’s what I was thinking originally, but wouldn’t that mean the answer could be “either or”?
s2000’s answer makes sense, but only if you assume that the risk-free rate changes and leaves the required return on the market unchanged. Look at required return on the market as the risk-free rate PLUS the market risk premium. The MRP is the additional amount OVER AND ABOVE THE RISK_FREE RATE that compensates an investor for taking on an “Average risk asset” (i.e. the market)
Assuming that the required return on the market will be unchanged is equivalent to saying that an increase in the risk-free rate will be offset by a lower market risk premium.
The problem is that a lot of people estimate the mkt risk premium based on historical results, and take the mkt return as a given.
This highlights the ambiguity of the question: is the market return constant (independent of the risk-free rate), or is the market risk premium constant (independent of the risk-free rate)? In the real world you might reasonably argue for the latter over the former, but in an exam question the assumption needs to be stated explicitly.
You are assuming that the increase in tax rates and Rf will not change your beta. Which is not true in most cases.
The higher your tax rate, the more debt you are inclined to to take, and the more leveraged your company becomes. Beta is a measurment of your company’s risk on asset returns, and an increase in debt will increase the levered beta. Therefore driving up your cost of equity along with it. There is a payoff on where the optimal ratio of debt/equity is to minimize the WACC, but any increases in debt beyond that point will increase your WACC because the tax shield savings are outweighed by the burden of interest and debt repayment. So beta cannot be held constant in this instance.
The higher the Rf, the more expensive it is to finance with debt. Thus driving your beta higher because you increase the market value of debt, thus multiplying your leverage, and increasing the required return on equity. So in reality, an increase in Rf will be accompined by a proportinate increase in beta to reflect the additional cost of debt. So what an increase in Rf does is spread out the levered betas of the company’s inside the economy around the market portfolio, but they should all nonetheless average out to 1 according to the CAPM theory. In turn driving up the absolute market return, and hence the equity risk premium, due to higher leverage and higher required rates on capital investments.
I hope this makes sense.