Beta Inc. wants to raise capital amounting to $550 million. It has a target debt-to-equity ratio of 1.2. The following table illustrates the company’s marginal cost of capital schedule:
**Amount of New Debt ( millions)****After-Tax Cost of Debt****Amount of New Equity ( millions)**Cost of Equity 0 – 100 3.5% 0 – 200 6.5% 100 – 250 4.5% 200 – 400 7.5% 250 – 450 5.5% 400 – 600 8.5%
The company’s weighted average cost of capital is closest to:
6.41%
5.86%
13.4%
Answer: A
Proportion of new debt raised = 550 × (1.2 / 2.2) = $300
Proportion of new equity raised = 550 (1 / 2.2) = $250
For cash flow of 300, it correspond to the after cod of 5.5% for cash flow 250-450, as 300 fall within this range. Similarly, 7.5% for equity as 250 correspond to 200-400.
I just came across a question that I am having trouble understanding why the answer to the question is what the schweser books says the answer is. . . .
The first part is asking if the tax rate were to increase, what happens to the cost of debt. Obviously the cost of debt decreases with an increase in the tax rate. This ultimately flows into a decrease in WACC.
What I don’t understand is why the book indicates that an increase in the risk free rate will increase the WACC. It would seem to me that an increase in the RFR would decrease the WACC.
Generally, expected return from market equal risk free rate plus market risk premium. In your case, you are increasing the risk-free rate but the expected market return is till the same i.e. you are decreasing the market risk premium. That might be leading to your erroneous conclusion that an increase in risk-free rate will decrease WACC.
Just think logically, amigo. If the risk-free rate increase, it would obvioulsy increase the cost of capital as expected return from other investment classes would also increase.
When dealing with questions like these keep in consideration the change in cost according to the range. this is nothing new. The concept of Marginanl cost of Capital is demonstrated using the ranges. Increament in raised capital increases the ost of capital. Thats what the ranges show.
You are not taking into consideration the change in the Market Risk Premium due to the change in RFR. If RFR increase, other things keeping the same, the market risk premium would rise (Market Risk Premium = Expected retrun from the market - RFR)
To assume that the RFR increases while the RROR on risky assets remain unchanged is a strange assumption. We typically think of the required rate on risky assets as (1) The required rate on risk-free assets, plus (2) various risk premiums (liquidity, exchange rate risk, maturity risk, etc…).
In the capm or SML, you often see the market risk premium as R(m) -R(f). So, if R(m) is increases AND THE REQUIRED RETURN ON THE AVERAGE RISKY ASSET (i.e. the market) IS UNCHANGED, the Market Risk Premium would decrease. But while that’s mathematically true, the assumption that the market risk premium would decrease is kind of strange.
I think it’s more useful to view the SML as R(e) = R(f) + beta x Market Risk Premium. So, an increase in the risk free rate would simply be a parallel shift upwards of the SML.