Cost of Capitol when interest increases

Q: If central bank actions caused the risk-free rate to increase, what is the most likely change to cost of debt and equity capital?

a. Both Decrease b. One increase and one decrease c. Both Increase

A: c: An increase in the risk-free rate will cause the cost of equity to increase. It would also cause the cost of debt to increase. In either case, the nominal cost of capital is the risk-free rate plus the appropriate premium for risk.

My guess was (b), that the cost of equity decreases because K = Rf + B (Rm - Rf)… so if Rf decreases, the market risk premium will increase, which will cause K to decrease… Why is the answer the cost of capital would also increase?

So for example, if Rf = 4, B = 1.2, and Rm = 10… K would be 11.2%

If we increase Rf to 5, K would be 11%, which is a decrease and NOT an increase… Whats going on?

( Rm - Rf ) is a risk premium and it should be relatively fixed because the amount of risk a certain stock bears compared to a risk-free asset is also fixed.

If Rf increase, an investor will demand a higher return on risky assets, so the risk premium keeps the same value (aproximately).

In other words, Rf is like your risk-free opportunity cost of capital. If you are meant to bear any risk, you will demand a marginal compensation (a return in addition to the risk-free asset return) to offset the risk of lose (i.e. risk premium).

C is the correct answer. The rfr is the base/risk-free/lowest of the low rate one will demand for compensation. Equity/Debt securities are obviously more risky than rfr. Thus, as the rfr floor moves higher, so does the required return for risky asset (all else equal), and–therefore–cost of capital also increases.

Don’t confuse what the Market Risk Premium IS with how you ESTIMATE it. For the first, what it IS is the additional return required for an asset with “average” systematic risk.

For the second, it is often ESTIMATED by using the historical difference between the returns on a broad market index and a risk-free asset (usually proxied for by Treasuries or some other sovereign debt). There are many other ways of estimating this - surveys, macroeconomic models like Ibbotsen-chen, those using CDS spreads (I think Damodaran explains this in mentions this in his SSRN paper on the equity risk premium). But you won’t see these others on the exam.

Bottom line - an increase in the risk free rate doesn’t change the ADDITIONAL return required for a risky asset OVER AND ABOVE that required for a risk-free one. It just means you’re adding the additional required return to a bigger risk-fee rate. So, the cost of equity will increase by the amount of the increase in the RF rate.