Risk free rate

[apcarlso]

If Fed actions caused the risk-free rate to increase, we would expect the cost of capital to:
A) decrease.
B) remain unchanged.
C) increase.
D) need more information to answer question.
Your answer: A was incorrect. The correct answer was C) increase.
An increase in the risk-free rate will cause the cost of equity to increase using the CAPM approach. It would also most likely cause the cost of raising new debt to increase as market rates increase based on the increase in the Fed Funds rate.
CAPM cost of equity = Rf + beta( E[Rm] - Rf)
10 + 1.3( 17 - 10) = 19.1
12 + 1.3 ( 17 - 12) = 18.5
Above, I see that all else equal, the increase in the risk free rate actually decreases the cost of equity. Someone set me straight here….

 

[aza]

apcarlso Wrote:
——————————————————-
> An increase in the risk-free rate will cause the
> cost of equity to increase using the CAPM
> approach. It would also most likely cause the cost
> of raising new debt to increase as market rates
> increase based on the increase in the Fed Funds
> rate.
>
>
> CAPM cost of equity = Rf + beta( E - Rf)
>
> 10 + 1.3( 17 - 10) = 19.1
>
> 12 + 1.3 ( 17 - 12) = 18.5
>
> Above, I see that all else equal, the increase in
> the risk free rate actually decreases the cost of
> equity. Someone set me straight here….
the answer is written in the sentence above: “It would also most likely cause the cost of raising new debt to increase as market rates increase based on the increase in the Fed Funds rate.”
the expected return on the market is comprised of risk-free rate and various risk premiums, like default risk premium, liquidity rp, and so forth. With the increase in Rf, the E(Rm) will increase as well.
in your example above: 12+ 1.3 (19 (approx) -12) = 21.1%.

 

[liaaba]

you’re using 1 specific example…
think about it, using your equation, you can rearrange to have
CAPM cost of equity = Rf*(1- beta)+ beta*E[Rm]
so if you choose beta to be >1, then for cost of equity, it could result in a lower number, but this is only looking at it from a math point of view….
think about it, if risk free rate is higher, wouldn’t people in general demand a higher return for their money to be invested in risky assets (I would since I can get more from RISK FREE asset now)? it doesn’t just affect cost of equity as alluded to by the answer, cost of debt will likely increase as well, as a matter of fact, when the fed raises the fed funds rate, the bond yield will follow higher (usually anyway), hence higher cost for debt…make sense?

 

[apcarlso]

So you are saying… it is incorrect to assume that the E(Rm) can stay constant with a change in the Rf rate?

 

[apcarlso]

liaaba - perfect sense… thanks for the clarification.

 

[alix12]

I think it is much better if you tackle the problem (or understand it) in a much more economic way rather than mathematical. That is the multiplier effect of the FED’s action in increasing the interest rate.