The yield on a three-month t-bill is 2.7%, and the yield on a 10-year t-bond is
ID: 2651687 • Letter: T
Question
The yield on a three-month t-bill is 2.7%, and the yield on a 10-year t-bond is 3.8%. The market risk premium is 6.1%. D'Amico Co. has a beta of 1.56. Using the Capital Asset Pricing Model (CAPM) approach, D'Amico's cost of equity is
a. 16%
b. 14%
c. 14.6%
d. 13.3%
Kuhn Co. is closely held and, consequently, cannot generate reliable inputs for the CAPM approach. Kuhn's bonds yield 11.5%, and the firm's analysts estimate that the firm's risk premium on its stock over its bonds is 3.5%. Using the over-own-bond-yield judgemental risk premium approach, find the firm's cost of equity:
a. 16.5%
b. 18.8%
c. 15%
d. 18%
Please show how you got the answer. Thanks!
Explanation / Answer
Capital asset pricing model is used to estimate cost of equity of a common stock. Here cost of equity will mean miimmum return that company has to pay to its common stock owner to keep them satisfied. It is ascertaned by adding some premium with the risk free return. Thus two terms requires explanation here.
1. Risk free rate: It is the return on government security. Here investment is government security will mean risk free investment. It is so called because it has no default risk. Here default risk will indicate the incapacity of the bond issuer to pay dues like interest or principal repayment in time. Suppose you will receive 10% interst at the end of a year. But due to liquidity crisis company has failed to pay it. It will create default risk. Government has no default risk. It is the authority of issuing notes. In a situation of liquidity crisis it can print note and circulate in the economy. Thus liquidity problem is not there.
In this problem two types of government security has been metioned. First one is 3 month short term T-bill. Second one is 10 years long term bond. Question is which one will be taken here as equivalent to risk free investment. Answer is you must consider 10 year bond. Common stock is a long term investment. But T bill is a short term ivestment. So you cannot consider it. Hence risk free return here is yield on 10 years t-bond. It is 3.8%
Risk premium: All ivestmets are more risky tha T- bod. So extra risk will require extra retur. It will be risk premium. This risk premium is calculated by multiplyig beta value of the commo stock with market portfolio return. ow you should kow the cocept of beta ad marlket portfolio.
Market portfolio is a well diversifierd portfolio of investmet. It includes varieties of securities that are listed in the stock exchange. This variation of security will eliminate company specific risk. It is known as unsystematic risk. A weel diversified portfolio has zero unsystematic risk. Thus only systematic risk is found here. It is a risk which causes from factors that are beyod the control of company of investors. Inflation, recession, natural disasters, etc. These factors will affect all firms in the ecoomy.
Now the question is which one is market portfolio. Answer is portfolio of market index. It includes best possible securities from all field of industries and services in the economy. So index is the market portfolio and return on market index is the market portfolio return.
Return on market index in excess of risk free return is market premium. If market index return is 8% and risk free return is 3%, then market portfolio premium is 8%-3%=5%. In this problem it is 6.1%.
Finally consider beta value. It is correlation between market portfolio return and return of the cocerned security. If it is 1 then both are equally risky. So premium will be equal. In this problem beta value is 1.56% So security is 156% more risky than market portfolio. Hece its premium will be 156% of market index premium.
Based on above ideas cost of equity under CAPM is calculated below:
Cost of equity = Risk free return + Beta value x market risk premium
= 3.8% + 1.56 x 6.1%
= 3.8%+9.516%
=13.316%
Answer: Cost of equity is 13.3% (rounded off). So correct option is (d).
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Answer of part (b):
In this problem it is not possible to estimate cost of equity by using CAPM approach. But company has a bond which requires an yield of 11.5%. Risk premium of the firm stock over this bond is 3.5%. Here stock must be more risky tha bond. Bond receives interest. It is payable, even there is a loss. But stock will get dividend. It is payable only when there is profit.
Thus add the premium with bond yield to get cost of equity. Hence the answer is:
Cost of equity = Yield on bond + Equity premium
= 11.5% + 3.5%
= 15.0%
Answer: Correct option is (c) where return is 15%.
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