Question

In​ mid-2009, Rite Aid had​ CCC-rated,66​-year bonds outstanding with a yield to maturity of 17.3%. At the​ time, similar maturity Treasuries had a yield of 4%.Suppose the market risk premium is 6% and you believe Rite​ Aid's bonds have a beta of 0.37. The expected loss rate of these bonds in the event of default is 54%.

a. What annual probability of default would be consistent with the yield to maturity of these bonds in​ mid-2009?

b. In​ mid-2015, Rite-Aid's bonds had a yield of 7.3%​, while similar maturity Treasuries had a yield of 1.7%. What probability of default would you estimate​ now? What annual probability of default would be consistent with the yield to maturity of these bonds in​ mid-2009? ​ (Round to two decimal​ places.)

c. Suppose​ Pepsico's stock has a beta of 0.57. If the​ risk-free rate is 3% and the expected return of the market portfolio is 6%, what is​ Pepsico's equity cost of​ capital?

Answer 1

a.) Calculation of Annual Probability of Default

Step -1 First step is to calculate Required Return on Investments

Required Return on Investment = Risk free rate + Beta * Market Risk Premium

Given Risk free rate = 4%

Beta = 0.37

Market Risk Premium =6 %

Required Return on Investment = 4 % + 0.37 * 6%

= 6.22%

Step -2 Calculation of Annual Probability of Default that would be consistent with yield to maturity of these bonds in mid-2009

YTM is the representation of probability of default and the current level of interest in the economy.

The Expected return if Probability is not zero should encompass the chances of default. When Deafault is zero, YTM = Expected / Required Return

Expected Return = YTM - p * Loss Rate

Given YTM = 17.3%

Expected Return ( as calculated) = 6.22 %

Loss Rate = 54 % or 0.54

Let p be the probability

6.22 = 17.3 - p* 0.54

p*0.54 = 17.3 - 6.22

p = 11.08 / 0.54

p = 20.52 %

The annual probability of default that would be consistent with the yield to maturity of these bonds in​ mid-2009 is 20.52 %

b.) Calculation of New Probability of Default

Expected Return = Risk free rate + Beta * Market Risk Premium

Expected Return = 1.7 % +.0.37 * 6%

Expected Return =3.92 %

Risk free Rate now is  1.7 %

Expected Return = YTM - p * Loss Rate

p = ( 7.3 -3.92 ) / 0.54

p = 6.26 %

Probability of default would you estimate​ now is 6.26 %

c.) Calculation of equity cost of​ capital

Equity cost of​ capital = Risk free rate + Beta * ( Return from market - Fisk free Rate)

Equity cost of​ capital = 3 % + 0.57 (6%-3% )

Equity cost of​ capital = 4.71 %