Question

In mid-2009, Rite Aid had CCC-rated, 17-year bonds outstanding with a yield to maturity of 17.3%. At the time, similar maturity Treasuries had a yield of 2%. Suppose the market risk premium is 6% and you believe Rite Aid's bonds have a beta of 0.38. The expected loss rate of these bonds in the event of default is 57%. What annual probability of default would be consistent with the yield to maturity of these bonds in mid-2009?

The required return for this investment is .......%.
(Do not round until the final answer. Then round to two decimal places.)

The annual probability of default is ......%.
(Do not round until the final answer. Then round to two decimal places.)

Answer 1

(a.) Required Return on Investments

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

Given Risk free rate = 2%

Beta = 0.38

Market Risk Premium =6 %

Required Return on Investment = 2 % + 0.38 * 6%

= 4.28%

(b.) 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 Default is zero, YTM = Expected ( Required Return)

Expected Return = YTM - p * Loss Rate

Given YTM = 17.3%

Expected Return ( as calculated) = 4.28 %

Loss Rate = 57 % or 0.57

Let p be the probability

4.28 = 17.3 - p* 0.57

p*0.57 = 17.3 - 4.28

p = 13.02 / 0.57

p = 22.84 %

The annual probability of default that would be consistent with the yield to maturity of these bonds in​ mid-2009 is 22.84 %