Question

In​ mid-2009, Rite Aid had​ CCC-rated,10​-year bonds outstanding with a yield to maturity of 17.3%. At the​ time, similar maturity Treasuries had a yield of 3%. Suppose the market risk premium is 4% and you believe Rite​ Aid's bonds have a beta of 0.31. The expected loss rate of these bonds in the event of default is 57%.

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

7.2 %7.2%​,

while similar maturity Treasuries had a yield of

1.4 %1.4%.

What probability of default would you estimate​ now?

Answer 1

We can calculate the desired result as follows

a) Yield to Maturity of bond = 17.30%

Risk Free rate = 3%

Market Risk Premium = 4%

Beta = 0.31

Loss on bond in case of default = 57%

The required rate of return = risk free rate +(beta*Market Risk Premium)

= 3% + (0.31*4%) = 4.24%

Probability of default as per Yield to maturity of bond:

= Yield to Maturity of bond - required rate of return / Loss on bond in case of default

= 17.30% - 4.24% / 57%

= 13.06% / (0.57) = 22.91%

The probability of default is 22.91%.

b) Probability of default when Yield = 7.2% and Risk free rate = 1.4% is

The required rate of return = risk free rate +(beta*Market Risk Premium)

= 1.4% + (0.31*4%) = 2.64%

= Yield to Maturity of bond - required rate of return / Loss on bond in case of default

= 7.20% - 2.64% / 57%

= 4.56 / 0.57 = 8%

So, the probality now is 8%.

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