The Dunley Corp. plans to issue? 5year bonds. It believes the bonds will have a BBB rating. Suppose AAA bonds with the same maturity have a 4% yield. If the market risk premium is 4% using the data in the tables LOADING... ?: a. Estimate the yield Dunley will have to? pay, assuming an expected 58% loss rate in the event of default during average economic times. What spread over AAA bonds will it have to? pay? b. Estimate the yield Dunley would have to pay if it were a? recession, assuming the expected loss rate is 77% at that time but the beta of debt and market risk premium are the same as in average economic times. What is? Dunley's spread over AAA? now? c. In? fact, one might expect risk premia and betas to increase in recessions. Redo part ?(b?) assuming that the market risk premium and the beta of debt both increase by 20%?, that is they equal 1.20 times their value in recessions.
Here is the chart
Annual Default Rates by Debt Rating? (19832011) 

?Rating: 
AAA 
AA 
A 
BBB 
BB 
B 
CCC 
?CCC 

Default? rate: 

Average 
?0.0% 
?0.1% 
?0.2% 
0.5 %0.5% 
?2.2% 
?5.5% 
?12.2% 
?14.1% 

In recessions 
?0.0% 
?1.0% 
?3.0% 
3.0 %3.0% 
?8.0% 
?16.0% 
?48.0% 
?79.0% 

Source?: ?"Corporate Defaults and Recovery? Rates, 1920dash–?2011," ?Moody's Global Credit Policy?, February 2012. 
Average Debt Betas by Rating and Maturity 

By rating 
A and above 
BBB 
BB 
B 
CCC 

Average beta 
?< 0.05 
0.100.10 
0.17 
0.26 
0.31 

By maturity? (BBB and? above) 
?15 Yr 
?510 Yr 
?1015 Yr 
?> 15 Yr 

Average beta 
0.01 
0.06 
0.07 
0.14 

Source?: S. Schaefer and I.? Strebulaev, "Risk in Capital Structure? Arbitrage," Stanford GSB working?paper, 2009. 
Answer)
As the chances of default in AAA bond is zero as per table 1, it can be consider as risk free return in calculation
answer a)
yield of Dunley ,using CAPM
R_{d}= R_{f} + B( R_{m} R_{f})
R_{d} = 4+ 0.01* 4 =4.04%
Actual yield net to chances of default , Y = R_{d} + P(L) ,where is P= probability of default , L = chances of loss
Y = 4.04 + 0.5 *(0.58) =4.33%
Spread over AAA rated bond
4.33  4 = 0.33 %
Answer b) in the recession period ,
Only change in value of P = 3%
Chance of loss , L= 77%
Y=4.04 + 3 *(0.77) = 6.35
Spread = 6.35 4 = 2.35%
Answer c)
Increse in Beta and market risk premium by 20%
new beta = 0.01 * 1.2= 0.012
risk pre = 4 *1.2 = 4.8
R_{d} = 4 + 0.012 *4.8 =4.0576
New yield ,
Y=4.0576 + 3 *(0.77) = 6.3676
Spread = 6.3676 4 = 2.3676%= 2.37%
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