Question

The Dunley Corp. plans to issue 5-year bonds. It believes the bonds will have a BBB rating. Suppose AAA bonds with the same maturity have a 5% yield. If the market risk premium is 4% using the data in the tables:

Rating:	AAA	AA	A	BBB	BB	B	CCC	CC-C
Default rate:
Average	0.0%	0.1%	0.2%	0.5%	2.2%	5.5%	12.2%	14.1%
In recessions	0.0%	1.0%	3.0%	3.0%	8.0%	16.0%	48.0%	79.0%
By rating	A and above	BBB	BB	B	CCC
Average beta	< 0.05	0.1	0.17	0.26	0.31
By maturity (BBB and above)		1-5 Yr	5-10 Yr	10-15 Yr	> 15 Yr
Average beta		0.01	0.06	0.07	0.14

a. Estimate the yield Dunley will have to pay, assuming an expected 55% 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 80% 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.

Answer 1

Risk free rate is not specified separately. In the absence of risk free rate, let's assume risk free rate = Yield of the AAA bonds with the same maturity = 5%. Market risk premium = 4%

a. Estimate the yield Dunley will have to pay, assuming an expected 55% loss rate in the event of default during average economic times. What spread over AAA bonds will it have to pay?

Yield on the bond = Risk free rate + Beta x Market Premium + Probability of default x Loss rate = 5% + 0.1 x 4% + 0.5% x 55% = 5.675%

Spread over AAA bonds = 5.675% - 5% = 0.675%

b. Estimate the yield Dunley would have to pay if it were a recession, assuming the expected loss rate is 80% 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?

Yield on the bond = Risk free rate + Beta x Market Premium + Probability of default x Loss rate = 5% + 0.1 x 4% + 3% x 80% = 7.800%

Spread over AAA bonds = 7.800% - 5% = 2.800%

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.

Beta = 1.20 x 0.1 = 0.12

Market premium = 1.2 x 4% = 4.8%

Yield on the bond = Risk free rate + Beta x Market Premium + Probability of default x Loss rate = 5% + 0.12 x 4.8% + 3% x 80% = 7.976%

Spread over AAA bonds = 7.976% - 5% = 2.976%