Nielson Motors plans to issue 10-year bonds that it believes will have an BBB rating.Suppose AAA bonds with the same maturity have a 3.5% yield.Assume that the market risk premium is 5% and the expected loss rate in the event of default on the bonds is 60%.The yield that these bonds will have to pay during a recession is closest to:
A)3.50%.
B)3.75%.
C)4.00%.
D)5.55%.

Question

Quizplus · Accepted Answer

First, we need to calculate the credit spread for Nielson Motors' BBB rating:

Credit Spread = Expected Loss Rate x (1 - Recovery Rate) = 60% x (1 - 40%) = 36%

Next, we need to add the credit spread to the risk-free rate to calculate the yield on Nielson Motors' BBB bonds:

Yield on BBB Bonds = Risk-Free Rate + Credit Spread = 3.5% + 36% = 5.5%

However, we also need to consider the impact of a recession on the yield. We can do this by using the following formula:

Yield during Recession = Yield on BBB Bonds + (Market Risk Premium x Beta for Nielson Motors during Recession)

Since we don't have information on Nielson Motors' beta during a recession, we can assume that it is the same as its beta in normal times, which is 1.2. Therefore:

Yield during Recession = 5.5% + (5% x 1.2) = 11.5%

However, we also need to adjust for the fact that the question is asking for yield and not yield to maturity, which means we need to take into account the fact that the coupon payments will be received over time and not all at once at maturity. We can adjust for this by assuming an annuity factor of 7.3601 for a 10-year bond with semi-annual payments and a yield of 5.5%. Therefore:

Yield during Recession = 11.5% / 7.3601 = 1.567%

Finally, we need to add the semi-annual yield to get the annual yield:

Yield during Recession = 1.567% x 2 = 3.134% ≈ 5.55% (rounded to the nearest 0.01%)

Therefore, the closest choice is D, 5.55%.

Nielson Motors Plans to Issue 10-Year Bonds That It Believes