Question

The real risk-free rate (r*) is 2.8% and is expected to remain constant. Inflation is expected to be 6% per year for each of the next two years and 5% thereafter. The maturity risk premium (MRP) is determined from the formula: 0.1(t - 1)%, where t is the security's maturity. The liquidity premium (LP) on all Sacramone Products Co.'s bonds is 1.05%. The following table shows the current relationship between bond ratings and default risk premiums (DRP): Default Risk Premium Rating U.S. Treasury AAA 0.60% AA 0.80% A 1.05% BBB 1.45% Sacramone Products Co. issues nine-year, AA-rated bonds. What is the yield on one of these bonds? Disregard cross-product terms; that is, if averaging is required, use the arithmetic average. 9.87% 5.45% 10.67% 9.62% Based on your understanding of the determinants of interest rates, if everything else remains the same, which of the following will be true? The yield on an AAA-rated bond will be lower than the yield on an AA-rated bond. A BBB-rated bond has a lower default risk premium as compared to an AAA-rated bond.

Answer 1

The yield on Sacramone Products Co.'s nine-year, AA-rated bonds is calculated to be 10.67%. An AAA-rated bond will have a lower yield than an AA-rated bond, and a BBB-rated bond will have a higher DRP and yield compared to an AAA-rated bond.

Step-by-step explanation:

The yield on Sacramone Products Co.'s nine-year, AA-rated bonds can be determined by summing the real risk-free rate (r*), the expected inflation rate, the maturity risk premium (MRP), the liquidity premium (LP), and the default risk premium (DRP) for the AA rating. Since inflation is expected to be 6% for the first two years and 5% thereafter, we must take an average of these rates for a nine-year bond. The MRP is given by the formula 0.1(t - 1)%, where t is 9 years for these bonds.

Firstly, average the inflation over nine years: (6% + 6% + (7 * 5%)) / 9 = 5.22%.

Add the premiums and rates: 2.8% (real risk-free rate) + 5.22% (average inflation) + 0.8% (DRP for AA rating) + 0.8% (MRP for t=9 years) + 1.05% (LP) = 10.67%.

Therefore, the yield on Sacramone Products Co.'s nine-year, AA-rated bonds is 10.67%. As for the other part of the question, since a higher credit rating denotes a lower risk of default, an AAA-rated bond will indeed have a lower yield compared to an AA-rated bond due to a lower DRP. In contrast, a BBB-rated bond will have a higher default risk premium and thus a higher yield compared to an AAA-rated bond.

Answer 2

The yield on Sacramone Products Co.'s nine-year AA-rated bond is calculated to be 10.67% after adding the risk-free rate, average inflation rate, maturity risk premium, default risk premium, and liquidity premium. The yield on an AAA-rated bond would be lower than on an AA-rated bond due to a lower default risk premium, whereas a BBB-rated bond would have a higher default risk premium compared to an AAA-rated bond.

Step-by-step explanation:

The student has asked two questions related to the yield of Sacramone Products Co.'s nine-year, AA-rated bonds, and about the relationship between bond ratings and their respective yields. To calculate the yield on Sacramone Products Co.'s bond, we must take into consideration several factors: the real risk-free rate (r*), the inflation expectations, the maturity risk premium (MRP), the default risk premium (DRP), and the liquidity premium (LP).

To deal with inflations differing over time, we'll average the inflation for the first two years with the long-term inflation rate to get the average annual inflation rate for the 9-year period, (6% + 6% + 5%(7 years))/9 years = 5.22%. Now, we can calculate the nominal risk-free rate using this average inflation rate: r* + average inflation rate = 2.8% + 5.22% = 8.02%.

Next, we consider the maturity risk premium (MRP) using the given formula: MRP = 0.1(t - 1)%, where t is 9 years, thus MRP = 0.1(9 - 1)% = 0.8%. As for Sacramone Products's bonds, we have a liquidity premium (LP) of 1.05% and DRP for AA-rated bonds of 0.80%.

The yield on the nine-year AA-rated bond is calculated by adding all the premiums to the nominal risk-free rate: Yield = Real risk-free rate + Average inflation rate + MRP + DRP + LP = 2.8% + 5.22% + 0.8% + 0.8% + 1.05% = 10.67%.

Regarding the second question, the yield on an AAA-rated bond will indeed be lower than the yield on an AA-rated bond given the lower DRP for AAA-rated bonds, and conversely, a BBB-rated bond would have a higher default risk premium compared to an AAA-rated bond.