Calculating interest rates The real risk-free rate (r*) is 2.8% and is expected to remain constant. Inflation is expected to be 8% per year for each of the next five years and 7% 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 Smith and Carter Inc.’s bonds is 1.05%. The following table shows the current relationship between bond ratings and default risk premiums (DRP): Rating Default Risk Premium U.S. Treasury — AAA 0.60% AA 0.80% A 1.05% BBB 1.45% Q1. Smith and Carter Inc. issues fifteen-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. a. 12.33% b. 13.38% c. 6.05% d. 11.98% Q2. Based on your understanding of the determinants of interest rates, if everything else remains the same, which of the following will be true? Option a. A BBB-rated bond has a lower default risk premium as compared to an AAA-rated bond. Option b. The yield on an AAA-rated bond will be lower than the yield on an AA-rated bond.
Calculating interest rates
The real risk-free rate (r*) is 2.8% and is expected to remain constant. Inflation is expected to be 8% per year for each of the next five years and 7% 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 Smith and Carter Inc.’s bonds is 1.05%. The following table shows the current relationship between bond ratings and default risk premiums (DRP):
| Rating | Default Risk Premium |
|---|---|
| U.S. Treasury | — |
| AAA | 0.60% |
| AA | 0.80% |
| A | 1.05% |
| BBB | 1.45% |
Q1. Smith and Carter Inc. issues fifteen-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.
a. 12.33%
b. 13.38%
c. 6.05%
d. 11.98%
Q2. Based on your understanding of the determinants of interest rates, if everything else remains the same, which of the following will be true?
Option a. A BBB-rated bond has a lower default risk premium as compared to an AAA-rated bond.
Option b. The yield on an AAA-rated bond will be lower than the yield on an AA-rated bond.
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