Question

**Calculating interest rates**

The real risk-free rate (r*) is 2.8% and is expected to remain constant. Inflation is expected to be 7% per year for each of the next four years and 6% 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 Gauge Imports 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% |

Gauge Imports Inc. issues 15-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.

12.32%

11.27%

6.05%

10.92%

Based on your understanding of the determinants of interest rates, if everything else remains the same, which of the following will be true?

A. An AAA-rated bond has less default risk than a BB-rated bond.

B. The yield on U.S. Treasury securities always remains static.

Answer #1

Inflation premium = (7%*4 years + 6%*11 years)/15 years = 6.2667%

Matrurity Risk premium = 0.1*(15-1)% = 1.4%

The liquidity premium (LP) = 1.05%

AA bond default premium = 0.80%

So,

Yield on 15 year AA bonds = 2.8%+6.2667%+1.4%+1.05%+0.80% =
12.31667% or **12.32% (1st option is correct)**

All else remaining same, the AAA rated bond has less default
risk than a AA rated bond. T**his statement is true as the
bonds are rated based on their default risk (Statement A is
true)**

The yield on U.S. Treasury securities always remains static.
This statement is not correct as yields on US treasury also changes
based on decisions of Central bank and market conditions
(**Statement B is false)**

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