Question

The real risk-free rate (r*) is 2.8% and is expected to remain constant. Inflation is expected to be 5% per year for each of the next two years and 4% 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 14-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.

8.79%

9.04%

10.09%

5.95%

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

A BBB-rated bond has a lower default risk premium as compared to an AAA-rated bond.

Higher inflation expectations increase the nominal interest rate demanded by investors.

Answer 1

Question 1

Nominal yield = Real risk free rate + Inflation premium + Maturity risk premium + Default risk premium + Liquidity premium

Real risk free rate = 2.8%

Inflation premium is average of the inflation over the life of bond = [(5% * 2) + (4% * 12)]/14 = 4.14%

Maturity risk premium = 0.1(14 -1)% = 1.3%

Default risk premium (from table for AA bond) = 0.80%

Liquidity premium = 1.05%

Nominal yield = 2.8% + 4.14% + 1.3% + 0.80% + 1.05% = 10.09%

Question 2

Statement 2 is true. Higher inflation implies the inflation premium would be higher and hence higher would be the nominal yield, which is the return that an investor requires/would get.

Statement 1 is false. BBB-rated bond has a higher probability of default and hence higher risk which would imply higher yield (or return).