7. Calculating interest rates The real risk-free rate (r*) is 2.80% and is expec

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7. Calculating interest rates

The real risk-free rate (r*) is 2.80% and is expected to remain constant into the future. Inflation is expected to be 5.10% per year for each of the next two years and 3.90% thereafter.

The maturity risk premium (MRP) is determined from the formula: 0.10 x (t – 1)%, where t is the security’s maturity. The liquidity premium (LP) on all Berth Construction Inc.’s bonds is 1.10%. The following table shows the current relationship between bond ratings and default risk premiums (DRP):

Berth Construction Inc. issues nine-year, AA-rated bonds. What is the yield on one of these bonds? (Hint: Disregard cross-product terms; that is, if averaging is required, use an arithmetic average.)

8.57%

8.87%

5.50%

9.67%

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 a AAA-rated bond will be higher than the yield on a BB-rated bond.

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

7. Calculating interest rates

The real risk-free rate (r*) is 2.80% and is expected to remain constant into the future. Inflation is expected to be 5.10% per year for each of the next two years and 3.90% thereafter.

The maturity risk premium (MRP) is determined from the formula: 0.10 x (t – 1)%, where t is the security’s maturity. The liquidity premium (LP) on all Berth Construction Inc.’s bonds is 1.10%. 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%

Berth Construction Inc. issues nine-year, AA-rated bonds. What is the yield on one of these bonds? (Hint: Disregard cross-product terms; that is, if averaging is required, use an arithmetic average.)

8.57%

8.87%

5.50%

9.67%

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 a AAA-rated bond will be higher than the yield on a BB-rated bond.

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

Explanation / Answer

1) Yield = r* + IP + MRP + LP + DRP

r* = 2.80%

IP (inflation premium) = (5.10% x 2 + 3.90% x 7) / 9 = 4.16666666% or 4.17%

MRP = 0.10 x (t - 1)% = 0.10 x (9 - 1)% = 0.80%

LP = 1.10%

DRP = 0.80%

Yield = 2.80% + 4.17% + 0.80% + 1.10% + 0.80% = 9.67%

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

The yield on AAA rated bonds will be actually lower than BB rated bonds, as the DRP for BB rated bonds would be higher.

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