Question

1. The real risk-free rate is 2.6%. Inflation is expected to be 2.15% this year, 4.15% next year, and 2.65% thereafter. The maturity risk premium is estimated to be 0.05 × (t - 1)%, where t = number of years to maturity. What is the yield on a 7-year Treasury note? Do not round your intermediate calculations. Round your answer to two decimal places.

2. A company's 5-year bonds are yielding 9.75% per year. Treasury bonds with the same maturity are yielding 4.85% per year, and the real risk-free rate (r*) is 2.25%. The average inflation premium is 2.2%, and the maturity risk premium is estimated to be 0.1 x (t - 1)%, where t = number of years to maturity. If the liquidity premium is 0.95%, what is the default risk premium on the corporate bonds? Round your answer to two decimal places.

3. A 5-year Treasury bond has a 4.85% yield. A 10-year Treasury bond yields 6.7%, and a 10-year corporate bond yields 9.75%. The market expects that inflation will average 1.5% over the next 10 years (IP₁₀ = 1.5%). Assume that there is no maturity risk premium (MRP = 0) and that the annual real risk-free rate, r*, will remain constant over the next 10 years. (Hint: Remember that the default risk premium and the liquidity premium are zero for Treasury securities: DRP = LP = 0.) A 5-year corporate bond has the same default risk premium and liquidity premium as the 10-year corporate bond described. What is the yield on this 5-year corporate bond? Round your answer to two decimal places.

Answer 1

Answer to Question 1:

Real Risk-free Rate = 2.60%

Inflation Premium = Average Inflation over next 7 years
Inflation Premium = [2.15% + 4.15% + 5 * 2.65%] / 7
Inflation Premium = 19.55% / 7
Inflation Premium = 2.79%

Maturity Risk Premium = 0.05 * (t - 1)%
Maturity Risk Premium = 0.05 * (7 - 1)%
Maturity Risk Premium = 0.30%

Yield on 7-year Treasury Note = Real Risk-free Rate + Inflation Premium + Maturity Risk Premium
Yield on 7-year Treasury Note = 2.60% + 2.79% + 0.30%
Yield on 7-year Treasury Note = 5.69%

Answer to Question 2:

Real Risk-free Rate = 2.25%
Inflation Premium = 2.20%
Liquidity Premium = 0.95%

Maturity Risk Premium = 0.10 * (t - 1)%
Maturity Risk Premium = 0.10 * (5 - 1)%
Maturity Risk Premium = 0.40%

Yield on 5-year Corporate Bond = Real Risk-free Rate + Inflation Premium + Liquidity Premium + Maturity Risk Premium + Default Risk Premium
9.75% = 2.25% + 2.20% + 0.95% + 0.40% + Default Risk Premium
Default Risk Premium = 3.95%