Final answer:
The average expected inflation rate over the next 4 years is 2.5%. The yield on a 4-year Treasury bond is 5.8%. The yield on a 4-year BBB-rated corporate bond with a liquidity premium is 7.6%. The yield on an 8-year Treasury bond is 6.2%. The yield on an 8-year BBB-rated corporate bond with a liquidity premium is 8%.
Step-by-step explanation:
(a) The average expected inflation rate over the next 4 years can be calculated by taking the average of the expected inflation rates for each year. For the next 3 years, the inflation rate is expected to be 2% per year, and for the following 5 years, it is expected to be 4% per year. Therefore, the average expected inflation rate for the next 4 years is [(2% + 2% + 2% + 4%)/4] = 2.5%.
(b) The yield on a 4-year Treasury bond can be calculated by adding the components of the interest rate: the real risk-free rate, the expected inflation rate, and the maturity risk premium. Given that the real risk-free rate is 3% and the average expected inflation rate is 2.5%, the nominal risk-free rate is 3% + 2.5% = 5.5%. Additionally, the maturity risk premium for a 4-year bond is 0.1 × (4 - 1)% = 0.3%. Therefore, the yield on a 4-year Treasury bond is 5.5% + 0.3% = 5.8%.
(c) The yield on a 4-year BBB-rated corporate bond with a liquidity premium can be calculated in the same way as the yield on a Treasury bond. However, we need to add the default risk premium and the liquidity premium. Given that the default risk premium for a BBB-rated bond is 1.3% and the liquidity premium is 0.5%, the total additional premium is 1.3% + 0.5% = 1.8%. Therefore, the yield on a 4-year BBB-rated corporate bond with a liquidity premium is 5.8% + 1.8% = 7.6%.
(d) The yield on an 8-year Treasury bond can be calculated using the same formula. The maturity risk premium for an 8-year bond is 0.1 × (8 - 1)% = 0.7%. Therefore, the yield on an 8-year Treasury bond is 5.5% + 0.7% = 6.2%.
(e) Finally, the yield on an 8-year BBB-rated corporate bond with a liquidity premium can be calculated by adding the default risk premium and the liquidity premium to the yield on a Treasury bond. Therefore, the yield on an 8-year BBB-rated corporate bond with a liquidity premium is 6.2% + 1.3% + 0.5% = 8%.