Calculating interest rates The real risk-free rate (r*) is 2.8% and is expected

Question

Calculating interest rates 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 four 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 Smith and Carter 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 Smith and Carter Inc. issues eight-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. Based on your understanding of the determinants of interest rates, if everything else remains the same, which of the following will be true? In theory, the yield on a bond with a longer maturity will be higher than the yield on a bond with a shorter maturity. The yield on a AAA-rated bond will be higher than the yield on a BB-rated bond.

Explanation / Answer

Answer:

a) Risk free rate = 2.8%

b) maturity risk premium = 0.1(8-1)% = 0.7%

c)Liquidity premium = 1.05%

d) default risk premium = for AA bonds = 0.8%

e) Average inflation during bonds life = (5%*4+4%*4)/8 = 4.5%

So the yield is the addition of all above =

2.8%+0.7%+1.05%+0.8%+4.5% = 9.85%

The true statement is the yield on longer maturity bond will be higher than yield on shorter maturity because of longer the duration higher the risk.

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