Question

Calculating interest rates problem:

3. Calculating interest rates The real risk-free rate (r*) is 2.8% and is expected to remain constant. Inflation is expected to be 6% per year for each of the next four years and 5% thereafter. The maturity risk premium (MRP) is determined from the formula: 0.1(t - 10%, where t is the security's maturity. The liquidity premium (LP) on all Harrington Horticulture Co.'s bonds is 1.05%. The following table shows the current relationship between bond ratings and default risk premiums (DRP): Default Risk Premium Rating U.S. Treasury AAA AA 0.60% 0.80% 1.05% 1.45% Harrington Horticulture Co. issues ten-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. 5.55% 9.90% O 10.05% O 10.95% 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 U.S. Treasury securities always remains static. In theory, the yield on a bond with a longer maturity will be higher than the yield on a bond with a shorter maturity.

Answer 1

Yield = real risk free rate + inflation premium + maturity premium + Liquidity risk premium + Default risk premium

Average inflation premium for next 9 years = (6% x 4 + 5% x 6) / 10 = 5.4%

Maturity premium for 10 years maturity = 0.1(t - 1)% = 0.1 x (10 - 1)% = 0.9%

Liquidity risk premium = 1.05%

Default risk premium corresponding to AA rating = 0.8%

Hence, Yield = 2.8% + 5.4% + 0.9% + 1.05% + 0.8% = 10.95%

Hence, the correct answer is the last option.

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The correct answer is :

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 longer maturity will have a relatively higher maturity premium, MRP and hence higher yield if every other variable remains constant.