Question

3. The real risk-free rate is 3%, and inflation is expected to be 4% for the next 2 years. A 2-year Treasury security yields 8.3%. What is the maturity risk premium for the 2-year security? Round your answer to one decimal place.

4. Renfro Rentals has issued bonds that have a 9% coupon rate, payable semiannually. The bonds mature in 6 years, have a face value of $1,000, and a yield to maturity of 7.5%. What is the price of the bonds? Round your answer to the nearest cent.

Answer 1

3. The maturity risk premium is computed as shown below:

= Yield on 2 year Treasury security - real risk free rate - inflation

= 8.3% - 3% - 4%

= 1.3%

4. The price of the bond is computed as shown below:

The value of the bond is computed as shown below:

The coupon payment is computed as follows:

= 9% / 2 x $ 1,000 (Since the payments are semi annually, hence divided by 2)

= $ 45

The YTM will be as follows:

= 7.5% / 2 (Since the payments are semi annually, hence divided by 2)

= 3.75% or 0.0375

N will be as follows:

= 6 x 2 (Since the payments are semi annually, hence multiplied by 2)

= 12

So, the price of the bond is computed as follows:

Bonds Price = Coupon payment x [ [ (1 - 1 / (1 + r)ⁿ ] / r ] + Par value / (1 + r)ⁿ

= $ 45 x [ [ (1 - 1 / (1 + 0.0375)¹² ] / 0.0375] + $ 1,000 / 1.0375¹²

= $ 45 x 9.522693919 + $ 642.898978

= $ 1,071.42 Approximately

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