Question

# Bond X is noncallable and has 20 years to maturity, an 8% annual coupon, and a \$1,000 par value. Your required return on Bond X is 9%; if you buy it, you plan to hold it for 5 years. You (and the market) have expectations that in 5 years, the yield to maturity on a 15-year bond with similar risk will be 7.5%.How much should you be willing to pay for Bond X today? (Hint: You will need to know how much the bond will be worth at the end of 5 years.)

Solution

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$\textbf{Analysis of given information:}$

You plan to hold a 20-year bond for 5 years. In 5 years, you expect similar bonds (at 15 years maturity at that time) to have a yield to maturity of 7.5%.

We can assume that you will sell the bonds in 5 years. The price at which you will sell the bonds will be equal to the price of the similar bonds after 5 years.

$\textbf{Solution:}$

We first compute for the price of similar bonds after 5 years $\textbf{\color{#4257b2}{(a)}}$, and then use it as the `future value' of the bonds that we are planning to buy today, and substitute it to the bond price formula $\textbf{\color{#4257b2}{(b)}}$.

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