Question

Bond X is noncallable and has 20 years to maturity, a 10% annual coupon, and a $1,000 par value. Your required return on Bond X is 8%; 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 10%. 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.) Do not round intermediate calculations. Round your answer to the nearest cent.

Answer 1

For 20 years non callable bond the price = $ 1196.36. And after 5 years its value is expected = $1171.2.

Now after 5 years its observed that a 15- year bond with same coupon payment has 10% YTM with face value of $1000 has price also = $1000.

So the net profit after 5 years would be of selling the 20 year bond for $ 1171.2 and buying a 15 year bond for $ 1000 so net profit = $ 171.2 and will be discounted for 5 years to find its PV using 8% yield. Its PV = $116.5.

So we would be willing to pay = $ 1312.87 today.