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 10%; 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 10.5%. 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.) Do not round intermediate calculations. Round your answer to the nearest cent.

Answer 1

Number of Years of maturity = 15
YTM is 10.5%
Coupon =10%*1000 = 100
We need to find price of this 15 year bond = PV of Coupons + PV of Par Value =100*(1-(1+10.5%)^-15 )/10.5% + 1000/(1+10.5%)¹⁵ = 963.03

Sales value of Bond after 5 years of purchase = 963.03
YTM = 10%
Current price of Bond X = PV of coupons + PV of Market value of bond after 5 years = 100*(1-(1+10%)^-5 )/10% + 963.03/(1+10%)⁵ = 977.05

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