Question

(Bond valuation​) You are examining three bonds with a par value of ​$1 comma 000 ​(you receive ​$1 comma 000 at​ maturity) and are concerned with what would happen to their market value if interest rates​ (or the market discount​ rate) changed. The three bonds are Bond Along dash a bond with 6 years left to maturity that has an annual coupon interest rate of 9 ​percent, but the interest is paid semiannually. Bond Blong dash a bond with 11 years left to maturity that has an annual coupon interest rate of 9 ​percent, but the interest is paid semiannually. Bond Clong dash a bond with 17 years left to maturity that has an annual coupon interest rate of 9 ​percent, but the interest is paid semiannually. What would be the value of these bonds if the market discount rate were a. 9 percent per year compounded​ semiannually? b. 7 percent per year compounded​ semiannually? c. 17 percent per year compounded​ semiannually? d. What observations can you make about these​ results?

Answer 1

9%:
1. Bond Along
=(9%*1000/9%)*(1-1/1.045^12)+1000/1.045^12=1000
2. Bond Blong
=(9%*1000/9%)*(1-1/1.045^22)+1000/1.045^22=1000
3. Bond Clong
=(9%*1000/9%)*(1-1/1.045^34)+1000/1.045^34=1000

7%:
1. Bond Along
=(9%*1000/7%)*(1-1/1.035^12)+1000/1.035^12=1096.63334334596
2. Bond Blong
=(9%*1000/7%)*(1-1/1.035^22)+1000/1.035^22=1151.67124835541
3. Bond Clong
=(9%*1000/7%)*(1-1/1.035^34)+1000/1.035^34=1197.00684233823

17%:
1. Bond Along
=(9%*1000/17%)*(1-1/1.085^12)+1000/1.085^12=706.212557212446
2. Bond Blong
=(9%*1000/17%)*(1-1/1.085^22)+1000/1.085^22=607.6081765985
3. Bond Clong
=(9%*1000/17%)*(1-1/1.085^34)+1000/1.085^34=558.790288342674

Higher the ytm lower is the price and longer maturity bond more sensitive to yield changes