(Bond valuation) You are examining three bonds with a par value of $1,000 (you r

Question

(Bond valuation) You are examining three bonds with a par value of $1,000 (you receive $1,000 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 A a bond with 5 years left to maturity that has an annual coupon interest rate of 1 1 percent, but the it rests paid semiannual Bond B -a bond with 11 years left to maturity that has an annual coupon interest rate of 11 percent, but the interest is paid semiannually. Bond C-a bond with 16 years left to maturity that has an annual coupon interest rate of 11 percent, but the interest is paid semiannually. What would be the value of these bonds if the market discount rate were a. 11 percent per year compounded semiannually? b. 6 percent per year compounded semiannually? c. 16 percent per year compounded semiannually? d. What observations can you make about these results?

Explanation / Answer

Value of bond = Interest*PVIFA(r%,nyear) + redemption value*PVIF

For Bond A:

For Bond B

For Bond C

Summary table

Observations :

1) Bond with higher maturity fluctuates more. It means bond having higher maturity is more sensitive to interest rate changes

2) If market rate = Interest rate of bond , Bond market price= Face value of Bond

Particulars Value of bond Value If R = 11% compounded semi annually (1000*5.5%)*PVIFA(5.5%,10) + 1000*PVIF(5.5%,10)
=55*7.538 + 1000*0.5854
=414.59 + 585.4 1000 If R = 6% compounded semi annually (1000*5.5%)*PVIFA(3%,10) + 1000*PVIF(3%,10)
=55*8.530 + 1000*0.7441
=469.15 + 744.1 1213.25 If R = 16% compounded semi annually (1000*5.5%)*PVIFA(8%,10) + 1000*PVIF(8%,10)
=55*6.710 + 1000*0.4632
=369.05 + 463.2 832.25

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