120 in annual interest, with a (Bond valuation) You own a bond that pays $120 in

Question

120 in annual interest, with a (Bond valuation) You own a bond that pays $120 in annual interest, with a $1,000 par value. It matures in 10 years. Your required rate of return is 11 percent. a. Calculate the value of the bond b. How does the value change if your required rate of return (1) increases to 15 percent or (2) decreases to 8 percent? c. Explain the implications of your answers in part (b) as they relate to interest rate risk, premium bonds, and discount bonds d. Assume that the bond matures in 4 years instead of 10 years. Recompute your answers in part (b) e. Explain the implications of your answers in part (d) as they relate to interest rate risk, premium bonds, and discount bonds

Explanation / Answer

Par Value of Bond(FV) = 1000

Periods to maturity, nper= 10 years

PMT = $120

Required return, YTM = 11%

a) Value of Bond = PV(11%,10,120,1000) = $ 1058.89

b)

1) YTM = 15%

Value of Bond = PV( 15%,10,120,1000) = $ 849.44

2) YTM = 8 %

Value of Bond = PV(8%,10,120,1000) = $ 1268.40

c)

As seen from b) as interest rates in the economy increases, the YTM increases which will reduce the value of underlying bond . This will ensure that the bond can be purchased at discount ie a Discount bond. The vice versa case when YTM decreases the value will increase providing the case for a premium bond. In the above case when the interest rate(YTM) rises above the coupon rate(120/1000=12%) it provides a discount bond and when the rate is below coupon rate it gives rise to a premium bond.

d)

Nper = 4

Value of Bond when YTM is 15% = PV(15%,4,120,1000) = 914.35

Value of Bond when YTM is 8% = PV(8%,4,120,1000) = 1132.49

e)

As seen from d) as interest rates in the economy increases, the YTM increases which will reduce the value of underlying bond . This will ensure that the bond can be purchased at discount ie a Discount bond. The vice versa case when YTM decreases the value will increase providing the case for a premium bond. In the above case when the interest rate(YTM) rises above the coupon rate(120/1000=12%) it provides a discount bond and when the rate is below coupon rate it gives rise to a premium bond. However there is one addition which is the maturity period. As observed, lower the maturity period, higher will be the value of higher yielding bond when compared to similar yielding bond and lower will be the value of lower yielding bonds of similar maturity.

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