New Generation Public utilities issued a bond with a $1,000per value that pays $

Question

New Generation Public utilities issued a bond with a $1,000per value that pays $30 in annual interest. It matures in 20 years. Your required rate of return is 4 percent.

a.       Calculate the value of the bond.

b.      How does the value change in your required rate of return (1) increases to 7 percent or 92) decreases to 2 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 10 years instead of 20 years. Re-compute 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

a. Value of bond can be calculated in Excel as =PV(4%,20,-30,-1000). This is equal to 864.10

b. Value at 7% can be calculated in Excel as =PV(7%,20,-30,-1000). This is equal to 576.24

Value at 2% can be calculated in Excel as =PV(2%,20,-30,-1000). This is equal to 1163.51

c. When yield (or required rate of return) is greater than the coupon rate (in this case 3%), then the bond becomes a discount bond (less than par value). When yield (or required rate of return) is lesser than the coupon rate (in this case 3%), then the bond becomes a premium bond (greater than par value). So we see when return rate increases from 4% to 7%, it goes further away from coupon rate and hence goes from a discount bond to a deep discount bond. Similarly, when it goes from 4% to 2%, the discount bond becomes a premium bond.

d. Value at 4% and 10 years can be calculated in Excel as =PV(4%,10,-30,-1000). This is equal to 918.89

Value at 7% can be calculated in Excel as =PV(7%,20,-30,-1000). This is equal to 719.06

Value at 2% can be calculated in Excel as =PV(2%,20,-30,-1000). This is equal to 1089.83

e. The values of discount bonds seen in (d) are higher than the corresponding prices in (a). Similarly, the value of the premium bond seen in (d) is lower than the corresponding price in (a). So when the duration is lower, the bond values tend to be closer to the par value as compared to high duration bonds. We also see that the variation in bond values among the 3 10-year bonds is lower as compared to the variation in the 3 20-year bonds. This is because the duration (or interest rate sensitivity) is higher in longer duration bonds.

Hope this helped ! Let me know in case of any queries.

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