Ross et al.: Fundamentals III. Valuation of Future 7. Interest Rates and Bond of Corporate Finance, Sixth Cash Flows Valuation

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CHAPTER 7 Interest Rates and Bond Valuation 207

tells us that a relatively small change in interest rates will lead to a substantial change in the bond's value. In comparison, the one-year bond's price is relatively insensitive to interest rate changes.

Intuitively, we can see that the reason that longer-term bonds have greater interest rate sensitivity is that a large portion of a bond's value comes from the $1,000 face amount. The present value of this amount isn't greatly affected by a small change in interest rates if the amount is to be received in one year. Even a small change in the interest rate, however, once it is compounded for 30 years, can have a significant effect on the present value. As a result, the present value of the face amount will be much more volatile with a longer-term bond.

The other thing to know about interest rate risk is that, like most things in finance and economics, it increases at a decreasing rate. In other words, if we compared a 10-year bond to a 1-year bond, we would see that the 10-year bond has much greater interest rate risk. However, if you were to compare a 20-year bond to a 30-year bond, you would find that the 30-year bond has somewhat greater interest rate risk because it has a longer maturity, but the difference in the risk would be fairly small.

The reason that bonds with lower coupons have greater interest rate risk is essentially the same. As we discussed earlier, the value of a bond depends on the present value of its coupons and the present value of the face amount. If two bonds with different coupon rates have the same maturity, then the value of the one with the lower coupon is proportionately more dependent on the face amount to be received at maturity. As a result, all other things being equal, its value will fluctuate more as interest rates change. Put another way, the bond with the higher coupon has a larger cash flow early in its life, so its value is less sensitive to changes in the discount rate.

Until recently, bonds were almost never issued with maturities longer than 30 years. However, in November of 1995, BellSouth's main operating unit issued $500 million in 100-year bonds. Similarly, Walt Disney, Coca-Cola, and Dutch banking giant ABN-Amro all issued 100-year bonds in the summer and fall of 1993. The reason that these companies issued bonds with such long maturities was that interest rates had fallen to very low levels by historical standards, and the issuers wanted to lock in the low rates for a long time. The current record holder for corporations appears to be Republic National Bank, which sold bonds with 1,000 years to maturity in October 1997. Before these fairly recent issues, it appears that the last time 100-year bonds had been sold was in May 1954, by the Chicago and Eastern Railroad.

We can illustrate our points concerning interest rate risk using the 100-year BellSouth issue and two other BellSouth issues. The following table provides some basic information on the three issues, along with their prices on December 31, 1995, July 31, 1996, and July 2, 2001.

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