Calculate the fair present values of the following bonds, all of which pay interest semiannually, have a face value of $1,000, have 12 years remaining to maturity, and have a required rate of return of 10 percent. ( LG 3-5 ) a. The bond has a 6 percent coupon rate. b. The bond has a 8 percent coupon rate. c. The bond has a 10 percent coupon rate. d. What do your answers to parts (a) through (c) say about the relation between coupon rates and present values? ( LG 3-5 ) An important factor that affects the degree to which the price of a bond changes (or the price sensitivity of a bond changes) as interest rates change is the time remaining to maturity on the bond. A bond’s price sensitivity is measured by the percentage change in its present value for a given change in interest rates. The larger the percentage change in the bond’s value for a given interest rate change, the larger the bond’s price sensitivity. Specifically, as is explained below, the shorter the time remaining to maturity, the closer a bond’s price is to its face value. Also, the further a bond is from maturity, the more sensitive the price (fair or current) of the bond as interest rates change. Finally, the relationship between bond price sensitivity and maturity is not linear. As the time remaining to maturity on a bond increases, price sensitivity increases but at a decreasing rate. Table 3–5 presents the bond information we will be using to illustrate these relationships. In Table 3–5, we first list the fair present values of the bonds analyzed in Example 3–4. We then repeat the present value calculations using three bonds with identical characteristics except for the time to maturity: 12 years versus 14 years versus 16 years.
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