Final answer:
The duration of a bond is a measure of its price sensitivity to interest rate changes and involves the present value weighted timing of cash flows. For a 5-year bond with a 5% annual coupon, the duration will be less than 5 years. If the yield to maturity rises, the bond price will decrease due to the inverse relationship between bond price and market interest rates.
Step-by-step explanation:
Calculating Bond Duration and Price Change
Let’s address the two parts of the question separately:
- Duration of the Bond: The duration of a bond measures the sensitivity of the bond’s price to changes in interest rates and serves as a weighted average time until the cash flows from the bond are received. Calculating the exact duration requires a formula that accounts for the present values of all the bond’s cash flows, weighted by the time until each cash flow occurs. However, as specific calculations are not provided here, we can state that the duration for a typical bond that pays an annual coupon is less than its actual term (less than 5 years in this case).
- Percentage Change in Bond Price: If the market-required yield to maturity (YTM) on a bond increases, the price of the bond decreases. This inverse relationship follows because the present value of the bond’s future cash flows is calculated using the required YTM. A 50 basis point increase in YTM will result in a price drop, but without specific calculations or the bond’s duration, the exact percentage cannot be determined.
For a similar example, when Ford Motor Company issues a bond with a 5-year maturity, the interest rate can be calculated by dividing the annual coupon payment by the bond's face value and then converting it to a percentage.
b. If the market interest rate rises, say from 3% to 4%, the value will decrease. This happens because as the market interest rates rise, new bonds are likely to be issued at higher rates, which makes existing bonds with lower rates less valuable.