Final answer:
To determine the bond's present value, you would discount each semiannual coupon and the principal using the 2.5% semiannual rate of return. The bond's duration is calculated by taking the weighted average time of the present values of the cash flows. Modified duration, representing the bond's volatility, is found by adjusting the Macaulay duration by the yield to maturity and number of periods.
Step-by-step explanation:
Present Value of the Bond
To calculate the present value (PV) of the bond, we use the present value formula for each semiannual coupon payment and the principal amount at the end of the bond's life. The annual coupon rate is 6%, so the semiannual coupon rate is 3%, which on a $1,000 bond equals $30 per payment. The bond pays these coupons every six months for four years, resulting in eight payments. To find the PV of the bond, we discount each of these cash flows back to the present using the semiannual required rate of return which is 5% annually or 2.5% semiannually.
Duration of the Bond
Duration measures the average time it takes to receive all the present value of the bond's cash flows and is expressed in years. It accounts for the time value of money and is useful for assessing a bond's sensitivity to interest rate changes. To compute duration, we need to calculate the weighted average time until the cash flows are received and weight each time period by the present value of the cash flow at that time.
Volatility and Modified Duration
The volatility of a bond, often measured by modified duration, indicates how much the price of a bond is expected to change with a 1% change in interest rates. To calculate modified duration, we take the Macaulay duration and divide it by (1+y/n), where y is the yield to maturity and n is the number of coupon periods per year. The result indicates the percentage change in the bond's price for a 1% change in yield. It helps investors understand the risk of a bond investment based on interest rate movements.