Final answer:
The problem involves calculating the Macaulay and modified durations of a bond with specific features. By discounting each cash flow and weighting it by the time, we get the Macaulay duration and further adjust it to calculate the modified duration. Bond price and yield are inversely related to interest rate movements.
Step-by-step explanation:
The student is asking how to calculate the Macaulay and modified durations of a $100 par value bond with an 8% coupon rate, semi-annual coupon payments, 2 years to maturity, and a yield to maturity (YTM) of 6%. To do this, one must calculate the present value (PV) of each cash flow, weight these by the time until the cash flow is received, and then sum these products to get the Macaulay duration. Modified duration is then calculated by dividing the Macaulay duration by (1 + YTM/m), where 'm' is the number of compounding periods per year.
For example, if we had a similar bond issued for $3,000 at an 8% interest rate, it would pay $240 annually in interest. If the discount rate is 8%, we could calculate the present value of its future cash flows to determine what the bond is worth today. Should the interest rates rise to 11%, the bond's present value would decrease, reflecting its lower price in a higher interest rate environment.
To further illustrate, when calculating bond yield, if you bought a $1,000 bond with a coupon rate of 8%, the yield is calculated based on the annual interest payments you'd receive, plus any capital gains or losses when selling the bond before its maturity. If interest rates rise, the market price of the bond falls, as newer bonds offer higher coupon rates, reflecting in a different yield calculation.