A 6% coupon bond with 7 years to maturity has a yield-to-maturity of 3%. Assuming the coupons are paid semi-annually and the principal amount is equal to 100, what is the Macaulay duration of the bond (in years)?
To calculate the Macaulay duration of a bond, you first need to understand what it represents. Macaulay duration measures the weighted average time it takes to receive the cash flows from a bond, including both coupon payments and the repayment of the principal.
Here are the steps to calculate the Macaulay duration of the given bond:
1. Determine the number of periods until the bond matures: Since the bond has 7 years to maturity and coupons are paid semi-annually, there will be 14 periods (7 years * 2 periods per year).
2. Calculate the present value of each cash flow: Starting from the first period, calculate the present value of each semi-annual coupon payment using the yield-to-maturity of 3%. Since the coupon rate is 6% and payments are semi-annual, each coupon payment would be 3% of $100 (coupon rate * principal amount / 2). Use the present value formula to calculate the present value of each coupon payment.
3. Calculate the present value of the principal payment: At the end of the 14th period, the bond will mature, and the principal amount of $100 will be returned. Calculate the present value of this principal payment using the same methodology as step 2.
4. Calculate the weighted average time of these present values: Assign weights to each present value calculated in steps 2 and 3. The weight is determined by dividing each present value by the bond's current market price (which is the present value of all future cash flows). Multiply each present value by the respective weight and sum them all up.
5. Finally, divide the result obtained in step 4 by the bond's current market price to get the Macaulay duration.
Since we don't have the bond's current market price in your question, we won't be able to provide the exact Macaulay duration. However, you can follow these steps using the given information and any bond pricing software or financial calculator to calculate the Macaulay duration.