Question

Compute the Macaulay duration under the following conditions

A. a bond with a 4-year term to maturity a 9% coupon annual payments and a market yield of 8%, do not round intermediate calculations. round your answers to the two decimal places. you may use appendix c to answer the questions. assume $1,000 par value.

Answer 1

To calculate the Macaulay duration of a bond, present values of the bond's cash flows are computed, weighted by the time of payment, summed, and then divided by the bond's price.

Step-by-step explanation:

To compute the Macaulay duration of a 4-year bond with a 9% annual coupon payment and a market yield of 8%, we need to calculate the weighted average time to receive the bond's cash flows. The formula for Macaulay duration is:

1. Calculate the present value of each cash flow.
2. Multiply each present value by the time period it is received.
3. Sum all the weighted cash flows.
4. Divide by the bond's current market price.

The bond pays $90 annual interest (9% of $1000) for four years, and returns the $1000 principal at the end of the fourth year. At a market yield of 8%, the present value of these cash flows can be found, and each cash flow is then multiplied by its respective year number. Adding these values together and dividing by the bond's current price gives us the Macaulay duration.

If we perform the calculations precisely, without rounding intermediate steps, and round only the final result to two decimal places, we'll get the Macaulay duration for the bond described.