A $1,000 par value, 5% annual coupon bond matures in 4 years.The bond is currently priced at $965.35 and has a YTM of 6.0%.What is the Macaulay duration?

Question

Quizplus · Accepted Answer

- First we need to calculate the semi-annual coupon payment: 
5% annual coupon rate x $1,000 par value = $50 annual coupon payment 
$50 / 2 (semi-annual payments) = $25 semi-annual coupon payment

- Using the YTM of 6%, we can calculate the semi-annual discount rate: 
6% / 2 (semi-annually) = 3% semi-annual discount rate

- Using the formula for Macaulay duration: 
Macaulay duration = (1 x CF1 / (1 + y)^1) + (2 x CF2 / (1 + y)^2) + ... + (n x CFn / (1 + y)^n) / Bond price

where CF is the cash flow (semi-annual coupon payment or par value at maturity) and n is the number of periods.

- Plugging in the numbers: 
Macaulay duration = (1 x $25 / (1 + 0.03)^1) + (2 x $25 / (1 + 0.03)^2) + (3 x $25 / (1 + 0.03)^3) + (4 x $1,025 / (1 + 0.03)^4) / $965.35 
Macaulay duration = 3.68 years

A $1,000 Par Value, 5% Annual Coupon Bond Matures in 4