Duration is the average time taken to recover the cash flows on an investment.
Duration measures the average time to recover the present value of the project (if cash flows are discounted at the cost of capital).
Duration captures both the time value of money and the whole of the cash flows of a project.
Projects with higher durations carry more risk than projects with lower durations.
Exam standard example (extract)
GNT Co is considering an investment in a corporate bond. The bond has a par value of $1,000 and pay coupon interest on an annual basis.
The market price of the first bond is $1,079•68.
Its coupon rate is 6% and it is due to be redeemed at par in five years.
Gross Redemption Yield is 4.2%.
Estimate the Macaulay duration of the bond.
Solution: Step by step
Determine Gross Redemption Yield
Calculate PV of the annual cash flows (interest + redemption value in the year 5)
Interest (6% x 1000=) 60 x 1•042^–1 + 60 x 1•042^–2 + 60 x 1•042^–3 + 60 x 1•042^–4 + 1,060 x 1•042^–5
PV of cash flows (years 1 to 5) = 57•58 + 55•26 + 53•03 + 50•90 + 862•91 = 1,079•68
Determine market price
Market price = $1,079•68
Calculate duration using PV calculated earlier and multiply them by number of year and then divided by market price
Duration = [57•58 x 1 + 55•26 x 2 + 53•03 x 3 + 50•90 x 4 + 862•91 x 5]/1,079•68 = 4•49 years