ACCA AFM Syllabus B. Advanced Investment Appraisal - Duration (Macauley duration) - Notes ^{11 / 19}

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%.

Required

Estimate the Macaulay duration of the bond.

Solution: Step by step

1. Determine Gross Redemption Yield

   = 4.2%

2. 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

3. Determine market price

   Market price = $1,079•68

4. 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