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Investment appraisal – Discounted cash flow techniques

Question 12

IRR of an annuity

A project will earn net cash flows of $4,000 for 5 years. The initial capital cost
of the project is $17,000. Calculate the project’s IRR.

An initial NPV calculation is set up as follows:

Time Cash flow discount factor Present value

t0 (17,000) 1 (17,000)

t1-5 4,000 ?

At the IRR, the NPV will be $0 so we can fill in more figures as follows:

Time Cash flow discount factor Present value

t0 (17,000) 1 (17,000)

t1–5 4,000 ? 17,000

–––––––

NPV 0

Now we can work out what the 5 year annuity factor must be:

$17,000/$4,000 = 4.25

Then look on the annuity tables to see what percentage has an annuity factor
closest to this for 5 years.

5% = 4.329, 6% = 4.212, 7% = 4.1

So the IRR is closest to 6%

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