BUSF_A01.qxd

Internal rate of return

Year Cash flow Present value

££

0 (20,000) (20,000)

1 3,509

2 4,617

3 4,050

4 4,145

5 3,116

NPV (563)

As the NPV when the cash flows are discounted at 14 per cent is negative, the dis-
count rate that gives this project a zero NPV lies below 14 per cent and apparently
close to the mid-point between 14 and 12 per cent. We can prove this by discounting
at 13 per cent:

Year Cash flow Present value

££

0 (20,000) (20,000)

1 3,540

2 4,699

3 4,158

4 4,293

5 3,257

NPV (53)

Given the scale of the investment, an NPV of minus £53 is not significantly differ-
ent from zero, so we can conclude that, for practical purposes, the IRR is 13 per cent.
If we wanted to have a more accurate figure, however, we could make an approx-
imation based on the following logic. Increasing the discount rate by 1 per cent (from
12 to 13 per cent) reduced the NPV by £532 (from plus £479 to minus £53). Thus,
increasing the NPV from minus £53 to zero would require a reduction in the discount
rate of 53/532 of 1 per cent, that is, about 0.1 per cent. So the IRR is 12.9 per cent. This
approach is not strictly correct because it assumes that the graph of NPV against
the discount rate is a straight line. This assumption is not correct, as can be seen in

6,000

(1 +0.13)^5

7,000

(1 +0.13)^4

6,000

(1 +0.13)^3

6,000

(1 +0.13)^2

4,000

(1 +0.13)

6,000

(1 +0.14)^5

7,000

(1 +0.14)^4

6,000

(1 +0.14)^3

6,000

(1 +0.14)^2

4,000

(1 +0.14)