BUSF_A01.qxd

Chapter 4 • Investment appraisal methods

What, though, if the project were £120 initial outlay, followed by inflows of £69 at

the end of each of the following two years?

Despite the total inflows still being £138, the IRR is not 15 per cent because this pro-

ject runs over two years, not one. Nor is it 7.5 per cent (that is, 15 ÷2) because much

of the £120 is repaid in year 1 and so is not outstanding for both years. In fact, the first

£69 represents a payment of the intereston the investment during the first year plus a

repayment of part of the capital(the £120). By the same token, the second £69 repres-

ents interest on the remaining capital outstanding after the end of year 1, plus a sec-

ond instalment of capital such that this second instalment will exactly repay the £120

initial outlay.

A moment’s reflection should lead us to conclude that the IRR is closely related to

the NPV discount rate. In fact, the IRR of a project is the discount rate that if applied

to the project yields a zero NPV. For our example it is the solution for rto the follow-

ing expression:

− 120 ++ = 0

This equation could be solved using the standard solution to a quadratic equation: not

a difficult matter. (The answer, incidentally, is r=0.099, or 9.9 per cent.)

When we look at, say, the Zenith (from Example 4.1), the IRR of an investment in

that machine is rin the following equation:

−20,000 +++++= 0

Solving for rhere is not so easy, and in fact some iterative (trial and error) approach

becomes the only practical one. Thus we solve for rby trying various values of runtil

we find one that satisfies, or almost satisfies, the equation. On page 84, we calculated

that the Zenith has an NPV of +£479 when discounted at 12 per cent. This tells us that

it must have an IRR of above 12 per cent, because the higher the discount rate, the

lower the present value of each future cash inflow. How much above 12 per cent we

do not know, so we just pick a rate, say 14 per cent.

6,000

(1 + r)^5

7,000

(1 + r)^4

6,000

(1 + r)^3

6,000

(1 + r)^2

4,000

(1 + r)

69

(1 + r)^2

69

(1 + r)

What is the IRR of a project where an initial investment of £120 is followed a year later by a

cash inflow of £138 with no further inflows?

Example 4.3

Obviously it is:

138 − (^120) × 100 =15%
120
Solution