This is the last of the four major methods of investment appraisal found in practice. It is closely related to the NPV method in that both involve discounting future cash flows. The internal rate of return (IRR) of an investment is the discount rate that, when applied to its future cash flows, will produce an NPV of precisely zero. In essence, it represents the yield, or percentage return, from an investment opportunity.
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INTERNAL RATE OF RETURN (IRR) 169
When we discounted the cash flows of the Billingsgate Battery Company machine project at 20 per cent, we found that the NPV was a positive figure of £24,190 (see p. 165). What does the NPV of the machine project tell us about the rate of return that the investment will yield for the business (that is, the project’s IRR)?
As the NPV is positive when discounting at 20 per cent, it implies that the project’s rate of return is more than 20 per cent. The fact that the NPV is a pretty large amount suggests that the actual rate of return is quite a lot above 20 per cent. The higher the discount rate, the lower will be the NPV. This is because a higher discount rate gives a lower discounted figure.
Activity 4.14
IRR cannot usually be calculated directly. Iteration (trial and error) is the approach normally adopted. Doing this manually can be fairly laborious. Fortunately, computer spreadsheet pack- ages can do this with ease.
Despite it being laborious, we shall calculate the IRR for the Billingsgate project manually.
We have to increase the size of the discount rate in order to reduce NPV. This is because a higher discount rate gives a lower discounted figure.
Let us try a higher rate, say 30 per cent, and see what happens.
Time Cash flow
£000
Discount factor 30%
PV
£000
Immediately (time 0) (100) 1.000 (100.00)
1 year’s time 20 0.769 15.38
2 years’ time 40 0.592 23.68
3 years’ time 60 0.455 27.30
4 years’ time 60 0.350 21.00
5 years’ time 20 0.269 5.38
5 years’ time 20 0.269 5.38
NPV (1.88) By increasing the discount rate from 20 per cent to 30 per cent, we have reduced the NPV from £24,190 (positive) to £1,880 (negative). Since the IRR is the discount rate that will give us an NPV of exactly zero, we can conclude that the IRR of Billingsgate Battery Company’s machine project is very slightly below 30 per cent. Further trials could lead us to the exact rate, but there is probably not much point, given likely inaccuracies with the cash flow estimates. For most practical purposes, it is good enough to say that the IRR is about 30 per cent.
The relationship between the NPV method discussed earlier and the IRR is shown graphically in Figure 4.5 using the information relating to the Billingsgate Battery Company.
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170 CHAPTER 4 MAKING CAPITAL INVESTMENT DECISIONS
In Figure 4.5, if the discount rate is equal to zero, the NPV will be the sum of the net cash flows. In other words, no account is taken of the time value of money. However, as the discount rate increases there is a corresponding decrease in the NPV of the project. When the NPV line crosses the horizontal axis, there will be a zero NPV. That point represents the IRR.
Figure 4.5 The relationship between the NPV and IRR methods
Source: Adapted from Atrill, P. and McLaney E. (2009) Accounting: An Introduction, 5th edn, Pearson Education.
When the NPV line crosses the horizontal axis, there will be a zero NPV. The point where it crosses is the IRR.
70 60 50 40 NPV 30 (£000)
20 10
0 0 10 20
Rate of return (%)
30 40
–10
What is the internal rate of return of the Chaotic Industries project from Activity 4.2? (Hint:
Remember that you already know the NPV of this project at 15 per cent (from Activity 4.12).)
Since we know that at a 15 per cent discount rate, the NPV is a relatively large negative figure, our next trial is using a lower discount rate, say 10 per cent:
Time Cash flows
£000
Discount factor 10%
Present value
£000
Immediately (150) 1.000 (150.00)
1 year’s time 30 0.909 27.27
2 years’ time 30 0.826 24.78
3 years’ time 30 0.751 22.53
4 years’ time 30 0.683 20.49
5 years’ time 30 0.621 18.63
6 years’ time 30 0.564 16.92
6 years’ time 30 0.564 16.92
NPV (2.46) This figure is close to zero NPV. However, the NPV is still negative and so the precise IRR will be a little below 10 per cent.
Activity 4.15
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INTERNAL RATE OF RETURN (IRR) 171
We could undertake further trials to derive the precise IRR. If done manually, this can be quite time-consuming. We can, however, get an acceptable approximation to the answer fairly quickly by first calculating the change in NPV arising from a 1 per cent change in the discount rate. This is achieved by taking the difference between the two trials (that is, 15 per cent and 10 per cent) that have already been carried out (in Activities 4.12 and 4.15):
Trial Discount factor
%
Net present value
£000
1 15 (23.49)
2 10 (2.46)
Difference 5 21.03
The change in NPV for every 1 per cent change in the discount rate will be:
(21.03/5) = 4.21
The reduction in the 10% discount rate required to achieve a zero NPV would therefore be:
(2.46/4.21) * 1%= 0.58%
The IRR is therefore:
(10.00 - 0.58)% = 9.42%
However, to say that the IRR is about 9 per cent or 10 per cent is near enough for most purposes.
Note that this approach assumes a straight-line relationship between the discount rate and NPV. We can see from Figure 4.5 that this assumption is not strictly correct. Over a relatively short range, however, this simplifying assumption is not usually a problem and so we can still arrive at a reasonable approximation using the approach taken. As most businesses have computer software packages to derive a project’s IRR, it is not normally necessary to make the calculations just described.
The following decision rules are applied when using IRR:
■ For any project to be acceptable, it must meet a minimum IRR requirement. This is often referred to as the hurdle rate and, logically, this should be the opportunity cost of capital.
■ If two, or more, competing projects meet the hurdle rate, the one with the higher (or highest) IRR should be selected
Real World 4.6 gives some examples of IRRs sought in practice.
Rates of return
IRRs for investment projects can vary considerably. Here are a few examples of the expected or target returns from investment projects of large businesses:
■ Merlin Entertainments plc, the entertainments business (cinemas, Legoland, Alton Towers) targets an IRR of 14 per cent for new facilities.
■ Next plc, the fashion retailer, requires an annual IRR of 30 per cent when appraising online advertising campaigns.
Real World 4.6
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172 CHAPTER 4 MAKING CAPITAL INVESTMENT DECISIONS
■ Rentokil Initial plc, the business services provider, has an after-tax required IRR of between 13 and 15 per cent for any investments that it may be considering.
■ Draper Esprit plc, a venture capital provider, seeks an IRR of 20 per cent on its investments.
These values seem surprisingly high. A study of returns made by all of the businesses listed on the London Stock Exchange between 1900 and 2017 showed an average annual return of 5.5 per cent. This figure is the real return (that is, ignoring inflation). It would probably be fair to add at least 3 per cent to it to compare it with the targets for the businesses listed above. Also, the targets for the four businesses are probably pre-tax (the businesses do not always specify). In that case it is probably reasonable to add about a third to the average Stock Exchange returns. This would give us around 11 per cent per year. In view of this, the targets for the businesses seem rather ambitious. Next’s target is very high, though it relates to advertising campaigns.
Sources: Merlin Entertainments plc, Preliminary results 2017; Next plc, Annual report 2016, p. 13; Rentokil Initial plc, Preliminary results 2017, p. 6; Draper Esprit plc, Final results 2018; Dimson, E., Marsh, P. and Staunton, M. (2018) Credit Suisse Global Investments Returns Yearbook, 2018, p. 35.
Problems with IRR
IRR shares certain key attributes with NPV. All cash flows are taken into account and their tim- ing is logically handled. The main problem of IRR, however, is that it does not directly address the question of wealth generation. It can therefore lead to the wrong decision being made.
The IRR approach will always rank a project with an IRR of 25 per cent, for example, above that of a project with an IRR of 20 per cent. Although accepting the project with the higher percentage return will often generate more wealth, this may not always be so. This is because IRR completely ignores the scale of investment.
With a 15 per cent cost of capital, £15 million invested at 20 per cent for one year will make us wealthier by £0.75 million (15 * (20 - 15)% = 0.75). With the same cost of capi- tal, £5 million invested at 25 per cent for one year will make us only £0.5 million wealthier (5 * (25 - 15)% = 0.50). IRR does not acknowledge this point.
Which other investment appraisal method ignores the scale of investment?
We saw earlier that the ARR method suffers from this problem.
Activity 4.16
Competing projects do not usually possess such large differences in scale and so IRR and NPV normally give the same signal. However, as NPV will always give the correct signal, it is difficult to see why any other method should be used.
A further problem with the IRR method is that it has difficulty handling projects with uncon- ventional cash flows. In the examples studied so far, each project has a negative cash flow arising at the start of its life and then positive cash flows thereafter. In some cases, however, a project may have both positive and negative cash flows at future points in its life. Such a pattern of cash flows can result in there being more than one IRR, or even no IRR at all. This can make the IRR method difficult to use, although it should be said that this problem is quite rare in practice.
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