Let us suppose that a company is considering two mutually exclusive options, option A and option B.
The cash flows for each would be as follows:
Year Option A Option B
$ $
0 Capital outlay (10 200) (35 250)
1 Net cash inflow 6 000 18 000
2 Net cash inflow 5 000 15 000
3 Net cash inflow 3 000 15 000
The company's cost of capital is 16 per cent.
Solution
The NPV of each project is calculated below:
Option A Option B
Year Discount factor at
16% Cash
flow Present
value Cash
flow Present value
$ $ $ $
0 1.000 (10 200) (10 200) (35 250) (35 250)
1 0.862 6 000 5 172 18 000 15 516
2 0.743 5 000 3 715 15 000 11 145
3 0.641 3 000 1 923 15 000 9 615
NPV = +610 NPV = +1 026
The DCF yield (IRR) of option A is 20% and the yield of option B is only 18% (workings not shown). On a comparison of NPVs, option B would be preferred, but on a comparison of IRRs, option A would be preferred.
This situation can be illustrated diagrammatically:
Figure 3
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Therefore, in the case of mutually exclusive projects where NPV and IRR rankings appear to conflict, the NPV approach should be used to decide between them.
Of course, if the projects were independent all this would be irrelevant since under the NPV rule both would be accepted and the organisation would be indifferent as to the order in which they were accepted.
4.4 The NPV method and shareholder wealth creation
The NPV method of project appraisal is consistent with the financial objective of maximising
shareholder wealth. Given certain assumptions, the value of a company should be expected to increase by the NPV of any projects that it undertakes.
The superiority of the NPV method of investment appraisal is that it provides a measurement of the expected increase in the value of a company, and so the increase in shareholder value, that might be expected from an investment. This is an important point, and is worth studying carefully.
Suppose that you invest $1 000 and want to earn a return of 10% per annum. If you are offered the chance to invest in a one-year project that will pay back $1 100 after one year, the investment will provide the 10%
return you are looking for, and you will therefore think that it is worth the $1 000 that it will cost.
Suppose, however, that you are offered an investment with exactly the same risk characteristics that will pay back $1 200 after one year, on a $1 000 investment. This second investment will be more attractive, because it will provide a return higher than the 10% you are looking for. In NPV terms, the investment would have a positive net present value.
Year Cash flow Discount factor at 10% Present value
$ $
0 (1 000) 1.000 (1 000)
1 1 200 0.909 1 091
NPV 91
If you acquire this investment for $1 000, another investor who also wants a return of 10% might
immediately offer to buy it from you. He will offer more than $1 000. To obtain a return of at least 10% on his investment, this other investor will be prepared to offer you up to $1 091 ($1 200/1.10). If you sell at this price, you will have made $91 on your investment. In other words, you will have increased your wealth by $91. This increase in wealth is the NPV of the investment.
The same principle applies to investments by companies, for the same reason. If a project earns a return in excess of the returns expected by the providers of finance, the surplus belongs to the shareholders. The shareholders will expect this additional return to be paid to them as dividends, or reinvested by the
company to provide even higher returns and dividends in the future. Either way, the perceived value of their investment will go up, and it should be expected to go up by the amount of the project NPV.
4.4.1 The fundamental theory of share values
The connection between a project NPV and changes in the total wealth of shareholders can be stated as a fundamental theory of share values.
Definition
The fundamental theory of share values states that the market price of shares reflects investors’
expectations of what the future returns from the shares will be. The share price represents the present value of all future returns, discounted at the investors’ yield requirements (the cost of equity).
We will consider this in more detail in Chapter 6.
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4.5 Summary of NPV and IRR comparison
NPV tells us the absolute $ increase in shareholder wealth from a project, assuming a given cost of capital.
IRR tells us the maximum amount that the company could afford to pay for the project finance, or the expected return of the project in % terms.
(a) Both methods give the same accept or reject decision for individual projects.
(b) The IRR method is more easily understood by non-financial managers.
(c) NPV is simpler to calculate than IRR.
(d) IRR ignores the relative sizes of investments.
(e) NPV is the preferred method for deciding between mutually exclusive projects.
Despite the advantages of the NPV method over the IRR method, the IRR method is widely used in practice. Even so, the NPV method is superior because it focuses on the measurement of shareholder wealth.
5 Multiple methods of investment appraisal
Section overview
• Some businesses employ multiple methods of investment appraisal. They may use
payback/discounted payback to demonstrate liquidity, NPV or ROCE to demonstrate commercial viability and IRR to demonstrate the risk inherent in the NPV assessment as a result of the potential for interest rate changes.
Throughout these first two chapters we have considered five different investment appraisal methods and each has its own advantages and disadvantages.
(a) Return on capital employed – The return on capital employed method has the advantages of being easy to calculate, easy to understand and clearly demonstrates profitability. However it takes no account of cash flow timings, differing project lives or the size of initial investment needed.
(b) Payback period – The payback period has the advantages of being easy to calculate and
understand. It also considers the earlier (more certain) cash flows and is useful if there are liquidity problems. However, the measure ignores completely all cash flows outside the payback period and completely ignores the timing of cash flows within the period.
(c) Discounted payback period – The discounted payback method of project evaluation is similar to the normal payback method, except that it allows for the time value of money as it will only
recommend a project for investment if its NPV is expected to be positive. It gives recognition to the fact that for many companies liquidity is important, and projects need to provide returns fairly quickly, however it still ignores cash flows outside the payback period and hence the overall return from the project.
(d) NPVs – NPVs consider all cash flow returns from a project and their timings, cash being a much less subjective measure than profits. Unfortunately, NPVs are harder to calculate and harder for non-financial managers to understand. In addition, a number of uncertainties arise, e.g. regarding exact cash flow timings or future interest rates, and it is often necessary to make some assumptions to complete any calculations.
(e) IRRs – The IRR or yield is an easier idea for non-financial managers to interpret than the NPV. It gives an indication of the sensitivity of the project to interest rate changes. It cannot, however, be
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liquidity, NPV to demonstrate commercial viability and IRR to demonstrate the risk inherent in the NPV assessment as a result of the potential for interest rate changes.
Where multiple methods are used, however, the question arises of how the results can be assessed to decide on a project or, more awkwardly, how to decide between projects. As we have already seen with mutually exclusive projects the highest IRR and the highest NPV do not necessarily coincide, and this fact can be extended to all of the techniques. The ideal project would have the highest ROCE, the shortest payback period, the highest NPV and highest IRR, but when assessing a range of alternatives this is unlikely to be the case.
If multiple methods are to be used then it will be important to have a pre-determined approach for prioritising the various results, although this will inevitably be somewhat subjective, based on opinions and experience.
6 Sensitivity analysis
Section overview
• Sensitivity analysis assesses how responsive the project's NPV is to changes in the variables used to calculate that NPV. This helps identify the critical estimates in the project forecast.
6.1 Need for sensitivity analysis
Definition
Sensitivity analysis is one method of analysing the risk surrounding a capital expenditure project and enables an assessment to be made of how responsive the project's NPV is to changes in the variables that are used to calculate that NPV.
Any investment appraisal technique is based on forecasts or estimates. The NPV could depend on a number of uncertain independent variables:
The basic approach of sensitivity analysis is to calculate the project's NPV under alternative assumptions to determine how sensitive it is to changing conditions.
An indication is thus provided of those variables to which the NPV is most sensitive (critical variables) and the extent to which those variables may change before the investment results in a negative NPV.
Therefore, sensitivity analysis provides an indication of why a project might fail. Management should review critical variables to assess whether or not there is a strong possibility of events occurring which will lead to a negative NPV. Management should also pay particular attention to controlling those variables to which the NPV is particularly sensitive, once the decision has been taken to accept the investment.
6.2 Approach to sensitivity analysis
A simple approach to deciding which variables are critical is to calculate the sensitivity of the NPV to each variable in turn:
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Formula to learn
The formula to apply is as follows:
Sensitivity =
The resulting percentage indicates how far the variable can change before the NPV becomes zero.
The lower the percentage, the more sensitive NPV is to that project variable as the variable would need to change by a smaller amount to make the project non-viable.