T

CD CL

i-1-1-1-1-1-1-1-1-1-1-1-r>ci-1-1-1-1-1-1-1-1-1-1-1

11 12

Discount rate (%)

Figure 3.3 Estimating the internal rate of return for project 1.

(one either side of the true value) and using the resulting NPVs (one of which must be positive and the other negative) to estimate the correct value. Note that this technique will provide only an approximate value but, in many cases that can be sufficient to dismiss a project that has a small IRR or indicate that it is worth making a more precise evaluation.

The internal rate of return is a convenient and useful measure of the value of a project in that it is a single percentage figure that may be directly compared with rates of return on other projects or interest rates quoted elsewhere.

Table 3.6 illustrates the way in which a project with an IRR of 10% may be directly compared with other interest rates. The cash flow for the project is shown in column (a). Columns (b) to (e) show that if we were to invest £100,000 now at an annual interest rate of 10% in, say, a bank, we could withdraw the same amounts as we would earn from the project at the end of each year, column (e), and we would be left with a net balance of zero at the end. In other words, investing in a project that has an IRR of 10% can produce exactly the same cash flow as lending the money to a bank at a 10% interest rate. We can therefore reason that a project with an IRR greater than current interest rates will provide a better rate of return than lending the investment to a bank. We can also say that it will be worth borrowing to finance the project if it has an IRR greater than the interest rate charged on the loan.

Table 3.6

A project cash flow treated as an investment at 10%

Year

Equivalent investment at 10%

Project cash flow forecast

Capital at Interest Capital at End of year start of year during year end of year withdrawal

-100,000 10,000 10,000 10,000 20,000 99,000

100,000 100,000 100,000 100,000 90,000 0

10,000 10,000 10,000 10,000 9,000 0

110,000 110,000 110,000 110,000 99,000 0

10,000 10,000 10,000 20,000 99,000 0

£100,000 invested at 10% may be used to generate the cash flows shown. At the end of the 5-year period the capital and the interest payments will be entirely consumed leaving a net balance of zero.

One deficiency of the IRR is that it does not indicate the absolute size of the return. A project with an NPV of £100,000 and an IRR of 15% can be more attractive than one with an NPV of £10,000 and an IRR of 18% - the return on capital is lower but the net benefits greater.

An often quoted objection to the internal rate of return is that, under certain conditions, it is possible to find more than one rate that will produce a zero NPV. This is not a valid objection since, if there are multiple solutions, it is always appropriate to take the lowest value and ignore the others. Spreadsheets will normally always return the lowest value if provided with zero as a seed value.

NPV and IRR are not, however, a complete answer to economic project evaluation.

• A total evaluation must also take into account the problems of funding the cash flows - will we, for example, be able to repay the interest on any borrowed money and pay development staff salaries at the appropriate time?

• While a project's IRR might indicate a profitable project, future earnings from a project might be far less reliable than earnings from, say, investing with a bank. To take account of the risk inherent in investing in a project, we might require that a project earn a 'risk premium' (that is, it must earn, say, at least 15% more than current interest rates) or we might undertake a more detailed risk analysis as described in the following sections of this chapter.

• We must also consider any one project within the financial and economic framework of the organization as a whole - if we fund this one, will we also be able to fund other worthy projects?