Resultados sobre aspectos concretos de la información y los rumores en

The proper cash flows to be included in NPV calculations are the incremental cash flows caused by the project. These include the side-effects on other projects. A new project or product can partly replace (cannibalize) sales from existing projects or products. That reduction should be included in the calculations. The opposite is also possible; selling new installations can increase sales of the maintenance and repair department that services the installations. Similarly, if a project leads to additional overhead costs, the increment should be included in the project.

When an investment is made in stages, the investment outlay is spread over time as well, so that the cash outflows of the later stages have to be discounted to present. These outflows are usually known in advance; if that is the case, they can be discounted at the risk-free rate. Note that the changes in net working capital are tied to sales and, hence, just as risky as the project itself. They should be discounted at the same rate as the cash flows.

In addition to producing cash flows, a project can also generate intangible assets such as growth opportunities and reputation. The technology in the example may be exported to countries where this type of purification plant is still in operation. Or the technology

can be adapted to next-generation purification plants. These follow-on investment oppor-tunities can be very valuable and they should be part of the investment decision. They are known as real options and are analyzed in Chapter 9.

Finally, we analyzed the project as if it was all equity financed. No interest or other debt payments are mentioned in the example. Although almost all projects are partly financed with debt, it is common practice to analyze investment decisions in this way. It allows us to concentrate on the investment decisions and to postpone the financing decision to a later stage. As we shall see in Chapter 6, the effects of the way a project is financed are mainly accounted for in the discount rate, not in the cash flows.

Other investment criteria

The NPV is a theoretically correct criterion with which to evaluate investment proposals.

This means that it leads to the correct decisions. The value of the firm will be maximized when all available proposals with a positive net present value are accepted. It rejects all proposals that do not ‘earn’ the opportunity cost of capital, for example the return on equal-risk investments available in the market.

In practice, some other investment criteria are used as well, but they do not live up to the same standard. One of these is the book rate of return in the bottom row of Table 2.6.

The average book return of the project is 17.5 + 84 + 21/(205 + 150 + 100) = 0.269 or 26.9 per cent. This criterion has three major deficiencies. First, it uses accounting returns instead of cash flows. Second, it ignores the fact that late returns are less valuable than early ones. Third, it contains no market-based required rate of return; the user has to set his or her own target rate.

A second criterion (apparently) used in practice is the payback period. This is defined as the time it takes to recover the investment outlay. The shorter that period is, the more attractive the investment is. For the example project the payback period is a little under two years, as the cumulative cash flow after two years is 72.5 + 134 = 206.5. Obviously, this method does not discount cash flows and it completely ignores the cash flows after the payback period. Since these later cash flows can be extremely large or extremely negative, it is hard to see the rationale for this method.

A third criterion used in practice is the internal rate of return (IRR). This is the discount rate that gives a net present value of zero. The IRR for the example project is found by solving:

−190 + 72.5

(1 + r) + 134

(1 + r)² + 121 (1 + r)³ = 0

for r, which gives r = .3 or 30 per cent. The IRR is often used in combination with the decision rule to accept a project when the IRR is greater than the opportunity cost of capital. This will lead to correct decisions for normal cash flow patterns. Normal means that the investment cash outflow comes first and the inflows later. If that order is reversed, a negative IRR may result, or the decision rule may have to be reversed (accept a project when the IRR is smaller than the opportunity cost of capital). If the cash flow pattern changes sign more than once, there are multiple rates of return that give zero NPV.

29 2.4 Utility and risk aversion Economic depreciation

Although not necessary for investment decisions, it is perfectly possible to calculate a cash flow present value for each year of the project’s life. The year-to-year differences between these values are known as economic depreciation, the loss in project value as time progresses and more and more of the project value is realized. The calculations are straightforward and shown in Table 2.8. As we have just calculated, the discounted cash inflows have a present (i.e. end-of-year-0) value of 205.7. After one year, the first cash flow of 72.5 is realized and the two remaining cash flows of 134 and 121 are then one and two years away. They have an end-of-year-1 value of:

134

1.25+ 121

1.25² = 184.6

The difference between both end-of-year values, 184.6 − 205.7 = −21.1, is the economic depreciation of the project over the first year. Similarly, after two years there is only one remaining cash flow, which has an end-of-year-2 value of 121/1.25 = 96.8. This gives an economic depreciation over the second year of 96.8 − 184.6 = −87.8, etc. The profit from the project in any year is the cash flow plus the change in project value. Expressed as a fraction of the beginning-of-year project value this is the return on investment.

Table 2.8 Economic depreciation of the project

year 0 1 2 3

1 Cash inflows from project 72.5 134 121

2 PV cash inflows, year end 205.7 184.6 96.8 0

3 PV cash inflows, year begin 0 205.7 184.6 96.8

4 Economic depreciation (2 − 3) – −21.1 −87.8 −96.8

5 Profit from project (1 + 4) – 51.4 46.2 24.2

6 Return on investment (5/3) 0.25 0.25 0.25

The economic depreciation in Table 2.8 changes from year to year, but the economic profits change in proportion to the remaining value of the project. Hence, the return on investment is constant and equal to the opportunity cost of capital. In this representation, each of the three years of the project’s life is as good as any other. In the account-ing representation of the project in Table 2.6, depreciation is constant while the return on investment goes wildly up and down. This makes the second year stand out as an exceptionally good one (probably with bonuses all around).

2.4 ... Utility and risk aversion

Utility is a central concept in economics and although its role in finance is more modest, it is used to make certain financial decisions. Risk aversion is at the heart of finance and many models are formulated to find the proper price of risk. This section introduces both concepts in a simple economic setting.