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Incorporating uncertainty

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‘Any long term major allocation of funds will be considered to be a capital investment’ (Hull 1980: 1). Examples are a five-year training programme, a major advertising campaign, an investment in R and D, as well as the classic investments in plant and equipment. Most litera- ture on capital budgeting is written as if all investments are indepen- dent, irreversible investments, the classic once-and-for-all, accept or reject, decisions based upon static expectations of cash flows and on a passive acquiescence by relevant managers in the implications of the The Investment Process and Decision Making: the Financial Perspective 75

decision. The usual starting point is a single project with, at least implicitly, a single decision maker and a single decision. A simple objective of profit or share price maximisation is commonly assumed.

Such a profile means an over-simplification of the relevant problems.

Dixit and Pindyck (1994: 3, 23–25) emphasise three characteristics shared by many investment projects:

• irreversibility – there is some element of sunk costs about any invest- ment which involves assets specific to the enterprise or industry,

• uncertainty – mostly about future net revenue streams,

• timing – there is flexibility about the timing of all investments.

The following offers a classification of relevant investments with these three factors in mind (Trigeorgis 1996: 2–3):

• Independent investments for which there is an option to defer, including staged investments, or investment by instalments, at each stage of which there is an option to delay (or to exit). Any single project involves discrete decisions spread out over time. The deliberate staging and pacing of decisions is an important matter (White 2004: 631–33). Sometimes there are natural stages in an investment project, e.g. in the exploration and development of an oil field, in the development and testing of a pharmaceutical drug or in the development of real estate. Part of such investment is the preliminary identification of a relevant project through research and development.

• Reversible investments where there is a realistic option to abandon, i.e. the relevant plant can be sold at close to its original cost. This might apply in a capital intensive industry, such as airlines, where there is a good market for the relevant capital equipment. The reversibility is limited where the investments are highly specific or where all enterprises within a sector experience the same cyclical fluctuations.

• Investments made to increase flexibility, allowing at low switching costs a change in either inputs or outputs, in some cases being based on modular development, or an expansion or contraction of scale, including a temporary closure. The first applies to any indus- try in which there is a significant energy input or in which product customisation has become important, e.g. automobiles. The second might include the fashion industry. The group includes invest- ments made as an insurance, for example deliberately built-in

overcapacity, where there is strongly seasonal demand, such as electricity generation.

• Growth investments, including any type of research and develop- ment expenditure. Such investments make possible other invest- ments, e.g. buying licenses in telecommunications, in mining exploration or development and testing in the pharmaceutical industry. They include deliberately interdependent investments, serving other investment projects, sometimes generating tem- porarily negative net cash streams. One option may be to acquire another option, creating a compoundedness of options.

The existing resources of the enterprise predispose decision makers to certain kinds of projects, already implicit in the knowledge developed in the implementation of operating projects. New projects are the result of a long process of development and learning but the trajectory of development of a new technology is not known in advance. The future learning process must be allowed for. It is illegitimate to think of the financial blueprint of an investment project as complete.

While all the factors important for domestic investment are impor- tant for international investment, there are other complicating factors (Moosa 2002):

• the different perspectives of home and host countries which may mean that the values of key variables are modified, e.g. the rate of time discount,

• greater complexity, e.g. more interactions between projects in a value adding chain,

• usually a much larger commitment of resources, raising the initial level of investment,

• greater risk, notably country risk.

The investment decision is the result of many determinants operating within the highly specific circumstances relevant to a given project. It is difficult to come up with all the information needed for an invest- ment appraisal, particularly the exact value of relevant inputs.

Uncertainty may result from an inadequate information strategy, an inability to forecast accurately, or a recognition of the unavoidable uncertainty about day-to-day returns and the likely occurrence of risk- generating events. This section considers how a company allows for the existence of such uncertainty in the valuation of an investment project.

The Investment Process and Decision Making: the Financial Perspective 77

A simple and well-tried method of taking account of the uncertainty is to vary the length of the target payback period. The greater the risk, the shorter the target period. In extreme cases the decision maker may require payback in a period as short as one to two years. This technique requires little information and little sophistication in its calculation, which explains its popularity and its weakness.

Uncertainty can be taken into account by a significant adaptation of the decision rule. There are two basic methods. They are both based on the assumption that an investment project can be delayed until uncer- tainty is reduced. The first method requires for immediate implementa- tion of the investment that its value covers the opportunity cost of losing the option of waiting. The second method includes in the esti- mation of net present value a term which allows for the value of waiting or of any other options specifically created by the investment project. The value of the option of waiting may convert a negative net present value into a positive value.

Alternatively uncertainty can be built into measurement of the inputs into net present value. Moosa refers to three – adjusting the dis- count rate, adjusting the cash flows and estimating the sensitivity of values to variations in relevant variables.

• The discount rate can include a risk premium. The problem is to determine the level of the risk premium. One rate can be applied to all cash streams or the discount rate can be varied according to the riskiness of the particular streams, with a higher premium for streams further into the future.

• Cash flows can be adjusted by ‘certainty equivalents’ which differ for different time periods. Discounting is then applied at the risk- free rate. This approach has the virtue of separating the time element from the risk element for discounting.

• Sensitivity analysis assumes an investment project with provisional values for all inputs and analyses the ability of the project to sustain positive net present values after changes in key variables. It is widely used to identify which variables have a significant effect on value. One approach is to extract from managers optimistic and pessimistic values for all key input variables, defining these in a consistent manner, for example as those for which there is a 95%

confidence that the variable will be less than the optimistic level or greater than the pessimistic level. It is not easy to extract such information from relevant managers. Doing this for all variables and estimating net present value can show whether it is worth con-

sidering the project, clearly not in the case of a negative overall outcome using optimistic inputs, or whether there needs to be time devoted to risk analysis at all, clearly not if there is a positive outcome using pessimistic inputs. It is possible to weigh the impor- tance of individual inputs and make as accurate as possible the most important variables. This is done by varying their value by a small amount, holding all others at their expected level, and esti- mating the impact on the net present value. If the results are trivial, the expected value can be used, ignoring the distribution of probabilities. Otherwise, the probabilities are important.

Such subjective probability distributions are constructed from the judgement and experience of one person or a group of people, often insider managers, but where appropriate, using the Delphi method, a panel of experts who have the ‘alleged’ virtue of objectivity. The result is a set of probability distributions for all key variables and for the key performance indicator, in this case net present value. Such distribu- tions can be constructed with the help of historical data, but the past is not often directly relevant to the future.

The procedure for extracting relevant information is critical. There are biases which can affect any information elicited from the relevant managers or stakeholders, some motivational and some cognitive (Hull 1980: 50–53). These result from the interests of the relevant managers or stakeholders and the spin they are likely to put on the estimates.

Probably the most common bias is the central bias, the tendency of managers to see too narrow a distribution for any performance indica- tor. Managers have most difficulty with extremes, particularly if the distribution is of its nature skewed.

An alternative technique is to use the Monte Carlo method to select random values for the variables in order to produce from such simulations a probability distribution of net present value. Ambitious simulations can be carried out with different values of key variables yielding a probability distribution of net present values. The level of any significant variable which produces a break-even net present value could be carefully analysed to see whether it represents a likely outcome.

A focus on the mean and variance is justified if the distributions are expected to be normal, not so under differing but likely conditions:

• if the investment has a number of associated and potentially valuable options (expansion, contraction, abandonment),

The Investment Process and Decision Making: the Financial Perspective 79

• if the relevant variables are non-linear in their impact,

• if there are dependencies between non-linear variables,

• if the number of uncertain variables is small, even just one.

All techniques share a common weakness in including uncertainty as a negative factor. They assume that in order to take account of uncer- tainty a larger risk premium should be included in the discount rate used to yield a present value, or lower cash flow values should be selected. In both cases the impact of higher risk is to reduce present value, in some cases converting a positive into a negative present value. Such techniques encourage decision makers to think of uncer- tainty as a factor always negative for any project. The greater the uncertainty, the lower the value of an investment project and the less likely that it will be implemented.

There is a sense in which the opposite it true – the greater the risk, the potentially more beneficial the project. There is usually an upside and a downside to any variation in a measure of risk. With a normal distribution, the outcomes are symmetrical. For most distributions, a larger variance offers the prospect of both more advantageous and more disadvantageous outcomes. If the downside could be avoided but the upside exploited, the project will be more advantageous, not less. The potential value of a riskier project is higher, provided that the increased upside is not matched by an increased downside. If there is flexibility in the timing of an investment the option to delay can deliver value, particular by revealing more information on the likely outcome. If the worse outcome occurs, the possibility of exit, at least at a low cost, can limit the downside. If the better outcome even- tuates, the project can go ahead. The so-called cone of uncertainty widens the longer we look into the future, so that the longer we wait the greater the possibility of an upside (Amram and Kulatikala 1999:

14), other things being equal such as the absence of pre-emption of an opportunity by a competitor.

Sometimes, it is useful not just to wait in a passive manner for information, but to make opportunities for acquiring relevant in- formation, particularly, if it involves a possible upside. This may involve deliberate strategies – implementing a relevant information strategy, developing a pilot project, or staging an investment in such a way that the immediate commitment is limited. It may be possible to modify the project in the process of learning more about the risk confronting the enterprise: for example, threatening risk factors can be mitigated.

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