So far, our capital budgeting analyses have assumed complete certainty, whereby relevant money cash flows and money discount rates can be specified in advance. But what if a plurality of future cash flows and discount rates are possible? How do management select investments that maximises shareholder wealth in this real world of risk and uncertainty?

Let us begin with a conceptual clarification and a few definitions.

Risk and uncertainty both refer to situations with more than one outcome. However, risk defines future events that can be objectively specified in advance based on prior knowledge; an obvious example being the throw of a dice. Uncertainty, which characterizes most business decisions, relates to events whose probabilities cannot be predicted with accuracy.

What management require, therefore, are quantitative techniques that transform uncertainty to quasi-risk, which assumes a range of possible outcomes and assigns subjective probabilities to the likelihood of each occurring.

We should also note that a project's overall uncertainty or total risk embraces:

- Business risk that relates to the variability of future cash flows arising from an investment's fundamental characteristics, as well as changing economic conditions.

- Financial risk associated with a project's funding and how the earnings distributed to investors determine the company's cost of capital (discount rate).

Since the former determines the latter (without profits how can you reward investors?) financial risk need not concern us yet. Cost of capital is also better left until we deal with security pricing in Part Three. So, first let us focus on the treatment of business risk,

4.1. Dysfunctional Risk Methodologies

The following risk techniques are popular with management. But unfortunately they fail to maximise shareholder wealth.

- Modifications to the cut-off rate for investment that adds a risk premium the discount rate.

- Point estimates such as best, worst or most likely net cash inflow; Minimax, which focuses upon the best outcome under the most adverse conditions; Laplace criteria, which select the most favorable simple average of a three point estimate; Probability estimation which applies probabilities to three point forecasts to produce the best weighted average (subject to the proviso that the sum of the probabilities equals one).

Suffice it to say that if the cut-off (discount) rate is based on a market rate, it already factors in business risk. So, adding a premium duplicates uncertainty. Turning to the variability of cash flows point estimations and their derivatives may also be counterproductive. The worst scenario may be improbable, but if it materializes then it may be catastrophic for the firm.

4.2. Decision Trees, Sensitivity and Computers

Look at any financial text and you will also find decision trees, sensitivity analyses and computer simulation techniques. However, these do not quantify risk. Rather they manipulate risk-adjusted data to assess their effect on an investment's viability.

Decision trees provide a mind map of uncertain project cash flows branch out from an investment (hence its name) and may proliferate beyond a three-point analysis. Conditional probabilities are attached to a sequence of likely future events. The branches of the trunk arise from previous managerial decisions (control factors) and chance (uncontrollable factors).

Sensitivity analysis deconstructs cash data that comprise an initial NPV computation into estimates of its component parts. Each variable is then analysed sequentially, using partial equilibrium analysis. By holding all other variables constant and gauging the impact on the appropriate investment criteria of percentage changes to the variable under observation, its critical value is established.

Computer simulation can be used in conjunction with decision trees, sensitivity analysis, or any technique, to calculate quickly innumerable permutations of probabilistic cash flows.

As tools, however, decision trees, sensitivity analyses and computer simulation are only as sound as the data upon which they are based. So, let us move beyond three point estimation.

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