2.3 Treatment of risk in cash flow
The Methodology assumes that the cash flows prepared for the PSC have been adjusted for all project risks. Risk is quantified in the PSC based upon Expected Values, which are inclusive of all risks (systematic and non-systematic). When we refer to cash flows being adjusted for risk we refer to the cash flows being adjusted to Expected Values. This applies regardless of whether the source of the variability is Systematic or Non-Systematic Risk.
Some practitioners consider that including risks in both the cash flows and the Discount Rate is double counting. This is not the case. The cash flows account for risk in the sense of considering all possibilities and deriving a mean, or Expected Value, but do not account for risk in the sense of providing specific compensation for the potential for returns to depart from those Expected Values due to Systematic Risk. For example, a project with a certain cash flow return of $50 per annum would have the same expected cash flow as a project with a 50 per cent probability of $0 return and 50 per cent probability of a $100 return per annum. Therefore, the Expected Value of the cash flows does not reflect the variance of the cash flows due to Systematic Risk, or the co-variance of those cash flows with the cash flows of a portfolio of projects. To the extent that the potential variance is sensitive to Systematic Risk this is taken account of through the Discount Rate.
In estimating cash flows, analysts often incorporate into projected cash flows estimates based on substantial realisation of expectations with little, or no allowance for the potential for the unexpected or unlikely. For example, cash flow projections may be based on a target or budget reflecting what 'should' happen, rather than a realistic balance of probable and improbable outcomes. This approach not only creates problems in terms of potentially biasing financial analysis, but may also suggest insufficient risk analysis to support project development and assessment more generally.
CAPM, upon which the Methodology for deriving the Systematic Risk transferred is based, requires that cash flow projections be adjusted to represent the Expected Value for each component. Ideally, the calculated Expected Value for each cash flow item is the probability weighted average of all potential outcomes for that item. However, in practice, analysts usually find it sufficient to identify a reasonable range of possible outcomes for each item, weight each possible outcome by an assessed likelihood of it occurring and then calculate a mean value to determine the Expected Value for each item. This process is best done as part of, or in close association with, risk analysis of procurement options. It is the Expected Value of cash flows that should be included in a DCF analysis.
Example - Simple Calculation of Expected Value |
Suppose that building costs are $500 if the weather is sunny but $1 000 if the weather is rainy. Suppose that three days out of four are sunny and one day out of four is rainy. Sunny days are more likely than rainy days, so the most likely building costs are $500. However, the Expected Value of building costs, which is the correct measure, are calculated as follows: 3/4*500+1/4*1000 = $625. ((the probability of a sunny day is ¾ times the building cost on a sunny day of $500) plus (the probability of a rainy day of ¼ times the building cost on a rainy day of $1 000). Note that all probabilities must add to 100 per cent or 1.) |
For more detailed discussion on this issue practitioners should refer to Volume 4: Public Sector Comparator Guidance.