The Green Book

APPRAISING THE OPTIONS

INTRODUCTION

5.1

The purpose of option appraisal is to help develop a value for money solution that meets the objectives of government action. Creating and reviewing options helps decision-makers understand the potential range of action that they may take.

5.2

The approach set out here explains how options can be created, and values estimated for the Base Case (i.e. the best estimate of the costs and benefits of an option). It goes on to state how the Base Case may be adjusted to account for uncertainty about the future, using sensitivity and scenario analyses, and how to consider non-monetised impacts.

CREATING OPTIONS

5.3

This step involves preparing a list of the range of actions which government could possibly take to achieve the identified objectives. The list should include an option where government takes the minimum amount of action necessary (the ‘do minimum option’), so that the reasons for more interventionist actions can be judged.

5.4

The range of options depends on the nature of the objectives. For a major programme, a wide range should be considered before short-listing for detailed appraisal. Both new and current policies, programmes and projects should be included as options. At the early stages, it is usually important to consult widely, either formally or informally, as this is often the best way of creating an appropriate set of options.

5.5

An option may affect, or be affected by, other expenditure across the public sector (for example, where its outputs or costs depend upon another project or the implementation of a related policy perhaps in another department). Where a number of expenditures or activities are linked together and the costs or benefits are mutually dependent, the proposal must be appraised as a whole. However, the contribution of the component parts of each proposal to achieving overall value for money must be taken into account.

BOX 8: CREATING OPTIONS

Establishing a range of options can be challenging. The following actions are suggested:

	Research existing reports, and consult widely with practitioners and experts, to gather the set of data and information relevant to the objectives and scope of the problem.
	Analyse the data to understand significant dependencies, priorities, incentives and other drivers.
	From the research, identify best practice solutions, including international examples if appropriate.
	Consider the full range of issues likely to affect the objective.
	Identify the full range of policy instruments or projects that may be used to meet the objectives. This may span different sorts or scales of intervention; regulatory (or deregulatory) solutions may be compared with self-regulation, spending or tax options.
	Develop and consider radical options. These options may not become part of the formal appraisal but can be helpful to test the parameters of feasible solutions. Well-run brainstorming sessions can help to generate such a range of ideas.

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BOX 9: EXAMPLES OF OPTIONS

Examples of strategic and operational options include:
	Varying time and scale
	Options to rent, build or purchase
	Changing the combination of capital and recurrent expenditure
	Refurbishing existing facilities or leasing and buying new ones
	Co-operating with other parts of government
	Changing locations or sites
	Provision of the service, such as maintenance, or facility by the private sector
	Co-locating, or sharing facilities with other agencies
	Using IT to improve delivery, as part of wider organisational changes
	Transferring service provision to another body, or improving partnership arrangements
	Varying the balance between outsourcing and providing services (or retaining expertise in-house)
	Engaging the voluntary sector
	Regulation, including private sector self regulation, and voluntary action
	Different standards or compliance procedures for different groups (e.g. large and small businesses)
	Varying quality targets
	Different degrees of compulsion, accreditation, monitoring, and inspection regimes, including voluntary codes, approved codes of practice or government regulation
	Action at a regional, national, or international level (e.g. European wide)
	Better implementation of existing measures or initiatives
	Information campaigns
	Deregulation and non-intervention
	Changes that will be permanent in the foreseeable future, or initiatives with specified time horizons

Short-listing options

5.6

A shortlist of options may be created, partly to keep the appraisal process manageable, usually at the preliminary stages of a policy appraisal, or during the strategic outline business case stage for a capital investment appraisal. However, there is a risk that the process of short-listing will eliminate the optimal solution before it is given full consideration. Therefore, shortlists should still try to cover a wide range of potential action.

5.7

The shortlist must always include the ‘do minimum’ option. Reasons behind the rejection of each excluded option should be recorded.

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VALUING THE COSTS AND BENEFITS OF OPTIONS

Introduction

5.8

The relevant costs and benefits to government and society of all options should be valued, and the net benefits or costs calculated. The decision maker can then compare the results between options to help select the best. It is important to avoid being spuriously accurate when concluding from, and presenting the results of, data generated by the appraisal. However, the confidence in the data provided by the analysis will need to increase, depending on the importance or scale of the decision at hand (for instance, depending on how much resource will be committed by the decision).

5.9

In this context, relevant costs and benefits are those that can be affected by the decision at hand. Although they will vary depending on the scope of the proposal, some general principles apply. It is useful early on in the appraisal process to consider widely what potential costs and benefits may be relevant.

5.10

Costs and benefits considered should normally be extended to cover the period of the useful lifetime of the assets encompassed by the options under consideration, although, if the appraisal concerns the contractual purchase of outputs and outcomes (e.g. in PFI), the appraisal period may be different.

5.11

Costs and benefits should normally be based on market prices as they usually reflect the best alternative uses that the goods or services could be put to (the opportunity cost). However, market prices may need to be adjusted for tax differences between options.

5.12

Wider social and environmental costs and benefits for which there is no market price also need to be brought into any assessment. They will often be more difficult to assess but are often important and should not be ignored simply because they cannot easily be costed. Annex 2 provides more information on how to take into account the wider impacts of proposals.

5.13

Cashflows and resource costs are also important in an appraisal, as these inform the assessment of the affordability of a proposal. However, they do not provide the opportunity cost and, therefore, cannot be used to understand the wider costs and benefits of proposals. Proposals are also likely to require resource budgets, so that it is clear how they will be funded, and, ex post, accounted for. Chapter 6 provides more information on resource budgets and the other accounting requirements of appraisals.

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Estimating costs

5.14

Costs should be expressed in terms of relevant opportunity costs. It is important to explore what opportunities may exist. An example of an opportunity is to use land in a different, more valuable, way than in its current use. Another is the alternative use of an employee’s time. Full time equivalent (FTE) costs should be used to estimate the costs of employees’ time to the employer¹, and should include pensions, national insurance and allowances, as well as basic salaries.

5.15

Costs of goods and services that have already been incurred and are irrevocable should be ignored in an appraisal. They are ‘sunk costs’. What matters are costs about which decisions can still be made. However, this includes the opportunity costs of continuing to tie up resources that have already been paid for.

5.16

It can be useful to distinguish between fixed, variable, semi variable and step costs:

	Fixed costs remain constant over wide ranges of activity for a specified time period (such as an office building);
	Variable costs vary according to the volume of activity (external training costs, for example, varying with the number of trainees);
	Semi-variable costs include both a fixed and variable component (maintenance is an example, where there is usually a set planned programme, and a responsive regime whose costs vary in proportion to activity, i.e. the number of call-outs); and,
	Semi-fixed, or step costs, are fixed for a given level of activity but they eventually increase by a given amount at some critical point (after telephone call volumes reach a certain level, a new call centre may be required).²

5.17

Categorising costs in this way can aid sensitivity analysis, but the categorisation should be used carefully. A cost that is fixed relative to one factor may change with another. More complex modelling may be required to describe how costs change over time and with different variables.

5.18

For substantial proposals, the relevant costs are likely to equate to the full economic cost of providing the associated goods and services, and for these proposals, the full economic cost should be calculated, net of any expected revenues, for each option. The full cost includes direct and indirect costs, and attributable overheads. The full cost of the Base Case, as built up in this way, should also equal the total of the analysis of costs into their fixed, variable, semi-variable and stepped elements. A dual cost analysis of this kind enables opportunity costs to be fully considered, and sensitivity analysis to be conducted later on.

5.19

Appraisals leading to short-term or non-strategic decisions are likely to have a smaller set of relevant costs. The relevant costs are likely to be those that are marginal to the organisation’s overall activity.

5.20

Cost estimation can be difficult, depending on the class of costs under consideration. It will normally involve input from accountants, economists and other specialists, depending on the type of appraisal. The appraiser needs to understand and communicate clearly the scope of the appraisal to ensure that specialists provide relevant cost information, whilst ensuring that opportunities have been thoroughly explored.

5.21

Depreciation and capital charges should not be included in an appraisal of whether or not to purchase the asset that would give rise to them (although for resource budgeting purposes they may be important). Depreciation is an accounting device used to spread the expenditure on a capital asset over its lifetime. Capital charges reflect the opportunity cost of funds tied up in capital assets, once those assets have been purchased. They are used to help test the value for money of retaining an asset. They should not be included in the decision whether or not to purchase the asset in the first place.

5.22

Even where an appraisal covers the full expected period of use of an asset, the asset may still have some residual value, in an alternative use within an organisation, in a second-hand market, or as scrap. These values should be included, and tested for sensitivity, as it may be difficult to estimate the future residual value at the present time.

5.23

Some projects expose the government to contingent liabilities – that is commitments to future expenditure if certain events occur. These should be appraised (and monitored if the proposal goes ahead). One class of contingent liabilities is the cancellation costs for which the government body may be liable if it terminates a contract prematurely. Such liabilities, and the likelihood of their coming about, must be taken into account in appraising the initial proposal. Redundancy payments fall into this category, but as the wider social and economic consequences of these should also be assessed, advice from economists should be sought.³

5.24

The purpose of valuing benefits is to consider whether an option’s benefits are worth its costs, and to allow alternative options to be systematically compared in terms of their net benefits or net costs. The general rule is that benefits should be valued unless it is clearly not practicable to do so. Even if it is not feasible or practicable to value all the benefits of a proposal, it is important to consider valuing the differences between options.

5.25

In principle, appraisals should take account of all benefits to the UK.⁴ This means that as well as taking into account the direct effects of interventions, the wider effects on other areas of the economy should also be considered. These effects should be analysed carefully as there may be associated indirect costs, such as environmental costs, which would also need to be included in an appraisal. In all cases, these wider effects should be clearly described and considered.

5.26

Real or estimated market prices provide the first point of reference for the value of benefits. There are a few exceptions where valuing at market prices is not suitable. If the market is dominated by monopoly suppliers, or is significantly distorted by taxes or subsidies, prices will not reflect the opportunity costs and adjustments may be required and specialist economic advice will be needed. An example of this is the effect of EU subsidies on the market for agricultural land.

5.27

The results of previous studies may sometimes be used to estimate the economic value of changes stemming from current programmes or policies. There will be increasing scope for using this ‘benefit transfer’ method as databases expand, though care must be taken to allow for different circumstances. The characteristics of the consumers or client group for which data exist may differ from those of the proposal under consideration. These factors can limit the extent to which values can be transferred or generalised.

5.28

In the absence of an existing robust (i.e. reliable and accurate) monetary valuation of an impact, a decision must be made whether to commission a study, and if so how much resource to devote to the exercise. Annex 2 sets out the key considerations that may govern a decision to commission research.

5.29

Where it is concluded that a research project to determine valuations is not appropriate, a central estimate, together with a maximum and minimum plausible valuation, should be included. These figures should be included in sensitivity analyses to give assurance that benefit valuation is not critical to the decision to be made. A plausible estimate of the value of a benefit or cost can often be drawn out by considering a range of issues which are summarised in Annex 2.

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Valuing costs and benefits where there is no market value

5.30

Most appraisals will identify some costs and benefits for which there is no readily available market data. In these cases, a range of techniques can be applied to elicit values, even though they may in some cases be subjective. There will be some impacts, such as environmental, social or health impacts, which have no market price, but are still important enough to value separately.

5.31

Box 10 summarises the main techniques that can be used to elicit these values. Annex 2 describes these techniques in more detail, and provides further information on how they are being applied in practice.

BOX 10: VALUATION TECHNIQUES

Determine whether

Impacts can be measured and quantified

AND

Prices can be determined from market data

If this cannot be readily done

Use ‘Willingness to Pay’ for a benefit

‘willingness to pay’

determined by

‘revealed
preference’
or a subset
of this called
‘hedonic pricing’

Inferring a price from observing consumer behaviour

If this does not provide values, determine whether:

Willingness to pay can be estimated by asking
people what they would be willing to pay for
a particular benefit

‘stated
preference’

or whether

In the case of a cost: identifying the amount of compensation consumers would demand in order to accept it

‘willingness
to accept’

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ADJUSTMENTS TO VALUES OF COSTS AND BENEFITS

5.32

Adjustments will often be required to take account of distributional impacts, and relative price changes to develop the Base Case. As for all adjustments, they should be shown separately, clearly and explicitly in any supporting tables of data.

Distributional analysis

5.33

It is important that the distributional implications of each option are considered during appraisal. This type of analysis enhances the understanding of the fairness of proposals, their social impacts and their scale.

5.34

The impact of a policy, programme or project on an individual’s well-being will vary according to his or her income; the rationale being that an extra pound will give more benefit to a person who is deprived than to someone who is well off. In economics, this concept is known as the ‘diminishing marginal utility of additional consumption’.

5.35

Other distributional issues may also arise, and should be considered during appraisal. A proposal may have differing impacts according to age, gender, ethnic group, health, skill, or location. These effects should be explicitly stated and quantified wherever feasible. For example, the costs and benefits of a proposal might be broken down according to the ethnic group they accrue to, providing appraisers with a basis for comparison and analysis.

5.36

Generally though, these other distributional issues are largely correlated with income. Therefore, if more in depth analysis is undertaken, it should focus on how the cost and benefits of a proposal are spread across different socio-economic groups.

5.37

For the purposes of project appraisal, relative prosperity may often be best defined by relative income, adjusted for household size, and divided into quantiles (e.g. quintiles or deciles).⁵ The equity impact of competing options can be compared by charting the impact each has on different ‘quantiles’ of the income distribution. Proposals that deliver greater net benefit to households or individuals in lower income quantiles are rated more favourably than those that benefit higher quantiles.

5.38

A more in depth analysis uses distributional weights to adjust explicitly for distributional impacts in the cost-benefit analysis. Benefits accruing to households in a lower quantile would be weighted more heavily than those that accrue to households in higher quantiles. Conversely, costs would be weighted more heavily for households in lower quantiles. Annex 5 provides further guidance in this area.

5.39

A project aiming to improve market efficiency through the correction of market failure needs also to consider equity outcomes. In this case, an explicit adjustment would be particularly helpful as an equity check for the proposal. Similarly, an adjustment is desirable when faced with a decision between competing equity motivated projects, aimed at regenerating areas containing different socio-economic populations.

5.40

Applying an explicit distributional adjustment requires quite detailed information about the affected population. A judgement must be made as to whether the necessary socio-economic information is available at an acceptable cost, given the importance of the proposal and the likely scale of the impact of distributional analysis.

5.41

Where appraisers decide not to adjust explicitly for distributional impacts, they must provide a justification for this decision. This judgement should be informed by the following considerations:

	The significance of the impact of distributional analysis to the proposal under consideration;
	The ease with which distributional impacts can be measured; and
	The scale of the impact associated with a particular project or proposal.

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Adjusting for relative price changes

5.42

The valuation of costs or benefits should be expressed in ‘real terms’ or ‘constant prices’ (i.e. at ‘today’s’ general price level), as opposed to ‘nominal terms’ or ‘current prices’.

5.43

If necessary, the effect of expected future inflation in the general price level should be removed by deflating future cash flows by forecast levels of the relevant deflator. Over a long-term period, the Bank of England’s annual inflation target⁶ is the appropriate measure of prices to use as a general deflator.

5.44

Where particular prices are expected to increase at significantly higher or lower rate than general inflation, this relative price change should be calculated. Examples where relative price changes may be material to an appraisal include:

	High technology products, prices for which may be expected to fall in real terms;
	Fuel prices, where the resource supply is scarce; and
	Wages, where productivity growth is expected to lead to wage increases above general inflation.⁷

5.45

It is helpful when anticipating relative price movements, to consider whether the value of a benefit or a cost will rise as incomes increase. The most direct evidence for this is evidence about how, in fact, revealed preference or stated preference valuations of the benefit in question have increased with income over time. In some cases there is reason to expect that the value of a benefit or cost will rise as incomes increase, for example because the good is in fixed supply (such as certain environmental assets), or because the units in which it is measured are such that its utility value can be expected to remain broadly constant, regardless of changes in income. In the absence of definitive data, the rate of increase in the real value of the benefit should be assumed to be positive, and only in unusual circumstances would it exceed the projected rate of increase of per capita real income.⁸ Where these assumptions are critical, they should be tested against any specific evidence.

5.46

For other costs and benefits, the factors listed below might be considered in determining whether their value would change by more or less than inflation.

	Scarcity. If a good is exhaustible, its relative price may be expected to rise at a faster rate than general prices, as it becomes increasingly scarce. Against this, developing technologies may enable more of a good to be extracted than initially thought possible.
	Substitutability. Where plenty of substitutes are available, any scarcity impact may be largely offset. Consideration should be given to whether substitutes are likely to develop over time, particularly in the case of exhaustible goods.
	Non-linearity. Some of the damage resulting from pollutants, for example, will be non-linear. If the quantity of a pollutant changes over time, this non-linearity will affect the rate at which its relative price changes.
	Increasing competition, or the removal of monopoly powers, would increase the availability of goods and services, and relative prices may be expected to decline.
	Economies of scale. If the size of the market for a particular good or service increases, then there is a greater potential for economies of scale, and relative prices may then also be expected to reduce.

5.47

Advice on likely relative price movements should be obtained from the appropriate expert bodies and from finance divisions or economists.

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DISCOUNTING

5.48

Discounting is a technique used to compare costs and benefits that occur in different time periods. It is a separate concept from inflation, and is based on the principle that, generally, people prefer to receive goods and services now rather than later. This is known as ‘time preference’.

5.49

For individuals, time preference can be measured by the real interest rate on money lent or borrowed. Amongst other investments, people invest at fixed, low risk rates, hoping to receive more in the future (net of tax) to compensate for the deferral of consumption now. These real rates of return give some indication of their individual pure time preference rate. Society as a whole, also prefers to receive goods and services sooner rather than later, and to defer costs to future generations. This is known as ‘social time preference’; the ‘social time preference rate’ (STPR) is the rate at which society values the present compared to the future.

The discount rate is used to convert all costs and benefits to ‘present values’, so that they can be compared. The recommended discount rate is 3.5%. Calculating the present value of the differences between the streams of costs and benefits provides the net present value (NPV) of an option. The NPV is the primary criterion for deciding whether government action can be justified.

5.50

The mathematical expressions used to calculate discounted present values are set out in the footnote below.⁹

5.51

For projects with very long-term impacts, over thirty years, a declining schedule of discount rates should be used rather than the standard discount rate. The schedule of long-term discount rates is shown in Annex 6.

5.52

Annex 6 also explains the derivation of the social time preference rate, why the rate declines over time, and the circumstances when exceptions to the standard discount rates are allowed.

5.53

Table 1 shows how the present value of £1,000 declines in future years with a discount rate of 3.5 per cent. More detailed discount rate tables are provided in Annex 6.

TABLE 1: PRESENT VALUES AND DISCOUNT RATE

Time (mid year)	0	1	2	3	4	5	6	7	8	9	10

PV of payment (mid year)	£1,000	£966	£934	£902	£871	£842	£814	£786	£759	£734	£709

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Required Rates of Return and Pricing Rules

5.54

Some central government bodies sell goods or services commercially, including to the government itself. These activities may be controlled by requiring prices to be set to provide a required rate of return (RRR) on the capital employed by the activity as a whole. Government policy is generally to set charges for goods and services sold commercially at market prices, and normally to recover full costs for monopoly services, (including the cost of capital as defined in the Treasury Fees and Charges Guide).¹⁰

BOX 11: CALCULATING THE NPV

Alternative projects, A and B, are both expected to improve the quality of a department’s work and reduce staff costs. The Base Case of each is being estimated.

Option A requires £10 million in initial capital expenditure to realise benefits of £2.5 million per annum for the following four years (£2 million in reduced staff costs and £0.5 million in quality improvements).

Option B requires £5 million in initial capital expenditure to realise benefits of £1.5 million per annum for the following four years (£1 million reduced staff costs and £0.5 million in quality improvements).

Calucation of Present values


Year	0	1	2	3	4	NPV

Discount Factor	1	0.9962	0.9335	0.9019	0.8714

Option A
Costs/Benefits (£)	-10.00m	2.50m	2.50m	2.50m	2.50m
Present Value (£)	-10.00m	2.42m	2.33m	2.25m	2.18m	-0.82m

Option B
Costs/Benefits (£)	-5.00m	1.50m	1.50m	1.50m	1.50m
Present Value (£)	-5.00m	1.45m	1.40m	1.35m	1.31m	0.51m

Project B yields a positive net present value of £0.51m compared to -£0.82m for project A and zero for the implicit ‘do minimum’ alternative. Therefore Project B is preferable.

ADJUST FOR DIFFERENCES IN TAX BETWEEN OPTIONS

5.55

The adjustment of market prices for taxes in appraisal is appropriate where it may make a material difference to the decision. In practice, it is relatively rare that adjustments for taxation are required, because similar tax regimes usually apply to different options. It can also be difficult in practice to estimate costs net of tax. However, where the tax regimes applying to different options vary substantially, this should not be allowed to distort option choice. In such cases it is important to adjust for any differences between options in the incidence of tax arising from different contractual arrangements, such as in-house supply versus buying in, or lease versus purchase. Options attracting different VAT rates, for example, should be compared as if either the same VAT payments, or no payments were made in all cases.

5.56

Where publicly financed options are compared to PFI options, taxation differences should be considered, and adjustments explicitly made if not doing so would materially distort the decision. Specific guidance is available on the Treasury Green Book homepage on how to do this in practice.

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INTRODUCTION TO RISK AND UNCERTAINTY

Introduction

5.57

In appraisals, there is always likely to be some difference between what is expected, and what eventually happens, because of biases unwittingly inherent in the appraisal, and risks and uncertainties that materialise. As a result, risk management strategies should be adopted for the appraisal and implementation of large policies, programmes or projects, but their principles can be applied to smaller proposals.

5.58

Appraisers should calculate an expected value of all risks for each option, and consider how exposed each option is to future uncertainty. Before and during implementation, steps should be taken to prevent and mitigate both risks and uncertainties. It is important to be transparent with sponsors about the potential impact of risks and bias on their proposals.

Risk management

5.59

Risk management is a structured approach to identifying, assessing and controlling risks that emerge during the course of the policy, programme or project lifecycle. Its task is to ensure an organisation makes cost-effective use of a risk process that has a series of well-defined steps to support better decision-making through good understanding of the risks inherent in a proposal and their likely impact. Risk management involves:

	Identifying possible risks in advance and putting mechanisms in place to minimise the likelihood of their materialising with adverse effects;
	Having processes in place to monitor risks, and access to reliable, up-to-date information about risks;
	The right balance of control in place to mitigate the adverse consequences of the risks, if they should materialise; and,
	Decision-making processes supported by a framework of risk analysis and evaluation.

5.60

Annex 4 provides more information on risk management.

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ADJUSTING FOR BIAS AND RISKS

Optimism bias

5.61

There is a demonstrated, systematic, tendency for project appraisers to be overly optimistic. This is a worldwide phenomenon that affects both the private and public sectors.¹¹ Many project parameters are affected by optimism – appraisers tend to overstate benefits, and understate timings and costs, both capital and operational.

5.62

To redress this tendency, appraisers should make explicit adjustments for this bias. These will take the form of increasing estimates of the costs and decreasing, and delaying the receipt of, estimated benefits. Sensitivity analysis should be used to test assumptions about operating costs and expected benefits.

5.63

Adjustments should be empirically based, (e.g. using data from past projects or similar projects elsewhere), and adjusted for the unique characteristics of the project in hand. Cross-departmental guidance for generic project categories is available, and should be used in the absence of more specific evidence.¹² But if departments or agencies have a more robust evidence base for cost overruns and other instances of bias, this evidence should be used in preference. When such information is not available, departments are encouraged to collect data to inform their estimates of optimism, and in the meantime use the available data that best fits the case in hand.

5.64

Adjusting for optimism should provide a better estimate, earlier on, of key project parameters. Enforcing these adjustments for optimism bias is designed to complement and encourage, rather than replace, existing good practice, in terms of calculating project specific risk adjustments. They are also designed to encourage more accurate costing. Accordingly, adjustments for optimism may be reduced as more reliable estimates of relevant costs are built up, and project specific risk work is undertaken. Both cost estimates and adjustments for optimism should be independently reviewed before decisions are taken. Annex 4 provides further detail on how to deal with optimism bias.

BOX 12: OPTIMISM BIAS EXAMPLE

The capital costs of a non-standard civil engineering project are estimated to be £50m NPC in a strategic outline business case (SOBC). No detailed risk analysis work has taken place at this stage, although significant costing work has been undertaken. The project team reports to the project board and applies an optimism bias adjustment of 70%, showing that, for the scope of work required, the total cost may increase by £35 million to £85 million in total. This is based on consultants’ evidence, and experience from comparable civil engineering projects at a similar stage in the appraisal process.

As this potential cost is unaffordable, the chief executive requests reductions in the overall scope of the project, and more detailed work for the outline business case stage (OBC). As the project progresses, more costs and specific risks are identified explicitly, despite the reduced scope. For the final business case, the optimism bias adjustment is reduced until there remains only a general contingency of 5% for unspecified risks.

Without applying optimism bias adjustments, a false expectation would have been created that a larger project could be delivered, and at a lower cost.

5.65

It is good practice to add a risk premium to provide the full expected value of the Base Case. As the previous section explained, in the early stages of an appraisal, this risk premium may be encompassed by a general uplift to a project’s net present value, to offset and adjust for undue optimism. But as the appraisal proceeds, more project specific risks will have been identified, thus reducing the need for the more general optimism bias.

5.66

An ‘expected value’ (EV) provides a single value for the expected impact of all risks. It is calculated by multiplying the likelihood of the risk occurring by the size of the outcome (as monetised), and summing the results for all the risks and outcomes. It is therefore best used when both the likelihood and outcome can be reasonably estimated.

BOX 13: EXAMPLE OF EXPECTED VALUE OF BENEFITS

A new policy was originally expected to generate significant benefits, but following concerns that the original predictions were over optimistic, further risk analysis has confirmed that there is now considerable uncertainty about some of these benefits being realised. Four potential outcomes are now considered possible, with NPVs and probabilities assessed as follows:

	NPV	Probability	Benefits – Expected Values

1	£10 million	0.2	£2 million
2	£20 million	0.4	£8 million
3	£30 million	0.3	£9 million
4	£40 million	0.1	£4 million

Expected value			£23 million

The costs of implementation have been more rigorously assessed at between £12-17 million, with an expected value of £15 million.

The expected net benefit is therefore £8 million NPV.

5.67

Decision trees can be useful in this context. They are graphical representations useful in assessing situations in which the probabilities of particular events occurring depend on previous events, and can be used to calculate expected values in these more complex situations. For example, the likelihood of a particular volume of traffic using a road in the future might be dependent on the probability of movements in the oil price. Different scenarios can be analysed in this way.

BOX 14: EXAMPLE – DECISION TREE

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ASSESSING UNCERTAINTY

5.68

An expected value is a useful starting point for understanding the impact of risk between different options. But however well risks are identified and analysed, the future is inherently uncertain. So it is also essential to consider how future uncertainties can affect the choice between options.

Sensitivity analysis

5.69

Sensitivity analysis is fundamental to appraisal. It is used to test the vulnerability of options to unavoidable future uncertainties. Spurious accuracy should be avoided, and it is essential to consider how conclusions may alter, given the likely range of values that key variables may take. Therefore, the need for sensitivity analysis should always be considered, and, in practice, dispensed with only in exceptional cases.

5.70

The calculation of switching values shows by how much a variable would have to fall (if it is a benefit) or rise (if it is a cost) to make it not worth undertaking an option. This should be considered a crucial input into the decision as to whether a proposal should proceed. It therefore needs to be a prominent part of an appraisal.

5.71

Examples of variables that are likely to be both inherently uncertain and fundamental to an appraisal are the growth of real wages, forecast revenues, demand, prices, and assumptions about the transfer of risks. A prior analysis of costs into fixed, step, variable, and semi-variable categories can help in understanding the sensitivity of the total costs of proposals.

BOX 15: EXAMPLE OF SENSITIVITY ANALYSIS

A new IT system costs £1million and is expected to yield staff savings of £150,000 per year over a period of 10 years. Discounting at 3.5 per cent the NPV of these costs and benefits is £247,000.

Suppose the estimates of staff savings assumed that the IT system would replace 15 staff with an average cost per person of £10,000. A possible sensitivity test is as follows: what if the IT system replaces only 10 staff? Staff savings would then fall to £100,000 per year and the NPV turns negative (minus £168,000).

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Scenarios

5.72

Scenarios are also useful in considering how options may be affected by future uncertainty. Scenarios should be chosen to draw attention to the major technical, economic and political uncertainties upon which the success of a proposal depends. Considering scenarios needs to be proportionate. It may take the form of asking simple ‘what if’ questions for small and medium sized projects, but extend to creating detailed models of future states of the world for major policies and large programmes. The expected NPV can be calculated for each scenario. It may also be helpful to undertake some sensitivity analysis within a scenario.

BOX 16: EXAMPLE OF SCENARIOS

Box 13 above shows that there is a 20 percent chance that there will be no net benefits (Outcome 1) but a 40 percent chance of net benefits of around £15 million NPV or more (Outcomes 3 and 4). Should it go ahead? Many other considerations then might play, such as whether there are other policies with