Step eight: calculate net present values and assess uncertainties

This page provides details on step eight of the economic appraisal process.

Net present values (NPVs)

2.8.1 In appraisals, we generally need to compare options that will impact over a period of years into the future. This raises the question of how future cost and benefits should be valued in today's terms. Normally people prefer to receive cash sooner rather than later, and pay bills later rather than sooner. This is true even after allowing for inflation. For an individual this time preference may be indicated by the real interest rate on money lent or borrowed.

2.8.2 In the public sector, likewise, we reflect social time preference by giving more weight to earlier than to later costs and benefits. This is usually given effect by applying a "discount rate" to future costs and benefits. The discount rate defines how rapidly the value today of a future real pound declines through time, just as a real rate of interest determines how fast the value of a pound invested now will increase over time. Guidance on the practical application of the discount rate is given in Basics of Discounting - including Discount Tables.

2.8.3 The standard discount rate is 3.5 per cent per annum in real terms. This rate also serves as the Resource Accounting and Budgeting Cost of Capital Charge (RABCCC). This rate should be applied in all but a few exceptional cases. The main exception concerns assistance to industrial and commercial activities (See 2.8.18 below).

2.8.4 The 3.5 percent rate should be applied to all costs and benefits expressed in real terms up to and including the 30th year of an appraisal. However, current practice is to discount longer term impacts less heavily. This is because uncertainty about the future can be shown to cause declining long-term discount rates over time. Thus, instead of applying 3.5 per cent to all future years, the following schedule should be used:

Years 0-30 31-75 76-125 126-200 201-300 300+
Discount Rate 3.5% 3.0% 2.5% 2.0% 1.5% 1.0%

2.8.5 In 2008, Her Majesty's Treasury (HMT) produced separate guidance providing for heavier discounting in projects with very large long-term effects on welfare of future generations. Such cases are likely to be relatively rare in Northern Ireland, but where they arise, the following schedule of annual discount rates is recommended:

Years 0-30 31-75 76-125 126-200 201-300 300+
Discount Rate 3.0% 2.57% 2.14% 1.71% 1.29% 0.86%

Treatment of inflation

2.8.6 The standard discount rate is defined in real terms, and should therefore be applied to values which are also expressed in real terms, as opposed to nominal or cash values. This means that the anticipated effects of general inflation should be removed from all the figures before discounting.

2.8.7 The most common assumption is that inflation will affect all prices equally, in which case all values are expressed in constant prices at a given date. This is adequate in a majority of appraisals. 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. The gross domestic product (GDP) Deflator is usually the most appropriate measure of prices to use as a general deflator in appraisals. See HMT's GDP Deflators for the latest figures.

2.8.8 In some cases, it may be anticipated that a certain cost or benefit item, for example wage earnings or oil prices, will experience inflation at a significantly different rate to that of general inflation. In such circumstances, the cost or benefit stream for that item should be adjusted accordingly before discounting. Specialist advice should be sought about how to do this if necessary.

Adjustment for optimism bias

2.8.9 The adjustment for optimism bias (OB) explained under step six above is usually made before the calculation of NPVs. The base case for each option is the best estimate of its costs and benefits after allowance for appraisal optimism. Thus the base case NPV for each option is its OB adjusted NPV.


2.8.10 Appraisals should generally include, for each option, a calculation of its NPV. This is the name given to the sum of the discounted benefits of an option less the sum of its discounted costs, all discounted to the same base date. Where the sum of discounted costs exceeds that of the discounted benefits, the net figure may be referred to as the Net Present Cost (NPC). Alternatively, the term 'negative NPV' may be used.

2.8.11 The NPV is the key summary indicator of the comparative value of an option. It not only takes account of social time preference through discounting, but also, by combining capital and recurrent cost and benefits in a single present day value indicator, enables direct comparison of options with very different patterns of costs and benefits over time. For instance, it solves the problem of how to compare a low capital cost/high running cost option with that of a high capital cost/low running cost alternative.

2.8.12 The decision rule is to select the option that offers to maximise NPV, or minimise NPC. This is subject to account being taken of those impacts which can not be valued in money terms. Conceptually, these also have an NPV or NPC, but inability to express them in money terms means that they must be judged by other means, as indicated at step seven, and weighed alongside the monetary values in coming to a decision.

2.8.13 The time horizon for NPV calculations should reflect the economic life of the services being appraised, or the useful life of relevant key assets, or the expected term of a contract, and should be sufficiently distant to cover all the important cost and benefit differences between options. For projects expected to have a very long life, the effect of shorter horizons should be illustrated for key years.

2.8.14 Discount calculations should be shown in detail. NPV calculations should show a breakdown of the main cost/benefit items covered, and how their incidence is distributed over time. All calculations should be conducted at up-to-date prices. In addition, DoF generally expects the calculations to show:

  • the discount factors used, year by year
  • the total NPV (or NPC) for each individual year
  • the cumulative total NPV (or NPC), for each year of the calculations

2.8.15 Appraisal reports should record both:

  • the price basis of the money values (that is, the date at which prices have been held constant)
  • the base date for discounting (that is, the date corresponding to start of the appraisal - usually the beginning of year 0 in the NPV calculations)

2.8.16 Discount calculations are facilitated by the use of software packages or a calculator. Departmental economists can advise about this and can normally supply spreadsheets suitable for adaptation to the needs of individual cases. A basic NPV spreadsheet is available on the DoF appraisal web pages.

Basics of discounting

2.8.17 The basic principles of discounting are explained further in Basics of Discounting - including Discount Tables, which also provides tables giving discount factors, equivalent annual cost factors and annuity factors.

Discount rate for commercial and industrial activities

2.8.18 The main exception to the use of the 3.5 per cent discount rate is where government is selling goods or services commercially, or is providing support to industrial or commercial activities. Where government is acting in a competitive environment, it should achieve a rate of return set neither to advantage nor disadvantage it against its competitors. Similarly, when it is supporting industrial or commercial activities, for example through financial assistance, the viability of the proposed activities needs to be assessed by reference to current commercial rates of return.

2.8.19 This requires the use of rates that reflect the commercial returns achieved by comparable businesses facing a similar level of risk. Currently the normal range of rates is 5-10 per cent but rates as high as 15 per cent may be appropriate for the very highest risk businesses.

Required rates of return and pricing rules

2.8.20 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 explained in Managing Public Money NI (MPMNI) (see discussion of financial objectives at A.6.2.5 in the annexes).

Assess uncertainties

2.8.21 The OB adjusted NPVs provide a starting point for understanding the impact of risk between different options. However, the future is inherently uncertain therefore no matter how thoroughly costs, benefits, risks and timing are identified and analysed, and even after best efforts have been made to adjust for optimism bias, there will remain uncertainty over the accuracy of the assumptions made. It is essential to test how these uncertainties may affect the choice between options. Whereas OB adjustment is primarily about ensuring NPVs are based on best estimates, assessment of uncertainty is chiefly about testing the robustness of the appraisal conclusions.

2.8.22 Sensitivity analysis is the key technique for this purpose and it is fundamental to appraisal. It is the process of examining how the balance of advantage among options is affected by reasonable variations in key assumptions. Its purpose is to influence the option selection decision; it is not something to be applied merely to a preferred option after it has been selected. The need for sensitivity analysis should always be considered, and, in practice, dispensed with only in exceptional cases. It is always potentially useful but is particularly valuable when the NPVs of options are relatively close to each other.

2.8.23 The basic procedure is to alter an assumption, recalculate the OB adjusted NPV for each option, and consider the impact on both the total net benefits, and on the balance of advantage between the options.

2.8.24 It is generally recommended to consider the effect of varying assumptions one at a time as this helps to isolate the assumptions that have the most impact. Some variations may have little impact on NPVs or option ranking, in which case they may not be regarded as a cause for much concern. Other variations may alter the ranking of options or significantly change the NPV. Such variations should be considered carefully and may require specific risk management actions. For example, it may be appropriate to seek to reduce the uncertainty over particular assumptions in order to make them more robust, and improve the chances of a good outcome. (See section on risk reduction strategies in step six above).

2.8.25 The calculation of 'switching values' is a particular form of sensitivity test. It shows by how much a variable would have to fall (if it is a benefit) or rise (if it is a cost) to switch the balance of advantage from one option to another, or switch the NPV from positive to negative. This may be a crucial input into the decision as to whether a proposal should proceed. For example, it can help answer key questions such as:

  • by how much can we allow benefits to fall short of expectations, if the project is to remain worthwhile? How likely is this?
  • how much can operating costs increase without jeopardising the VFM of the proposal? How likely is this?

2.8.26 In any particular case, judgement in the light of past experience should be used to decide upon the assumptions that are worth subjecting to sensitivity analysis, and the range of variation to be examined for each assumption. 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. Examples of the assumptions which should be considered for sensitivity analysis include:

  • projections of need or demand e.g. school enrolments, traffic forecasts, projected sickness incidence rates
  • estimates of key costs and benefits; for example, items of capital or recurrent costs, forecasts of revenue income
  • estimates of land or property valuations, particularly in periods of property market volatility
  • changes in real prices; for example, growth of real wages or real oil prices
  • weights and scores attached to non-monetary factors
  • the phasing of costs or benefits
  • the time horizon for the appraisal

2.8.27 The reasons for choosing the assumptions investigated and the range of variations examined should be recorded. Slavish analyses of variations of plus or minus some arbitrary percentage in every assumption should be avoided.

2.8.28 Presentation of sensitivity analyses is important, particularly when many are undertaken. Summary tables should generally be provided, comparing the key results of all the sensitivity tests undertaken. Inclusion of large numbers of spreadsheets that repeat most of the rows of figures in the main spreadsheets is not very helpful. Sufficient information should be provided to facilitate checking of sensitivity calculations.

2.8.29 Departments should explain the implications of sensitivity analysis for option selection. It is not good practice simply to append sensitivity analyses to appraisal reports without explaining their significance.

Scenarios and expected values

2.8.30 It can sometimes be helpful to group potential variations into scenarios, for example, to enable consideration of "optimistic" and "worst case" scenarios. "Scenario planning" looks at the consequences of various possible states of the world for anything from an individual investment project to an entire corporate strategy. Scenario planning supplements sensitivity analysis by describing alternative internally consistent possible future economic and political environment, and outcomes. Scenarios are often useful for planning an investment programme and may also be justified for exceptionally large and complicated projects, or for policies that are very sensitive to the external environment.

2.8.31 Scenarios should be chosen to draw attention to the major technical economic and political uncertainties upon which the success of the project or option or strategy depends. Generally the best approach is to set up two or three scenarios that differ in important dimensions. The expected NPV can be calculated for each scenario. It may also be helpful to undertake some sensitivity analysis within and between scenarios.

2.8.32 Where there are a number of possible NPV scenarios or outcomes whose probability can be reasonably estimated, or where a number of NPVs are considered to be equally probable, then the expected value of NPV should be calculated and used as the base case NPV.

2.8.33 The expected value NPV is the average of the possible outcomes weighted by their probabilities. For example, suppose there are three scenarios with NPVs and probabilities estimated as follows:

Scenario NPV Probability NPV x Probability
1 £5m 0.2 £1.0m
2 £4m 0.3 £1.2m
3 £3m 0.5 £1.5m
    Expected Value £3.7m

2.8.34 More sophisticated techniques should be used as appropriate in particularly large or complex appraisals and in private finance initiative (PFI) projects. For example,

  • in PFI cases, it may be appropriate to use Monte Carlo analysis to calculate expected values rather than single point estimates for NPVs. Specialised computer software and expert assistance may be required
  • proposals requiring sequential decisions can be analysed using decision trees, which are graphical representations of the set of possible strategies. Different strategies result in different NPVs depending on the events (or states of the world) that occur. An extension of the technique can be employed when the probability of any particular risk is assigned
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