Discounting and Social Time Preference
5.32 Discounting is a technique used to compare costs and benefits occurring over different periods of time on a consistent basis. Discounting should be applied to all future costs and benefits. Discounting in appraisal of social value is based on the concept of time preference - that generally people prefer to receive goods and services now rather than later.
5.33 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 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. This is known as 'social time preference'. The discount rate used in the Green Book is known as the 'social time preference rate' (STPR). It is the rate at which society values the present compared to the future.
5.34 The STPR has two components:9
'time preference' - the rate at which consumption and public spending are discounted over time, assuming no change in per capita consumption. This captures the preference for value now rather than later.
'wealth effect' - this reflects expected growth in per capita consumption over time, where future consumption will be higher relative to current consumption and is expected to have a lower utility.
5.35 The STPR used in the Green Book is set at 3.5% in real terms, with exception for risk to life values which use a lower rate of 1.5%. The derivation of the discount rate can be found in Annex 6. Table 2 shows the present value of £1,000 declines in future years with a discount rate of 3.5%.
Table 2. Present Values and Discount Rate
| Year | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| Value | £1,000 | £966 | £934 | £902 | £871 | £842 | £814 | £786 | £759 | £734 | £709 |
5.36 The main role of discounting is to put interventions with different time spans and benefit cost profiles on to a common "present value" basis. In the longer term (over 30 years), the STPR declines in a series of steps to allow for future uncertainty in the value of its constituent parts, as explained in Annex 6. The approach to discounting where there are inter-generational wealth transfers is also described in Annex 6. The accompanying tables in Annex 6 and associated tables on the Green Book web pages show both the discount rate and discount factors that can be used to calculate a present value.
5.37 Discounting is solely concerned with adjusting for social time preference and is separate from adjusting for inflation. The recommended Green Book discount rate applies to real values, with the effects of general inflation already removed. To promote transparency the best practice approach is to first convert costs or benefits to a real price basis, and then perform the discounting adjustment. The inflation rate and discount rate should not be added and applied to costs and benefits.10
5.38 In appraisal, discounting should never be applied retrospectively to costs and benefits that have already occurred. Values do not increase simply because activities took place in the past (although of course the value of some assets may tend to increase over time). Discounting and the calculation of NPSV are illustrated further in Box 10.
5.39 Costs to government of raising funds (either through taxation or borrowing) are not a decision variable when considering whether to go ahead with a project or not. The STPR is therefore not linked to the costs of raising funds (either through taxes or borrowing).
Box 10. NPSV and Discounting Worked Example
| Alternative options, A and B, are both expected to improve the quality of a department's work and reduce staff costs. 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). | |||||
| Year | 0 | 1 | 2 | 3 | 4 |
| Option A (£m) | |||||
| Costs | -10.00 | 0 | 0 | 0 | 0 |
| Benefits | 0 | 2.50 | 2.50 | 2.50 | 2.50 |
| Net Benefit | -10.00 | 2.50 | 2.50 | 2.50 | 2.50 |
| Discounted net benefits | -10.00 | 2.42 | 2.33 | 2.25 | 2.18 |
| Net Present Social Value -0.82 | |||||
| Option B (£m) | |||||
| Costs | -5.00 | 0 | 0 | 0 | 0 |
| Benefits | 0 | 1.50 | 1.50 | 1.50 | 1.50 |
| Net Benefit | -5.00 | 1.50 | 1.50 | 1.50 | 1.50 |
| Discounted net benefits | -5.00 | 1.45 | 1.40 | 1.35 | 1.31 |
| Discount factor | 1 | 0.9662 | 0.9335 | 0.9019 | 0.8714 |
| Option B has positive NPSV of £0.51m compared to -£0.82m for Option A. | |||||
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9 Based on Ramsey F.P. (1928) "A Mathematical Theory of Saving" Economic Journal, Vol. 38, No 152, pp. 543 559.
10 Some automated systems to calculate costs and benefits are not set up in line with this approach. As long as the calculation provides the same result this is acceptable on grounds of proportionality for this to continue until established data systems are redeveloped.