A4.1 Using a discount rate has the effect of reducing the value of future costs and benefits in present day terms. If society has a discount rate of 3.5% per annum, this implies that it values £1 today equally with the certainty of £1.035 in a year's time. Another way to express this is to say that £1 in a year's time is worth only 96.62p now, because 1/1.035 equals 0.9662. The 96.62p figure is called the Present Value (PV) of the £1, and the 0.9662 figure is the relevant 'discount factor'.
A4.2 The following figures show how the PV of £1 declines in future years when the rate of discount is 3.5% per annum.
Year of Payment | Present Value |
0 | £1.0000 |
1 | £0.9662 ( = £1 x 1/1.035) |
2 | £0.9335 ( = £1 x 1/1.0352) |
3 | £0.9019 ( = £1 x 1/1.0353) |
10 | £0.7089 ( = £1 x 1/1.03510) |
A4.3 It is important to remember that the discount rate should generally be applied to figures that are:
• expressed in real terms i.e. excluding allowance for general inflation (See 2.8.5 above); and
• adjusted for appraisal optimism (See 2.6.15 above)
A4.4 In most appraisals it is sufficient to carry out discounting on costs and benefits identified at annual intervals. For example, it is common to identify streams of costs and benefits assumed to occur in the middle of Years 1, 2, 3 etc and to discount them all back to the middle of Year 0. Similarly, they may be assumed to commence at the start of Year 1, 2, 3 etc and discounted back to the start of Year 0.
A4.5 Table 1 of this appendix (see below) shows the discount factors needed to calculate PVs at 3.5% per annum. Table 2 provides discount factors for discount rates from 1% to 10% per annum. Detailed discounting calculations are facilitated by the use of suitable computer software, avoiding the need to refer to discount tables. However, tables can be useful in some circumstances, for instance when simple calculations are required. Departmental economists can advise on the design of spreadsheets to suit particular cases.