Discount rates and net present value

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’.

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 mathematical expressions used to calculate discounted present values are set out below.

Year 0 is the present. Accordingly, the present value, at the middle of year 0, of a payment of £1 made at the middle of year n is given by:

D_n=1/(1+r)^n

where r is the discount rate and  is the discount factor. The discount rate is used to convert all costs and benefits to ‘present values’, so that they can be compared. The recommended UK public service discount rate is 3.5%. For example, a payment of £150 at the middle of year 5 has a present value at the middle of year 0 of:

150 x 1/〖1.035〗^n = 150 x 0.8420 = 126.30

Present values and discount rate

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. The following table shows how the present value of £1,000 declines in future years with a discount rate of 3.5 per cent.

Time

(mid year)

PV of payment

(mid year)

0

£1,000

1

£966

2

£934

3

£902

4

£871

5

£842

6

£814

7

£786

8

£759

9

£734

10

£709

Long-term discount rates

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 below.

The declining long term discount rate

Period of years

Discount rate

0–30

3.5%

31–75

3.0%

76–125

2.5%

126–200

2.0%

201–300

1.5%

301+

1.0%

Exceptions to the discount rate schedule

The standard schedule of discount rates may not be appropriate in the following circumstances.

For international development assistance projects, a discount rate derived from estimates of the social time preference rate appropriate to the recipient economy should be used.

When undertaking sensitivity analysis, the impact of changing the precise value of the discount rate can be analysed in the same way as for other parameters in the appraisal. The rationale for undertaking sensitivity analysis on the discount rate should be clearly explained.

More information is available in HM Treasury’s The Green Book (2003).