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Discounting

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Discounting is the technique used to compare costs and benefits that occur at different points in time.  Its purpose is to express in present values the flow of costs and benefits that arise across the full lifetime of a scenario or project.

Discounting involves three main steps:

  1. specification of the discount rate to be used;
  2. application of the selected discount rate to the costs and benefits identified for each year in the assessment period;
  3. summation of the discounted costs and benefits to give the total costs and benefits in present value terms.

Scope

Purpose: 

Immediate impacts of a policy or other intervention are often considered to be valued more highly than the same impacts at some future date. Discounting is therefore designed to adjust the value of future impacts to present values, in order to allow costs and benefits to be aggregated and compared in a consistent form.  

Boundaries: 

Discounting can be used whenever long-term impacts need to be assessed, and when suitable discount rates can be identified to reflect the opportunity cost of being able to make use of benefits now, or defer costs until later.  The degree to which this is valid in the case of health impacts needs to be carefully considered before discounting is done.  In the case of long-lasting impacts, care is also needed because the extended application of discounts can greatly influence the results of an assessment, and may bias the outcomes.  Care is needed, likewise, when inter-generational costs and benefits are involved, for discounting implies a transfer of benefits from future generations to present ones (and costs in the reverse direction), neither of which may be appropriate or acceptable when viewed from the perespective of those affected in the future.    

Method description

Input: 

Data are required on two main sets of attributes:

1) Discount rates:

  • Financial: maximum rate of return of capital obtained from alternative investments (opportunity costs)
  • Social: pure time preference, rate of growth of real consumption per capita, or elasticity of marginal utility of consumption

2) Present value of future costs:

  • Cost incurred in year t, rate of discount
Output: 

Analysis generates two primary outputs:

  1. Discount rate
  2. Present value of future costs or benefit streams
Rationale: 

Discount rates are generally based on one of two measures: the social opportunity cost of capital or the social time preference rate.   The former is based on observed behaviour; the latter derives from ethical consideration as to how future preferences should be valued.  Some disagreement exists about which is more appropriate, especially for assessments, though currently the majority of EU countries tend to apply social time preference rates.

Controversy also exists about the use of pure time preference rates, particularly in inter-generational assessments (e.g. impacts of long term pollution or climate change).   It has been argued, for example, that public policy should reflect collective, not private, interests (Sen, 1982), so in these cases pure time preferences should not be allowed to influence social discount rates.  The associated ethical argument is that, to ensure impartiality in pursuit of intergenerational equity, requires that the well-being of one generation should not be counted differently from that of any other. There are therefore arguments for paternalism.

An alternative reason for re-examining the appropriateness of the standard discount rate in applications over longer time periods is given by Weitzman (1998), who argues that, for any period, the real rate of interest is determined by the marginal opportunity cost of capital and this is constant over time.  By applying constant discount rates, economists are implicitly assuming that the productivity of investment will be the same in the distant future as in the recent past, and Weitzman sees no fundamental reasons why this should not be so.  However, the distant future is totally uncertain.  Uncertainty about future interest rates provides a strong generic rationale for using certainty-equivalent social interest rates that decline over time (starting beyond the short-term range within which it can be expected that current rates will prevail).  Certainty-equivalent discount rate can be found by taking the average of the discount factor, rather than the discount rate itself.  One such set of certainty-equivalent social interest rates has been adopted by the UK Government (see Table 1, below).  

Table 1.  Suggested discount rates for long term impacts (from UK Treasury)

Period (years ahead) Discount rate (%)
0-30  3.5
31-75 3.0
75-125 2.5
126-200 2.0
201-300 1.5
>300 1

A related issue is that of changes in unit values over time: because incomes are expected to rise over time, so should the WTP valuations be expected to increase.  This raises the question of whether the two should be assumed to increase at the same rate.  A number of studies have reported a positive relationship between income and WTP values (e.g. Hammitt and Liu 2004).  In combining this information with the need for discounting it seems reasonable to discount using only a pure rate of time preference (PRTP), for example of 1.5% .  The logic for this is that benefits, such as a reduction in the risk of death, might be seen as having a broadly constant utility value over time, regardless of changes in income.  If so, then such future benefits can be valued in current values and discounted at the pure time preference rate, so avoiding the need to calculate separately a rate of increase in their value over time.

Method: 

Discount rates are calculated and applied as follows:

1) The discount rate is calculated as:

\[i = z + n \times g \]

where: i is the social discount rate;

z is the social rate of pure time preference;

n is the elacticity of the marginal utility of consumption;

g is the growth rate of per capita consumption.

2) The present value of future costs or benefit streams is then estimated as:

\[PV = \sum_{t=0}^T C_t \times \frac{1}{(1+r)^t} \]

where: PV is the present value of the future costs/benefits;

Ct is the estimated cost in year t;

r is the ....

In applying discount rates as part of an environmental health impact assessment, it is recommended that:  

  • A common discount rate regime should be used across all study areas (e.g. countries).  The central rate used in the EU by the Directorate General for Environment is 4%, and this provides an appropriate guide rate for many applications.
  • Sensitivity analyses should usually be conducted to check that the discount rate is not biasing the analysis excessively.  Values of 2% and 6% are applied for the purpose by DG Environment, and these, too, may be appropriate as lower and upper bands for many environmental health impact assessments.
  • For the purpose of sensitivity analysis, also, a declining discount rate shoud be applied for longer term health impacts.  The discount regime used in the UK (see Table 1, above) provides guideline values for this purpose.