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Reconciling cost-benefit analysis and time

This is complicated because a given unit of currency (£, €, $, etc) worth of costs or benefits ten years from now is not the same as a unit of currency worth of costs or benefits today. As a project may provide benefits and take costs at different times during its lifespan, comparisons of these costs and benefits need a consistent denominator over time (i.e. a common currency). To ensure this feature is taken into account in CBA, a process called discounting is used.

Discounting is used to translate the present value of our monetary unit to that in x number of years into the future and therefore allow all future costs and benefits to be expressed in their present value equivalent.

For example, at a constant 10% interest rate, the present value of £1 11 years from now is equivalent to about 35p and the present value of £1 50 years into the future is just over half of one penny.

Does that sound right?

The proof is shown in table 1.1.

Table 1.1

Year ValueDiscount (=10% interest)DifferenceFollowing year's value
Year 1 £1.00 10p (100-10) 90p
Year 2 90p 9p (90-9) 81p
Year 3 81p 8.1p (81-8.1) 72.9p
Year 4 72.9p 7.29p (72.9-7.29) 65.61p
Year 5 65.61p 6.52p (65.61-6.52) 59.09p
Year 6 59.09p 5.91p (59.09-5.91) 53.18p
Year 7 53.18p 5.32p ( 47.86p
Year 8 47.86p 4.86p (47.86-4.86) 43p
Year 9 43p 4.3p (43.99-4.3) 38.7p
Year 10 38.7p 3.9p (38.70-3.9) 34.8p

Inflation (i.e. the rate at which money loses its value) can change massively over time - inflation ran at 12 to 13% in the 80s. What is today's rate? The ability to predict this accurately is not particularly well developed. You could try to devise a spreadsheet to carry this on for 50 years or with different interest rates, but, in general, the longer the time frame and the higher the discount rate, the smaller the impact will be of any given year on total net benefits. This gives rise to one of CBA's main weaknesses - one that is even recognised by economists. The final result is that any decision is based on the identification of the correct discount rate.

Another very significant problem rarely recognised is that because the discounting process calculates the results from the present generation's perspective, one needs to be concerned about temporal equity issues - that is, to the fairness of the decision to future generations. In fact, costs that occur far into the future may be given little weight in traditional CBA. The pound may be worth less in the future, but clean air, for example, may not be worth less - it may be worth an awful lot more. Environmental sustainability has developed as an additional consideration for public policy decision-making. This is because of the very real concern that the process of discounting future environmental considerations may steer us towards policies that overly emphasise short-term gain.

Just to reiterate, CBA does not and should not be seen as a tool through which it is possible to decide on the most sustainable option. This is an important point which is generally missed by decision-makers. However, that is enough on the problem of value and time. The next issue when carrying out a CBA is the choice of input values.