Appendix 3: Converting Values to Their "Present Value"
Suppose that an option has costs that are incurred over the next two years and benefits that are realised in ten years, or from now into the future indefinitely (for example, an option to build a new road). In order to compare costs and benefits across time, all costs and benefits need to be converted to their present value, which means the value of the cost or benefit is converted to its value as if it was incurred/received today. The need for such a conversion arises from the simple observation that the value of a dollar received today is normally valued more highly than a dollar received at some time in the future. Converting values to their present value (i.e. discounting values that will be realised in the future) means you are comparing apples with apples. There are three major reasons for this difference:
- The "rate of time preference". Most people are impatient and prefer consumption undertaken now rather than later. Thus, a dollar available now is more highly valued than one received later.
- Uncertainty. There is necessarily some degree of uncertainty as to whether a future dollar will actually be received. Its value is lessened in proportion to the expected size of this uncertainty factor. Hence the discount rate may depend on the degree of uncertainty.
- Wealth. People will be wealthier in the future than they are now, so impacts incurred now are valued more than the same impacts incurred in the future.
Note: all costs and benefits must be real (inflation adjusted) values.
The discount rate seeks to capture the sum of the above factors. A standard formula for the discount rate is d=ρ+μ.w where ρ is the rate of time preference (including uncertainty), μ is the marginal utility of consumption (how much value an additional dollar is worth - a value of 1 implies that a generation with twice as much wealth will value a dollar at half that which the current generation does) and w is the per capita growth rate. For example, if ρ=0.03 (3%), μ=1, and w=0.02 the discount rate, d, equals 0.05 or 5%.
To calculate the present value of a cost or benefit, multiply the magnitude of the cost or benefit by 1/(d+1)t where:
- d = discount rate;
- t = the time period.
The time period is defined with reference to the discount rate. For example, if d=5% per year, and t=2, 2 represents the second year. If d=5% per month, and t=2, 2 represents the second month.
While conceptually simple, there is considerable debate about how discount rates should be calculated. The discount rate used may depend on the type of benefit or cost being discounted. The discount rate applied to Government expenditure can be the cost of capital to the Crown, or the Government bond rate appropriate to the term of the project. This incorporates the opportunity cost of resources forgone to pursue the proposal or project. Further, it may be possible to justify applying much lower discount rates to environmental values in the expectation that as people become wealthier and the extent and nature of the environment decline, people in the future can be expected to place greater value on the natural environment. Social projects can be particularly sensitive to discount rates, and accordingly many health projects often use a low discount rate of 3% because of the long length of time before benefits accrue. Using a range of discount rates to demonstrate the sensitivity of your project to the discount rate, rather than just choosing one discount rate, is often recommended.
Care needs to be taken in the choice of discount rates. Across Government, these choices can impact on:
- the allocation of resources between the private and public sectors;
- the extent to which it is possible to support the imposition of regulatory costs on business and community interests;
- the extent to which the interests of current generations may be favoured over those of future generations; and
- More guidance on the net present value concept and discount rates is available in Treasury's Cost Benefit Analysis Primer [link to Treasury website].
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