### Discounting and the Importance of the Right Discount Rate

The discount rate is the percentage rate that is used to convert future values to present values. A discount rate of 4% (0.04) means that one dollar received in one year is worth $1/1.04 = 96 cents today. A discount rate of 10% (0.10) means that one dollar received in one year is worth $1/1.10 = 91 cents per day. Due to the geometric nature of discounting, the difference in present values becomes increasingly significant the further into the future that the dollar is received. For example, one dollar received in 15 years' time is worth $1/1.04^{15}= 56 cents with a discount rate of 4%, but only $1/1.10

^{15}= 24 cents with a discount rate of 10%. The choice of discount rate clearly makes a very significant difference to the present value of future costs and benefits.

Discount rates can be categorised into investor discount rates and social discount rates. Investor discount rates are used for calculating the value of an investment to an investor. Social discount rates are used for calculating the value of a project or course of action to society as a whole, such as an investment in a public hospital, or public transport or other infrastructure. Using a discount rate that is too high will result in under-investment in socially beneficial projects.

### Social Rate of Time Preference

When the calculation is for a private investment, then all costs associated with the investment will be displacing other investment that could be undertaken by the investor, and the appropriate discount rate is the opportunity cost of private investment. When the calculation is for a social net benefit assessment, the costs may be displacing (“crowding out”) private investment, or they may be displacing private consumption. When private consumption is displaced, the appropriate social discount rate is the "social rate of time preference"; when private investment is displaced the appropriate social discount rate is the "social opportunity cost".The rate at which individuals are willing to trade consumption now for consumption in the future is the individual consumer’s marginal rate of time preference. Just as the rate at which investors are willing to trade value now for value in the future is the appropriate discount rate for their decisions, the appropriate discount rate for an individual is the rate at which they are willing to trade consumption now for consumption in the future (i.e., the marginal rate of time preference).

There are two main ways for calculating the SRTP:

- Calculating an estimate of an individual’s marginal rate of time preference from observed interest rates; and
- Calculating the “consumption rate of interest” from more fundamental data.

### The Effect of Uncertainty

Suppose that we did not know which of the earlier discount rates, 4% or 10%, was the "correct" rate, and therefore assign an equal likelihood to them both. The resulting implied discount rate is*not*the arithmetic mean of the two values (which would be 7%). Instead, it is closer to the lower of the two estimates. Take, for example, the calculation over 15 years: the mean present value is (56c + 24c)/2 = 40c, which implies a discount rate of 6.3%. The effect is even more pronounced over long time periods, with the average discount rate over 50 years being just 5.3%. As the chart below shows, the further into the future that benefits and costs occur, the more that uncertainty over the right discount rate suggests that a low discount rate is more correct than a high discount rate.

**Chart: Uncertainty Means that Future Discount Rates should be Lower than the Average**

### The Social Discount Rate in New Zealand

The New Zealand Treasury recommends a default discount rate of 8%, including "for projects that are difficult to categorise including regulatory proposals."^{[1]}The New Zealand Institute of Economic Research (NZIER) considers that this default discount rate is probably too high, and that a lower rate consistent with the above concepts should be used.

^{[2]}

In 2007, Andrew Shelley co-authored a paper that examined the social discount rate for New Zealand in detail.

^{[3]}That study estimated a post-tax real discount rate for New Zealand of 3.5%, with a range of 2% to 6%. This range incorporates both the “social rate of time preference” approach to the discount rate and the more conventional (from an investor’s perspective) opportunity cost approach.

### International Practice

A social discount rate of 3.5% is consistent with practice in other advanced economies. In the United Kingdom, the “Green Book” recommends a real social discount rate of 3.5% based on a calculation of the social rate of time preference, for application in “all policies programmes and projects”.^{[4]}The social discount rate adopted by France is 4% and by Germany is 3%.

^{[5]}In the United States the rate currently mandated by the Department of Energy for certain federal programmes is 3%.

^{[6]}

### Conclusion

Cost-benefit analysis for public good projects should be conducted using a social discount rate. The current default rate of 8% suggested by the NZ Treasury is too high. A more suitable value for New Zealand is 3.5%, within a range of 2% to 6%, based on the social rate of time preference. This rate is consistent with the rate used in other advanced economies for social cost-benefit analyses. Uncertainty over the "correct" discount rate also suggests that a lower rather than higher rate should be used for long-horizon analyses.**Endnotes**

[1] New Zealand Treasury,

*Cost Benefit Analysis including Public Sector Discount Rates*, http://www.treasury.govt.nz/publications/guidance/planning/costbenefitanalysis, page updated 29 October 2010, accessed 2 February 2014.

[2]Chris Parker, “Economics like there’s no tomorrow”, NZIER Insights 32, 2011, http://nzier.org.nz/system/files/NZIER Insight 32 - Economics like there's no tomorrow.pdf

[3]Andrew Shelley, Jeremy Hornby, and Michael Thomas,

*Discount Rate for the Grid Investment Test*, CRA International, 29 March 2007, available online at http://www.ea.govt.nz/dmsdocument/3429.

[4] HM Treasury (2003)

*The Green Book: Appraisal and Evaluation in Central Government*, Treasury Guidance: London

[5] Evans, D.J. (2006)

*Social Discount Rates for the European Union*, Working Paper n. 2006-20, Università degli Studi di Milano, October, pp. 1-2.

[6] Rushing, A.S., J.D. Kneifel and B.C. Lippiatt (2013) "Energy Price and Discount Factors for Life-Cycle Cost Analysis – 2013 Annual Supplement to NIST Handbook 135 and NBS Special Publication 709", NISTIR 85-3273-21, Prepared for United States Department of Energy Federal Energy Management Program, National Institute of Standards and Technology, U.S. Department of Commerce, June, p. 1.