Discount rate

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This editable Main Article is under development and subject to a disclaimer.

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A mathematical form of this article is available on the tutorials subpage.

Discount rates are used in economics to allow for the reduced current values that are ascribed to deferred occurrences, and have applications both to the cost-benefit analysis of public sector projects and to the appraisal of private sector investments. They are also used in financial theory in connection with the management of interest rates by central banks. The choice of discount rate for the evaluation of the effects of global warming has major policy implications.

## Contents

* 1 Discounting criteria
* 2 Discount rates in cost/benefit analysis
* 2.1 The social opportunity cost rate
* 2.2 The social time preference rate
* 2.3 The discount rate for transfers between generations
* 3 The discount rate for investment appraisal
* 4 References

## Discounting criteria[edit]

The preferred method of applying discount rates to cost-benefit analysis and to investment appraisal is by the calculation of the net present value of future flows of cost and benefits. Allowances for risks are made, either by adjustments to the risk-free discount rate, or by using specific probability estimates to calculate a net present expected value

## Discount rates in cost/benefit analysis[edit]

### The social opportunity cost rate[edit]

Many public sector authorities have evaluated their investments using discount rates based upon market rates, or other rates that are used in the private sector, in order to avoid crowding out private sector investments. Some authorities have used surveys of discount rates used for investment appraisal in the private sector, and in some cases, reductions to the resulting estimates have been introduced to allow for externalities that are socially significant, but are not allowed for in company accounts, such as noise and pollution, and for monopoly profits resulting from the exercise of market power. In view of its economic importance, the diversity of choices of discount rate has been remarkable. From 1972 to 1992, the rate which the United States Office of Management and Budget required federal agencies to use was 10 per cent, based upon an early estimate of private sector rates of return. In 1992, after a protracted debate among the government's economic advisers [1], it adopted the use of the real interest rates on Treasury notes and bonds, which are revised annually, and which in 2008 ranged from 2.1% for 3 years to 2.8% for 30 years [2]. Social opportunity cost rates imposed by the British Treasury between 1972 and 2003 ranged from 10 per cent to 5 per cent, based upon surveys of the discount rates used by British companies.

### The social time preference rate[edit]

The social time preference concept of discounting, arises from the behavioural observation that people prefer immediate satisfaction to deferred satisfaction. Thus the term “discount rate” refers to the compensation in terms of increased utility that a person requires as inducement to defer consumption (usually as a percentage per annum). The discount rate that a person experiences assuming no expectation of changing circumstances, is sometimes termed his “pure time preference rate” - to distinguish it from the inducement that he would require if he expected his consumption to increase. In that case, he would take account of the fact that, as his total consumption increased, he would experience a reduction in the marginal utility of any further increase [3]. According to the Ramsey equation[4], the proportionate further compensation that a person requires to take account of its diminishing marginal utility is referred to as that person’s “elasticity of the marginal utility of consumption”. A community’s discount rate, taking account of rising consumption, is termed its “social time preference rate”. The social discount rate of a community togeher with its liquidity preference are major determinants of its market interest rate. The social time preference discount rate adopted by the British Treasury in 2003 was 3.5 per cent for the first 30 years and declining thereafter to allow for increasing uncertainty [5].

### The discount rate for transfers between generations[edit]

The Stern Review of the economics of climate change [6] adopted the controversial [7] assumption that there should be no difference between the values attributed to a benefit (or cost) now and, the provision of the same benefit (or cost) to someone living at some remote time in the future. After allowing for an assumed probability of the survival of the human race, that implied a pure social time preference rate of 0.1 per cent. Together with the review's other assumptions and estimates [8], that led in turn to a discount rate of 2.1 per cent.

## The discount rate for investment appraisal[edit]

The appropriate discount rate for investment appraisal of an investment is the cost of capital to the investor, with an appropriate adjustment for the riskinness of the investment. A company' s cost of capital is the weighted average of its cost of capital and its cost of debt, where the proportion of debt is limited by the risk of insolvency [9].

## References[edit]

1. ↑ Matthew Goldberg Discount rates for government investment projects: The economic logic behind OMB circular A-94 The Engineering Economist Summer 1998
2. ↑ 2008 Guidelines and Discount Rates for Benefit-Cost Analysis of Federal Programs.,OMB Circular No A-94 revised 2008, Office of Management and Budget, 2008
3. ↑ See the article on supply and demand
4. ↑ Frank Ramsey “A Mathematical Theory of Saving” Economic Journal Vol. 38 1928
5. ↑ The Green Book, Annex 6, HM Treasury 2003
6. ↑ Stern Review on the Economics of Climate Change - Final Report HM Treasury 2006
7. ↑ See the Tutorials subpage for an account of the controversy
8. ↑ Noted on the tutorials subpage
9. ↑ The considerations governing a company's gearing are discussed in the article on financial economics