Discount rate: Difference between revisions

Latest revision as of 11:01, 7 August 2024

Discounting criteria

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

The social opportunity cost rate

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

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

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

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

↑ Matthew Goldberg Discount rates for government investment projects: The economic logic behind OMB circular A-94 The Engineering Economist Summer 1998
↑ 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
↑ See the article on supply and demand
↑ Frank Ramsey “A Mathematical Theory of Saving” Economic Journal Vol. 38 1928
↑ The Green Book, Annex 6, HM Treasury 2003
↑ Stern Review on the Economics of Climate Change - Final Report HM Treasury 2006
↑ See the Tutorials subpage for an account of the controversy
↑ Noted on the tutorials subpage
↑ The considerations governing a company's gearing are discussed in the article on financial economics

[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

[1]

[2]

[3]

[4]

[5]

[6]

[7]

[8]

[9]

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 {{subpages}}
+{|align="left" cellpadding="10" style="background:lightgray; width:90%; border: 1px solid #aaa; margin:20px; font-size: 92%;"
+| A mathematical form of this article is available on the [[/Tutorials|tutorials subpage]].
+|}
-==Definition==
-In economics, the concept of discounting, as used for the purpose  of [[cost/benefit analysis]], 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 <ref>See the article on [[supply and demand]]</ref>.  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”.  (The derivation of that concept is attributed to a 1928 paper by the economist [[Frank Ramsey]] <ref> Frank Ramsey “A Mathematical Theory of Saving”  Economic Journal Vol. 38 1928</ref>.  There is a note on the “Ramsey equation”, and the estimation of the associated elasticity measure, on the tutorials subpage.).  A community’s discount rate, taking  account of rising consumption, is termed its “social time preference rate”. The social discount rate of a compunity togeher with its [[liquidity prefernce]] are major determinants of its market [[interest rate]].
-In financial theory, the uses of the term “discount rate” include its application to a variety of interest rates, including the rate charged for loans made to a country’s banks by its central  bank <ref> See the article on [[financial economics]]</ref>, and the rates of return that are used as investment criteria by companies <ref> See the article on [[business economics]]</ref>  and by government agencies <ref> See the article on [[cost/benefit analysis]]</ref>.
+'''[[Discount rate]]s''' 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.
-==Financial implications==
+==Discounting criteria==
-"Time is money". Financial theory has tried to implement the fact that one [[cash flow]] received in the future is worth less than the same cash flow received today (i.e. one [[dollar]] in one year vs. one dollar received today). Any investor preferring to receive a cash flow sooner rather than later can put his money in a riskless [[saving account]]. The general formula for the [[discount]]ing of a cash flow is given by:
+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 value/Tutorials#Net present expected value|net present expected value]]
-<math>NPV_0=\frac{FV_t}{(1+k)}</math>
+==Discount rates in cost/benefit analysis==
+===The social opportunity cost rate===
+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 [[externality|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 <ref>[http://findarticles.com/p/articles/mi_qa3621/is_199807/ai_n8799084  Matthew Goldberg Discount rates for government investment projects: The economic logic behind OMB circular A-94 The Engineering Economist Summer 1998]</ref>, it adopted the use of the real interest rates on [[Financial system#Bonds|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
+<ref>[http://www.whitehouse.gov/omb/memoranda/fy2008/m08-08.pdf ''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]</ref>. 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.
-where <math>NPV_0</math> is the [[Net Present Value]],
+===The social time preference rate===
-<math>FV_t</math> is the Future value (i.e. of a cash flow) received at time <math>t</math>
+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 <ref>See the article on [[supply and demand]]</ref>. According to the [[/Tutorials#The social time preference rate|Ramsey equation]]<ref> Frank Ramsey “A Mathematical Theory of Saving”  Economic Journal Vol. 38 1928</ref>, 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 <ref>[http://greenbook.treasury.gov.uk/annex06.htm  ''The Green Book'', Annex 6, HM Treasury 2003]</ref>.
-and <math>k</math> is the discount rate.
-Rearranging this equation we have that:
+===The discount rate for transfers between generations===
+The Stern Review of the economics of climate change <ref>[http://www.hm-treasury.gov.uk/independent_reviews/stern_review_economics_climate_change/stern_review_Report.cfm ''Stern Review on the Economics of Climate Change - Final Report HM Treasury 2006]</ref> adopted the controversial <ref> See the Tutorials subpage for an account of the controversy</ref> 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 <ref> Noted on the tutorials subpage</ref>, that led in turn  to a discount rate of 2.1 per cent.
-<math>k=\frac{FV_t}{NPV}-1</math>
+==The discount rate for investment appraisal==
+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 <ref> The considerations governing a company's gearing are discussed in the article on [[financial economics]]</ref>.
-The '''discount rate''' is the interest rate that links a future cash flow received a time <math>t</math> to the same cash flow received now, at <math>t = 0</math>. It takes into account the length of the time period (the longer time it is, the higher it should be) and the risk related to the cash flow (the more uncertain it is, the higher the discount rate is).
-Assume I have $80, and I buy a [[government bond]] that pays me $100 in a year's time. The discount rate represents the discount on the future cash flow:
-<math>\frac{(100)}{80}-1= 25%</math>
-==Economic Policy==
-One of the major issues in economics is what is an appropriate discount rate to use under various circumstances. For example, in assessing the impact of very long-term phenomena such as climate change, use of any discount rate much more than 1% per annum renders long-term damage (occurring in, say, 200 years time) of negligible importance now.
-Conversely, governments often take a short-term view of things, effectively applying discount rates of perhaps 20% p.a. or higher, on the grounds that anything they do or fail to do which has detrimental effects in (say) 10 or more years' time won't prevent their re-election sooner than that.
-In practice, discount rates such as 2%, 3%, 5% and 10% are widely used in economics. However there is little consensus on what value is appropriate in any given circumstance, and it often makes a significant difference.
-==Context Specific Uses==
-;Credit cards : {{main|Merchant account}}
-:The discount rate is a percentage of the dollar amount of the transaction that a merchant is charged for each credit card transaction.
-;Monetary Policy : The discount rate is the rate that an eligible depository institution (such as a [[bank]]) is charged to borrow short term funds directly from the [[central bank]] through the [[Discount_window|discount window]]. This is also known as the '''base rate''', '''repo rate''' and/or '''primary rate''', as a profit-making bank will need to charge rates higher than this to its customers.
-==External links==
-*[http://www.richmondfed.org/publications/economic_research/instruments_of_the_money_market/ Instruments of the Money Market: Table of Contents]
-**[http://www.richmondfed.org/publications/economic_research/instruments_of_the_money_market/ch03.cfm Instruments of the Money Market: Chapter 3 - The discount window]
 ==References==
-<references/>
+<references/>[[Category:Suggestion Bot Tag]]