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Economics of Climate Change Adaptation Training - Session 9

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Economics of Climate Change Adaptation Training - Session 9

  1. 1. Photo credit: UNDP Climate Change Adaptation ECONOMICS OF CLIMATE CHANGE ADAPTATION BLOCK 2 TRACK 2 Cost-Benefit Analysis of Investment Projects and of Climate Change Adaptation Investments SESSION 9 Discounting
  2. 2. 8/21/2017 2 Session 9 Outline of presentation 2.1 What is T? 1 General methodology 2.2 What if T is infinite? 2.3 What about inflation? (nominal vs. real?) 2.4 Which discount rate to use: theory and practice 2 Four questions
  3. 3. 8/21/2017 3 Session 9 Outline of presentation 2.1 What is T? 1 General methodology 2.2 What if T is infinite? 2.3 What about inflation? (nominal vs. real?) 2.4 Which discount rate to use: theory and practice 2 Four questions
  4. 4. 8/21/2017 4 Session 9 General methodology Principle of discounting Discounting is simply a technique that allows us to compare costs and benefits that happens at different point in time into a common unit of measurement. Assume 10% return on investment Year 0 Year 1 Year 2 110 121100 Compounding Discounting Calculate Present Value
  5. 5. 8/21/2017 5 Session 9 General methodology Typically, the flows of costs and benefits of a project look like this: C0 1nvestment costs Benefits C1 C2 C3 C4 C5 C6Costs C7 Operational costs 0 0 0 B3 B4 B5 B6 B7
  6. 6. 8/21/2017 6 Session 9 General methodology Net benefits Benefits Costs
  7. 7. 8/21/2017 7 Session 9 General methodology C0 Benefits C1 C2 C3 C4 C5 C6Costs C7 0 0 0 B3 B4 B5 B6 B7 PV of Costs PV of Benefits
  8. 8. 8/21/2017 8 Session 9 General methodology C0 C1 C2 C3Costs PV of Costs Technique of discounting r Is referred to as the discount rate (in real terms). Is referred to as the discount factor. 3 3 2 21 0 )1()1()1( r C r C r C C      = t r)1( 1 
  9. 9. 8/21/2017 9 Session 9 General methodology PV = More generally Suppose a flow of benefits (or costs) Bt from t = 0 until t = T, then the present value of this flow is: T T r B r B r B r B B )1( ... )1()1()1( 3 3 2 21 0             Tt t t t r B 0 )1(PV =
  10. 10. 8/21/2017 10 Session 9 General methodology PV of costs = So, for any given project or policy, we will have: PV = T T r C r C r C r C C )1( ... )1()1()1( 3 3 2 21 0             Tt t t t r C 0 )1( T T r B r B r B r B B )1( ... )1()1()1( 3 3 2 21 0        PV of benefits =     Tt t t t r B 0 )1( PV =
  11. 11. 8/21/2017 11 Session 9 Outline of presentation 2.1 What is T? 1 General methodology 2.2 What if T is infinite? 2.3 What about inflation? (nominal vs. real?) 2.4 Which discount rate to use: theory and practice 2 Four questions
  12. 12. 8/21/2017 12 Session 9 Outline of presentation 2.1 What is T? 1 General methodology 2.2 What if T is infinite? 2.3 What about inflation? (nominal vs. real?) 2.4 Which discount rate to use: theory and practice 2 Four questions
  13. 13. 8/21/2017 13 Session 9 Four questions What is T? In theory, all benefits and costs of a project should be measured, even when they extend indefinitely. However, at least in the case of infrastructure project, the common practice is set the time horizon of the analysis (T) to coincide with the expected lifetime of the key (most important) component of the infrastructure project. For example: • Expected lifetime of a road (before it needs major repair – so major that it may as well be considered a new road): 40 years • Expected lifetime of a bridge: 75 to 100 years • Expected lifetime of a coal-fired power plant: 25 to 40 years And so, the time horizon of the analysis is set to coincide with these expected lifetimes.
  14. 14. 8/21/2017 14 Session 9 Four questions What is T? Or in situation where the Government will provide a concession to build and run a project (e.g. a power plant, a forestry or mining concession), then very often the time horizon of the cost-benefit analysis is set to coincide with the duration of the concession. For example if: • Duration of a concession of a build and operate power plant 25 years. Or if: • Duration of a mining concession: 40 years • Then the time horizon of the analysis is set to coincide with these durations (25 years or 40 years respectively).
  15. 15. 8/21/2017 15 Session 9 Four questions What is T? Warning: As a principle, this approach for setting the time horizon of the economic analysis is wrong. The selection of the time horizon for the CBA should be guided by one question: How long will the impacts (positive or negative) last? And the answer to this question may or may not coincide with the lifetime of the infrastructure or duration of the concession. This may or may not matter in terms of assessing the economic desirability of the project or policy. If the infrastructure lifetime or duration of the concession is long enough, and if the discount rate being used is relatively high, then whatever happens after the CBA is truncated (after say 40 years) may not matter very much.
  16. 16. 8/21/2017 16 Session 9 Outline of presentation 2.1 What is T? 1 General methodology 2.2 What if T is infinite? 2.3 What about inflation? (nominal vs. real?) 2.4 Which discount rate to use: theory and practice 2 Four questions
  17. 17. 8/21/2017 17 Session 9 Four questions $A $A $A $A $A $A $A Year $A What if T is infinite? Suppose the following: 0 1 2 3 4 5 … ∞ For example, if A = $100 and if r = 10%, then the present value of A is: 100*(1.1)/0.1 = $1,100. PV = PV =          )1( ... )1()1()1( 32 r A r A r A r A A r r A )1( * 
  18. 18. 8/21/2017 18 Session 9 Four questions $A $A $A $A Year $A What if T is infinite? Suppose the following: 0 1 2 3 4 5 … ∞ How would you calculate the PV of $A?
  19. 19. 8/21/2017 19 Session 9 Four questions $A $A $A $A Year $A What if T is infinite? Suppose the following: 0 1 2 3 4 5 … ∞ Discounted to Year 0, it will be: r r A )1( *  )1( 3 r PV to Year 3 = A * (1+r) r
  20. 20. 8/21/2017 20 Session 9 Outline of presentation 2.1 What is T? 1 General methodology 2.2 What if T is infinite? 2.3 What about inflation? (nominal vs. real?) 2.4 Which discount rate to use: theory and practice 2 Four questions
  21. 21. 8/21/2017 21 Session 9 Four questions What about inflation? (nominal vs. real?) Should we include inflation in this work? If we do, then what discount rate to use? So, suppose that prices are expected to rise at rate ‘g’ for the duration of the project. Suppose that the nominal discount rate is m (the real discount rate is r).
  22. 22. 8/21/2017 22 Session 9 Four questions PV = What about inflation? (nominal vs. real?) Then, the present value of a flow of benefits from t = 0 to t = T is: According to Fisher’s Law: (1 + m) = (1 + r)(1 + g). So we have: T T T m gB m gB m gB m gB B )1( )1( ... )1( )1( )1( )1( )1( )1( 3 3 3 2 2 21 0             PV = TT T T gr gB gr gB gr gB gr gB B )1()1( )1( ... )1()1( )1( )1()1( )1( )1)(1( )1( 33 3 3 22 2 21 0             Which is the same as: PV = T T r B r B r B r B B )1( ... )1()1()1( 3 3 2 21 0        
  23. 23. 8/21/2017 23 Session 9 Four questions What about inflation? (nominal vs. real?) If all costs and benefits are measured in nominal values, then use nominal discount rate. If all costs and benefits are measured in real values, then use real discount rate. It does not matter. However, in practice, most of the time we do the analysis in real terms. In doing so, there is one less variable we need to make projections for, the annual inflation rate for each year of the time horizon of the analysis. Note: Doing the analysis in real terms does not necessarily in constant prices. . Message is:
  24. 24. 8/21/2017 24 Session 9 Four questions Adjust past value for US inflation to find today’s US value Taking values from the past What about inflation? (nominal vs. real?) Today Do analysis in real terms Taking values from the past Adjust past value for national inflation to find today’s value Use exchange rate today to transfer in national value today Do analysis in real terms Do analysis in real terms
  25. 25. 8/21/2017 25 Session 9 Outline of presentation 2.1 What is T? 1 General methodology 2.2 What if T is infinite? 2.3 What about inflation? (nominal vs. real?) 2.4 Which discount rate to use: theory and practice 2 Four questions
  26. 26. 8/21/2017 26 Session 9 Four questions Which discount rate to use: theory Consumers have utility function defined over consumption today and in the future. Where and stand for consumption today and tomorrow. Two things about this function: In a perfect world: 1 The higher or , the higher is utility. 2 The marginal utility of consumption is declining. It implies that consuming everything today or tomorrow will not maximize utility (consumption smoothing is preferred).
  27. 27. 8/21/2017 27 Session 9 Four questions Which discount rate to use: theory The Marginal Rate of Substitution (MRS) tells us by how much future consumption must be increased to compensate for a loss of consumption today. Where U is marginal utility with respect to C and U with respect to C The MRS is also interpreted as the individual’s rate of time preference. In a perfect world: It is the slope of the indifference between present and future consumption. 1100
  28. 28. 8/21/2017 28 Session 9 Four questions The slope of this Indifference curve is the marginal rate of substitution. However, if I have a limited amount of C0 and you are taking one unit away, I will need a large increase in C1 to be compensated. If I have lots of C0 and you take away one unit of C0, I do not need a large increase in C1. In a perfect world: C0 C1 -1 -1 Which discount rate to use: theory
  29. 29. 8/21/2017 29 Session 9 Four questions We can transform today’s consumption into future consumption. In a perfect world: If we invest one unit of C0, we will obtain additional units of C1 according to the marginal productivity of capital. Which discount rate to use: theory
  30. 30. 8/21/2017 30 Session 9 Four questions The slope of this Indifference curve is the marginal rate of substitution. The slope of this function is the marginal rate of transformation. In a perfect world: C0 C1 Which discount rate to use: theory
  31. 31. 8/21/2017 31 Session 9 Four questions In a perfect world: C0 C1 Which discount rate to use: theory C1 C0
  32. 32. 8/21/2017 32 Session 9 Four questions The optimal consumption path (which maximizes lifetime utility) is such that the marginal rate of transformation is equal to the marginal rate of substitution. In a perfect world: Marginal rate of transformation Which discount rate to use: theory If we introduce perfectly competitive capital markets, we can show that a competitive equilibrium in capital markets is such that the market interest rate (which is the opportunity cost of capital) equals the marginal productivity of capital. Individual’s rate of time preference Opportunity cost of capital Marginal productivity of capital = =
  33. 33. 8/21/2017 33 Session 9 Four questions And so now we finally have: In a perfect world: Market interest rate Which discount rate to use: theory Opportunity cost of capital Individual’s rate of time preference = = Marginal productivity of capital =
  34. 34. 8/21/2017 34 Session 9 Four questions Suppose G comes in and wants to undertake a public project. The project will decrease consumption and/or private investment today, and increase consumption tomorrow. In a perfect world: Which discount rate to use: theory What should be the discount rate to evaluate the benefits of future additional consumption? Answer is: The project will either displace consumption or private investment. Hence, the discount rate to use will depend on what G project is displacing.
  35. 35. 35 Session 9 Four questions If the project displaces current consumption, the discount rate should be the rate of time preference. In a perfect world: Which discount rate to use: theory If the project displaces other investments, the discount rate should be the marginal productivity of capital. If the project displaces both consumption and investment, the discount rate should be a weighed average of the marginal productivity of capital and the rate of time preference. But in this perfect world, both the rate of time preference and the marginal productivity of capital equals the market interest rate. Thus we get: Discount rate = Market Interest Rate (risk free)
  36. 36. 36 Session 9 Four questions We may base the selection of the discount rate either on the rate of society’s time preference or on the social opportunity cost of capital or on a weighed average of those two. In a less than perfect world: Which discount rate to use: theory Most financial/treasury/planning institutions would understand using the social opportunity cost of capital to set the discount rate. For example, from ADB’s CBA guidelines: “A project investment is economically justified if the estimated economic internal rate of return (EIRR) exceeds the economic opportunity cost of capital (EOCC) for the country.”
  37. 37. 37 Session 9 Four questions All of welfare economics is based on the presumption that policy choices aim to maximize society’s welfare. However: Which discount rate to use: theory If this is correct, then upon noting (1) that society’s welfare is made of some aggregation of individual’s welfare (utility) and (2) that utility is defined over consumption, then the value of the social discount rate should be based the rate of society’s time preference – not the opportunity cost of capital. This approach gives rise to the Ramsey Rule.
  38. 38. 38 Session 9 Four questions Ramsey Rule (from Ramsey), 1928) Where: is the social discount rate is the rate at which society discounts the utility of present versus future consumption (impatience) is the relative aversion to intertemporal inequality. is the growth rate of per capita consumption.
  39. 39. 8/21/2017 39 Session 9 Four questions Upon applying the Ramsey Rule: Which discount rate to use: theory Weitzman (2007) 2% 2 2% 6% Nordhaus (2005) 1% 2 2% 5% Stern (2006) 0.1% 1 1.3% 1.4% U.K. (since 2003) 1.5% 1 2.0% 3.5% France (since 2005) 0% 2 2.0% 4.0%
  40. 40. 8/21/2017 40 Session 9 Four questions MDBs: MDBs Discount rates World Bank 10% Asian Development Bank 12% Inter-American Development Bank 12% European Bank (EBRD) 10% Note: All projects, irrespective of sectors (be it transport, energy, environment, health, water supply, agriculture, etc.) and irrespective of countries, must use the same discount rate. Which discount rate to use: practice
  41. 41. 8/21/2017 41 Session 9 Four questions MDBs:: MDBs: MDBs Discount rates World Bank 10% Asian Development Bank 12% Inter-American Development Bank 12% European Bank (EBRD) 10% ADB: “Given the difficulty of estimating country-specific economic opportunity costs of capital (EOCC), the EOCC for all ADB DMCs is 12%.” World Bank: “ It is justified as a notional figure for evaluating Bank-financed projects. This notional figure is not necessarily the opportunity cost of capital in borrower countries, but is more properly viewed as a rationing device for World Bank funds" (Operational Core Services Network Learning and Leadership Center, 1998). Which discount rate to use: practice
  42. 42. 8/21/2017 42 Session 9 Four questions Some countries Countries Discount rates Philippines 15% India 12% Pakistan 12% Which discount rate to use: practice
  43. 43. 8/21/2017 43 Session 9 Four questions Line ministries (or operational departments in MDBs) would prefer to have their policies or projects accepted. Incentives to over-estimate benefits and under-estimate costs. Set a high discount rate. Which discount rate to use: practice Strategic reaction from those who allocate resources:
  44. 44. 8/21/2017 44 Session 9 Four questions Some countries Which discount rate to use: practice Countries Discount rates Philippines 15% India 12% Pakistan 12% New Zealand 10% (until 2008); now 8% United States OMB: 10% (until 1992); 7% (until now); 3% for sensitivity (since 2003); NOAA: 3%: EPA: 3% European Union 6% (until 2006); now 5% Germany 4% (until 2004); now 3% France 8% (until 2005); now 4%
  45. 45. 8/21/2017 45 Session 9 Four questions In the USA: On the selection of 7% in 1992: “This new rate of 3% is justified by the social rate of time preference. If we take the rate that the average saver uses to discount future consumption as our measure of the social rate of time preference, then the real rate of return on long-term government debt may provide a fair approximation” (OMB, (2003). The 3% corresponds to the average real rate of return of 10- year Treasury notes between 1973 and 2003. Which discount rate to use: practice On the selection of 3% in 2003: “7% is an estimate of the average before-tax rate of return to private capital in the U.S. economy” (OMB (2003).
  46. 46. 8/21/2017 46 Session 9 Four questions U.K. since 2003 Which discount rate to use: practice 0.5% 1.0% 1.5% 2.0% 2.5% 3.0% 3.5% 100 200 300 400 500 Rationale: We cannot presume that future generations will be better off than today’s generation.
  47. 47. 8/21/2017 47 Session 9 Four questions Canada: TBS currently recommends the use of 3% (“social” rate) and 7% (“real” rate) as CBA discount rates. TBS now allows for the option to use 3% discount rate as a central value for health and environmental CBAs. Which discount rate to use: practice
  48. 48. 8/21/2017 48 Session 9 Four questions Applying the Ramsey Rule in Canada: Which discount rate to use: practice Mid - point 1% 1.5 1.7% 3.5% Range 1 – 2 1.5% – 2.0% 2.5% - 5.0% Source: Boardman et al (2008)
  49. 49. 8/21/2017 49FOOTER GOES HERE Thank you

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