Discounting How should the future benefits of a project be weighed against present costs Generic Group Project You are making a recommendation about using catchment basins for groundwater recharge in LA Costs now provide water in future offsetting future water costs Good idea Big issue comparing costs today with benefits tomorrow Contractor wins 314 9 million Powerball Winner opts for 170 million lump sum payoff instead of 30 annual payments of about 10 5 million per year Question Why would someone choose 170 million over 315 million Answer The time value of money Future earnings must be discounted Outline What is discounting Why do we discount The mechanics of discounting The importance controversy of discounting Discounting in practice What is discounting Public and private decisions have consequences for future Private Farmer invests in water saving irrigation High up front cost benefits accrue over time Public Dam construction decommissioning Regulating emissions of greenhouse gases wetlands restoration etc Need method for comparing costs benefits over time Why do we discount Put 100 in bank today get about 103 next year Why does money earn positive interest People generally prefer to consume sooner rather than later impatience If we invest we can get more next year Productivity of capital Example Carol s Forest Assume forest grows at a declining annual rate Annually 4 3 9 3 8 When should she cut her forest If she s patient wait and get more wood If she s impatient cut now Tension impatience to consume vs waiting and producing more Interest rate is an equilibrium between impatience of consumers and productivity of the forest Mechanics of discounting Money grows at rate r Invest V0 at time 0 V1 V0 1 r V2 V1 1 r Future Value Formula Vt V0 1 r t Present Value Formula V0 Vt 1 r t This is compounded annually Continuous V0 Vtexp rt Other formulae available in handout The drip irrigation problem Farmer has to decide whether to invest in drip irrigation system should she Basic Parameters of Problem Cost 120 000 Water savings 1 000 Acre feet per year forever Water cost 20 per acre foot Calculate everything in present value alternatively could pick some future date and use future value formula Investing in drip irrigation r 05 Year Costs Benefits Cumulative Net Gain 0 120 000 20 000 100 000 1 0 19 048 80 952 2 0 18 141 62 811 3 0 17 277 45 534 When does she break even Drip Irrigation Project 200000 Net Payoff 150000 100000 50000 0 50000 0 5 10 15 100000 150000 Year 20 25 Concept of Present Value annual discount rate r What is the present value of a stream of costs and benefits x t x0 x1 xT 1 PV x1 1 r 1x2 1 r 2x2 1 r T 1 xT 1 If PV 0 stream is valuable Annuity Opposite of present value convert a lump sum into a steam of annual payments Eg spend 1 000 000 on a dam which is equivalent to 96 000 per year for 30 years check it Eg Reverse mortgages for seniors Where does inflation come in Inflation is the increase in the cost of a basket of goods over time Your grandpa always says An ice cream cone only cost a nickel in my day the fact that it s now 2 is inflation Want to compare similar values across time by controlling for inflation Correct for inflation Real Don t correct for inflation Nominal The Consumer Price Index CPI is the way we account for inflation CPIt 100 Ct C0 Ct cost of basket of goods in year t C0 cost of basket of goods in year 0 E g Year CPI 1990 100 1991 104 2 1992 107 4 Some other discounting concepts Net Present Value NPV The present value of a stream of values over the life of the project e g NPV of B C Internal Rate of Return IRR The interest rate at which project would break even NPV 0 Scrap Value The value of capital at the end of the planning horizon Importance of discounting Discounting the future biases analysis toward present generation If benefits accrue later project less likely If costs accrue later project more likely Speeds up resource extraction E g lower discount rate increases desirability of reducing GHG now WHY Risk adjusted discount rate Risky rate projects may justify increasing discount Social vs private discount rate Private discount rate easily observed It is the outcome of the market for money Depends on risk of default on loan Social rate may be lower People care about future generations Public projects pool risk spread losses among all taxpayers Argues for using risk free rate of return Social discount rate in practice Small increase in r can make or break a project Typical discount rates for public projects range from 4 10 Usually do sensitivity analysis to determine importance of discount rate assumptions Be clear about your assumptions on r Weitzman s survey 2160 Economists Taking all relevant considerations into account what real interest rate do you think should be used to discount over time the benefits and costs of projects being proposed to mitigate the possible effects of global climate change Mean 4 Median 3 Mode 2 Far distant costs or benefits Many important environmental problems have costs and or benefits that accrue far in the distant future Constant rate discounting has 3 disadvantages in this case Very sensitive to discount rate Far distant consequences have little or no impact on current policy Does not seem to fit empirical or experimental evidence very well Constant rate discounting New Innovations Uncertainty If uncertain over future value of r then as if rate was lower Hyperbolic discounting Gives much more weight to future Formula PV FV 1 at g a But is time inconsistent If social decisionmakers were to use people s 1998 hyperbolic rates of time preferences plans made in 1998 would not be followed because the low discount rate applied to returns in say 2020 will become a high discount rate as the year 2020 approaches Cropper and Laibson Quasi hyperbolic discounting can be time consistent Hyperbolic vs Const Rate