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 V 0 at time 0: V 1 =V 0 (1+r) V 2 =V 1 (1+r),… Future Value Formula: V t =V 0 (1+r) t. Present Value Formula: V 0 = V t /(1+r) t. This is compounded annually Continuous: V 0 = V t exp(-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) YearCostsBenefitsCumulative Net Gain 0120,00020, , ,048-80, ,141-62, ,277-45,534

When does she break even?

Concept of Present Value (annual discount rate r) What is the present value of a stream of costs and benefits, x t : x 0, x 1,…,x T-1 PV= x 1 + (1+r) -1 x 2 +(1+r) -2 x 2 +…+(1+r) -(T-1) x T-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. CPI t = 100*(C t /C 0 ) C t = cost of basket of goods in year t. C 0 = cost of basket of goods in year 0. E.g. YearCPI

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 projects may justify increasing discount rate.

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