Discounting & Finance

1. Discounting & Finance How should the future benefits of a project be weighed against present costs?

2. 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 acquisition costs. [2001 Group Project on urban stormwater runoff] • Good idea? • Big issue: comparing costs today with benefits tomorrow

3. Example 1: “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?

4. Example 1: “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.

5. Outline • What is discounting? • Why do we discount? • The mechanics of discounting. • The importance & controversy of discounting. • Discounting in practice.

6. 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.

7. Why do we discount? • Simple answer: Put $100 in bank today, get about $103 next year.

8. Why a positive discount rate? • Impatience – • I would rather have that ice cream cone today than tomorrow • Decreasing marginal value of wealth • An extra dollar is less important if I am richer • Productivity of capital • Letting Carol’s forest grow another year generates more lumber • Risk • Will I live to see the money I put in the bank?

9. Example 2: 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

10. Combining impatience with capital productivity Slope=“rate of exchange” between wood today and wood tomorrow [eg, 1 cord today = 1.1 cords tomorrow] Wood today Indifference curve for consumers Forest Productivity Wood tomorrow

11. 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. • Other formulae available.

12. Example 3: 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)

13. Investing in drip irrigation (r=.05)

14. When does she break even?

15. Concept of Present Value (annual discount rate r) • What is the present value of a stream of costs and benefits, xt: 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

16. 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”

17. What is the risk free rate?US Tresury Yield Curve January 16, 2009

18. 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.

19. Some other discounting concepts • Net Present Value (NPV): The present value of a stream of values over the life of the project (eg, 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.

20. 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 • Eg, lower discount rate increases desirability of reducing GHG now (WHY?) • “Risk-adjusted discount rate” • Risky projects may justify increasing discount rate.

21. Social vs. private discount rate • Private discount rate—for private decisions • A positive concept • Result of market – supply and demand • Social rate – for societal decisions • A normative concept • Usually lower than private rate • How should we make intertemporal decisions? • Moving resources between generations different than between years for same person

22. Intergenerational decisions • Choice of discounting an ethical decision • We do have a preference for consumption earlier rather than later • We also tend to think a dollar is more important to a poorer person than a richer person • Result: r = η g + δ • η: elasticity of marginal utility of consumption wrt income • δ: pure rate of time preference • g: growth rate of income • Example (η = 1; g = 2%; δ = 0%) • r = 2%

23. Social discount rate in practice • Small increase in r can make or break a project. • Typical discount rates for public projects range from 2% - 10%. • Usually do “sensitivity analysis” to determine importance of discount rate assumptions. • Be clear about your assumptions on r.

24. What is the discount rate?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%

25. Distribution of responses

26. 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

27. Constant-rate discounting

28. Stern Review of Economics of Climate Change • Conclusion: Benefits of action outweigh costs of inaction • Controversies • Low discount rates for benefits • What does this do? • Different discount rate for costs and benefits • What does this do?

29. What’s the big deal?So what if we do a little more climate protection than necessary? • Money diverted from education • Developing countries have less well-educated population in 2050 • Savings diverted from other projects • Research into cancer gets shortchanged