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# Discounting

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

2. “Construction company owner wins \$314.9 million Powerball” • Winner opts for \$170 million lump-sum payoff instead of 30 annual payments. • Question: Why would someone choose \$170 million over \$315 million? • Answer: The time value of money. Future earnings must be discounted.

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

4. 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, Regulating emissions of SOx, etc. • Need method for comparing costs & benefits over time.

5. Why do we discount? • Put \$100 in bank today, get about \$105 next year. • Why does money earn positive interest? • People generally prefer to consume sooner rather than later (impatience), • Productivity of capital (if we divert some money to investment, may yield higher future consumption).

6. 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 in handout.

7. The drip irrigation problem • Farmer has to decide whether to invest in drip irrigation system: • Cost = \$120,000. • Water savings = 1,000 Acre-feet per year • Water cost = \$20 per acre foot. • Calculate everything in present value (alternatively, could pick some future date and use future value formula)

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

9. When does he break even?

10. Where does inflation come in? • Inflation is the increase in the cost of a “basket of goods” at different times. • Your grandpa always says “An ice cream cone only cost a nickel in my day”….that’s inflation. • Want to compare similar values across time by controlling for inflation • Correct for inflation: “Real” • Don’t correct for inflation: “Nominal”

11. The “Consumer Price Index” • CPI is the way we control 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.

12. Some other discounting concepts • Net Present Value (NPV): The present value of B-C over the life of the project. • Internal Rate of Return (IRR): The interest rate at which project would break even. • Scrap Value: The value of capital at the end of the planning horizon.

13. 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 • “Risk-adjusted discount rate” • Risky projects may justify increasing discount rate.

14. 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.

15. 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.