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## Discounting

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**Discounting**How should the future benefits of a project be weighed against present costs?**“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.**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, Regulating emissions of SOx, etc. • Need method for comparing costs & benefits over time.**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).**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.**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)**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”**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.**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.**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.**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.