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

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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 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. 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)

Investing in drip irrigation (r=.05) YearCostsBenefitsCumulative Net Gain 0120,00020,000-100,000 1019,048-80,952 2018,141-62,811 3017,277-45,534

When does he break even?

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. 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 1990100 1991104.2 1992107.4

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.

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