1. Net Present Value Analysis Rich Sweeney (rich_sweeney@hksphd.harvard.edu)rich_sweeney@hksphd.harvard.edu (Based on Notes from Avinash Kishore) February 08, 2013 Review Section Note from Rich: Feel free to print the slides or bring your laptop to class. If you feel comfortable with this material already, no need to come!

2. Agenda  Fundamental Theories of Welfare Economics  Static Efficiency vs. Dynamic Efficiency (NPV)  Internal Rate of Return  Equivalent Annual Net Benefits  Readings on Benefit-Cost Analysis  Practice Problem(s)  Excel Workbook Embedded Here: 1

3. Fundamental Theories of Welfare Economics: Pareto Criterion and Pareto Optimality  Pareto Criterion: A policy change is an improvement if at least some people are made better off and no one is made worse off  Pareto Optimality: No other feasible policy could make at least one person better off without making anyone else worse off 2 Adam’s Payment Beth’s Payment Status Quo Policy A Policy B Policy C Policy D Feasibility Frontier Possible Payments to Adam and BethWhich satisfy Pareto Criterion? ‒ Policy A does ‒ Policy B does not ‒ Policy C does not ‒ Policy D does ‒ All policies in light gray triangle Which satisfy Pareto Optimality? ‒ Policy A does not ‒ Policy B does not ‒ Policy C does ‒ Policy D does ‒ All policies on feasibility frontier (because nothing “better” from there) $25 $100 $25 $100

4. Fundamental Theories of Welfare Economics: Kaldor-Hicks Criterion  Kaldor-Hicks Criterion: A policy change is an improvement if the “winners” could fully compensate the “losers” and still be better off themselves –Also known as Potential Pareto Improvement Criterion  Kaldor-Hicks Criterion rules out policies with total benefits smaller than total costs (that is, policies with negative net benefits, where NB = TB - TC)  When the Kaldor-Hicks Criterion is used to compare all feasible policy options, the best is that which maximizes net benefits –If all policies have negative net benefits, keep the status quo 3

5. Static Efficiency (Single time period)  Undertake policy to the point at which TB – TC is the highest  marginal benefit = marginal cost 4 Total Benefits Total Costs Marginal Benefits Marginal Costs Net Benefits Q*Q* Total Benefits and Total CostsMarginal Benefits and Marginal Costs Q*Q*

6. Dynamic Efficiency: when B and C in different time periods  To achieve dynamic efficiency (multiple time periods), undertake policy with highest net present value  If all policies have negative NPV, keep the status quo  Discount rate should reflect social opportunity cost  U.S. Office of Management and Budget (OMB) published guidance on discount rate and benefit-cost analysis in Circular A-4 (September 2003): http://www.whitehouse.gov/omb/assets/regulatory_matters_pdf/a-4.pdf http://www.whitehouse.gov/omb/assets/regulatory_matters_pdf/a-4.pdf 5

7. OMB Guidelines on C-B Analysis  “For transparency’s sake, you should state in your report what assumptions were used, such as the time horizon for the analysis and the discount rates applied to future benefits and costs.  It is usually necessary to provide a sensitivity analysis to reveal whether, and to what extent, the results of the analysis are sensitive to plausible changes in the main assumptions and numeric inputs”. 6

8. Why do we need discounting? (Circular A4, OMB)  Benefits or costs that occur sooner are generally more valuable –Resources invested earn a positive return, so current consumption is more expensive than future consumption, since you are giving up that expected return on investment when you consume today. (Opportunity Cost). –Postponed benefits also have a cost because people generally prefer present to future consumption. (Positive time preference). –Also, if consumption continues to increase over time, as it has for most of U.S. history, an increment of consumption will be less valuable in the future than it would be today (Principle of diminishing marginal utility). 7

9. What is the appropriate discount rate?  “a real discount rate of 7 percent should be used as a base-case for regulatory analysis”.  Why? –“The 7 percent rate is an estimate of the average before-tax rate of return to private capital in the U.S. economy. –the returns to real estate and small business capital as well as corporate capital. –It approximates the opportunity cost of capital –it is the appropriate discount rate whenever the main effect of a regulation is to displace or alter the use of capital in the private sector”. 8

10. The appropriate discount rate ?  The effects of regulation do not always fall exclusively or primarily on the allocation of capital.  When regulation primarily and directly affects private consumption (e.g., through higher consumer prices for goods and services), a lower discount rate is appropriate.  The alternative most often used is sometimes called the social rate of time preference  …the rate at which society discounts future consumption flows to their present value. –the rate that the average saver uses to discount future consumption as a measure  Real rate of return on long-term government debt ( = 3%) 9

11. How does discounting work?  Reciprocal of compounding  Benefits and costs far in the future are more sensitive to discount rate than near-term benefits and costs –Run discounting program in Excel workbook 10 r = 3% → NPV = $29M r = 10% → NPV = -$10M

12. How does discounting work?  When costs are incurred up front and benefits occur in the future, low discount rates result in higher NPVs than high discount rates 11 Relationship between Discount Rate and NPV with Upfront Costs and Future Benefits

13. Steps for NPV Analysis  Pick a discount rate  Estimate the static net benefits of the project in each year for the entire life of the project.  Convert each period’s net benefits into present value terms by dividing by (1+r)^t  Sum the discounted stream of net benefits to get the present value over the project.  Select the project with the greatest NPV 12

14. Dynamic Efficiency: Power Plant Example  You are a special assistant to Gov. Schwarzenegger of California. He wants to shut down a coal-fired power plant and replace it with either a hydropower plant or a natural gas- fired plant. He asks you to analyze the options.  Assumptions (unrealistic…) –Both plants can be built in 1 year and operate for 5 years –Both plants yield annual benefits of $50M relative to coal –Hydropower plant has upfront fixed costs of $100M and annual operating costs of $5M –Natural gas plant has upfront fixed costs of $40M and annual operating costs of $20M –Discount rate is 7 percent, but also try 3 and 10 percent 13

15. Dynamic Efficiency: Power Plant Example  Hydropower has a slightly higher NPV than natural gas at 7 percent discount rate, but lower at 10 percent 14

16. Discounting & Climate Change: The Stern Report  A time scale of centuries, so the brute power of compound interest –Manhattan purchase: 60 guilders ($ 1000) in 1626 –@ 7%: ~$80 trillion; @ 3%: ~ 15 million(5 million times)  The Stern Report conclusions are driven mainly by the low assumed discount rate : (r = 1.4%) –If r = 6%, the PDV of global-warming loss 100 years hence is <1/100 th  Question: Is it worthwhile to sacrifice costs C =1% of GDP now to remove damages D = 5% of GDP a 100 years from now?  Stern’s B/C ratio = 4.5 (upper bound 5 if zero discount rate is chosen)  B/C ratio (@ r = 6%) = 0.1  Prof Martin Weitzman: “In fact, it is not an exaggeration to say that the biggest uncertainty of all in the economics of climate change is the uncertainty about which interest rate to use for discounting” 15

17. Health related costs and benefits  Question: is discounting even appropriate? –lives saved today cannot be invested in a bank to save more lives in the future.  Answer: Yes! –People have been observed to prefer health gains that occur immediately to identical health gains that occur in the future. –If future health gains are not discounted while future costs are, then what happens? –an attractive investment today in future health improvement can always be made more attractive by delaying the investment 16

18. Equivalent Annual Net Benefits  Suppose the hydropower plant replacing the coal plant in California can operate for 10 years and the natural gas plant can still only operate for 5 years –At r = 7 percent, NPV hydro = $216M and NPV gas = $83M –At r = 32* percent, NPV hydro = $32M and NPV gas = $30M * This is an unusually high discount rate, but it illustrates the point for the example numbers  Calculate equivalent annual net benefits to compare these projects of different duration –At r = 7 percent, EANB hydro = $27M and EANB gas = $16M –At r = 32 percent, EANB hydro = $8M and EANB gas = $9M 17

19. Readings on Benefit-Cost Analysis: Arrow et al. (1996)  Benefit-cost analysis is a important framework for making regulatory decisions –Careful consideration of benefits and costs –Common unit of measurement for disparate impacts (dollars) –Useful tool for improving effectiveness of regulation –Techniques for incorporating uncertainty  But benefit-cost analysis should not be the sole basis for making regulatory decisions –Consideration of distributional impacts as well –Perhaps not necessary to perform benefit-cost analysis for minor regulations 18

20. Readings on Benefit-Cost Analysis: Goulder and Stavins (2002)  Discounting does not shortchange the future, so long as an appropriate discount rate is used –It simply puts current values and future values of benefits and costs in equivalent monetary terms; apples-to-apples comparison –It accounts for time value of money (interest) and not inflation: r nominal ≈ inflation + r real  When the “winners” of a policy do not actually compensate the “losers,” the Kaldor-Hicks criterion carries less weight  Lowering the discount rate to increase NPV is problematic because it mixes efficiency and equity 19