Net Present Value Analysis Andrew Foss Economics 1661 / API-135 Environmental and Resource Economics and Policy Harvard University February 13, 2009 Review Section

Agenda  Fundamental Theories of Welfare Economics  Static Efficiency  Dynamic Efficiency  Cost-Effectiveness Analysis and Benefit / Cost Ratios  Internal Rate of Return  Equivalent Annual Net Benefits  Readings on Benefit-Cost Analysis  Private Goods and Public Goods  Excel Workbook Embedded Here: 1

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

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

Static Efficiency  To achieve static efficiency (single time period), undertake policy to the point at which marginal benefits equal marginal costs 4 Total Benefits Total Costs Marginal Benefits Marginal Costs Net Benefits Q*Q* Total Benefits and Total CostsMarginal Benefits and Marginal Costs Q*Q*

Dynamic Efficiency: Overview  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): 5

Dynamic Efficiency: Discounting  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 embedded on p. 1 6 r = 3% → NPV = $29Mr = 10% → NPV = -$10M

Dynamic Efficiency: Discounting  When costs are incurred up front and benefits occur in the future, low discount rates result in higher NPVs than high discount rates 7 Relationship between Discount Rate and NPV with Upfront Costs and Future Benefits

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 8

Dynamic Efficiency: Power Plant Example  Hydropower has a slightly higher NPV than natural gas at 7 percent discount rate, but lower at 10 percent 9

Cost-Effectiveness Analysis and Benefit / Cost Ratios  Cost-effectiveness analysis answers the question, “Does the policy achieve its purpose at least cost?”  Benefits and costs over time should be discounted  When benefits are not monetized, undertake projects in increasing order of cost per unit of benefit  When benefits are monetized, calculate benefit / cost ratios and undertake projects in decreasing order of benefit / cost ratios, provided they are greater than 1  There are problems with both these rules, however 10

Cost-Effectiveness Analysis and Benefit / Cost Ratios  Cost-effectiveness analysis is less robust than NPV –Insensitive to scale –Sensitive to impact definitions (e.g., costs as negative benefits) 11 Reducing Nitrogen Oxide (NO x ) Emissions at Ports ‒ Unclear what scale of benefits could result from each measure ‒ Unclear to what degree policies should be undertaken ‒ Unclear whether one or several policies should be undertaken ‒ Unclear what probability distributions underlie uncertainty bars

Internal Rate of Return: Overview  Internal rate of return answers the question, “What discount rate would make NPV zero?”  When costs are incurred up front and benefits occur in the future, undertake project if IRR > r  In the first discounting example (p. 7), IRR ≈ 8 percent  Internal rate of return is less robust than NPV, and it should not be used to rank projects when constraints make it impossible to undertake them all 12

Internal Rate of Return: Power Plant Example  A nuclear power plant can be built in 1 year for $100M, can operate for 5 years, yields annual benefits of $55M relative to coal, has annual operating costs of $5M, and has decommissioning costs of $155M in Year 6 13 IRR??  IRR is not useful in this case because there are costs in the future

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 14

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 15

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 16

Private Goods and Public Goods: Beekeeper and Farmer Example  A beekeeper and a farmer are neighbors. The bee- keeper’s bees help pollinate the farmer’s orchard.  The beekeeper’s marginal benefit from Q beehives is MB beekeeper (Q) = 10 – Q  The beekeeper’s marginal cost is constant at MC beekeeper (Q) = 7  The farmer’s marginal benefit from Q beehives is MB farmer (Q) = 5 – Q  If the beekeeper ignores impacts on the orchard, how many beehives will the beekeeper have? What if the beekeeper takes impacts on the orchard into account? 17

Private Goods and Public Goods: Beekeeper and Farmer Example  If the beekeeper treats the beehives as a private good, the beekeeper will have 3 beehives 18 Q*Q* MC beekeeper MB beekeper = MC beekeeper 10 – Q = 7 Q* = 3 beehives MB beekeeper

Private Goods and Public Goods: Beekeeper and Farmer Example  If the beekeeper treats the beehives as a public good, the beekeeper will have 4 beehives –Public goods are underprovided by private decision-making 19 Q*Q* MB beekeeper MC beekeeper MB society = MB beekeeper + MB farmer (vertical sum of MBs for public goods) For 0 ≤ Q ≤ 5 (where both MBs ≥ 0), MB society = (10 – Q) + (5 – Q) = 15 – 2Q MC society = MC beekeeper MB society = MC beekeeper 15 – 2Q = 7 Q* = 4 beehives MB society MB farmer

Private Goods and Public Goods: Beekeeper and Farmer Example  If the beekeeper and farmer can negotiate without transaction costs, what outcome would we expect? 20  Increasing the number of beehives from 3 to 4 gives the beekeeper extra benefits of $6.50 (area under MB beekeeper ) but extra costs of $7 (area under MC beekeeper ), so the beekeeper’s profit decreases by $0.50  Increasing the number of beehives from 3 to 4 gives the farmer extra benefits of $1.50 (area under MB farmer ) and does not impose extra costs on the farmer  By the Coase Theorem, the farmer could give the bee- keeper between $0.50 and $1.50 to have 4 beehives

Private Goods and Public Goods: Steel Mill and Laundry Example  A steel mill generates $1000 in profits and can install technology to eliminate its emissions at a cost of $400  A laundry can operate either upwind or downwind of the steel mill, with different building sizes at the locations –If the laundry operates upwind of the steel mill, It can generate $400* in profits if mill releases emissions It can generate $600* in profits if mill releases no emissions * Suppose profits differ even when upwind because emissions depress local economy –If the laundry operates downwind of the steel mill, It can generate $200 in profits if mill releases emissions It can generate $1000 in profits if mill releases no emissions 21

Private Goods and Public Goods: Steel Mill and Laundry Example Laundry UpwindLaundry Downwind Steel Mill Emissions Steel Mill$1000 Laundry$400$200 Joint$1400 (= $ $400)$1200 (= $ $200) No Steel Mill Emissions Steel Mill$600 (= $ $400) Laundry$600$1000 Joint$1200 (= $600 + $600)$1600 (= $600 + $1000) 22 Steel Mill and Laundry Profits

Private Goods and Public Goods: Steel Mill and Laundry Example  What is the socially efficient arrangement? 23 –The socially efficient arrangement has highest joint profits for the steel mill and laundry –Joint profits are highest ($1600) when the steel mill has no emissions and the laundry operates downwind

Private Goods and Public Goods: Steel Mill and Laundry Example  Suppose the steel mill and laundry cannot bargain  What arrangement will occur if the steel mill has the right to release emissions? 24 –The steel mill will release emissions, because its profits are higher if it releases emissions ($1000) than if it does not ($600) –The laundry will operate upwind, because its profits are higher if it operates upwind ($400) than if it operates downwind ($200)  What arrangement will occur if the laundry has the right to clean air? –The steel mill will have to install the technology to eliminate its emissions, leaving it with $600 in profits –The laundry will operate downwind, because its profits are higher if it operates downwind ($1000) than if it operates upwind ($600)

Private Goods and Public Goods: Steel Mill and Laundry Example  Suppose the steel mill and laundry can bargain costlessly  What arrangement will occur if the steel mill has the right to release emissions? 25 –The laundry can increase its profits from $400 operating upwind with emissions to $1000 operating downwind without emissions. The laundry is willing to pay the steel mill up to the difference, $600, to install the technology. The steel mill is willing to accept anything more than $400, so they make some deal in this range.  What arrangement will occur if the laundry has the right to clean air? –The steel mill is willing to pay up to $400 to avoid installing the technology, but the laundry is only willing to accept $600 or more to allow emissions and operate upwind, so there is no deal.  With bargaining, steel mill installs technology and laundry operates downwind (the efficient arrangement) regardless of allocation of rights (Coase theorem)