Cost Benefit Analysis, G ch. 8 Estimate a project's net benefit ($ value) for a community. Net benefit = user benefit + indirect benefit cost. 1.

Transcription

1 Cost Benefit Analysis, G ch. 8 Estimate a project's net benefit ($ value) for a community. Net benefit = user benefit + indirect benefit cost. 1. Specify community (city, region, country, or other group). 2. Consider present (discounted) value of costs and benefits or else costs and benefits per period (usually 1 year). Present value of cost or benefit adjusts for the date it occurs. $100 paid now has bigger burden than $100 paid in a year if interest can be earned during the year. Gross return on $100 after 1 yr at 5% = 5/100 interest is (5/100) = 105. Present value of $105 in 1 yr at 5% interest is $100 = investment now that gets gross return of $105 in 1 yr.

2 Gross Return and Present (Discounted) Value At interest rate i, gross return on V invested for 1 yr is V + Vi = V(1+i) = principal + interest. Gross return on V invested for 2 yrs is the return on V(1+i) invested for one more yr: V(1+i)(1+i) = V(1+i) 2 Gross return on V invested for n yrs is V(1+i) n Present value of benefit or cost x in n yrs is investment now that yields gross return x in n yrs. It is V with V(1+i) n = x. Present value of benefit or cost x in n yrs at interest rate i is V = x/(1+i) n. Present value of benefit and cost stream benefit B 0 and cost C 0 now; benefit B 1 and cost C 1 in 1yr; benefit B 2 and cost C 2 in 2 years; etc., at interest rate i is B 0 C 0 + (B 1 C 1 )/(1+i) + (B 2 C 2 )/(1+i)

3 Present (Discounted) Value Present value at interest rate i of net benefit stream of N in every yr starting in 1 yr, continuing forever is N/(1+i) + N/(1+i) 2 + N/(1+i) = N/i since N/i invested forever yields interest payment N each yr Exercises: 1. Find the present value of a cost of $1600 in 3 yrs at interest rate 7%. 2.a. Find the present value of a $100,000 benefit in 60 yrs at 2% interest. b. Find its present value at 8% interest. 3. Find the present value of the net benefit of the following streams of costs and benefits at 7% interest: a. $100,000 cost now, $50,000 benefit in 1 yr and $50,000 benefit in 2 yrs. b. $100,000 cost now and a $14,000 benefit every yr starting in 1 yr.

4 Present (Discounted) Value Exercise Answers: The present value asked for is labeled V. 1. 7%= =1.07. V = $1600/(1.07) 3 $ a. (1.02) V = $100,000/(1.02) 60 $30, b. (1.08) V = $100,000/(1.08) 60 $ a. V = $100,000 + $50,000/(1.07) + $50,000/(1.07) 2 $100,000 + $ $ = $9, b. At interest rate i, the present value of the stream of benefits of N each year starting in 1 year is N/i. Here, N=$14,000 and i = 0.07, so N/i =$14,000/0.07 =$200,000. Subtracting the cost of $100,000, we get the present value V = $100,000 + $200,000 = $100,000. Other way to get present value of $14000/yr benefit stream: At 7% interest, $200,000 invested forever pays $14,000/yr.

5 Cost Benefit Summary Net benefit to community = user benefit + net generated income + net value of other externalities cost. user benefit to community = benefit from locals' use = user surplus, usually area under MB (demand) curve. Indirect benefit = net generated income + net externalities. Net Generated Income = (net new spending on LVA) (multiplier) (profit rate) (net new spending on LVA) (1+c) (0.2) in normal times. c = real local income created by locals' spending on LVA out of $1 of new income. NET new spending on LVA = spending on LVA with project (what would have spent on LVA without project). Convert all repeated benefits and costs into present values or convert one-time cost into annual cost (of debt repayment).

6 Estimating Expressions in Present Value Formulas A. 1/1.06 = For small interest rate i, 1/(1+i) 1 i. Note that 1/(1+i) < 1 if i > 0. B = (0.06). For small interest rate i, (1+i) n 1+ ni = (0.06) = This approximation gets bad when n is big: (1.06) (1.06) , not 1+50(0.06) = 4. C. (1.06) 50 = [(1.06) 10 ] 5. (1+i) nm =[(1+i) n ] m D. Estimating (1+i) n when i is small and n is big: An investment of $1 at interest rate of x % doubles to $2 in about 70/x yrs. (1.07) 70/7 = (1.07) 10 = , so (1.07) 50 = [(1.07) 10 ] 5 [2] 5 = 32. Really (1.07) 50 = E. Remember the formula: (1.02)

7 Cost Benefit Analysis, G ch Specify community (city, region, country, or other group). 2. Consider present value of costs and benefits or else costs and benefits per period (usually 1 year). Future costs and benefits are usually estimated ignoring inflation (in "real" prices at date of analysis). But interest rate is higher if inflation is expected. If estimated costs and benefits are in current prices, USE REAL (inflation adjusted) interest rate r with 1+r = (1+i)/(1+j) if interest rate is i and inflation rate is j. (Gross return 1+i in 1 yr buys only 1+r units of a good that costs 1+j in 1 yr.) 3. Estimate user benefit to community members. User benefit of private good to community users of project area under their SMB curve up to output Q demanded. For most projects, user benefit is the biggest benefit. off, so there is no Pareto improvement.

8 3. User benefit of private good to community users of project area under their SMB curve up to output Q demanded. Bridge Example: Q = # locals' crossings With linear demand, toll P, choke price P*, User benefit = area of triangle + rectangle = CS + R = (1/2)(P* P)Q + PQ P* SMB CS = consumer surplus R = toll revenue P Q #crossings

9 3. User benefit of private good to community users of project area under their SMB curve up to output Q demanded. Bridge Example: Q = # locals' crossings With linear demand, toll P, choke price P*, User benefit = area of triangle + rectangle = CS + R = (1/2)(P* P)Q + PQ P* P SMB CS = consumer surplus R = toll revenue SMC (With this SMC, P is optimal price) Q #crossings

10 3. User benefit of private good to community users of project area under their SMB curve up to output Q demanded. Bridge Example: Q = # locals' crossings With linear demand, toll P, choke price P*, User benefit = area of triangle + rectangle = CS + R = (1/2)(P* P)Q + PQ off, so there is no Pareto improvement. P* SMB CS = consumer surplus R = toll revenue Optimal P = 0 when SMC = 0. P Q #crossings

11 Bridge Example 1 (Estimating user Benefit) Suppose locals' bridge demand has choke price = $6 and suppose that at price P=0, 7 million locals cross per yr. If SMC=0, then optimal price =0 and user benefit = consumer surplus = $(1/2)(6)(7)=$21 million/yr. Assuming this benefit occurs every year, we convert it to present value to compare it to a one-time cost of construction. Present value of $21 million/yr for 50 yrs at 7% interest is approximately the same as $21 million/yr forever, which is $21/(.07) = $300 million.

12 3. Alternative measure of user benefit of bridge or road: value of time saved. Time saving estimated by traffic studies. Value of time estimated from surveys, revealed preference [example: time people wait in line to get lower price.], or as a fraction (between 1/2 and 1) of ave. wage rate. DON'T COUNT BOTH the surplus measure (area under SMB) and time saved. Doing that counts value of saved time twice since much of the surplus is due to saved time.

13 3. Other possible user benefit: safety. --may already be counted in surplus. Example: $ value of life saved; implicit in such policies as speed limits, asbestos regulation, seatbelt+bike helmet laws,... $ value from foregone wages, surveys, revealed preference (compensating differentials in jobs with different riskiness) Methods yield typical estimates in range: $4 to $8 million per life. Can use QALY: Quality adjusted life year.

14 3. Gov policies value lives very differently: Raising interstate speed limits from 55 to 65mph values a life < $4 million. Banning asbestos values a life > $20 million (one study says > $85 million, but part of that cost improves quality of life). 4. Other included benefits go to community members not from direct use of project. Examples: businesses might make more profit, land values might rise, community might be more congested (this "benefit" is negative),... MANY COST BENEFIT ANALYSES MISTAKENLY EXAGGERATE THESE INDIRECT BENEFITS.

15 Indirect Benefits 4. Net generated income + net value of other externalities. Net Generated Income = (net new spending on local value added) (multiplier) (profit rate)

16 Indirect Benefits 4. Net generated income + net value of other externalities. Three Aspects of Net Generated Income Example 1 (continued): Outsider (federal gov) pays $100 million to local firm to build bridge in city. G1 Community (city) does not keep all the $ spent. Pays for some inputs bought from outside (steel). $ community keeps: Local Value Added (LVA). G2 Some $ community keeps are spent again on LVA, making more income for locals: multiplier effect. G3 $ spent on LVA pays for costly inputs provided by community (e.g., labor). Only "profit" is net benefit.

17 Indirect Benefits Bridge Example 1: Outsider (federal gov) pays $100 million to local firm to build bridge in city. G1. Local Value Added (LVA) = value of community output for project value of inputs from outsiders. LVA: mostly labor. Locals only keep $ spent on LVA. Example: Firm pays outsiders $40 million for steel, cement. Net new spending on LVA = $60 million. G2. Locals spend a fraction of these $ again on LVA. Let c = real local income from locals' spending on LVA out of each $1 of new local income. c 0 if local production near capacity (inputs taken from other local production).

18 Indirect Benefits Bridge Example 1: Outsider (federal gov) pays $100 million to local firm to build bridge in city. G2. Locals spend a fraction of these $ again on LVA. Let c = real local income from locals' spending on LVA out of each $1 of new local income. c 0 if local economy near capacity (inputs taken from other local production). With lots of extra capacity, c MPC (marginal propensity to consume LVA) = $ locals spend on LVA out of $1 of new income. MPC estimate 0.3 for 1 million population; 0.7 for US. More $ generated by these $? Usually reach capacity, so at next stage, c 0. $1 for LVA adds 1+c income.

19 Indirect Benefits Bridge Example 1: Outsider (federal gov) pays $100 million to local firm to build bridge in city. G2. Locals spend a fraction of these $ again on LVA. Let c = real local income from locals' spending on LVA out of each $1 of new local income. c 0 if local economy near capacity (inputs taken from other local production). With lots of extra capacity, c MPC (marginal propensity to consume LVA) = $ locals spend on LVA out of $1 of new income. Multiplier 1+c. Each $1 new spending on LVA generates 1+c new local income.

20 Indirect Benefits Bridge Example 1: Firm pays outsiders $40 million Net new spending on LVA = $60 million. G2. Each $1 spent on LVA creates 1+c income: $60 million new income if economy near capacity (c 0). $60(1+c) 60(1.3) = $78 million if city of 1 million has lots of excess capacity. G3. $ spent on LVA in G2 pays for labor or other inputs owned by community. Subtract these inputs' opportunity cost. What remains is community "profit." Only this profit is net benefit. For labor, opportunity cost = reservation wage = minimum amount worker must be paid to be willing to work.

21 Indirect Benefits G3. $ spent on LVA in G2 pays for labor or other inputs owned by community. Subtract these inputs' opportunity cost. What remains is community "profit." Only this profit is net benefit. For labor, opportunity cost = reservation wage = minimum amount worker must be paid to be willing to work. Subtract this opportunity cost from income to get profit. Profit rate = profit / income 0.2 for many inputs in normal times; higher when unemployment is high. If worker with reservation wage $15/hr is paid $20/hr, profit rate is (20 15)/20=0.25.

22 Indirect Benefits Net Generated Income = (net new spending on local value added) (multiplier) (profit rate) Example: $60 million new spending on LVA. In normal times, multiplier 1; profit rate 0.2; net generated income $12 million. With high unemployment, net generated income might be $60(1+c)(profit rate) =$60(1.3)(.5) = $39 million. Then net generated income is 39% of total spending of $100 million. G0. ONLY NET new spending on LVA creates net generated income. Other spending leaves community. All spending on LVA may be new if outsider pays it. If community pays part, subtract what they would have spent on LVA without project.

23 NET new spending = spending on LVA with project (what would have spent on LVA without project). Example 2. Same as Bridge Example 1, except that outsiders pay half the construction cost and community pays rest. Of the $50 million community pays, it would have spent $50 MPC 50(.3)=$15 million on LVA without the project. $60 million is spent on LVA, but net new spending on LVA is $60 15 = $45 million (spending on LVA minus what locals would have spent without project). Net generated income from construction is around $45(1)(.2)=$9 million in a normal economy; maybe $45(1.3)(.5)= $29.25 million if unemployment is high.

24 NET new spending = spending on LVA with project (what would have spent on LVA without project). Include outsiders' increased spending on LVA induced by project: includes increased spending at local businesses if more outsiders use bridge to enter city to shop. Example 3. Same as Example 2, except that outsiders use the bridge and spend $5 million/yr more on LVA. Net generated income from this net new spending $5 (1) (.2) = $1 million/yr in normal times (maybe $5(1.3) (.5) = $3.25 million/yr in big recession). Net benefit repeats each yr. We must change it to present value to add it to the one-time net generated income from project construction. Present value of $1 million/yr forever at 7% interest rate is $1/(.07) $14.3 million.in normal times, total net generated income $9+14.3=$23.3 million. If locals buy more outside city since bridge makes leaving easier, count this change in spending on LVA.

25 Indirect benefit = net generated income + value of other externalities Examples of other externalities: pollution, construction noise + congestion, training for newly employed workers, demonstration effect (``area on the move"), change in real estate values. DON'T DOUBLE COUNT: Don't count change in business property values if they are due to project's effect on business income, already counted in net generated income. Don't count change in residential property values if they are due to benefits from use of project services. These benefits should be included in user benefits.

26 Uncertainty and Insurance A risk averse consumer is willing to pay for insurance. If benefit levels are 100, 200 and 400, with probabilities 1/6, 1/2, 1/3, respectively, then expected value of benefit = (100/6)+(200/2)+(400/3) = 250. Actuarially fair insurance: Insurer's expected net payout = 0. With actuarially fair insurance, consumer can replace risky benefit with sure benefit of same expected value. Risk averse consumer does this, replaces risky benefit above by sure 250 Certainty equivalent of a risky benefit is the sure benefit that the consumer considers just as good. For risk averse consumer certainty equivalent of benefit < expected benefit since certainty equivalent is just as good as risky benefit, but getting the expected benefit for sure is better.

27 Uncertainty and Insurance In cost benefit analysis with risk averse consumers, replace risky benefits and costs by consumers' certainty equivalents. Since certainty equivalent < expected consumption risky benefits are reduced below their expected values. But costs are negative benefits. Replacing risky costs by their certainty equivalent makes them more negative (bigger in absolute value), so Uncertainty reduces benefits below their expected value, increases costs above their expected value. Investment in technology or other policy to reduce greenhouse gases (GHG) is investing now to reduce future uncertainty (possible big future costs from climate change). Here uncertainty raises expected net benefit of current investment since it provides insurance (reduces risk).

28 Cost Benefit Summary Net benefit to community = user benefit + net generated income + net value of other externalities cost. user benefit to community = benefit from locals' use = user surplus, usually area under MB (demand) curve. Indirect benefit = net generated income + net externalities. Net Generated Income = (net new spending on LVA) (multiplier) (profit rate) (net new spending on LVA) (1+c) (0.2) in normal times. c = real local income created by locals' spending on LVA out of $1 of new income. NET new spending on LVA = spending on LVA with project (what would have spent on LVA without project). Convert all repeated benefits and costs into present values or convert one-time cost into annual cost (of debt repayment).

29 Times Union Center, Albany County, pop. 0.3M Economic Impact Analysis 1984, construction '87-'90. Arena seats 6000 to Est. costs in millions of $: construction 36, infrastructure 4, admin+maintenance 1/yr Predicted 100 events/yr, ave attendance 5000, $12 per ticket, 60% of spectators from outside county. Average variable cost to county: $8 per ticket (event costs) Impact statement claimed generated income: Ticket profit: $4/ticket 500,000 tickets/yr = $2 million/yr. From construction: $80 million = $40 million multiplier of 2. Extra spending: $8 spent locally per spectator (food, parking,..) $8 500,000 spectators/yr multiplier of 2 = $8 million/yr. Borrow at 10%/yr nominal interest over 40 years; finance repayment with higher county property tax. Inflation rate 4%.

30 Correcting Errors in Times Union Center Analysis Economic Impact Analysis claimed $40 million benefit from construction + ($8+2 1= $9 million/yr) other income. Present value= $40 + (9/.1) = = $130 million WRONG! For corrected cost benefit analysis, estimate user benefit + indirect benefit cost. user benefit = consumer surplus of local users. Assume linear demand, locals same as outsiders, choke price = 3 ticket price (estimated from scalper prices) For net generated income: assume profit rate = 0.2, construction: 50% local value added, c = 0.2 (high estimate) Discount using real interest rate 10 4$ = 6%/yr

31 Correcting Errors in Times Union Center Analysis User benefit + Indirect benefit cost. user benefit = consumer surplus of local users. Assume linear demand, locals same as outsiders, choke price = 3 ticket price (estimated from scalper prices) Choke price = $36. At $12/ticket,.5 million sold, 40% to locals, cost to county $8/ticket. 36 User benefit = Locals' consumer surplus = $.5(36 12)(.2) + 4(.2) = $3.2 million/yr

32 Correcting Errors in Times Union Center Analysis To find indirect benefit, estimate net generated income: assume profit rate = 0.2, c = 0.2 (high estimate) 50% of construction spent on local value added (LVA). Net generated income from $40M construction+infrastructure: $20M spent on LVA (50%). County would have spent 40 MPC on LVA without project. If MPC on LVA =.3, county would have spent (.3)40 million =$12 million. NET NEW spending on construction is $20 12 = $8 million (one time). Net generated income from construction =(net new spending on LVA) (1+c) (0.2) 8(1.2)(.2) $1.9 M. Other generated income: $8/ticket extra spending in community. Some of this money would be spent without the arena. As a guess, assume locals would spend it anyway, but full $8 spent by outsiders is net new spending.

33 Correcting Errors in Times Union Center Analysis Outsiders' extra spending (on food, drink,..) is not all on LVA. Assume 75% on LVA. Outsiders buy 60% of.5m tickets. Outsiders' extra spending on LVA: (.75)($8) (.6)(.5M)=$1.8M/yr. Net generated income from outsiders' extra spending (1.8) (1+c) (profit rate)/yr (1.8)(1.2)(.2) /yr $.43M/yr. Ticket profit: $4 (.3M tickets to outsiders) = $1.2M/yr (profit from locals is locals paying locals, not new income). Divide by interest rate to get present value of repeated net benefits. Net benefit in millions of $: User benefit+net generated income cost [3.2/(.06)] [.43/(.06)] + [1.2/(.06)] [1/(.06)] 40 $24M present value. County estimated 440% higher net benefit, but net benefit may be even lower: Deadweight loss from tax raises cost; most omitted externalities are negative (congestion, construction).