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AEM 2500 2010 Lec 18 discounting and GC sv

AEM 2500 2010 Lec 18 discounting and GC sv - This This Or...

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Unformatted text preview: This This Or This Which is Socially Desirable? Benefit Benefit Cost Analysis • • Grand Canyon Canyon Discounting Benefit and Cost Estimates: Grand Canyon Benefit Estimates of Benefits and Costs of Controlling Sulfur Dioxide at Navajo Generating Station 1. Contingent valuation estimate of WTP for greater visibility in the Grand Canyon th 2. Construction cost for sulfur removal equipment equipment. 3. Operation and maintenance cost. 4. Sulfur reduction at 70% effectiveness $210 million annually $330 million investment $75 million annually 25,000 tons annually. Source: Chapman, 2000; USEPA 1990 Com Compounding Compounding: Compounding: Translating a present payment (PV) or cost into a value in the future (FV). FV = (1 + r ) × PV t Basic Basic Idea: Opportunity Cost of Investment (Mankiw #2). (Mankiw • • Someone you trust borrows $100 today and promises to pay you back $106 in a year. On a purely financial basis would you be better off in a year by loaning the money or putting it in the bank? money Your decision should depend on the interest rate: If If the bank’s interest rate (r) is 5%, the $100 today should be worth $105 a year from now (t=1). If If the bank’s interest rate (r) is 10%, the $100 today should be worth $110 a year from now (t=1). How about $114 two years from now? How about $114 two years from now? Note: We will return to appropriate social discount rate (Harris, pp. 118-119) when we discuss Global Warming Discountin Discounting Discounting: Discounting: Translating a future payment (FV) or cost into a value in the present (PV). th (PV) • Reverse of compounding. Basic Basic Idea: Opportunity Cost of Investment (Mankiw #2). • • Someone you trust promises you an IOU of $106 in a year. How much is that IOU worth to you today? that IOU worth to you today? It It would be less than $106 because you could put an amount less than $106 in the bank now and get more than at the end of a year. Exact amount depends on the interest rate: amount depends on the interest rate: If If the bank’s interest rate (r) is 5%, the $106 a year from now (t=1) should be worth $100.95 today if you had put $100.95 in the bank. That is, after rounding, $100.95 plus interest payments of $5.05 (=100.95*0.05) equals $106 (=100.95*1.05). Note: We will return to appropriate social discount rate (Harris, pp. 118-119) when we discuss Global Warming Balancing Balancing Present and Future: Present Value (PV) and The Notion of Discounting (PV) Th Di Basic Basic idea is that a dollar today is worth more than a dollar in the future. future. We We would like a way to compare present costs (benefits) with future benefits (costs). B = future benefit t = time (in, say, years, present = 0) r = discount rate. 1 PV = * FVt FV t (1 + r ) The discount factor is 1 (1 + r ) t Grand Grand Canyon Equivalent to Harris Fig. 6-2 6Net Present Value Criteria (NPV) = PV[B] – PV[C] If the NPV > 0 then the project is desirable. the NPV then the project is desirable. Costs (-) and Benefits (+) Contingent valuation estimate of WTP for greater visibility in the Grand Canyon, $210 annually t=1,2…30 annually 1 2 3 4 0 Operation and Maintenance Costs, Constr. $75 mil. annually t=1,2…30 Cost for Cost for Sulfur Sulfur Removal Equip at t=0, $330 mil. Time (in years) Present Value Costs = PV [C ] = ∑ Value t =0 Period Period Future Cost Discount Factor Present Value Period T Future $ in Period t (1 + r ) t Future Cost Discount Factor Present Value 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 330 75 75 75 75 75 75 75 75 75 75 75 75 75 75 75 75 1 0.909 0.826 0.751 0.683 0.621 0.564 0.513 0.467 0.424 0.386 0.350 0.319 0.290 0.263 0.239 0.218 330.00 68.18 61.98 56.35 51.23 46.57 42.34 38.49 34.99 31.81 28.92 26.29 23.90 21.72 19.75 17.95 16.32 17 18 19 20 21 22 23 24 25 26 27 28 29 30 Total 75 75 75 75 75 75 75 75 75 75 75 75 75 75 0.198 0.180 0.164 0.149 0.135 0.123 0.112 0.102 0.092 0.084 0.076 0.069 0.063 0.057 14.84 13.49 12.26 11.15 10.13 9.21 8.38 7.61 6.92 6.29 5.72 5.20 4.73 4.30 10 % Discount Rate Used Following USFS Guidelines (Chapman, 2002) 2002) PVC =$1,037.02 Present Value Bens. = PV [ B ] = ∑ Value t =0 Period Period Future Benefit Discount Factor Present Value Period T Future $ in Period t (1 + r ) t Future Cost Discount Factor Present Value 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 0 210 210 210 210 210 210 210 210 210 210 210 210 210 210 210 210 1 0.909 0.826 0.751 0.683 0.621 0.564 0.513 0.467 0.424 0.386 0.350 0.319 0.290 0.263 0.239 0.218 0.00 190.91 173.55 157.78 143.43 130.39 118.54 107.76 97.97 89.06 80.96 73.60 66.91 60.83 55.30 50.27 45.70 17 18 19 20 21 22 23 24 25 26 27 28 29 30 Total 210 210 210 210 210 210 210 210 210 210 210 210 210 210 0.198 0.180 0.164 0.149 0.135 0.123 0.112 0.102 0.092 0.084 0.076 0.069 0.063 0.057 41.55 37.77 34.33 31.21 28.38 25.80 23.45 21.32 19.38 17.62 16.01 14.56 13.24 12.03 10 % Discount Rate Used Following USFS Guidelines (Chapman, 2002) 2002) PVB =$1,979.65 Net Net Present Value Approach (i.e. Benefit Cost Analysis) I. Present value of initial construction cost scrubber removal equipment. II. Present value of annual operation and maintenance costs. costs Present value of all costs (sum of I and II) $ 330 million PV[C1] $ 707 million PV[C2] $ 1,037 million PV[C1+ C2] $ 1,980 million PV[B] III. Present value of annual WTP for visibility cleanup benefits. IV. Net present value (III-I-II) (IIISource: Chapman, 2000 $ 943 million PV[B] PV[C PV[B] - PV[C1+ C2] Note: We do not use benefit/cost ratio – it can be misleading/uninformative in some cases. Source: Chapman, 2000. Note that these have been converted to annualized (AKA levelized) values) ...
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