Unformatted text preview: This Or This Which is Socially Desirable?
Benefit Cost Analysis Benefit
• • Grand 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 $210 million annually for greater visibility in the Grand Canyon 2. Construction cost for sulfur removal equipment. 3. Operation and maintenance cost. 4. Sulfur reduction at 70% effectiveness $330 million investment $75 million annually 25,000 tons annually. Source: Chapman, 2000; USEPA 1990 Compounding Compounding
Compounding: Translating a present payment (PV) or cost into a Compounding: value in the future (FV). FV = (1 + r ) × PV
t
Basic Idea: Opportunity Cost of Investment (Mankiw #2). Basic
• • 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. Your decision should depend on the interest rate: If the bank’s interest rate (r) is 5%, the $100 today should be worth $105 a If year from now (t=1). If the bank’s interest rate (r) is 10%, the $100 today should be worth $110 If a year from now (t=1). How about $114 two years from now? How
Note: We will return to appropriate social discount rate (Harris, pp. 118119) when we discuss Global Warming Discounting Discounting Discounting: Translating a future payment (FV) or cost Discounting: into a value in the present (PV).
• Reverse of compounding. Basic Idea: Opportunity Cost of Investment (Mankiw #2). Basic
• • Someone you trust promises you an IOU of $106 in a year. How much is that IOU worth to you today? It would be less than $106 because you could put an amount less It than $106 in the bank now and get more than at the end of a year. Exact amount depends on the interest rate: If the bank’s interest rate (r) is 5%, the $106 a year from now (t=1) If 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 That (=100.95*0.05) equals $106 (=100.95*1.05). Note: We will return to appropriate social discount rate (Harris, pp. 118119) when we discuss Global Warming Balancing Present and Future: Balancing Present Value (PV) and The Notion of Discounting
Basic idea is that a dollar today is worth more than a dollar in the Basic future.
We would like a way to compare present costs (benefits) with future We benefits (costs). B = future benefit t = time (in, say, years, present = 0) r = discount rate. $50 10 0.10 1 PV = * FVt t (1 + r ) Grand Canyon Equivalent to Harris Fig. 62 Grand Net Present Value Criteria (NPV) = PV[B] – PV[C]
Costs () and Benefits (+) Contingent valuation estimate of WTP for greater visibility in the Grand Canyon, $210 annually t=1,2…30 1 2 3 4 0 Operation and Maintenance Costs, Constr. $75 mil. annually t=1,2…30 Cost for Sulfur Removal Equip at t=0, $330 mil. Time (in years) Present Value Costs = PV [C ] = ∑
t =0
Period Future Cost Discount Factor Present Value Period T Future $ in Period t t (1 + r )
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) PVC =$1,037.02 Present Value Bens. = PV [ B ] = ∑
t =0
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) PVB =$1,979.65 Net Present Value Approach (i.e. Benefit Cost Analysis) Net
I. Present value of initial construction cost scrubber removal equipment. II. Present value of annual operation and maintenance 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 (IIIIII)
Source: Chapman, 2000 $ 943 million 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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 Fall '07
 POE,G.
 Net Present Value

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