#### Economic efficiency criteria Static efficiency – Maximize net benefits of one optimal rotation Dynamic efficiency – Maximize net benefits from continuous series of optimal rotations, where the.

download report#### Transcript Economic efficiency criteria Static efficiency – Maximize net benefits of one optimal rotation Dynamic efficiency – Maximize net benefits from continuous series of optimal rotations, where the.

Economic efficiency criteria Static efficiency – Maximize net benefits of one optimal rotation Dynamic efficiency – Maximize net benefits from continuous series of optimal rotations, where the net benefits from future rotations are discounted back to present value terms. Net benefits maximum where, level of output where TB - TC is greatest i.e. where MC = MB Define MC Opportunity cost to hold timber for one more unit of time Opportunity is to harvest timber and use proceeds for some other purpose – – – Assume it will earn a guaranteed r% in a bank, the alternative rate of return Net Revenue = P * Q - Harvesting Costs (assumed to be zero) MC = NR * r Example of MC calculation for 50 to 60 year period Let, P = $5 per ft3, Let r = 4% From growth function Q 50 = 1,400 ft3 Therefore, – – NR50 = $5/ft3 * 1,400 ft3 = $7,000 Interest on $7,000 over 10 years is – – (1.04)10 * $7,000 - $7,000 = $3,361.71 But need to discount back to year 50 MC50 =$3,361.71/(1.04)10 = $2,271.05 Time line for MC calculation $2,271.05 $7,000 50 $3,361.71 earn compound interest on $7,000for 10 years 55 60 MR calculation for 10 year period MR = NR = P * Q60 - P * Q50 Assume P = $5per ft3 NR50 = $5 * 1,400 ft3 = $7,000 NR60 = $5 * 2,100 ft3 = $10,500 MR = $5 * 700 = $3,500 received in year 60 MR50 = $3,500 / (1.04)10 = $2,364.47 Time line for marginal benefit calculation $10,500 - $7,000 $3,500 $2,364.47 50 55 60 What rate of return has been earned by holding for 10 years? We know that Vn = V0 (1+r)n Solve for r, – r = (Vn/V0)1/n - 1 r = (10,500/7,000)0.1 - 1 r = 1.5 0.1 - 1 = 4.14% since IRR > discount rate, optimal policy is to hold the resource and let it grow Interpretation of rate of return If alternative rate of return is 4% then can do better financially by letting stand grow If alternative rate of return is greater than 4.14% then should cut stand key point: is rate of growth of stock greater than the rate of growth of an alternative? (should you cut now and put the money in the bank where it will grow faster?) Determine economically optimal length of one rotation Assume – – $100 establishment cost in year zero $10 per year annual cost Components of NVP calculation Present Present Present Present Value Value of Value of Value of Timber Establishment Annual 1st rotation Cost Cost @$10 PV(V) PV(EC) PV(AC) NPV $ $ 100.00 $ 81.11 $ (181.11) $ 171.15 $ 100.00 $ 135.90 $ (64.76) $ 308.32 $ 100.00 $ 172.92 $ 35.40 $ 781.08 $ 100.00 $ 197.93 $ 483.16 $ 984.99 $ 100.00 $ 214.82 $ 670.17 $ 998.13 $ 100.00 $ 226.23 $ 671.90 $ 818.80 $ 100.00 $ 233.95 $ 484.85 $ 629.07 $ 100.00 $ 239.15 $ 289.92 $ 468.94 $ 100.00 $ 242.67 $ 126.27 $ 341.55 $ 100.00 $ 245.05 $ (3.50) $ 244.12 $ 100.00 $ 246.66 $ (102.54) $ 171.69 $ 100.00 $ 247.74 $ (176.05) $ 119.04 $ 100.00 $ 248.47 $ (229.43) $ 81.45 $ 100.00 $ 248.97 $ (267.52) $ 55.37 $ 100.00 $ 249.30 $ (293.93) $ 37.41 $ 100.00 $ 249.53 $ (312.12) Present value of one rotation $800.00 $600.00 $400.00 $200.00 $$(200.00) $(400.00) 1 3 5 7 9 11 13 15 Dynamic efficiency Optimal rotation length for a perpetual series of uniform rotations Use multiplier for capital value (CV) of a periodic series – Let, a = value of periodic payment t = length of time between payments r = interest rate – CV = a/((1+r)t -1) Perpetual series of rotations of length R ft3 R1 R2 R3 Ri time Soil expectation value (SEV) Identified by Faustman Capital value of a perpetual series of forest rotations Dynamic efficiency is achieved when SEV is maximized Represents the value of the soil to produce the timber crop Key point: optimal rotation length is shorter for SEV than for NPV $1,000.00 $800.00 $600.00 $400.00 $200.00 NPV SEV $$(200.00) 1 $(400.00) 3 5 7 9 11 13 15 Three opportunity costs Timber 1. interest on income from timber revenue if cut sooner rather than later 2. interest on delay of start of next rotation if lengthen rotation Land 3. interest on income from sale of land if sold sooner rather than later SEV formula t SEV = (Ij - Cj) (1 + r) t-j t- 1 (1 + r) j=0 j = index on time t = rotation length I = revenue r = interest rate c = cost Operation of SEV formula Discount income minus costs back to year 0 It Year 0 C0 Ct Compound costs forward to rotation R Sensitivity analysis of SEV Price of timber Planting cost Interest rate