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Economic efficiency criteria

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.

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Economic efficiency criteria

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  1. 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.

  2. Net benefits maximum where, level of output where TB - TC is greatest i.e. where MC = MB

  3. 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 Define MC

  4. 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 Example of MC calculation for 50 to 60 year period

  5. Time line for MC calculation $2,271.05 $3,361.71 $7,000 earn compound interest on $7,000for 10 years 60 50 55

  6. 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 MR calculation for 10 year period

  7. Time line for marginal benefit calculation $10,500 - $7,000 $2,364.47 $3,500 50 55 60

  8. 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 What rate of return has been earned by holding for 10 years?

  9. 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?) Interpretation of rate of return

  10. Assume $100 establishment cost in year zero $10 per year annual cost Determine economically optimal length of one rotation

  11. Components of NVP calculation

  12. Present value of one rotation

  13. 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) Dynamic efficiency

  14. Perpetual series of rotations of length R ft3 Ri R1 R2 R3 time

  15. 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

  16. Key point: optimal rotation length isshorter for SEV than for NPV

  17. 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 Three opportunity costs

  18. SEV formula t (Ij - Cj) (1 + r) t-j  SEV = (1 + r) t - 1 j=0 j = index on timet = rotation length I = revenuer = interest rate c = cost

  19. Operation of SEV formula Discount income minus costs back to year 0 It Year 0 R C0 Ct Compound costs forward to rotation

  20. Price of timber Planting cost Interest rate Sensitivity analysis of SEV

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