Optimal Rotation-Pt 2

1. Optimal Rotation-Pt 2 February 27, 2014

2. Adam Smith Born: June 5, 1723, Kirkcaldy, United Kingdom Died: July 17, 1790, Edinburgh, United Kingdom David Ricardo Born: April 18, 1772, London, United Kingdom Died: September 11, 1823, Gatcombe Park, United Kingdom Alfred Marshall Born: July 26, 1842, Bermondsey, London, United Kingdom Died: July 13, 1924, Cambridge, United Kingdom John Maynard Keynes Born: June 5, 1883, Cambridge, United Kingdom Died: April 21, 1946, East Sussex, United Kingdom Ronald Coase Born: December 29, 1910, Willesden, London, United Kingdom Died: September 2, 2013, Chicago, Illinois, United States

3. Post lecture slides before class Identify equations and graphs to be used in problem sets Examples of how to use them Better labeling of graphs Feedback

4. Harry Nelson 2010 Optimal Rotation for a Series of Harvests What then is the present value of a series of recurring harvests every 60 years (where p=Revenues-Costs)? p p p p 240 60 120 180 • Perpetual Periodic Series • (pg. 129 in text)

5. Harry Nelson 2011 Associated Math This is the formula for calculating the present value of an infinite series of future harvests. Pearse calls this “site value”. It can also be called “Soil Expectation Value (SEV)”, “Land Expectation Value (LEV)”, or “willingness to pay for land”. p V0= (1 + r)t - 1 p Vs= (1 + r)t - 1 If there are no costs associated with producing the timber, Vs then represents the discounted cash flow-the amount by which benefits will exceed costs

6. Present value of a series of infinite harvests, excluding all costs • Evaluated at the beginning of the rotation Land Expectation Value p Vs= (1 + r)t - 1 So if I had land capable of growing 110 m3/ha at 100 years, and it yielded $7 per m3, evaluated at a discount rate of 6% that would give me a value of $42.26/ha

7. Harry Nelson 2011 Calculating Current Value and Land Expectation Value at Different Harvest Ages LEV maximized at 70 years

8. Harry Nelson 2011 Associated Math So in order to maximize LEV the goal is to pick the rotation age (t*) that maximizes this value. p At 90 years, only 109 m3/ha and worth $6 per m3, but LEV is higher-$49.17 Vs= (1 + r)t* - 1 This can be done in a spreadsheet by putting in different rotation ages and seeing which generates the highest value

9. Harry Nelson 2011 Further Modification Imagine you have a series of intermittent costs and revenues over the rotation along with annual costs and revenues -how do you calculate the optimal rotation then? Commercial thinning - net revenue (NRt) Harvesting - net revenue (NRh) Reforestation-Cr Pre-Commercial Thin -Cpct 80 0 20 50

10. Harry Nelson 2011 For problem set For periodiccosts and revenues over the rotation: Commercial thinning - net revenue (NRt) Harvesting - net revenue (NRh) Reforestation-Cr Pre-Commercial Thin -Cpct 80 0 20 50 You can compound all the costs and revenues forward to a common point at the end of the rotation-this then becomes p + + P = (1 + r)80 *Cr + (1 + r)60*Cpct (1 + r)30*NRt NRh p Vs= (1 + r)t - 1

11. Harry Nelson 2011 For problem set Recurring annual revenues and costs can be are included in a2ndexpression p a - c + Vs= r (1 + r)t* - 1

12. Adding Carbon What happens if we manage for Carbon? Carbon payment schemes pay for either C sequestered or avoided C emissions. In forestry focus has been on sequestration (trees are efficient C storage mechanisms) • It is not the biological side that makes C accounting complex-it is the market side. • Baseline • Leakage • Buffer • Harvest

13. Interest rate • Higher the interest rate the shorter the optimum rotation Impact of Different Factors

14. Interest rate • Higher the interest rate the shorter the optimum rotation • Land Productivity • Higher productivity will lead to shorter rotation Impact of Different Factors

15. Interest rate • Higher the interest rate the shorter the optimum rotation • Land Productivity • Higher productivity will lead to shorter rotation • Prices • Increasing prices will lengthen the optimal rotation Impact of Different Factors

16. Interest rate • Higher the interest rate the shorter the optimum rotation • Land Productivity • Higher productivity will lead to shorter rotation • Prices • Increasing prices will lengthen the optimal rotation • Reforestation costs • Increase will increase the optimal rotation length Impact of Different Factors

17. What if there are other values? Annual costs & returns Incremental growth in value or ∆p/p(t) i* T* Rotation age (t)

18. Harry Nelson 2011 Amenity Values and Non-Monetary Benefits Growth in value without amenity values “Perpetual rotation” Rate of growth in the value of timber (%/yr) Growth in value with amenity values Growth in value with amenity values i or MAR Rotation age Rotation age In this case you’d never harvest

19. Assessing Risk Cost of outcome: S1 Cost of outcome: S2 Selection didn’t work P=0.2 P=0.3 No infestation Selection works infestation Cost of outcome: S3 Selection P=0.8 P=0.7 P=0.2 No infestation Cost of outcome: NS1 No selection P=0.8 infestation Cost of outcome: NS2 p. 124 in text

20. Cost of improving the stand -$1000 per hectare • Result-doubling of growth (an additional 995 cubic metres) • Standard cost-benefit: • Discounted Benefit: $13,187/1.0558=$778 • Cost: $1000 • So NPV =-$222; B/C = 0.78 • From Chapter 8, 163-65 Allowable Cut Effect

21. If you can take additional volume over the 58 years… ($13,187/58) • Then it looks quite different • Using a formula, the present value of a finite annuity • NPV = ($13,187/58)*((1.05)58-1) .05*(1.05)58 • Or $4,546 Introducing ACE

22. Using ACE as an incentive

23. Experience with ACE