1. Stand-Level Management Planning
ISA Presentation
Stand-Level Management Planning
Lecture 3 –Financial Analysis and The Optimal Financial Rotation
Wednesday, November 17, 2016

2. Lecture Outline Importance of the Land Expectation Value (LEV)
What is the LEV?
Notation
Calculating the LEV
Examples

3. Lecture Outline The Optimal Financial Rotation
Marginal analysis of the decision to wait one year before harvesting
Effects on the financially optimal rotation and the LEV due to changes in the economic variables
Stumpage price ● Establishment Cost
Interest Rate ● Taxes
Recommended Reading:
Deacon, Robert T "The Simple Analytics of Forest Economics" in R.T. Deacon and M.B. Johnson (eds.). Forestlands, Public and Private. Ballinger Publishing Co.

4. Lecture Outline The Forest Value… Example The Forest Value Formula
What if we cut immediately?
What if we wait to harvest?
The Forest Value Formula

5. Importance of the LEV The LEV …
provides a method of estimating the value of forest land (excluding the value of the standing timber) for land that is used primarily for growing timber on an even-aged basis.
The LEV (or various generalizations of it) …
is the main tool used to identify optimal even-aged management regimes, including rotation decisions, thinning regimes, stand establishment effort and intermediate treatments, when the primary objective of the landowner is to maximize their financial return.
can be generalized to include other values and concerns in addition to financial return.

6. What is the LEV?
The Land Expectation Value (LEV) is the present value, per unit area, of the projected costs and revenues from an infinite series of identical forest rotations, starting initially from bare land.

7. What is the LEV? (continued)
Assumptions:
the forest land is used primarily for growing timber on an even-aged basis,
each rotation is of equal length,
the sequence of events within each rotation is the same, and
the net revenue associated with a particular event within a rotation is the same for all rotations.
Are these assumptions realistic?

8. Calculating the LEV
There are four basic types of costs and revenues involved in calculating LEVs:
Establishment cost (E),
Net revenue from a timber sale at the end of the rotation ( )
Annual net revenues (A), and
Miscellaneous intermediate costs and revenues (It ) that occur at various times (0 < t < R ) within the rotation.
Note: You won’t necessarily see all of these different types of costs and revenues in every LEV calculation, but this basically covers all the possibilities.

9. Calculating the LEV (continued)
Notation:
R = the length of a rotation (in years),
E = the stand establishment cost per unit area,
A = the net revenue per unit area from all annual costs and benefits,
It = an intermediate cost or revenue per unit area,
Yp,R = the expected yield per unit area of product p at age R,
Pp = the price of product p,
Ch = costs associated with the harvest, and
r = the real interest rate.

10. Calculating the LEV (continued)
Notation (continued)
PVR1 = the present value of the costs and revenues from the first rotation.
FVR1 = the future value at the end of the rotation of the costs and revenues from the first rotation.

11. Calculating the LEV (continued)
Method 1
Calculate the present value of the first rotation.
Convert the present value of the first rotation into a future value.
Apply the infinite periodic series formula.
Method 2
Calculate the future value of the first rotation.

12. Calculating the LEV (continued)
Method 3
Calculate the future value of the first rotation directly, ignoring the annual net revenue.
Apply the infinite periodic payment formula for the future value of the first rotation calculated in step 1, and
Use the infinite annual series formula for the net annual revenue.

13. Calculating the LEV (continued)
Method 3
Calculate the future value of the first rotation directly, ignoring the annual net revenue:
Apply the infinite periodic payment formula for the future value of the first rotation calculated in step 1, and use the infinite annual series formula for the net annual revenue:

14. Calculating the LEV (continued)
Method 3 (continued)
Combining these equations gives:

15. Example: A Southern Pine LEV
Consider the following per-acre expected incomes and costs associated with managing a hypothetical stand of southern pine:
Amount
Year
Reforestation Cost
$125
Brush Control Cost
$50 5
Thinning Cost
$75 10
Property Tax $3
annual
Hunting Revenue $1
Thinning Revenue
$200 20
Final Harvest
$3000 40

16. Example: A Southern Pine LEV
Calculate the LEV for this stand assuming that the real alternative rate of return is 6%.
ANSWER
First, calculate either the present value of the first rotation (Method 1) or the future value of the first rotation (Method 2).
It is useful to organize the information in a table as follows:

17. Example: A Southern Pine LEV
Amount
Year
Present Value
Future Value
Reforestation Cost
$125
Brush Control Cost
$50 5
Thinning Cost
$75 10
Property Tax $3
annual
Hunting Revenue $1
Thinning Revenue
$200 20
Final Harvest
$3000 40
Total
-$125.00
$1,285.71
-$37.36
-$384.30
-$41.88
-$430.76
-$45.14
-$464.29
$15.05
$154.76
$62.36
$641.43
$291.67
$3,000.00
$119.69
$1,231.12

18. Example: A Southern Pine LEV
Compound the present value of the first rotation forward 40 years to get the future value of the first rotation.
This is the same value as the future value that was calculated directly.

19. Example: A Southern Pine LEV (continued)
Now, the LEV can be calculated using the formula for an infinite periodic series.

20. Example: A Southern Pine LEV (continued)
The problem can also be solved using Method 3, as follows:

21. Example 2: Pennsylvania Oak Stand
Calculate the Land Expectation Value (LEV) of a medium-site oak stand managed on a 90-yr rotation using the following assumptions:
No establishment cost,
The average stumpage price is $345/mbf,
A shelterwood harvest occurs at age 80 that will produce 3.1 mbf/ac,
The overstory removal harvest occurs at age 90 produces 6.4 mbf/ac,
The real alternate rate of return is 3%,
Annual property taxes are $2/ac, and
All costs and prices are expected to increase at the rate of inflation.

22. Pennsylvania Oak Stand Example
Using Method 3:

23. The Optimal Forest Rotation
What is the best time to harvest an even-aged stand and start a new stand?
Alternatively, how long should you grow an even-aged cohort of trees before harvesting it and starting a new cohort?
This is a classic question in forest management and economics.

24. Multiple Perspectives on the “Optimal Forest Rotation”
When a stand reaches its…
Maximum Yield
Maximum Annual Growth
Maximum Mean Annual Increment
This is a favorite among foresters
The rotation that maximizes the Land Expectation Value
Aka the “Optimal Financial Rotation”
Aka the “Faustmann Rotation”
Emulating natural disturbance regimes

25. The Rotation that Maximizes LEV – aka, the Faustmann Rotation
It’s called the Faustmann rotation because it’s based on the LEV formula, which was first proposed in 1849 by a German forester, Martin Faustmann
It’s the rotation that forest economists (and regular economists) have shown to be the optimal rotation for forests grown primarily for growing timber for profit
The approach can be generalized to apply to a wide range of management objectives
So, let’s return to our discussion of the LEV…

26. Another LEV Example
Assume that the sawtimber yield (Y) of the stand, in thousands of board feet per acre, is given as a function of age (A) by the following equation:
Also assume that:
the price of sawtimber is $600/mbf;
the cost of establishing the stand is $200/ac;
the annual property tax is $2/ac;
the annual management cost is $1/ac;
the marginal tax rate on income is 22%; and
the real alternate rate of return is 3%.

27. Another LEV Example (continued)
Finally, assume that all of these values are unchanging and that the landowner is interested in maximizing the financial return on the forest land.
Using Method 3, we can express the LEV, as a function of the rotation age, as follows:
And we can graph the LEV as a function of the rotation…

28. The LEV and the Optimal Rotation
Figure 6.3 – Yield and LEV for the example over a range of rotation ages

29. The LEV and the Optimal Rotation
Marginal analysis of the decision to wait one year before harvesting.
What is the marginal benefit of waiting one year before harvesting?
The value of one year’s growth,
Plus any annual revenues (or values) earned each year (in this case, there are none).

30. The LEV and the Optimal Rotation (continued)
What is the marginal cost of waiting one year before harvesting?
The taxes and other annual costs paid each year,
The rent on the land for one year, and
The interest on the inventory (value of standing timber).

31. Marginal Analysis of the Decision to Wait One Year
Figure 6.4 – Marginal Analysis of the Optimal Rotation Age

32. Note the Shape of the Annual Increment Curve

33. Marginal Analysis of the Decision to Wait One Year
Figure 6.4 – Marginal Analysis of the Optimal Rotation Age

34. The LEV and the Optimal Rotation (continued)
Effects on the financially optimal rotation and the LEV due to changes in economic variables R*
LEV r
Negative P
C=0
C>0
Neg.
Positive C A
tprop
tinc
tsever
Pos.

35. Definition of the Forest Value
The Forest Value is the present value, per unit area of forest, of the projected costs and revenues from a forested tract with or without an existing stand of timber, and on which an infinite series of identical future even-aged forest rotations will also be grown.
The Forest Value includes the value of both the trees and the land.
Unlike the LEV, the Forest Value can be applied to uneven-aged stands with only minor adjustments.

36. Definition of the Forest Value (continued)
In the case of even-aged forests, it is assumed that:
the current stand will be harvested, either now or at some point in the future, and
it will be replaced with a new stand, and
all future rotations (after the current one) will be identical, with rotations of equal length and identical net revenue streams within a rotation.

37. How does the forest value generalize the LEV?
It applies to forested properties at any stage of development, not just at the beginning of the rotation.
It includes the value of both the land and the trees.
It allows you to make different assumptions about the current rotation than those made about future rotations.
E.g., it allows you to assume that prices will change, at least during the current rotation.

38. The Forest Value - Example
You are planning to purchase a timbered tract that you plan to harvest immediately, with the intention of regenerating the stand for future timber crops.
The tract is a northern hardwood stand,
...with 18 mbf of sawtimber and 14 cords of pulpwood per acre.
Current northern hardwood stumpage prices are $325/mbf and $7/cord.

39. The Forest Value – Example (continued)
Questions:
How much can you afford to pay for this tract?
What is the value of the timber on the tract?
What is the value of the land?
Should the timber be cut now?

40. The Forest Value – Example (continued)
If cut now, the timber is worth:
Timber Value = 18mbf×$325/mbf + 14cd×$7/cd
= $5,948
But the tract consists of both land and timber, so we also need to know the value of the land...
To calculate the value of the land, we need to calculate the LEV for the future rotations.

41. Calculating the Value of the Land –Example (continued)
To calculate the LEV for the future rotations, we need some additional information regarding the future management of the stand:
You plan to regenerate the stand naturally, and there is no regeneration cost.
A timber stand improvement cut will be made in 30 years, yielding about 12 cds of hardwood pulpwood.
In another 30 years (i.e., at age 60), you expect to clearcut the stand again, yielding 13 mbf of sawtimber and 25 cords of pulpwood.
Annual taxes on the property are $5 per acre.
You want to earn a real rate of return on your investment of at least 5%.
All of your cost estimates are in real dollars, and you expect real stumpage prices and management costs to remain constant.

42. Calculating the Value of the Land –Example (continued)
Calculate the LEV:

43. The Forest Value – Cutting Now
Thus, the forest value of the stand, if it is harvested now, is:
Forest Valuecut now = Timber value + Land value
= $ $169.42
= $6,117.42
So, is it best to harvest the stand now, or should we wait?
To answer this, we need to calculate the forest value under the assumption that we will wait to cut the stand (the alternative to cutting now).

44. Forest Value – Waiting to Harvest
In the previous example, perhaps the stand should not be harvested immediately.
Consider waiting 10 years to harvest the stand.
You estimate that the stand volume would increase to
24 mbf of sawtimber and
12 cords of pulpwood per acre.
Recall that the stand had 18 mbf of sawtimber and 14 cords of pulpwood per acre.
Assume constant prices.
What is the forest value in this case?

45. Present Value of the First Harvest
Assuming constant prices, in ten years you will be able to sell the timber for:
Of course, you have to wait ten years before you can realize this timber value, so this value needs to be discounted:

46. Costs that Occur Before the Next Harvest
Taxes will have to be paid on the property over the next ten years.
To account for this, subtract the present value of ten annual tax payments:
Thus, the net present value for the remainder of the current rotation is $4, ($4, $38.61)

47. Accounting for Future Rotations
After harvesting in ten years, you will have bare land.
The LEV calculated earlier indicates that the value of this bare land will be $
This gives the discounted value of all of the future rotations on the site.
But it is a future value that occurs in ten years.
Because the future rotations won’t start for another ten years.

48. Accounting for Future Rotations (continued)
The bare land value (LEV) must also be discounted for ten years before it is added to the present value of the current rotation:

49. The Forest Value – Waiting to Harvest
The Forest Value when the harvest is delayed is:
the present value of the costs and returns from the current rotation,
plus the present value of all future rotations.
Thus, the Forest Value when the harvest is delayed for 10 years is $4, ($4, $104.01)
Compare this with the Forest Value if the tract is harvested now — $6,
You would lose $1, per acre if you delay harvesting the stand for ten years.

50. The Forest Value Formula
First, some new notation:
T0 = the time when the current stand is to be harvested,
YCp, To = the expected yield of product p from the current stand at time T0,
ChC = the cost of selling the current stand of timber.
Now, the Forest Value formula:

51. The Forest Value Formula (continued)
Consider the Forest Value formula:
If a stand is going to be harvested right now (i.e., if T0 = 0), then the above formula simplifies to:
In this case, the Forest Value is just the liquidation value of the timber plus the LEV.

52. Even-aged Management Review
LEV
Good for estimating the value of bare land used primarily for growing timber
Good for evaluating alternative management regimes over a full rotation
Forest Value
Useful for calculating the value of land plus timber (especially immature timber)
Useful for evaluating alternative management regimes when you already have a growing stand