Economics of Pre-commercial and Commercial Thinning

Michael Stone
Economics and Trade Branch
British Columbia Forest Service

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1. Introduction

This paper reviews the method of assessing the economic feasibility of pre-commercial and commercial thinning, presents some results derived from growth and yield simulations, and offers some management guidelines.

2. Economic Assessment

In assessing the economics of silviculture investments, we are concerned not only with the stand's net value at each harvest age but also with any costs associated with establishing and managing the stand. We also require some means of comparing costs and benefits which occur in different time periods. These comparisons can be made by converting the future benefits and costs to equivalent present values. To do this, we discount the future values using a discount rate which reflects society's or an individualís preferences for present versus future consumption. The discount rate allows us to compare various flows of benefits and costs occurring over time in a logical and consistent manner. Thus, we estimate the expected flow of benefits and costs from a stand management regime, and then discount them to equivalent present values in order to determine the net present value and site value of that regime.

A silviculture treatment's net present value (NPV) will be the sum of the discounted benefits yielded by a treatment minus the sum of the discounted costs of the treatment. This can be written mathematically as:

where Ri = a revenue, or benefit, received at stand age i, Ci = a cost incurred at stand age i, r = the discount rate, and A = the age of harvest.

Stand regeneration costs occur in year zero, stand tending costs at the prescribed age and the conversion value in the year of harvest. Unless otherwise stated a real discount rate of 4% is used below.

NPVs based on a single rotation cannot be compared with regimes having different harvest ages because use of the land differs over time. The problem is overcome by considering the value of the site. Site value (SV) represents the maximum amount that someone would be willing to pay for bare land if the land was devoted to producing an infinite series of rotations of identical growing regimes (Faustmann, 1849). It is the net present value of this infinite series of growing regimes. The general formula for determining the SV is (Gregory, 1972):

The harvest age will obviously affect the estimated SV for a stand and the harvest age which maximizes the stand's SV is known as the economic rotation age. To assess alternative stand management regimes, compare the SVs of the alternatives at their respective economic rotation ages. The management alternative which yields the highest SV is the optimum regime. However, when some forest management constraint or objective requires that the stand be harvested at an age other than the economic rotation age (e.g. the culmination of MAI) then the SVs of the alternative regimes should be compared at the desired rotation age. You can also determine the economic loss of not harvesting at the economic rotation age by comparing the SV at the economic rotation age to the SV achieved at the desired rotation age.

The base age to which all benefits and costs are discounted to in calculating NPVs and SVs is typically age zero. However, we may wish to examine only the impacts of the pre-commercial or commercial thinnings and not the regeneration costs. Thus, when examining the each type of thinning below we discount all costs and benefits to the age at which the thinning would take place. Note that all silviculture costs and other costs occurring prior to the thinning age are treated as sunk costs and are ignored in both the NPV and SV calculations which follow.

3. Source of Simulations

The simulations used in this paper come from two interrelated growth and yield models: TASS (Tree And Stand Simulator) and TIPSY (Table Interpolation Program for Stand Yield). TASS is an individual tree distance dependent growth and yield model which simulates the growth of trees in three dimensions (Mitchell, 1975). It is the BC Ministry of Forestsí managed stand growth and yield model which also provides the yield table data base from which TIPSY operates. The commercial thinning simulations were based on TASS output while the pre-commercial thinning simulations were derived from TIPSY (Mitchell et al., 1993). TIPSY contains an economic analysis module, known as the TIPSY Economist (Stone et al., 1996), with which the economic analyses of pre-commercial thinning were calculated.

4. Pre-Commercial Thinning

A pre-commercial thinning (pct) is of course an investment in the future development of a stand. Naturally we would only undertake such an investment if the monetary value of the stand increased sufficiently to at least offset the cost of the thinning. Now suppose we undertook a pre-commercial thinning at age 15. Figure 1 shows the return required from every dollar invested in pre-commercial thinning at rotation ages of up to 100 years where the required rate of return is 3%, 4% and 5%. At age 75 you would require a return of $5.89 for each dollar invested if your interest rate was 3%, $10.52 at 4% and 18.68 at 5%. Thus, if pct costs were $600/ha the net stand value when harvested at age 75 would have to have increased by $3,534/ha, $6,312/ha and $11,208/ha at discount rates of 3%, 4% and 5% respectively. This would represent the minimum monetary value which the treatment must provide at harvest in order for the treatment to be economically viable at a 75 year rotation age.

With this in mind we examine three different pct scenarios: thinning in a managed stand (i.e. an initial density of 10,000 sph); thinning in a high density fire origin stand with an initial density of 250,000 sph prior to the onset of height growth repression; and thinning in the same high density stand but after the onset of repression.

Figure 1 Increase in stand net revenue required for
every dollar spent on a pre-commercial thinning at age 15

Thinning in a Managed Stand

The earlier presentation by Mitchell et al. (1997) showed that there was little evidence to suggest that there would be significant volume gains, and likely volume losses, associated with pre-commercial thinning as currently practiced in western Canada in lodgepole pine. Instead we trade off a small gain in volume in the dominant trees for a potentially large volume loss in the smaller trees. Volume losses increases dramatically as residual densities drop below 1,200 sph in lodgepole pine.

Does then the value added to the larger trees offset the value lost from the loss of the small trees? Figure 2A shows the total revenue, conversion cost and conversion return for a site index 18 lodgepole pine stand with an initial density of 10,000 sph, which was pre-commercially thinned when it reached a top height of 4 m to residual densities ranging from 331 sph to 4,00 sph and then harvested at age 60. Figure 2B shows average revenue, average conversion cost and average conversion return. The dotted lines show the same values for the unthinned stand. The results suggest that only a relatively modest increase in the standís net value at harvest, the conversion return, would be achieved and only for some residual densities. Conversion return would be maximized at a residual density of 1,600 sph and would fall below the net value of the unthinned stand at residual densities below approximately 800 sph. Note that we have not yet taking into account the cost of the pct.

The average values shown in Figure 2B show that average revenue can be increased significantly at the lower densities but that this entails such a loss in volume that total revenue falls. Average conversion cost also increases at these low densities because the fixed road development and overhead costs are amortized over a smaller volume which totally offsets the lower tree-to-truck costs associated with the larger piece sizes attained at the lowest densities. The average cost results might change somewhat if you are dealing with a site with low development and overhead costs and/or are employing a harvest system which is more sensitive to piece size than the ground based skidding assumed in our simulations.

The reason for this relatively modest economic gain at harvest is again the limited biological response of the stand to the thinning. This is demonstrated in Figure 3 which shows the economic and physical rotation ages and the mean annual increments of the stand at different residual densities. The dashed lines are again the values for the unthinned stands.

Figure 2 Revenue, conversion cost and conversion return at age 60 for
pre-commercially thinned stands by residual density
(SI 18 lodgepole pine initial density 10,000 sph)

Figure 3 -Economic and physical rotation ages and mean annual increment for SI 18

Still, if it is possible to increase conversion return, what would be the maximum feasible pct cost that would still ensure a rate of return on our thinning investment of 4%? We calculate this by first setting actual pct costs to zero and calculating the NPV of the thinned stand discounted back to the age of the thinning. Similarly we calculate the NPV of the unthinned stand also discounted back to the age at which the pct would take place. The maximum feasible pct cost is the difference between the NPV of the thinned stand and the NPV of the unthinned stand.

The results of this procedure are shown in Figure 4 for lodgepole pine stands with an initial density of 10,000 sph at three site indexes; 20, 18 and 16 m. Panel A shows the results if the stands were harvested at their economic rotation age while panel B shows the results if the stands were harvested at their physical rotation. The maximum feasible pct cost would be only $250/ha at site index 20, $200/ha at site index 18 and $150/ha at site index 16 if the stands were harvested at their economic rotation age. Note this maximum feasible cost drops off quickly as you move away from the optimum residual density of 1,600 sph. If harvested at their physical rotation age the maximum feasible pct cost would be even lower.

Maximum feasible pct cost results are not very sensitive to the discount rate used as changing the discount rate would affect both the thinned and unthinned results. For example, decreasing the discount rate from 4% to 3% increases the maximum pct costs for our site index 18 stand by only $90/ha from $200/ha to $290/ha at a residual density of 1600 sph.

Figure Maximum allowable spacing costs when harvested at economic and physical rotation ages

Thinning In High Density Stands Subject to Height Growth Repression

Thinning in a high density stand prior to the onset of height growth repression does produce a biological response by allowing the site to achieve its potential height growth (Mitchell and Goudie, 1980; J.S. Thrower and Assoc. Ltd., 1993a,b,c,d). We simulated this impact by examining the impact on two sites with initial densities of 250,000 sph using the repression module contained in TIPSY. One site has a site index of 18 m but due to the effects of repression would have a height at index age of only 15.4 m, while the other stand has a site index of 20 m but would achieve a height at index age of 17.1 m. If a pct allows a site to achieve its potential height growth then the pct would have a large volume impact. Remember that site index is a non-linear measure of site productivity and thus the volume impact is greater the higher the site index. However, the restoration of the stand to its potential height growth is only possible if the stand is thinned prior to the onset of repression which occurs at a top height of approximately 1 m. Thinning after this critical height is attained would produce a negligible height growth response.

Figure 5 shows the maximum feasible pct cost if the stand is thinned prior to the onset of height growth repression. Maximum feasible pct costs have increased dramatically from the mere $200/ha shown earlier for a site index 18 stand to almost $500/ha if the stand is harvested at its economic rotation age. The increase in the allowable pct cost is even greater for our SI 20 stand which now reaches $700/ha. Again the optimum residual density is approximately 1,600 sph. Feasible pct costs drop sharply for residual densities below the optimum density but fall off slowly at the higher residual densities shown. Note that the maximum allowable pct cost is higher if the stands were harvested at their physical rotation age rather than then at the economic rotation. The reason for this is discussed later.

Figure 5 Maximum allowable spacing costs for repressed stands thinned
prior to the onset of repression and harvested at economic and physical rotation ages

If the stand is thinned after the onset of height growth repression then the maximum feasible pct cost drops sharply as shown in Figure 6. In this case the pct fails to return the site to its potential productivity and the residual stand cannot quickly reoccupy the site.

Figure 6 Maximum allowable spacing costs for repressed stands thinned after
the onset of repression and harvested at economic and physical rotation ages

Figure 7 shows the effects of pct on the physical and economic rotation ages for thinning both before and after the onset of repression. Thinning before repression significantly reduces both the physical and economic rotation ages compared to the unthinned rotations but the effect on the physical rotation is the most dramatic. Thinning after repression has little effect on the economic rotation age but does reduce the physical rotation, but not by as much as when thinning prior to repression.

The significantly greater decline in the physical rotation for the high density stands is the reason why maximum allowable pct costs were higher at the physical rotation age than at the economic rotation age, as shown in Figures 5 and 6. As you move past the economic rotation age the NPV of the stand quickly begins to drop off. By decreasing the period between the economic and physical rotation age the drop in NPV becomes relatively smaller. This increases the NPV of the thinned stands when calculated at the physical rotation more than it does when the NPV is calculated at the economic rotation. This in turn makes the difference between the thinned and unthinned NPVs greater at the physical rotation than at the economic rotation.

The higher allowable pct costs at the physical rotation is not an economic justification for harvesting at the physical rather than the economic rotation. The economic rotation is still the economically superior harvest age. However, if you are constrained to harvest at the physical rotation then there is an added benefit from thinning high density stands which results from the significantly greater decrease in the rotation age.

Figure 7 Economic and physical rotation ages and mean annual increment for SI 20

Pre-Commercial Thinning Conclusions

• Thinning in managed stands (<15,000 sph initial density) will likely be economically viable only on better sites in areas with low pct costs.
• Residual density will be a key determinant of the economic success of thinning with approximately 1,600 sph being the optimum residual density for lodgepole pine. Significant volume losses should be expected at residual densities below 1,200 sph.
• Thinning in high density stands prior to the onset of height growth repression can support substantially higher pct costs. The maximum allowable cost increases with site index.
• Thinning after the onset of repression is unlikely to be viable.

5. Commercial Thinning

A commercial thinning can be defined as a partial harvest of trees in older immature stands where some portion of the trees removed has reached a merchantable size and where the sale of the timber harvested will earn a positive financial return (Worthington and Staebler, 1961).

Research Branch's Tree and Stand Simulator (TASS) was used to simulate the development of natural origin lodgepole pine stands of site index 20, 18 and 16 m, with an initial density of 5,000 sph. Commercial thinnings were simulated at age 40, 50, 60 and 70 years to residual densities of 900 and 600 sph. The simulations suggested that the thinnings can provide at best only a marginal increase in the cumulative merchantable volume available from a stand over a rotation and if not planned correctly could reduce cumulative volume. While cumulative volume may increase, the final harvest of the thinned stands was reduced below that of the unthinned stand. Commercial thinnings must therefore be justified based on the increase in value of the stand resulting from the concentration of the standís growth on fewer trees or on the earlier financial return obtained from the thinnings. Further details of these and other commercial thinning simulations can be found in Stone (1996).

The estimated site value (SV), calculated at a standard age of 40 years, for each growing regime and thinning intensity are displayed in the Figures 8 to 10. Harvest revenues and costs were estimated in 1994 dollars and were based on the procedures used in BCís Interior Appraisal Manual. They show that the choice of the rotation age for the final harvest will be critical when assessing the economics of commercial thinning lodgepole pine. When comparing the optimum economic rotation age of an unthinned stand to that of a thinned stand, the unthinned stand almost always dominates. However, the optimum economic rotation age for unthinned stands occurs between ages 50 to 70 with the longer economic rotations occurring on the lower quality sites. Typically these economic rotation ages are shorter than those that maximize the standís merchantable volume. However, comparison of SVs at optimum economic rotation ages may not be particularly relevant as BCís provincial forests are managed to achieve a number of goals other than the strict maximization of economic return. These goals include the maximization of sustained yield and the maintenance of non-timber forest values. These multiple objective goals typically extend rotation ages to or past the culmination of MAI. In cases where the optimum economic rotation age cannot be selected, because of conflicts with other forest management goals, then the forest manager should select the regime which maximizes the SV while meeting the other forest management goals. This constrained maximization problem will in practice mean that the forest manager will be selecting the maximum SV at a rotation age greater than the economic rotation age. The diagrams show that when rotation ages are planned for ages greater than 80 to 90 years the SVs of the thinned simulations would dominate.

The diagrams also show that for all growing regimes the stand's SV begins to quickly fall soon after it passes its economic rotation age. However, the decline is not as rapid for the thinned regimes. The slower decline in SVs provided by the commercial thinning regimes can be attributed to two factors. First, the thinnings concentrated the stand's growth on the larger dominant trees which produced a higher value per m^_ of wood grown. Second, the thinnings produced interim revenues through the harvesting of trees who's timber values would have grown at a rate lower than the social discount rate. Using an investment analogy, if the stand is viewed as an investment portfolio and each tree as a separate stock than the commercial thinning may be viewed as the liquidation of those stocks producing the poorest investment yields. In addition, the thinning would have the added advantage of increasing the returns on the remainder of the investment portfolioóthe leave trees.

In considering only the commercially thinned simulations we can conclude that generally the lighter thinnings would provide a higher SV when the final harvest is planned for ages below 90 to 100 years while the heavier thinnings dominate for final harvest ages greater than 90 to 100 years. A comparison of the results by site index suggests the following regimes would be optimal for the commercially thinned regimes:

site index 20 - a light or heavy thinning at age 50;

site index 18 - a light thinning at age 50 or a heavy thinning at age 60; and,

site index 16 - either a heavy or a light thinning at age 60.

Figure 8 Site values discounted to age 40 of alternative growing
regimesósite index 20, initial density 5,000 sph

Figure 9 Site values discounted to age 40 of alternative growing
regimesósite index 18, initial density 5,000 sph

Figure 10 Site values discounted to age 40 of alternative
growing regimesósite index 16, initial density 5,000 sph

Those familiar with economic evaluations of forestry investments in British Columbia may be surprised by the robustness of the commercial thinning results, as the analysis of investments, such as forest regeneration, typically show a low return due to the long rotation ages. This means that the revenues received at final harvest from such projects are heavily discounted. However, for commercial thinnings discounting is working in favor of the thinnings as the revenue from the thinning is received at the beginning of the evaluation period while the cost of the reduced final harvest is incurred at the end of the period. Thus, there is a reversal in the ordering of costs and revenues in that the net revenues of the commercial thinning are not discounted while the net costs at final harvest are discounted.

The discussion above does not mean that calculation of SVs for the economic rotation ages are without policy relevance, for they can show us the opportunity cost of extending rotation ages past the economic rotation age or the opportunity cost of selecting an alternative growing regime. For example, consider an unthinned stand with an SV of $3,000/ha at its economic rotation age of 55, but due to other forest management constraints the stand could not be harvested before age 95. For a harvest age of 95 the unthinned stand's SV would be $1,500/ha which implies that the opportunity cost of meeting the forest management objective which extended the rotation age was $3,000/ha minus $1,500/ha or $1,500/ha. If, on the other hand, the stand was commercially thinned to 600 sph at age 60, the SV of the stand at age 95 might be $2,000/ha which would reduce the opportunity cost of meeting the constraining objective to $1,000/ha.

Comparison Between Thinning Ages

Note that the SVs for each regime were calculated using age 40 as the base year, to which all values were discounted. This provides the appropriate comparison when attempting to determine the optimum age at which to commercial thin a stand. However, it does not provide an appropriate comparison when attempting to determine which of two stands, one age 50 and one age 70, should receive priority for thinning. To do this type of comparison the SV for each stand should be calculated using its current age as the base year to which all costs and benefits are discounted. This would be the same as compounding the SV calculated at age 40 forward to each standís current age. If this was done then, for a given site index and initial density, it would show that the older the stand the higher will be its SV when calculated at its current age. This means that when comparing two stands, one of which is older, the older stand should receive priority for commercial thinning provided that clearcutting the older stand is not feasible.

Commercial Thinning Sensitivity Tests

The economic results for the commercial thinning simulations are highly sensitive to four factors:

• Planned Rotation Age - If you are free to harvest the unthinned stand at its economic rotation age you should do so. However, if other forest management constraints prevent this then commercial thinning becomes an economically feasible option at longer rotation ages.
• Road Development Costs - If road development costs are high or if the road build for the thinnings is not available for the final harvest then the economic advantage from thinnings will be lost. However, if because of adjacency requirements you must leave stands unharvested in roaded areas then a commercial thinning of these stands may well be warranted.
• Prices Received for Small Diameter Timber - The markets for pulp logs and sawlogs are cyclical thus commercial thinning may only be feasible during market upturns.
• Future Price Expectations - If you expect an increase in real timber prices in the future then it would be better off to forgo thinning the stand and clearcut harvest the entire stand later.

References

Faustmann, M., 1849. "Calculation of the value which forest land and immature stands possess for forestry." Allegeine Forst- und Jagd-Zeitung pp. 441-455. The English translation can be found in Linnard, W. and M. Gaine (1968) Martin Faustmann and the evolution of discounted cash flow, Commonwealth Forestry Institute, Institute Paper No. 42, University of Oxford.

Gregory, R.G., 1972. Forest resource economics. John Wiley & Sons. Inc., New York.

J. S. Thrower and Assoc., Ltd. 1993a. Growth and yield effects of juvenile spacing lodgepole pine in the Gold Fire near Cranbrook, B.C. Unpub. Rep., B.C. Min. For., Silv. Br., Stand Tending Field Trip, Victoria, B.C. 17 p.

J. S. Thrower and Assoc., Ltd. 1993b. Growth and yield effects of juvenile spacing in three fire-origin lodgepole pine stands 12-15 years after treatment. Unpub. Rep., B.C. Min. For., Silv. Br., Min. Serv. Contr. No. 107735, Project No. 92-19-RW, Victoria, B.C. 87 p.

J. S. Thrower and Assoc., Ltd. 1993c. Paired-plot sampling for height growth repression and recovery in three older juvenile spacing projects in fire-origin lodgepole pine. Unpub. Rep., B.C. Min. For., Silv. Br., Min. Serv. Contr. No. 21812, Project No. 92-18-NDb, Victoria, B.C. 36 p.

J. S. Thrower and Assoc., Ltd. 1993d. Paired-plot repression and recovery in three older juvenile spacing projects in fire-origin lodgepole pine. Unpub. Rep., B.C. Min. For., Silv. Br., Victoria, B.C. 36 p.

Mitchell, K.J, 1975. Dynamics and simulated yield of Douglas-fir. Forest Science Monogram No. 17.

Mitchell, K. J. and J. W. Goudie. 1980. Stagnant lodgepole pine. Unpubl Man., Final Rep. FY-1979-1980 on EP850.02, B.C. Min. For., Res. Br, Victoria, B.C. 31 p.

Mitchell K.J., J. Goudie, and l. Herring. 1997. The Emperorís new clothes. Presentation given at the Stand Density Management: Planning and Implementation Conference, November 6-7, 1997, Edmonton, Alberta.

Mitchell, K.J., S.E. Grout, R.N. Macdonald, and C.A. Watmough. 1993. Userís guide for TIPSY: A Table Interpolation Program for Stand Yields, Version 2.0 beta. Ministry of Forests, Research Branch, Victoria, B.C.

Stone, M.S. 1996. Commercial thinning lodgepole pine: An economic analysis. FRDA Working Paper WP-6-017. Canadian Forest Service/BC Ministry of Forests, Pacific Forestry Centre, Victoria, B.C.

Stone, M.S., S.E. Grout, and C.A. Watmough. 1996. The TIPSY Economist: An economic analysis module for WinTIPSY. Ministry of Forests, Victoria, B.C.

Worthington, N.P., and G.R. Staebler. 1961. Commercial thinning of Douglas-fir in the Pacific Northwest. US Depart. Of Agriculture, Forest Service, Technical Bulletin No. 1230. Washington, D.C.