Discounted Cash-Flow Model for Western Washington Forest Products

Transcription

1 Discounted Cash-Flow Model for Western Washington Forest Products FORSight Resources, LLC 3813 H Street Vancouver, WA Prepared for: John Dough Woodlands & Procurement Manager Western Washington Forest Products June 8, FORSight Resources, LLC

2 Executive Summary Western Washington Forest Products (hereafter, WWFP ) contracted with FORSight Resources (hereafter, FORSight ) to develop a discounted cash-flow model in support of on-going management of its Big Timber Tree Farm. The total area of the Big Timber Tree Farm is 76,414 acres comprised of four tracts: Whitman (14,426 ac), Walker (20,440 ac), Euclid (18,393 ac) and Estevan (23,154 ac). The majority of the area (42%) is western hemlock. Douglas-fir stands constitute another 36%. Non-commercial timberlands, including buffer areas, wetlands, and other unmanaged acres, make up 10% of the total acreage. Across all tracts, a majority of the area (76%) is moderate to good sites (Site Index greater than 95). In the Walker tract, fully 50% percentage of the acres have Site Index values greater than 115. Conversely, more than 13% of the Whitman tract is comprised of Site Index values of 55 or less. The age class distributions of the four tracts have some significant differences: eastern tracts (Euclid & Estevan) have significantly more acres in the below-10 and age ranges than the western tracts (Whitman and Walker). Conversely there are more acres in the age range on the western tracts than the eastern ones. Overall, the age distribution is somewhat bimodal, with a moderate age-class gap in the age range. As part of the modeling process, FORSight Resources conducted rigorous screening and cleaning of data received from WWFP staff. Overall, the data were relatively clean. The issue of greatest concern is that it appeared that some height, TPA, and basal area data had been populated based 10-year age class averages, which if not corrected, could cause issues when projecting them forward with growth and yield models. Current forest inventory for the Big Timber Tree Farm was projected forward for years using the Stand Management Cooperative (SMC) variant of ORGANON. Regenerated Douglasfir plantations were modeled using the SMC variant of the CONIFERS simulator, which is designed to model the effects of various levels of competing vegetation on the development of young Douglas-fir stands. Stands were grown in conifers until their age was at least 18 years, at which time grown treelists were fed into ORGANON for further projection. FORSight developed a strategic harvest scheduling model using the Remsoft Spatial Planning System. The model maximized discounted cash flows over a planning horizon of 101 annual planning periods. The first year of the model planning horizon incorporated remaining harvest blocks to be harvested by WWFP for FY 2008, to bring the inventory to current (year-end 2008). There were four actions defined in the model (clear-cut, site preparation, natural regeneration and planting), corresponding to activities undertaken to manage the forest: final harvest, site preparation, stand establishment. The clear-cut action determines the timing of the regeneration harvests in stands labeled as commercial forest. No clear-cuts were permitted in non-forested areas, nor in management zones such as SMZs, easements, etc. Average logging costs were associated with logging system (cat/cable) and elevation (high/low) yielding a 2x2 matrix of logging costs associated with clear-cut harvests. Site preparation was assumed to occur one year following final harvest. Individual costs were provided for site preparation associated with planting (low elevation) and with natural i

3 regeneration (high elevation). Stand establishment was assumed to occur 1 year following site preparation. Planting density was assumed to be 500 Douglas-fir trees per acre. Natural regeneration was assumed to occur 3 years after final harvest, with hemlock and Douglas-fir stands regenerating to hemlock, and all others regenerating to mixed conifer. Five model runs were completed by FORSight as well as an unconstrained base run. Alternative 1 established a floor on conifer log volume of 55 MMBF/ year. For Alternative 2, sequential flow constraints (± 5%) were added to the floor constraints of Alternative 1 to smooth out harvests in the early years. Alternatives 3 and 4 explored WWFP management goals of geographically dispersing the harvest and tightly controlling product mix, respectively. Alternative 5 constrained high elevation harvests to no more than 60% of the annual total. All of the model runs were feasible and produced optimal solutions. The unconstrained base run was important because significant variability in annual harvests was exhibited, so much so that it defies practical implementation. The constrained runs all addressed this variability directly and as a result, the constraints were binding in many periods, yielding significant reductions in NPV. 50 Year Results: Harvest Volumes (MMBF) Base Alt1 Alt2 Alt3 Alt4 Alt5 Df 12" Df 8" Df 5" Df Pulp Wh 12" Wh 8" Wh 5" Wh Pulp Ww 12" Ww 8" Ww 5" Ww Pulp Rc 12" Rc 8" Rc 5" Ra 12" Ra 8" Ra 5" Ma 12" Ma 8" Ma 5" Hw Pulp Average Merchantable Inventory Harvest Revenues 12"+ $ 473,573,467 $ 415,626,848 $ 703,915,305 $ 700,857,170 $ 695,213,890 $ 700,857,169 8"+ $ 752,421,509 $ 758,872,022 $ 616,415,735 $ 605,870,801 $ 595,281,071 $ 605,870,800 5"+ $ 129,917,931 $ 171,387,689 $ 49,441,021 $ 49,333,621 $ 58,959,323 $ 49,333,621 Pulp $ 90,977,164 $ 98,015,268 $ 74,927,159 $ 75,038,219 $ 74,610,659 $ 75,038,219 Harvest statistics Avg clearcut age (years) Avg acres clearcut (ac/yr) 1,690 1,906 1,198 1,198 1,210 1,198 Avg annual logging cost $ 8,025,711 $ 7,923,584 $ 8,289,691 $ 8,213,673 $ 8,221,085 $ 8,213,673 Avg logging cost ($/ac) $ 4,748 $ 4,158 $ 6,921 $ 6,858 $ 6,793 $ 6,858 Avg logging cost ($/mbf) $ $ $ $ $ $ Avg annual hauling cost $ 5,514,983 $ 5,511,784 $ 5,683,019 $ 5,640,787 $ 5,604,841 $ 5,640,787 Avg hauling cost ($/mbf) $ $ $ $ $ $ Annual costs Avg WA B&O tax $ 1,389 $ 1,386 $ 1,387 $ 1,374 $ 1,367 $ 1,374 Avg WA Forest Excise tax $ 874,763 $ 868,272 $ 896,737 $ 889,536 $ 883,092 $ 889,536 Avg site preparation cost ($) $ 91,034 $ 109,932 $ 68,800 $ 68,703 $ 69,328 $ 68,703 Avg planting cost ($) $ 365,188 $ 430,992 $ 281,020 $ 280,374 $ 281,067 $ 280,374 Contribution to Net Present Value 50-yr NPV $ 341,212,663 $ 309,576,584 $ 218,373,238 $ 215,293,018 $ 212,862,869 $ 215,293, yr NPV $ 364,060,044 $ 324,653,759 $ 263,850,323 $ 260,591,743 $ 257,535,003 $ 260,591,743 per-acre basis $ 4,764 $ 4,249 $ 3,453 $ 3,410 $ 3,370 $ 3,410 After considering all of the alternative model runs, WWFP management determined that Alternative 5 best met their management objectives and they deemed it their preferred alternative. ii

4 Table of Contents Executive Summary... i Table of Contents...iii List of Figures...iii List of Tables... v 1 Introduction Background Description of Forest Analysis Assumptions and Parameters Data Auditing Growth & Yield Generation Model selection Stratification Merchandising Planning Model Model Assumptions Classification Scheme Silvicultural Treatments/Management Regimes Model Outputs and Reports Objective Function and Constraints Sensitivity Testing and Model Validation Development of the preferred alternative Discussion Conclusions List of Figures Figure 1. Spatial distribution of Big Timber Tree Farm, identifying individual tracts Figure 2. Big Timber timberlands by tract... 2 Figure 3. Big Timber timberlands acreage by broad cover type... 2 Figure 4. Big Timber timberlands total acreage by land classification Figure 5. Age class distribution of the Big TimberTree Farm... 4 Figure 6. Spatial distribution of harvest areas past & present (hatched), as well as associated green-up restrictions (solid) Figure 7. Conifer log harvest volume over 101-year planning horizon (no ending inventory constraint) Figure 8. Changes in merchantable inventory over 101-year planning horizon (no ending inventory constraint) iii

5 Figure 9. Average harvest age trend over 101-year planning horizon (no ending inventory constraint) Figure 10. Conifer log harvest volume over 251-year planning horizon (no ending inventory constraint) Figure 11. Conifer log harvest volume over 101-year planning horizon (with PTHC) Figure 12. Changes in merchantable inventory over 101-year planning horizon (with PTHC) Figure 13. Clearcut acres in Maximize NPV base run (no flow constraints, with PTHC) Figure 14. Conifer log harvest volume in Maximize NPV base run (no flow constraints, with PTHC) Figure 15. Clearcut acres in Maximize NPV Alternative 1 run Figure 16. Conifer log harvest volume in Maximize NPV Alternative 1 run Figure 17. Conifer log harvest volume in Maximize NPV Alternative 2 run Figure 18. Harvest acres by tract in Maximize NPV Alternative 2 run Figure 19. Softwood product mix in Maximize NPV Alternative 2 run Figure 20. Harvest acres by elevation in Maximize NPV Alternative 2 run Figure 21. Harvest volume by tract in Maximize NPV Alternative 3 run Figure 22. Harvest acres by tract in Maximize NPV Alternative 3 run Figure 23. Softwood product mix in Maximize NPV Alternative 4 run Figure 24. Harvest volume by tract in Maximize NPV Alternative 4 run Figure 25. Harvest acres by tract, in Maximize NPV Alternative 5 run Figure 26. Percentage of volume by elevation in Maximize NPV Alternative 5 run Figure 27. Harvest acres by logging system and elevation, in Maximize NPV Alternative 5 run Figure 28. Variability in conifer log volume harvested over 50 years Figure 29. Displacement of harvest volume via sequential flow constraints Figure 30. Variability in total inventory over 50 years iv

6 List of Tables Table 1. Summary of data irregularities isolated in Big Timber timberlands data... 5 Table 2. Species-specific merchandising specifications provided by WWFP... 7 Table 3. Prices and costs used in the Big Timber model Table year summary of results for discount rate effects sensitivity testing Table year summary of results for discount rate effects sensitivity testing Table year summary of results for base run and Alternatives Table year summary of results for base run and Alternatives v

7 1 Introduction Western Washington Forest Products (hereafter, WWFP ) contracted with FORSight Resources (hereafter, FORSight ) to develop a discounted cash-flow model in support of ongoing management of the Big Timber Tree Farm. 1.1 Background The Big Timber Tree Farm is located in the northern Cascades of Washington State, and as is typical of the region, is characterized by higher elevations, steep terrains and plentiful annual precipitation conducive to tree growth. Douglas-fir plantations dominate the lower elevations and hemlock-true fir-mixed conifer stands are at the higher elevations. Figure 1. Spatial distribution of Big Timber Tree Farm, identifying individual tracts Description of Forest The total area of the Big Timber Tree Farm is 76,414 acres comprised of four tracts: Whitman (14,426 ac), Walker (20,440 ac), Euclid (18,393 ac) and Estevan (23,154 ac). The property is dominated by western hemlock and Douglas-fir stands (see Figure 3). The majority of the area (42%) is western hemlock. Douglas-fir stands constitute another 36%. Non-commercial timberlands, including buffer areas, wetlands, and other unmanaged acres, make up 10% of the total acreage (see Figure 4). 1

8 Big Timber Tree Farm by Tract Whitman 19% Estevan 30% Walker 27% Euclid 24% Figure 2. Big Timber timberlands by tract. BigTimber Tree Farm by Forest Type Non-Productive Whitewoods Hemlock Forest type Red Alder Other Hardwood Douglas-Fir Red Cedar Acres Whitman Walker Euclid Estevan Figure 3. Big Timber timberlands acreage by broad cover type. 2

9 Figure 4. Big Timber timberlands total acreage by land classification. Across all tracts, a majority of the area (76%) is moderate to good sites (Site Index greater than 95). In the Walker tract, fully 50% percentage of the acres have Site Index values greater than 115. Conversely, more than 13% of the Whitman tract is comprised of Site Index values of 55 or less. BigTimber Tree Farm Site Quality by Tract Acres I II III IV V Site Quality Whitman Walker Euclid Estevan Figure 4. Big Timber timberlands acreage by Site Index class and block. 3

10 Age Class Distribution Acres Age (years) Whitman Walker Euclid Estevan Figure 5. Age class distribution of the Big TimberTree Farm. The age class distributions of the four tracts exhibit some significant differences, as shown in Figure 5. The eastern tracts (Euclid & Estevan) have significantly more acres in the below-10 and age ranges than the western tracts (Whitman and Walker). Conversely there are more acres in the age range on the western tracts than the eastern ones. Overall, the age distribution is somewhat bimodal, with a moderate age-class gap in the age range. There is a large spike in the age class distribution at age 51 that corresponds to a significant windthrow and salvage event in

11 2 Analysis To ensure that any harvest scheduling analysis provides credible results, it is necessary to start with a solid foundation, based on clean inventory data and appropriate growth models. Once these steps are completed, a set of silvicultural regimes are agreed upon, and they are projected using the growth models to develop yield tables. The yield tables are evaluated, looking for projections that fall outside biologically reasonable bounds, and where necessary, adjustments are made to bring them in line with expectations. The yield tables are then incorporated into a planning model framework where alternative objective functions and/or constraints can be tested in order to develop a preferred management alternative Assumptions and Parameters WWFP provided FORSight staff with the assumptions, parameters, and management regimes/silvicultural treatments to be included in the model formulation for the Big Timber property. This information also included an appropriate range of alternative treatments and activity timing choices. From these alternatives, the model selected the financially optimal mix of activities to best meet WWFP s stated management objectives and constraints. 2.2 Data Auditing As part of the modeling process, FORSight Resources conducted rigorous screening and cleaning of data received from WWFP s inventory system. Data were validated in a number of different ways. First, missing or null data were identified. Second, data were examined to determine whether stated conditions were likely to exist in nature (i.e., outside lower and upper bounds considered biologically reasonable for the region). If conditions were considered unlikely, data were flagged for further examination. These flagged stands do not necessarily constitute erroneous data, but rather suspect data that merit further examination. Table 1 summarizes the data errors revealed after FORSight examined the data provided by WWFP. It should be noted that these errors are not cumulative. There are instances where a given forest stand record qualifies for more than one type of anomaly. As FORSight identified data issues, WWFP personnel were contacted to provide a collaborative process to address data concerns. Table 1. Summary of data irregularities isolated in Big Timber timberlands data. Error Description Stands affected Acreage Affected Affect on Inventory High Basal Area per Acre ,972 Overstate value Low Basal Area per Acre 1 22 Understate value Low Trees per Acre Understate value High Volume per Acre 154 6,105 Overstate value Low Volume per Acre Understate value High Board Feet per Acre 340 2,594 Overstate value Dominant Species Mismatch 2 27 Unknown Very Old Stands Unknown Weighted Avg Height too High Overstate value Low Height/DBH Ratio High Height/DBH Ratio 106 DBH records affected 110 DBH records affected According to WWFP field staff, there is a lot of standing timber on the Tree Farm due to WWFP s historically conservative forest management strategy. With this in mind, it could be possible that many of the flagged stands having abnormally high values are correct. Data were 5

12 screened based on reasonable thresholds, but these thresholds may be too conservative based on this property. Overall, the inventory data were relatively clean. The issue of greatest concern is not directly shown in the above table. It appeared that some height, TPA, and basal area data had been populated based on 10-year age class averages. This could cause issues, especially, with the younger age stands, when using the growth and yield models. 3 Growth & Yield Generation This section briefly describes the process used to generate the Woodstock yield tables. It also describes the assumptions used in the growth and yield process Model selection Current forest inventory for the Big Timber Tree Farm was projected forward for years using the Stand Management Cooperative (SMC) variant of ORGANON. ORGANON is an individual tree, distance independent growth simulator. It takes existing tree list data and projects changes in heights, diameters, and other tree parameters through time. Other models considered for use in projecting growth were the Forest Vegetation Simulator (FVS) (the Western Cascade variant) and the Forest Projection System (FPS). ORGANON was chosen for its ability to accurately model growth in a wide range of stand conditions. In addition, ORGANON is available in the public domain and has been through an extensive peer review process, ensuring that the model has undergone scrutiny by the scientific community. Although the SMC ORGANON variant was developed using stand data ranging in age from 1 to 80 years, many stands in the dataset were 20 years and older. As a result, projections for stands less than 20 years may be questionable. The CONIFERS simulator was used to project young stands less than 18 years old. The CONIFERS project is run by the Pacific Southwest Experiment Station of the U.S. Forest Service in Redding California. The SMC variant of the CONIFERS simulator is designed to model the effects of various levels of competing vegetation on the development of young Douglas-fir stands. Stands were grown in CONIFERS until their age was at least 18 years, at which time grown treelists were fed into the ORGANON model for further projection. Yield curves for regenerated Douglas-fir plantations were also simulated using the CONIFERS model for the first 20 years. Planting density was assumed to be 500 trees per acre with an endemic mortality rate of 1.05% (yielding approximately 20% mortality at age 20). The resulting grown treelist was again fed into ORGANON for further projection. Yield curves for naturally regenerated stands were simulated in ORGANON using data from existing natural stands years of age. Although the resulting curves do not begin until at least age 18, this was deemed acceptable as stands less than 35 years of age are not considered merchantable. 6

13 3.1.2 Stratification There are two common methods for representing strata conditions; the first uses the average value of all of the stands within the strata while the second uses the stand closest to the centroid to represent strata conditions. The first method requires the same degree of accuracy in the data for all stands. Since this is rarely true in general and never true in projected data, the second method was chosen. Stratification parameters consist of the biological conditions present in the stands as well as the possible silvicultural conditions and product breakdowns. The stands were divided into classes by primary species cover type (based on basal area), site index, basal area, per acre tree count and 10-year age class. Stands without basal area were assumed to be recently planted and were aggregated into bare-ground strata. Within each stratum the stand having conditions nearest to the average of the stratum values was selected to represent stratum conditions. In the calculation of the average values individual strata were weighted by their size. In addition selection probability was increased by stand area. Thus when two stands were equidistant from the stratum centroid, the stand with the larger area was selected to represent the stratum Merchandising Once tree lists are grown, they are merchandised by predicting the number and size of the logs in each tree record and dividing these logs into product categories. Board Foot volumes are determined by selecting a minimum top diameter, trim allowance, stump height, and log length. Stump height and trim allowance were set to one foot. The minimum top diameter and log length were species specific values provided by Western Washington Forest Products (see Table 2). Table 2. Species-specific merchandising specifications provided by WWFP. Minimum Pulpwood Sort 3 Sort 2 Sort 1 Species Merchantable DBH Min. DIB Min. Len. Min. DIB Min. Len. Min. DIB Min. Len. Min. DIB Min. Len. Alaska Yellow Cedar Big Leaf Maple Cherry Species Cottonwood Species Douglas-fir Grand Fir Misc. Conifers Misc. Hardwoods Mountain Hemlock Noble Fir Pacific Silver Fir Pacific Yew Red Alder Sitka Spruce Sugar Pine Western Hemlock Western Red Cedar Western White Pine White Fir Depending on the species, taper functions from ORGANON or the Forest Service National Volume Estimator Library (NVEL) were used to determine the number of logs per tree and their associated scaling diameters. The volumes from the logs were accumulated into the four product classes outlined in Table 2. Yield tables were then constructed based on these volumes for use in the Woodstock planning model. 7

14 After all the yield tables for the modeling effort were produced, WWFP silviculturists evaluated them to be sure that they fell within the range of values expected on the Big Timber Tree Farm. A total of seven yield tables were found to exceed expected values, and after some adjustments to the representative stand parameters, new yields were generated for these 7 cases. WWFP then signed off on the yields as acceptable. 3.2 Planning Model FORSight Resources developed a strategic forest management scheduling model as part of the acquisition analysis utilizing the Remsoft Spatial Planning System (Model-II linearprogramming formulation), growth and yield models, a range of silvicultural alternatives, forest management objectives and constraints, and an appropriate land classification scheme. Woodstock is a very flexible modeling environment that allows for a wide-range of silvicultural treatments, detailed tabular and graphical reports on outputs and relatively easy integration with other analytical tools. 3.3 Model Assumptions The strategic harvest schedule provided to WWFP specifies harvest years, harvest acres, and harvest volumes for final harvests and thinning by stratum (a population of similar stands) over a planning horizon of 50 years. This schedule is a proper subset of the full planning horizon used in the full Woodstock harvest scheduling model. At the time the modeling process was started, WWFP had not completed a final year-end inventory update of 2008; silvicultural history was updated to Q3 of Rather than wait until the New Year for the final update, FORSight began the modeling process with the existing inventory. The first planning period was designated 2008, and to account for harvesting that was in the final stages only the in-progress harvest blocks were eligible to be harvested in the first planning period. This was accomplished by hard-wiring those blocks in the Woodstock LPSchedule section and excluding the generation of clearcut decision variables in that period. The result is that the model will complete the designated harvests, update the inventory to yearend internally, and commence full harvest scheduling for Based on birth year information in the inventory database, harvest areas for the past five years were also identified, and using Spatial Woodstock s proximal analysis feature, commercial forest stands within 300 feet of the harvest areas were identified as inoperable for 5 years following the year of harvest 1. 1 For example, the neighboring stands of a block that was harvested in 2004 would be ineligible for harvest in 2008 and 2009, but they would be eligible for harvest in 2010 when the green-up period of 5 years had elapsed. 8

15 Figure 6. Spatial distribution of harvest areas past & present (hatched), as well as associated green-up restrictions (solid). In Figure 6, the colored polygons with hatching indicate implemented ( ) or planned ( ) harvest blocks. The polygons without hatching indicate stands that are ineligible for harvest due to green-up and adjacency requirements associated with the implemented and planned harvest areas. The circle with cross-hairs indicates a 300 diameter. With a 5-year greenup interval, if any portion of a stand is within 300 feet of a 2009 harvest block, that entire stand is ineligible for harvest until at least While this methodology is conservative -- entire stands are locked out rather than just the 300 buffer -- it does ensure that at least the stands adjacent to pre-existing harvest areas will not violate restrictions set forth by Washington s Forest Practices Act Classification Scheme To develop an effective harvest schedule, one needs three types of information: an accurate initial inventory of forest types (e.g., age, site quality, volume, etc.), growth and yield estimates for a range of different intermediate and final silvicultural treatments, and accurate cost and revenue information. To link these different kinds of information within a harvest-scheduling model, one needs a concise classification scheme. This scheme should include both biological and management components. Stands that will or should be treated similarly should be grouped accordingly. The classification parameters used in this model are as follows: 9

16 Theme I: Dominant species (DF, WH, WW, RA, RC, HW) Theme II: Site class (I-V) Theme III: Basal area class (5 classes) Theme IV: Trees per acre class (6 classes existing; 2 classes regenerated) Theme V: Age class (10 year breaks to 80, 81+) Theme VI: Stand origin (existing or regenerated) Theme VII: Stand condition (clearcut, site prepared, stocked) Theme VIII: Logging system (caterpillar, cable) Theme IX: Elevation (2500 ft break) Theme X: Tract (Whitman, Walker, Euclid, Estevan) Silvicultural Treatments/Management Regimes The heart of the strategic model is the assignment of management regimes and harvest/treatment timing choices to strata. For that reason, the selection of candidate regimes and their impacts on growth, yield and economics is one of the most critical aspects of building a harvest scheduling model. There were four actions defined in the model (clear-cut, site preparation, natural regeneration and planting), corresponding to activities undertaken to manage the forest: final harvest, site preparation, stand establishment. Each action had associated timing choices, and while three distinct activities would be expected to be carried out by WWFP management (clearcutting, site preparation, planting), natural regeneration was modeled as a decision variable to facilitate the incorporation of regeneration lag into the conceptual model. The clear-cut action determines the timing of the regeneration harvests in stands labeled as commercial forest. Clear-cuts were not permitted in non-forested areas nor were they permitted in management zones such as SMZs, easements, etc. Average logging costs were associated with logging system (cat/cable) and elevation (high/low) yielding a 2x2 matrix of logging costs associated with clear-cut harvests. Site preparation was assumed to occur one year following final harvest. Individual costs were provided for site preparation associated with planting (low elevation) and with natural regeneration (high elevation). Stand establishment was assumed to occur 1 year following site preparation. Planting density was assumed to be 500 trees per acre. Only Douglas-fir was assumed to be planted. Natural regeneration was assumed to occur 3 years after final harvest, with hemlock and Douglas-fir dominated stands assumed to regenerate to hemlock, and with all others assumed to regenerate to mixed conifer. 3.4 Model Outputs and Reports The model has a significant number of outputs defined. Most of these were required to calculate volumes and financial results which drive the optimization process. Several outputs were classified as accounting variables to display model results. The model was formulated to track timber harvest volumes and revenues by log sort and origin (logging system/elevation), harvest and silvicultural treatment acres, costs by treatment and non-silvicultural costs. Outputs were grouped by category as follows: 10

17 Acreage and Activity related Harvest Volumes Standing Inventory Revenues Costs Discounted Revenues Discounted Costs Several reports were developed to allow for quick review of specific results and to assist in model interpretation and diagnosis. Summary reports for each individual tract as well as the entire property were also produced. Specific volume reports for each tract were also provided detailing log sort harvest volumes by species, volumes by logging/elevation combination, and acres harvested, site prepared and planted each year. Table 3 details the assumed prices and costs used in the Big Timber model. WWFP is interested in maximizing discounted net revenue from its timberlands and wanted to incorporate current mill prices into its analysis. However, FORSight staff pointed out that current prices are wellbelow historic trend prices and that long-term management planning should be based on longterm price trends. WWFP management acknowledged this, and suggested a 5-year trend back to normality from the current prices. Table 3 summarizes the prices and costs used in the analysis (real, net of inflation). Table 3. Prices and costs used in the Big Timber model. Current Trend Douglas-fir 12" $/mbf Logging Costs < 2500' CAT 130 $/mbf Douglas-fir 8" $/mbf Logging Costs < 2500' CABLE 180 $/mbf Douglas-fir chip&saw $/mbf Logging Costs > 2500' CAT 90 $/mbf Douglas-fir pulp $/mbf Logging Costs > 2500' CABLE 140 $/mbf western hemlock12" $/mbf western hemlock8" $/mbf Site prep < 2500' 65 $/acre western hemlockchip&saw $/mbf Site prep > 2500' 35 $/acre western hemlockpulp $/mbf Planting 313 $/acre white woods 12" $/mbf white woods 8" $/mbf Forest Excise Tax $/mbf white woods chip&saw $/mbf WA B&O Tax white woods pulp $/mbf Company overhead 20 $/mbf red cedar 12" $/mbf red cedar 8" $/mbf red cedar chip&saw $/mbf red alder 12" $/mbf red alder 8" $/mbf red alder chip&saw $/mbf red alder pulp $/mbf maple 12" $/mbf maple 8" $/mbf maple chip&saw $/mbf hardwood pulp $/mbf 3.5 Objective Function and Constraints To meet WWFP s management objectives, the model objective function maximized discounted revenues from mill delivered volumes minus discounted logging, hauling and silvicultural costs. Property taxes, management fees, lease payments and other fixed costs that depend only on property acres were excluded, since they do not affect forest management decisions. However, an estimate of Washington timber severance taxes (WASEV) and business and occupation 11

18 (WABO) taxes were included in the discounted cash flows. WASEV was estimated using a value of $13.25/mbf harvested and WABO was based on a rate of % of revenue. These costs were included in the calculation of overall net present value Sensitivity Testing and Model Validation Previously, WWFP used the binary search harvest scheduler included in its inventory system to estimate allowable cuts and to help determine a harvest plan. To satisfy their curiosity, management asked FORSight to conduct a run that maximized the harvest volume of conifer logs (excluding cedar) over 50 years, consistent with their previous harvest scheduling analyses. Since the yields generated for the modeling exercise were deemed realistic, management recognized that any changes in the allowable cut must be due to the scheduling algorithms, rather than inherent differences in volume estimates. In their last analysis, the maximum even-flow volume for conifer logs was 46.3 MMBF per year Maximum even-flow conifer logs Maximum even flow of conifer logs volume (excluding red cedar) is 63.4 MMBF annually over the 101 year planning horizon (year 1=2008 is merely to bring the inventory to year-end 2008). This represents a 37.5% increase in volume over previous estimates using binary search. Figure 7. Conifer log harvest volume over 101-year planning horizon (no ending inventory constraint) However, under that scenario, the standing inventory of the forest is essentially liquidated. This is a common artifact of harvest scheduling models with finite planning horizons. Because standing inventory at the end of the planning horizon cannot be used to increase the objective function (harvest volume) there is no value in retaining any excess inventory for years 102 and beyond. 12

19 Figure 8. Changes in merchantable inventory over 101-year planning horizon (no ending inventory constraint). One might be tempted to simply ignore the impact on inventory since the harvest is maintained for many decades. However, an examination of average harvest age shows a decreasing trend (harvesting younger and younger stands) until finally the merchantable inventory is exhausted. While a trend to younger harvest ages is expected, the rapid decrease in the last ten years is clearly indicative of a depleting inventory. Average Harvest Age over Time Figure 9. Average harvest age trend over 101-year planning horizon (no ending inventory constraint). One method of countering the end-of-planning-horizon effect is to is to extend the planning horizon; a common rule of thumb is average rotations. This does not eliminate the endof-planning-horizon effect of depleting inventory, but it does effectively eliminate any potential 13

20 changes to how the existing forest will be managed for the next 2 full-rotations because all currently existing stands will have been harvested at least twice. FORSight implemented a 251-year planning horizon to determine the maximum even flow of conifer logs, and found it to be 59.1 MMBF annually, a decline of 6.8% from the previous estimate. Figure 10. Conifer log harvest volume over 251-year planning horizon (no ending inventory constraint). The drawback to this approach is that with longer-lived species, the number of years required for the planning horizon results in a much larger LP model, and often these models are too large to solve unless planning periods are adjusted to multi-year periods. While the multi-year planning period approach works well enough for strategic planning (i.e., estimating allowable cuts), it makes tactical planning (implementation on the ground) more difficult, particularly when green- planning up periods are not equal to the planning period width. WWFP preferred to continue using annual periods. An alternative to extending the planning horizon is to implement a perpetual timber harvest constrain (PTHC). The PTHC originated in the U.S. Forest Service when non-declining yield was mandated in their planning models. The constraint simply requires that the ending inventory be no less than the average inventory over the entire planning horizon, under the assumption that an even-flow of timber should be available in perpetuity so long as the average is maintained. After implementing the PTHC in the BigTimber model, the maximum even flow volume of logs was found to be 59.7 MMBF annually, marginally higher thans the 251-year planning horizon result. 14

21 Figure 11. Conifer log harvest volume over 101-year planning horizon (with PTHC). The PTHC is a good compromise in this situation, because it achieves an allowable harvest that is comparable to the result of the much longer planning horizon and the inventory at the end of the planning horizon is not only unimpaired, but actually improves on the initial conditions. Figure 12. Changes in merchantable inventory over 101-year planning horizon (with PTHC). Discount rate effects Next, FORSight first ran a base scenario that maximized NPV subject to no constraints. Such scenarios facilitate the understanding of results by providing a baseline from which to determine the costs of additional constraints. As part of our standard modeling procedure, a number of alternative model runs were completed varying one or more of the initial assumptions. Solutions were generated at higher and lower discount rates to test the robustness of the model. For example, at lower discount rates, one would expect to carry higher levels of inventory and lower rates of harvest due to the lower hurdle rate; conversely, at higher discount rates, one expects lower levels of inventory and higher rates of harvest early on. By establishing a base run, it is possible to estimate the costs of additional constraints or changes in operability limits on harvests or silvicultural activities. 15

22 Moreover, it is easier to determine if model behavior is normal in the absence of constraints; the addition of multiple constraints can result in atypical behaviors that defy conventional wisdom and risk the loss of buy-in on the model results. Table year summary of results for discount rate effects sensitivity testing. Unconstrained Unconstrained Unconstrained 4.5% discount rate 5.5% discount rate 6.5% discount rate 10 Year Results: Harvest Volumes (MMBF) Sens Run 1 Sens Run 2 Sens Run 3 Df 12" Df 8" Df 5" Df Pulp Wh 12" Wh 8" Wh 5" Wh Pulp Ww 12" Ww 8" Ww 5" Ww Pulp Rc 12" Rc 8" Rc 5" Ra 12" Ra 8" Ra 5" Ma 12" Ma 8" Ma 5" Hw Pulp Average Merchantable Inventory (MMBF) Harvest Revenues 12"+ $ 293,016,922 $ 289,617,200 $ 287,606,635 8"+ $ 274,825,058 $ 287,938,591 $ 299,366,807 5"+ $ 27,854,684 $ 31,193,815 $ 33,770,287 Pulp $ 33,414,640 $ 35,029,655 $ 36,080,975 Harvest statistics Avg clearcut age (years) Avg acres clearcut (ac/yr) 3,306 3,537 3,726 Avg annual logging cost $ 17,196,338 $ 17,710,530 $ 18,084,022 Avg logging cost ($/ac) $ 5,201 $ 5,007 $ 4,854 Avg logging cost ($/mbf) $ $ $ Avg annual hauling cost $ 12,202,202 $ 12,478,728 $ 12,732,346 Avg hauling cost ($/mbf) $ $ $ Annual costs Avg WA B&O tax $ 3,020 $ 3,090 $ 3,153 Avg WA Forest Excise tax $ 1,858,936 $ 1,902,778 $ 1,941,705 Avg site preparation cost ($) $ 171,778 $ 185,235 $ 201,172 Avg planting cost ($) $ 685,939 $ 743,485 $ 796,964 Contribution to Net Present Value 10-yr NPV $ 233,794,912 $ 227,989,107 $ 221,231,035 As expected, the 10-year and 50-year results show higher rates of harvest, and lower standing inventories associated with higher discount rates. The long-run sustained yield average (MMBF/yr) over the planning horizon at the 4.5%, 5.5% and 6.5% discount rates was 48.63, and 41.41, respectively. The effect of discounting is readily apparent in the proportion of the total net present value that is achieved in the first 10-years as discount rates increase. For example, only 64% of the total 100-year NPV is achieved by the end of the 10 th year when the discount rate is 4.5%; at a discount rate of 6.5%, more than 77% of the total 100-year NPV is achieved by the end of the 10 th year. 16

23 Table year summary of results for discount rate effects sensitivity testing. 50 Year Results: Harvest Volumes (MMBF) Sens Run 1 Sens Run 2 Sens Run 3 Df 12" Df 8" Df 5" Df Pulp Wh 12" Wh 8" Wh 5" Wh Pulp Ww 12" Ww 8" Ww 5" Ww Pulp Rc 12" Rc 8" Rc 5" Ra 12" Ra 8" Ra 5" Ma 12" Ma 8" Ma 5" Hw Pulp Average Merchantable Inventory (MMBF) Harvest Revenues 12"+ $ 473,573,467 $ 415,626,848 $ 374,690,566 8"+ $ 752,421,509 $ 758,872,022 $ 720,045,863 5"+ $ 129,917,931 $ 171,387,689 $ 194,647,888 Pulp $ 90,977,164 $ 98,015,268 $ 97,879,235 Harvest statistics Avg clearcut age (years) Avg acres clearcut (ac/yr) 1,690 1,906 1,992 Avg annual logging cost $ 8,025,711 $ 7,923,584 $ 7,580,206 Avg logging cost ($/ac) $ 4,748 $ 4,158 $ 3,806 Avg logging cost ($/mbf) $ $ $ Avg annual hauling cost $ 5,514,983 $ 5,511,784 $ 5,278,243 Avg hauling cost ($/mbf) $ $ $ Annual costs Avg WA B&O tax $ 1,389 $ 1,386 $ 1,332 Avg WA Forest Excise tax $ 874,763 $ 868,272 $ 832,362 Avg site preparation cost ($) $ 91,034 $ 109,932 $ 114,067 Avg planting cost ($) $ 365,188 $ 430,992 $ 469,033 Contribution to Net Present Value 50-yr NPV $ 341,212,663 $ 309,576,584 $ 282,139, yr NPV $ 364,054,606 $ 318,885,266 $ 286,846,549 per-acre basis $ 4,764 $ 4,173 $ 3,754 4 Development of the preferred alternative As requested by WWFP management, a real discount rate of 5.5% was used in all subsequent model runs. Using the second discount rate sensitivity run as a base model provided a means for establishing the costs of various constraints that were necessary to develop a preferred management alternative. As the main provider of timber to WWFP s sawmill, the Big Timber Tree Farm needs to provide a steady supply of logs. The base model was not constrained in this manner and harvests occurred at the economic optimum time for every stand. The result was a harvest flow profile that fluctuated wildly each period: there is no harvest scheduled at all for the period followed by a jump to almost 18,000 acres in 2012 and over 7,000 acres in Over one-third of the total forest area and over one-half the merchantable volume is harvested in just two years; clearly this harvest schedule is not operationally feasible. 17

24 Figure 13. Clearcut acres in Maximize NPV base run (no flow constraints, with PTHC). Figure 14. Conifer log harvest volume in Maximize NPV base run (no flow constraints, with PTHC). To meet mill demand, the Big Timber Tree Farm needs to produce at least 40 MMBF of conifer logs annually. Since the maximum even-flow volume of conifer logs was determined to be almost 60 MMBF annually, WWFP managers were interested in a solution that guaranteed at least 55 MMBF of conifer logs annually a level that was considerably higher than previous estimates but appeared to be conservative relative to the analysis thus far. FORSight implemented the mill demand as a floor constraint on the annual conifer log harvest and reran the model; these results were deemed Alternative 1 (Alt1). 18

25 Figure 15. Clearcut acres in Maximize NPV Alternative 1 run. Figure 16. Conifer log harvest volume in Maximize NPV Alternative 1 run. While the floor constraint provided the minimum necessary volume in all planning periods, the volume spike in 2012 is still far too high to be operationally feasible. After consulting with WWFP staff, FORSight implemented a sequential flow constraint on total harvest limiting periodic changes to no more than ± 5% in addition to the floor constraint on conifer logs. These results were deemed Alternative 2 (Alt2). 19

26 Figure 17. Conifer log harvest volume in Maximize NPV Alternative 2 run. WWFP considered Alternative 2 sufficient for their needs, but FORSight encouraged them to examine the solution to Alternative 2 more deeply, to determine if it truly met all their needs. Upon closer examination, various members of the WWFP management team expressed some concerns about the solution. Figure 18. Harvest acres by tract in Maximize NPV Alternative 2 run. WWFP s woodlands manager expressed a concern that harvests should be relatively proportional across the four tracts (see Figure 18) to geographically disperse harvests and to minimize variations in hauling costs. FORSight advised them that the model already considered average hauling cost in the determination of net present value, and so it was unlikely that a constraint to balance the harvests in proportion to the area of the tracts would improve the answer in terms of hauling costs. However, in order to address the spatial dispersal issue, FORSight agreed to implement a constraint to better balance volume flows from the tracts. In general, WWFP s mill manager thought the product mix was acceptable coming out of Alternative 2, but the volumes in years 2023, 2034 and 2037 seemed to produce too much 12+ material and insufficient 5+ material (see Figure 19). He asked if it were possible to constrain the product mix within ± 2% of their historic averages of 52:45:3 for 12+, 8+ and 5+, respectively. 20

27 FORSight advised that such constraints were possible, but could not suggest whether the cost of these constraints would be too high. Figure 19. Softwood product mix in Maximize NPV Alternative 2 run. Finally, WWFP procurement foresters were concerned that a high proportion of timber from some years was coming from high elevation stands (see Figure 20), and they believed that no more than 60% of the harvest volume in any year should come from high elevation stands. Given that only a few years exhibited a propensity for high elevation stands, FORSight advised that this constraint be included in the analysis because its impact would likely be low. Figure 20. Harvest acres by elevation in Maximize NPV Alternative 2 run. For Alternative 3, FORSight implemented a constraint on harvest flows from each tract to match their relative proportion of the total forest. The Whitman tract comprised 18% of the productive forest land and therefore harvests from Whitman should comprise no less than 16% and no more than 20% of the total harvest volume. Similar constraints (± 5%) were implemented for the other three tracts. 21

28 Figure 21. Harvest volume by tract in Maximize NPV Alternative 3 run. The constraints on volume flows from each tract were successful, as shown in Figure 21. However, due to site quality differences among the tracts the volume harvested per acre can vary a great deal, resulting in more variation in harvest acres year to year (Figure 22). Figure 22. Harvest acres by tract in Maximize NPV Alternative 3 run. The cost of these constraints, relative to Alternative 2, was $3.7 million in net present value, or roughly $49/acre. For Alternative 4, FORSight implemented constraints on product mix that would maintain product mixes within narrow bands about the historic averages provided by WWFP staff. However, these constraints were added to those from Alternative 2 so that their costs could be compared directly with those from Alternative 3. Results indicate that the product mix can be maintained within the ranges desired by WWFP mill managers (see Figure 23) but its cost is two-fold. First, the cost in terms of net present value is $6.3 million (or $83/acre), almost double the cost of the Alternative 3 constraints. Second, the constraints seem to work at cross-purposes to Alternative 3, with significant variations in the proportion of harvest volume coming from each tract (Figure 24). 22

29 Figure 23. Softwood product mix in Maximize NPV Alternative 4 run. Figure 24. Harvest volume by tract in Maximize NPV Alternative 4 run. After considering the results of Alternatives 3 and 4, WWFP management instructed FORSight to implement a new run based on Alternative 3 but with the additional constraints on highelevation harvests discussed earlier. This run was deemed Alternative 5. Figure 25 and Figure 26 provide evidence that the constraints functioned as expected: the proportions of harvest volume from each tract are consistent in all years and the volume from high elevation harvests never exceeds 60% of the total volume in a given year. 23

30 Figure 25. Harvest acres by tract, in Maximize NPV Alternative 5 run. Figure 26. Percentage of volume by elevation in Maximize NPV Alternative 5 run. As expected, the addition of the high-elevation constraint did not have a significant impact. In fact, alternative harvests low-elevation harvests were available to make up for virtually all the reductions in high-elevation harvests in the years affected; the only detectable differences between this alternative and Alternative 3 was $2 in harvest revenue (see Table 7). Moreover, the constraints on the spatial distribution of harvest volume had collateral benefits in terms of product mix. Compare Figure 27 to Figure 19 and it becomes clear that the product mix is more balanced in Alternative 5 (and Alternative 3) than in Alternative 2. 24

31 Figure 27. Harvest acres by logging system and elevation, in Maximize NPV Alternative 5 run. 5 Discussion All of the model runs were feasible and produced optimal solutions. Table 6 and Table 7 summarize the results of the various runs over 10 and 50 years respectively. Table year summary of results for base run and Alternatives 1-5. Unconstrained Base + Alt1 + Alt2 + Alt2 + Alt % discount rate 55MMBF floor SEQ5%(logs) tract-proportional ±2% historical high elevation harvest product mix logs < 60% of total 10 Year Results: Harvest Volumes (MMBF) Base Alt1 Alt2 Alt3 Alt4 Alt5 Df 12" Df 8" Df 5" Df Pulp Wh 12" Wh 8" Wh 5" Wh Pulp Ww 12" Ww 8" Ww 5" Ww Pulp Rc 12" Rc 8" Rc 5" Ra 12" Ra 8" Ra 5" Ma 12" Ma 8" Ma 5" Hw Pulp Average Merchantable Inventory Harvest Revenues 12"+ $ 293,016,922 $ 289,617,200 $ 205,821,644 $ 196,429,560 $ 204,776,615 $ 196,429,560 8"+ $ 274,825,058 $ 287,938,591 $ 166,082,086 $ 165,061,434 $ 158,651,900 $ 165,061,434 5"+ $ 27,854,684 $ 31,193,815 $ 11,763,782 $ 13,023,521 $ 10,899,147 $ 13,023,521 Pulp $ 33,414,640 $ 35,029,655 $ 18,243,752 $ 18,283,939 $ 17,028,885 $ 18,283,939 Harvest statistics Avg clearcut age (years) Avg acres clearcut (ac/yr) 3,306 3,537 2,081 2,046 1,965 2,046 Avg annual logging cost $ 17,196,338 $ 17,710,530 $ 10,889,092 $ 10,439,558 $ 10,398,813 $ 10,439,558 Avg logging cost ($/ac) $ 5,201 $ 5,007 $ 5,233 $ 5,101 $ 5,293 $ 5,101 Avg logging cost ($/mbf) $ $ $ $ $ $ Avg annual hauling cost $ 12,202,202 $ 12,478,728 $ 7,895,457 $ 7,515,103 $ 7,672,427 $ 7,515,103 Avg hauling cost ($/mbf) $ $ $ $ $ $ Annual costs Avg WA B&O tax $ 3,020 $ 3,090 $ 1,929 $ 1,885 $ 1,879 $ 1,885 Avg WA Forest Excise tax $ 1,858,936 $ 1,902,778 $ 1,207,145 $ 1,177,565 $ 1,171,006 $ 1,177,565 Avg site preparation cost ($) $ 171,778 $ 185,235 $ 114,785 $ 113,106 $ 108,958 $ 113,106 Avg planting cost ($) $ 685,939 $ 743,485 $ 441,447 $ 432,937 $ 424,744 $ 432,937 Contribution to Net Present Value 10-yr NPV $ 233,794,912 $ 227,989,107 $ 128,964,356 $ 127,557,539 $ 127,454,216 $ 127,557,539 25

32 Table year summary of results for base run and Alternatives Year Results: Harvest Volumes (MMBF) Base Alt1 Alt2 Alt3 Alt4 Alt5 Df 12" Df 8" Df 5" Df Pulp Wh 12" Wh 8" Wh 5" Wh Pulp Ww 12" Ww 8" Ww 5" Ww Pulp Rc 12" Rc 8" Rc 5" Ra 12" Ra 8" Ra 5" Ma 12" Ma 8" Ma 5" Hw Pulp Average Merchantable Inventory Harvest Revenues 12"+ $ 473,573,467 $ 415,626,848 $ 703,915,305 $ 700,857,170 $ 695,213,890 $ 700,857,169 8"+ $ 752,421,509 $ 758,872,022 $ 616,415,735 $ 605,870,801 $ 595,281,071 $ 605,870,800 5"+ $ 129,917,931 $ 171,387,689 $ 49,441,021 $ 49,333,621 $ 58,959,323 $ 49,333,621 Pulp $ 90,977,164 $ 98,015,268 $ 74,927,159 $ 75,038,219 $ 74,610,659 $ 75,038,219 Harvest statistics Avg clearcut age (years) Avg acres clearcut (ac/yr) 1,690 1,906 1,198 1,198 1,210 1,198 Avg annual logging cost $ 8,025,711 $ 7,923,584 $ 8,289,691 $ 8,213,673 $ 8,221,085 $ 8,213,673 Avg logging cost ($/ac) $ 4,748 $ 4,158 $ 6,921 $ 6,858 $ 6,793 $ 6,858 Avg logging cost ($/mbf) $ $ $ $ $ $ Avg annual hauling cost $ 5,514,983 $ 5,511,784 $ 5,683,019 $ 5,640,787 $ 5,604,841 $ 5,640,787 Avg hauling cost ($/mbf) $ $ $ $ $ $ Annual costs Avg WA B&O tax $ 1,389 $ 1,386 $ 1,387 $ 1,374 $ 1,367 $ 1,374 Avg WA Forest Excise tax $ 874,763 $ 868,272 $ 896,737 $ 889,536 $ 883,092 $ 889,536 Avg site preparation cost ($) $ 91,034 $ 109,932 $ 68,800 $ 68,703 $ 69,328 $ 68,703 Avg planting cost ($) $ 365,188 $ 430,992 $ 281,020 $ 280,374 $ 281,067 $ 280,374 Contribution to Net Present Value 50-yr NPV $ 341,212,663 $ 309,576,584 $ 218,373,238 $ 215,293,018 $ 212,862,869 $ 215,293, yr NPV $ 364,060,044 $ 324,653,759 $ 263,850,323 $ 260,591,743 $ 257,535,003 $ 260,591,743 per-acre basis $ 4,764 $ 4,249 $ 3,453 $ 3,410 $ 3,370 $ 3,410 The very high harvests in the first few periods are indicative of significant excess inventory arising from WWFP s admittedly conservative management in the past. To maximize net present value, the base model solution includes rapid harvesting of these high-valued, high volume stands right away, which clearly cannot be implemented (see Figure 28). Conifer Log Harvest by Alternative Conifer Volume (board feet) Millions Year Alt1 Alt2 Alt3 Alt4 Alt5 Base Figure 28. Variability in conifer log volume harvested over 50 years. 26

33 The constrained runs all addressed this variability directly and as a result, the constraints were binding in many periods, yielding significant reductions in NPV (see Table 6). For example, imposing the floor constraint of 55 MMBF/yr on conifer log volume in Alt1 significantly reduced the volume spike in but did not completely eliminate it. Still that constraint alone reduced net present value by over $500/acre. Figure 29. Displacement of harvest volume via sequential flow constraints. In Figure 29, we have zoomed in on the conifer log volume graph to illustrate how the ± 5% sequential flow constraints were able to distribute the harvest volume over approximately 20 years. The volume under the spike (light blue) is reallocated to some earlier periods (darker blue), but most of the volume must be harvested well after the spike, indicating a deferred harvest. While the the addition of the sequential flow constraints on conifer log volume eliminated the spike, they also contributed to a further reduction in net present value of about $800/ac or more. The stands being deferred are mostly older, high volume but slow-growing stands, and even if there is no volume loss to mortality, the effects of discounting result in a significant loss in net present value. If WWFP were able to log this excess inventory at a faster rate (through internal consumption or external log sales), there could be significant returns to the firm without impairing long-term wood supplies. When there are no flow constraints on harvest, the model solution exhibits an immediate reduction in inventory through harvesting (Figure 30) and once the excess is liquidated, total inventory remains well below the initial level thereafter. In contrast, the constrained alternatives retain an essentially constant inventory over time. Alternative 1 has a different trajectory than the other alternatives at first but over time it tends toward the others. Clearly the floor constraint is driving the maintenance of inventory since it is common to all alternatives. Alternative 4 must retain an even higher level of inventory to provide each year sufficient logs of each size class to maintain the product mix within the specified bounds. After considering all of the alternative model runs, WWFP management determined that Alternative 5 best met their management objectives and they deemed it their preferred alternative. 27

34 Changes in Total Inventory by Alternative Millions Board Feet Year Alt1 Alt2 Alt3 Alt4 Alt5 Base Figure 30. Variability in total inventory over 50 years. 6 Conclusions Overall, the base model performed as expected (PTHC constraints only). Older stands, high volume stands that are growing at the hurdle rate of 5.5% annually or less are immediately harvested, but otherwise stands are harvested at their economic rotation. However, this harvest schedule produces untenable fluctuations in annual harvest from year to year. Placing a constraint on the annual conifer log harvest at 55 MMBF provides much of the stability in log flow desired by WWFP management (Alternative 1). However, additional flow constraints (Alternatives 2-5) on harvest were necessary to smooth out the liquidation harvest of excess inventory, allowing WWFP loggers and markets to adjust to the changing harvest levels. Tight constraints on product mix (Alternative 4) proved to be too costly in terms on net present value as well as working at cross purposes to WWFP s desire to geographically disperse harvests across the tree farm. The constraints to proportionally distribute the harvest across the four tracts (Alternative 3 & 5) had a collateral benefit to product mix; although the product mix variations were higher than in Alternative 4, they were still an improvement over Alternative 2. WWFP staff indicated that because of limitations associated with high elevation logging, no more than 60% of the annual harvest could practically come from high elevation stands. While the schedule of stands differed in Alternatives 3 and 5, the impact of this constraint was negligible. However, this constraint may be more costly when spatial restrictions on harvest are considered, and may be further exaggerated by access issues on the steep ground at higher elevations. 28

35 7 Appendix A Woodstock Runtime Graphs, Preferred Alternative 29

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