69- 20,889 MARTIN, Allen J effrey , 1943EVALUATING TIMBER STAND IMPROVE­ MENT OPPORTUNITIES IN NORTHERN LOWER MICHIGAN USING THE DECISIONTREE APPROACH. Michigan State U n iversity, P h.D ., 1969 A griculture, fo restr y and w ild life University Microfilms, Inc., Ann Arbor, Michigan EVALUATING TIMBER STAND IMPROVEMENT OPPORTUNITIES IN NORTHERN LOWER MICHIGAN USING THE DECISION-TREE APPROACH By A. Jeff Martin A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Forestry 1969 ABSTRACT EVALUATING TIMBER STAND IMPROVEMENT OPPORTUNITIES IN NORTHERN LOWER MICHIGAN USING THE DECISION-TREE APPROACH By A. Jeff Martin Data were collected from 25 small privately-owned woodlands within a five-county area of northern Lower Michigan which had received a timber stand improvement treatment in 1962 and remuneration for part of the esti­ mated cost through the Agricultural Conservation Program, The stands were second-growth northern hardwoods. In the analysis, each stand was reconstructed as it appeared before and after the timber stand improvement treatment. This afforded a means for simulating the d ec i­ sion-making sequence faced b y each individual owner in 1962. The decision-tree approach was employed for purposes of evaluating the formulated model, describing a total of 30 alternatives available to each ownership. Physical growth projections were made under the four major assumptions A. J. Martin of: 1) No TSI in 1962, and no future thinnings, in 1962, but future thinnings would be performed, in 1962, but no future thinnings, future thinnings. costs, and 2) No TSI 3) TSI 4) TSI in 1962, with Additional assumptions concerning prices, cull defect, mortality, and quality change were then applied to the decision model. To evaluate the model, internal rates of return were calculated for each opportunity, and used as a measure of effectiveness for ascertaining the relative desirability of the various options. IRR values ranged from less than 1 percent to over 20 percent, "best" five alternatives. averaging 8 1/2 percent for the The highest returns were associ­ ated with timber stand improvement subsidized b y ACP p a y ­ ments, followed by a regular schedule of periodic thinnings, terminating in the marketing of cut products from the w o o d ­ land. the original Subsequent to the initial evaluation, model was subjected to sensitivity analysis, providing some insight as to how incremental changes in certain parameter values influence the optimal sequence of alternative courses of action. Of the various factors tested, the internal rate of return appeared most sensitive to changes in the annual cost assumption. ACKNOWLEDGMENTS The project was supported b y federal funds from the Mclntire-Stennis Law (P.L. 87 - 788). In addition, the Michigan Department of Natural Resources provided valuable suggestions and assistance in both the planning and imple­ mentation of the investigation. I sincerely appreciated the cooperation of Ronald Auble, Daniel Bonner, and Barrie Lightfoot of the Forestry Division, Michigan Department of Natural Resources in helping to locate ownerships and neces­ sary r e c o r d s . I am deeply indebted to Dr. Victor J. Rudolph, my major professor, for the opportunity of undertaking the study and for the enjoyable and stimulating research envi­ ronment. I also gratefully acknowledge the helpful sugges­ tions offered b y other members of* the guidance committee; namely, Dr Bruce T. Allen, Dr. R. Keith Hudson, Dr. Robert S. Manthy. Janice, Above all, for her understanding, e n c o u r ag em en t . and I am grateful to my wife patience, and constant TABLE OF CONTENTS Page ACKNOY7LEDGEMENTS............. ii LIST OF T A B L E S ......................................... iv LIST OF F I G U R E S ........................................ viii LIST OF A P P E N D I C E S ............. ix Chapter I. II. III. IV. V. VI. VII. VIII. IX. INTRODUCTION. . 1 THE STUDY A R E A ............. SAMPLING PROCEDURES 5 ......................... 18 FIELD P R O C E D U R E S .............................. 24 COMPILATION OF FIELD D A T A .......... . 30 GROWTH PREDICTION AND VOLUME PROJECTION . . THE DECISION-TREE MODEL AND UNDERLYING A S S U M P T I O N S ................................ EVALUATION OF THE DECISION-TREE MODEL . . . 43 60 113 CONCLUSIONS AND R E C O M M E N D A T I O N S .............. 143 LITERATURE CITED. . ................................... 149 A P P E N D I C E S ................................................ 159 iii LIST OF TABLES Table 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. Page Total and forest area in the five counties, 1 9 6 6 .................................... 12 Hardwood growing stock volume on commercial forest land, by counties and species groups, 1 9 6 6 ................ 14 Population and original sample distribution by individual stratum ....................... 20 Population and final sample distribution by individual stratum. . . . . ................ 22 Population and sample distribution by stratum size and administrative area. . . . . . . . 23 Site index for all referrals, using average heights and average ages for all species, based on Curtis's c u r v e s ............. 32 Summary of volume data for Referral No. 2G01, 1 9 6 6 ................................. 34 Volume summary for each of the 2 5 referrals (ownerships) in the study a r e a .......... 35 Summary of diameter, height, age, and basal area data for the 2 5 ownerships, 1966 . . . 37 Data for material removed in the TSI operation during 1962, for each ownership . 39 iv List of T a b l e s . — C o n t . Table 11. Page Additional referral measurements and c h a r a c t e r i s t i c s ................ 40 12. Additional referral characteristics 13. Species composition of each referral by cubic-foot volume per acre, 1 9 6 6 ........... 42 Basal area growth calculations for Referral 2G01 using the before treatment growth r a t e .................................... 46 Basal area growth calculations for Referral 2G01 using the after treatment growth rate. 47 Annual basal area growth for each referral wi th and without T S I ......................... 51 Basal area data for stand conditions before TSI, removed in TSI, after TSI, and in 1966 for each o w n e r s h i p ..................... 52 Computation of volume removed by TSI in 1962 on Referral No. 2g 0 1 ......................... 56 Volume by species and size class for Referral No. 2G01 in 1966— per acre b a s i s ........... 57 Volume by species and size class for Referral No. 2G01 in 1962— per acre b a s i s ........... 58 Log grade yield from trees of given butt-log tree grades for sugar maple and "other h a r d w o o d s " .................. 83 Computational steps in volume projection and calculation of final yield by species and log grade, for Referral No. 2G01, w i t h no TSI and no future thinnings, per acre basis 88 14. 15. 16. 17. 18. 19. 20. 21. 22. v . . . . . 41 List of T a b les.— C o n t . Page Table Computational steps in volume projection and calculation of final yield by species and log grade, for Referral No. 2G01, w i t h TSI in 1962, but no future thinnings were per­ formed, per-acre b a s i s ....................... 89 Computational steps in volume projection and calculation of final yield by species and log grade, for Referral No. 2G01, w i t h no TSI in 1962, however, future thinnings were performed, per acre basis. . . . . . . 90 Computational steps in volume projection and calculation of final yield by species and log grade, for Referral No. 2G01, w i t h TSI in 1962, and future thinnings, per acre b a s i s ....................................... .. 92 Volume per acre at rotation age for each of the four major alternatives for Referral No. 2g 01, by species and log grade after cull and quality adjustments were made. . . 95 Production costs on a per-unit basis for an owner choosing to market sawlogs and cordwood at the mill s i t e ........... .. . . . . 97 28. Schedule of hauling and unloading costs 98 29. Prices for sawlogs delivered at the mill site, and for sawtimber stumpage, per MBF . 109 Prices for pulpwood delivered at the mill site, and for pulpwood stumpage, per cord . 110 Internal rates of return for each referral for the 30 alternatives, under "medium" or average conditions for all parameters . . . 116 23. 24. 25. 26. 27. 30. 31. vi . . . List of Tables.— C o n t . Page Table 32 . 33. 34. 35. Number of cells by desirability rank for each alternative in the "best" set. . . . „ 119 The summarized "best" set for the most favorable a l t e r n a t i v e s ......... .. 123 Regression coefficients and simple correla­ tion coefficients for the 11-term regres­ sion on average IRR v a l u e s ................ .. 126 Results of the sensitivity analysis for Referral No. 2G01, values are internal rates of r e t u r n ......................... 132 . . Changes in the optimal sequence of investment opportunities as a result of the sensi­ tivity analysis of selling price, Referral No. 2 G 0 1 ......................... .. 133 Changes in the optimal sequence of investment opportunities as a result of the sensi­ tivity analysis of annual cost, Referral No. 2 G 0 1 ....................................... 134 Changes in the optimal sequence of investment opportunities as a result of the sensi­ tivity analysis of periodic costs, Referral No. 2 G 0 1 .............. ...................... .. 135 39. Stocking levels by administrative area. 139 40. Basal area growth rate with and without TSI in the two areas, 1962-1966 ................ 36. 37. 38. 41. . . . Internal rate of return comparisons b y area 141 . 141 LIST OF FIGURES Page Figure 1. MICHIGAN'S LOWER PENINSULA, SHOWING THE STUDY AREA SUBDIVIDED INTO AREA I AND AREA II. . . . .............................. 6 PRIMARY H IG HWAY NETWORK FOR THE FIVE-COUNTY STUDY AREA, SHOWING U.S. AND STATE ROUTES. 9 THE POINT-SAMPLE DISTRIBUTION A N D ORIENTA­ TION FOR A N ORTH-SOUTH D E S I G N .............. 26 BASIC DECISION TREE FOR A WOODLAND OWNER FACED W I T H A DECISION ON TIMBER STAND IMPROVEMENT IN 1 9 6 2 ......................... 63 DECISION TREE SHOWING ADDITIONAL A L T E R N A ­ TIVES FACING A TYPICAL OWNER IN 1962 . . . 68 6. TH E DECISION T R E E IN ITS FINAL F O R M ......... 74 7. GR OW T H FOR A TYPICAL REFERRAL FROM 1962 UNTIL THE END OF THE ROTATION 70 YEARS H E N C E .................................. . . . 79 2. 3. 4. 5. viii LIST OF APPENDICES Appendix Page «>**. I. Common and Scientific Names of Tree Species Encountered in the S t u d y ............ 160 II. Distance from Referral to Mill Site by Road Surface Type for Each of the 2 5 R e f e r r a l s ..................................... 162 III. Internal Rates of Return Resulting from the Sensitivity Analysis, for the Six Selected R e f e r r a l s ............................ 165 IV. The Modified Version of Clark Row's Computer Program (1963) Which Was Used in the Present S t u d y .......................... 208 ix CHAPTER I INTRODUCTION The small woodland segment of Michigan's forest land represents a substantial source of potential timber supply. Of the total commercial forest land in M i c h i g a n , 66 percent is in some form of private ownership — by full- and part-time farmers. 20 percent is owned The farm-woodland category alone contributed timber products valued at $16.3 million in 1957 — 1960). 22 percent of the total from all forests (James, The amount from all "small" private ownerships would be significantly greater. Generally, when a woodland owner undertakes forestry practices, he is interested in making a net return from his forest lands. He is usually constrained b y a limited budget for investment purposes, and the best procedures for ma xi ­ mizing returns are not specifically known to him. Reliable data concerning the possible fluctuations in net returns from' various forest management activities are relatively scarce in all regions, Lake States. and are practically non-existent in the Such data are needed to determine where forestry 2 can be practiced most profitably# and the kinds and inten­ sities of management that can be justified economically. But aside from justifying small woodland research on the basis of improving the owner's welfare# come-generating potential# and/or his in­ such efforts should strive to achieve more abundant production of consumer goods from small ownerships# products which are more economical and competitive than so-called woo d substitutes (Schallau# 1964). Schallau proposes the implementation of small-tract produc­ tion and marketing research# searching for strategic prob­ lems to investigate rather than attempting to study all phases of growing and selling timber. The present investigation was oriented towards the production phase. It sought to compile needed information on net returns from actual forest stands which have had v a r y ­ ing degrees of cultural practices applied to them in keeping with the goals of ownership. The major objective of this study was to establish management priorities and guidelines ment practices. for timber stand improve­ Such a set of recommendations would be d e ­ signed for the forest landowner and/or the consulting for­ ester, to use in the management of small northern hardwood stands in northern Lower Michigan. 3 In attaining this goal/ were fulfilled in the process; certain secondary objectives 1) establishing a working model for decision-making b y the small forest landowner# con­ cerning the implementation of various cultural activities; 2) determining the effects of cultural treatments in northern hardwood stands on developmental patterns and financial pros­ pects; and 3) ascertaining the relative influence of indi­ vidual ownership characteristics on the expected net re­ turns . To accomplish the stated objective# the following steps were required; 1. Select an area for concentrated study. 2. Determine which woodlands should be sampled in the finite population of private landownerships and what sampling intensity should be applied to each. 3. Undertake field measurements to determine the effects of past treatments and to provide a basis projections 4. for stand into the future. Compile the collected data in a form suitable for growth projection and subsequent analysis. 4 5. Establish a growth projection procedure for pre­ dicting future volumes under various intensities of management. 6. Formulate a model for decision-making by d ev elop­ ing a set of possible alternatives facing a given woodland owner and to predict future volume growth* as modified by various assumptions regarding mor ta l­ ity* cull defect* quality* etc., for each o ppor­ tunity . 7. Add various economic assumptions concerning costs and prices to the decision-model. 8. Evaluate the various alternatives for each owner­ ship and establish a list of priorities based on a commonly accepted measure of effectiveness. 9. Based on results of the evaluation* formulate a series of recommendations w h i c h would guide a forest landowner in making future management decisions. 10. Identify those factors that are most critical in making such an economic evaluation, by judging their influence on the measure of effectiveness. CHAPTER II THE STUDY AREA General Description The area selected for study included Benzie, Grand Traverse, Leelanau, Manistee, and W ex fo rd counties in the northern portion of Michigan's Lower Peninsula (Figure 1). The Michigan Department of Natural Resources sub­ divides the State into various Regions, Districts, for administrative purposes, and Areas and the entire study area is within Region II and District 6. Benzie, Leelanau, and Manistee Counties comprise the Betsie River Area and will be referred to as Ar ea I in this study, and Wexford Counties and Grand Traverse form the Fife Lake Area, which will be designated as Ar ea II in this project (Figure 1). The five-county b l ock contains 1,440,000 acres of land (4 percent of the state's total), (8 percent of the state's total) and 60,160 acres of water (Myers and Van Meer, 1966) . The past h is to ry of the study area is quite similar to that witnessed throughout the northern half of Michigan's 6 ■illtn?r |M M t M M M "P I l* M •• u u m Im * "T " «*i S #* « FIGURE 1 MICHIGAN'S LOWER PENINSULA, SHOWING THE STUDY AREA (CROSS-HATCHED) S U B ­ DIVIDED INTO A RE A I AND AREA II. 7 Lower Peninsula# with most of the region owing its "develop­ ment" to the lumbering era. Portions of two state forests and one national forest are located in the study area. Fife Lake State Forest extends into Benzie# Manistee# The and Wexford Counties# and the Betsie River Forest is located in Leelanau and Manistee Counties. The Manistee National Forest extends into the southern portion of the s t ud y area# comprising a large share of Manistee and Wexford Counties. The five-county area# Northern Lower Peninsula# as with many sections of the shows extreme contrasts in home dwellings and general economic prosperity within the span of a few miles. A typical shoreline abounds with recreation centers and large# expensive dwellings (generally in ab sen­ tee o w n e r s h i p ) # whereas evident prosperity decreases rapidly upon leaving the vicinity of the lake. The area b e t w e e n lakes is largely devoted to farming and fruit orchards, in the case of many orchard ownerships, and# except the properties are rapidly deteriorating into "rural slums." Buildings in d i s ­ repair# and croplands reverting to wildlands add testimony to a decline in "small-parcel" farming. The 1960 population of 88,153 for the five counties comprised 1 percent of the state's total# with ne ar l y half 8 (42 percent) of Cadillac (18#432) of the area's population residing in the cities (10#112)# Manistee (Myers and Van Meer, (8#324) and Traverse C i t y 1966). Four of the five counties ed adjacent to Lake Michigan and# in the study area are locat­ therefore# experience a modified marine climate most of the year. W ex fo r d County# approximately 20 to 25 miles from the Lake's shore has a climate that alternates between the continental and semima­ rine# with changing meterological conditions (USDA# 1941). Three soil associations encompass most of the five counties: 1) Montcalm#^Kalkaska# Emmet; ford, Emmet; and# 2) Montalm# W e x ­ 3) Rubicon# Roselawn# Grayling side, et al_. # 1968) . (White­ The soils on the sampled ownerships ranged from medium to very high in potential productivity for northern hardwoods# based on their woodland suitability classification (USDA# 1966) . The region has a well-developed transportation sys­ tem# with a network of hard-surfaced roads providing excel­ lent access to most areas (Figure 2). In fact# the study area has a higher concentration of main trunklines than any similar-sized area in northern Lower Michigan. 9 U.S. STATE ROUTES ROUTES C ad illac M an istee FIGURE 2 PRIMARY HIGHWAY NETWORK FOR THE FIVE-COUNTY S TUDY AREA# SHOWING U.S. AND STATE ROUTES 10 M a j o r roadways Highways 131 and 31# 109, 110, that traverse the area include U.S. and Sta t e H i g h w a y s 113, 115# 186# and 204. 22# 37# 42, 55# 72# This p r i m a r y n e t w o r k is a dequately supported b y a g o o d s y s t e m of s e c o n d a r y roads, which# in the case of most c o u n t y roads# are h a r d surfaced. The median income of families living within the study area is somewhat below that for the state and em p l o y ­ ment data show that a larger percentage of the study area's labor force is unemployed# (Myers and Van Meer, 1966). relative to the entire state General agriculture# forestry# and fisheries comprise nearly 8 percent of the total emp lo y­ ment for the study area# compared to 3.4 percent for the state. Farming is quite important w he n considering the scope of this study. The woodland areas sampled in the investigation were generally part of a farm ownership. The ties between farming and forestry in the area are further highlighted when it is noted that 88 percent of the farming units include woodland acreage (James# 1960) . Almost one- third of the total acreage in the area was classified as farmland in 1966. In this same year# the total farm o wn er ­ ships numbered 2#547# with an average size of 160 acres# 11 slightly larger than the state average o£ 145 acres and Van Meer, (Myers 1966) . The recreational picture has been considerably en ­ hanced since the da ta were collected in 1966 b y the intro­ duction of Coh o salmon to several streams in the five-county region. This region is also the location of Sleeping Bear Sand Dunes, proposed. for w hi ch a National Lakeshore status has been A s with most of Michigan, the recreation aspects in the area are largely water-oriented; and the five coun­ ties ha ve approximately 30 lakes which provide excellent facilities for boating, fishing and camping. Timber Resources The five counties contain 13 percent of the total land area in the northern h a l f of Michigan's Lower Peninsula, and 12 percent of the total forest land. In the study area, commercial forest land comprises 99 percent of all forest land, and represents 12 percent of the commercial forest in the northern Lower Peninsula sents additional (Ostrom, 1967). Table 1 p r e ­ forest-land information from the most recent Forest Survey in Michigan. 12 TABLE 1.— Total and forest area in the five counties, 1966 Total Land Area County All Forest Land Non­ commercial Forest Land Commercial Forest Land Commercial Forest as a Percent of Land Area Percent Benzie 202.2 124.7 2.7 122.1 60.3 Grand Traverse 297.0 161.7 0.6 161.1 54.2 Leelanau 223. •* 114.2 1.0 113.2 50.7 Manistee 357.1 221.3 1.1 220.2 61.7 Wexford 360.3 221.9 1.5 220.4 61.2 Total 1,440.0 843.8 6.9 836.9 57.6 11,387.4 7,051.7 57.7 6,994.0 61.4 Northern Lower Peninsula Source: Ostrom, 1967. In a study of Michigan's farm woodlands (James, 1960), it was pointed out that 36 percent of the farm area was w o o d ­ land in northern Lower Michigan, with the average size of each woodlot being 67 acres. In this same area, the farm woodlot sector represents 18 percent of the total forest area. Yoho's classic wor k involving private forest land ownership in northern Lower Michigan (1957) , estimated that 13 in the "Cadillac Block" of counties,^- 31 percent of the pri­ vately held commercial forest acreage was owned b y full-time farmers, 13 percent by part-time farmers, industry. Thus, and 7 percent by farm ownership constitutes a large share of the commercial forest land in this region and undoubtedly, (44 p e r c e n t ) , a similar pattern holds throughout the study area. The No rthern Lower Michigan Unit, as designated in the Third Forest Survey, 31 counties 1964 to 1966, coincides with the included in Y o h o 's study; hence, quite comparable. the data are The Forest Survey data subdivided the commercial forest land area into various cover types, northern hardwood component accounts of the forest land in the study area, and the for nearly 27 percent (Ostrom, 1967). This type, designated as cover Type 2 5 b y the Society of American Foresters (1962), this study. basswood, esters, provided nearly all of the sample data in Associated types included Type 26, Sugar maple- and Type 27, Sugar maple (Society of American F o r ­ 1962) . Benzie, Grand Traverse, and Wexf or d Counties. Kalkaska, Manistee, Missaukee, 14 The growing stock volume of sugar maple and yellow birch was 89.4 million cubic feet in the five-county study area (Table 2), which represented 16.8 percent of the total for these species in the northern 31 counties of the Lower Peninsula (Chase# 1968). Table 2.— Hardwood growing stock volume on commercial forest land, by counties and species groups, 1966. County Species Total Benzie Grand „ Traverse " T , Leelanau Manistee Wexford -Million cubic feetAspen Paper birch Oak Sugar mapleYellow birch Other soft hardwoods a Other hard hardwoods Total Source: 126.4 20.7 17.2 19.3 34.1 35.1 33.7 5.6 5.7 6.9 7.3 8.2 108.9 11.4 25.9 8.6 42.4 20.6 89.4 16.1 16.2 16.2 17.1 23.8 168.2 33.8 30.7 24.7 36.8 42.2 62.5 12.8 11.7 9.5 13.6 14.9 589.1 100.4 107.4 85.2 151.3 144.8 Chase, 1968. a Other soft hardwoods— primarily red maple, black ash, balsam poplar, cottonwood, yellow poplar, basswood, black cherry, the elms, hackberry, and sycamore. b Other hard hardwoods— primarily hickory, beech, white ash, and black walnut. .1 15 The northern hardwood cover type yellow birch# and beech) (sugar maple* contributed 23.6 percent of the total hardwood sawtimber volume in the five-county area (Chase# 1968). Two associated species that formed a significant portion of the sample d a t a — basswood and elm consituted another 20.8 percent of the board-foot volume total. This five-species group# making up nearly one- half of the hardwood sawtimber, accounted for 37.4 p e r ­ cent of the board-foot volume for all species study area (Chase# 1968). From these data# dent that the northern hardwood cover type# associated types, in the it is evi­ and other comprise the largest share of timber volume in the study area# and represent a ve ry important forest resource for economic research. Allowable cut data from the Forest Survey co m ­ pleted in 1954 indicate that# component# for the northern hardwood the actual cut of 26 million board feet slightly exceeded the allowable cut of 25 million board feet in the Northern Lower Michigan Survey Unit This relationship probably holds for the study area as well. Annual net growth for the northern Lower Peninsula was 296*300 cords or approximately 24 million cubic feet 16 in 1955 in the northern hardwood type (Findel/ et al.< 1960). When compared to the 2 5 million cubic feet of annual allow­ able cut» it appears that cutting has be en maintained at a level approximately consonant with recommended practices/ and a similar situation probably existed in the study area in regards to the growth-cut relationship. As with most of the northern Lower Peninsula/ aspen was the principal pulpwood species harvested in the study area/ contributing 54 percent of the total in 1966 1963; and Blyth/ 1967) . In 1964/ (Horn/ a total of 290 farms in the study area sold a mix of forest products valued at $426/306 (U.S. Department of Commerce/ 1967). cluded sawlogs/ veneer l o g s , pulpwood/ trees, maple sap and maple sirup. These in­ fuelwood/ Christmas Manistee Cou nt y contri­ buted 36 percent of the value of all forest products sold/ 60 percent of the pulpwood volume/ and 61 percent of the sawtimber and veneer-log volume which wa s marketed from farm ownerships within the study area during 1964. Thus/ timber production from farm woodlands seems to be concen­ trated in the southwestern portion of the study area/ pro­ bably influenced b y the large pulp and papermill in nearby Filer City. In the present study# this mill was considered to be the sole purchaser of pulpwood from the five counties. The number of sawmills located within the region is between 30 and 35# and nearly all have an annual production of less than 3,000 M B M (Michigan Department of Conservation, 1964). CHAPTER III SAMPLING PROCEDURES Two important questions ha d to be answered before actual field investigation could commence# namely# how many properties should be chosen for sampling# and ho w intensively should each ownership be sampled? A fter consultation with personnel in the Forestry Division of the Michigan Department of Natural Resources, and examination of their records, it was decided to confine the study to ownerships which had applied timber stand im­ provement (TSI) in 1 9 6 2 , Conservation Program government. Michigan# the B-10 (ACP) and had obtained Agricultural cost-sharing payments from the During that year# 774 farms in the State of totaling 9#574 acres# received remuneration under (timber stand improvement) ACP program. forestry practice of the The greatest concentration of these farms that had applied timber stand improvement to northern hardwoods was located in the five counties selected as the study area. The entire population of woodland ownerships that received A C P payments for the B-10 practice in 1962 within 18 19 the five-county block totaled 78 referrals. records, exact locations, 2 . . Additional and aerial photographs were ob­ tained from Department of Natural Resources Field Offices in Beulah and Traverse City. A f ter considering distance from East Lansing to the study area, estimated time for sampling a referral, length of time available for data collection, and the it was decided that 30 referrals should be sampled from the population of 78. The 78 referrals ranged in size from 1 acre to 30 acres. Before the samples were chosen, the population was strati­ fied on the basis of acreage per ownership into three strata as follows: 11 to 20 acres; Stratum I, 1 to 10 acres; Stratum II, and Stratum III, 21 to 30 acres. The sam­ ple allocation to each stratum was in proportion to the total number of referrals per stratum for the entire popu­ lation. The original 30 samples were selected in a random fashion from the three strata, using a table of random digits (Table 3) . 2 Referral is the term applied to an ownership that has applied for assistance under the Agricultural Conserva­ tion Program. 20 Table 3 - — Population and original sample distribution by individual stratum Stratum No. in population Size Percent of total Samples per stratum Acres Number Percent Number I II III 0-10 11-20 21-30 49 22 7 63 28 9 19 8 3 Total --- 78 100 30 Because the referrals were selected in a random manner and without replacement# random sampling: the method was not independent i.e., the probabilities for each remain­ ing choice were changed after a sample was drawn from the population. Thus, it was not a simple random sample with all units having an equal probability of selection, although the sampling design did provide the randomness necessary for statistical analysis (Clelland, ej: a l . , 1966) . A fter an initial trial with the field measurement procedures, it was decided that two BAF 10 point samples would be established on each ownership. Such a design per­ mitted the sampling of one referral in 3 to 4 hours, thus enabling the two-man crew to complete two properties in one working day including the necessary travel time. 21 When 14 referrals had been measured# a preliminary statistical analysis was made to determine the required sample size needed for a specified sampling error, which would then provide sufficient confidence in the reliability of the data. Two statistical procedures were applied to the preliminary data: 1960), and 1) The range-mean ratio (Allen, et a d . , 2) The standard sample-size formula for strati­ fied sampling (Cochran, 1953; Freese, 1962). In both cases, average basal area was chosen for the calculations, because this parameter is of most concern to a woodland owner when thinnings or other intermediate cuttings are contemplated for a forest stand. To obtain a sampling error of 10 percent or less, the range-mean ratio calculations indicated that 2 5 samples would be necessary. computations, By the standard sample-size formula it was found that 22 samples would be needed. Thus, on the basis of these independent computations, it was decided that the sample size would be reduced to 25 ownerships (Table 4). Five referrals were removed from the list in a random procedure similar to that used in the first selection process. 22 Table 4 . — Population and final samjple distribution b y individual stratum Stratum I II III Total Number in the population Percent of the total Samples taken in each stratum Referrals Percent Referrals 49 22 7 63 28 9 16 7 2 78 100 25 The study area was divided into two "Areas," based on the administrative units employed by the Michigan Department of Natural Resources. Table 5 presents sample data and average referral size, b y stratum for the two areas. 78 referrals totaled 847 treated acres, The and the 2 5 sampled referrals totaled 268 acres. After 2 5 samples had been taken, the range-mean ratio was again computed to obtain a final check on sample adequacy. The results indicated that 20 samples would have been s u ffi­ cient to obtain a sampling error of 10 percent or l e s s . Hence, the actual sample provided somewhat greater accuracy. 23 Table 5.— Population and sample distribution by stratum size and administrative area. Area Total in Pop­ ulation Area in Population Total Average Number in Sample Area in Sample Total Average Number Acres Acres Number Acres Acres 1-10 11-20 21-30 Total 9 5 0 14 49.5 66.0 0.0 115.5 5.50 13.20 3.5 0.0 0.0 3.5 3.50 8.25 1 0 0 1 Leelanau 1-10 11-20 21-30 Total 9 7 4 20 66.0 135.0 108.5 309.5 7.34 19.29 27.12 15.45 4 2 1 7 35.0 40.0 26.0 101.0 8.75 20.00 26.00 14.42 Manistee 1-10 11-20 21-30 Total 9 0 1 10 58.0 0.0 30.0 88.0 6.44 30.00 8.80 3 0 1 4 15.0 0.0 30.0 45.0 30.00 11.25 1-10 11-20 21-30 Total 27 12 5 44 173.5 201.0 138.5 513.0 6.42 16.75 27.70 11.66 8 2 2 12 53.5 40.0 56.0 149.5 6.69 20.00 28.00 12.46 1-10 11-20 21-30 Total 14 5 0 19 78.0 84.0 0.0 162.0 5.66 16.80 22.5 44.0 0.0 66.5 5.63 14.67 8.52 4 3 0 7 1-10 11-20 21-30 Total 8 5 2 15 46.0 76.0 50.0 172.0 5.75 15.20 25.00 11.46 4 2 0 6 21.0 31.0 0.0 52.0 5.25 15.50 1-10 11-20 21-30 Total 22 10 2 34 124.0 160.0 50.0 334.0 5.64 16.00 25.00 9.83 8 5 0 13 43.5 75.0 0.0 118.5 5.44 15.00 1-10 11-20 21-30 Total 49 22 7 78 297.5 361.0 188.5 847.0 b. 07 16.40 26.90 10.87 16 7 2 25 97.0 115.0 56.0 268.0 6.06 16.43 28.00 10.72 County Stratum Acres I Benzie Totals for Area I II Grand Traverse Wexford Totals for Area II Total for Both Areas --- --- 3.50 5.00 --- --- 9.50 8.67 --- 9.12 CHAPTER IV FIELD PROCEDURES The field information collected from each referral was obtained from ten mechanically located BAF 10 point samples within the treated area. A wedge prism was used to determine which trees should be included in the tally. The sampling design required establishment of two major point samples and eight minor point samples on each owner­ ship. The data obtained from the two major point samples were quite detailed# and were recorded on an individual tree basis, whereas the information gathered from the eight minor point samples involved only tree and stump counts for calculating the basal area. The initial major point, which determined the loca­ tion of all other point samples on the ownership, was esta­ blished by rectangular coordinates. approximately square, If the woodlot was the first point was located two chains from one of the corners and two chains into the woodlot (measured along cardinal compass d i r e c t i o n s ) . 24 For 25 properties having a rectangular shape# the point was located two chains from a corner and one chain into the woodlot. If the woodlot was very small# acres# such as one or two the coordinate dimensions were changed to one chain by one chain to confine the samples to interior portions of the treated area. The second major point sample was s ys­ tematically placed two chains from the first# in one of the four cardinal compass directions# depending on orienta­ tion of the area and position of the initial point. The minor point samples were arranged in circular fashion one chain from the major point, four minor points to each major point on predetermined compass bearings (Figure 3). For ownerships in which the two major point samples had to be oriented east-west# the sampling scheme was oriented accordingly. Fr o m the selected trees at each major point# a subsample of five was chosen from which increment cores were then taken for age determination. lied at the major points# For all trees tal­ the following information was obtained: 1. Species. 2. DBH (diameter at breast h e i g h t ) — using a diameter 26 c 0 X u u «s FIGURE 3 THE POINT-SAMPLE DISTRIBUTION AND ORIENTATION FOR A NORTH-SOUTH DESIGN; THE AZIMUTH READINGS ARE MEASURED CLOCKWISE FROM DUE NORTH tape, and recorded to the nearest 1/10 of an inch— on all trees 1 inch D BH and larger. Total height to the nearest foot, using the BlumLiess Altimeter. Merchantable height to the nearest foot for all sawtimber-sized stems, 9.5 inches DB H or larger, m e a ­ sured to a variable top diameter determined in the field. The merchantable height for all stems less than 9.5 inches D B H (merchantable as cordwood only) was measured to a 3 -inch top DOB (diameter outside bark) . G r a d e — determined in accordance with the Northern Hardwoods Tree-Grading Classification Service, 1949), (U.S. Forest for trees 9.5 inches DBH and larger. C u l l — estimated for each tree according to the seven cull defect classes established for this cover type, for trees 9.5 inches DBH and larger and Gevorkiantz, (Zillgitt 1946). C r o w n class— determined for all stems, using the Society of American Foresters' (1958) definitions; 28 i.e., dominant, pressed 8. codominant, intermediate, or sup­ (overtopped). V i gor class— established in accordance with the four northern hardwoods tree vigor and risk classes, all stems (Goetzen, for 1943). All stumps from trees cut during the 1962 operation and located "within" the point sample in 1962 before cutting were also measured and tallied by species. whether a cut tree was To ascertain "in" or "out" of the point sample in 1962, each stump in the immediate area of the point center was measured, and its diameter at stump height (DSH) was co n ­ verted to a DBH value b y means of a previously constructed table. From the distance of the stump to the point center, and the reconstructed DBH, it was established whether the tree would have b e e n tallied in 1962 or not. The D S H -DBH conversion table was prepared b y regres­ sion analysis from tree data collected in the sample area. The equation was: Estimated DBH = 0.15 + 0.833 5 (DSH) 29 In addition# each stump was classified on the basis of existing stump sprouts and their level of abundance and vigor into one of four "sprouting-level" classes. Increment cores were extracted from five trees at each major point for age determination and growth information, DBH, and the other at stump height. one at The trees selected were the first two encountered in a clockwise direction from a line due north from point center. Trees 3 and 4 were the first two en­ countered in a similar manner from a line extending due south of point center. The fifth was the one closest to the point center. Data from the core at breast height consisted of the radial growth for the past 10 years, which was subdivided into the 4-year growth after treatment 6-year growth prior to treatment. (1962 through 1966), and the The measurements were made to the closest 0.01 inch. A separate tally sheet was used for each major point to record crown closure, and reproduction, condition class, sprouting, cover type, understory operability, topography-site, availability of commercial products, incidence of insects and disease, mortality, and silvicultural needs. stand structure, These items were purely subjective in nature based on observ­ able characteristics of the stand immediately adjacent to the point center. 31 Site Index Determination The standard concept of site index is generally reserved for even-aged stands of one species. theoretical grounds, Thus# on such a concept would not apply to the study area; however, it was believed that a measure of site, obtained from quantifiable field data, or based on published data, would be useful as a predictive tool in this study. Since the major species in most referrals was sugar maple,^ site index curves for that species by Curtis were used for site index determination (1962) (Table 6) . Volume Computation The merchantable volume in cubic feet, board feet, and cords, was estimated for each measured tree on all refer­ rals, using the tables prepared by Gevorkiantz and Olsen (1955). The individual tree volumes were then converted to per acre volumes for each ownership. 3 See Appendix 1 for a listing of common and scientific names for all tree species encountered in the present investi­ gation . 32 Table 6.— Site index for all referrals, using average heights and average ages for all species, b ased on Curtis's curves. Site index Referral number*3 Frequency Number 50 Percent of the total Percent 1L04 1L16 2 8 55 2W18 1 4 60 2G01 1L13 2W17 2W23 1M24 5 20 2G02 1L06 2W09 2G10 2G15 1M21 6 24 65 70 75 85 2G03 1L0 5 2W07 2G08 1B14 1M19 1L2 5 7 28 2W11 1L12 2G22 3 12 1M20 1 4 8<%% ----100 Total 25 a Estimates obtained from the formula presented by Curtis (1962), for sugar maple in V e r m o n t . The Referral Number is coded as follows: The first digit indicates the Area, and the letter represents the county in w h ich the referral was located. The last two digits indicate the referral's number— 1 to 25. 33 Volume in board feet was ascertained for all trees in the 10-inch diameter class and larger. Merchantable '( ' cubic-foot and cordwood volumes were determined for the 5inch diameter class and larger. Appropriate cull deductions as presented by Zillgitt and Gevorkiantz (1946) for northern hardwoods were applied to gross board-foot volumes to obtain net volumes. Individual tree volumes/ and per acre values were computed for the two major points for each ownership. The volume data were then grouped b y species# grade# diameter class, as shown in Table 7. and By subdividing total stand volume into grade and species categories# the appli­ cation of differential selling prices was facilitated in the economic analysis portion of the study. Wh e n stand volume is considered solely in terms of board feet# merchantable cubic feet# cords, or some combin­ ation thereof# some additional cordwood volume will be avail­ able in the tops and larger limbs of sawtimber-sized trees. To determine the amount of such volume# b y Chase and Gevorkiantz the method presented (1953) was utilized. The authors present a table of factors for estimating top and limbwood volume per M bd. wood species. ft. (International 1/4-inch Rule) for h a r d ­ The volume information for each referral# cluding this additional volume# is summarized in Table 8. in­ Table 7.— Summary of volume data for Referral No. 2G01, 1966 Species DBH class Volume b y tree grade 2 3 - Sugar maple - Bd. Ft. - 3 4 5 6 8 9 12 0 Total Basswood - 9 10 11 12 13 — — 1091 454 0 0 434 1091 572 — 322 — Total Volume - - Bd.ft. C u .f t . Cords 1.28 2.08 1.31 1.38 1.26 362 362 110.5 130.1 98.5 90.3 113.8 362 362 543 .2 7.31 434 1413 1663 454 110.6 114.1 445.8 357 .5 109.3 1.41 1.14 4.74 3 .84 1.30 — — — Total 1545 2097 322 — 3964 1137.3 12.43 Grand Total 1545 2097 322 362 4326 1680.5 19.74 35 Table 8.— Volume summary for each of the 2 5 referrals (ownerships) in the study area. The entire volume is expressed in three different f o r m s j b o ard feet, cubic feet, and cords; in addition the available volume in topwood (expressed in cords) is also presented. (data for 1966) Total volume of stand expressed i n : Referral b oard feet per acre cubic feet per acre cords per acre Additional volume in topwood3 cords/acre 2G01 2G02 2G03 1L04 1L05 1L06 2W07 2G08 2WO 9 2G10 2W11 1L12 1L13 1B14 2G15 1L16 2W17 2W18 1M19 1M20 1M21 2G22 2W2 3 1M24 1L2 5 Average 4, 326 4,070 6, 529 3,875 7,111 698 7,186 6, 318 1,476 165 722 9,164 4,52 3 6,989 5, 556 5,631 5,493 1,259 4,365 5, 555 6,940 8, 359 6,933 2,993 2,998 1,680.5 2,698.6 2,383.4 1,923.4 2,573.9 1,368.7 2,662.5 3,076.2 2,441.6 869.7 1,675.0 4,091.1 2,393.2 2,721.2 2,488.7 2,038.5 2,347.0 1,364.2 1,977.7 2,244.2 2,611.8 3,157.5 2,831.9 1,746.7 1,413.8 19.74 26.64 23.98 24.58 24.71 15.05 24.05 32 .03 28.46 11.34 20.83 38.91 2 5.84 27.48 22 .32 21.15 21.82 16.98 19.01 21.49 23.11 29.01 30.60 19.71 15.35 2.52 3.74 3.01 2 .07 2.90 1.27 4.51 3.20 1.64 0.18 0.78 4.49 2.06 3.12 3.92 3.18 2.84 1.69 2.70 2.03 4.84 4.27 5.22 2 .62 2.65 4,804 2,263.8 23.21 2 .90 aMaterial w h i c h is also available when the stand volume is expressed in terms of board feet; however, this is in­ cluded in the cubic-foot and cordwood volume figures. 36 Additional Stand Measurements and Characteristics Additional stand data including average DBH# mean DBH# average tree height# average age# number of trees per acre# and basal area per acre were compiled for all 25 referrals. Each parameter was weighted by the number of trees per acre and summarized in Table 9. The basal area estimate was determined from the 10 point samples# whereas other data were tabulated solely from the two major points.. Table 10 summarizes the improvement cutting opera­ tions performed in 1962. Stump tallies at each point sam­ ple provided information for obtaining the number of trees and basal area removed in the cutting. Information for each ownership including tree class, vigor# cull percentage# distances to mills, soils# topography# sprouting# reproduction# insects and disease# mortality is listed in Tables 11 and 12. and Table 13 presents species composition information b y cubic-foot volume for' each ownership. Table 9.— Summary of diameter# height# 25 ownerships# 1966. Average D B H Referral All trees Inches age# and basal area data for the Mean D B H a Dom. and Codom. Number Basal Average Age of trees/ acre area per acre All trees Dom. & codom. trees Inches Inches Inches Feet Years Number Sq.ft. Dorn. & codom. trees Average Height trees 2G01 2G02 2G03 1L04 1L05 1L06 2WO 7 2G08 2WO 9 2G10 2W11 1L12 1L13 1B14 4.9 8.7 9.8 8.2 9.8 8.3 6.2 8.0 6.1 2.9 4.1 5.0 4.9 9.7 9.0 10.7 11.7 9.4 11.1 8.3 12.2 10.7 9.0 6.4 7.0 10.5 9.7 12.2 5.6 9.2 10.2 8.5 10.2 8.5 7.7 8.4 6.5 3.5 4.6 3 .4 5.8 10.2 9.2 10.9 11.9 9.6 11.2 8.5 12.6 10.8 9.2 6.6 7.2 10.6 10.0 12.4 62.0 71.8 78.6 58.4 79.0 65.6 79.8 80 .8 71.2 58.0 67.1 85.0 73 .5 81.2 54.6 58.0 62.8 69.5 61.8 54.4 64.4 66.0 57.0 39.9 41.2 64.2 77.9 66.0 597 .0 228.9 166.6 330.1 156.8 171.2 369.0 336.0 627.2 1 # 0 9 5 .2 1»001.2 1#128.7 862.6 180.5 92 128 85 77 89 77 118 115 128 94 107 99 87 83 Average 6.9 9.8 7.3 10.0 72.3 59.8 517.9 98 Table 9 . — (Continued) Average D B H Referral 2G15 1L16 2W17 2W18 1M19 1M20 1M21 2G22 2W23 1M24 1L25 Average All trees Dom. & codom. trees Mean D B H a All trees Dom. & codom. trees D o m . and Codom. trees Average He ight Number Basal Average Age of trees/ acre area per acre S g .f t . Inches Inches Inches Inches Feet Years Number 9.2 8.7 4.7 5.2 9.0 6.6 13 .0 8.2 4.8 5.3 5.1 15.6 10.1 10.6 8.8 10 .5 11.3 15.6 11.9 10.7 9.3 9.1 10.5 9.2 5.6 6.0 9.6 7.2 13.4 9.0 6 .0 5.9 5.9 15.8 10.6 10.9 9.0 10.8 11.7 15.8 12.4 11.0 9.5 9.3 81.8 69.0 65.0 57.4 73 .8 84.1 81.6 87.7 70.8 65.6 68.2 74.2 97 .0 61.1 53 .0 54.2 49 .8 80.3 66.4 64.2 57 .4 47 .9 155.8 218.2 592 .6 461.2 171.2 507 .4 91.2 270 .4 1,582.4 568.4 393 .2 99 84 104 98 92 100 94 111 118 90 79 7.3 11.2 8.0 11.5 73 .2 64.1 455.6 97 a Diameter of the tree of mean basal area. 39 Table 10.— Data for material removed in the TSI operation during 1962, for each ownership. Material removed in TSI in 1962 Referral Basal area per acre Sq. ft. 2G01 2G02 2G03 1L04 1L05 1L06 2WO 7 2G08 2W09 2G10 2W11 1L12 1L13 IB 14 2G15 1L16 2W17 2W18 1M19 1M20 1M21 2G22 2W23 1M24 1L25 Average Number of trees per acre Average DBH of cut trees Number Inches Percent of cut by species Sugar maple Ironwood Elm Beech Othera Percent - - - 37 18 25 17 31 25 23 28 25 31 24 20 31 13 43 18 14 19 47 22 13 28 22 37 23 115.8 16.6 26.6 637.0 116.8 483.9 161.5 117.4 134.4 266.0 119.4 298.2 32.3 6.5 32.7 27.4 50.8 141.1 101.1 13.4 56.8 55.6 47.0 15.0 251.2 7.0 12.4 13.6 3.4 6.9 6.7 7.0 8.5 3.6 5.3 7.1 5.4 10.9 16.9 14.2 11.0 8.4 6.2 10.0 14.1 9.0 11.8 6.1 11.0 5.6 —— — — 3 37 98 — 53 100 34 79 — — 100 25.5 126.4 9.0 — — — — 70 — — 77 — 100 3 55 2 — 24 — 52 21 — — — — — — 12 100 41 86 — 47 4 78 — 100 — — .— — 72 — 92 — 24 — 7 — 59 — 28 — —— 31 23 18 59 — 94 — — 3 41 — — 8 — — 23 — 1 — — 9 — 100 8 — — 5 — — 11 — — 20 — — — — — 100 — — 13 — 30 91 — — 14 76 — 76 — — 3 — 53 4 8 20 a The category of "other" species includes the following: basswood, red maple, yellow birch, white ash, black cherry, red oak, and aspen. Table 11.— Additional referral measurements and characteristics A v e . A v e . t r e e R e f e r r a l c l a s s A v e . D i s t a n c e % v i g o r N e a r e s t P a p e r - c u l l c l a s s s a w m i l l m i l l o f r e f e r r a l M i l e s M-U.es t o : a S t a t u s N e a r e s t t o w n A v e . t o l e r a n c e * 3 o f R e p r o d u c t i o n A v e . a b u n d a n c e 0 A ve . d e s i r a b i l i t y 4 M i l e s 2 G 0 1 2 .2 22 3 . 4 13. 5 6 7 . 0 4 . 2 V T M L 2 G 0 2 2.2 13 2 . 5 7 .2 5 8 . 8 6 . 5 V T S H H 2 G 0 3 2.2 15 2.7 6 .0 60. 5 6 . 0 V T A 1 L 0 4 2 . 1 6 3 . 4 7 .0 6 1 . 2 4 . 5 T A L 1 L 0 5 2.2 16 2 .2 5.8 6 7 . 0 2 .2 T A L H 1 L 0 6 3 . 5 4 5 2.3 2 . 8 73 .8 4 . 5 V T s 2W O 7 2.3 21 3 . 4 4 . 8 4 8 . 0 2 . 5 T S L 2 G 0 8 1 . 9 14 2 . 8 4 . 8 65. 5 5.8 T A H H 2W O 9 3 . 5 42 3 .2 3.2 5 5. 2 7.2 V T S 2 G 1 0 2 .0 7 3 . 5 6 .0 62. 5 5.8 V T S H 2 W 1 1 2.3 7 3 . 4 7 .2 4 9 . 2 3 . 5 V T S H 1 L 1 2 2 . 4 14 2.7 1 5 . 2 8 0 . 2 5.5 V T M H 1 L 1 3 2 . 5 24 3 .1 2 . 5 6 0 . 2 3 .5 I A L 1 B 1 4 2 . 4 22 2.3 2 .2 3 8 . 0 3 .2 T A H 2 G 1 5 2.2 23 3 . 1 1 3 . 8 5 5. 0 2 .8 V T M H 1 L 1 6 2.0 10 2 . 9 7 .0 6 1 . 2 4 . 5 T A L H 2 W 1 7 2 . 6 13 3 .0 4 . 5 3 8 . 8 1.0 T S 2 W 1 8 3.2 42 3 .4 4 . 8 3 9 . 0 1.0 T s L 1 M 1 9 2 . 5 20 2 . 4 6 .2 3 3 .2 7 .8 T M H H 1 M 2 0 2 .1 10 3 .0 8 . 0 2 0 . 2 6 .0 T S 1 M 2 1 2 .0 11 3.3 7.0 3 5 . 2 6 . 2 T A L 2 G 2 2 2 . 6 14 3 .1 8 . 8 6 5 . 2 5.8 V T M H 2 W 2 3 2 . 7 18 3 .6 1 3 . 0 4 9 . 8 5.5 V T M L 1 M 2 4 2 .0 9 2 . 8 1 1 . 0 3 9 . 5 6 .2 V T A L 1 L 2 5 2 .1 18 2.7 8 . 0 6 4 . 8 5.8 V T A L S e e A p p e n d i x °VT» T, I; 2 V e r y _M « A, S; H. L; H i g h , f o r c o m p l e t e t o l e r a n t , M o d e r a t e , a n d a l o w d e s c r i p t i o n t o l e r a n t , a b u n d a n t , a n d d e s i r a b i l i t y a n d s c a r c e , o f m i l e a g e to i n t e r m e d i a t e , r e s p e c t i v e l y . r e s p e c t i v e l y . m i l l s b y r o a d - s u r f a c e r e s p e c t i v e l y . type. O 41 Table 12.— Additional referral characteristics Relative Relative . .^ proximity 1 . i to roads0 _ , , Referral portion „ , .. Relative , b slope® stand, Relative of no. of a F, M, C C; M S S M S M S M S H S S M S S S s M s M S s of incidence® L L M H H H M H H H H H H L M L M M H L M M M suitability classification? £ mortality L H N H M N N H N M M N L L L M L M H L E A C C C A A E C E C C E E D C C C C C L L L H L M M M H H M M L L M M M M H M H M L L U U C L M U u M L L L C L S M N M c H Greater road disease sprouts'3 Woodland amounts c c M c M M M M M nearest b L, L U L U u H L L L U H H U U H U H F C M C C M C C M M C M C Relative and stump sprout o ri gi n 0 2G01 2G02 2G03 1L04 1L05 1L06 2W07 2G08 2W0 9 2G10 2W11 1L12 1LI3 IB 14 2G15 1L16 2W17 2W18 1M19 1M20 1M21 2G22 2W23 1M24 1L25 Insect of than 1 M mile, between 1/4 and H N M 1 mile, and less E C A than 1/4 mile from the respectively. U, H; Level, undulating, and hilly S, M, H; Slight, L, M, H; Low, moderate, and high L, M, H; Low, moderate, and high respectively. c moderate, and high incidence of sprout origin respectively. d amount of stump sprouting respectively. e spectively. *"L, M, H; N — Low, No indication moderate, and of incidence insects high or mortality of insect disease and/or disease infestation re­ present. respectively. g Woodland tivity or more (i.e., suitability for northern than 1.2 275-325 potential classification; hardwoods cords/acre bd. per ft./A/yr.; productivity (i.e., (i.e., or Soils a year); Groups 0.8-1.2 200-275 in growth bd. group rate B A of and have more C c o r d s / A / y r .); ft./A/yr.; or have very than high Grouns 0.5-0.8 high 325 D potential bd. potential and E produc­ ft./acre/year; productivity have cords/A/yr.) medium (USDA, 1966.) 42 Table 13.— Species composition of each referral by cubic-foot volume per acre, 1966. Percent of each referral by species Referral Sugar maple Beech Yellow ,. , birch Elm Bass. wood , , Ash Black , cherry Other Percent ■ 2G01 2G02 2G03 1L04 1L05 1L06 2W07 2G08 2W09 2G10 2W11 1L12 1L13 1B14 2G15 1L16 2W17 2W18 1M19 1M20 1M21 2G22 2W23 1M24 1L25 a 32 39 94 35 57 91 — 54 70 20 80 — 98 92 49 37 31 30 28 67 17 78 39 53 34 — — — — — — 14 — 7 — — — — 3 38 12 20 — 13 — 6 . 11 18 — 10 — — — — — — — — — — — — — — — — — — — — — — — — —— 52 6 41 37 9 — 31 — 13 16 2 — 5 7 41 21 22 33 7 77 — 4 3 68 9 — 24 6 — — 15 5 9 — 37 — — — — 23 40 — — — — 29 4 8 — — — — — — — — 6 58 — 31 — — — 7 5 — 26 7 — 6 10 — 43 Includes oak, aspen, ironwood, hemlock, and red maple. —— — — — — — — 12 — — — — — 6 3 — — — — — — — 6 —— — — — — — 86 — — — 4 30 2 — — — — 8 — 19 — 5 — 34 5 a C H A P TER VI GROWTH PREDICTION AND VOLUME PROJECTION Basal Area and Height Growth After comparing the results of several different methods of growth p r e d i c t i o n # Spurr's Two-Way Growth Pre­ diction Procedure (Spurr# 1952) was selected for use. Re­ sults using his procedure were about the same as those from the stand table projection procedure/ is considerably faster in application. and the two-way method Predicting volume by means of yield tables would have necessitated less time; however# existing tables contained no provision for the in­ fluence of management activities. The two-way method pr o ­ vided a measure of volume growth which was more sensitive to changes induced b y various management regimes# thus# was more responsive to the results of each alternative investi­ gated in the study. Although basal area growth projection was of a straight-line nature# assumptions, tempered only b y mortality the resulting volume predictions indicated accurate relative differences even though the absolute values m a y be somewhat inflated. 43 44 The two-way approach combines separate estimates of basal area and height growth as the basis for determining future volume. Growth in average stand height was esti­ mated from the appropriate site index curve applicable to each ownership. Basal area growth was estimated by the method out­ lined in the Service Forester Handbook (USDA, 1961) using the following formula: Rob = where: [1 - Z ( D BH - 2r f Rob = DB H = n /n] 100 the ratio of 10-year basal area increment to present basal area per acre expressed as a percent. the present diameter at breast height. = the number of growth sample trees. r « the 10-year radial growth in inches. The radial growth for the 6-year period before timber stand improvement# and for the 4-year period after treatment were converted to a 10-year basis by multiplying b y 1.667 and 2.5# respectively. A modification involved a 5 percent addition to the radial wood growth to adjust for bark growth. for the factor (DBH - 2r) 2 Values were available in tabular form in the Service Forester Handbook (USDA, 1961) # and were 45 multiplied by the number of trees in each diameter class within the five-tree growth subsample of each point sample. An example of the basic computations using the before treatment growth rate is given in Table 14, an d for the after treatment growth rate in T a ble 15, for Referral 2G01. The results in Tables 14 and 15 were used to co m ­ pute the basal area growth percents for before and after treatment conditions. treatment conditions, Point No. For Referral No. 2G01, for the before the computations were as follows: 1 Rob = [1-(163.70/261.40)] 100 Rob = 37.38% Point No. 2 Rob = [1-(91.85/128.60)] 100 Rob = 28.58% The Referral Average Rob = (37.38 + 28.58)/2 Rob = 32.98% (the 10-year growth p e r c e n t ­ age; or 3.298% per year) For the after treatment condition for the same referral, the computations w e r e : 46 Table 14.— Basal area growth calculations for Referral 2G01 using the before treatment growth rate. N o . of trees DBH class per acre (1) In. Past Past radial radial growth growth adjusted to 10-year basis (3) (2) Number Inches (4) Inches 10-year radial (DBH-2r) 2 growth 2 weighted (DBH-2r) a d j . for b y no. bark of trees growth (6) (7) (5) Inches Point sample no. 1 11 5 11 6 4 16.0 79.4 16.0 51.0 99.0 Total 261.4 5 8 9 12 62.9 30.1 23.1 12.5 Total 128.6 .35 .27 .42 .32 .28 .583a .450 .700 .533 .467 — --- .31 .24 .32 .34 — .61b .48 .74 .56 .49 — Point sample no. 2 .54 .517 .42 .400 .533 .56 .59 .567 --- — .79C .64 .76 .64 .56 — 12.64d 50.82 12.16 32.64 55.44 163.70 .64 .81 .74 .81 40.26 24.38 17 .09 10.12 — 91.85 aColumn (3) X 1.667, to adjust the 6-year growth before treatment in 1962 to a 10-year basis. Column (4) X growth. .0 5, to adjust for 5 percent bark Q From the Service Forester Handbook ^Column (2) X column (6) . (USDA, 1961). 47 Table 15.— Basal area growth calculations for Referral 2G01 using the after treatment growth rate. No. of Past Past radial trees growth DBH radial adjusted class per growth to 10-year acre basis (1) (2) IITU Number (4) (3) Inches Inches 10-year radial growth a d j . for bark growth (5) (DBH-2r) weighted (DBH-2r)2 b y no. of trees (6) (7) Inches Point sample no. 1 11 5 11 6 4 16.0 79.4 16.0 51.0 99.0 Total 261.4 .27 .20 .28 .14 .17 .6 7 5 a .500 .700 .3 50 .425 .71 .52 .74 .39 .44 .76° .64 .76 .74 .64 --- ----- --- --- 12.16d 50.82 12.16 37.74 63 .36 176.24 Point sample no. 2 62.9 30.1 23 .1 12.5 .21 .28 .19 .29 .525 .700 .475 .725 .55 .74 .50 .76 .58 .67 .77 .74 36.48 20.17 17 .79 9.25 Total 128.6 --- ---- --- --- 83 .69 5 8 9 12 aColumn (3) X 2.5* to adjust the 4-year growth after treatment in 1962 to a 10-year basis. b Column (4) X growth. c .05* to adjust for 5 percent bark From the Service Forester Handbook Column (2) X column (6) . (USDA/ 1961). 48 Point No. 1 Rob = [X-(176.24/261.40)] 100 Rob = 32.58% Point No. 2 Rob = [1-(83.69/128.60)] 100 Rob = 34.92% The Referral Average Rob = (32.58 + 34.92)/2 Rob = 33.75% (the 10-year growth percentage? or 3.375% per year) The basal area growth percents were then used to compute past and future basal area v a l u e s . area* immediately after the TSI in 1962 The past basal (the residual basal area) , was determined as follows: Basal area growth Past basal _ Present basal percent for length area per acre ~ area per acre of projection period For Referral No. 2G01# Present basal area per acre these computations became: Basal area Basal area per in acre after TSI * 1962 in 1962 4 annual basal area years X growth X in percent 1962 49 = 92 - (4 X 3.375 X 92) =92-20 = 80 square feet per acre. The basal area per acre before the TSI in 1962 was obtained b y adding the basal area removed in the TSI to the residual basal area. For Referral No. 2G01, the cut-stump tally totaled 37 square feet of basal area per acre Table 10). Thus, (from the basal area before TSI in 1962 was: 80 + 37 = 117 square feet per acre. The future basal area at the end of any desired projection period was obtained as follows: Future basal area per acre Present basal area per acre Basal area growth Present percent for length X basal area of projection per acre period If Referral No. 2G01, wi t h 117 square feet of basal area in 1962, had not been treated, its basal area by 1966 would have become: Basal area per Basal area acre in 1966 = in + 1962 4 years X Annual growth percent X Basal area in 1962 50 = 117 + (4 X 3.298 X 117) = 117 + 15 = 132 square feet per acre. Annual basal area growth values for each ownership are presented in Table 16. Basal area data on a per acre basis for stand conditions before TSI, TSI, removed in TSI, after and four years later at the time of measurement in 1966, are presented in Table 17. By comparing the average growth rates before treat­ ment and after TSI in 1962, very little difference can be observed. ment) The basal area increment without TSI was 2.86 percent, ment) was 2.92 percent. and the figure with TSI (before treat­ (after treat­ These values were so close that no statistical difference could be noted; hence, it can not be stated that timber stand improvement caused any acceler­ ation in growth. However, measurement was very short, yet to be realized. the period between cutting and so perhaps the true response has 51 Table 16.— Annual basal area growth for each referral with and without TSI. Referral Basal area increment with TSI treatment Basal area increment without TSI treatment 2G01 2GD2 2G03 1L04 1L0 5 1L06 2WO 7 2G08 2WO 9 2G10 2W11 1L12 1L13 1B14 2G15 1L16 2W17 2W18 1M19 1M20 1M21 2G22 2W23 1M24 1L25 3 .38 2.27 2.44 1.90 2 .52 2 .76 3 .71 3 .08 3 .79 4.40 3 .45 2.38 3 .01 2.74 3 .20 2.66 2.64 2.97 3 .13 2.88 1.37 3 .81 2.43 2 .33 3 .81 3.1 2.9 2.1 1.5 2.2 2.1 4.4 3.5 4.8 4.1 , 3.7 2.4 2.6 2.3 3.2 2.2 2.7 2.9 2.9 2.9 1.3 4.2 2.9 2.1 3 .0 3 .30 2.68 2.76 1.96 3 .11 2.82 3 .97 2 .79 3 .84 3 .95 3 .03 2 .51 3 .43 2 .98 2 .65 2 .21 2 .05 2 .98 2 .61 2 .80 1.63 3 .00 2 .55 2 .95 3 .58 3.9 3.6 2.8 1.7 3.4 2.7 4.9 3.6 5.1 4.3 3.5 2.7 3.7 2.6 3 .4 2.1 2.2 3.1 3.3 3.1 1.7 3.7 3 .3 3.5 3.2 Average 2.92 2.86 2.86 3 .21 52 Table 17.— Basal area data for stand conditions before TSI# removed in TSI# after TSI# and in 1966 for each ownership. Referral Basal area per acre 1 o Before TSI Removed in After TSI In 1966 TSI in 1962 in 1962 in 1962 Sq. 2G01 2G02 2G03 1L04 1L05 1L06 2W07 2G08 2WO 9 2G10 2W11 1L12 1L13 1B14 2G15 1L16 2W17 2W18 1M19 1M20 1M21 2G22 2W23 1M24 1L25 - Average ft. 117 134 102 . 88 111 94 123 129 134 109 116 109 108 87 129 93 107 105 127 110 102 122 128 119 90 112.0 Sq. ft . 37 18 25 17 31 25 23 28 25 31 24 20 31 13 43 18 14 19 47 22 13 28 22 37 23 25.5 Sq. ft. Sq. f t . 80 116 77 71 80 69' 100 101 109 78 92 89 77 74 86 75 93 86 80 88 89 94 106 82 67 92 128 85 77 89 77 118 115 128 94 107 99 87 83 99 84 104 98 92 100 94 111 118 90 79 86.5 97.5 53 Volume Projection The volume in cubic feet per acre formed the basis for all volume projections. The past or future volume per acre was computed by the following equation USDA# (Spurr# 1952; 1961): V (H ) p where: V E (BA ) p V = (H ) n IL (BA ) n = the present cubic-foot volume per acre P V n = the cubic-foot volume per acre in year n. Hp = the present stand height. = the average stand height in year n. BAp = the present basal area per acre. BA n = the basal area per acre in year n. These computations were made to obtain an estimate of volume for each referral in 1962# both before and after the TSI operation, as well as predicting volume for any year in the remaining portion of the rotation. Referral No. The basic data for 2G01# and the computation of the volume in 1962 after timber stand improvement is as follows: 54 The present volume = 1/680.5 cubic feet per acre Present basal area = 92 square feet per acre The present stand height = 62 feet Stand height in 1962 = 60 feet curves) (from site index Residual basal area in 1962 = 80 square feet per acre 1,680.5 ______________ V _ _______ n 62 X 92 V n = 1,414.2 60 X 80 cubic feet per acre, The volume per acre in 1962 before TSI could also be c o m ­ puted easily by merely replacing the 60 square feet of residual basal area with 117 square feet, which was the basal area before the TSI. However, the volumes b y individual species, by a simple backward projection. that the 37 square feet of it was desired to have and this was not possible The reason for this is basal area removed was tallied from the stumps of trees cut in the thinning operation, and backward projection would provide only the total volume before TSI — not b y each individual species. Therefore, the volume removed in timber stand improvement was estimated separately, and then added to the residual volume. 55 To accomplish the initial volume calculation, a sep­ arate regression was first computed for each referral, gressing height on DBH. re­ By determining the DBH of a "cut" tre'e from its stump diameter (as previously described) , and then calculating its height b y the regression equation, its cubic-foot contents could, be read directly from the volume table. Individual tree volumes were then multiplied b y the representative number of trees per acre and summed to obtain the total volume per a c r e . were averaged to obtain the referral mean For Referral No. The two point-sample estimates (Table 18). 2G01, this amounted to 514.2 cubic feet per acre removed in the TSI activity (Table 18); hence, the volume before TSI was 1,414.2 + 514.2, or 1,928.4 cubic feet per acre. Thus, the volume of 1,928.4 cubic feet in 1962 had been reduced b y TSI by 514.2 cubic feet, and the re­ sidual volume of 1,414.2 cubic feet per acre ha d grown to 1,680.5 cubic feet per acre by 1966. From these and earlier computations, it was a simple matter to portray the stand volume for each species and size class in 1966, as shown for Referral No. 2G01 in Table 19, and also the residual volume after TSI in 1962, in TSI, and the volume before TSI, the volume removed as shown in Table 20. 56 Table 18.— Computation of volume removed by TSI in 1962 on Referral No. 2G01 Number Merchantable Total Total _ a Stump Species „. f DBHb e Diameter of volume Merchantable heightc per treed trees volumee Inches In. Feet 52 11.4 9.7 62 19.5 9.7 189.2 52 7.1 6.1 51 49.3 2.5 123.2 52 6.2 5.3 49 65.4 1.7 111.2 52 7.5 6.4 52 44.8 3.2 143 .4 60 7.4 6.3 52 46.3 3.2 148.2 62 20.4 17.2 84 6.2 50.5 313.1 Totals No. for 2 point samples Total per acre a 52 = elm; b 60 = basswood; Cubic feet C ubic feet 231.5 ---- 1,028.3 115.8 ---- 514.2 and 62 = b e e c h . From the regression equation: DBH = 0.15 + (.8335)(DSH). From the regression equation: H T . = 33.3 + (2.976)(DBH). Q ^From Gevorkiantz and Olsen DBH and height v a l u e s . (1955), using the estimated 0 (Number of trees) X (Volume per t r e e ) . Table 19.— Volume b y species and size class for Referral No. 2G01 in 1966— per acre basis. Item Maple Species c-----Basswood Total Total volume; cubic feet Percent of total Percent b y size 543.2 32.3 1,137.3 67.7 1,680.5 100.0 100.0 100.0 100.0 Volume in poletimber-sized t r e e s , cubic feet Percent of total Percent by size 431.3 25.7 79.4 30.7 1.8 2.7 462.0 27.5 27.5 Volume in sawtimber-sized t r e e s , cubic feet Percent of total Percent by size 111.9 6.6 20.6 1,106.6 65.9 97.3 1,218.5 72.5 72.5 Table 20.— Volume b y species and size class for Referral No. 2G01 in 1962— per acre basis. Maple Elm Species *■-----Basswood Total initial vol .# cubic feet Percent of total Percent by size 456.8 23.7 100 .0 283 .5 14.7 100.0 1,031.5 53 .5 100.0 156.6 8.1 100.0 1,928.4 100.0 100.0 Poletimber volume # cubic feet Percent of total Percent b y size 362.7 18.8 79.4 188.9 9.8 66.6 99.9 5.2 9.7 ------- 651.5 33 .8 33.8 94.1 4.9 94.6 4.9 931.6 48.3 156.6 8.1 1,276.9 66.2 283 .5 74.1 156.6 514.2 Item Sawtimber volume# Percent of total cubic feet Volume removed in TSI# Residual volume# cubic feet cubic feet 456.8 957.4 Beech Total 1 1414 .2 59 At this point# the volume and growth computations did not include adjustments for mortality/ cull defect/ or quality changes throughout the projection period. Also/ the basis for converting cubic-foot volume into either board feet or cords had not been determined. Such steps were needed before the economic analysis could be made; however/ before these aspects of the prediction model could be developed and merged for application/ analysis model itself had to be identified/ the formal and the basic alternatives and decision-making framework specified. CHAPTER VII THE DECISION-TREE M O DEL AND UNDERLYING ASSUMPTIONS Development of the Model The formulation of a model for prediction and eval­ uation purposes b e g a n with the premise that each of the 2 5 woodland owners was faced with a set of alternative courses of action in 1962 and, therefore, was confronted with the necessity of making a set of decisions. of decisions would, over time, Such a sequence influence the physical p r o ­ cesses of stand growth and development and consequently, financial returns to the owner. In order to provide a clear representation of the various alternatives facing an owner, as well as providing a means for evaluating the different opportunities, tree analysis was selected. decision The decision tree approach is a relatively new analytical tool of applied statistical deci­ sion theory. Foundations of statistical decision theory were pioneered b y Robert Schlaifer of the Harvard Business School 61 (1959)# and the decision tree technique received its greatest impetus from John Magee# also of Harvard (1964). A decision tree accomplishes two functions with its implementation. First# it provides a clear visual represen­ tation of the complete decision-making process faced by a business manager# the various tives. as it is actually composed on paper, "tree branches" portray the relevant alterna­ It contains the available courses of action# associated costs and possible outcomes# occurrence# and probabilities of and the consequences involved# decision-making sequence. Second# their for an entire the method employs a computational algorithm for evaluating each opportunity# and determining which course of action should be pursued. This "best" set of policies is the optimal sequence# in terms of expected net returns for the duration of a plan­ ning horizon. The decision tree approach recognizes that longrange planning consists not of one decision--but rather a series of d e c i sions— made at various times throughout the planning period. As expressed b y Peter F. Drucker (1959) # "Long-range planning does not deal with future decisions. It deals with the futurity of present decisions." 62 The decision tree for the study at hand was prepared in stages/ outcomes, starting with fundamental alternatives and chance to which were added various modifications tive of the model's many ramifications. indica­ In this analysis, there were two basic decisions which affected the potential physical yields from a given referral: 1) In 1962, the owner had to decide whether he was going to undertake a timber stand improvement operation or not; and 2) In future years he would have to decide whether the woodland would be allowed to grow unmanaged for the remainder of the rotation. paired, these two options resulted in four general to the owner's decision tree When "branches" (Figure 4). This created the need of four separate schedules to project the physical data for each ownership. this requirement, To fulfill individual growth projections were made for each of the following situations: 1. The assumption that TSI was performed in 1962, and that thinnings would be interspersed throughout the balance of the rotation. This was based on the basal area growth rate measured after the actual TSI operation. FUTURE THINNINGS TSI IN 1 9 6 2 NO FUTURE "t h i n n i n g ? FUTURE THINNINGS NO TSI IN 1 9 6 2 NOFUTURE "Th i n n i n g s " Decision point figure 4 BASIC DECISION TREE FOR A WOODLAND OWNER FACED W I T H A D ECISION ON TIMBER STAND IMPROVEMENT IN 1962. 2. The assumption that TSI was performed in 1962; however* no thinnings would occur in the future. This also relied on the growth rate determined after TSI/ but projection was greatly simplified as compared to No. (1) since the stand was allowed to grow directly to the end of the rotation before a cut was m a d e . 3. The assumption that TSI was not undertaken in 1962; however/ future thinning operations would be performed when warranted b y physical and finan­ cial characteristics of the stand. This schedule was based on growth rate calculations for the period preceeding the actual TSI program. 4. The assumption that TSI was not undertaken in 1962/ and that future thinnings would not be part of the management plan. No cultural work whatsoever would be applied in the intervening years before a final harvest cut. The next phase in the model-building process was to extend the basic framework into a more sophisticated repre­ sentation of the decision-sequence which would confront a woodland owner. It was impossible to include all of the myriad alternatives available to a manager/ because many such avenues would not be recognized b y the analyst or even the owner himself. included/ If a complete enumeration were the computational phase would be extremely time- consuming/ even with the aid of high-speed computers. addition/ many alternatives In in such an exhaustive list would be extraneous to the major objective of evaluating timber stand improvement opportunities. For example/ it was assumed that the woodland owner would retain his woodlot in a forested condition until commercial products were available. Thus, investment (or disinvestment) natives which w o uld remove the timber, for farmland, alter­ such as clearing selling for residential construction, etc., although possibly hi g h l y profitable in the long run, were not included in the decision tree. The "branch" dealing with TSI in 1962 was expanded as to: tion, 1) Who assumed the financial burden and actuality, for the opera­ 2) How the undesirable stems were removed. In all 25 referrals received monetary reimbursement through the Agricultural Conservation Program (ACP), and all TSI consisted of cutting trees, with only a small portion 66 of the cut material removed and sold in product form. ever, this pattern was not the only recourse; How­ the owner could have assumed the financial responsibility himself, and the stems might have been girdled, cide, or cut and sold. Therefore, treated with silvi- two additional points of decision were added to the basic "tree" for each ownership. Initially, it was thought that the costs of TSI should be differentiated by the method of removal, whether girdled, cut, or treated with silvicide. of the research on this aspect 1956; MacConnell, 1962; (Chaiken, Lindmark, 1965), However, most 1951; Walker, reported the results on a per acre or diameter-inch basis only. Such information was inadequate for application to different ownerships, where the stocking, material to be removed, species composition, ferent, because, age, growth rate, etc., were all d i f ­ regardless of these parameters, cost figure would be used. the same The most useful guidelines that were available gave a cost schedule dependent on the amount of basal area removed, most germane to this study, of removal method (USDA, and in the recommendations cost structure was 1961; Haskins, 1961). independent 67 For these reasons/ and for further simplification in model construction/ only two alternatives were considered in the removal of undesirable stems/ namely/ selling the material/ cutting and and deadening the stems. adding these alternatives/ and whether the TSI was self- financed or ACP cost-shared/ total of ten "branches" Thus, by the decision tree now had a (Figure 5). Additional modifications concerned the manner of selling merchantable products from an ownership. The two primary opportunities available to an owner were the sel­ ling of stumpage/ or the marketing of cut products. was conceivable that an owner/ It contemplating several future thinning operations plus a final harvest/ would select both means of sale over the rotational period/ and cordwood and sawlogs could be handled differently for a given thinning. For example/ an owner might sell all of the material from the first thinning/ which would consist mainly of cordwood/ as stumpage/ whereas when the second thinning was undertaken/ he could market cut products/ cluding more sawlogs than before/ at the mill site. in­ When a subsequent thinning or final harvest cut was made/ he could sell his merchantable pole-sized stems as cordwood 68 Decision 1 D ecision 2 Decision 3 D ecision 4 Jn ^ I m Ju w ""TnSnlnis In 1962 Im Im h th inn in g* H ^future th in n in g s Cu^and th inn in g* AC^coet•h n rin f Hefuture ^ th in n in g * P e a d e n ls •tense on l lu»*r* thinning* TSI in 1962 N ^future thinning* Cut and future^ thinn ing * Self financing N^luter* th in n in g * I— D e c isio n •te m « o n ly p o in t Puture^_ th in n in g * FIGURE 5 DECISION TREE SHOWING ADDITIONAL ALTERNATIVES FACING A TYPICAL OWNER IN 1962. 69 stumpage along with the poorer saw-timber-sized trees, and market the higher grade sawlogs delivered at the local mill. Thus, it was readily apparent that a realistic pat­ tern of choice would be infinitely variable and extremely complex for analytical p u r p o s e s . by owner, The pattern would vary and w o uld be determined by many factors which were not included in the study. Because of their nature, many would be non-quantifiable or at best semi-quantifiable, such as length of tenure, bound children, uncertainty, age of owner, educational levels, number of college- aversions to risk and and b a sic attitudes towards forest management. Such complexities would increase the number of com­ putations at a geometric rate. For example, starting with one of the 5 "branches" dealing with future thinnings, decision occurred at the time of thinning No. 1: to sell stumpage or market the cut material. a whether If it is then assumed that each alternative has the potential of either a low, medium, or high income "branches" w o uld be created. (a chance e v e n t ) , six additional This process would then be repeated for thinning No. 2, and each of the six "branches" for the first thinning would J e s u i t in an additional six for the next cutting opera tion— a new total of 6 X 6, or 36 70 "branches." If three thinnings were planned before the final harvest, this compounding would involve 1,296 "branches" at the end of the rotation; however, possible, if another thinning was the number would spiral to 7,776; and this, only one of the "future-thinnings branches I" for If this se­ quence were applied to all the "future-thinnings" alterna­ tives, and the "no-thinning" alternative added, total would be approximately 39,000 more, "branches!" this excluded many other possibilities, owner selling only cordwood, bination of the two products; of his timber as stumpage, Therefore, Further­ such as the or only sawtimber, and, the grand or a com­ the owner selling part and marketing the remainder. it was necessary to restrict the system by cer­ tain simplifying assumptions. One very important assumption was that, once an owner had determined the manner in which his products would be harvested and sold for the first thinning, he would con­ sistently follow such a procedure for all additional cutting operations. The author believes that such an assumption is quite realistic for most small woodland owners; unless a man goes bankrupt in an initial timber transaction, it seems quite reasonable that subsequent ventures would exhibit 71 identical characteristics. If a substantial loss were ex­ perienced by the owner, he w o u l d probably avoid further forestry activities, rather than seek professional ass i s t ­ ance for his management p r o b l e m s . Another assumption was that all yields from thin­ nings w o u l d be treated as cordwood in the estimation of product value. Alt h o u g h this aspect ma y become less r e a l ­ istic as the stand matures, it should suffice for the early thinnings, w h i c h remove the smaller stems, and even with later cuts w h i c h take larger trees, low and cull percentage high, marily for pulpwood. the quality w ould be thus necessitating usage p r i ­ The final yield was considered to be sawtimber, wi t h cordwood from the tops and larger limbs. Hence, part of this assumption was that all owners were aiming toward an eventual crop of quality hardwood sawtimber stumpage or harvested sawlogs. Obviously, this assumption may not be realistic for some owners, because properties change hands, goals ass o c i ­ ated with ownership fluctuate, ogy change, etc. However, product markets and technol­ the evaluation of alternatives using the discounted cash flow technique, resulted in a m e a ­ sure of expected future value in 1962, when the initial decision had to be made. This expectation about potential returns must form the basis for present-day decision-making concerning future changes in management objectives or p r o p ­ erty useage (e.g.# disposal of forest land by selling or clear i n g ) ; it becomes a form of opportunity cost when d e v i ­ ations are made from the optimum schedule. It was questionable whether the stumpage-sale alter­ native should be included# as much past research showed this to be less profitable than marketing products at roadside or mill site However# (Filip and Leak# 1962; Aughanbaugh# 1963). at least one investigation indicated the opposite case in some instances (Fenton and Broomall# 1963) # and it was quite likely that many owners would sell stumpage re­ gardless of the monetary consequences, because they lack either the time and/or the equipment for harvesting and hauling timber products. For these reasons it was decided that the stumpage provision should be retained. A n o t h e r facet concerned the absence of explicit probability data on the decision tree. In the literature dealing with statistical decision theory and the concepts of decision trees# probability estimates are applied to each chance event. This information is used to obtain the 73 discounted value from each "branch#" and the alternative yielding greatest expected returns mum path to pursue. However# is selected as the o p t i ­ a recent investigation in Christmas tree investment opportunities (Bentley and Kaiser, 1967) # employed the decision tree approach without directly using probability estimates. They were applied implicitly by using average or "most likely" values for certain p a r a ­ meters in the initial solution# w hich was then followed by sensitivity analysis of various factors to gauge their influence on the optimal sequence. This latter approach was followed in the present analysis# using "medium" or "most probable" estimates each parameter in the model's initial solution. means of sensitivity analysis# allowed to vary# sequence. for Later# by certain parameters were to judge the responsiveness of the optimal Such techniques eliminated the need for formally grappling with probability estimates# and they would give a manager some insight as to which factors have the greatest impact# and thus require the most attention in measurement and/or estimation. The -final form of the decision tree used in this vestigation is presented in Figure 6. It contains 30 in­ 74 Decision 1 Decision 2 Decision 3 Decision 4 Decision 3 Chance event S e l l tCom^^ur£lui 1962 No TS I i 1 products Future t h i n n i n g s S e l l l o n v . s u rp lus S e l l ^Convj_ij»ur£lus Cut ond s e l l *products th i n n i n g s S e l l ACP c o s t s h o r in g S e l l 1A ve. p rice Conv s u r p l u s Future t h i n n i n g s S e l l T S Ii n 1962 M arket thinnings S e l l 1 products 1Ave. pr ice io n v _ s u r £ l u s i Cut and s e l l *products Future thinnings 1Ave. p ri c e S e l l No ACP i 1products____ thinnings , o n v . s u r p l u s ■ —Decision point 0—Chance event stems only M arket S e l l 1A v e . price o n v . FIGURE 6 THE D E C I S I O N TREE IN ITS FINAL FORM. 75 "branches," indicative of the alternatives available to each of the 25 owners evaluation began, in the sample. additional assumptions about certain physical and economic aspects, quality, prices, However, before the including mortality, cull, costs, etc., were needed. Rotation Length and Thinning Interval The rotation used in the initial formulation was 120 years. This guideline was consistent with management recommendations for even-aged stands of northern h a r d w o o d s . "Even-aged, sites, second-growth forests, especially those on good can yield high-value products. are mostly yellow birch, beech, Where the species and sugar maple, high-value yields will be associated with long, rotations years) ..." (Gilbert and Jensen, 1958). (100 to 120 This permitted the projection of all referrals at least 20 years future into the (one ownership averaged 93 years of age in 1962). The interval between successive intermediate cuts was 10 to 20 years, and Filip Jensen as advocated b y Arbogast (1963), Eyre and Zillgitt (1958), and Zon and Scholz (1957), Blum (1953), Gilbert and (1929). Gilbert and 76 Jensen (1958) state that most stands composed of sugar maple and other tolerant species will respond to a thinning even after age 60; therefore, all ownerships were considered to be suitable for thinning, even though response might be ne g ­ ligible in some of the older stands. In making each hypothetical cut throughout the pr o ­ jection period, a guideline of 92 square feet of residual basal area per acre was followed Zillgitt, (Arbogast, 1957; Eyre and 1953; Society of American Foresters, 1959) . Mortality After consulting several research reports dealing with mortality (Conover and Ralston, 1951; Eyre and Zillgitt, 1953; Meteer, 1959; Eyre and Longwood, 1953; Leak, 1961; Longwood, 1953; Meyer, 1954; Stott, 1965), 1952, the assump­ tions used in the model were derived primarily from studies conducted at the U. S. Forest Service Northern Hardwoods Research Laboratory in Michigan's Upper Peninsula. Their results indicated that in uncut stands over a period of 20 to 25 years, the mortality loss was nearly 70 percent of the net growth— hence, a net increase in total stand volume of 77 30 percent of the net growth. ent study, However, this seemed a b i t severe. for use in the pres­ Most of the uncut stands at the Northern Hardwoods Research Laboratory were mature or over-mature old-growth northern h a r d w o o d s , whereas ownerships in the present study were immature to mature second-growth stands. Therefore, it was assumed that uncut stands in the study area would lose only 50 percent of the growth to mortality; one-half the projected growth would be lost and the remainder would be the net increase. Eyre and Longwood (19 51) also reported, "... that the average mortality on all the cutting plots was only 1/4 of that in uncut timber is perhaps the most noteworthy fea­ ture of the entire study." tigation, Therefore, in the present inves­ the assumption was made that 1/4 of 1/2, or 1/8 of the growth w ould be lost to mortality when partial cuts were made at relatively frequent i n t e r v a l s . W h e n only one thinning was performed, as in the case of an initial TSI treatment not followed b y future thinning operations, the mortality, although reducing growth by 1/8 after cutting, w o u l d gradually approach the 50 percent loss level in an uncut stand. Therefore, it was decided that a reduction factor of 1/4 should be applied to the growth 78 when a stand received the TSI treatment in 1962# but no additional intermediate cuts in the future. This provided an average b e t w e e n the 1/8 mortality loss corresponding to intensive management# stands. and the 1/2 mortality loss for uncut Examples of the various assumptions concerning mortality are presented in Figure 7. Converting Cubic-Foot Volume to Cordwood or Board Feet In computing the growth for each alternative# cubic-foot volumes were used; however# involving future thinnings# converted to cords# for those schedules the cubic-foot volumes were so that appropriate monetary v a l u a ­ tions could be made. It was assumed that one standard cord would b e equivalent to 92 cubic feet of wood and bark (Gevorkiantz and Olsen# 1955). Therefore# matter to divide the cubic-foot volume deduction) b y 92# it was a simple (less the mortality and obtain the volume in cords at the time a thinning was made. For converting cubic-foot volumes to board feet# yield tables for northern hardwoods in the Lake States by Gevorkiantz and Duerr (1937)# were used. From their SO 110 130 (R) 70 SO •O 100 iio no (R) (a) -j VO so 100 *0 110 130 (R) (d) FIGURE 7. GROWTH FOR A TYPICAL REFERRAL FROM 1962 UNTIL THE END OF THE ROTATION 70 YEARS HENCE, (a) NO TSI IN 1962, AND NO FUTURE THINNINGS; (b) TSI IN 1962, BUT NO FUTURE THINNINGS; (c) NO TSI IN 1962, HOWEVER FUTURE THINNINGS WERE PERFORMED; (d) TSI IN 1962, AND FUTURE THINNINGS. LINE AB IS THE VOLUME AVAILABLE FOR HARVEST AT THE END OF THE ROTATION. 80 information# the following conversion factor for a stand at 120 years of age was obtained: Y = 2.924 X where: Y = the net board-foot volume per acre. X = the merchantable cubic-foot volume per acre for all trees. Changes in Cull Defect Several researchers have discussed the amount of cull expected in old-growth northern hardwood stands and Longwood# Gevorkiantz# 1951; Eyre and Zillgitt# 1946)# 1953; Zillgitt and indicating that the deduction may range from 30 to 50 percent of the gross volume for very defective old-growth s t a n d s ) . ceived some type of partial cut# to 24 percent# (Eyre (45 to 50 percent On areas which re­ the cull varied from 15 and was approximately 3 7 percent on uncut areas. With these findings serving as a rather rough g uide­ line# the following assumptions concerning cull reduction at the end of a rotation were applied: 81 1. If no initial TSI was performed# nings were made# and no future thin­ the deduction for cull at the h a r ­ vest cut w o uld be 3 5 percent. In the case of a referral having more than 3 5 percent cull in 1962# the deduction was increased to 4j3^^rcent. 2. If TSI was performed in 1962# but no intermediate cuts were made in the remaining years# cull deduc­ tion at the time of final cut was 2 5 percent of the gross volume. In the case of a referral having more than 3 5 percent cull in 1962# was increased to 3 5 percent# the deduction so that there would be no change in the projected net volume. 3. In the case of a management schedule with no timber stand improvement in 1962, but with periodic thin­ nings in the future# cull deduction would be 10 percent of the gross volume. In stands where the cull defect was greater than 3 5 percent in 1962# the deduction would be 20 percent of the harvest volume. 4. For ownerships that had TSI in 1962# and would be managed very intensively over the remainder of the rotation# the cull deduction would be 5 percent# 82 except for ownerships where the 1962 level of cull defect exceeded 3 5 percent# where the deduction w o uld be set at 15 percent. Changes in Quality During the stand inventory# each tallied tree was classified b y tree grade# based on the log grade of the butt log. 1962# This distribution was projected "backwards" to assuming no change in the grade proportion of the residual stems during the intervening four years. two major alternatives involving no TSI# For the the material actu­ ally removed in 1962 was added# with the simplifying assump­ tion that it was all in tree grade 4. The next phase was to establish log-grade conversion factors for each of the three tree grades. in Northern Michigan# Meteer (1966) In a recent study constructed tables show­ ing the percentage of each log grade in a given tree grade for individual species and species g r o u p s . The percentages from his report which were used in the present study are shown in Table 21. 83 Table 21.— Log grade yield from trees of given butt-log tree grades for sugar maple and "other hardwoods" Tree Grade Species Proportion of the volume by log grade: #2 #1 - sugar maple Meteer, --------- 1 2 3 4 other hardwoods Source: 47.4 1 2 3 4 #3 Percent - 33.8 68.4 4.4 ----- ----- 59.1 ----- 28.3 68.3 ----- ----- —— —— — —— — 12.6 31.7 100.0 100.0 1966. With these factors, the board-foot volumes b y log grade and species at the beginning of the projection ment) 18.8 31.6 95.6 100.0 (invest­ period in 1962, and at the end of the rotation were c om­ puted for each of the four major alternatives. In reference to the assumptions dealing with cull defect, mortality, and quality, Farrell (1964) has stated: "Such adjustments are somewhat arbitrary, but are necessary to reduce gross yield estimates to realistic levels before applying value. For specific tracts, foresters may apply experience values of their own choice." Other authors 84 advancing a similar viewpoint made the following statement: "Projection of quality may sometimes be difficult because information about the effect of time and treatment on quality is less abundant than information on volume and size. it is necessary to make these projections, basis is at best doubtful. subjective one" even when the An objective estimate, though b a s e d on limited data, Yet even is better than a completely (Marty, ert a^L. , 1966) . The only available information on quality changes following partial cutting in northern hardwoods was the 20-year study b y Eyre and Zillgitt (1953) which compared the results of nine different forms of thinning with an u n ­ cut reserve area. Their findings indicated that the volume in grade 1 logs remained fairly constant, whether the stand was thinned or not. regardless of On the other hand, thinning to this level increased the volume in grade 2 logs by 15 percent, and decreased the grade 3 category b y approx­ imately 15 percent. This information provided a rather gen- eral guideline for the following grade change assumptions: 1. If there were no initial TSI and no future thinnings, there w o uld be a 5 percent increase in the amount of material in log grade no. 2, and a 5 percent decrease in grade 3. occur, It was assumed that some change would even though the stand received no cultural treatment; primarily due to the increase in size of individual t r e e s . Improvement in grade through in­ creased size w ould slightly offset any decline in quality caused b y increases in cull defect. The in­ crease in defect would be reflected more by an in­ crease in cull, rather than a change in log grade. If there were no initial TSI, but future thinnings were applied, there would be a 15 percent increase in the volume of grade 2 logs, and a 15 percent d e ­ crease in the grade 3 category. If initial TSI were applied but no future thinnings, there would be a 10 percent reduction in log grade no. 2, and a 10 percent reduction in log grade no. 3. With initial TSI and future thinnings, there would be a 15 percent improvement in log grade no. 2, and a 15 percent decrease in log grade 3. it was Thus, assumed that a TSI operation followed by periodic thinnings would result in the same grade distribution 86 as periodic thinnings without an initial TSI treatment. Once the projection of volume was accomplished, based on the grade distribution in 1962, the quality im­ provement factors were applied to obtain an estimate of net board-foot volume in each species-log grade category at rotation age. Determination of the Additional Volume in Topwood Wh e n the projected cubic-foot volume was converted to board feet per acre at the end of the rotation, it was possible to determine h o w much additional cordwood volume would be available in the tops and limbs of sawlog trees, using the procedure recommended b y Chase and Gevorkiantz (1953), as outlined in an earlier chapter (page 33). To facilitate this conversion on a per acre basis, using the board-foot volume at the time of final harvest, the follow­ ing regression equation was computed and utilized: Y = 0.746 + 0.000367 X where; Y = the additional cordwood volume per acre in topwood. X = the net board-foot volume per acre. Computational Steps in Volume Projection The calculations of volume per acre at the time of each proposed thinning# and at the time of final harvest# for Refer­ ral No. 2G01# are presented in Tables 22,to 25. Percentages in these computations indicate the volume in each species category, and changes in species composition induced by each thinning operation# since the cuttings were designed to encourage high-value species and to remove those of lower value. The percentages, which changed after each cut was made# were u t i ­ lized to determine the volume distribution b y species before the next scheduled thinning. For example# sugar maple in Referral No. 2G01 would increase from 23.7 percent to 81.3 percent of the total volume over the remaining years of the rotation# schedule of intermediate cutting were fallowed each proposed thinning# (Table 24). For data are given for the volume per acre before thinning# volume removed# acre. if the and the residual volume per The board-foot volumes are not adjusted for the assumed Table 22.— Computational steps in volume projection and calculation of final yield by species and log grade, for Referral No. 2G01, with no TSI and no future thinnings, per acre basis. Age Ave. Ht. Basal Area Gross Volume Mor­ tality Gross Vol. Less Mortality Yrs. Ft. Sq.Ft. Cu.Ft. Cu.Ft. Cu.Ft. 51 60 117 1,928.4 120 89 386a 9,437.1 3,754.4 Volume by SpeciSs— Cords & Percent Sugar Bass­ Entire Elm Beech Maple wood Stand 1,928.4 100% 21.0 23.7% 5.0 53.5% 11.2 14.7% 3.1 8.1% 1.7 5,682.7 100% 61.8 23.7% 14.6 53.5% 33.1 14.7% 9.1 8.1% 5.0 5.8 1.4 3.1 0.8 0.5 Additional volume in topwood— -cords*5 Distribution of final board-foot yield by tree and log grades based on the initial distribu­ tion in 1962: Species Sugar Maple Basswood Elm Beech Total Total Net Volume0 3,938 8,890 2,443 1,345 16,616 Volume by Log Grades Volume by Tree Grades 1 2 ---- ---- 3,467 4,703 ------- ------- 3,467 4,703 3 4 1 2 3,938 ---- ---- ---- 2,049 4,193 ------- 2,443 1,345 ------- r^ — — ---- 720 7,726 2,049 4,193 ---- 720 aThis represents the basal area corresponding to the projected volume, before a reduction for mortality had been applied. ^Cordwood available at the time of final harvest in addition to the sawtimber volume. Based on the cull defect percentage in 1962. 3 3,938 2,648 2,443 1,345 10,374 Table 23.— Computational steps in volume projection and calculation of final yield by species and log grade, for Referral No. 2G01, with TSI in 1962, but no future thinnings were performed, per acre basis. Age a Yrs. 51l 51c 51k 120 Ave. Ht. Basal Area Gross Volume Mor­ tality Gross Vol. Less Mortality Ft. Sq.Ft. Cu.Ft. Cu.Ft. Cu.Ft. 60 60 60 117 37 80 1,928.4 514.2 1,414.2 89 Vv .. .D 294 Volume by Species— Cords & Percent Sugar Bass­ Entire Elm Beech wood Maple Stand 1,928.4 514.2 1,414.2 - 7,709.1 1,573.7 6,135.4 Additional volume in topwood— -cordsc 14.7% 3.1 3.1 5.0 53.5% 11.2 0.8 10.4 --- --- 100% 66.7 32.5% 21.7 67.5% 45.0 ----- ----- 7.1 2.3 4.8 --- --- 100% 21.0 5.6 15.4 23.7% 5.0 --- 8.1% 1.7 1.7 Distribution of final board-foot yield by tree and log grades based on the initial distri­ bution in 1962: Species Total Net Volume Sugar Maple Basswood Total Volume by Log Grades Volume by Tree Grades 1 2 3 5,831 12,109 4,723 6,406 980 17,940 4,723 6,406 980 4 1 2 3 2,791 5,712 5,831 3,606 2,791 5,712 9,4.37 5,831 5,831 ai, C, and R indicate ijiitial stand conditions, material cut, and residual stand conditions respectively at a given age. ^This represents the basal area corresponding to the projected volume, before a reduction for mortality had been applied. c Cordwood available at the time of final harvest in addition to the sawtimber volume. ^Based on the cull defect percentage in 1962. Table 24.— Computational steps in volume projection and calculations of final yield by species and log grade, for Referral No. 2G01, with no TSI in 1962, however, future thinnings were performed, per acre basis. . a Age Ave. ht. Basal area Gross Volume Ft. Scr.ft . C u .f t . Mortality Gross vol. less mortality Volume by species-cords & percent Entire Stand Sugar Maple 1,928.4 100% 21.0 23.7% 5.0 53.5% 11.2 14 .7% 3 .1 8.1% 1.7 2,321.2 678.5 1,642.7 100% 25.2 7.3 17.9 23.7% 6.0 53.5% 13.5 1.6 11.9 14 .7% 3 .7 3 .7 -— 8.1% 2.0 2.0 2,908.9 1,038.7 1,870.2 100% 31.6 11.3 20.3 33.5% 10.6 3,229.7 1,157.3 2,072.4 100% 35.1 12.6 22.5 3,510.7 3,716.2 152 205.5 120 89 Additional volume in topwood - cordsc 100% 38.2 5.1 Yrs. 60 51 C u .f t . 1,928.4 117 60c 60 r 80 8 °C 80 r 100 ioo: 100 R 65 65 65 74 74 74 82 82 82 152 60 92 152 60 92 152 60 92 2,714.0 392.8 ------------ 1,642.7 3,089.8 180.9 ------------ 1,870.2 3,423.9 ----------- 2,072.4 194.2 Elm Beech C u .f t . V 60 t Basswood ------ 6.0 66.5% 21.0 11.3 9.7 -— - -— - -— ----- -— - -— - -— ----- 18.3 47.8% 16.8 12.6 4.2 81.3% 31.1 4.1 18.7% 7.1 1.0 ------ 10.6 52.2% 18.3 ------ -— - —— - -— - -— -— - Table 24.— (Continued) Distribution of final board-foot yield by tree and log grades based on the initial distribution in 1962: Species Sugar maple asswood Total Total net volume Volume by tree grades: 1 2 3 4 Volume b y log grades: 1 2 8,345 8,345 8,345 3 1,920 749 1,016 155 433 906 571 10,265 749 1,016 155 8,345 433 906 8,916 a i» C, and R indicate jLnitial stand conditions, material cut, and residual stand conditions respectively at a given age. ^This represents the basal area corresponding to the projected volume, before a reduction for mortality had been applied. c Cordwood available at the time of final harvest m the sawtimber volume. Based on the cull defect percentage in 1962. addition to Table 25.— Computational steps in volume projection and calculations of final yield b y species and log grade, for Referral No. 2g 01, with TSI in 1962, and future thinnings, per acre basis. A a Age Yrs. 51T 51c 51P 7 0 I 70c 70r 90 90 9 0 P. 120 Ave. ht. Basal area Gross Volume Ft. S q .ft . C u .f t . 60 60 60 70 70 70 78 78 78 89 117 37 80 _ 139 47 92 154 62 92 185 Mortality Cu.ft. 1,928.4 514.2 1,414.2 Vi D 2,866.7 181.6 ------------------ --------------- 1,897.4 3,539.1 -------- 205.2 ------- 2,114.2 4,850.9 342.1 Additional volume in topwood - cordsc Gross vol. less mortality Volume b y species-cords & percent Entire Stand Sugar Maple 1,928.4 514.2 1,414.2 100% 21.0 5.6 15.4 23.7% 5.0 2,685.1 787.7 1,897.4 100% 29.2 8.6 20.6 32.5% 9.5 3,333.9 1,219.7 2,114.2 100% 36.2 13.2 23.0 4 6.1% 16.7 4,508.8 100% 49.0 Basswood Elm Beech C u .f t . 6.6 53.5% 11.2 0.8 10.4 14.7% 3.1 3.1 ------- ------- 67.5% 19.7 8.6 11.1 ------- ------- ------- ------- ------- ------- ------- ------- ------- ------- --- ------- ------- ------- 16.7 53.9% 19.5 13.2 6.3 ------- ------- 7 2.6% 35.6 2 7 .4% 13.4 ------- ------- ------- ------- 4.8 1.8 ------- ------- ------- 5.0 ------- 9.5 ----- 8.1% 1.7 1.7 Table 25.— (Continued) Distribution of final board-foot yield by tree and log grades based on the initial distribution in 1962: Species Total net volume Volume b y tree grades: 1 3 2 4 1 1 2 3 833 1,704 1,075 833 1,704 10,647 9,572 Sugar maple 9,572 Basswood 3,612 1,409 1,911 292 13,184 1,409 1,911 292 Total Volume by log grades: 9,572 a i, C, and R indicate j.nitial stand conditions, material cut, and residual stand conditions respectively at a given age. ^This represents the basal area corresponding to the projected volume before a reduction for mortality had been applied. Q Cordwood available at the time of final harvest in addition to the sawtimber volume. ^Based on the cull defect percentage in 1962. 94 changes in cull and quality; however# it is subdivided by tree grade and log grade# b a sed on the 1962 distribution. The next step incorporated the various assumptions concerning cull defect changes and log-grade improvement (Table 26). Although the changes are presented in Table 26, they were actually applied in the computer program used in the economic evaluation. This was much simpler, eliminated many preparatory calculations. pected changes# since it With these ex­ the assumptions involving physical yield data were concluded# and the remaining aspects of model formulation entailed various economic considerations. Periodic Cost Assumptions The completed decision-tree model (Figure 6) consid­ ered two alternative methods that an owner might use for sel­ ling his timber products: or# 1) Marketing sawlogs and cordwood, 2) Selling the material as stumpage. The harvesting costs would be quite different for the two possibilities. If the decision were made to market the products at either a sawmill or pulpmill# of felling# bucking# skidding# the owner would incur the costs loading# hauling# and unloading# Table 26.— Volume per acre at rotation age for each of the four major alternatives for Referral No. 2G01, by species and log grade after cull and quality adjustments were made. Net volume by alternative cutting schedule: Species and Log Grade No TSI and no future thinninqs No TSI, TSI in 1962 but but no future thinnings future thinninqs - - - - - Board Feet - - - - TSI in 1962 and future thinnings Sugar maple: Grade 1 2 164 3,116 1,444 8,186 561 5,048 1,749 9,910 Basswood: Grade 1 2 3 1,707 3,603 2,096 511 1,145 560 2,685 5,842 3,122 1,015 2,271 1,113 Grade 3 2,035 ---- ----- ----- Grade 3 1,120 ---- ---- ----- Elm: Beech: Total adjust ed net volume 13,841 11,846 17,258 16,058 or else enlist the services of a contractor. The per unit costs for each operation in the production process are pre­ sented in Table 27 . Although a recent study was made of timber har v e s t ­ ing costs in northern hardwoods (Gardner/ mation from the Service Forester Handbook 1966) # the infor­ (USDA/ 1961)/ was considered to be more applicable# because only the data available for consideration by the owner in 1962 would be relevant# and information from the Handbook would usually provide the basis for actual cost determination b y the con­ sulting Service Forester for ACP cost-sharing purposes. Hauling and unloading costs were based on a differ­ ential rate depending on the type of road surface (Table 28). Rates were in dollars per unit of volume per unit of distance therefore# accurate determination of the mileage from each ownership to a market location was needed. The market for sawtimber was assumed to be the closest sawmill to each property. It was assumed that all pulpwood would be sold to the mill in F i ler City. The requisite mileage was ascer­ tained from county maps b y road-surface category (Appendix 2) 97 Table 27.— Production costs on a per-unit basis for an owner choosing to market sawlogs and cordwood at the mill site. Cost Ope ra L ion Sawtimber per MBF Pulpwood per cord $5.99 variable $4.28 variable Skidding3 5.70 variable 3 .71 variable Loading 1.40 variable .47 variable Hauling and unloading F i x ed— based on the mileage and type of road surface Fixed— based on the mileage and type of road surface Total logging cost Summation of the previous items Summation of the previous items Marking# felling# and bucking# including supervision Overhead (20 percent of the logging cost) Total production cost Source: USDA# Fixed Summation of the previous items Fixed Summation of the previous items 1961. a The cost of $5.70 represents the expense of skidding sawlogs with a small tractor# on slopes of 10 percent or less# for a distance of 200 feet# and for a stand with an average D B H of 16 i n c h e s . i. See Table 28. 98 Table 28.— Schedule of hauling and unloading costs Cost ^ .. Operation Sawtimber: ($7.00/hour and a load of 2 MBF) Per MBF per mile Standby# delay# and unloading Pulpwood: ($7.00/hour and a load of 6 cords) Per cord per mile $1.40 $ .47 .16 .28 .44 .88 .05 .09 .15 .29 Hauling: Highway (45 mph) Main haul (25 mph) Secondary (15 mph) Woods road (8 mph) Source: a USDA# 1961. . The minimum hauling costs including unloading m $2.00 per cord and $4.00 per MBF. 1961 were The computations of harvesting costs for Referral No. 2G01 are as follows: 99 Sawtimber, per M B H : Marking, bucking, felling, and including supervision ............. $5.99 S k i d d i n g .......................................... 5.70 L o a d i n g .......................................... 1.40 Hauling and unloading: Standby, delay, and unloading . . $1.40 Highway (6 m i l e s ) ..................... 96 Main (6 m i l e s ) ....................... 1.68 Secondary (.5 m i l e s ) .............. .22 Woods road (1 m i l e ) .............. .88 Total . . . . 5.14 Total logging c o s t ........... $18.23 Overhead (20 percent of the logging cost) Total production cost Pulpwood, . 3.65 . . . . $21.88 per c o r d : Marking, bucking, felling, and including supervision ............. $4.28 S k i d d i n g ..........................................3.71 L o a d i n g ....................................... .47 Hauling and unloading: Standby, delay, and unloading . . $ .47 Highway (64.5 miles) . ............ 3.22 Main (1 m i l e ) ..........................09 Secondary (.5 m i l e s ) .............. .08 Woods road (1 m i l e ) .............. .29 Total . . . .4.15 Total logging c o s t ............. $12.61 Overhead (20 percent of the logging cost) Total production cost . . . . . 2.52 $15.13 100 If an owner decided to sell stumpage# he would still have the responsibility of marking timber for cutting# supervising the harvesting operation. and Such items# whether done b y the owner himself or b y a professional consultant# would involve a cost that must be included in the analysis. In the present study it was assumed that marking and super­ visory costs w ould be $1.50 per MBF for the final harvest of sawtimber# and $.40 per cord for each intermediate cut (Marty and Trimble# 1967). The sawtimber cost was applied to the gross volume removed at the time a harvest cut was made. Costs of Timber Stand Improvement A wo o d l a n d owner contemplating timber stand improve­ ment# was assumed to have four possibilities available. The associated costs and their computation differ somewhat for each alternative. One alternative would be a TSI operation completely financed b y the owner# where the marked trees were either cut and left where they fell# or where the undesirable stems were girdled or treated with silvicide. The actual cost for 101 such a program was determined from the Service Forester Handbook (USDA, 1961), which provided data on TSI cost per acre per square foot of basal area to be removed. For Referral 2G01, the computation of total cost per acre for this option proceeded as follows: DBH class Inches Basal area removed Sq. Ft. Cost per square foot of basal area removed Total cost per acre 6 10 18 25 6 6 $.588 .3-62 .214 $14.70 2.17 1.28 Total Thus, 37 $18. 15 if the owner of Referral No. 2G01 had chosed to fi­ nance timber stand improvement from his own pocket, unwanted trees were not sold for pulpwood, and the the cost would be $18.15 per acre. It was possible, however, that an owner might have been able to cut and sell the undesirable stems, and there­ fore, generate a monetary return which might offset the cost involved. This opportunity would have hinged primarily on prevailing market conditions, and the costs would have been computed in the same manner as for other commercial thinnings If the material was marketed at a mill site, the total 102 production costs would be applied to the volume removed* or# if a stumpage sale was selected b y the owner# marking and supervision would be involved. the costs of In the case of Referral No. 2G01# where 5.6 cords per acre were removed in 1962# the total cost of TSI per acre would be; 5.6 X $15.13 = $84.73 per acre if the cordwood was marketed at a mill site. 5.6 X $ .40 = $2.24 per acre if the cordwood was sold as stumpage. Actually# the option taken b y all referrals study area was cost-sharing payments program. for TSI under the ACP In general# A C P payments are 80 percent of the Service Forester's estimate of total cost per acre# the payment is not to exceed $25.00 per acre. Michigan# in the and However# in the Department of Natural Resources# which admin­ isters the program on a local level* has established a sys­ tem of reducing the total estimated cost when merchantable products will be obtained from the thinning. Thus, an 80 percent payment could not be realized by ownerships which removed a volume greater than the specified minimum? nearly all sampled referrals did not receive the full 80 percent remuneration. 103 The appropriate payment schedules for 1962 were ob­ tained from the Michigan Department of Natural Resouces. "Generally, volumes of less than 2 standard cords per acre will not be considered merchantable. Otherwise, the fol­ lowing is suggested as the amount to reduce the total esti­ mated cost in computing the Federal Cost Share" (Haskins, 1961): Cords per acre Approximate allowance per acre $ 0.00 1.00 1.50 3.00 2 3 4 5 and over -$ 1.00 - 1.50 - 3.00 - 4.00 Although the actual cost of a TSI operation may differ from the estimated expense, the Service Forester computed each cost-share on the basis of his own determina­ tion of total cost. would then The reduction for merchantable volume be applied to his estimate, as described above. The Michigan D e p artment of Natural Resources used the fol­ lowing schedule for estimating costs of timber stand improve­ ment prior to 1964 (Haskins, 1961): 104 $1.25 per square foot of basal area— saplings 1 to 5 inches DBH cut or girdled. $ .75 per square foot of basal area— poletimber 5 to 11 inches D B H cut or girdled. $ .50 per square foot of basal area— sawtimber over 11 inches DBH cut or girdled. The federal cost-share payment was equal to 80 per­ cent of the difference between total estimated cost and the reduction for merchantability. For Referral No. 2G01# the cost-share was calculated as follows: 1. Estimate total cost per acre: Size class Saplings Poletimber Sawtimber Total 2. Basal area Sq. ft. — Cost per sq. ft. Total cost per acre --- ---- 31 $.75 $23.25 6 .50 3.00 37 $26.25 Determine the reduction for merchantable products; 5.6 cords were cut; hence# the reduction would be $3.50 per cord# or a total reduction of $3.50 X 5.6 = $19.60 per acre. 105 3. Determine the federal cost-share: The total estimated cost minus the reduction allow­ ance: $26.25 - $19.60# leaves $6.25; and 80 per­ cent of $6.25 is $5.32. This is the cost-share p ay­ m e n t per acre for the owner of Referral No. 2G01. Once the cost-share had been computed# it was deducted from the actual cost per acre# to find the true cost of the owner's TSI operation. For example# if the owner of Refer­ ral No. 2G01 had chosen to obtain ACP reimbursement for deadening the undesirable stems, the true cost would equal the actual cost of eliminating the trees either b y cutting# girdling# or treating with silvicide# minus the cost-sharing payment: $18.16 - $5.32# or $12.83 per acre. On the other hand# if the owner had decided to cut and sell the marked material# his true cost would have been: $84.73 - $5.32# or $79.41 per acre if the pulpwood was marketed at the mill site. $2.24 - $5.32# or - $3.08 per acre if the pulpwood was sold as stumpage. This re­ sulted in a negative cost# thus it was actually an income of $3.08# due to the federal cost-share. In all cases# the actual cost of timber stand improve­ ment as determined from information in the Service Forester Handbook was lower than the actual Service Forester's estimate. 106 This fact has caused the Michigan Department of Natural Resources to revise its cost estimates downward beginning in 1961. The latest reduction in 1964 dropped the cost in each size class b y $.20 to $.25 per square foot of basal area (Haskins, 1965), which now makes the actual costs of TSI and the basis for determining cost-sharing payments closer together. A similar discrepancy between actual costs and ACP-estimated costs was also observed in a Wisconsin study of timber stand improvement b y Montambo and Sylvester (1965) . Their findings for three woodlots ranging from 7.5 acres to 8.8 acres in size, indicated the actual ex­ pense of TSI b y girdling was from 8 to 43 percent below the ACP estimate. Annual Cost Assumptions With the computer program used in the evaluation phase of this study (Row, 1963), it was possible to investi­ gate several annual cost assumptions simultaneously. Also, it was permissable to start with a base annual cost, and to increase it every year by a predetermined p e r c e n t a g e . 107 C o n s e q u e n t l y # the following assumptions were selected for evaluation# representing a low# medium# Beginning base annual cost Low and high annual cost. Annual Increase Applied to the base Percent 0 $0.00 Medium 1.00 1 High 1.50 3 The annual cost included taxes, tection# administration, fire pro­ etc.# w hich would be paid each year regardless of whether any cultural activities were performed or not. The annual increase was a simple interest rate# and in the case of the "medium" assumption# would be $1.00 the first year# $1.02 in the third year# $1.01 the annual cost in the second year# and so on for the entire investment period. Selling Price Assumptions The various prices used were obtained from several sources (Michigan Department of Conservation# sity of Wisconsin# 1963; Univer­ 1967; Wisconsin Department of Agriculture# 108 1963; Office of Iron Range Resources and R e h a b i l i t a t i o n # 1965; Stott# 1965) which were coalesced into a single price for each species and grade category (Tables 29 and 30). Major emphasis was given to the 1963 data from the M i c h i ­ gan Department of Conservation (presently the Department of Natural R e s o u r c e s ) , which were published for the n orth­ ern portion of Michigan's Lower Peninsula. The various opportunities concerned with selling stumpage# instead of marketing cut products# were handled in a twofold manner with respect to stumpage price. first was termed an average price; The i.e., the price which usually prevailed in the study area (Tables 29 and 30). The second set of stumpage prices was calculated in the "textbook" plus fashion. (or residual) They were computed as conversion su r ­ prices; i.e.# what was "left over" after the costs of production plus a margin for profit were d e ­ ducted from the final selling price. was calculated in the following manner 1. Conversion surplus (USDA# 1961): Calculation of Margin for Profit: Margin for Profit = 10 percent of the selling price of final product which in this case was either sawlogs or pulpwood . 109 Table 29.— Prices for sawlogs delivered at the mill site, and for sawtimber stumpage, per MBF. Species Sawlog prices by log grade: 1 2 3 Stumpage prices b y log grade: 3 1 2 $ 70 $40 $25 $19.80 $10.00 $1.65 Aspen 40 30 15 6 .00 3 .00 .50 Basswood 85 50 25 24.00 12 .00 2 .00 Beech 60 30 20 15.60 7.75 1.30 Yellow birch 140 60 25 10 .80 5.50 .90 Black cherry 85 45 30 24.00 12 .00 2 .00 Elm 60 40 25 19 .80 10.00 1.65 H em l o c k 3 --- 45 — 10 .00 ---- Hard maple 100 60 35 33 .00 16.50 2.75 Red oak 85 50 30 15.00 7 .50 1.25 Soft maple 70 40 20 13 .20 6.75 1.10 Ash Source: a Michigan Department of Conservation (1963-1965); Minnesota Forest Products Marketing and Pricing Review (1965); Wisconsin Department of Agr i c u l ­ ture (1963); Stott (1965). Hemlock was not priced by g r a d e s . 110 Table 3 0 . — Prices for pulpwood delivered at the mill site» and for pulpwood stumpage# per cord. Delivered at the mill Species Sold as Stumpage $14.50 $1.30 Basswood 14.00 .80 Hemlock 19.00 3 .00 Mixed hardwoods 16.00 1.00 Oak 15.00 1.00 Aspen Source: Michigan Department of Conservation (1963 1965) ? Minnesota Forest Products Marketing and Pricing Review (1965); Wisconsin D e p a r t ­ ment of Agriculture (1963); Stott (1965). Ill For example: the selling price of grade 1 ash sawlogs was- $70 per MBF (Table 29)» hence the margin for profit would be: 10% of $70 = $7.00 2. Calculation of total operating costs: Total operating costs = total production costs + margin for profit; and# to continue the example# using cost figures from Referral No. 2G01: Total operating costs = $21.88 + $7.00 = $28.88 3. Calculation of the conversion surplus stumpage price per unit of v o l u m e ) : (i.e.# the Stumpage price = Selling price - Total operating costs = $70.00 - $28.88 Stumpage price = $41.12 per MBF The calculation of conversion surplus resulted in a considerably higher stumpage price than was usually paid on the average; e.g.# $41.12 compared to $19.80 (see Table 29). However# w i t h pulpwood# because of the cost structure involved# the reverse was often noted; i.e.# average stumpage price was higher than conversion surplus for some species. As with the annual cost assumption# program prices. (1963) Row's computer facilitated investigating various changes To provide a low# medium# in and high range in expected 112 future prices, differing annual-percentage changes were applied to the base price for each species-grade category. The following changes were applied, and permitted some insight into the model's sensitivity to potential v a r i a ­ tion in price: Annual increase applied to _______ the base price_______ Sawtimber Percent Pulpwood Percent Low 0 0 Medium 1 1/2 High 2 1 To simplify matters, the changes were allocated uniformly to each species and grade combination. C H A PTER VIII EVALUATION OF THE DECISION-TREE M O D E L The Computer Program The computer program published b y Row (1963) was used to evaluate each "branch" of the decision tree. sequent to Row's original publication# certain modifications Sub­ the program received (Marty# e £ a l .# 1966) which increased its sophistication and computational capacity. its use in the present investigation, Prior to the program was streamlined somewhat to save compilation time on the com­ puter# and the output format was modified to minimize the lines of print and number of pages (see Appendix 4). The program's structure permitted simultaneous evaluation of six alternatives from one data deck. fore# T h ere­ five sets of data cards were required for each refer­ ral to accomodate the complete schedule of 30 a l t e r n a t i v e s . The data cards, mation# containing both physical and economic infor­ numbered nearly 4,000 for the entire analysis. 113 114 Measure of Effectiveness The measure of effectiveness was the internal rate of return (IRR). This is the compound interest rate which equates the discounted value of all future returns to the discounted value of all future costs; i.e./ generates a present net worth of zero. the rate which This criterion enables the analyst to rank various alternatives on the basis of their financial desirability; the higher the IRR# the more attractive the investment. The essence of the evaluation phase was to compute an internal rate of return for each alternative under "medium" conditions for all parameters. This established rates of return which could be expected as payoffs for each of the 30 "branches" on the decision tree. The "branch" possessing the highest IRR value is the one which should have been followed# if it can be assumed that the "medium" or average conditions were valid. Once various alternatives are ranked in descending order on the basis of their rates of return# a decision­ maker can then guage the relative desirability of all o p por­ tunities. Such a ranking w ould permit hi m to see the 115 financial loss# in terms of a percent# that would result if he were to pursue another alternative in lieu of the optimal c h o i c e . The Initial Solution Results of the initial solution for average or "medium" conditions are presented in tabular form for all alternatives or "branches" In several tables for each referral in Table 31. in this chapter# category of "cut-leave" is used. and Appendix 3# the This mere l y refers to all removal methods which simply deaden the undesirable stems in place# with o u t any utilization or sale of the material thus eliminated from the stand. Although the optimum alternative varied somewhat from ownership to ownership# trends. the results indicated certain This was especially true when the top five alter­ natives from each referral were considered. To extract meaningful information from the initial results, the values were considered in terms of an initial solution (IS) matrix. The matrix dimensions were 30 x 25# representing the 30 al­ ternatives and the 25 referrals, for a total of 750 cells. 116 Table 31.— Internal rates of return for each referral for the 30 alternatives, under "medium" or average conditions for all parameters. Alternative I. (A) 2G02 2G03 4.6 4.8 6.6 1.6 3.6 1.6 3.2 3.6 5.8 5.2 8.4 1.4 3.0 1L04 Referral No. 1L05 1L06 2W07 2G08 2W09 2G10 4.4 2.0 No TSI in 1962 Future Thinnings (1) Market Products (2) Sell Stumpage A. Ave. Price B. Conv. Surplus 6.4 3.2 CO m No Future Thinning (1) Market Products (2) Sell Stumpage A. Ave. Price B. Conv. Surplus CO RQ.BUCJ5 (2) SILL STUMPAGE A. AVI, PRICE B. CONY, SURPLUS I I , TSI I N 1962 (A) NO FUTURE THINNINQ MEDIUM I. 3,2 0,2 0,2 0,2 2,2 1,6 5,2 0,2 1,« 1,0 3,2 0,2 0,2 0,4 0,2 4,2 3,4 A 4,4 0,2 0,2 0,2 0,2 0,2 0,2 0,« 0,2 1.6 1,0 4,0 1,6 3,2 2,4 A 3,2 2,2 1,6 3,6 2,4 5,2 0,2 0,2 0,2 0,2 I,4 0,6 A l,4 2,0 li4 A 2,2 3,6 2,8 A 3,6 MARKET products................. A»NO ACP. CUT«SBLL B-ND ACP, CUT-LBAVE C*ACP, CUT»SELL D*ACP,CUt-LEAVE (2) SELL STUMPAOE A. AYE,.. PRICE 1-NO ACP, BUT*SELL 2-NQ ACP, CUT-LEAVE S.ACP, CUT»SBLL 4 . ACP, CUT« B, CONY, SURPLUS 1»NQ acpv i ut - sell 2.N0 acp; BUT*LEavE 3-ACP. CUT-SELL 4-ACP, CUT-LBAVE (B) FUTURE THINNINGS (1) MARKET PROOUCTS A?NO ACP, CUT*SELL B.NO acp, cut- lbave C-ACP, CUT*8EU D-ACP, CUT-LEAVE (2) SELL STUMPAGE A, AVE, PRICE A*NO ACP. fUT-BELL 2-NO ACP, OUT'LEAVE 3-ACP, CUT-SELL 4 . ACP, CUT*LEAVE B, CQNV, SURPLUS 1-NO ACP, CUT-SELL 2.N0 ACP, SUT-LEAVE 3-ACP,CUT-SELL 4-ACPi CUT-LBAVE V VI, ...........( 1 ) 0,2 1.6.7 TABLE B. REFBRRAL NO, 2W09, SENSITIVITY ANALYSIS OF THE SELLING PRICE ASSUMPTION, VALUES ARE INTERNAL RATES OF RETURN FOR BACH OPTION, Low I , NO TSI IN 1962 J A). JO., JFUlUfit JHj NNJJG (1) MARKET PROOUCTS (2) SELL STUMPAOE A, AVE, PRICE r.CONV, SURPLUS ( B) FUTURE THINNINGS (2) SELL STUMPAGE A, AVE, PRICE B, CONV, SURPLUS I I , TSI IN 1962 U) MO FUTURE THINNING J .D MIMJEI PROOUPT?,..... A.NO ACP, CUT-SELL B-NOACP, CUTiLEAVf C-ACP, CUT-SELL D-ACP, CUT-LEAVE (2) SELL STUMPAOE A, AVR* PRICE 1 . NO acp; ...CUT"SELL 2•NO ACPi SUJ • LEAVg 3-ACP* CUT-SELL 4-ACP, CUT-LEAVE B, CONV, SURPLUS 1-NO ACPL CUT-SELL 2i NO” ACP{...BuT-LEAvE 3-ACP, CUT-SELL 4-ACP, CuT-LEAv'E IB) FUTURE THINNINGS (1) MARKET PROOUCTS A-NO ACP. CUT-SELL I^NFACP, CUT-LEAVE C-ACP, CUT-SELL O-ACP,CUT-LEAVE (2) SILL STUMPAGE A, AV§, PRICE 1-NO ACP* CUT-SELL 2.N0 ACP,BUT-tEAVE 3-ACP, CUT-SELL 4-ACP, CUT-LEAVE B, CONV, SURPLUS 1-NO ACPV BUT-SELL 2-NO ACP1, BUT-LEAVE 8-ABP,CUT-SELL 4-ACP, CUT-LEAVE medium HIGH 0,2 4,4 6,0 0,2 1,8. 0,2 3,6 6,4 3 *6 7 *8 M VO,8 0,2 1,4 1,4 2,8 2,0 1,2 2,0 2,2 6,2 4,8 6,2 6,6 7,6 0,2 0,2 0,2 0,2 2,4 1,4 2,4 2,6 3.4 2.4 3.4 3,8 3,6 2,6 3,6 4,0 5,0 3,8 5,o 5,4 6,0 4,4 3,0 4,4 5,0 0 4 5,8 8,4 8,8 11,4 0,2 0,2 q,2 0,2 2,4 1,2 2,4 2,8 2,0 3,6 2,6 3i§ 3,8 i,4 2,0 2,2 2.8 3,8 6,0 7 ,4 8,0 }•* 6,0 6.4 j h 13,8 3.6 2,2 3.6 4,2 4.4 3 4 4.4 4 6 table c. referral no, ?G10, sensitivity a * a l m i o £ the sell iNfi h m assumption, values are internal ......................RATIt ftF R|TURN FOR..BACH..OPTION, LOW medium HJG! I, NO TSI I N 1962 . (1) MARKET PRODUCTS .... .(.21 SILL STUMPAOE A, AVS, PRICE t.CONV, SURPLUS future thinn I nos MARKET PRODUCTS A.NO ACP, CUT-SELL "SLNO acp *CUT-LEAVE C-ACP; CUT-SELL O-ACp, CUT-LEAVE (2) SELL STUMPAOE A, AVE, PRICE 1-NO ACP, CUT-SELL S^NiTAcp; WUT*LEAVE 3-ACP, CUT-SELL 4-ACP, CUT-LEAVE B, CONV, SURPLUS 1-NO ACP, SUT-SELL 2-NO ACP, SUT-LEAVE 3-ACP,CUT-SELL 4-ACP, CUT-LEAVE 2,* 5,2 6,2 0,4 3,2 2,2 4,4 3,0 5,2 6,4 10,0 *2,8 3,4 4,2 4,6 5,4 9,6 6,2 17,8 3,6 17,8 3,6 18,8 5,4 5,4 20,0 6,4 20,0 6,4 I,4 1,2 3,2 2,6 3,2 2,6 4,0 3,4 4,0 3,4 4,6 3 6 4,8 3,6 6,2 4,6 6,2 4,6 7,0 5,4 7,0 5,4 19,0 8,2 19,0 5,2 21,0 8,0 21,0 8,0 22,8 9,6 22,8 9,6 1,2 O,8 1,2 0,8 3,2 2,4 3,2 2,4 4,2 3,4 4,2 3,4 5,8 3,4 8,8 3,4 A 4,6 1 4,6 1,4 18,6 5,4 5,4 172 table G. REFfiRRAL NO, 1L06, SENSITIVITY ANAl.tfi?. Pf Th e . a M U A L COM. ASSUMPTION. VALUES ARE INTERNAL RATES Q£ RETURN FOR |A qh OPTION, LOw MedT uM HlGl 1, NO TSI IN 1962 lAi M.Q JF IN 8 (1) MARKET PRODUCTS (2) SELL STUMPAOE A, AVE, PRICE B, CONV,SURPLUS FUTURE THINNINGS JU.MB41&T PMflUCTS (2) SELL STUMPAOE A, AVE, PRICE B, CONV, SURPLUS I t , TSI IN 1962 (A) NO FUTURE THJNNINQ (1) MARKET PROOUCTS A.NO ACP, CUT-SELL B-NO ACP* CUT»LBAVg C-ACP' CUT-SELL D-ACP, CUT-LEAVE (2) SELL STUMPAOE A, AVE, PRICE 1-NO ACP, BUT 2-NO ACP| CUT-LEAVE 3-ACP# CUT-SELL 4-ACP, CUT-L|AVE B, CONV, SURPLUS 1-NO ACP, SUT-SELL * M O ACP, fQf-LEAVE 3 - acp, cut- sell 4-ACP, cut-lbave (B) FUTURE THINNINQS (1) MARKET PROOUCTS A.NO ACP, CUT-SELL B-NO ACP, CUT-LEAvE C-ACP, CUT-SELL O-ACP, CUT-LEAVE 12) SELL STUMPAOE A, AVE, PRICE 1-NQ ACP, SUT-SELL 2-NOAOF, SUT-LEAVE 3-ACP, CUT-SELL 4-ACP, cut- leave B, CONV, SURPLUS 1-NO ACP, SUT-SELL 2-NQ ACP, SUT-LEAVE 5-ACP, CUT-SELL 4-ACP, cut- leave 16,2 3,2 1,2 13,2 16,0 0,2 2,2 0,2 0,2 10,8 5,2 Si 8 A 9,4 1,0 3,2 0,2 1,4 9,0 A A 4,2 3 14 A 4,4 2,8 2.4 3.4 2,« A.... 2,4 A A 0,2 0,2 0,8 0,2 0,2 0,2 0,2 0,2 8,2 4,2 A A M 8,0 9,8 A A A 3,2 A 8,0 Y * Y M 0, J 3,2 1,2 V A 5,6 3,8 3,2 9.0 4.0 0,8 A 1,8 0,2 0,2 0,2 0,2 3,6 2, E A 3,8 i,» i,4 *•* i,® 173 TABLE H. REFIRRAL NO, 2W09, SENSITIVITY ANALYSIS OF THE ANNUAL COST ASSUMPTION, VALUeS ARE INTERNAL RATES OF RETURN FOR BAQH OPTION, LOW MEDIUM HIGH I, NO TSI IN 1962 J i l J A m m J i d M N I . ( t ) MARKET PROOUCTS (2) SILL STUMPAGI A, AVE, PRICE 8, CONY, SURPLUS (B) FUTURE THINNINGS <1J MARKET PRODUCTS ?*> SELL STUMPAGE A, AVE, PRICE B, CONV, SURPLUS I I , TSI IN 1962 (A) NO FUTURE THINNING (1) MARKET PROOUCTS T i w r o ^ m i s i t L B-NO ACP, CUT-LEAVE c- acp, cut- sell D-ACP, CUT-LEAVE 11) SILL STUMPAGE A, AVE, PRICE i w N O ~m t CUT«SELL 2-NO ACP, 0UT«LEAVE 3-ACP, CUT-SELL 4-ACP, CUT-LEAVE B. CONV, SURPLUS UNO ACP. CUT-SELL ' UNO AGP,'"GOT. LEAVE 3-ACP, CUT-SELL 4 - acp , cut- leave (8) FUTURE THINNINGS (1) MARKET PRODUCTS A-NO ACP| CUT-SELL B- nS A cp , CUT C-ACP, CUT-SELL D-ACP, CUT-LEAVE (2) SILL STUMPAGE AvE, PRICE 1-NO ACP, 0UT-SELL UNO ACP; CUT¥l6AV6 3-ACP, CUT*SELL 4-ACP, CUT-LEAVE B, CONV, SURPLUS 1-NO ACP, CUT-SELL 2-NO ACP, CUT-LEAVE 3LACP,CUT-SILL 4-ACP, CUT-LEAVE 16,0 4,4 2,6 13,2 17,6 0,2 3,6 0,2 1,4 14,6 7,6 A 6,6 I,4 2,8 5,2 0,2 1.0 19,6 6,0 1*.* A 6,2 4,8 6,2 6,6 4,8 4,0 4,« 4,8 16,6 3,4 2.4 1,4 2,4 2,8 0,2 0,2 0,2 8,2 19,0 5,2 3,0 3 8 5,0 5.4 3! 4 2| 6 3,4 3,6 14,8 7,2 14,6 23,4 8.4 5,8 0,4 6,0 a; 6 6,0 6,4 A 3,8 A A 2,4 1,2 2,4 2,« 0,2 8,2 8,2 0,2 7,0 4,0 T,6 A 3,6 2,6 3,6 3,0 1,8 I,4 1,8 2,0 16,6 A lY 17.4 TABLE I . REFIRRAL NO, 2G10, SENSITIVITY analysis Of The annual cost ASSUMPTION. values are INTERNAL RATES OF RETURN FOR EACH OPTION, LOW I, NO TSI IN 1962 ( i L J G L FUTURE..THINNING ( I ) MARKET PRODUCTS (?) SELL STUMPAGE A, AVE, PRICE B . CONV. SURPLUS FUTURE THINNINGS ..... (.11 JU.AfiKETLMOJDM.TS (2) SELL1STUHPAGE A, AVE, PRICE 8 , CONV, SURPLUS I, TSI IN 1962 (A) NO FUTURE THINNING 11 MARKET PRODUCTS A*NO ACP* Cut•SlLL B-NO ACP,..CUT-LEAVE C-ACP, CUT-8ELL P-ACP, CUT«LEAVE (2) SELL STUMPAGE ..A,..AVI,..PRICE ............. 1-NO ACP, CUY-SEIL 2-NO ACP, CUT*LEAvE 3-ACP, CUT«8ELL 4-ACP, CUT«LEPV6 B, CONV, SURPLUS 1-NQ ACP, CUT-SELL 2»NO ACP, ISClT-tEAVE 3-ACP, CUT-SELL 4.ACP, CUT-LEAVE (B> FUTURE THINNINGS ( t) MARKET PRODUCTS A-NO ACP, CUT-SELL 8-NO ACP, CUT-LEAVE C-ACP, CUT-SELL D-ACP, CUT-LEAVE^ (2) SELL STUMPAGE A, AVI, PRICE 1-NQ ACP, CUT-SELL 2-NO ACP, CUT-LIAvE 3-ACP, CUT-SELL 4-ACP, CUT-LEAVE B, CONV, SURPLUS 1-NO ACP, CUT-SELL 2-NO ACP, CUT-LEAVE S-ACP, CUT-SELL 4- acp, cut- leave ...... (. . . medium high 13,0 2,0 0, 2 10,8 11,2 0,2 0,2 0. 2 0, 2 16,4 Ai 4 2, 2 A 5,2 0,2 0,2 0, 2 0, 2 9,2 3,0 2,2 5 ,2 2,0 I 2 t 0 1 A 3,4 0•| 0,2 0,2 0,2 0 0 0 0 2 2 2 2 5,2 2,A A A,2 0,2 0,2 0,4 0,2 0 0 0 0 2 2 2 2 11,0 5.2 A 8,2 5,0 3,4 33,4 A,2 2 2 3 2 6 0 4 4 A 2,4 A 5,2 0.2 0*2 0,2 0,2 0 0 0 0 2 2 2 2 4,8 1,0 0,8 I.6 1*0 0 0 0 0 2 2 2 2 Y 5,6 A Y A,2 1 4 1 0 175 TABLE J . REFERRAL NO, 1814, SENSITIVITY ANALYSIS OF THE ANNUAL COST ASSUMPflON, VALUES ARB INTERNAL rates 0? Return for bach option , LOW mioiuh HIGH I , NO TSI IN 1962 ■ (A) VO FUTURE THINNING nr'MiiRiff'TrewefS (2) SELL' STUMPAOE A, AVE, PRICE 8, CONV, SURPLUS (B) Future thinnings UPMARKET PRODUCTS r a y S i u r STUMPAOE A, AVE, PRICE 8 , CONV, SURPLUS I I , TSI IN 1962 (A) VO Future thinning U > MARKET PRODUCTS a;w acp ,"“cut< 8 . NO ACP, CUT-LEAVE C-ACP’,CUT-SELL D-ACp , cut- leave <2) SILL STUMPAOE A, AVE. PRICE ■— ...... .. i . N O A e p ; cut- sell 2-NO ACP, SUT*lEAvE 3-ACP, CUT-SELL 4-ACP, CUT-LEAVE B, CONV, SURPLUS 1-NO ACP, CUT-SELL 2~*~N8ACP', SUT-LEAVE 3-ACP, CUT-SELL 4-ACP, CUT-LEAVE (8) future thinnings (1)MARKET PRODUCTS A-NO ACP, CUT-SELL b l w a c f ; cot- le *ve C-ACP, CUT-SELL D-ACP, CUT-LEAVE (2) SELL STUMPAOE A, AyE, PRICE 1-NO ACP, CUT-SELL 2 - NU ACP, BUT-LBAVE 3-ACP, CUT-SELL 4-ACP, CUT-LEAVE 8, CONV, SURPLUS 1-NO ACP, cut- sell 2-NO ACP, CUT-LEAVE '3-ACP, COT-SELL...... 4-ACP, CUT-LEAVE — 23,0 7,0 5,4 20,6 22,6 4,0 6,4 1,8 4,6 29,8 10,4 8«2 A A 5 ,4 3,2 5,8 7,6 22,0 1 0 ,4 22,0 10,4 8,8 6,8 8,8 6,8 ...A ' 8,6 A 8,6 5.2 4,8 5.2 4,6 A 10,2 A 10,2 7.6 6,8 7.6 6,8 22,6 13.8 22,6 13.8 12,6 9,4 12,6 ’ ,4 A 9.8 A 9.8 6,0 A l Ym 11,4 6,0 5,4 8,6 7,4 ........n A 7,4 s 176 table k . REFERRAL NO, 1L16, ANALTSI? of assumption, SENSITIVITY THE a n n u a l COST values are internal RAlls 91 RETURN FOR lACH OPTION, I, NO TSI IN 1962 m.N^rUI.URE..mNNlNl (1) MARKET PRODUCTS (2) SELL STUMPAOE A, AVE, PRICE . . . . . . B. CONV, SURPLUS (B) FUTURE THINNINGS SILL STUMPAOE A, AVE, PRICE 1-NO ACPi fUT.SflL 2.N0 ACP, OUt»LEAVE 3-ACP, CUT-SELL 4-ACP# CUT-LEa'Ve B, CONV, SURPLUS 1-NO ACP, CUT-SELL 2-NQ ACP, CUT-LEAVE 3-ACP, CUT-SELL 4-ACP, CUT-LEAVE 177 REFERRAL NO, 1M20, SENSftJVITY ANALYSES OF THE ANNUAL CQST assumption , Values are internal rates of return FOR EACH option , TABLE L. low medium h| qh I, NO TSI IN 1962 J H m„£uxuM miNNiNo (1) MARKET PRODUCTS <2) SELL STUMPAGE A, AVE, PRICE B.CONV. SURPLUS (B) FUTURE THINNINGS .... i l l . MARKiT_PM0yCTS (2) SELL STUMPAGE A, AVE, PRICE B, CONV, SURPLUS 11,.Til IN 1962 (A) NO future thinning -......i l L MARKET PRODUCTS A-NO ACP* CUT-SELL B-NO ACP, CUT-LE*VE C-ACP; CUT-SELL D-ACP, CUT-LEAVE <2> SILL STUMPAGE A. AVE. PRICE ....... riNO“T c R T W Ti5ILL" 2-NO ACP, BUT*LEAve 3-ACP* CUT-SlLL 4-ACP, CUT-LEAVE B, CONV. SURPLUS 1-NO ACP, BUT-8ELL ...y-'NO“-«eft'"BITTitf*VE 3-ACP. CUT-SELL 4-ACP, CUT-LEAVE (B) FU1ruRE Thinnings (1) MARKET PRODUCTS A-NO ACP* CUT-SELL " l - W ajjjp, CUT- LEAVE C-ACP, CUT-SELL D-ACP, CUT-LEAVE <*> SELL STUMPAOE A. AVE, PRICE 1-NO ACP* CUT-SELL 2-NO "ACP, “BUTWLEAVE 3-ACP* CUT-SELL 4- acp * cut- leave B, CONV, SURPLUS 1-NO ACP* SUT-SELL 2-NO ACP, SUT-LEAVE 3-ACP, CUT-SELL 4-ACP, CUT-LEAVE 17,4 5,2 3, S 15,2 17,0 2,2 4,4 0,2 2,8 31,0 10,0 8,8 A A 4,8 5,4 2,8 3,2 27,6 7,8 27,6 7,8 18,8 5,4 18,8 5,4 5,6 A*4 5,8 V A 5 ,8 A 5,8 3,2 2,8 3,2 2,8 M 0,8 1,0 0,8 A 7,o A 7,0 6,2 4,8 8,2 4,8 41° 3,4 4,0 3,4 27,8 12,4 27,8 12,4 21,0 8,0 21,0 8,0 14,2 A 6, 8 A 6,8 312 2,4 3,2 2,4 0,2 0,2 0,2 0,2 A 8,6 A 8,6 A 4,8 A 4,8 3,6 2,8 3,6 2,8 14,2 5,8 178 table m TABLE M. referral no» ;*nsitivity 7 Na l y S|S OF T«E RfRlODJC COST ASSUMPTION, VALUES ARE INTERNAL RATES OF RETURN TOR |ACW OPTION* MEDJuM HIGH 3,6 3,2 0,2 2,2 0,2 2,2 2.6 0,2 2 18 6,0 1,0 3,2 5.2 1,0 3,2 4 .4 0,8 3,2 4,8 3,8 A 4,8 4 »2 3,4 A 4.4 3,6 3,2 6,6 4,2 0,2 0,2 1,0 0,2 0,2 0,2 0*8 0,2 0,2 0,2 0,8 0,2 3,2 4 3.2 2,4 A 3,2 3,2 2,2 A 3,2 6,4 4 ,® A 6.2 5,2 43 ,48 LOW I . NO TSI IN 1962 >ELL STUMPAGE i, AVE, PRICE 1-NQ ACP| CUT-SELL 2-NOACP, COT-LEAVE 3-ACP, CUT-SELL 4-ACP, CUT-LE a VE I, CONV, SURpLUS 1-NO ACP', CUT-SELL 2-Np ACP, CUT-LEAVE S.ACP, CUT-SELL 4-ACP, CUT-LEAVE S.4 181 TABLE P. REFIRRAL NO, 1B14, SENSITIVITY analTSI® of the periodic co^t ASSUMPfI ON, RATES VALUES ARE INTERNAL of r e t u r n FOR each LOW I, NO TSI IN 1962 -IJlLJISL £UIilRf...IH tN.N I.N G (1) market products <2) SELL STUMPAOE A, AVE, PRICE B, CQNy, SURPLUS (B) FUTURE THINNINGS <11 MARKET PRODUCTS (I) SILL STUMPAOE A, AVE, PRICE B, CONV. SURPLUS ORTJON. MEDfUM HJQH 7,4 7,0 6,8 4,0 6,4 4,0 6,4 4,0 6,4 11,4 10,4 5,6 7,8 5,4 7,6 5,4 7,6 23,6 7,0 23,6 7,0 8,6 6,6 8,8 6,6 7,4 6,6 7,4 6,6 5,2 4,6 5,2 4,6 5,2 4,6 5,2 4,6 5,2 !•! *•* 4,6 7 j® 6,8 7,8 6,8 7,6 6,8 7,6 6,8 7j 6 6,6 7,6 6,6 25,2 1C,2 25,2 10,2 12,6 9,4 12,6 9,4 9, 6 8,8 6 6,8 6,2 5,4 6,2 5,4 6,0 5,4 6,0 5,4 6,0 6,6 7,4 8,6 7,4 6,6 7,4 6,6 7,4 6,6 7,4 8,6 V H i TSI IN 1962............... MARKET PRODUCTS A*NO ACP, B-NO ACP, CUT-LEAVE C-ACP, CUt-SELL D-ACP, CUT-LEAVE <2) SELL STUMPAOE A, AVE, PRICE 1-NO TCPrWT-iELL 2-NO ACP, «UT*LEAvE 3-ACP, CUT-SELL 4-ACP, CUT-LEAV e B, CONV, SURPLUS 1-NO ACP, CUT-SELL 2-no acp; tiifntm 3-ACP, CUT-SEll 4-ACP, CUT-LEAVE IB) FUTURE THINNINGS <1) MARKET PRODUCTS A-NO ACP, CUT-SELL I-NOACP, Cur-tEWf C-ACP, CUT-SELL D-ACP,CUT-LEAVE (2) SELL STUMPAGE A, AVE, PRICE *•**0 ACP* CUT-SELL 2 - W ACP* trUT-LEAVE 3-ACP, CUT-SELL 4-ACP, CUT-LEAVE B. eONV, surplus 1-NO ACP. CyT-SELL 2-NQ ACP, 6UT-LEAVE 3- AC P, cun s s l l 4-ACP, C U T - L M v E 6,0 5,2 182 TABLE Q. REFERRAL NO, 1L16, SENSITIVITY ANALYS],? OF THE PERIODIC COST ASSUMPTION, VALUES ARE INTERNAL RATES OF return FOR EACH OPTION. medium HjflH 11,4 10,2 8,8 6,6 10,2 6,4 10,2 6,2 10,0 1.6.,.6 15,4 14,0 10,4 13,6 10,2 13,4 10,2 13,4 15.0 1|,2 15.0 12.2 11,2 ll,4 11,2 U, 4 10 *6 8,8 11,8 7.2 11,8 7.2 11.4 7.0 11.4 7.0 11,8 6,6 11,8 10,6 11.8 10.4 11,8 10.4 11,6 10 * 11,6 10,2 10,8 l6,8 l 4 ,6 13.2 13.8 13.2 13.8 1.4,8. 9,2 14,8 ’ ,2 14.4 ’ ,0 14.4 ’ ,0 13.8 13.6 12,2 13.6 12,2 LOW I, NO TSI IN 1962 .„.lA.jL„m.lUlURf IH1NNINR (1) MARKET PROOUCTS (2) SELL STUMPAOE A. AVE, PRICE B, CONV.SURPLUS FUTURE THINNINGS .J.ll„,W,ARKEI~t.R OPilC TS (2) SELL STUMPAOE A. AVE, PRICE B, CONV. SURPLUS Til IN 1962 II (A) NO FUTURE THINNING . (1). N AR KJ|T „PR 0.0U C TS A.NO ACP, CUT-SSLL B-NO ACP, CUT-LEAVE C-ACP* CUT-SELL D.ACp; CUT-LEAyE (2) SELL STUMPAOE A t AVE, PRJCE “T-NO ACPi CUT-S6LL ?»N0 ACP, CUT*L£AVE 3-ACP, CUT-SELL 4- acp, cut- leave B,I, CONV, SURPLUS 1-NOA lCRj CUT-SELL 2-NO ACP, SUt«LEAvfc 3-ACP, CUT-SELL 4-ACP, cut- leave (B) FUTURE THINNINGS (1) MARKET PRODUCTS 1-JNO ACP, CUT-SELL B-NO ACP, CUT-LEAVE C-ACP'. CUT-SELL D-ACP, CUf-LEAVE SILL STUMPAOE (?) A # AVE, PRICE 1-NO ACP, c u t - s e l l 2-NO ACP, OUT-LEAVE *-ACP, CUT’“BCI * 4-ACP, CUT-L^AVfe 1. CONV. SURPLUS 1-NO ACP, CUT-SELL 2-NQ ACP, SUT-LEAVE 3-ACP, CUT-SELL 4-ACP, cut- leave l10,6 U l 16,8 Xt 'U 13.8 12,4 18.6 11,0 S.6 1 0 ,® 13,0 li;S 13.4 12,0 13.4 12,0 183 TABLE R. REFERRAL NO, lM2p, SENSITIVITY ANALTSj? Of THg PERIODIC COST ASSUMPTION, VALUES ARE INTERNAL * RATESjiF RETURN FOR EACH OPTION, LOW medium HIGH I, NO TSI IN 1962 . (1) MARKET PRODUCTS (2) SELL’ STUMPAOE A, AVE, PRICE B, CONY, SURPLUS (B) FUTURE THINNINGS 11). „MARKf T ..PROOyCTS i t ) SELL STUMPAOE A, AVE, PRICE B, CONV, SURPLUS III. TSI IN &962 (A) VO FUTURE THINNING <1) MfRK|T PRODUCTS A.NO ACP, 60T• S'ELL B-NO ACP, CUT-LEAVE C-ACP, Cut**8ELL D-ACP', c u t -l e a v e i t ) SELL STUMPAOE A. AVE, PRICE 1- n o T c p ; c u t - s e l l 2-NO ACP, CUT-LEAVE 3-ACP, CUT-SELL 4.ACP, CUT-LEAVE B. CONV, SURPLUS 1-NO ACP, CUT-SELL 2- n o ACP;CUT-LEAVE 3-ACP, CUT-SELL 4-ACP, CUT-LEAVE (B) FUTURE THINNINGS (1) MARKET PRODUCTS A-NO ACP, CUT-SELL B-NO ACP,CUT-LEAVE C-ACP', CUT-SELL D-ACP, CUT-LEAVE (2) SELL STUMPAGE A, AVE, PRICE 1-NO ACPj. SUT-SELL 2-NO ACPI CUT-LEAVE 3-ACP, CUT-SELL 4-ACP, CUT-LEAVg 8, CONV, SURPLUS 1-NO ACP, SUT-SELL 2-NO ACP, SUT-LEAVE 3-ACP,CUT-SELL 4-ACP, CUT-LEAVE 5,4 5,2 5,0 2,2 4,4 2,2 4,4 2,0 4,A 12,8 10,0 8,0 4,8 5,4 4,8 5,4 4,8 5,4 36,0 16,6 5.4 6 3I 6 ,' n 5,6 18,8 5.4 3.2 3.2 2,6 3.2 2,6 2,6 6.2 6.2 6,2 4.8 6,2 A,6 36.4 9.6 36.4 9.6 21,0 10 8.0 6 21,0 10 8.0 6 4.8 .312 2,6 3,2 2,6 A 4,6 A A,8 3.2 2,6 * ,6 3.2 2.4 3.2 2.4 A 4,6 ’J1 6,6. 184 TABLES. REFERRAL NO, TL06. SENSITIVITY ANALYSIS RESULTING FRQH A 9 - ' ' PERCENT “CHANGE ITT'TREQU AL'ITY INDEX, VALUES ARE INTERNAL -------------------- irJT^---QT™-|TETI,K|^ijR ETlJR'"TTPTl'trNr LOW HIGH medium I, NO TSI IN 1962 (1) MARKET 3*2 3,0 products (2j m t STUMPAGE 0*2 A. AVE, PRICE 1?8 ~ ■ B. CCNV, SURPLUS ( B) FUTURE THINNINGS - — r n ra"rret'"prcducT's .....- .........~ " m ..* (2) SELL STUMPAGE OT® ............ A7 AVE. PRICE ...................... 2,8 8. CONV, SURPLUS TT7 T S I I N 1962............. (A) NO FUTURE THINNING — - . — ”~-^tX"RARKET"'PRODtrCTS ....... .- A-NO ACP, CUT-SELL B'.W ACP,CUT-LEAVE C.ACP*. CUT-SELL - C»ATP,7'CUT«LE*VE (2) SFLL STUMPAGE ^ ^ . T ^ T V T 7 ^ pnTX:^ — 4,0 3*4 A 4,4 1-NQ ACP. CUT-SELL 2 •NO ACP*. CUT-LEAVE 3-ACP, CUT-SELL ----4-ACR71CUT-LEAVE B, CONV, SURPLUS 0,2 0*2 0,2 0, 2 ■ xm v 0,2 2,4 --- 5 7 *------ -- . ll» 3*2 - A -r,~ir 1,8 3,6 .... — ..— 4,2 3,4 4,4 4,4 3,6 A 4,6 „ icr r ^cu'T-seu:— 2-NO ACP, CUT-LEAVE 3-ACP,CUT-SELL 4-ACP, CUT-LEAVE TS) FUTURETWINNINGS (1) MARKET PRODUCTS AriW-ACRT'CUT-^EtL ~ B-NO ACP, CUT-LEAVE •*« 2i2 - 8*8 Of* 8,» 0, 2 ...... 2,2 * 3#2 0,6 0,2 2,4 0,4 -37 * - ■"»**• 2,6 A 3,2 2,6 A 3,4 T,V ............9*f*.... 4,2 4,4 * ,6 4,4 C-ACR; ~CUT-S£LL. . . . . . . . . A. . . . . . A. . . . . . . A ' D-ACP. CUT-LEAVE (21SELL" STUMPAGE A. AVE. PRICE - ....... . * ~~ acp ; 'T?ur*^EtL 2-NO acp; CUT-LEAVE 3-ACP. CUT-SELL 4-ACP, CUT-LEAVE B.CONV, SURPLUS l-NO ACP, CUT-SELL ----------gswo-■i cp;~'CUT4T g AVF 3-ACP, CUT-SELL 4-ACP, CUT-LEAVE 5?4 5*6 -ovrOf? 1*8 0{4 it 3f2 ~T¥*“ A 3f2 *” 8*6 A 1*4 3,6 “2*fS A A 3,6 5,8 - ~ -trr 1,2 A 2,0 . “ ......- “ 3,2 4,0 ~. T , T 4,0 185 -ta b le t . ---------- - h e f e r r a l wo'i z n c 9 , 3 1r s t t t v t Tr RESULTING from A 5 PPRCCNT “CMANGE IN"fMEBU ALTTY INDEX* VALUES ARE INTERNAL analysis LOW medium high I. NO TSI IN |962 (1) MARKEf PRODUCTS 4*8 4*4 4,6 --- -- (ET SFCC STUMP AGE ' "........ '................ ......... A, AVE, PRICE Of? 8*2 0,8 “ ------------ B r t r O N ? . S U R P t U S 3f* 3*6 3,6 (B> FUTURE THINNINGS --- -- It) MARKEf PRODUCTS”"' «TT" ---7?*“ (2) SELL STUMPAGE ~— ---------- A; AVE. PRTCE ... ".......... 0T*........* f4........... 3 »*. B, CONV, SURPLUS 2*2 2*0 3,6 ------- rt- T SI -IN T T 6 2 - -...... ........... (A) NO FUTURE T A N N I N G __ __ _ _ " . — A-NO ACP, CUT-SELL 6*0 6*8 6,2 ------ --9 i N G A G P , C U T ’’LEAVfe........ 4*8....... 4*6 .... 4,8 C-ACP', CUT-SELL 6*0 6*2 6,2 -------- - TTsrACP* "CUT*"t€AVE... ... 6f6....... 6*6........ 6,6 (2) SELL STUMPAGE « rr AVg-, -PR I C E-- — --------------- - ..— — ...... .. 1-NO ACP* CUT-SELL 1*8 2*4 2,8 .. — ..... .... ...2-NC ACP» C U T - L E A V E 0 , 8 ....... 1*4..... ... 1 ,f 3-ACP, CUT-SELL 1H 2*4 2,8 - -- ----------4-ACP,..CUT-LEAVE..... 1X8....... 2 , 6 ........ 3,0‘ B.----CONV. SURPLUS _— ---- — — ------- 1 »NO ACP , "CUT'»EELt~~~" ... 9T0“.... ..— ----- 2-NO ACP', CUT-LEAve 3*6 3*0 4,0 ■-- ---- --- 3- ACP,..C U T - S E L t ......... 5TQ....... 3*0........ 9 , 2 4-ACP, CUT-LEAVE 5*2 5*4 5,6 t t r F U T U R E T«INNINGS (1) m a r k e t p r o d u c t s ■•■x«fNC~“ACPr~cuTRSPtt"* .. — .— t t *-- ----- or4” tour B-NO ACP, CUT-LEAVE 5*2 5** 6,2 C*ACP> -CUT-GftLTi4 8?4 tG,0 D-ACP, CUT-LEAVE 8*2 9*0 12,2 <21 Sfttr STUMPA GE A, AVE, PRICE 1-MOTCP*—CUT-- 66LL-----------6t 0--------- 2f4“—.......—4~,~6~ 2-NO ACP, CUT-LEAVE 012 1»« 2,2 3-ACP, CUT-SELL OH 2t* 4,6 4-ACP, CUT-LEAVE 1*0 2*0 7,0 B , C O N V , SURPLUS 1-NO ACP* CUT-SELL 2*0 3*6 4,4 ---------- y-rMQ ACP V CU T-ttfcA>VB~.— 2TT Br*----------- * r f ‘ 3-ACP, CUT-SELL 2*9 3*6 4,4 4-ACP, CUT-LEAVE 3*0 3H 4,0 ' 186 TABLE REFERRAL NO, 2GT0.SENSITIVITY ANALYSIS RESULTING FROM A 5 PERCENT t?HATlGE“ 11^ TWE- SUALTTY INDEX, VALUES ARE INTERNAL •' “ --------- ------ — R^TFg-^^Tt;irN"'FCirEicwn3WtJtrr LOW I, NO TSI IN i962 T A )~ND"Tl) TI3R E "THINNING------------------(1) MARKEt PRODUCTS lr8 T2 J SELL" STUMPAGE A, AVE, PRICE 012 -------- ¥| CONV, SURPLUS 0,2 (8) FUTURE THINNINGS C1I MARKET 'PR'PDU' C 'TS--- r~ nnr~ (2) SELL STUMPAGE - ---- A-; rvEV PRICE 01* B, CONV, SURPLUS 012 TT , TST IN IV62 .............. (A) N° f u t u r e t h i n n i n g A.NO ACP, CUT-SELL B A N C ACP, CUT-LEAVE C,ACP*, CUT-SELL D'-ACP, CUTS LEAVE (2) SELL STUMPAGE -------j C E - ---------------------- — M6PJUM “ _ 2*8 2,2 8*2 0*» 0,2 0,2 ....^ 0,2 Of* ' 2,8 2,2 4*2 2T6 ..... HIGH --- --~ ~ 5 T F 0 ,2 0,8 ' 3,0 Z*2 5*2 2*6 3,2 2,4 39,0 2,8 .............. ......... . 1-NO ACP', CUT-SELL 0*2 0*2 0,2 2-73C ACP*, CUT-LEAVE 07 2 0*2 0,2 3 .ACP, CUT.SELL 0,2 8*2 0,2 -4VACP; CUT-LEAVE 0*2 0,2 0,2 8. CONV. SURPLUS ------ — .. r5-N'0 i'cppcur.sett— - .“072-".. - ~ T * r - — -uvr 2-NO ACP, CUT.LEAVE 0*2 8,2 0,2 ~ 3-ACP, CUT-SELL 012 0 *« 1,0 4-ACP. CUT-LEAVE 0*2 0*2 0,4 (BT FUTURE THINNINGS (1) MARKET PRODUCTS -------- A L W ^ A C F r T T F T - S E L L ................. 3 * 8 ~ ~.3*6 8-NO ACP, CUT-LEAVE 3*2 3*4 3,6 C-ACPV^UT-SELL 27 fU 33*4 38,8 D-ACP, CUT-LEAVE 4*0 4,2 4,6 1 2 ) SELLSTUMPAGE A, AVE. PRICE ------------ .----- I8W~ACP7"TrVT-SlLL .......... O'f2 ......... ... T * t " ............. t f f r 2-NO ACP, CUT-LEAVE 0*2 0*2 0,2 3-ACP. CUT-SELL 0,2 0*2 1,8 4-ACP, CUT-LEAVE 08* 0*2 0,2 8. CONV, SURPLUS 1-NO ACP, CUT-SELL 0*6 1*0 1,6 - - - - - - - - CUT-LEAVE 3 -ACP, 4-ACP. ~0T*. . . . . . . . . . . CUT-SELL CUT*LEAV6 1*0 0*6 -. -. *,T lfR lf« 2.4 1,4 187 TABLE 7 . REFERRAL WO, IB1 4 , SENSITIVITY 5 analysis resulting prom a PERCENT CHANGE TN THE BOALTTT INDEX, VALUES ARE INTERNAL RATE5™^r"NETURN FOR EACH' CRT |PNT LOW ---- I, NO TSI IN £962 "TAT" NO FUTURE”THINNTNO---------<1> MARKET PRODUCTS f27 STOMP aC E . A. AVE, PRICE • - - ----------- E.CONV.SURPLUS _ 7»0 3.8 6*2 medium high —------------------- ---7|fl 7,2 4*8 6*4 4,2 6,4 FUTURE THINNINGS --(1). MARKET PRODUCTS-- -- - -- TfT~” * U t l (2) SELL STUMPAGE - - - - - - - A . AYE". “PRICE . . . . . . . . . . 4 ,2. . . . . 4*8. . . . . 5, 6 B. CONV, SURPLUS 4*6 5*4 6,4 “. . . Tt, TSt TN 1-982 .. . (A) NO FUTURE THINNING — — f t T T ARKer PRODU CTS....... -..— — — ----A.NO ACP, CUT-SELL 9*2 18*8 24,6 - - - - - - - B-NB ACPy COT-LEAVE. . . . . . 5,4... '5f4 -. . . . . . 5,6 C.ACP: CUT.SELL 9|2 18*8 24,6 —- - -------------- ^CtHTrtEAYE’ ............................5*4.............. 5*4...............5,6 (2) SELL STUMPAGE « -A; AV'ft* t fil t t — — •. . . . . — - -— 1.NO ACP, CUT-SELL 2*8 3*2 3,6 - - - - - - - - ' 2*^0 ACP, CUT-LEAVE... 2T4 . . . . 2*4. . . . . 2,8. 3-ACP, CUT-SELL 2*8 3*» 3,6 —. . . . -.. . . . . 4* ACP* CUT-t*AVE. . . . . 2.4. . . . . 2*6 2', 8 B. CONV, SURPLUS - - - - - - - - - - - — — fwNO""^?';— eUT-SELfcr. . . -*Bt 6— -6f-8“— - - ... 2.NO ACP, CUT-LEAVE 4,6 4*6 4,8 —. . . . — ... .. 3-ACP.'CUT*SELL ‘.. 5,6 6*2 7,4. 4-ACP, CUT-LEAVE 4*6 4*6 4,8 (Br fUTUBE TH'T'tW'TNGS ~ (1) MARKET PRODUCTS —- - - - - - - - - ~~ATNO“ ACP, -CUTwSEt.t - . . . 18 ,~4 .. ~2* t E--- E5y8r8.NO ACP, CUT-LEAVE 7*4 0*0 8,4 ..... ... ....Ci-AUPi"-LfeAVE 0 #2 0,4 3-ACP, CUT-SELL 0,2 A --------------4*ACP# CUT-LEAVE .0T2......... ......0 , 2 ............ 1,0 B. CONV. SURPLUS - - — - ~ l - W A CF‘, “CUT»SEttr ------? r r ..-......... "3f2-...—...- 3,8 2,4 2,0 2-NO ACP, CUT-LfcAVE 2,6 .... A .......... .......A .............. ...A .... s - acp, cutasell 3*2 4 . ACP. CUT-LEAVfc 3,6 3?Q ............. TBT FUTURE THINNINGS (1) market products ........476" A-NO ACP. CUT-SELL ~97«” 4,4 4,6 4 jo B.NO ACP, CUT-LEAVfc .... A............. ..A... 37 ff Ci ACRVCUT¥SELt 5,6 6,0 5, a D.ACP, CUT-LEAVE ..................(2) SELLSTUMPAGE A, AVE, PRICE ............ . ..... ...... ‘... TGNG... ACFV CUT-SELt ...... *t f i ~ ..... ... Y»"4" ..... 3.2 0*6 0,2 1,8 2-NO ACP, CUT-L6AVE ........A ' A SiACP,CUT-8ELL 0*2 1*4 2,8 0J2 4 -ACP, CUT-LEAVE B. CONV. SURPLUS 2,8 3*6 4,4 1-NO ACP; CUT-SELL ... - ........ ..... “2-W ICF# CUT-LEAVE ........2 .2 ....... - ...2 i 2 .......... . .3"i'2“' 4,4 A A 3 -ACP« CUT-SELL 3*6 4-ACP, CUT-LEAVE 3T0 4,2 TABLE Z. REFERRAL NO, 2«09, StRSITTV|tr ANALYSIS RESULTING FROM A 10 PEECERT CHANGE | n fRE 0UALTTT INDEX, VALUES ARE INTERNAL LOW MEDIUM HIQh I, NO TSI IN £962 -TXr''NO“FDTURE"TFTT}NT"RG' (1) MARKET PRODUCTS --------- <2r SELL STOPPAGE A. AVE. PRICE 8, COW,SURPLUS f u ture 7,2 3*6 6*2... 4,8 6,4 4,4 6, 6 — ___— .— ( f - - - ™---t t f * .— .. 4 TO 6f 8 ....5 * 4 .... 7,6 6,8 8.6 7,6 8,8 6,®.... 6,® 6,6 12,8 7.0 12,8 7.0 5.2 4,6 ... 5.2 4,6 6,2 5.0 6,2 5.0 6 j 6 ... 7 f6 4T 8 ~ 1-NO ACP* CUT-SELL 7,8 t h in n i n g s (2) SELL STUMPAGE A. AVE. PRICE B. CONV, SURPLUS It,' TSt IN 1962 (A) NO FUTURE TWINNING — — ft7~ rf-IpKf T'“PR0 0UCTS~— .. A.NO ACP. CUT-SELL r# NU ACP, -CUTwt EAVfe C.ACP; CUT-SELL ........ &-*CP. CUTwLEAVE (2) SELL STUMPAGE — 7 f0 414 .4ff. 4 |4 ■“Aft -■ « r 8 ... ...— 6*6 61® 6 #6 ....... . ... 9,0 6,6 6,8 7.6 9,0 6,8 6.6 future thinnings (1) market products CUT^SELt'..... ACP. CUT-LEAVE C-ACp;CUT-SELL D-ACP, CUT-LEAVE (2) SELLSTUMPAGE A. AVE, PRICE ----------- irwW’"ACPT~CUT-»Sfciit“ 2-NO ACP‘, CUT-LEAVE 3-ACP,CUT-SELL 4-ACP, CUT-LEAVE 8. CONV, SURPLUS 1-NO ACPp CUT-SELL ---------- j— 8-NO 3-ACP. CUT-SELL 4-ACP. CUT-LEAVE ~ " t ........lEf®... ...19,0 9*0 9,« 10,0 0.2 I2f6 19.0 9,4 10.0 9 A’0 -- - ---- -6nfS—..- ... 9yt~ 5.4 6.4 4*2 9,2 6,8 4t4 5.4 4,2 6.4 6,6 7 #0 ~6-f8--- .- .7-4-. 8,6 7,0 7,4 6*8 A — .~*t 0. A 8,0 194 TABLECC. REFERRAL NO. I t 16. SINSITIVJTT ANALYSIS RESULTING FROM A IB PERCENTCHANGETN THE 8UALITY INDEX* VALUES ARE INTERNAL "Re t u r n -t o r -e i w o f t t r n t LOW ^ MEDIUM high I, NO TSI IN 1962 (1) MARKET PRODUCTS TZT SETL STUMPaGE A. AVE, PRICE ' B .' CCW. SURPLUS (B) FUTURE THINNINGS 9»6 1# 12 10,8 5 10 9,4 6,4 1B * 2 7,6 18,8 n i r * ... ~ x 5 T * — .. ..1«“,E <2) SELL STUMPAGE AT AVE. PR ICE B. CONV, SURPLUS I I , T S I TW1V62 (A) NO FUTURE THINNING Si 6 12 *4 IB,2 13,4 11,1 14,6 9,8 11*0 9 t8 11 VO H,2 11,6 11,2 11,4 13,2 11,6 13*2 11,6 710 6,0 7,0 6*0 11.4 7.6 11.4 7.6 A 7,6 A 7*6 -T r j - HiR-KiT P R O D U C T S " A . NO ACP, CUT-SELL B.NU ACP, CUT-LEAVE C-ACP; CUT.SELL --------- D¥ACF7 CUTiXFAVE (2) SELL STUMPAGE "-rr-AVFT-RRTCE" 1-NO ACP, CUT-SELL 2 -NO ACP, C U T -LEAVE 3-ACP, CUT-SELL 4-ACP. CUT-LEAVE B. CONV, SURPLUS ------------- l ^ t j “ 5nTFi"“CCT^ELL • 2-NO ACP, CUT-LEAVE 3-ACP, CUT-SELL 4-ACP. CUT-LEAVE m FUTORE THINNINGS (1) MARKET PRODUCTS ....A~-W~ ACP, CUT-SELL 8-NO ACP, CUT-LEAVE C-ACP*CUT* SELL D-ACP, CUT-LEAVE (2) SELLSTUMPAGE A. AVE, PRICE t 2-NO ACP, CUT-LEAVE 3-ACP, CUT-SELL 4-ACP. CUT-LEAVE B. CONV, SURPLUS 1-NO ACP, CUT-SELL ------------3-ACP. CUT-SELL 4-ACP, CUT-LEAVE -”9',2 10,0 9,2 10f0 .... I T , * .. .. tr,! 16.4 10,8 17,4 11,8 10.4 10,8 11 -ft 13 f4 1116 13 f4 .1 3 , 1 .... ..15,0 14.2 13,» 13,1 13,0 14.2 13,8 9 jr0 8,0 9 TO 8*0 10,6 11 if 10,6 1116 .... IPV4.. 9*8 14,4 9,1) ■ ... A''’ 9.8 A 9.8 13.6 20,2 .IS", 8 .... ...... .. 13.6 20,2 12 ,a 12,6 195 TABLE DD. ” . REFERRAL NO, 1M20. SiNSITTVITY ANALYSIS HESULTINO FROM A 10 PERCENT CHANGE INDEX, TN THEQUALITT VALUES ARE INTERNAL - - - - - - - - RTAT ESTF " RETURN FOR" EIGH QpTTtmr- - medium LON I. m NO TSI IN 1962 W 7 U TCTRE~THTNNTNG' <1) market products ~t * t SELL" STUMPAGE A.’ AVE. PRICE — — r t o w r i t m v s - (8) FUTURE THINNINGS TtT~HTRHe-t™PRTWCTS ---- ~ (2 ) SELL STUMPAGE A, AVE. PRrCE ................ B. CONV, SURPLUS 1 1 , TCT I N 1962 (A) NO FUTURE THINNING — -- (IT N AR K6T’“PRClJtrCTS - ' A-NO ACP. CUT-SELL " ‘ PiNO ACP.CUT* LEAVE C-ACPj CUT-SELL -------------- ITiACP-, CUT«tt*VP (2) SELL STUMPAGE _ — .— AT-TYrr-pR-rcr--— - 1-NO ACP. CUT-SELL hioh 5*8 5*8 5,2 1*6 . 472 2,8 ... 4,4 2,6 . . . 4,6 , , “~TJ — • i n .a . 376 4*0 4t« 5,4 6,4 7,4 714 514 7f 4 5t 4 I8f« 5 14 18t» 5f 4 29,6 5.6 29,6 5,6 3*8 4,2 2*6 — '........ 2 - N O ACP# CUT-L2AVE 3,0 3,2 3-ACP, CUT-SELL A,2 2 ,6 4*ACP.CUT^LPAVfe 3,0 B. CONV, SURPLUS ..... „ , , „a.. ,..... --------- .........— jprWC“ACP'# "iTUT -r9'ErLL-. -5* 2 ...... z.trr* ........ Hr 4*6 4*6 4,8 2-NO ACP', CUT-LEAVE 6 *2 A 5-ACP,CUT-SELL 5 t2 4,6 4*6 4,8 4-ACP. CUT-LEAVE tBv futurethtnnings (1) market products — ------ /r-fl^rO ArC^i CUT-Gfrtfc 12f 2 ........21*8 ......... 30,2 8*0 6*6 B.N0 ACP, CUT-LEAVE 9,0 30,2 2118 12 f 2 C-*CPy CttT-Gftt 8*0 6*6 D.ACP. CUT-LEAVE 9,0 <2) SPtLSTUMPAGf A. AVE, PRICE --B-jTf------ -------—t wfijQ"ACP>—CUT-GfeLL TfO 2*4 2-N0 ACP, CUT-LEAVE 4.0 110 A 3 - ACP, CUT-SEtte If 9 3*« 4.0 2,4 4-ACP, CUT-LEAVE 1.0 B. CONV, SURPLUS A 4*2 1-NO ACP, CUT-SELL A .. 2-N O— ACPi— CtfT-teEPVfr 3 - ACP, CUT-SELL' 4-ACP, CUT-LEAVE 2*4 .2,3 2*4 ’272 --GfO-' 4*2 3?6 ~4'i|r4'*. A 4,6 A 5.8 196. be . •re fe r ral w y tots . siretttvitt analysis resulting from a 15 FERGEWr~ CW*NUTTN TRE~ID7fCTTY — INDEX, VALUES ARE INTERNAL RATES ofr..h^TURNTt3E'“' E l W ‘O F n W T “.. LOW MEDIUM HIGH . I. N° TSI I N J 962_ _ _ _ _ _ _ __ __ . _ _ _ __ (1) MARKET PRODUCTS 2,8 3,8 3,4 ~ m m i STUMP A"Gi. . . . . . . . . . . . . . . . . . . . . . . . . . . . A. AVE. PRICE 0,2 0*2 0,2 B, CONV, SURPLUS 114 2,2 2,6 (B) FUTURE THINNINGS — " m “RTEKBT PRODUCTS — — ~ ~Tff ~ ~5Tf 8TT* (2} SELL STUMPAGE . . . 1 7 1 T B , PPT OE .... .. ... 012. . . . . 1, B. . . . . 3,2 9. CONV. SURPLUS 2.5 3*8 4,4 IT, TSI IN 1962. . . . . ... (A) NO FUTURE TWINNING ftT -'7^-Rrprgy--pgoUU CT S" “ . . .. . . .. . — . — -. A-NO ACP, CUT-SELL 3*8 4,2 4,8 9-NO' AGP, CUT-LEAVE 31? 3*4 3,6 C.ACP; CUT-SELL 6,0 A A dmACP, CUT-LEAVE 412 4,4 4, B <2) SELL STUMPAGE “— T7-T7F7“FfrrCi. ... . . . . . ~~ 1-NO ACP, CUT-SELL 0?2 0*2 1,8 2 -NOACP,CUT-LEAVE 0T2 0*2 0 ,8 3-ACP, CUT-SELL 012 0*8 A 4.ACP.CUT-LEAVE 012 0*2 1,4 B. CONV. SURPLUS — — t - w c Acp; PUT- S'ei r ~ ~... 2 7 *........ - -st*....—.....T r n r 2-NO ACp; CUT-LEAVE 2,0 2*4 2,8 J *ACP» C UT-S EL L 4,4 A A 4-ACP. CUT-LEAVE 218 3,2 3,6 f B) FUTURE THINNINGS (1) MARKET PRODUCTS . . ~ ' A‘"»^O tCP7"CUT-SELL . - 4,4 . . . 5,*. '.. 6,2‘ 8-NO ACP, CUT-LEAVE 3*8 4,4 4,0 C-ACPJ,CUT-SELL 6,6 A A D-ACP’, CUT-LEAVE 4*8 5,6 6,2 ( 2 ) SELLSTUMPAGE A. AVE, PRICE - - - 1-mr ACF; CUT-SELL'' -.. 012. . . . . 1 , 4 . . . 4,2 2-NO ACP, CUT-LEAVE 012 0*6 2,2 3-ACP, CUT-SELL 012 A A 4-ACP. CUT-LEAVE 0*2 1*4 3,4 8. CONV. SURPLUS 1-NO ACP, CUT-SELL 2*4 3,6 5,0 — .. .... 7-swirc'PV'''tnrniLEAVE-'''' 3-ACP. CUT-SELL 4-ACP, CUT-LEAVE 27 a 3*4 216 ... 2 *8 — A 3»6 .... »,« A 4,6 197 TABLE FF. REFERRAL NO, 2W09, SENS I T] Vf YY analysis RESULTING FROM A 15 PERCENT TWANOtr t NTHE0UAHTY „ _ -------- INDEX, VALUES ARE INTERNAL LOW I, no TSI nrrwFU MEDIUM high IN 1962 t o r f ~m w r m y — ~~ -— ---- — .— — (1) MARKET PRODUCTS 4f0 4,4 4,8 ....“ .."TFT..SELL..STUMPAGE............................................................................... A, AVE, PRICE 0<2 0,2 1,8 " .. B. CONV, "SURPLUS 2T8 3f6 4,0 (B)--------- FUTURE THINNINGS -------- (11 MARK'ET" PRODUCTS ~ — ----- ?T*'---- * 3 , r (2) SELL STUMPAGE ............ A. AVE, PRICE 0j f Tf ♦ 28,6 8. CONV, SURPLUS U0 2,8 6,2 .. T T r TS1 IN 1“9 62 (A) NO FUTURE THINNING A*NO ACP, CUT-SELL 5?8 6,2 6,4 B«NtT ACPi CUT»tEAVE 4<6 4,8 5,0 C«ACP‘, CUT.SELL 5 A8 6,2 6,4 ........... —-DwACP'r-'CUTwLEAV-E...................... 6 ,4 .............. 6,6...............6, 8 (2)-------------- SELL STUMPAGE ------ ATTYtriWtW — ...... — .. ...— 1-NO ACP', CUT-SELL 0,2 2,4 3,6 - ........... 2-NO ACP* CUT• LEAVE UT2 *,♦ 2,4 3-ACP, CUT-SELL 0*8 2*4 3,6 0T2 2 ,6 3,8 4•AOP7 CUT-LEAVE 0. CONV, SURPLUS —------- ------- ^lT»Nt)“1ltrpV™Ct^*rSfeL'L *-4t 6“~ • '5t R~~ -HErn 2-NO ACP, CUT-LEAVE 3?4 3,8 4,2 3-ACP, CUT-SELL 4T6 9,0 9, 4 4-ACP, CUT-LEAVE 5f0 5,4 5,8 < 8 7 FUTURETHINNINGS (1> MARKET PRODUCTS -----------------------------------5i«.8 ,4...... -.1 4,2 8 . NO ACP, CUT-LEAVE 4f4 5,8 7 ,f C-ACPy CUTi.S8tt 8-ft 8 f4 14,2 D-ACP, CUT.LEAVE 6f2 9,8 19,8 ( 2 ) SELL STUMPASe A, AVE, PRICE ----------------------- f . NO ACP?—OUT-S-ELL- - S'pt'-.....- — —...... —24t §' 2 . NO ACP, CUT-LEAVE 0*2 1|2 4,2 3- ACP» eOT-SELL* 0t« 21* 2 6 ,6 4 . ACP, CUT-LEAVE Of2 2,6 A 8v CONV,SURPLUS 1-NO ACP, CUT-SELL 1?6 3,6 7,2 f NO ACPi CUT»bEAV€" — —........ 4 rt“ 3-ACP, CUT-SELL 1*6 3,6 7,2 4 . ACP* CUT-LEAVE 1,8 3,8 A 198 T*BLE'~ GG. REFERRAL P C ,2G 10. analysis resulting SENSTTIV|fY FROM A 15 PERCENT CHANGE I N T R E BUALTTT INDEX, Wk TEs ^o r .VALUES ^ ETy1r^ ARE {NlfRNAL uow I, NO TSI IN 1962 — ( AI N'CT'TUTBRE THTNUTNG ~....... (1) MARKET PRODUCTS T2) SI L L S TUMPAGE A, AVE, PRICE ■ — ™ _ — HIGH 2f« 0|2 0*2 0*2 8*2 1.0 2,0 D«ATP,CUT« LE A VE 2*4 2*0 3*4 2*4 3,0 2*2......... 5*2 2*6 3,8 2, 4 A 3,0 A¥XCP, “CUT-LEAVE 0*2 012 0,2 0*2 0*2 0*2 0,2 0*2 0,4 0,2 1,0 0,2 . 2 *4 0,2 0*2 0** 0,2 0*2 Of 2 "3,~2..... ...— pyr~...... — ^ -T - su rplu s (B> FUTURE THINNINGS "TTTl^RPET'lWDUCTS (2) SELL STUMPAGE ■ ----------- a; AVE, PRICE 0, CONV. SURPLUS XT, TSI IN 1962 (A) NO FUTURE THINNING _ (2) MEDIUM 1*6 b; c o w *- - - — . A-NO ACP, CUT-SELL B iW ACP, CUT*LEAVE C.ACP^ CUT-SELL SELL STUMPAGE j~ AVE'"," PRICE 1-NO ACP, CUT-SELL 2iR0 ACP’, CUT-LEAVE 3-ACP, CUT-SELL 0. CONV, SURPLUS ..... 2-NO ACP, CUT-LfAVE 3-ACP, CUT-SELL 4-ACP. CUT-LEAVE (BYFUTURE THINNINGS (1) market products -------------- TANTTAUP; CUT-BELL B-NO ACP, CUT-LEAVE CiACPi BUT*SELL D.ACP. CUT-LEAVE ( 2 1 SELL STUMPAGE A. AVE. PRICE ------------------- s r s w A c r , 'n r u r - “B tL L 2-NO ACP, CUT-LEAVE 3 -A C P , CUT-SELL 4-ACP. CUT-LEAVE B. CONV, SURPLUS 1-NO ACPji CUT-SELL ----------- --------2^1^- -jfCPA ~CUT»LBATE 3-ACP, CUT-SELL' 4-ACP, CUT-LEAVE ~ u r e ... ...... 0*2 ...... ...Ayr" 0,6 0,2 0*2 0*4 on 2,0 0,2 1,0 0*2 .3*4..... .... -...* 7 * - ..‘.... .. 4 3*4 2*0 412 33*4 4,6 A 3*4 4*2 5.2 ~DT* 3,8 0*2 6*2 0f2 8*2 A 0*2 6*2 1,6 0,2 1*0 0 i t ..................... tfP................. 0,2 or* 1*6 lf-6 1,0 3,0 1,6 A 2,4 __________________________ a a a _____ __ ____________ TABLE HH.~ WHRPTl. NO, I B IT. SfNSTTTVJTY ANALYSIS RESULTING FROM A 15 ~ “ PERCENT'~CHANCE"TN TKE SU'AU'TTY INDEX, VALUES ARE INTfiRNAL --------RATES 0F"NrrONN'n3W''Ein?ffnJFTTWr LOW MEDIUM HIGH I, NO TSI IN 1962 f Aj-' NO-pUTirRB - TH'TNNTW- "---- ’---- -------- ----------- -- ----------------------- (1) MARKET PRODUCTS ----------fE)SELtT STUHP'AGE~ ' A. AVE, PRICE -------------— CtJlT>r^“"STJRFttXS 7i 0 7* fl '........ ......... 7,2 3*2 6X2 4,6 6,6 4*8 6*4 (B) FUTURE THINNINGS (1) "HIRKET PRODUCTS — -----~-------- 9T2----- ----ITT*— '----- t t y f <2) SELL STUMPAGE ------------------r - 1SYF# p*TCE~“ ‘..................... “3T«.............5*4 ..............7 ,6 B. CONV. SURPLUS 6,4 7,6 9,2 ---- f T | -T S T T l q T T 6 2 - (A) NO FUTURE THINNING ----------~Tt7~'H~ATfKET"~PNt rDtrCTS —’ A.NO ACP, CUT-SELL ■' ...BXNC ACE, CUT-LETVE C.ACPl CUT.SELL ----------------ms acpv c irr - t e *ve (2) SELL STUMPAGE — — ------ A7-"*rrr"p* 1eg— — — - - — 7,2 “frft 7,2 ex 6 -— - -............. ~...™“.. 8*8 22,0 6 *8 ?-0 8*8 22,0 6* e 7,0 — ■ — — — — — - 1-NO ACp, CUT-SELL 3,8 5,2 7,2 ------- -------- -2-NO AC?', CUT-LEAVE........... 4*0 " ........4*6 .......... 5,0 3-ACP, CUT-SELL 3*8 5*2 7,2 ... .— r-jtcN-x ctrt*t&Ave - - 4,0. . . . 4*6. . . . . 5,0 B. CONV, SURPLUS —------- — t T>trO'’'''>CP» "CU Tw'StLL— -™-lgrT6-— — -ff-6' — ~~Ar 2-NO ACP, CUT-LEAVE 6*6 6,8 7,0 —............. 3-ACP* CUT-SEtt 8X6 7,6 A 4-ACP. CUT-LEAVE 6*6 6*8 7,0 TBT^TUTtJNt^ TN1NN1NC5 (1) MARKET products —- - -- - - - - r«NC TrCPT"CUT*S€Lt- ~ — ~9r* - - 12*T -23 *8 B-NO ACP, CUT-LEAVE Bfft 9*4 3,0,2 ............ C»AC^i”Tt^T«SELL ......... ................ 9 ,4 ........... 12*6........... 23,8 D.ACP. CUT-LEAVE 8*6 9*4 10,2 ■ "-•■-■T^-SEtt-'-'STONPxCf -.. A, AVE, PRICE —...------------------------- !hrN^~ACFiimC1^T^feirt - S t* ------------ 6fT-----------------A.... 2-NO ACP, CUT-LEAVE 3,8 5*4 6,8 3-ACP, XCT-Sttt3*6 6*8 A 4-ACP. CUT-LEAVE 3*8 5*4 6,8 B. CONVx SURPLUS' 1-NO ACP‘, CUT-SELL 6*4 8*6 A -------- -------- -------- 2-NO~~ArgpX"-CUT-'fc E AX 5 ------ -6x*~------------ 7yT -------------- 8y4- 3-ACP, CUT-SELL* 4-ACP* CUT-LEAVE 6*4 6*4 8*6 7*4 A 8,4 200 TABLE II. ~ --------------— REFERRAL NO, 1 0 * 7 ” SENSITIVITY ANALYSIS RESULTING FROM A 15 PERCENT ONAWJe 1N T E E ffU ALTT Y INDEX, VALUES ARE INTERNAL Rj TeS- 0r - W ETUiriT"Tcrr"ETrij'H"~apTiON» LOW medium WIQ( 1, NO TSI IN |962 ■ . *. m "n o '"rnTWFTHTPi t w ~. .. . ~ 9(2 11,2 (1) MARKET p r o d u c t s 18*2 ' - - - - - - C2r SELL STUMPAGE 6,4 4*0 A. AVE. PRICE 8,2 11,0 — — ~ 1", CORV 7 "SURPLUS . 9(0.. 10*2 (B) FUTURE THINNINGS . .. ... - •nrrr*iPFEf~FmnnjcTs. ~~— . — . rrr*— . T5y0-- . . T07? (2) SELL STUMPAGE 12,6 10*2 . 7(6 . - - - -- - — . A .' TVT. FR TOE. .. . . 13*4 11(8 15,0 B. CONV. SURPLUS . . . . .. IT, "TST. IN.1V62.. . .. . . . . . ■ '. .. . (A) NO FUTURE THINNING . . “T t T . WAR K'Et" PRODUCTS. . . . 14,4 9(0 lit* A*NO ACP, CUT-SELL 11,8 B-.NITTCP;“CUTSfETTVE IDT® . U * 4.. 14,4 9,0 C-ACP^ CUT*SELL 11*2 . . 11*4.. II,? . 10 i8. . — - - - - - - - - - TOreP7~C0T¥tEEVE. . . (2) SELL STUMPAGE _ . ---- - " -Tr * VF7~"PPTCE.. . . . . — . . . . — -- - - - -- - - — — ~— -■ 1-NO ACP, CUT-SELL A 5*6 11* 4 770 “ 2-NOACp;CUT-LEAVE . '5(0 " 8,0 11*4 5*6 A 3-ACP, CUT-SELL 7,0 .. . . . " ■" ~ 4-ACP, CUT-LEAVE . . 57?.. 8,0 B. CONV, SURPLUS - — .. . — r 4 W . I'cpr-'coT-sTOr. .. - B y r ~ . . . 717® .. A 10,4 9*8 2-NO ACPI CUT-LlAVE 11,0 3-ACP. CUT-SELL ... A 074 11,8 10,4 9(8 4-ACP, CUT-LEAVE 11,0 (BV FUTURE THINNINGS (1) m a r k e t p r o d u c t s - - — ““ ~~ — — ATNtr-ITCPr'C’OT'iiSELL--... . . it*o. . . I3y0. — . . 1®,2 14,4 13,8 B-NO ACP, CUT-LEAVE 13*2 CiACPV-CUt-SftL m o . . 137*. . 16,2 13*8 14,4 D-ACP', CUT-LEAVE 13*3 ( 2 ) SELL*STUMPAGE A. AVE. PRICE - - - - - - -“'l-iiKrO” ACF*,“"CUT-SELL. . . 14*4.. . . . A 7i« 7*4 9*0 10,2 2-NO ACP, CUT-LEAVE 14,4 7T4 A 3-ACP, CUT-SELL 7*4 9*8 10,2 4-ACP, CUT-LEAVE B. CONV, SURPLUS 9*8 13*6 A 1-NO ACP‘, CUT-SELL ~ . — - - - - - - 7 - m ACP7 "OUT*trEATE. . 117?.. . -127'®. . . 1370 13*6 9*8 A 3-ACP, CUT-SELL 12*8 11*4 4-ACP, CUT-LEAVE 13,0 REFERRAL NO,1M2Q, SENSITIVITY ANALYSIS RESULTING FROM A 15 P E RC E N T C H A N G E I N THE QUALITY INDEX* VALUES ARE INTERNAL — ^^■jgy-^f-trETURN'"TCR™EAEH~'OPT| ON T ......... - TABLE JJ. LOW " MEDIUM HIGH 5f0 5,2 5,4 1 ff2 4ft 2*2 2,8 4 ,6 I, NO TSI IN 1962 <1> MARKET PRODUCTS mSELLSTURPAGE A. AVE. PRICE 'B. C O N V * SURPLUS (Q) f u tu r e th in n in g s _ (2) SELL STUMPAGE ~ A, AVE, PR ICE B. CONV. SURPLUS It, TS| IN 1V62. . . . . . . . <_A> NO FUTURE THINNING ^ ^ 4*4 ^ ^ 311 316 4*8 5*4 ^ ^ 7,6 8,0 A-NO ACP* CUT-SELL. 6*6 18*0 34,2 8 - N O ACP,CUT"LEAVE 5*4 5,4 5,6 C*ACP: CUT-SELL 6,6 18,0 34,2 — D-ACP, CUT-LEAVE 5f4 5*4 5,6 (2) SELL STUMPAGE ------- r r -A-VtT-pRTCe-~ ..... ... -.... ....... .... ........ 1-NO ACP, CUT-SELL ' — 2-NO ACp, CgT-tEAVE 3-ACP, CUT-SELL 4-ACP. CUT-LEAVE B. CONV, SURPLUS Tr-NO ACP, CUT-w-SEtt -. . 2-NO ACP, CUT-LEAVE 3-ACP, CUT-SELL 4-ACP. CUT-LEAVE tST fUTUPE THTNRINGC (1) MARKET PRODUCTS — A-NC“ACP", CUT'*“SCLL — B.NO ACP. CUT-LEAVE C-ACP* CUT-SELL D-ACP, CUT-LEAVE <2) SELL STUMPAGE A. AVE. PRICE - - - - - - - _— v eUT-SEL t 2-NO ACP, CUT-LEAVE 3-ACP, O U T S E L L 4-ACP. CUT-LEAVE 8. CONV.SURPLUS 1-NO ACP, CUT-SELL 2,0 3*2 2#Q 2*6 2*0 3*2 2,02 * 6 3 , 2 5,0 3,2 5,0 4*8. . . . . . 6,2. . 4,4 4,6 4?« 0,2 416 4,6 An~ 4,0 A 4,8 — • • S f t ' .............. 4 - ,* ..................4 ,4 — ---------- -- — 2 » Nfr-ACP~,—CUT - LfcAVE 3-ACP, CUT-SELL' 4-ACP, CUT-LEAVE TTO.... 21%8 6*4 8*0 9tO 21* 8 6*4 8*0 ihrt" 0 ff2 0*t 0|8 3,4 3 |4 3fft 34, 09,6 34,6 9,6 "3'r8--- -- ~k" ■ 2,4 4,8 3,2 A 2*4 4,8 A A 6*6 A A 6,4 202 TABLE KK. — -------------- REFERRALNO, 1L06. SENSITIV$?Y ANALYSIS RESULTING FROM A 28 PERCENT CHANGEtN TRE QUALITY INDEX, VALUES ARE INTERNAL -0f- ttETURR FOR'"EIER' “CPT10 NT LOW medium high I, NO TSI IN j 962 rATlVDrTUTURE“THTWI'NQ" 3,8 2,6 3,6 (1) MARKEf PRODUCTS " " (2>SILLSTUMPAGE 0*2 0,6 0,2 A, AVE, PRICE 2,2 2,8 1,0 " 87 COW,SURPLUS (B) FUTURE THINNINGS ...'4V?...... ... ....S’* * '....... H6r,4 ^ r r ‘^XRKEf“~pRtnjucTs............ (2) SELL STUMPAGE 1,0 Off 4,0 ........... ..A, "AVF. PRICE...................... 3,2 B. CONV, SURPLUS 4,8 1 ,4 11 , TSI IN 1952 (A) NO FUTURE THINNING —...-•»•••*... *........... ------- fty-iTIRRBtrTR01JTjm..... 4,2 3,6 5,0 A.NO ACP, CUT-SELL ...... 3,4 _ B.NOACPVCUT-LEAVE 3,8 3,2 A 5,4 A C-ACP* CUT-SELL ......4 , 4........ .... 4,8 --- ----------D* ACP* 'CUTCLEAVE 4,0 (2) SELL STUMPAGE ............. ----....... .......... A"."A-VEV* PRICE.... ........ .......... 0,2 1-NO ACP* CUT-SELL 0*2 2.2 Git 2-NO ACP', CUT-LEAVE 0,2 1,0 A 0,6 3-ACP, CUT-SELL 0,2 1,8 4-ACP,CUT-LEAVfe 0,2 0,2 8. CONV, SURPLUS ----------— .... -i tfwo..ACPf^’CUT'^'Setl:....... ....2 i t ...-. ....... 3 ,2 .......... .... 4J T 2,4 2,8 2-NO ACP, CUT-LEAVE 1f 8 A A ....3,6 3-ACP,CUT-SELL 3,8 2,6 4-ACP, CUT-LEAVE 3,8 TBI FUTURETHINNINGS (1) MARKET PRODUCTS ...4","2..... ...... 5,« ........ .... 6,6 ------------- A'^TNC'~lADP'n:UT*SELL '...... 4,4 4,8 3,6 8-NO ACP, CUT-LEAVE A 5,8 A C-ACP‘, CUT-SELL 5,6 4,6 6,4 D-ACP, CUT-LEAVE (2 J SELL STUMPAGE A. AVE, PRICE 1*4 5,4 “ — — ....-'"i'-RQ" ACP,.CUT-SELL"' ..... Off 0,6 0*2 2-NO ACP, CUT-LEAVE 2,6 A A 0,2 3-ACP, CUT-SELL 1*4 4-ACP, CUT-LEAVE 012 4,0 9. CONV, SURPLUS 3*6 1-NO ACP, CUT-SELL 5,6 2*0 .. ...... ............. 2 - NO'■XCpy TJUT-t?ErAVE.... .. 1*4... ..... ......... .. 3, 6 A 2,6 A 3-ACP, CUT-SELL 3«6 4-ACP, CUT-LEAVE 2T2 5,0 TABLE LL. REFERRAt NO, 2W09. SENS!TTV|?Y 20 F€RCENT“ CMAHG&-JNVMS WAL I™ I N D E X VALUES^ARE^| N T g R N A L ^ ^ ^ analysis resulting prom a ______ _ LOW I , NO TSI * M * * 2 . MEDIUM HJ9h _ ..._ ..._................. .......... (1) MARKET PRODUCTS 3;0 4*6 4,8 f P > S Ett'STUKPAOE A, AVE, PRICE 0(2 0,2 2,2 9, CONV, SURPLUS 2,6 3*6 4,2 (B) FUTURE THINNINGS — “TtT^TTRirEt^tTITUTTTS”-" *" ~T r r — "'Tf*™ tSyS (2) SELL STUMPAGE ‘ A, AVE, PRICE ................ 0*2................ 1*4.........' 36,2 0, CONV, SURPLUS 0(6 2*0 10,6 I t , TSI IV 1962........................................................................................... (A) NO FUTURE THINNING ~ — ’— m MTRRSt~*PRt)'DU CTS— “ ... .. ........................ ...... ............. A-NO ACP, CUT-SELL 5(8 6*2 6,4 ‘ B-NO ACP, CUT*LEAVE 4, 4 4,6 5, o C.ACPl CUT.SELL 5*8 6*2 6,4 D¥A^,-'-1^JT¥UBRtt 6t 2 6,6 7,0 (2) SELL STUMPAGE VFT~PRT'CE~^~ ~ “ ' ” ..... ~----------------1-NO ACp; CUT-SELL 0*2 2*4 3,8 2-NOAOp; CUT-LEAVE 0,2 I*4 2,8 3-ACP, CUT-SELL 0(2 2*4 3,8 4-ACP, CUT-LEAVE 0«2 2*6 4,2 9. CONV, SURPLUS R’Cp;—CU'TwS'Et b'........ —Vf # ..............St*".~.... ....5-jfr 2-NO ACp, CUT-LEAVE 3(2 3*8 4,g 3-ACR,CUTwSftfe 4-ACP. CUT-LEAVE te r 4(4 4,8 5*8 5*4 5,6 6,0 future thinnings <1) MARKET PRODUCTS - ------ y -' NG-A-CPy - eut ’ w t g Lt -.. 9 j t .-..... ~&r*..... 8-NO ACP, CUT-LEAVE 4,2 C-ArCPV CUT-Sftt "'St* D-ACP. CUT-LEAVE 5*4 1 2 ) SELL STUMPAGE A, AVE, PRICE t*wr~KCPir cu T*s e l l .......... or* 2-NO ACP, CUT-LEAVE 0*2 3»ACP,CUT*Sttt 0(2 4-ACR, CUT-LEAVE 0(2 " By CONV. SURPLUS 1-NO ACP', CUT-SELL ---------- f-rN'O ACP» gUT*tfe A'V'E 3-ACP. CUT-SELL' 4-ACP*"CUT » t SAY6 1,2 Dr*' 1(2 I f* 5** 8*4 9*0 7,8 16, r 25,0 ............• 1*2 5,2 2*6 36,2 2*» A 3*6 13,0 ........2f*..........— •v*' 3*6 13,0 3*0 A “T A B L E MH. REFERRALNO,2G10.SENSITIVITY ANALYSIS RESULTING FROM A 20 PERCENT CHAN G E IN THE GUALITY INDEX, VALUES ARE INTERNAL LOW I, NO TSI IN 1962 medium ___ ________ high _ (1) MARKET PRODUCTS If* 2,0 2,4 ” U )SELL STUHPAGE A. AVE, PRICE 0,2 0*8 0,2 “B7 CONVV “SURPLUS 0 ,2 0*2 0,4 (B) wi y !^ n n u u ~ z ^ _____ ^ (2) SELL STUMPAGE ---------A, AVF.PRICE 012 0,2 3,0 B. CONV. SURPLUS 0*2 0,2 2,6 IT, TSI IN 1962 ....... ................................................................................ (A) NO FUTURE TWINNING “— f lr j HTRKEt PRODUCTS ' A.NO ACP, CUT-SELL 0-NO SCR, CUT-LEAVE C»ACP, CUT-SELL ~ ------------ CAACP, “CUT-LEAVE (2) s„ SELL STUMPAGE r T V .F r .p R I .C F „ 1-KO ACP. CUT-SELL 2-NOACPV CUT-LEAVE 3-ACP, CUT-SELL “ 4-ACP, CUT-LEAVE 0. CONV, SURPLUS -----------------|SN'0- y c prr- gy-T-'SgLX:— .................. ' 2,2 1*8 3,0 2.4 4,0 2,6 A 3,0 _ . 0,2 0fS 0,2 0 .2 0*2 0,2 0,2 0,2 ----0 * T ~ .... ...Tf**~” 2-NO ACP, CUT-LEAVE 0f 2 3-ACP, 0 (2 CC T^SELt 3,0 2,2 5*2 2,6 0*2 0 *« 0,8 0,2 2,0 0,4 ~tTW" 0,8 2 ,8 4-ACP, CUT-LEAVE 0,2 0,2 1,2 (B) FUTURE THINNINGS (1) MARKET PRODUCTS --- -------XiNC“ACP","“"CUT-"SRLt .........1 * 0 ' ...... .. 3 , 0...... 11,2 B-NO ACP, CUT-LEAVE 2*6 3,4 4,4 C-ACP, CUT-SELL 3,8 33,4 A D-ACP’, CUT-LEAVE 3,0 4,2 5,6 m SPLL“ STUMPAGE A. AVE. PRICE ' .......- 1-NO ACF‘r~CUT*S*tL 0,2 -...... "“t T * * “ A'“ 2-NO ACP1, CUT-LEAVE 0,2 8*8 1,6 3-ACP,CUT-SELL 0,2 0,8 A 4-ACP, CUT-LEAVE 0|2 0,2 2,6 B. CONV* SURPLUS 1-NO ACP, CUT-SELL 0«2 1*0 4,0 ~~---------- -~~ “^ i R t r ACPa CUT-tt*Vf~ ~0*2.......... “ST*—............2V'2~ 3-ACP, CUT-SELL 012 1,6 A 4-ACP, CUT-LEAVE 0,0 1*0 2,8 TABLE m . ------------ REFERRAL* 0 * 1B14, SENSITIVITY ANALYSIS RESULTING FRCH a 29 PERCENTtWftNttE |N m QUALITY INDEX, VALUES ARE INTERNAL RXTES" CP-^TIW-TW-EirBTr-CPTt^T.... LOW MEDIUM HIGH I, NO TSI IN i962 ~ — t t ) MARKET PRODUCTS 6,0 l 2 y ”SPLL STUMPAGE a ; AVE, PRICE ~. B , CONV . SURPLUS 7*0 7,4 3#0 4,9 4,8 610 6,4 6 ,6 (B) FUTURE THINNINGS — — T t r MARR'E T PR0 DOCTS— “ — — " r # r -------- "X V T*— ~ ..... f * ', T r <2) SELL STUMPAGE - ~ ‘ A . AVf, pPTCE 2it 5,4 8 ,4 B, CONV, SURPLUS 610 7*6 9,6 It, TS1 IN 1 V « 2 - — (A) NO FUTURE THINNING TtT~MARKET' PRODUCTS .. A.NO ACP, CUT-SELL 7*0 0*8 27,8 B¥NO~ A CPi CUT-LEAVE 4 *6 6*5 7,2 C.ACP; CUT-SELL 7*0 8*8 27,8 ■— — -DwACPv CUT-LEAVE 6,6 6*0 7 ,2 (2) SELL STUMPAGE — — -- r r A Y f r m c r -. . . . . . . . -. - . — 1-NO ACP, CUT-SELL 3,4 5*2 9,0 . . . . . . 2-NO ACP', CUT*LEAVE 3*6. . . . . A*6.. 5,2 3-ACP, CUT-SELL 3,4 5*2 9,0 4-ACP, CUT-LEAVE 3*6 4*6 5,2 B, CONV, SURPLUS - - - - - ,- - - f gfvo”'ACP, CUT •'SELL— ’. -“Ot*. ... . . . . . " t" 2-NO ACp; CUT-LEAVE 6*4 6,0 7,0 3-ACP, CUT-SELL 6*2 7,6 A 4-ACP, CUT-LEAVE 6*4 6*0 7,0 TBTFUTURETHINNINGS <1> MARKET p r o d u c t s ----------- ^-Ntnrcp-r'CUT-sttr -.... ~«r«.... -..i t , 6 .... tt, s. B-NO ACP, CUT-LEAVE 8*4 9,4 X0,4 C-ACP}CUT-SELL 8 f8 l*f* 28,6 D-ACP, CUT-LEAVE 8,4 9,4 1,0,4 121 CELL- STUMPAGE A. AVE, PRICE - - - - - — 1-NO ACP, CUT-SEL L - — Sr9" ~~ ~“frf9 — “A ~ 2-NO ACP, CUT-LEAVE 3*8 5,4 7,2 3-AflP, CUT*SELL 3*0 6*0 A 4-ACP, CUT-LEAVE 318 5*4 7,2 8. CONV, SURPLUS 1-NO ACP*. CUT-SELL 6*0 8*6 A --------------- ...... A C P ' *— CU T - L E A V E 3-ACP, CUT-SELL 4-ACP, CUT-LEAVE - ~4-ff 6,0 6,2 7f 4L ....... 8-*-B 8*6 7,4 A 8,8 -- 20i> TABLE 00. — “F E F E R F X t N O , XL 16, SENSITIVITY ANALYSIS HESULTING FROr A 20 FERCENT CHANGE IN T N E QUALITY INDEX( VALUES ARE INTERNAL ------------------- MEDIUM LOW I. NO TSI IN 1962 — . .. . TXT"WTTfTB RE" TH'T NNTNQ. . . . . “ (1) MARKET PRODUCTS " - - - - m seicstumpage A. AVE, PRICE ■ ‘ b; co nv. surplus (B> f u t u r e t h i n n i n g s — . - .. {TT~M XRK Ef ,j"P R OW C T S ’ .. . “ (2) SELL STUMPAGE ' ““ A, XVF. PRICE 8 . CONV, SURPLUS IT,TSI |N 1962 (A) NO FUTURE THINNING ■— . . . ... r n " “H*Nm^pffomjcrs". . A.NO ACP, CUT-SELL B i W B T W , CUT.LEAVE C.ACPl CUT-SELL . . . D-ACP,CUT-LEAVE (2) SELL STUMPAGE ~ n r:-w w rlFwuE~~' *. '. . . . 1-NO ACP!, CUT-SELL “ 2iN0 ACP*, CUT-LEAVE 3-ACP, CUT-SELL ---*¥ACF. CUT-WE AVE B. CONV. SURPLUS . — ~ -- “ '1-WO. XCPt '"CUT-Sttt. . 2-NO ACP, CUT-LfcAVE 3-XCP, CUT-SELL 4-ACP, CUT-LEAVE ~ I B IFUTURETHINNINGS (1) m a r k e t p r o d u c t s .. . . .... “A'iNO" XUF,'" CUT «^ELLT. . . B-NO ACP, CUT-LEAVE C.ACPV'CUTiSELL D-ACP. CUT-LEAVE ( ? ) SELLSTUMPAGE A. AVE, PRICE — ~. . — — . ■r-wo'"xcpr"Cur-s«tr. . 2-NO ACP, CUT-LEAVE 3-ACP, CUT-SELL 4-ACP, CUT-LEAVE B. CONV. SURPLUS 1-NO ACP; CUT-SELL - - - - - - ~- — . TsNtT’XCP, “TUTwttAVE. 3-ACP, CUT-SELL 4-ACP, CUT-LEAVE 9|0 10,2 HIGH 11,4 6,4 6,6 11,4 Itff . I3',~l. ~ . .. T3?*. .. . 16,or 13,2 6,6 18* * 13*4 11,4 15,6 3,0 " e,4 " .. . . .. . . . 8,6 10,8 8,6 10*8 11*2 .. .. . 4*4 510 4*4 5*0 U,« lit? 11*4 .. . 11*4 7,8 11,4 7*9 . .. 15,8 12,0 15,8 12,0 A 6,2 A 8,2 .. 7,6. . . . It*#' . ... A. 18,4 9,6 11,2 7,6 ... A ' 1 1 *# 10*4 916 11,2 .. . .«. . ' 1UT4. . ... ....13, 13,0 13*# 13*1 10 f4 13*8 1310 17,6 14,6 17,6 14,6 . 6,0. . . . 14,-4. . ... A. ’ 9*8 10,6 6*8 14,4 A 6*0 9,0 6,8 10,6 9,0 11 TO 9,0 11*0 13,6 .. It!*. . 13*6 12 *« A 3*2 A 13,2 ... 1 207 TABLE PP. REFERRALNO, 1M20. SSNSITIVI TY ANALYSIS HESULTING FROM A 28 PERCENT CHANGEIN THE DUALITY INDEX, VALUES ARE INffiRNAL ----------LOW MEDIUM hiqm I, NO TSI IN £962 5*2 5.4 (1) MARKET PRODUCTS 5 f0 t2) SltL STUMPAGE 2,2 0;8 3,0 A. AVE, PRICE ... 4f 4 . ........ 4|2 - - - 0. COW. SURPLUS 4,8 FUTURE THINNINGS tT-i'P CI t MARKft” products . . . . . . •"“STS-(2) SELL STUMPAGE 4f» 6,6 2 ,6 A, A V E , PRTCE 5*4 10,2 3fQ B. CONV. SURPLUS t t i TS1IN 1962 (A) NO FUTURE THINNING ... •---- --------------------■ ---- ---- ---------( ly wj-RKtt""PR0 DUCTS------ ---------- — 6,2 36,6 18*» A-NO ACP, CUT-BELL 5*4 ...... 5,6 ..... 5*4.... BVNO" ACP, CUT-LEAVE l8*8 38,6 6*2 C.ACP'f CUT-SELL St 4........ ... 5*4.. 5,6 - -- ---------- tr-ACP, CUT-LEAVE (2) SELL STUMPAGE . ---- ------- -----... . ------------.. _ _ --------- --------------------------- ------------ -----------— .... 3*2 19 6 A 1-NO ACP’. CUT-SELL 2*6 — ... -.... ..... -............. 2-NO..ACp, CUT-LEAVE •■■•- 116 3,2 3*2 1 ♦6 A 3-ACP, CUT-SELL 3.2 .........— ....... ...-.......4-ACPv.CUT-LEAVE.............. 1.6 2*6 B; CONV. SURPLUS , —^ . „ — - - — ^ ^ 0 "£Cp-j—CUT—"SELL-..... . .4f6 ... ..-6t U-.-.— ... A 4*6 4 14 2-NO ACP, CUT-LEAVE 5,0 6,2 .......A ~...... -...... ... -.3 - ACP;.CUT-8ELE.... . ... ' 4 1 6.... 4,6 4 A4 4-ACP, CUT-LEAVE 5,0 — it) FUTtrFfTNtNNlNOS (1) MARKET products ain^~SCF~, CUT-BEtt- B-NO ACP, CUT-LEAVE CiACF> CUT-wSEtL D-ACP, CUT«LEAVE (2) ~SEt L" BTUMPA15E A. AVE, PRICE ----------- fryttO~“yCF~~CU TwE fefet~ 2-NO ACP', CUT-LEAVE 3» ACP, CUT"Bfh.t 4-ACP, CUT-LEAVE B.CONV.SURPLUS 1-NO ACP, gUT-SELL 3-ACP, CUT-SELL 4-ACP, CUT-LEAVE ... T*~4... ......t t f t ...... ■“ W r t “ 8*0 6J0 .7*4... ... 21* 9 8*0 6*0 ..-6t2.... --- -"3"f 2*4 0*2 3*8 0|2 2*4 092 2*8 2,8 2.8 A 10,2 ........ 38*8 10,2 ...— --- A~. 8,8 A 5,8 A . -- --4*r6~.. .... *,* A A 4*6 7.2 APPENDIX IV The Modified Version of Clark Row' Computer Program (1963) Which Was Used in the Present Study. 209 »K0QR**1 INVEST 01MENS!on ANC<10>,:aNC|10>,NC(4(2QO>,PICO<6,200),N1»6,200),T1.01<6, lJU«),QJALl(6,200),V 2 ( * , 2 B O > . O U A l 2 ( * . 2 0 0 ) , N 3 ( * , 2 B O ) , T L e i ( * , 2 0 0 ) , B V A «I.A(6,2f)0),PH(3,20).CANil',20>,rv*L(2>>,*ATi(200),STLo8I20P),VALlN( 34.200>,LYIA1.KCXC6),KlxI*),K2X<6),*3X<*>,A(26),lI(6),YIDK*#20Q> OMEN-SION P l N T < 3 > , « l & K < * > 01SC(X)aRTLOl**X *nint 75 lb t'U^MAT(lHl,10X,*SevStTtVITT ANALVIlE OP THE PRICE AE«V*PT1ONa,//> na read itoooi(RInt(I).i»i»s)»iout l/OUO fURMAT <3F4,3,I2> TATE(1)«RINT(1) OU l7oni Ia2,200 IF{RATS(l-l)»RINT<1)> t7eo2(17003,1/003 1/0U2 RATE 30 TO 17001 I700J '„tVQTH«I-l IFfHO0/2 30 TO 137 1/I1U5 itNQTHaLENOTM/? 30 TO j37 . 1/OJi CONTINUE 137 DO 13S I»1,LENGTH 138 RTLQG( I ) » 1 , * R A T E ( I ) READ 11, NO.L2.LX, (Li <1)’ .1*1.6 ),(LT(L),Lb1,A),KX,KCxX, KXCX(l),lb1,6),K1X«, (KlXll.),L«1,6),a2XX,(K2X,lal,6) • 2<3XX, <<3X(L).L»1»6>, J X , « X , N Z , N X II lb n lb 132 13 \)b 160 162 14 rORNAT(3I2,6A4,6l3,12/7111/713,412) *R1NT 76.NO,(LI(I).L»l,*l formAt(1H0,5X,I2,10X.6<6X.A4)) SNINT 77 rURHAT'l*t 1 READ 15,(A,CANC(J),Jal,JX) DO 161 Nal.NX 1200 EORMAT(6^9,3 I 191 READ 1200, (PR(K,M),CPR(K',M).Kal.KX) 192 IMN7.1 >195,195,193 193 READ 1 3 , (FVAL(N),N»l'.NX) 196 DD 39q Jbi.JX DO 39g Nai.HX .LLXaNX IF(NX.EQ,0ILLLXal 198 DO 390 Na1,LLLX ?10 DO 3*5 La 1,LX ic«0.0 ot»Nu»n,o DAC»0,1 D M ■ n ,n 0k ^»n ,i DM«o,n Df i/Al.rl),0 O I ^ t l o o i I) D i $ c n « * T u O D < I )* * X L ^ r i l IMAMC(J)) 226,230.226 226 damc*(arjc*ANCIJ)«(D|SCO«XLY*HA|E(I)-l,))/(RATEtl)** I M K CX A ) 260.2*0.241 DO 2*6 K C « 1 .KCYA < y ;«f l :i a t (n <:< l »k c >) If ( X f ' C - l . l P ? * * , ? 4 4 , 2 4 6 230 ?3S 2Au 2* U J S U U ) ? 2*6 DJMTlNJb 230 (I- (A1YA) ?oaf2on,»5l 2 2 1 D O 2 * 6 M M ,Kj,yA X Y1«f L D A T f U U . K l ) ) ?66 DAitl-K1*(YUU(L.lM)«QUAUl(l.»Kl)*(l,*CPR(l,"IJ ?oo 261 1*AY1))/DISC(XNJ) If ( X 2 » A ) 2 ? a , 2 7 0 . 2 6 1 DO 2*5 K ? M , K 2 X A X N 6«( L D A T ( M 2 ( L » K 2 ) ) i>oo DA?»r.K?*« YI.J?(L»'<2I*PHf2'.M)*0UAL2 )2 lDISC ?/U ?/l 2 /8 If28P,280,271 x 3M , K 3 y A X'YX«FLDAT(N3(L,K.1) l D M « r i K « * ( Y I ii.ML , K 3 > * P R » 3 , M > * 0 u A L 3 ( l . . K 3 » * < l , * C P R ( 3 , “ ) » K N a ) ) Oj 27b l/UlSr< »N3) 2ofl TUYAI s IKIfnKPx'K.UPANC.DCAMC'DKi: If ( N 7 . 1 ) ? V P , ? ' ) C . 2 9 5 2vp YAU i>i(.ti)»rnv4i..(i.*i./ 3J TO 14(1 2V3 Df >'AI b -*VAL('Y)/PISC1 YAuIM.t I ) « r n v » L * D P Y A L loo i p o If ( V t L ’ M I L , I ) ) 7 3 0 . 3 4 0 » 3 4 n 9 Ai, !*■ ( . , I ) » o . 0 A s s j r - N 3.10 TO ‘7fcRi : j ' ' T !, < j e :
f A (1 ,3F10 .1) 30 T'l •6 66 3M N ) 776,tXtROll),L»1,6) !-v/4MAT(lH ,i 5X,•MEDIUM#,F6.I.5F i O,1) 30 rr »6A5 3M N T 7B6,IXIRP(L),L»1,6» 708 7J0MATUO ,17X. • « ! "«H», T6. 1 , 5 F 1 0 .1 ) 4 6 6 6 DJ 41.67 111 , LE’ltiTH 4607 4 A T E ( I )« 9 A T b ( I ) / 1 0 0 , 0 JvO 30 iT IN /E 4c»U 11, IF xD If I I H p . 9 8 ) 4 0 3 , 1 * 2 , 4 1 0 4 d0 34 INT *2 42 •d R M A T ( ? 3 « 0 4x0 s n p FRO07 IN INPJT CARDS) 211 P A T * I NP UT I ' S T R H C T I O n S CAHU columns ITfcM F IfcUU c C U N I R u l 1- A 5-B 9-1? -1 M A r 13-1A c u n i r o l - A W C A u 5-6 7-3n 2 c c 3 1- a r 49-50 C U M T R U l 1-J -3 V A - 21 ?2-24 A ?5*4? 2 NR A A 3 - AS 46-63 1-3 A - 21 CU imIRUu -A 2 2 2 2 2 ?2-2 1 ?A-?S 36-27 ?B-?9 p h u b , na E 1-73 PMUIJ , .,AM| -s XXX XXX XXX XXX XXX XXX MAX. NO, r e t u r n s f o r p r o d u c t t h r e e NO, HETURNS - EACH A - T E H N A T I V E - P R O D U C T T n R E t NO, SETS OF ANNUAL C j S T S ( 0 - 1 0 ) NO. SFTS OF PRODUCT “ R I C E S ( 0 - 2 0 ) TYPP OF T ERMI NAL C A L C U L A T I O N ( 0 1 - I F pfcRPfc1 UAL S E R I E S , 0 2 - I f F I N A L v A l UE) NO, UF F I N A L VALUES ( 0 - 2 5 ) XXX xxx xx XX 1-2M n a m e n a m e ~ a - 6n name PcRIO uIC COSTS n u 2 2 2 2 2 2 2 35-27 ?8-3A 37-io AO- AH 49-51 s2-60 A l-63 XA-7? 2 2 (Ni), ; P 2 P C 1U R N S m 0* CAOUS of product of product OF PRODUCT YEAR OF I T h COST YEAR OF I T h COST YEAR OF I T h COST YEAR OF I T h cost YEAR OF ITh c o s t YEAR OF I T h COST 1-3 4-1? 13-1S 1 = MAX, XX XX OF PROBLEM n a m e ?l-An 2 XX MAX, NO, P E R I O D I C C O s T s NO, P E R I O D I C C OSTS, sACH A L T E R N A T I V E MAX, NO, RETURNS F O R ’ PRODUCT ONE NO, RETURNS FOR EACH A l T E H N A T I V E - P R O U U C T UNE MAX, NO, RETURNS FOR PRODUCT TWO NO, RETURNS FOR EACH A L T E H N A T I V E - P R O U U C T TWO 2 i , XXX . XXX , XXX PROBLEM NUMBER ( 1 TO 9 9 ) FOR I D E N T I F I C A T I O N XX A L T E R N A T I V E TYPE ( O l - R O T A T I ON, 0 2 - S I T E I N U E X , XX 0 3 - » H O D U C T I J N SYSTEM) XX NUM9EH OF A L T E R N A T I V E S ( 0 1 TO 0 6 ) 4 O I U I T NO, I D E N T I F Y I N G EACH A L T E R N A T I V E XXXX LFNOHT OF EACH A L T E R N A T I V E ( 1 - 9 9 9 YEARS) XXX XX MAX. NO. OF D I F F E R E N T PRODUCTS ( 0 - 3 ) 1-2 3-4 e c A RATE OF I N T E R E S T I N T F H E S T RATE JNCREMeNT MAXI MUM RATE OF I N T E R E S T (00 FOR I N T . HATE ONL T , 01 FOR P,H. AND I N T E R E S T R A T E , 02 F O r PRESENT WORTHS ON L Y ) MINIMUM NO, one Two THHEe I T H COST FOR A l T . FON A L T , 1 I T H COST FOH A L T , FOR a l T , 2 I T H COST FOR A L T , FOR a l t , 3 I T H COST FOR A L T , for a lt , a I T H COST FOH A L T , Fur a l t . 5 I T H COST FOR A L T , for ALT. 6 UF PtRIODIC COSTS xxx x x x x x x . xx xxx X X X X X X , XX xxx xxxxxx,XX xxx X X X X X X , XX xxx X X X X X X . XX xxx x x x x x x , xx 1 2 3 4 5 6 IN ANY A L T , ) YEAR OF JTH RETURN FJ R THE KTH PRODUCT• A L ) , 1 XXX xxx.x VOLUME OF JTH y i e l d - O r HTh PROD UC T - A L T , 1 9-1? quality i n d e x , j t h return for kth p r o d . - A L l ,1 x.xx --AND SO FORTH FOR A „ L S I X A L T E R N A T I V E S I n O. OF CAGyc I N A SET » SAX. NO, OF RETURNS FROM THE PRUUUCT I n ANY A U r W A T I t t - n o , OF SETS a NO, OF P r ODUCT s ( 1 TO 3 ) ) U u u CI »»NJAL Ou S I 1-3 4- M 1-0 10-1“ I T h ANNUAL I T h C h ANUE anu P " 1LF a 1-9 10- 1 “ sn COST ASSUMPTI ON I N a n n u a l COST ASSUMPTI ON f o s Th , foh jp to i n sets X*X*X,X XX XXXXX.XXX I T h U N I T PHl Uf c A S S U M - T I O n - PRODUCT ON t XXXXX.XXX I T h ANNUAL Oh x NUE I N ' u n I T P R I C E ASSUME!) FOR PRODUCT JNfc XXXXX.XXX A I D SO FORTH FOR A . l t h r e e PRODUCTS ( A U U I T 1 O r a l CARPS OF OTHER S E T s OF P P J C F ASSUMPTI ONS T j a MAXIMUM OF 2u> IINAL VAlUes Z Tckm I**l 1-9 I T w F I N A L VALUE ASSUMPTI ONS XXXXX.XXX AND SO FORTH FOR a m a X I M j m OF 2 5 ( J O NOT USE I f TERM, C A L C, I S P FHPETUAL S t W l f c S ) 1-? T E R MI N A L C J d E ( V b - A N j T m ER PROP. 9 9 - AFTER T h e F I N A . PROB l FM) F O L L Ohs XX VITA A. Jeff Martin Candidate for the degrde of Doctor of Philosophy Final Exam: May 6, 1969 Guidance Committee: Dr. Dr. Dr. Dr. Vi c t o r J. Rudolph# Chairman Bruce T. Allen R. Keith Hudson Robert S. Manthy Dissertation: Evaluating Timber Stand Improvement Opportunities In Northern Lower Michigan Using the Decision-Tree Approach. College Education: BS in Forestry from Michigan State University in 1965. MS in Forest Management from Michigan State University in 1966. Biographical Sketch: Born# March 29# 1943 in Elsie Michigan; Attended Elsie High School and graduated in 1961. En­ rolled at Michigan State University in the fall of 1961# majoring in Forestry. Married in 1965. 212 213 Graduate Studies: Economics# 36 credits Statistics# 26 credits Computer Science# 10 credits Operations Research# 18 credits Experience: Forestry A i d - U. S. Forest Service, Wyoming# summer of 1962. Forestry A i d - U. S. Forest Service# California# Summer of 1963. Salesman at a retail lumber yard# summer of 1965. Graduate Research Assistant with the Department of Forestry# Michigan State University# from 1965 to 1968. Instructor in the Department of Forestry, Michigan State University during the fall of 1968 and the spring of 1969; teach­ ing a 5-credit course in forest biometrics# and a 3-credit course in woodland forestry. Member of: Society of American Foresters# Sigma Xi# Sigma Pi. and Xi