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Martin Forest Biometrician WA Dept. Natural Resources Olympia, WAJJTJProphecy versus Perspective*Predictions are fictional constructs that may have applications in the real world. "Prediction is difficult, especially if it concerns the future." Francis Crick.  Expositions of the future tell more about what we are, than about what we will become. Daniel Gilbert. Some clients view model results as predictions of what is to come - belief in absolute values. "To try to do something which is inherently impossible is always a corrupting enterprise." Michael Oakshott.<`(knVLProphecy versus Perspective: 4"Models provide a means to better represent existing information." Al Stage. "The purpose of calculation is insight, not numbers." Unknown "I believe the best test of a model is how well can the modeler answer the questions 'What do you know now that you did not know before?' and 'How can you find out if it is true?'" James M. Bower. Some clients use models to choose among alternative actions or directions - acceptance of relative values.  The myth of comprehensive planning versus the science of muddling through. Richard Behan. pP( Why Econ - Motivating Questions Given an existing stand, when is the economically efficient harvest time? What is the value of forestland for timber production? Given an existing stand and its forestland value, when is the economically efficient harvest time? Given harvest deferral of an existing stand until a target condition is achieved, what is the forestland value for timber production that maintains the target condition? Given an existing immature stand having a known land value, what is the value of the immature trees ( reprod value)? `( ZN8Example 1  when to harvest?Objective - maintain continuous tree cover. Assume 400 pole-sized trees per acre. Prescription: harvest 90% of the basal area between diameter limits that vary over time, e.g.: In 2004 harvest 90% of the basal area in trees 6-16 DBH. In 2054, harvest 90% of the basal area in trees 6-22 DBH.  Pretend harvest simulated each cycle. Z`(u0P()`(u( 0Example 1  FVS Measures2Example 1  ECON MeasuresExample 2 - forestland value?What is the soil expectation value (SEV) of a perpetually repeating prescription? Initial conditions: residual 16 TPA, 5-21 DBH. Prescription: plant & natural regeneration, commercial thinning 2034, & final harvest to replicate initial stand conditions.  Pretend final harvests simulated each cycle beginning in 2044. Each  pretend cycle is a mutually exclusive prescription, e.g., a repeating 80-year rotation, or a repeating 90-year rotation, but not both. pP(,Table 2  FVS Measures 2Example 2  ECON Measures!BExample 3  future prescription? ""  @When to replace a current stand with a perpetual prescription? Assume 400 pole-sized trees per acre. Prescription: reserve 16 large TPA.  Pretend harvest each cycle. SEV from Example 2 ($154). Influence of future stands is considered. "Value of forest" measures the economically efficient time to convert the existing stand.  Value of forest equals PNV plus the discounted SEV (value of trees plus value of land). @#2Example 3  ECON Measures$LExample 4  maintain a future forest? ''If harvest deferred until some stand target; what is SEV that maintains the target condition? Assume 400 pole-sized trees per acre. Prescription: harvest all but 16 sixteen largest trees when 10% of trees >= 21 DBH, and regenerate stand. Event Monitor tracks target condition to determine time of harvest, and  triggers ECON keywords (SEVSTART and PRETEND).  Pretend harvest at each cycle is mutually exclusive perpetual management alternative of different harvest age. `(%0Example 4  FVS Measures*#2Example 4  ECON Measures ' 4Example 5   reprod value Value of immature trees (  reprod value) when bare land value (SEV) is known? Well-stocked pole-size stand with little merchantable volume & SEV of $154. Value has two components, NPV of existing timber & discounted SEV of future stand. Value as of today if sold or destroyed   value at risk. Value depends on expected harvest date & hence delay of future prescription (SEV). }pZ(}\>64Example 5   reprod value  ("FIntegrated Example  FVS, FFE, ECON$$>Examine economic and biological effects of alternative fuel strategies. Young, mixed-species stand.  No Fuel Treatment thinned at 10, 30, 50 and 80 years, with wildfire in year 60.  Fuel Treatment same thinning & wildfire, but pile/burning treatments following 10 & 30-year thinning. `( hSIntegrated ExampleQGEconomic Summary Table FVS/ECON EXTENSION VERSION 1.0 STAND ID: Example_4 MANAGEMENT CODE: NONE - Dynamically initiate a future perpetual prescription --------------------------------------------------------------------------------------------------------------- ECONOMIC ANALYSIS SUMMARY TABLE (DISCOUNT RATE: 4.0%) --------------------------------------------------------------------------------------------------------------- INVEST- PRETEND UNDISCNTED VALUES PRESENT VALUES INTERNAL REALIZABLE MENT MODE IS ----------------- ---------------- RATE OF B/C RATE OF VALUE OF VALUE OF YEAR PERIOD ACTIVE COSTS REVENUES COSTS REVENUES PNV RETURN % RATIO RETURN % SEV FOREST TREES --------------------------------------------------------------------------------------------------------------- 2004 10 NO 0 0 0 0 0 2014 20 NO 0 0 0 0 0 2024 30 NO 0 0 0 0 0 2034 31 NO 1062 6361 315 1886 1571 > 50.0 5.99 10.2 2035 9 NO 50 0 48 0 -48 0.00 -162 2044 19 YES 50 0 48 0 -48 0.00 -92 2054 29 YES 50 0 48 0 -48 0.00 -71 2064 39 YES 50 0 48 0 -48 0.00 -61 2074 49 YES 50 0 48 0 -48 0.00 -56 2084 59 YES 684 1622 137 228 91 6.3 1.66 4.9 101 2094 69 YES 1110 3337 149 317 168 6.7 2.13 5.1 180 STAND ID: Example_3 MANAGEMENT CODE: NONE - Economically efficient time to implement perpetual prescription -------------------------------------------------------------------------------------------------------------- ECONOMIC ANALYSIS SUMMARY TABLE (DISCOUNT RATE: 4.0%, FOREST/TREE VALUES BASED ON USER-SUPPLLIED SEV: $154) --------------------------------------------------------------------------------------------------------------- INVEST- PRETEND UNDISCNTED VALUES PRESENT VALUES INTERNAL REALIZABLE MENT MODE IS ----------------- ---------------- RATE OF B/C RATE OF VALUE OF VALUE OF YEAR PERIOD ACTIVE COSTS REVENUES COSTS REVENUES PNV RETURN % RATIO RETURN % SEV FOREST TREES --------------------------------------------------------------------------------------------------------------- 2004 10 YES 1181 1407 1131 1352 221 > 50.0 1.20 5.9 391 237 2014 20 YES 1454 1828 946 1187 241 46.6 1.25 5.2 356 202 2024 30 YES 1620 2328 723 1022 298 21.2 1.41 5.2 375 221 2034 40 YES 1753 3082 543 914 370 14.8 1.68 5.4 422 268 2044 50 YES 1801 3868 395 775 380 11.4 1.96 5.4 415 261  P  -&Program FeaturesPretend Harvests Commercial vs. Pre-commercial Thinning Multiple Types of Costs & Revenues Value Rate Changes & Durations Specifying ECON Start Times & Re-initialization Volume Valuation`( 8PFHARVEST VOLUME & GROSS VALUE[ HARVEST VOLUME AND GROSS VALUE TABLE ------------------------------------------------------------------------------------------------------- YEAR = 2034 - PRETEND HARVEST: NO SMALL-END DIB TREE DBH TPA TPA TONS/ CU FT CU FT BD FT BD FT TOTAL SPECIES MIN MAX MIN MAX REMOVED VALUE $ ACRE REMOVED VALUE $ REMOVED VALUE $ VALUE $ ------- ------------- ------------- ------- -------- ------- ------- -------- ------- -------- -------- DF 6.0 10.0 14 0 0 DF 10.0 20.0 65 0 0 DF 20.0 999.9 10 0 0 DF 4.0 10.0 5203 780 780 DF 10.0 16.0 14497 4349 4349 DF 16.0 18.0 1055 369 369 DF 18.0 20.0 115 46 46 DF 0.0 999.9 3783 0 0 WH 0.0 999.9 10 0 0 WH 6.0 10.0 407 20 20 WH 10.0 20.0 5889 589 589 WH 20.0 999.9 795 199 199 WH 4.0 8.0 111 0 0 WH 8.0 12.0 925 0 0 WH 12.0 999.9 104 0 0 ------- -------- ------- ------- -------- ------- -------- -------- Totals 99 0 4923 0 27960 6353 6353 \ P\  idef6ee@7ECON FunctionalityBAbility to evaluate multiple harvest scenarios within a single simulation. Ability to dynamically initiate and value future management prescriptions. Ability to schedule management activities with the Event Monitor based on economic measures. Ability to compute special costs and revenues in response to simulated events. C`(CFVS-ECON Integration NDLessons LearnedThe FVS modeling environment or framework is the critical element. Value lies in examining as wide a range of actions & measures as possible. Growth precision is secondary to model operation and flexibility. Outputs are less a statement of future conditions than quantification of marginal effects. User s need to understand sequence and cycling of model operation. npZ(2nRH Suggestions B Plug & Play for growth generators to encourage better science  empirical and mechanistic. Evolve the framework  refactor and deprecate. Refactoring: a disciplined process that improves system structure but does not change behavior or introduce bugs. Deprecate: computer statements made invalid and obsolete overtime. Establish coordinating group to oversee model evolution, not just new features. Paradigm shift - FVS as a modeling environment not just a growth model. Competition needed among growth generators not modeling environments. ]0Z(10F2r`Cp_0Z2]1rC  ,t [PModel/Modeler Limitations"At times I even persuade myself that I can glimpse some of the answers, but this is a common delusion experienced by anyone who dwells too long on a single problem." Francis Crick. "Give me a fruitful error any time, full of seeds, bursting with its own corrections. You can keep your sterile truths for yourself." Vilfredo Pareto. "66% of teenagers will have sex before they graduate from high school, 32% will have sex sometime later in life, and the remaining 2% will become statisticians." 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 ?"6@ NNN?NEc \ z0___PPT10:___PPT9 s1338(" d#" @` G HR  ?"6@ NNN?Nc E\ z0___PPT10:___PPT9 u 1018(" d#" @` G H8]  ?"6@ NNN?Nc \ z0___PPT10:___PPT9 t20748(" d#" @` G H i  ?"6@ NNN?N`j c z0___PPT10:___PPT9 v14,6408(" d#" @` G Hr  ?"6@ NNN?Njj `c z0___PPT10:___PPT9 r138(" d#" @` G H~  ?"6@ NNN?Ns j jc z0___PPT10:___PPT9 s1238(" d#" @` G H  ?"6@ NNN?Nj s c z0___PPT10:___PPT9 v19,2648(" d#" @` G HT  ?"6@ NNN?NEj c z0___PPT10:___PPT9 s1078(" d#" @` G H8  ?"6@ NNN?Nj Ec z0___PPT10:___PPT9 u 1078(" d#" @` G H   ?"6@ NNN?Nj c z0___PPT10:___PPT9 t20648(" d#" @` G H̪  ?"6@ NNN?N`q j z0___PPT10:___PPT9 v10,1678(" d#" @` G H  ?"6@ NNN?Njq `j z0___PPT10:___PPT9 r 88(" d#" @` G H  ?"6@ NNN?Ns q jj z0___PPT10:___PPT9 s1118(" d#" @` G H  ?"6@ NNN?Nq s j z0___PPT10:___PPT9 v13,7708(" d#" @` G H  ?"6@ NNN?NEq j z0___PPT10:___PPT9 s 818(" d#" @` G H  ?"6@ NNN?Nq Ej z0___PPT10:___PPT9 u 1138(" d#" @` G H  ?"6@ NNN?Nq j z0___PPT10:___PPT9 t20548(" d#" @` G H\  ?"6@ NNN?N`xq z0___PPT10:___PPT9 u6,7928(" d#" @` G H  ?"6@ NNN?Njx`q z0___PPT10:___PPT9 r 58(" d#" @` G H|  ?"6@ NNN?Ns xjq z0___PPT10:___PPT9 s 908(" d#" @` G HD  ?"6@ NNN?Nxs q z0___PPT10:___PPT9 v 9,3768(" d#" @` G HT!  ?"6@ NNN?NExq z0___PPT10:___PPT9 s 578(" d#" @` G H4  ?"6@ NNN?NxEq z0___PPT10:___PPT9 u 1228(" d#" @` G Hh@  ?"6@ NNN?Nxq z0___PPT10:___PPT9 t20448(" d#" @` G H(A  ?"6@ NNN?N`xz0___PPT10:___PPT9 w 1,842*8(" d#" @` G H8V  ?"6@ NNN?Nj`xz0___PPT10:___PPT9 r 28(" d#" @` G HV  ?"6@ NNN?Ns jxz0___PPT10:___PPT9 s 658(" d#" @` G Hb  ?"6@ NNN?Ns xz0___PPT10:___PPT9 v 7,9938(" d#" @` G Hh  ?"6@ NNN?NExz0___PPT10:___PPT9 s1068(" d#" @` G H  ?"6@ NNN?NExz0___PPT10:___PPT9 u1,3888(" d#" @` G H  ?"6@ NNN?Nxz0___PPT10:___PPT9 t20348(" d#" @` G H  ?"6@ NNN?N`z0___PPT10:___PPT9 u 08(" d#" @` G Hԡ  ?"6@ NNN?Nj`z0___PPT10:___PPT9 r 18(" d#" @` G H  ?"6@ NNN?Ns jz0___PPT10:___PPT9 s1338(" d#" @` G H  ?"6@ NNN?Ns z0___PPT10:___PPT9 v 4,4538(" d#" @` G Hl  ?"6@ NNN?NEz0___PPT10:___PPT9 s 428(" d#" @` G H  ?"6@ NNN?NEz0___PPT10:___PPT9 u1,8058(" d#" @` G H8  ?"6@ NNN?Nz0___PPT10:___PPT9 t20248(" d#" @` G H|  ?"6@ NNN?N`z0___PPT10:___PPT9 u 08(" d#" @` G H8  ?"6@ NNN?Nj`z0___PPT10:___PPT9 r 08(" d#" @` G H  ?"6@ NNN?Ns jz0___PPT10:___PPT9 s 428(" d#" @` G H  ?"6@ NNN?Ns z0___PPT10:___PPT9 v 3,3028(" d#" @` G H  ?"6@ NNN?NEz0___PPT10:___PPT9 s 198(" d#" @` G H  ?"6@ NNN?NEz0___PPT10:___PPT9 u1,4648(" d#" @` G H,  ?"6@ NNN?Nz0___PPT10:___PPT9 t20148(" d#" @` G H,  ?"6@ NNN?N`z0___PPT10:___PPT9 u 08(" d#" @` G H5  ?"6@ NNN?Nj`z0___PPT10:___PPT9 r 28(" d#" @` G H?  ?"6@ NNN?Ns jz0___PPT10:___PPT9 s 188(" d#" @` G HK  ?"6@ NNN?Ns z0___PPT10:___PPT9 v 2,3508(" d#" @` G HL  ?"6@ NNN?NEz0___PPT10:___PPT9 s 148(" d#" @` G H_  ?"6@ NNN?NEz0___PPT10:___PPT9 u 168(" d#" @` G Hi  ?"6@ NNN?Nz0___PPT10:___PPT9 t20048(" d#" @` G Ht  ?"6@ NNN?N`L___PPT10,$___PPT9tl Harvest Bd Ft /Acre(" d ( " d### # #  @` G Hh  ?"6@ NNN?Nj`L___PPT10,$___PPT9tl Mortality Cu Ft/ Acre/Yr (" d( " d ### # # @` ~G H  ?"6@ NNN?Ns jL___PPT10,$___PPT9tl Accretion Cu Ft /Acre/Yr (" d( " d ### # # @` }G Hh  ?"6@ NNN?Ns L___PPT10,$___PPT9tl Total Bd Ft /Acre(" d ( " d### # ##  @` |G H  ?"6@ NNN?NEL___PPT10,$___PPT9tl Basal Area/ Acre(" d ( " d### # ## @`I {G H  ?"6@ NNN?NED___PPT10$r___PPT9TL  Trees /Acrer(" d( " d###   @` yG H  ?"6@ NNN?N8___PPT10N___PPT90( vYear:(" d## @`B G 6o ?"0@NNN?NB G 6o ?"0@NNN?NNNB G 61?"0@NNN?NB G 61?"0@NNN?NB M 61?"0@NNN?NB M 61?"0@NNN?NB M 61?"0@NNN?NB  N 61?"0@NNN?NB  N 61?"0@NNN?NB N 61?"0@NNN?NB N 61?"0@NNN?NxB %N 61?"0@NNN?NxB 'N 61?"0@NNN?Nxq B 3N 61?"0@NNN?Nxq B 5N 61?"0@NNN?Nq j B AN 61?"0@NNN?Nq j B CN 61?"0@NNN?Nj c B ON 61?"0@NNN?Nj c B QN 61?"0@NNN?Nc \ B ]N 61?"0@NNN?Nc \ B _N 61?"0@NNN?N\ U B kN 61?"0@NNN?N\ U B mN 61?"0@NNN?NU NB yN 61?"0@NNN?NU NB N 6o ?"0@NNN?N  N <   ?"6@ NNN?NZ v b* Actual harvest(plFZ N  @TUA#&Be]C4&DEF1m?TU3&U3&U(&U#&-X% [#&d]#&@  "    ? $? 4|F̛]  h FXTO"!d HDEa1Fa1W  e2pB3HB~A~A Kp+Ye,r), ,`#sb.TeYeʛ,P;P, ?@"34 8Z. < N  @A *B2C*DEpF1m? *g *5**."*e *+*4*0*;*?F*_P*[*h*z*z*)z*B*e**_*z*t*o*j*e*j*1j* @         "     ? $? 4|F̛] h FXTO"!d HDEa1Fa1W  e2pB3HB~A~A CY#e¥%E,.lŅ%YbC%JJX ?@"5be 8 C  H D 0޽h ? ̙3ff___PPT10i. 5+D='  = @B +Q " 0 h``(  Px P c $|     6 `a  #">2 `a   ~S HdT  ?"6@`NNN?N@h az0___PPT10:___PPT9 t 1318(" d#" @` }S H  ?"6@`NNN?N@o h z0___PPT10:___PPT9 t 1528(" d#" @` |S H  ?"6@`NNN?N@v o z0___PPT10:___PPT9 t 1548(" d#" @` {S H8  ?"6@`NNN?N@} v z0___PPT10:___PPT9 t 1458(" d#" @` zS H.  ?"6@`NNN?N@ } z0___PPT10:___PPT9 t 1378(" d#" @` yS H9  ?"6@`NNN?N@ z0___PPT10:___PPT9 t 1368(" d#" @` xS H:  ?"6@`NNN?N@z0___PPT10:___PPT9 t -768(" d#" @` wS HB  ?"6@`NNN?N@z0___PPT10:___PPT9 t-1168(" d#" @` vS HO  ?"6@`NNN?N@z0___PPT10:___PPT9 t-1418(" d#" @` uS Hb  ?"6@`NNN?N@z0___PPT10:___PPT9 t-2098(" d#" @` tS Ho  ?"6@`NNN?N@8___PPT10N___PPT90( wSEV<8" dP## @` P Hz  ?"6@`NNN?Nh `az0___PPT10:___PPT9 i5.3.8" d(c @` P H  ?"6@ NNN?Np h @az0___PPT10:___PPT9 s1288(" d#" @` P H$  ?"6@ NNN?Nh p az0___PPT10:___PPT9 v32,7568(" d#" @` P H  ?"6@ NNN?Nh az0___PPT10:___PPT9 s1008(" d#" @` P H  ?"6@ NNN?Nh az0___PPT10:___PPT9 t20948(" d#" @` P H  ?"6@`NNN?No `h z0___PPT10:___PPT9 i5.5.8" d(c @` P H$  ?"6@ NNN?Np o @h z0___PPT10:___PPT9 s1488(" d#" @` P H   ?"6@ NNN?No p h z0___PPT10:___PPT9 v26,5388(" d#" @` P H  ?"6@ NNN?No h z0___PPT10:___PPT9 s 908(" d#" @` P H  ?"6@ NNN?No h z0___PPT10:___PPT9 t20848(" d#" @` P H  ?"6@`NNN?Nv `o z0___PPT10:___PPT9 i5.7.8" d(c @` P H`  ?"6@ NNN?Np v @o z0___PPT10:___PPT9 s1478(" d#" @` P H  ?"6@ NNN?Nv p o z0___PPT10:___PPT9 v19,9648(" d#" @` P H  ?"6@ NNN?Nv o z0___PPT10:___PPT9 s 808(" d#" @` P H  ?"6@ NNN?Nv o z0___PPT10:___PPT9 t20748(" d#" @` P H  ?"6@`NNN?N} `v z0___PPT10:___PPT9 i5.9.8" d(c @` P H"  ?"6@ NNN?Np } @v z0___PPT10:___PPT9 s1368(" d#" @` P H#  ?"6@ NNN?N} p v z0___PPT10:___PPT9 v14,6408(" d#" @` P Hh9  ?"6@ NNN?N} v z0___PPT10:___PPT9 s 708(" d#" @` P HA  ?"6@ NNN?N} v z0___PPT10:___PPT9 t20648(" d#" @` P HN  ?"6@`NNN?N `} z0___PPT10:___PPT9 i6.2.8" d(c @` P HtX  ?"6@ NNN?Np @} z0___PPT10:___PPT9 s1248(" d#" @` P H\Y  ?"6@ NNN?N p } z0___PPT10:___PPT9 v10.1678(" d#" @` P Hln  ?"6@ NNN?N } z0___PPT10:___PPT9 s 608(" d#" @` P Hv  ?"6@ NNN?N } z0___PPT10:___PPT9 t20548(" d#" @` P H  ?"6@`NNN?N` z0___PPT10:___PPT9 i6.6.8" d(c @` P H  ?"6@ NNN?Np @ z0___PPT10:___PPT9 s1178(" d#" @` P H  ?"6@ NNN?Np z0___PPT10:___PPT9 u6,7928(" d#" @` P HL  ?"6@ NNN?N z0___PPT10:___PPT9 s 508(" d#" @` P H  ?"6@ NNN?N z0___PPT10:___PPT9 t20448(" d#" @` P H   ?"6@`NNN?N`z0___PPT10:___PPT9 j<0.0.8" d(c @` P Ht  ?"6@ NNN?Np @z0___PPT10:___PPT9 s-608(" d#" @` P H4  ?"6@ NNN?Np z0___PPT10:___PPT9 w 1,842*8(" d#" @` P H  ?"6@ NNN?Nz0___PPT10:___PPT9 s 408(" d#" @` P HL  ?"6@ NNN?Nz0___PPT10:___PPT9 t20348(" d#" @`  P H  ?"6@`NNN?N` b 0(C  @` P H  ?"6@ NNN?Np @z0___PPT10:___PPT9 s-808(" d#" @` P HL  ?"6@ NNN?Np z0___PPT10:___PPT9 u 08(" d#" @` P H\  ?"6@ NNN?Nz0___PPT10:___PPT9 s 308(" d#" @` P HH  ?"6@ NNN?Nz0___PPT10:___PPT9 t20248(" d#" @`  P H"  ?"6@`NNN?N` b 0(C  @` P Hp+  ?"6@ NNN?Np @z0___PPT10:___PPT9 s-768(" d#" @` P Hx3  ?"6@ NNN?Np z0___PPT10:___PPT9 u 08(" d#" @` P H?  ?"6@ NNN?Nz0___PPT10:___PPT9 s 208(" d#" @` P H?  ?"6@ NNN?Nz0___PPT10:___PPT9 t20148(" d#" @`  P HS  ?"6@`NNN?N` b 0(C  @` P H]  ?"6@ NNN?Np @z0___PPT10:___PPT9 s-688(" d#" @` P H^  ?"6@ NNN?Np z0___PPT10:___PPT9 u 08(" d#" @` ~P Hq  ?"6@ NNN?Nz0___PPT10:___PPT9 s 108(" d#" @` }P H~  ?"6@ NNN?Nz0___PPT10:___PPT9 t20048(" d#" @` |P HP  ?"6@`NNN?N`L___PPT10,$___PPT9tl Internal Rate of Return 8" dP8 " dPccc c cC @` {P H$  ?"6@ NNN?Np @8___PPT10N___PPT90( wPNV<8" dP## @` zP H|  ?"6@ NNN?Np L___PPT10,$___PPT9tl Harvest Bd Ft /Acre8" dP 8 " dP### # ##  @`S tP H  ?"6@ NNN?ND___PPT10$r___PPT9TL Investment Periodv 8" dP8 " dP ###   @` sP H  ?"6@ NNN?N8___PPT10N___PPT90( xYear<8" dP## @`B P 6o ?"0@NNN?N`B P 6o ?"0@NNN?Na`aB P 61?"0@NNN?NB P 61?"0@NNN?N``B XS 6o ?"0@NNN?N`B  61?"0@NNN?NB  61?"0@NNN?N``B  61?"0@NNN?NB  61?"0@NNN?N``B  61?"0@NNN?NB  61?"0@NNN?N``B  61?"0@NNN?NB  61?"0@NNN?N``B  61?"0@NNN?N B  61?"0@NNN?N`` B  61?"0@NNN?N } B  61?"0@NNN?N` `} B  61?"0@NNN?N} v B  61?"0@NNN?N`} `v B  61?"0@NNN?Nv o B  61?"0@NNN?N`v `o B  61?"0@NNN?No h B  61?"0@NNN?N`o `h B  61?"0@NNN?Nh aB  61?"0@NNN?N`h `a   <  ?"6@ NNN?NZ v b* Actual harvest(plFZ   @CA6BIC6DE(F1m? C6C6C6C6C6C6D6E6G6I6@   "    ? $? 4|F̛]v  h FXTO"!d HDEa1Fa1W  e2pB3HB~A~A Jo"H(Ye, 6XPK.l-ͅX+\ ?@" 8g bk  H P 0޽h ? ̙3ff___PPT10i. 5Т+D='  = @B +} " 0 X$(  Xr X S <, O    r X S - #   H X 0޽h ? ̙3ff___PPT10i. 50o +D='  = @B +M " 0 d\0a,g(  dr d S 0:     H | )g #">2 6|   d H=  ?"6@ NNN?NL z0___PPT10:___PPT9 r918(" d#" @` d H?  ?"6@ NNN?N Lz0___PPT10:___PPT9 s1408(" d#" @` d H@  ?"6@ NNN?N= z0___PPT10:___PPT9 s1358(" d#" @` d HS  ?"6@ NNN?NZ = z0___PPT10:___PPT9 v44,3768(" d#" @` d H^  ?"6@ NNN?N Zz0___PPT10:___PPT9 s1008(" d#" @` d Hdk  ?"6@ NNN?N z0___PPT10:___PPT9 t20948(" d#" @` d H$l  ?"6@ NNN?NL  z0___PPT10:___PPT9 r818(" d#" @` d H<  ?"6@ NNN?N L z0___PPT10:___PPT9 s1978(" d#" @` d H  ?"6@ NNN?N=  z0___PPT10:___PPT9 s1908(" d#" @` d HX  ?"6@ NNN?NZ = z0___PPT10:___PPT9 v43,3578(" d#" @` d H0  ?"6@ NNN?N Z z0___PPT10:___PPT9 s 908(" d#" @` d H<  ?"6@ NNN?N  z0___PPT10:___PPT9 t20848(" d#" @` d H  ?"6@ NNN?NL  z0___PPT10:___PPT9 r718(" d#" @` d Hh  ?"6@ NNN?N L z0___PPT10:___PPT9 s2608(" d#" @` d H  ?"6@ NNN?N=  z0___PPT10:___PPT9 s2498(" d#" @` d H@  ?"6@ NNN?NZ = z0___PPT10:___PPT9 v42,3778(" d#" @` d H  ?"6@ NNN?N Z z0___PPT10:___PPT9 s 808(" d#" @` d H  ?"6@ NNN?N  z0___PPT10:___PPT9 t20748(" d#" @` d H   ?"6@ NNN?NL  z0___PPT10:___PPT9 r618(" d#" @` d H  ?"6@ NNN?N L z0___PPT10:___PPT9 s3398(" d#" @` d Ht  ?"6@ NNN?N=  z0___PPT10:___PPT9 s3228(" d#" @` d H  ?"6@ NNN?NZ = z0___PPT10:___PPT9 v40,2518(" d#" @` d H!  ?"6@ NNN?N Z z0___PPT10:___PPT9 s 708(" d#" @` d H%  ?"6@ NNN?N  z0___PPT10:___PPT9 t20648(" d#" @` d H  ?"6@ NNN?NL  z0___PPT10:___PPT9 r518(" d#" @` d HC  ?"6@ NNN?N L z0___PPT10:___PPT9 s3878(" d#" @` d HM  ?"6@ NNN?N=  z0___PPT10:___PPT9 s3638(" d#" @` d HJ  ?"6@ NNN?NZ = z0___PPT10:___PPT9 v36,9238(" d#" @` d H`  ?"6@ NNN?N Z z0___PPT10:___PPT9 s 608(" d#" @` d Hk  ?"6@ NNN?N  z0___PPT10:___PPT9 t20548(" d#" @` d Hc  ?"6@ NNN?NL z0___PPT10:___PPT9 r418(" d#" @` d H|  ?"6@ NNN?NL z0___PPT10:___PPT9 s4158(" d#" @` d H  ?"6@ NNN?N=  z0___PPT10:___PPT9 s3808(" d#" @` d H  ?"6@ NNN?NZ= z0___PPT10:___PPT9 v33,9578(" d#" @` d Hܘ  ?"6@ NNN?NZ z0___PPT10:___PPT9 s 508(" d#" @` d H|  ?"6@ NNN?N z0___PPT10:___PPT9 t20448(" d#" @` d H  ?"6@ NNN?NLz0___PPT10:___PPT9 r318(" d#" @` d H|  ?"6@ NNN?NLz0___PPT10:___PPT9 s4228(" d#" @` d HT  ?"6@ NNN?N= z0___PPT10:___PPT9 s3708(" d#" @` d H  ?"6@ NNN?NZ= z0___PPT10:___PPT9 v30,4388(" d#" @` d H\  ?"6@ NNN?NZz0___PPT10:___PPT9 s 408(" d#" @` d H  ?"6@ NNN?Nz0___PPT10:___PPT9 t20348(" d#" @` d H!  ?"6@ NNN?NLz0___PPT10:___PPT9 r218(" d#" @` d Hh  ?"6@ NNN?NLz0___PPT10:___PPT9 s3758(" d#" @` d H!  ?"6@ NNN?N= z0___PPT10:___PPT9 s2988(" d#" @` d H!  ?"6@ NNN?NZ= z0___PPT10:___PPT9 v26,2488(" d#" @` d H%!  ?"6@ NNN?NZz0___PPT10:___PPT9 s 308(" d#" @` d H,!  ?"6@ NNN?Nz0___PPT10:___PPT9 t20248(" d#" @` d H8!  ?"6@ NNN?NLz0___PPT10:___PPT9 r118(" d#" @` d HB!  ?"6@ NNN?NLz0___PPT10:___PPT9 s3568(" d#" @` d HO!  ?"6@ NNN?N= z0___PPT10:___PPT9 s2418(" d#" @` d HP!  ?"6@ NNN?NZ= z0___PPT10:___PPT9 v21,6788(" d#" @` {d Hb!  ?"6@ NNN?NZz0___PPT10:___PPT9 s 208(" d#" @` zd H,n!  ?"6@ NNN?Nz0___PPT10:___PPT9 t20148(" d#" @` yd Hw!  ?"6@ NNN?NLz0___PPT10:___PPT9 r 18(" d#" @` xd H8!  ?"6@ NNN?NLz0___PPT10:___PPT9 s3918(" d#" @` wd HH!  ?"6@ NNN?N= z0___PPT10:___PPT9 s2218(" d#" @` vd H̏!  ?"6@ NNN?NZ= z0___PPT10:___PPT9 v17,0068(" d#" @` rd Hԛ!  ?"6@ NNN?NZz0___PPT10:___PPT9 s 108(" d#" @` qd H!  ?"6@ NNN?Nz0___PPT10:___PPT9 t20048(" d#" @`N pd H!  ?"6@ NNN?NL|D___PPT10$r___PPT9TL  Delay Periodv(" d( " d### #  @`Q od H|!  ?"6@ NNN?N|LD___PPT10$r___PPT9TL Value of Forestv (" d( " d### #  @` nd H!  ?"6@ NNN?N= |8___PPT10N___PPT90( uPNV:(" d## @` md Ht!  ?"6@ NNN?NZ|= L___PPT10,$___PPT9tl Harvest Bd Ft/ Acre(" d ( " d### # ##  @`S id H"  ?"6@ NNN?N|ZD___PPT10$r___PPT9TL Investment Periodv (" d( " d ### #  @` hd H!  ?"6@ NNN?N|8___PPT10N___PPT90( vYear:(" d## @`B d 6o ?"0@NNN?N||B d 6o ?"0@NNN?NB d 61?"0@NNN?N|B d 61?"0@NNN?N|B f 61?"0@NNN?NB f 61?"0@NNN?NB f 61?"0@NNN?NB f 61?"0@NNN?NB f 61?"0@NNN?NB f 61?"0@NNN?NB f 61?"0@NNN?NB f 61?"0@NNN?NB f 61?"0@NNN?N B f 61?"0@NNN?N B f 61?"0@NNN?N B f 61?"0@NNN?N  B f 61?"0@NNN?N B f 61?"0@NNN?N  B f 61?"0@NNN?N B f 61?"0@NNN?N  B f 61?"0@NNN?N B g 61?"0@NNN?N  B g 61?"0@NNN?N B g 61?"0@NNN?N B g 6o ?"0@NNN?N *g  @~8A+B4>C+DE@F1m?~8+8+8+8+8+8+8+=:+J+>+3>+@     "     ? $? 4|F̛]v  h FXTO"!d HDEa1Fa1W  e2pB3HB~A~A Ee t9e,łP6(YRʄb[,@F E  `(P    +g  @EA!'BKC2'DEF1m?E!'5G!'I&J1'J>'XY+X]+XY+\YY+ @      "    ? $? 4|F̛]V  h FXTO"!d HDEa1Fa1W  e2pB3HB~A~A =O+1,łT6YR R*Tرe"cE`RP ?@"tm 8 VD  H d 0޽h ? ̙3ff___PPT10i.5oS~+D=' ! = @B +} " 0 Pl$(  lr l S " '  "  r l S " V  "  H l 0޽h ? ̙3ff___PPT10i.5}+D=' ! = @B +8 " 0 OG`r:ߞ(  px p c $?"   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HZ0  ?"6@ NNN?N5z0___PPT10:___PPT9 s1118(" d#" @` g( Hf0  ?"6@ NNN?Nz0___PPT10:___PPT9 r108(" d#" @` f( Hg0  ?"6@ NNN?Nz0___PPT10:___PPT9 t20048(" d#" @`P e( Hy0  ?"6@ NNN?Np]D___PPT10$r___PPT9TL Value of Treesv 8" dP8 " dP###   @` d( H0  ?"6@ NNN?Npz0___PPT10:___PPT9 Value of Forest:8" dP#" @` c( H,0  ?"6@ NNN?Nwpz0___PPT10:___PPT9 uPNV:8" dP#" @` b( H0  ?"6@ NNN?N pwL___PPT10,$___PPT9tl Harvest Bd Ft/ Acre8" dP 8 " dP### # #  @` a( HD0  ?"6@ NNN?N5p L___PPT10,$___PPT9tl Total Bd Ft /Acre8" dP 8 " dP### # #  @` `( H00  ?"6@ NNN?Np5L___PPT10,$___PPT9tl Basal Area/ Acre8" dP 8 " dP### # # @`v _( H@0  ?"6@ NNN?NpD___PPT10$r___PPT9TL Invest-ment Periodv 8" dP8 " dP ###   @` ^( H0  ?"6@ NNN?Npz0___PPT10:___PPT9 vYear:8" dP#" @`B ( 61?"0@NNN?NppB ( 6o ?"0@NNN?No]oB ( 6o?"0@NNN?NpB ( 61?"0@NNN?N]p]B l* 61?"0@NNN?NB m* 61?"0@NNN?NB + 61?"0@NNN?NppB + 61?"0@NNN?Np5pB + 61?"0@NNN?N5p pB + 61?"0@NNN?N pwpB + 61?"0@NNN?NwppB + 61?"0@NNN?NppB + 61?"0@NNN?Np]pB  + 61?"0@NNN?N]]B -+ 61?"0@NNN?N]]B ;+ 61?"0@NNN?N]]B J+ 61?"0@NNN?N]]B Y+ 61?"0@NNN?N]] B h+ 61?"0@NNN?N] ] B w+ 61?"0@NNN?N] ] B + 61?"0@NNN?N] ]} B + 61?"0@NNN?N]} ]v B + 61?"0@NNN?N]v ]oB + 6o ?"0@NNN?N]B , 61?"0@NNN?NB , 61?"0@NNN?NB , 61?"0@NNN?N B , 61?"0@NNN?N B , 61?"0@NNN?N B , 61?"0@NNN?N } B , 61?"0@NNN?N} v B , 61?"0@NNN?Nv oH ( 0޽h ? ̙3ff___PPT10i.8+D=' 0 = @B +} " 0 $(  r  S 1 T  1  r  S T1   1  H  0޽h ? ̙3ff___PPT10i.5Y'+D=' 0 = @B +  " 0   f(  x  c $L1 h  1   0  F0e0eA h    ? @  5% 8c8c     ?A)BCD|E||# "0e@       @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abZZJ h 1  0  F0e0eA i    ? @  5% 8c8c     ?A)BCD|E||# "0e@       @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abZZ,  i 1  0  F0e0eA j    ? @  5% 8c8c     ?A)BCD|E||# "0e@       @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab ZZ j 1 B  BDg ?"0@NNN?N~[ ~  <1  ?"6@ NNN?N f :  \FIRE.plFZ2  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