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Microstand : a computerized learning tool for evaluating forest stands Masse, Sylvain 1989

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M I C R O S T A N D : A C O M P U T E R I Z E D L E A R N I N G T O O L F O R E V A L U A T I N G F O R E S T S T A N D S By S Y L V A I N M A S S E B . S c , Laval University, Quebec, 1980 A THESIS S U B M I T T E D IN P A R T I A L F U L F I L L M E N T O F T H E R E Q U I R E M E N T S F O R T H E D E G R E E O F M A S T E R O F S C I E N C E i n T H E F A C U L T Y O F G R A D U A T E STUDIES Department of Forestry We accept this thesis as conforming to the required standard T H E UNIVERSITY O F BRITISH C O L U M B I A October 1989 (c) Sylvain Masse, 1989 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of f~c?R fj.\7'fi Y The University of British Columbia Vancouver, Canada Date OCTOPKK I 7), / W DE-6 (2/88) i i A B S T R A C T T h e main ob jec t ive of this thesis was to deve lop a c o m p u t e r i z e d s tand m a n a g e -ment analysis p rogram based on the Lo tus 1 - 2 - 3 T ^ m i c r o c o m p u t e r so f tware that would be sui table for use as a s tumpage appra isa l l earn ing too l for U n i v e r s i t y of Br i t ish C o l u m b i a ( U B C ) undergraduate fores t ry e c o n o m i c s courses . A secondary ob jec t ive was to assess the appropr ia teness of L o t u s 1 -2 -3 T M f o r deve lop ing in te rac t i ve and u s e r - f r i e n d l y stand management analysis p rograms . M I C R O S T A N D is a stand l e v e l p rogram c o m p o s e d of s tumpage appra isa l s u b -models fed by a growth and y ie ld s imula tor and l inked to some f i n a n c i a l analysis d e v i c e s . T h e genera l condi t ions being s imu la ted are C r o w n t imber of Br i t i sh C o l u m -bia's c o a s t a l a r e a ; pure stands c o m p o s e d of one of four impor tan t c o m m e r c i a l spec ies ; three basic scenar ios cor responding to th inning only , f ina l harvest on ly , and thinning fo l lowed by f ina l harvest ; a s imula t ion per iod ranging f r o m one to 100 years ; and a 1985 base year f o r costs and revenues. F o r each scheduled harvest , the growth and y i e l d s imu la to r generates output y ie ld var iables which are then used by the t i m b e r - l o g convers ion s imula tor to t rans -f o r m the t imber harves ted into logs . T h e l o g grad ing s imula tor then es t imates a grade d is t r ibut ion , and the revenue s i m u l a t o r then appl ies l o g pr ices to the grade d is t r ibu t ion . T h e costs assoc ia ted wi th e a c h harvest (d irect costs per de l ivery phase, re turn on c a p i t a l and a s p e c i a l r isk a l lowance) are then e s t i m a t e d by the de l ivery cost s imu la to r . F i n a l l y , u s e r - s p e c i f i e d average rea l ra te of change in revenues, average rea l ra te of change in cos ts , and rea l d iscount rate are used by the f i n a n c i a l analysis s i m u l a t o r to produce the fo l lowing da ta : cash f low of rea l revenues and costs over the s imu la t ion per iod , res idua l t imber va lue at each harvest , and net present value and b e n e f i t - c o s t ra t io for the stand management scenar io . T h e reac t ions to th inning, the d is t r ibut ion of l o g vo lume a m o n g grades , and the return on c a p i t a l are genera ted by unsophis t ica ted s imula t ion procedures that were not tes ted with e m p i r i c a l da ta nor va l ida ted models . T h e p r o g r a m - u s e r in te rac t ions are c o n t r o l l e d through menu opt ions, growth and y ie ld graphs can be p r o d u c e d , and i n f o r m a t i o n notes can be d isp layed . Sens i t iv i ty analysis on appra isa l de te rminants can be c o n d u c t e d by re turn ing to previous input phases. M I C R O S T A N D is a sui table s tumpage appra isa l l earn ing too l fo r U B C under -graduate fores t ry e c o n o m i c s courses due to seven c h a r a c t e r i s t i c s : s imula t ion of representa t ive Br i t i sh C o l u m b i a c o a s t a l cond i t ions , u s e r - f r i e n d l y o p e r a t i o n , inc lus ion of c r i t i c a l appra isa l de te rminan ts , genera t ion of de ta i l ed outputs , f l ex ib i l i t y , and recogn i t ion of both uncer ta in ty and re levant e c o n o m i c c o n c e p t s . T h e inc lus ion of unsophis t ica ted and nonva l ida ted s imula t ion procedures does not prevent M I C R O S T A N D f r o m revea l ing the nature and the in ter re la t ions of the main appra isa l p a r a m e t e r s , wi th the sole excep t ion of t ree s ize var ia t ions in a stand and the consequent e f f e c t s on l o g revenues . R e c o g n i t i o n of t ree s ize v a r i a -t ions could be obta ined wi th a va luat ion procedure based on e m p i r i c a l data and regression techniques . A l i m i t a t i o n of M I C R O S T A N D is its re la t i ve ly slow process ing speed which is main ly due to two c h a r a c t e r i s t i c s of Lo tus 1 -2 -3 ™ : the r e c a l c u l a t i o n o f a l l the ce l ls in a worksheet when a va lue or a f o r m u l a in one of the ce l ls changes , and the necess i ty to t ranspose D O L O O P S through i te ra t ive p rocedures . Lo tus 1 -2 -3 T M proved to be an appropr ia te med ium for deve lop ing i n t e r a c t i v e and u s e r - f r i e n d l y stand management analysis p r o g r a m s , despi te cod ing c o m p l i c a t i o n s and possible slow process ing speed . T h e p r o g r a m m i n g approach deve loped for M I C R O S T A N D appears to be a f lex ib le f r a m e w o r k sui table for a va r i e ty of i n t e r a c -t ive programs re la ted to forest management and o ther f ie lds . S imu la to r s i m p l i f i c a -t ion by regression techniques is r e c o m m e n d e d in order to i m p r o v e program p e r f o r -m a n c e . It is a lso suggested that the deve lopment of mul t is tage programs such as M I C R O S T A N D cou ld benef i t f r o m a mul t id isc ip l inary t e a m a p p r o a c h . R E S U M E iv L 'ob jec t i f p r i n c i p a l de c e t t e these consiste a e laborer un p r o g r a m m e duplica-t ion (progiciel ) s imulant l ' amenagement de peuplements forest ie rs et pouvant serv i r c o m m e m a t e r i e l d 'apprent issage pedagogique pour r e v a l u a t i o n de la va leur (du bois) sur p ied . C e p r o g r a m m e sera i t c o n c u pour les cours d 'economie f o r e s t i e r e , de n iveau pregradue , a l 'Un ivers i te de l a C o l o m b i e - B r i t a n n i q u e . L e l o g i c i e l Lo tus 1 - 2 - 3 ™ pour m i c r o - o r d i n a t e u r s serv i ra i t d 'outil de p r o g r a m m a t i o n . L 'ob jec t i f secondai re consiste a eva luer le po ten t ie l de Lo tus 1 - 2 - 3 ™ pour l 'e laborat ion de p r o g r a m m e s d'analyse i n t e r a c t i f s et f a c i l e s d 'ut i l isat ion dans le domaine de l ' amenagement de peuplements fo res t i e rs . M I C R O S T A N D s imule l ' amenagement d'un seul peup lement fo res t ie r a l a fo is . L e p r o g r a m m e est c o m p o s e de modeles d e v a l u a t i o n de la valeur sur p ied et d 'analyse f inanc ie re qui sont a l imentes par un genera teur de c ro issance et de rendement . L e s condi t ions generates s imulees sont: (1) des si tes du domaine publ ic si tues dans, l a region co t i e re de l a C o l o m b i e - B r i t a n n i q u e ( G - B . ) ; (2) des peuplements purs composes d'une des quatre essences c o m m e r c i a l e s d ' importance retenues pour le p r o g r a m m e ; (3) t rois scenar ios de base correspondant a une e c l a i r c i e seu lement , a une coupe f ina le seu lement ou a une e c l a i r c i e suiv ie d'une coupe f ina le ; (4) un hor izon de s imu la t ion d'un a 100 ans; et (5) l 'annee de r e f e r e n c e 1985 pour les couts et revenus. Pour cheque r e c o l t e s imu lee , le genera teur de c ro issance et de rendement produi t des var iab les de rendement qui sont ut i l isees par un second s imula teur pour t rans fo rmer les t iges reco l tees en b i l lo ts . U n t ro is ieme s imu la teur d istr ibue le vo lume des bi l lots par c lasse de qua l i te . Des pr ix sont alors appl iques aux classes de qual i te par un quat r ieme s imula teur . L e s couts associes a chaque reco l te (les couts d i rec ts par phase d 'explo i ta t ion et de t ranspor t , le rendement du c a p i t a l et une a l l o c a t i o n spec ia le pour les risques) sont evalues par un c inqu ieme s imula teur . E n f i n , un s ix ieme s imula teur ut i l ise un taux moyen de var ia t ion des couts ree ls , un taux moyen de var ia t ion des revenus ree ls et un taux ree l d ' interet - tous trois spec i f i es par l 'ut i l isateur - pour produire les donnees suivantes: un f lux f inanc ie r (cash f low) de revenus de couts ree ls pour l 'hor izon de s i m u l a t i o n , la va leur res iduel le sur p ied a chaque reco l te a insi que l a va leur ac tua l isee net te et le ra t io a v a n t a g e -cout pour le scenar io d 'amenagement . L e s reac t ions a l ' ec la i rc ie , l a d is t r ibut ion du vo lume des b i l lo ts par c lasse de qual i te et le rendement du c a p i t a l sont generes par des procedures de s imula t ion peu sophist iquees n'ayant pas e te testees a l 'aide de donnees empi r iques ou de modeles va l ides . L ' in te rac t ion entre le p r o g r a m m e et l 'ut i l isateur est cont ro lee par des opt ions de menus; des graphiques peuvent e t re produits a par t i r des donnees de c r o i s s a n c e ; et des notes d ' in format ion peuvent e t re v isua l isees . Des analyses de sensib i l i te sur des paramet res a f f e c t a n t la va leur sur p ied peuvent e t re rea l isees en re tournant a des phases precedentes d'entree d' inputs. M I C R O S T A N D est un ou t i l adequat d 'apprent issage de l a va leur sur p ied pour les cours d 'economie fo res t i e re de l 'Un ivers i te de la C o l o m b i e - B r i t a n n i q u e g r a c e a sept ca rac te r i s t iques : la s imu la t ion de condi t ions representa t ives de la region co t ie re de l a C . - B . ; l a f a c i l i t e d 'ut i l isat ion; l ' inclusion de paramet res c r i t iques d 'eva luat ion; la p roduct ion de resul ta ts de ta i l l es , la f l ex ib i l i t e d 'operat ion , la r e c o n -naissance des concepts economiques per t inents et l a cons idera t ion de l ' incer t i tude . E x c e p t i o n fa i te de l a var ia t ion des d imensions de t iges et des e f fe ts de ce t te var ia t ion sur les revenus provenant des b i l lo ts , l ' inclusion de procedures de s imula t ion peu sophist iquees et non va l idees n 'empeche pas M I C R O S T A N D de reve le r la nature et les re la t ions rec iproques des pr inc ipaux p a r a m e t r e s d 'evaluat ion de la valeur sur p ied . L a reconna issance de l a var ia t ion des d imensions de t iges pourra i t e t re obtenue a l 'aide d'une procedure d 'evaluat ion des revenus basee sur des donnees empir iques et des techniques de regress ion . U n f a c t e u r l i m i t a t i f de M I C R O S T A N D est sa v i tesse d 'operat ion r e l a t i v e m e n t lente qui est due p r inc ipa lement a deux c a r a c t e r i s t i q u e s de L o t u s 1-2 _ 3 T M . lorsque la va leur ou l a f o r m u l e d'une ce l lu le change , le c a l c u l de toutes les ce l lu les d'un f i ch ie r est e f f e c t u e a nouveau , et i l est necessa i re de t ransposer les « D O L O O P S » par le biais de procedures i t e ra t i ves . Lotus 1 - 2 - 3 ™ s'avere un med ium adequat pour l 'e laborat ion de p rogrammes d'analyse in te rac t i f s et f ac i l es d 'ut i l isat ion dans le domaine de l 'amenagement de peuplements fo res t ie rs , en depit de c o m p l i c a t i o n s de p r o g r a m m a t i o n et d'une vi tesse d 'operat ion po ten t ie l l ement l en te . L 'approche de program mat ion deve loppee pour M I C R O S T A N D appara i t const i tuer un cadre f lex ib le qui pourra i t e t re ut i l ise pour la p rogram mat ion d'une var ie te de p r o g r a m m e s i n t e r a c t i f s ayant t ra i t a l ' amenage-ment fo res t ie r ou a d'autres d isc ip l ines . L a s i m p l i f i c a t i o n de modeles par l 'emploi de techniques de regression est tou te fo is r e c o m m a n d e e pour a m e l i o r e r la p e r f o r -mance des p r o g r a m m e s . II est ega lement suggere d 'employer une approche m u l t i -d isc ip l ina i re pour le deve loppement de log ic ie ls a plusieurs phases te l M I C R O S T A N D . vi i T A B L E O F C O N T E N T S Page A B S T R A C T ii R E S U M E iv T A B L E O F C O N T E N T S vi i L IST O F T A B L E S ix L IST O F F I G U R E S xi A C K N O W L E D G E M E N T S xi i 1. I N T R O D U C T I O N 1 P A R T I: M I C R O S T A N D : O V E R V I E W , D E S C R I P T I O N , A N D E V A L U A T I O N O F T H E S I M U L A T O R S 4 2. A N O V E R V I E W O F T H E S I M U L A T O R S 5 3. T H E G R O W T H A N D Y I E L D S I M U L A T O R 7 3.1 Equat ions fo r U n m a n a g e d Stands 7 3.2 Equat ions for R e a c t i o n s to Th inn ing 11 3.3 E v a l u a t i o n 14 4. T H E T I M B E R - L O G C O N V E R S I O N S I M U L A T O R , 17 4.1 Input and Output D a t a 17 4.2 E v a l u a t i o n 18 5. T H E L O G G R A D I N G A N D R E V E N U E S I M U L A T O R S 21 5.1 S imula t ion P r o c e d u r e 21 5.1.1 H ighest Possible G r a d e per L o g (Step 1) 22 5.1.2 V o l u m e D is t r ibu t ion per G r a d e (Step 2) 24 5.1.3 Basis for R e v e n u e C a l c u l a t i o n 26 5.2 E v a l u a t i o n 27 vi i i Page 6. T H E D E L I V E R Y C O S T S I M U L A T O R 29 6.1 D i r e c t C o s t s per Phase 29 6.1.1 R o a d D e v e l o p m e n t 30 6.1.2 T r e e - t o - T r u c k 33 6.1.3 O t h e r O p e r a t i o n a l Phases 38 6.2 T o t a l D e l i v e r y C o s t 41 6.3 E v a l u a t i o n 43 7. T H E F I N A N C I A L A N A L Y S I S S I M U L A T O R 47 7.1 C a s h F low of R e a l C o s t s and R e v e n u e s 47 7.2 F i n a n c i a l A n a l y s i s 48 7.3 E v a l u a t i o n 51 P A R T II: M I C R O S T A N D : P R O G R A M M I N G A S P E C T S , C A S E S T U D Y , E V A L - U A T I O N , A N D C O N C L U S I O N S 54 8. P R O G R A M M I N G A S P E C T S 55 8.1 P r o g r a m m i n g M I C R O S T A N D wi th Lo tus 1 -2 -3 55 8.2 E v a l u a t i o n of Lo tus 1 -2 -3 57 9. C A S E S T U D Y U S I N G M I C R O S T A N D 61 10. P R O G R A M E V A L U A T I O N 76 11. C O N C L U S I O N S 81 L I T E R A T U R E C I T E D 84 A P P E N D I X I: Input and Output Var iab les of the Program's S imula tors 86 A P P E N D I X II: D e r i v a t i o n of E q u a t i o n 39 90 ix LIST O F T A B L E S Page T a b l e I L o g P r i c e s by Spec ies U s e d in M I C R O S T A N D 21 Tab le II L o g G r a d i n g R e q u i r e m e n t s by Spec ies for the D e t e r m i n a t i o n of the Highest Possible G r a d e 23 T a b l e III P ropor t ion D is t r ibut ions of L o g V o l u m e by L o g Q u a l i t y and G r a d e 25 T a b l e IV R o a d D e v e l o p m e n t C o s t ( R D C S T ) for a V o l u m e C l a s s of 200 m 3 / h a and a R o a d D e n s i t y ( R D E N S ) o f 0.05 k m / h a 31 T a b l e V Propor t ion D is t r ibu t ion o f H a r v e s t i n g Systems for an A v e r a g e L o g V o l u m e of 0.25 m 3 33 T a b l e VI D i r e c t T r e e - t o - T r u c k C o s t for Th inn ing 34 T a b l e VII Hour ly C o s t by H a r v e s t i n g Sub Phase 38 T a b l e VIII E x a m p l e o f Input D a t a S e l e c t i o n for the G r o w t h and Y i e l d S imu la to r 62 T a b l e IX E x a m p l e of Values fo r G r o w t h and Y i e l d Var iab les E s t i -m a t e d by M I C R O S T A N D 63 T a b l e X E x a m p l e of Values for T i m b e r R e m o v e d Var iab les E s t i m a t e d by M I C R O S T A N D 64 T a b l e XI E x a m p l e o f Values for L o g Var iab les o f the A v e r a g e H a r -ves ted T r e e E s t i m a t e d by M I C R O S T A N D 67 T a b l e XII E x a m p l e of V o l u m e D is t r ibu t ions by G r a d e E s t i m a t e d by M I C R O S T A N D 68 T a b l e XIII E x a m p l e o f Input D a t a (Part 1) for the R e v e n u e , C o s t , and F i n a n c i a l A n a l y s i s S imula tors 69 T a b l e X IV E x a m p l e o f Input D a t a (Part 2) for the R e v e n u e , C o s t , and F i n a n c i a l A n a l y s i s S imula tors 71 X Page Tab le X V E x a m p l e of C a s h F low of R e a l C o s t s and Revenues E s t i -ma ted by M I C R O S T A N D 72 Tab le XV I E x a m p l e of F i n a n c i a l R e t u r n A n a l y s i s of C a s h F low E s t i -ma ted by M I C R O S T A N D 73 xi LIST O F F I G U R E S Page F igure 1 Bas ic Des ign of M I C R O S T A N D 5 F igure 2 T h e M e t h o d U s e d to E s t i m a t e Basa l A r e a A f t e r Th inn ing . . . . 12 F igure 3 A l t e r n a t i v e H a r v e s t i n g Systems fo r F i n a l Harves t 35 F igure 4 E x a m p l e s of G r o w t h and Y i e l d Graphs P r o d u c e d by M I C R O -S T A N D 65 A C K N O W L E D G E M E N T S I would l ike to acknowledge the cont r ibut ion of my superv isor , D r . P . H . P e a r s e , throughout my graduate studies and the deve lopment of this thesis . H is pa t ience was par t i cu la r ly a p p r e c i a t e d . I would also l ike to thank D r . D . H . Wi l l i ams , c o - s u p e r v i s o r of this thesis , for his c o m m e n t s , his he lp , and in pa r t i cu la r for mak ing ava i lab le his exper t ise in the f i e ld of de l ivery cost s i m u l a t i o n . T h e he lp fu l suggest ions and cons t ruc t i ve c r i t i c i s m s of D r s . D . H a l e y and P . L . M a r s h a l l , m e m b e r s of the thesis c o m m i t t e e , are a p p r e c i a t e d . M y thanks are also ex tended to M r . G . G . Y o u n g for his t e c h n i c a l ass is tance in the in i t ia l stages of this thesis . I would l ike to acknowledge the support of F o r e s t r y C a n a d a dur ing my d e v e l o p -ment l eave fo r graduate studies . F i n a l l y , a s p e c i a l ment ion is due to D r s . C . H . Winget and L . W . C a r l s o n of F o r e s t r y C a n a d a fo r their help and e n c o u r a g e m e n t . 1. I N T R O D U C T I O N "The purpose of s tumpage appra isa l is to e s t i m a t e , at a pa r t i cu la r point in t i m e , the value of s tanding t i m b e r ava i lab le for cu t t ing on a p a r t i c u l a r a rea" (Davis 1966, 381). T h e value of s tanding t i m b e r is c a l c u l a t e d "by sub t rac t ing f r o m the es t i ma t ed value of the products that can be r e c o v e r e d f r o m it the costs necessary to rea l i ze those va lues , inc lud ing a re turn to the opera tor" (Pearse et a l . 1974, 9). S tumpage appra isa l requires the in tegra t ion of s e v e r a l b i o l o g i c a l , t e c h n i c a l , and e c o n o m i c paramete rs in a dec is ion mak ing process ( B C M o F 1985, 1986). A p p r a i s a l is main ly under taken pr ior to harvest in order to e i ther d i r e c t l y establ ish a s tumpage ra te or to e s t i m a t e a m i n i m u m rate above which c o m p e t i n g logging opera tors can tender bids (Pearse et a l . 1974). H o w e v e r , s tumpage appra isa l is a lso a major de te rminant for most f o r m s of fores t management analysis inc lud ing land va lua t ion , s e l e c t i o n of a l t e rna t i ve s i l v i c u l t u r a l p rescr ip t ions , o p t i m i z a t i o n of - ro ta t ion age , and mode l l ing of e c o n o m i c t i m b e r supply . A t the U n i v e r s i t y of Br i t i sh C o l u m b i a ( U B C ) , undergraduate fo res t ry students are in t roduced to s tumpage appra isa l through fo res t ry e c o n o m i c s courses . Y e t , exposure to this impor tan t c o n c e p t is genera l ly l i m i t e d to the re levant e c o n o m i c pr inc ip les , whereas the nature and the in te r re la t ions of the ma in appra isa l pa ramete rs are par t ia l ly s tud ied in other courses dea l ing wi th forest ha rves t ing , forest m e n s u r a -t ion , and b i o m e t r i c s . A more in tegra ted exposure to s tumpage appra isa l in U B C undergraduate f o r -estry e c o n o m i c s courses cou ld be a c h i e v e d through the use of a c o m p u t e r program fea tur ing both a s tumpage appra isa l s i m u l a t o r and a design a l lowing sens i t i v i ty a n a l y -sis on key independent var iab les . Such a program would be adapted to the c h a r a c t e r -is t ics of Br i t i sh C o l u m b i a ' s forest resource and u t i l i za t ion technology as wel l as to the undergraduate learn ing con tex t . In this p e r s p e c t i v e , the author rev iewed cur ren t ly ava i lab le compute r p rograms incorpora t ing paramete rs of fo res t ry e c o n o m i c s . T h e rev iew ind ica ted that D F S I M WITH E C O N O M I C S (Fight et a l . 1984) is the only i n t e r a c t i v e and u s e r - f r i e n d l y program that a l lows for the s imu la t ion of the value of s tanding t i m b e r at e a c h scheduled h a r v e s t ^ ) . D F S I M WITH E C O N O M I C S s imula tes O r e g o n and Washington State condi t ions which are s imi la r to those encounte red in Br i t i sh C o l u m b i a . T h e program is based on a D o u g l a s - f i r (Pseudotsuga menz ies i i var . menzies i i ) growth and y ie ld stand s imu la to r . R e v e n u e s vary wi th d i a m e t e r at breast he ight . L o g g i n g costs are s imu la ted for a single harvest ing sys tem (shor t -span cable) . H o w e v e r , the other de l ivery cost components such as road d e v e l o p m e n t , t ruck and water hau l , and crew t ransport must be prov ided by the user , thus r e d u c i n g cons iderab ly the po ten t ia l usefulness of D F S I M WITH E C O N O M I C S as a too l to study s tumpage appra isa l . T h e other programs r e v i e w e d f a l l into two c a t e g o r i e s . T h e f i rs t ca tegory regroups comprehens ive forest management analys is programs (as opposed to stand management programs) that m a y be used to s imula te s tumpage appra isa l , but whose c o m p l e x s t ruc ture and opera t ion are not adapted to an undergraduate con tex t . A n example of such programs is D E F O R P L A N (Johnson n.d.) that was being deve loped for l o n g - r a n g e p lanning of the U n i t e d States na t iona l fo res ts . T h e second ca tegory regroups inves tment analysis programs which do not fea ture a de l ivery cost s imu la to r . In most cases , the s t ruc ture and the input f o r m a t of these programs do not assume a pa r t i cu la r contex t f o r the ana lys is . C o n s e q u e n t l y , input data consist of costs , revenues , and ident i fy ing i n f o r m a t i o n . E x a m p l e s of inves tment analysis programs are IVST (Chappe l le 1969) and M T V E S T (Zuur ing and Schuster 1980). Some inves t -ment analysis programs such as E c o n o m i c Gu ide l ines for L o b l o l l y P ine Management 1. T h e program SIMIN2 WITH E C O N O M I C S can be used to prepare in te rac t i ve ly the input da ta in the f o r m a t requ i red by D F S I M WITH E C O N O M I C S . in V i rg in ia (Thompson et a l . 1973) and Y i e l d 1.4 (Forest R e s o u r c e s Systems Institute n.d.) fea ture in addi t ion a growth and y ie ld s imu la to r . T h e main ob jec t ive of this thesis is to deve lop a c o m p u t e r i z e d stand m a n a g e -ment analysis p rogram based on the L o t u s 1 - 2 - 3 ™ m i c r o c o m p u t e r sof tware that would be sui table for use as a s tumpage appra isa l l earn ing too l for U B C undergrad -uate fores t ry e c o n o m i c s courses . A s is the case for D F S I M WITH E C O N O M I C S , the context that the program s imula tes would be deve loped f r o m a growth and y ie ld s imula tor . Revenues and de l ivery costs would be e s t i m a t e d at each scheduled har -vest , the res idual value would cor respond to the va lue of s tanding t im b er . A secondary ob jec t ive of this thesis is to assess the appropr ia teness of Lo tus 1 - 2 - 3 ™ for deve lop ing i n t e r a c t i v e and u s e r - f r i e n d l y stand management analysis p rograms. Lo tus 1 - 2 - 3 ™ is a t y p i c a l example of a second genera t ion spreadsheet so f tware wh ich provides the n o n p r o g r a m m e r wi th a f l ex ib le med ium for designing a n a l y t i c a l sys tems ( K e e t c h 1982; C o o n e y 1985). Th is thesis is c o n c e p t u a l i z e d in two par ts . P a r t I (Chapters 2 to 7) is c o n c e r n e d wi th the six s imula tors compos ing the s t r u c t u r a l e lements of M I C R O S T A N D , the program deve loped in this pro jec t . C h a p t e r 2 presents an overv iew of these s i m u l a -tors which are subsequent ly descr ibed and eva lua ted in C h a p t e r s 3 to 7. Pa r t II (Chapters 8 to 11) is c o n c e r n e d wi th the p rogram as a whole and Lo tus 1 - 2 - 3 ™ as a p r o g r a m m i n g m e d i u m . C h a p t e r 8 descr ibes the p r o g r a m m i n g approach deve loped for M I C R O S T A N D and examines the advantages and l im i ta t ions of Lotus 1 - 2 - 3 ™ as a p r o g r a m m i n g m e d i u m . C h a p t e r 9 presents a case study that i l lust rates a t y p i c a l example of p rogram use. T h e strengths and weaknesses of the p rogram are d iscussed in C h a p t e r 10. F i n a l l y , C h a p t e r 11 assesses both the usefulness of M I C R O S T A N D as a s tumpage appra isa l l earn ing too l and the appropr ia teness of Lo tus 1 - 2 - 3 ™ for deve lop ing stand management analys is p rograms . 4 P A R T I M I C R O S T A N D ; OVERVIEW, D E S C R I P T I O N , A N D E V A L U A T I O N O F T H E S I M U L A T O R S 2. A N OVERVIEW O F T H E S I M U L A T O R S M I C R O S T A N D is a stand l e v e l p rogram c o m p o s e d of s tumpage appra isa l s u b -models fed by a g rowth and y ie ld genera tor and l inked to some f i n a n c i a l analysis d e v i c e s . T h e genera l condi t ions being s imu la ted are as fo l lows: C r o w n t imber of Br i t i sh C o l u m b i a ' s c o a s t a l a r e a ^ ) ; pure stands composed of D o u g l a s - f i r (Pseudotsuga menz ies i i va r . menz ies i i ) , cedar (Thuja p l i c a t a Donn) , h e m l o c k (Tsuga he te rophy l la (Raf . ) Sarg. ) , or ba lsam (Abies spp.); three basic scenar ios cor responding to th inning only , f ina l harvest on ly , and thinning fo l lowed by f ina l harvest ; a s imu la t ion per iod ranging f r o m one year to 100 years ; and m e t r i c measurements and a 1985 base year fo r costs and revenues . F igure 1 shows the basic design of M I C R O S T A N D wi th the program s imula tors p e r f o r m i n g sequent ia l ly downwards. Inputs are those p rov ided by the user whereas outputs re fe r to the tables and graphics g e n e r a t e d by the p r o g r a m ^ ) . Figure 1. Basic Design of M I C R O S T A N D Inputs > Inputs > Inputs > Inputs > G r o w t h and Y i e l d S i m u l a t o r > I T i m b e r - l o g C o n v e r s i o n S i m u l a t o r > i L o g G r a d i n g S i m u l a t o r > R e v e n u e and D e l i v e r y C o s t S i m u l a t o r s F i n a n c i a l A n a si/ ysis S i m u l a t o r Outputs Outputs Outputs Outputs With a few except ions , the c o a s t a l a rea re fe rs to that part of Br i t i sh C o l u m b i a (BC) l y ing to the west of the C a s c a d e Mounta ins ( B C M o F 1985). In order to s i m p l i f y the text , the t e r m "Br i t ish C o l u m b i a ' s c o a s t a l a r e a " w i l l be r e p l a c e d throughout this thesis by "the C o a s t " . A c o m p l e t e l is t ing of the s imulator 's input and output var iab les can be found in A p p e n d i x I. F o r each scheduled harvest , the growth and y ie ld s imu la to r generates output y ie ld var iab les which are then used by the t i m b e r - l o g convers ion s imula tor to t r a n s -f o r m the t imber harvested into logs . T h e l o g grad ing s imu la to r then es t imates a grade d is t r ibut ion , and the revenue s imu la to r then appl ies l o g pr ices to the grade d is t r ibu t ion . T h e costs assoc ia ted wi th each harvest (d irect costs per de l ivery phase, re turn on c a p i t a l and a s p e c i a l r isk a l lowance) are then e s t i m a t e d by the de l ive ry cost s imu la to r . F i n a l l y , u s e r - s p e c i f i e d average rea l ra te of change in revenues , average rea l ra te of change in c o s t s , and r e a l d iscount ra te are used by the f i n a n c i a l analysis s imu la to r to produce the fo l lowing d a t a : cash f low of r e a l revenues and costs over the s imu la t ion p e r i o d , res idua l t i m b e r va lue at e a c h harves t , and net present value and b e n e f i t - c o s t ra t io for the stand management s c e n a r i o . E a c h of these s imula tors is descr ibed and e v a l u a t e d in C h a p t e r s 3 to 7. 3. T H E G R O W T H A N D Y I E L D S I M U L A T O R This f i rst s imu la tor es t imates growth p a r a m e t e r s over the s imu la t ion per iod and y ie ld paramete rs at scheduled harvests . A s imu la t ion per iod can c o v e r up to 100 years (1, 10, 20, 30.. . or 100 years) . T h e f i rs t year s i m u l a t e d is year z e r o . T h e condi t ions s imu la ted are pure stands of the C o a s t . A stand can be c o m -posed of D o u g l a s - f i r , c e d a r , h e m l o c k or b a l s a m . T h e three basic scenar ios that can be s imu la ted are th inning only , f i n a l harvest on ly , and thinning fo l lowed by f ina l harvest . N a t u r a l regenera t ion fo l lows f ina l harvest a f t e r wh ich no fur ther t ree r e m o v a l can be s i m u l a t e d . T h e growth and y ie ld s imu la to r was deve loped f r o m the ground measurement equat ions of the B C F o r e s t Serv ice var iab le densi ty y ie ld equat ions ( B C M o F 1983a). Sec t ion 3.1 presents the growth and y ie ld equat ions for unmanaged stands, S e c t i o n 3.2 descr ibes equat ions deve loped to s imu la te reac t ions to th inn ing, and Sec t ion 3.3 discusses the strengths and l im i ta t ions of the growth and y ie ld s i m u l a t o r . 3.1 Equations for Unmanaged Stands Unless otherwise s t a t e d , this s e c t i o n is based on B C M o F (1983a). T h e B C Min is t ry of Fores ts var iab le densi ty y i e l d equat ions were deve loped f r o m the C h a p m a n - R i c h a r d s n o n - l i n e a r growth m o d e l : V = b ! (1 - e b 2 A ) b 3 where V is the stand vo lume (m^/ha); A is the stand age (years); bi, b£ and b3 are regression c o e f f i c i e n t s . T h e C h a p m a n - R i c h a r d s mode l is sui table for broad planning purposes ( U B C 8 1983). H o w e v e r , a c c o r d i n g to the same s o u r c e , more re f ined y ie ld pred ic t ions are needed for de ta i led planning and s tand t rea tment prescr ip t ions . T h e r e f o r e , the basic C h a p m a n - R i c h a r d s mode l has been m o d i f i e d by the B C Min is t ry of Fores ts by the addi t ion of s i te index (SI), s tand basal a rea (BA) , and stand d i a m e t e r (D), as shown in the fo l lowing func t iona l re la t ionships and equat ions: B A = f (A , SI) D = f (A , SI, B A ) V = f (A , SI, B A , D) B A = b i S K l - e b 2 A ) b 3 e b 4 S I (1) D = D L I M + b!SI B A (1 - e b 2 A ) b 3 e b 4 S I e b 5 B A (2) V = b iS I B A D (1 - e b 2 A ) b 3 e b 4 S I e b 5 B A e b 6 D (3) where B A is the mean stand basal a r e a (m^/ha); D is the quadra t ic mean s tand d i a m e t e r at breast height ( c m ) d ) ; V is the stand vo lume (m^/ha); SI is the s i te index (m) cor respond ing to stand height at a r e f e r e n c e age (100 years fo r c e d a r , h e m l o c k and b a l s a m , 50 years for D o u g l a s - f i r ) ; D L I M is the d i a m e t e r l i m i t (7.5, 17.5 or 22.5 cm) cor responding to both the m i n i m u m d i a m e t e r at breast height for a t ree to be cons idered for growth and y ie ld va lues , and also to a u t i l i za t ion s tandard . A 7 . 5 - c e n t i m e t r e d i a m e t e r l i m i t re fe rs to a whole s tem u t i l i za t ion s tandard , whereas 17 .5 -c e n t i m e t r e and 2 2 . 5 - c e n t i m e t r e d i a m e t e r l im i ts cor respond to two i n t e n -s i t ies of c lose u t i l i za t ion exc lud ing decay v o l u m e ^ ) ; 1. T h e quadra t ic mean stand d i a m e t e r is the d i a m e t e r cor responding to a t ree of average basal a r e a . 2. C l o s e u t i l i za t ion means a 3 0 - c e n t i m e t r e s tump height and a 1 0 - c e n t i m e t r e d iamete r inside bark top . b j to bQ are regression c o e f f i c i e n t s that d i f f e r for e a c h equat ion , s p e c i e s , d i a m e t e r l i m i t , and forest inventory zone (FIZ) group. T h e F IZ groups cor responding to the C o a s t are A B C for D o u g l a s - f i r , cedar and b a l s a m , and B C for h e m l o c k . Var iab le densi ty y ie ld pro jec t ion c o e f f i c i e n t s for pure stands in Br i t i sh C o l u m -bia were not deve loped for combina t ions of d i a m e t e r l im i ts and u t i l i za t ion standards other than those descr ibed above . T h e a c t u a l s tand basal a rea fo r the in i t i a l year of a s imu la t ion per iod can be s p e c i f i e d , thus the name "var iable densi ty y ie ld equat ions" . If the in i t i a l year value is s p e c i f i e d , the basal a rea is e s t i m a t e d by equat ion 4 which is c o m p o s e d of the basal a rea equat ion 1 mul t ip l i ed by the re la t i ve basa l a rea ( R B A ) : B A = R B A b 1 S I ( l - e b 2 A ) b 3 e b 4 S I (4) where R B A = B A s p e c i f i e d for the in i t i a l age (5) C a l c u l a t e d basal a rea f r o m in i t i a l age and s i te index When no a c t u a l s tand basal a rea is s p e c i f i e d for the in i t i a l yea r of a s i m u l a t i o n , R B A takes a va lue of one, and equat ions 1 and 4 are equ iva len t . C o n s e q u e n t l y , only equat ion 4 is used in the program to e s t i m a t e basal a r e a . E x a m i n a t i o n of the d i a m e t e r equat ion 2 ind ica tes that the s p e c i f i e d d i a m e t e r l i m i t is the m i n i m u m value the equat ion can take . In order to avo id an unrea l is t ic ser ies of d i a m e t e r values equal to or s l ight ly over the d i a m e t e r l i m i t for the ear ly years of a s tand , D is set to zero when the value c a l c u l a t e d wi th equat ion 2 is s m a l l e r than the d i a m e t e r l i m i t plus 0.499 c m (8.0, 18.0 or 23 cm) . In such a c a s e , the stand basal a rea and vo lume are also set to z e r o . Th is const i tu tes a m o d i f i c a t i o n of the o f f i c i a l var iab le densi ty y i e l d equat ions descr ibed in B C M o F (1983a). T h e stand height (H) is c a l c u l a t e d f r o m equat ion 6 taken f r o m B C Min is t ry of Fores ts da ta ( B C M o F 1980). N o t e that the height e s t i m a t i o n does not use c o e f -f i c ien ts s p e c i f i c fo r d i f f e ren t u t i l i za t ion s tandards . 10 H = f (A , SI) H = b i S I 1 0 0 (1 - e b 2 A ) b 3 (6) where H is the to ta l s tand height (m); S I J Q O * S T N E s ^ e index (m) wi th a 100 -year r e f e r e n c e age; bi, b2 and b 3 a re regression c o e f f i c i e n t s that d i f f e r for each spec ies and forest inventory zone group. Equa t ion 7 is used for D o u g l a s - f i r to t r a n s f o r m the si te index value s p e c i f i e d by the user , w i th a r e f e r e n c e age of 50 y e a r s , into i ts equiva lent wi th a r e f e r e n c e age of 100 years , as requi red by equat ion 6(3). Six oo = 1.34318 S l 5 0 (7) T h e number of s tems per h e c t a r e (N) is e s t i m a t e d f r o m the m a t h e m a t i c a l re la t ionship that exists between the s tand basa l a rea and the quadra t ic mean stand d i a m e t e r (of t rees wi th a d i a m e t e r g rea te r than or equal to the d i a m e t e r l imi t ) . N = 12732.4 B A (8) D 2 T h e annual vo lume i n c r e m e n t (m3 /ha per year) is c a l c u l a t e d as the stand vo lume at the cur ren t age A minus the stand vo lume at age A - l . T h e mean annual vo lume i n c r e m e n t (m3 /ha per year) is c a l c u l a t e d as the vo lume per h e c t a r e d iv ided by the cor responding stand age . G r o w t h values for na tura l regenera t ion fo l lowing f ina l harvest are for a s tand of the harves ted spec ies wi th the same s i te index and re la t i ve basal a r e a . 3. Equa t ion 7 can be der ived f r o m equat ion 6 by subst i tu t ing SI50 for H at age 50, and by r e p l a c i n g A by 50 years and the c o e f f i c i e n t s by the i r respec t ive va lues . 3.2 Equations for Reactions to Thinning T h e growth and y ie ld mode l fo r unmanaged stands presented in Sec t ion 3.1 does not i m p l i c i t l y incorpora te hypotheses on the causes of m o r t a l i t y and the i n f l u -ence of densi ty on growth processes such as the anabol ic (construct ive) and c a t a b o l i c (destruct ive) metabo l isms ( B C M o F 1983a; P ienaar and T u r n b u l l 1973). C o n s e q u e n t -ly , s tand reac t ions to th inning cou ld not be handled by the m o d e l as s u c h , and it was necessary to deve lop a method using a m a t h e m a t i c a l manipu la t ion of the e q u a -tions for unmanaged stands to s imu la te stand reac t ions to th inn ing. T h e procedure for this man ipu la t ion , wh ich has not been tes ted with e m p i r i c a l measurements nor va l ida ted mode ls , revo lves around values and annual i n c r e m e n t s for basal area(4). T h e thinning age (TA) and the pe rcen tage of s tand basa l a rea r e m o v e d at t h i n -ning (TP) are s p e c i f i e d by the user . Basa l a rea at th inning age ( B A T A ) is c a l c u l a t e d f r o m equat ion 4, and the res idua l basal a rea a f te r th inning ( R E S B A ) is c a l c u l a t e d as: R E S B A = B A T A (1 - T P / 1 0 0 ) (9) T h e stand age cor responding to a basal a rea equa l to the res idua l basal a rea a f te r th inning is c a l l e d the th inning cor responding age ( T C A ) , and is c a l c u l a t e d by iso la t ing the age var iab le (A) in equat ion 4. T C A = round [ln(l - 1 0 l ° g < R E S B A / K > / b 3 ) / b 2 ] (10) Where K = bi R B A SI e b 4 S I T h e assumed i m m e d i a t e e f f e c t of th inning on the s tand basal a rea es t ima t ion is a re turn to condi t ions of an unmanaged s tand at a younger age: the th inning c o r -responding age . Thus the s tand basal a rea one year a f te r th inning is c a l c u l a t e d f r o m equat ion 4 wi th the age T C A + 1. A c c o r d i n g l y , the age T C A + 2 is used for the second 4. T h e s imu la t ion method descr ibed in this s e c t i o n was deve loped with the help of P . L . M a r s h a l l o f the U n i v e r s i t y of Br i t i sh C o l u m b i a . 12 year a f te r th inn ing, T C A + 3 for the th i rd year a f te r th inn ing , and so f o r t h , as i l l u s -t ra ted in F igure 2. Figure 2. The Method Used to Estimate Basal Area After Thinning 4 TCA+1 TA+1 Stand A g e (years) T h e age value used in equat ion 4 to es t imate the basa l a r ea a f te r th inning is c a l l e d the cur ren t cor responding age ( C C A ) c a l c u l a t e d as: C C A = T C A + A - T A (11) Suppose, fo r e x a m p l e , that the cur ren t s tand age (A) is 50 y e a r s , the th inning age (TA) is 45 years , and the th inning cor responding age ( T C A ) is 35 years . In such a c a s e , 40 years is the cur rent cor responding age ( C C A ) used in equat ion 4 to c a l c u l a t e the basal a rea at yea r 50. Th is method to s imu la te basal a r ea a f te r th inning wi l l s o m e t i m e s generate annual inc rements (at C C A ) sma l le r than those of unmanaged condi t ions (at A ) . Such s i tuat ions wi l l genera l ly resul t f r o m an excess ive reduc t ion of the basal a r e a at th inning (TP of equat ion 9). It should however be noted that the basal a rea i n c r e -ment a f te r th inning is d is t r ibuted on a reduced number of t rees , a cond i t ion that may par t ia l ly o f fse t possible i n c r e m e n t reduct ions due to th inn ing. T h e quadra t ic mean s tand d i a m e t e r a f te r th inning is e s t i m a t e d by equat ion 12 using d i a m e t e r values c a l c u l a t e d by the d i a m e t e r equat ion 2 for unmanaged stands. D a f te r th inning = R D * D at C C A (12) Where R D is the re la t i ve d i a m e t e r d e t e r m i n e d as: R D = D at T A (13) D at T C A With this s imu la t ion m e t h o d , th inning is assumed not to a f f e c t the d i a m e t e r d is t r ibut ion of a s tand nor , consequent ly , i ts quadra t ic mean d i a m e t e r . Th is can be demonst ra ted by examin ing the d i a m e t e r va lues p r e d i c t e d when the cur rent s tand age (A) equals the thinning age ( T A ) . In such a c a s e , equat ion 11 shows that the cur ren t cor responding age ( C C A ) is a lso the th inning cor respond ing age ( T C A ) . C o n -sequent ly D at C C A of equat ion 12 and D at T C A of equat ion 13 are equ iva lent , and D a f te r th inning equals D at th inning a g e . A n a l te rna t ive approach to e s t i m a t e the mean s tand d i a m e t e r a f te r th inning was e x a m i n e d . It cons is ted of using equat ion 2, an equat ion designed to e s t i m a t e the mean d i a m e t e r of unmanaged stands, but wi th basal a r ea values c a l c u l a t e d as the basal a rea at th inning age ( B A T A ) plus the s u m m a t i o n of the basal a r ea i n c r e -ments a f t e r th inning ( A B A / A A ) up to the cur ren t s tand age . T h e basal a r e a values thus used in equat ion 2 are genera l ly g rea te r than those for an unmanaged s tand . T h i s approach had to be abandoned because equat ion 2 is not s u f f i c i e n t l y sensi t ive to the resul t ing increases in B A va lues . Stand v o l u m e , he ight , number of s tems per h e c t a r e , annual vo lume i n c r e m e n t , and mean annual vo lume i n c r e m e n t a f te r th inning are c a l c u l a t e d wi th the same equat ions as those used for unmanaged stands, but wi th basal a rea and d i a m e t e r values e s t i m a t e d by the equat ions descr ibed in this s e c t i o n . 3.3 Evaluation Th is s e c t i o n examines the strengths and l im i ta t ions of the growth and y ie ld s imu la to r . T h e groupings "strengths" and " l imi ta t ions" represent in i t i a l eva luat ions of the s imulator 's c h a r a c t e r i s t i c s taken at f a c e va lue . H o w e v e r , fu r ther analysis of the c h a r a c t e r i s t i c s may r e v e a l less obvious advantages or ig ina t ing f r o m an a p p a r -ent " l im i ta t ion" or v i c e v e r s a . T h i s r e m a r k also appl ies to the eva lua t ion of the other s imu la to rs . Strengths Simulation of representative B C coastal conditions Th is is a c h i e v e d through the e s t i m a t i o n of g rowth and y ie ld paramete rs for i m m a t u r e , m a t u r e , or o ld g rowth e v e n - a g e d stands c o m p o s e d of impor tan t c o m m e r -c i a l s p e c i e s . Flexibility T h e numerous possible combina t ions of s p e c i e s , s i te indexes, d i a m e t e r l i m i t s , in i t i a l s tand ages and basa l a reas , harves ts , and lengths of the s imula t ion per iod provide the user wi th a f lex ib le basis for the s imu la t ion of s tumpage appra isa l . Detailed description of stand conditions Stand height , d i a m e t e r , number of s t e m s , basal a r e a , v o l u m e , annual i n c r e m e n t and mean annual i n c r e m e n t are e s t i m a t e d every year of a s imu la t ion pe r iod . Incorporation of strategies to offset wood supply deficits C l o s e r u t i l i za t ion and the i m p l e m e n t a t i o n o f s i l v icu l tu re p r a c t i c e s are the two main s t ra teg ies ava i lab le in Br i t i sh C o l u m b i a to o f fse t a c t u a l and an t ic ipa ted supply d e f i c i t s in te rms of to ta l supply , spec ies or qual i ty ( U B C 1983). Such s t r a t e -gies are i ncorpora ted in the s imula tor through the three possible d i a m e t e r l im i t opt ions and the th inning op t ion . T h e d i a m e t e r l i m i t s e l e c t i o n opt ion re fe rs to the concep t of e c o n o m i c marg in of u t i l i z a t i o n , the th inning opt ion to the concep t of c o m m e r c i a l pa r t i a l cu t t ing^ 5 ) . F u r t h e r m o r e , con t ra ry to other fo rms o f intensive s i l v i c u l t u r e , the th inning opt ion is we l l su i ted to such a s tumpage appra isa l p rogram because the s imula tors are a lmost equal ly app l icab le at th inning or f ina l harves t . Limitations Unsophisticated and nonvalidated procedure to simulate reactions to thinning T h e procedure descr ibed in S e c t i o n 3.2 can be cons idered as unsoph is t ica ted , notably because only one th inning can be s i m u l a t e d be fore f ina l harvest , because the d i a m e t e r l i m i t be fore and a f te r th inning is the s a m e , and because thinning is not assumed to a f f e c t the d i a m e t e r d is t r ibut ion of a s tand . F u r t h e r m o r e , the r e a c -t ions to th inning p r e d i c t e d wi th the procedure have not been c o m p a r e d to those of e m p i r i c a l da ta or to other mode ls . H o w e v e r , even the da ta and models that do exist are of a par t i a l or e x p e r i m e n t a l na tu re . In f a c t , " m u c h more work remains to be done be fore a s y s t e m is deve loped that can pred ic t cons is tent ly the response of a s tand to s p e c i f i c management a c t i v i t i e s " (Marsha l l 1987, 167). T h e procedure to s imula te reac t ions to th inning has, however , two c h a r a c -te r is t i cs which appear to make it appropr ia te for the in tended purpose of the p r o -g r a m . F i r s t , the procedure is based on basal a r ea annual inc rements cor responding to the s imu la ted s tand but at younger ages . C o n s e q u e n t l y , the method generates react ions to th inning which are s p e c i f i c to e a c h c o m b i n a t i o n of s p e c i e s , s i te index, 5. By d e f i n i t i o n , c o m m e r c i a l pa r t i a l c u t t i n g is e x p e c t e d to provide a re turn over costs or to at least break e v e n . densi ty , and d i a m e t e r l i m i t . S e c o n d , the vo lume a f te r th inning is e s t i m a t e d by e q u a -t ion 3 that uses the cur rent s tand age , and not the cur ren t cor responding age . Th is prevents unrea l is t ic react ions for mature stands that al low l i t t l e opportuni ty for th inning. These two c h a r a c t e r i s t i c s w i l l ce r ta in ly not prevent the growth and y ie ld s i m u -la tor f r o m o c c a s i o n a l l y p r e d i c t i n g unrea l is t ic reac t ions to th inning. Y e t , the n o n -l inear f o r m of the equat ions and their c o m p l e x in te rac t ions wi l l not ind ica te such possible b ias , i n a c c u r a c y , or i m p r e c i s i o n . C o n s e q u e n t l y , users should try to s imu la te rea l i s t i c th inning condi t ions ( p r e c o m m e r c i a l or c o m m e r c i a l ) , and use their knowledge and judgement to d e t e c t possible unrea l is t ic y ie ld p red ic t ions . No prediction of diameter distribution T h e growth and y ie ld s imu la to r used in M I C R O S T A N D is a t y p i c a l w h o l e - s t a n d model in that pred ic t ions cor respond to average v a l u e s ^ ) . Th is l i m i t s the possib i l i ty of tak ing into a c c o u n t the f i n a n c i a l i m p o r t a n c e of the d i a m e t e r d is t r ibut ion of t rees , espec ia l l y for the la rger t rees of a s tand . Th is point w i l l be fur ther examined in C h a p t e r s 4 and 5. 6. O ther w h o l e - s t a n d models inc lude a d i a m e t e r d is t r ibut ion which "may be based on an assumed d is t r ibu t ion , or a g e n e r a l d is t r ibut ion f u n c t i o n , such as the W e i -bul l p robabi l i ty densi ty f u n c t i o n . . . . " Th is l a te r func t ion "is one of a number of m a t h e m a t i c a l funct ions used to descr ibe d i a m e t e r d is t r ibut ions , i.e. f r e -quencies by d i a m e t e r c lass" (Ti tus and M o r t o n 1985, 21). 4. T H E T I M B E R - L O G C O N V E R S I O N S I M U L A T O R 17 T h e t i m b e r - l o g convers ion s imu la t ion corresponds to the buck ing a c t i v i t y dur ing a harvest ing o p e r a t i o n . Its purpose is to conver t the average harves ted t ree (whose dimensions are e s t i m a t e d by the growth and y i e l d s imulator ) into logs. A s wi l l be seen in C h a p t e r 5, the output values genera ted by the t i m b e r - l o g convers ion s i m u l a -tor const i tu te the basic inputs of the l o g grad ing s i m u l a t o r . T h e t i m b e r - l o g convers ion s imu la to r is an adapta t ion of a t ree pro f i l e p r e d i c -t ion sys tem deve loped by D e m a e r s c h a l k and K o z a k (1977) and based on two m a t h e -m a t i c a l func t ions : one for the butt swe l l to the point of i n f l e c t i o n , the second for the point of i n f l e c t i o n to the top of the t ree . S e c t i o n 4.1 presents the input and output d a t a of the s imu la to r . T h e d e r i v a -t ion and nature of the vo lume and taper equat ions can be found in D e m a e r s c h a l k and K o z a k (1977). S e c t i o n 4.2 examines the s imulator 's s t rengths and l i m i t a t i o n s . 4.1 Input and Output Data Input da ta for the adapted vers ion used in M I C R O S T A N D are the spec ies , m a t u -r i ty class (stands older than 120 years are c l a s s i f i e d as mature) , s tand height and d i a m e t e r , log length for b reakdown, as we l l as top d i a m e t e r and s tump height for u t i l i z a t i o n . L o g length for breakdown corresponds to a f i x e d length for the buck ing opera t ion tak ing p lace f r o m the butt end to the top end of the s t e m . E x c e p t for log length fo r breakdown ( f ixed at 10 metres) the other input values c o m e f rom the growth and y ie ld s imu la to r^ 1 ) . Outputs genera ted for e a c h log f r o m the average harves ted t ree are the log length (m), the top d i a m e t e r inside bark (cm), and the gross inside bark vo lume ( m 3 ) . 1. T o p d i a m e t e r and s tump height for u t i l i za t ion are ind i rec t l y s p e c i f i e d v i a the d i a m e t e r l i m i t . It should be noted that to speed up c o m p u t e r process ing t i m e for this c o m p l e x m o d e l , the top d iamete r for the whole s tem vo lume u t i l i za t ion is f i xed at 3 ra ther than 0 c e n t i m e t r e s . Th is results in a s l ight underes t imat ion of vo lume when whole s tem vo lume u t i l i za t ion is s p e c i f i e d ; however the process ing t i m e saved was d e e m e d more impor tan t as the p rogram is being designed for use as a learn ing t o o l . C o n -stra ints assoc ia ted wi th process ing t i m e wi l l be fur ther deve loped in Par t II dea l ing with the program as a whole . 4.2 Evaluation Th is s e c t i o n examines the strengths and l im i ta t ions of the t i m b e r - l o g c o n v e r -sion s imu la to r . Strengths Excellent tree-profile prediction system C o n s i d e r i n g that the s y s t e m is based on only two y i e l d inputs , height and d i a m e -ter at breast he ight , the pred ic t ions are r e m a r k a b l y prec ise and a c c u r a t e ( D e m a e r -schalk and K o z a k 1977). F u r t h e r m o r e , by r e c o g n i z i n g the d i a m e t e r l i m i t , the sys tem establ ishes a d i rec t re la t ionship be tween the s p e c i f i e d u t i l i za t ion standard and the appra ised p r ice that is e s t i m a t e d by the l o g grad ing and revenue s imu la tors . H o w -ever , the t r e e - p r o f i l e p red ic t ion s y s t e m does not al low for decay vo lume when c lose u t i l i za t ion is s e l e c t e d (17.5 and 2 2 . 5 - c m d i a m e t e r l im i ts ) . In such a c a s e , log vo lumes are o v e r e s t i m a t e d but as wi l l be seen in C h a p t e r 5, the l o g grad ing s imula tor is d e -signed to c o r r e c t this b ias . 19 Weaknesses Fixed log length for breakdown With its f i xed 1 0 - m e t r e length for breakdown, the t i m b e r - l o g convers ion s i m u -la to r may appear to be an o v e r s i m p l i f i e d representa t ion of the buck ing a c t i v i t y for the C o a s t . Indeed, the cur rent s t a t e - o f - t h e - a r t buck ing programs use o p t i m i z a -t ion techniques to es t imate the c o m b i n a t i o n of l o g length that w i l l m a x i m i z e net revenues, based on i n f o r m a t i o n such as l o g p r ice for e a c h log grade , buck ing and haul ing c o s t s , and const ra in ts on log l eng th , d i a m e t e r , and po ten t ie l grade r e c o v e r y (Rogler and C a n h a m 1986). Y e t , p red ic t ions genera ted by such buck ing systems using o p t i m i z a t i o n techniques m a y not be appropr ia te in a t i m b e r appra isa l contex t where the "operator o f average e f f i c i e n c y " concep t should be recogn ized^ 2 ) . In f a c t , the approved method for p red ic t ing l o g and t ree vo lumes fo r purposes of a p -pra is ing the s tumpage value of C r o w n t i m b e r in the C o a s t also uses the same f ixed 1 0 - m e t r e l o g length for breakdown and the t r e e - p r o f i l e p red ic t ion sys tem deve loped by D e m a e r s c h a l k and K o z a k (1977) ( B C M o F 1980). F u r t h e r m o r e , the f i xed log length fo r breakdown does not necessar i l y resul t in an underes t imat ion of l o g grades: the cru is ing procedure (s imulated in M I C R O S T A N D by the growth and y i e l d , t i m b e r - l o g c o n v e r s i o n , and log grad ing s imulators) does not incorpora te i n f o r m a t i o n regard ing l i m i t a t i v e grad ing f a c t o r s such as the l o c a t i o n of s t e m d e c a y and outside d e f e c t s ( B C M o F 1980). C o n s e q u e n t l y , the f i xed 1 0 - m e t r e l o g length for breakdown appears an appropr ia te basis for s imu la t ing the buck ing a c t i v i t y in a s tumpage appra isa l con tex t . 2. " A n appra isa l must es t imate the revenues that c a n be r e a l i z e d f r o m a t rack of t imber and the costs that must be i n c u r r e d to rea l i ze t h e m . But the a p -pra ised p r ice should not vary a c c o r d i n g to en t repreneur ia l sk i l l o f d i f fe rent l i c e n c e e s . R a t h e r , it should approx imate the amount that a c t i v e c o m p e t i t i o n a m o n g e f f i c i e n t enterpr ises would y ie ld - the fu l l e c o n o m i c rent . . . . C o n s i s -tent wi th the "operator of average e f f i c i e n c y " c o n c e p t , the se l l ing pr ices used in the appraisals should re la te to type and quant i ty of the products that are c u s t o m a r i l y p roduced f r o m that type of t imber" (Pearse et a l . 1974, 26-27). It should be noted that the 1 0 - m e t r e l o g length fo r breakdown al lows fo r the c a l c u l a t i o n of the average 1 0 - m e t r e log v o l u m e , an input var iab le for the de l ive ry cost s imula tor that is used to es t imate the t r e e - t o - t r u c k cost at each harvest (Ref . Sec t ion 6.1.2). No recognition of tree size variations By conver t ing into logs the average harves ted t ree , the s imu la to r does not recogn ize the var ia t ions of t ree s ize wi th in a s tand . T h e imp l i ca t ions of this l i m i t a -t ion wi l l b e c o m e more apparent wi th the log grad ing s imu la t ion and they wi l l be discussed in S e c t i o n 5.2 deal ing wi th the strengths and l im i ta t ions of the log grad ing and revenue s imu la tors . 5. T H E L O G G R A D I N G A N D R E V E N U E S I M U L A T O R S 21 Sec t ion 5.1 presents the s imu la t ion used in M I C R O S T A N D to process the logs of the average harves ted t ree (whose d imensions are genera ted by the t i m b e r - l o g convers ion s imula tor ) into a grade d is t r ibut ion to wh ich log pr ices are app l ied . Strengths and l im i ta t ions of this method are d iscussed in S e c t i o n 5.2 5.1 Simulation Procedure Simula t ion of l o g grad ing is based on the grad ing rules of the B C F o r e s t Serv ice sca l ing manua l ( B C M o F 1983b) and on the average 1985 pr ices for the Br i t i sh C o l u m -bia "major c o a s t a l l o g marke t type sa le" . T a b l e I shows these pr ices for e a c h of the four spec ies of the p r o g r a m . T h e major c o a s t a l p r ices are those used in Br i t i sh C o l u m b i a for se t t ing C r o w n t i m b e r s tumpage ra tes for both forest and t ree f a r m l i c e n c e s ( B C M o F 1986). Table I. Log Prices by Species Used in M I C R O S T A N D * Douglas-f i r Cedar Hemlock Balsam G r a d e P r i c e ( $ /m3) G r a d e P r i c e ( $ / m 3 ) G r a d e P r i c e ( $ / m 3 ) G r a d e P r i c e ($/m3.) A 182 .74 D 84 .07 D 61 .48 C 50 .89 B 118.06 F 82 .40 H 48 .24 D 59.88 C 67 .47 H 61 .99 I 42 .43 H 48 .03 D 129 .14 I 50 .26 J 34 .05 I 42.51 H 57 .59 J 40 .16 X 25 .63 J 34.71 I 49 .46 K 63 .19 Y 12.41 X 25 .67 J 35 .57 L 51 .72 Y 14 .30 X 20 .23 M 38 .00 Y 6 .19 X Y 17 .25 3.98 These values are average pr ices f o r the twe lve months ending D e c e m b e r 20, 1985 that were produced by the B C F o r e s t S e r v i c e f r o m log sale invo ices for the V a n c o u v e r L o g M a r k e t (sale type : major c o a s t a l l o g market ) . These pr ices are assumed to cor respond to the program's cost base of J u l y 1, 1985. 22 T h e l o g grad ing method deve loped fo r M I C R O S T A N D has two s teps . F i r s t , for each log of the average harvested t ree , the highest possible grade is e s t i m a t e d a c c o r d i n g to log length and top inside bark d i a m e t e r . T h e values for these two v a r -iables are genera ted by the t i m b e r - l o g convers ion s i m u l a t o r . S e c o n d , the vo lume assoc ia ted wi th each log is d is t r ibuted a c c o r d i n g to the log qual i ty s p e c i f i e d by the user (good, med ium or low) f r o m the highest possible grade to grade re jec ts . T h e log qual i ty s e l e c t i o n is designed to take into a c c o u n t other grading requ i rements in addi t ion to length and top d i a m e t e r . T h u s , c o m p a r e d to a lower qual i ty op t ion , the high qual i ty opt ion assumes bet ter c h a r a c t e r i s t i c s f o r the o ther grad ing r e q u i r e -ments and , consequent ly , the mode l generates a be t te r d is t r ibut ion of l o g vo lume by log grade . Th is t w o - s t e p procedure is de ta i led in Sect ions 5.1.1 and 5.1.2. 5.1.1 Highest Possible Grade per Log (Step 1) T a b l e II i nd ica tes , in te rms of l o g d imens ions , the grad ing requ i rements that are used to de te rmine the highest possible grade r e c o v e r a b l e f r o m e a c h log of the average harvested t ree . L o g grades fo r e a c h spec ies are d isp layed in order of d e -c l in ing values a c c o r d i n g to the pr ices o f T a b l e I. N o t e that the m i n i m u m length requ i rements in T a b l e II a re a l l s m a l l e r than 10 met res which means that the log length c r i t e r i o n only a f f e c t s the grade es t ima t ion of the smal les t l o g of a t ree , the only one wi th a length less than or equal to 10 m e t r e s . When more than one c o m b i n a t i o n of l ength and top d i a m e t e r requ i rements exists for a g r a d e , the least s t r ingent c o m b i n a t i o n of requ i rements is s e l e c t e d . T h e least s t r ingent combina t ions appear in T a b l e II. M o r e o v e r , when the m i n i m u m length and top d i a m e t e r requ i rements are the same for more than one grade of a spec ies , only the grade wi th the highest cor respond ing p r i c e is cons idered as a p o s -sible highest g rade . Th is is the case of cedar logs for wh ich grades I, L , and M have the same m i n i m u m length and top d i a m e t e r r e q u i r e m e n t s . S ince grade L c o m m a n d s Table JL Log Grading Requirements by Species for the Determination of the Highest Possible Grade Dimens ions Spec ies G r a d e L e n g t h T o p D i a m e t e r * ( m ) ( c m ) D o u g l a s - f i r A > 5 .2 > 75 D > 5 .0 > 75 B > 5 .2 > 59 C > 5 .2 > 37 H > 5 .0 > 29 I > 3 .8 > 37 J > 5 .0 > 10 and < 37 X > 2 .6 > 10 Y - -R e j e c t s - -C e d a r D > 5 .0 > 59 F > 5 .0 > 49 K > 3.8 > 49 H > 5 .0 > 37 L > 3.8 > 37 I > 3.8 > 37 J > 5 .0 > 10 and < 37 M > 3 .8 > 37 X > 2 .6 > 10 Y - -R e j e c t s - -B a l s a m and H e m l o c k D > 5 .0 > 65 > 5 .2 > 37 H > 5 .0 > 49 I > 3 .8 > 37 J > 5 .0 > 10 and < 37 X > 2 .6 > 10 Y - -R e j e c t s - -Inside bark B a l s a m o n l y the highest p r i c e of these three grades ( i l l u s t r a t e d by i t s higher p o s i t i o n i n Table I I ) , i t i s considered to be the highest possible grade. S i m i l a r l y , a log cannot be graded lower than Y at t h i s step. 5.1.2 Volume Distribution per Grade (Step 2) A proportion d i s t r i b u t i o n of volume i s generated from the estimated highest grade of a log to grade r e j e c t s f or each combination of q u a l i t y , species, and estimated highest log grade. These d i s t r i b u t i o n s are generated through i n d i v i d u a l binomial p r o b a b i l i t y d i s t r i b u t i o n s with three p r o b a b i l i t i e s of success each corresponding to a log q u a l i t y : 90 percent for good q u a l i t y , 80 percent f o r medium q u a l i t y , and 70 percent for low q u a l i t y . Table III shows the proportion d i s t r i b u t i o n s of log volume from each possible highest grade to the lowest grade for each species and log q u a l i t y . This procedure for d i s t r i b u t i n g log volume among grades i s not based on empirical data. The r a t i o n a l e f or using the binomial d i s t r i b u t i o n i n t h i s context i s that each possible grade (from the highest possible grade to grade r e j e c t s ) can be compared to a t o t a l number of successes (n, n-1,..., 0) i n n t r i a l s where success i n any t r i a l i s defined as meeting grading requirements other than length and top diameter. The p r o b a b i l i t y of success i s 90, 80 or 70 percent, depending on the selected q u a l i t y . Note that the summation of each proportion d i s t r i b u t i o n (column) of Table III i s unity (1), r e f l e c t i n g the f a c t that a l l possible outcomes have been considered, and that 100 percent of the log volume has been d i s t r i b u t e d . Assume, f o r example, that the estimated highest grades f o r the three logs of an average Douglas-fir tree harvested at a thinning are J , J , and X, and that the log q u a l i t y selected i s medium. The volume corresponding to each log would then be d i s t r i b u t e d according to Table III i n the following manner. For the two logs with an estimated highest grade of J , the proportions would be 0.512 for J logs, 0.384 for X logs, 0.096 f o r Y logs, and 0.008 f o r r e j e c t s . For the log with an e s t i -Table HI. Proportion Distributions of Log Volume by Log Quality and Grade* G r a d e by Species Propor t ion D is t r ibu t ion by Q u a l i t y C e d a r D - f i r B a l . H e m l . Good Qual i ty D .349 F A .387 .387 K D .194 .387 .430 H B D .057 .172 .389 .478 L C C D .011 .045 .143 .372 .531 I H H H .001 .007 .033 .124 .354 .590 J I I I .000 .001 .005 .023 .098 .328 .656 M J J J .000 .000 .000 .003 .015 .073 .292 .729 X X X X .000 .000 .000 .000 .001 .008 .049 .243 Y Y Y Y .000 .000 .000 .000 .000 .000 .004 .027 R e j . R e j . R e j . R e j . .000 .000 .000 .000 .000 .000 .000 .001 Medium Qual i ty D .107 F A .268 .134 K D .302 .302 .168 H B D .201 .302 .336 .210 L C C D .088 .176 .294 .367 .262 I H H H .026 .066 .147 .275 .393 .328 J I I I .006 .017 .046 .115 .246 .410 .410 M J J J .001 .003 .009 .029 .082 .205 .410 .512 X X X X .000 .000 .001 .004 .015 .051 .154 .384 Y Y Y Y .000 .000 .000 .000 .002 .006 .026 .096 R e j . R e j . R e j . R e j . .000 .000 .000 .000 .000 .000 .002 .008 Low Qual i ty D .028 F A .121 .040 K D .233 .156 .058 H B D .267 .267 .198 .082 L C C D .200 .267 .296 .247 .118 I H H H .103 .172 .254 .318 .303 .168 J I I I .037 .074 .136 .227 .324 .360 .240 M J J J .009 .021 .047 .097 .185 .309 .413 .343 X X X X .001 .004 .010 .025 .060 .132 .265 .441 Y Y Y Y .000 .000 .001 .004 .010 .028 .076 .181 R e j . R e j . R e j . R e j . .000 .000 .000 .000 .001 .002 .008 .027 .800 These vec to rs of proport ions are f r o m a table of ind iv idua l b inomia l p r o b a b i l i -t ies (Wonnacott and Wonnacot t 1984). mated highest grade of X , the proport ions would be 0.640 for X logs , 0.320 for Y logs, and 0.040 for re jec ts . T h e vo lume per hec ta re assoc ia ted wi th e a c h log of an average harves ted t ree (and d is t r ibuted among grades) is c a l c u l a t e d as: LVj ( m 3 / h a ) = LVj ( m 3 ) N ( V G Y ) (14) V c where LVj is the vo lume ( m 3 and m 3 / h a ) cor responding to l o g i. Values expressed in cub ic metres are genera ted by the t i m b e r - l o g convers ion s imu la to r ; N is the number of s tems harves ted (/ha) c a l c u l a t e d by the growth and y ie ld s imu la to r ; V Q Y is the vo lume harves ted ( m 3 / h a ) c a l c u l a t e d by the growth and y ie ld s i m u -la tor ) ; Vc is the vo lume harvested ( m 3 / h a ) c a l c u l a t e d by the t i m b e r - l o g convers ion s imu la to r as the number of s tems harves ted mul t ip l i ed by the s u m m a t i o n of e a c h l o g v o l u m e . No te that the te rm ( V Q Y / V Q ) is a c o r r e c t i o n f a c t o r designed to o f fse t the vo lume o v e r e s t i m a t i o n of the t i m b e r - l o g convers ion s imu la to r when c lose u t i l i za t ion is s e l e c t e d (Re f . S e c t i o n 4 .2 )d) . Th is f a c t o r also ensures that the vo lume r e m o v e d at e a c h harvest is cons tan t , independent of whether i t is c a l c u l a t e d by the growth and y ie ld s imu la to r or as the s u m m a t i o n of l o g vo lumes per g rade . 5.1.3 Basis for Revenue Calculation Revenues per h e c t a r e assoc ia ted wi th e a c h harvest are c a l c u l a t e d by apply ing the log pr ices ( $ / m 3 ) of T a b l e I to the l o g grad ing d is t r ibut ion ( m 3 / h a per grade) 1. Th is c o r r e c t i o n f a c t o r is s i m i l a r to the d i a m e t e r c lass decay fac to rs used in c o m p i l i n g net vo lumes for c ru ise samples on the C o a s t ( B C M o F 1976). genera ted by the s imu la to r . Revenues per cub ic met re are c a l c u l a t e d by d iv id ing revenues per h e c t a r e by the vo lume harves ted per h e c t a r e . A s w i l l be fur ther de ta i led in C h a p t e r 6 which deals with the f i n a n c i a l analysis s imu la to r , the user can s p e c i f y an average year ly rea l ra te of change in l o g pr ices over the s imula t ion pe r iod . In such a c a s e , the revenues c a l c u l a t e d wi th the above method are mul t ip l i ed by a compound ing f a c t o r r e f l e c t i n g p r ice changes . 5.2 Evaluation Th is s e c t i o n examines the st rengths and l im i ta t ions of the log grad ing and revenue s imu la to rs . Strengths Recognition of the prescribed utilization standard O n l y the m a t e r i a l wi th in the p r e s c r i b e d u t i l i za t ion s tandard is cons idered in d e t e r m i n i n g the l o g grad ing d is t r ibut ion at e a c h harvest and the consequent c o r r e -sponding revenues . Log quality as an input variable Due to its e f f e c t on the d is t r ibut ion of l o g vo lume per log g rade , s e l e c t i o n of l o g qual i ty for e a c h harvest brings a rea l i s t i c qua l i ta t i ve de te rminan t into the revenue c a l c u l a t i o n of the s tumpage appra isa l . In add i t ion , this fea ture a l lows the user to s i m u l a t e an a l te ra t ion of the s t e m qual i ty of a s tand through th inning (e.g. med ium qual i ty at th inning fo l lowed by good qual i ty at f ina l harvest ) . Limitations Limited recognition of tree size variations A t f i rs t g l a n c e , the nonva l ida ted procedure used to d ist r ibute log vo lume f r o m the e s t i m a t e d highest grade to grade re jec ts seems to be equiva lent to r e c o g n i z i n g the var ia t ions of t ree s izes in a s tand . T h i s is not en t i re ly so , par t i cu la r ly because the es t imat ion of the highest grade of the logs is based on the d imensions of the average harves ted t ree . Th is may resul t in an underes t imat ion of the range of l o g grades at e a c h harvest . In such a c a s e , M I C R O S T A N D cannot r e v e a l the i m p o r t a n c e of the f i n a n c i a l cont r ibut ion of the la rger t rees of a s tand , for example those in the upper 10 to 20 percent of the d i a m e t e r d is t r ibu t ion . A n o t h e r consequence of this l i m i t a t i o n is the presence of jumps in g rad ing d ist r ibut ions as the s tand age increases . Indeed, a o n e - y e a r d i f f e r e n c e in harvest ing t i m e may resul t in a marked ly d i f f e ren t e s t i m a t e d highest possible grade of a l o g . No te that grad ing d is t r ibut ion jumps over t i m e may s t i l l o c c u r wi th models r e c o g n i z i n g s tem d imension d i s t r i b u -t ions. In the l a t t e r c a s e , however , such jumps would be a t tenua ted and would not result f r o m a mode l l ing l i m i t a t i o n . No te that recogn i t ion of t ree s ize var ia t ions is obta inable wi th a va luat ion procedure based on e m p i r i c a l da ta and regress ion techn iques . Such a procedure was deve loped for the F o r e s t E c o n o m i c s and P o l i c y A n a l y s i s ( F E P A ) R e s e a r c h Un i t at the U n i v e r s i t y of Br i t i sh C o l u m b i a as part of a p rogram of studies of e c o n o m i c t imber supply (Gasson and Wi l l iams 1986). Limited reliability of the price base T h e pr ices used for d e t e r m i n i n g the value of logs are f r o m the V a n c o u v e r L o g M a r k e t . T h e i m p e r f e c t i o n s of this marke t have been e x a m i n e d by authors (e.g. Pearse et a l . 1974, Pearse 1976). Y e t , the l i m i t e d re l i ab i l i t y of the p r ice base does not prevent the program f r o m revea l ing the nature and the in ter re la t ions of the main appra isa l p a r a m e t e r s . C o n s e q u e n t l y , this l i m i t a t i o n has l i t t le i m p a c t in the present c o n t e x t . 6. T H E D E L I V E R Y C O S T S I M U L A T O R This s e c t i o n is c o n c e r n e d wi th the cost es t ima t ion of those operat ions that are necessary to obta in the se l l ing pr ices used in the appra isa l . T h e de l ivery cost es t imat ion at e a c h harvest is c o m p o s e d of the d i rec t costs ( including deprec ia t ion) per opera t iona l phase, re turn on c a p i t a l , and a s p e c i a l r isk a l lowance . C o n s i s t e n t wi th the "operator of average e f f i c i e n c y " concep t descr ibed in S e c t i o n 4.2, the d e l i v -ery cost s imula t ion is in tended to r e f l e c t the costs that are incur red in harvest ing a par t i cu la r s tand by an opera tor of average e f f i c i e n c y . S e c t i o n 6.1 presents the equat ions used to e s t i m a t e the d i rec t costs for e a c h opera t iona l phase. S e c t i o n 6.2 descr ibes the method deve loped to genera te both a re turn on c a p i t a l and a s p e c i a l r isk a l lowance at e a c h harves t . Strengths and l im i ta t ions of the de l ivery cost s imu la to r are e x a m i n e d in S e c t i o n 6.3. 6.1 Direct Costs per Phase T h e d i rec t cost s imula t ion is main ly designed f r o m the C o a s t a l L o g - B a s e d A p p r a i s a l Manuals ( C L B A M ) of 1985 and 1986 ( B C M o F 1985, 1986) used for the de te rmina t ion of s tumpage for the purchase of C r o w n t i m b e r on the C o a s t . C o m -posed of opera t ing costs and d e p r e c i a t i o n , d i r e c t costs are e s t i m a t e d for e a c h of nine opera t iona l phases: road deve lopment ; t r e e - t o - t r u c k ; t ruck hau l ; road m a i n -tenance ; dump, sor t , boom and s c a l e ; towing or barg ing; crew t ranspor ta t ion ; c a m p and cookhouse; and overhead . Values cor responding to prev ious cost bases are t rans -f o r m e d into the program's cost base of J u l y 1, 1985 through the opera t ing cost t rend a l lowances s p e c i f i e d in B C M o F 1985 and 1986. Equat ions presented below are designed to e s t i m a t e d i r e c t costs per opera t iona l phase in dol lars per cub ic m e t r e . T h e de l ive ry cost s imula tor also es t imates these costs in dol lars per h e c t a r e . T o do so , values in dol lars per cub ic met re are mul t ip l ied by the vo lume per h e c t a r e r e m o v e d at each harvest . 6.1.1 Road Development E s t i m a t i o n of costs assoc ia ted wi th road deve lopment is based on a mode l that s imula tes the deve lopment phase cost a l lowances descr ibed in the C L B A M 1986 for the C o a s t (Wi l l iams 1986a). T h e deve lopment phases o f the appra isa l p rocedure are subgrade e x c a v a t i o n , haul ing and p l a c e m e n t of s tab i l i z ing m a t e r i a l , and c o n s t r u c -t ion of br idges and c u l v e r t s . When Wi l l iams's mode l is used to e s t i m a t e road deve lopment cost per k i l o m e t r e of r o a d , its pa ramete rs are the average bal last haul d is tance , the f requency of br idges and cu lver ts per k i l o m e t r e of r o a d , the average br idge span and c r ib he ight , and the average uphi l l side slope (U). U corresponds to the average slope encounte red in roadbui ld ing , and was e s t i m a t e d by Wi l l iams (1986a) to be t w o - t h i r d s of the a v e r -age stand slope (S): U (%) = .67 S (%) (15) Wi l l iams (1986a) suggests average values fo r the other p a r a m e t e r s . By using average values in the m o d e l , road deve lopment cost per k i lomet re of road can be expressed as a func t ion of uphi l l s ide s lope . Th is is the genera l approach that was adopted to s imu la te the d i rec t costs of road deve lopment in M I C R O S T A N D . More s p e c i f i c a l l y , s ix teen uphi l l s ide slope and cor respond ing road deve lopment cost ( R D C S T ) va lues genera ted by Wi l l iams's mode l (Table IV) were used to produce a regression equat ion where R D C S T ($/km) is expressed as a func t ion of U (%). T o do so, it was f i rs t necessary to t r a n s f o r m R D C S T ( $ / m 3 ) values of T a b l e IV into R D C S T ($/km) va lues . Th is was done through equat ion 16: R D C S T ($/km) = R D C S T ( $ / m 3 ) V ( m 3 / h a ) (16) R D E N S (km/ha) 31 Table IV. Road Development Cost (RDCST) for a Volume Class of 200 m 3 / h a and a Road Density (RDENS) of 0.05 km/ha U p h i l l Side S l o p e D e v e l o p m e n t C o s t (%) ( $ /m3) 0 17.68 10 17 .14 20 16 .93 30 17.02 40 17 .09 50 17 .40 60 18 .23 70 19.11 80 21 .25 90 23 .75 100 25 .35 110 27.06 120 28 .27 130 29 .47 140 30.68 150 31 .87 S o u r c e : D . H . Wi l l i ams, F o r e s t E c o n o m i c s and P o l i c y A n a l y s i s R e s e a r c h U n i t , U n i v e r -s i ty o f Br i t i sh C o l u m b i a , V a n c o u v e r , B . C . where V ( m 3 / h a ) is the vo lume harves ted (200 m 3 / h a f r o m the regression data); R D E N S is the road densi ty (0.05 k m / h a f r o m the regression data) . T h e resul t ing regression equat ion is as fo l lows: R D C S T ($/km) = 72706 - 580.67 U + 12.914 U 2 - 0.044 U 3 (17) where U < 150% Equa t ion 17 has a R - s q u a r e va lue of 0.994. T h e three c o e f f i c i e n t s and the constant t e r m are s ign i f i can t ly d i f f e ren t f r o m ze ro at a 99 percent c o n f i d e n c e l e v e l . Values c a l c u l a t e d f r o m equat ion 17 cor respond to a cost base of J u l y 1, 1984. T h e y are increased by a cost t rend a l lowance of one percent ( B C M o F 1986) to c o r -respond to the program's cost base of J u l y 1, 1985. R o a d deve lopment cost per cub ic met re can now be e s t i m a t e d for any c o m b i n a -t ion of road densi ty , vo lume harves ted per h e c t a r e , and stand slope using equat ions 15 and 17 and the re la t ionships expressed in equat ion 16. T h e vo lume harvested is genera ted by the growth and y ie ld s imu la to r whereas the stand slope is s p e c i f i e d by the user . T h e defau l t value for the road densi ty (0.05 km/ha) can be mod i f i ed by the u s e r ^ ^ . Th is opt ion is espec ia l l y re levant at f i na l harvest where , as wi l l be seen in Sec t ion 6.1.2, the road densi ty and the s e l e c t e d harvest ing sys tem can be r e l a t e d . In add i t ion , the deve lopment cost s u b - m o d e l a l lows for scenar ios where a propor t ion of roads a l ready exists or where only par t of the t ranspor ta t ion i n f r a -s t ruc tu re is charged against the i m m e d i a t e harves t . Depend ing on the presumed state of the roads or cost share a r r a n g e m e n t , the user spec i f i es the appropr ia te percentage of the fu l l road deve lopment c o s t . 1. Th is va lue is the average road densi ty de r ived f r o m a sample of forest roads c o l l e c t e d f r o m a wide range of loca t ions on the C o a s t for the purpose of e s -tabl ishing the cost a l lowances i n c o r p o r a t e d into C L B A M 1986 (Wi l l iams 1986a). 6.1.2 Tree- to -Truck T h e t r e e - t o - t r u c k a c t i v i t i e s encompass fa l l i ng , buck ing , yard ing or sk idding, and load ing . T w o t r e e - t o - t r u c k cost s u b - m o d e l s are used in M I C R O S T A N D : one fo r th inning and another fo r f ina l harvest . 6.1.2 a Sub-model for Thinning Th is s u b - m o d e l is based on a single regression func t ion of d i rec t t r e e - t o - t r u c k cost using es t imates fo r th inning cor responding to the B C c o a s t a l condi t ions^ 2 ) . These cost es t imates are der ived f r o m data with a l o g vo lume base of 0.25 cub ic m e t r e , a c o m b i n a t i o n of three harvest ing sys tems , and a 1984 cost base. T h e three harvest ing systems and their cor responding cost per cub ic met re are as fo l lows: H a r v e s t i n g Sys tem C o s t ($/m.3) Hand f a l l i n g and buck ing p l u s yard ing 27.30 Hand f a l l i n g and buck ing p l u s sk idding 23 .09 M e c h a n i c a l f a l l i n g and fo rward ing 20.30 F o r each of three average stand slope c lasses , the proport ions of harvest ing systems ind ica ted in T a b l e V mul t ip l i ed by the cor responding costs g ive the t r e e - t o -t ruck costs for an average l o g vo lume of 0.25 cub ic met re l i s ted in the c e n t r a l c o l u m n of T a b l e VI. D a t a for the other four average log vo lumes were e s t i m a t e d by logging engineers . Table V . Proportion Distribution of Harvesting Systems for an Average Log Volume of 0.25 m 3 Propor t ion D is t r ibu t ion Stand S l o p e C l a s s H a r v e s t i n g S y s t e m 0-20% 21-50% 51%+ Hand f a l l i n g and buck ing p l u s yard ing .3 .5 1.0 Hand f a l l i n g and buck ing p l u s sk idding .2 .3 M e c h a n i c a l f a l l i n g and fo rward ing .5 .2 2. These es t imates were obta ined f r o m a c o n f i d e n t i a l forest industry s o u r c e . 34 Table VI. Direct Tree- to -Truck Cost for Thinning* D i r e c t C o s t ( $ / m 3 ) Stand S l o p e A v e r a g e L o g V o l u m e ( m 3 ) C l a s s 0 .15 0 .20 0 .25 0 .30 0.35 0 -20% 28.70 25 .25 22.96 21.89 21.81 21 -50% 32 .03 28 .33 24 .64 23.41 22.18 51%+ 40 .95 32.76 27.30 25 .94 24.57 * These es t imates cor respond to a 1984 cost base. T h e da ta presented in T a b l e VI were used to regress s tand slope c lass (the m i d - p o i n t s of the two slope c lasses , 10 and 35 p e r c e n t , and 50 percent ) and average log vo lume as a funct ion of d i rec t t r e e - t o - t r u c k cost ( T T T C S T , $ / m 3 ) . T h e resu l t ing equat ion is as fo l lows: T T T C S T = exp(2.6574 + 0.00515 S + 0 .10392/LV) (18) where S is the average stand slope (%) s e l e c t e d by the user , wi th m i n i m u m and m a x i -m u m values of 10 and 50 p e r c e n t ; L V is the average 1 0 - m e t r e l o g vo lume ( m 3 ) , wi th a m i n i m u m value of 0.15 m 3 . L V is e s t i m a t e d f r o m equat ion 19 whose de te rminants are genera ted by the t i m b e r - l o g convers ion s i m u l a t o r . L V = Z l o g vo lumes (19) ( Z l o g lengths) /10 Equa t ion 18 has an R - s q u a r e va lue of 0.926. T h e two c o e f f i c i e n t s and the constant t e r m are s ign i f i can t ly d i f f e ren t f r o m ze ro at a 99 percent c o n f i d e n c e l e v e l . T h e d i rec t t r e e - t o - t r u c k cost c a l c u l a t e d f r o m equat ion 18 corresponds to a 1984 cost base. Its va lue is inc reased by a cost t rend a l lowance of one percent ( B C M o F 1986) to cor respond to the program's cost base of J u l y 1, 1985. 6.1.2 b Sub-model for Final Harvest E s t i m a t i o n of d i rec t t r e e - t o - t r u c k costs for f ina l harvest is based on a m o d e l that s imula tes the t r e e - t o - t r u c k cost a l lowances descr ibed in the C L B A M 1985 for the C o a s t (Wi l l iams 1986b). T h e s imula t ion approach consists of app ly ing equ ip -ment hourly costs to p r o d u c t i v i t y es t imates of the fa l l ing and buck ing , yard ing or sk idding, and load ing a c t i v i t i e s . Wi l l iams's mode l was deve loped for reg iona l inventory da ta and , consequent ly , operates wi th a v e c t o r of proport ions for d i f f e ren t harvest ing sys tems . In the cur ren t s u b - m o d e l , this v e c t o r of proport ions is r e p l a c e d by the s e l e c t i o n of a s ingle h a r v e s t -ing system apply ing to a s tand . With this e x c e p t i o n , p r o d u c t i v i t y and hour ly cost equat ions presented below are those of Wi l l iams's m o d e l . T h e four a l te rna t ive harves t ing systems i n c o r p o r a t e d into the s u b - m o d e l are shown in F i g u r e 3 taken f r o m Wi l l i ams (1986b). No te that the fa l l ing and buck ing a c t i v i t i e s are assumed to be manua l . Figure 3. Alternative Harvesting Systems for Final Harvest F a l l i n g — > B u c k i n g — > H igh L e a d Y a r d e r -G r a p p l e Y a r d e r — R u b b e r T i r e d Skidder -Soft T r a c k e d Skidder • —•> H e e l B o o m L o a d e r —•> F r o n t - E n d L o a d e r T h e harvest ing sys tem is d e t e r m i n e d by the user through the se lec t ion of one of the four sk idd ing or yard ing s y s t e m s . N o t e that the average stand slope (Ref . S e c t i o n 6.1.1) is a p a r a m e t e r a f f e c t i n g the c h o i c e of the harvest ing equ ipment . T h e produced log vo lume ( P L V , m 3 ) is a p a r a m e t e r c o m m o n to some of the p roduct iv i ty equat ions descr ibed be low. P r o d u c e d log vo lume re fers to the average log vo lume adjusted to r e f l e c t ya rd ing losses and cur ren t u t i l i za t ion s tandards. It is es t i ma ted as: P L V = 2.6103 In (1 + L V ) (20) where L V is the average 1 0 - m e t r e log vo lume ( m 3 ) e s t i m a t e d by equat ion 19 of Sec t ion 6.1.2 a . P r o d u c t i v i t y es t imates per harves t ing sub phase are c a l c u l a t e d f rom equat ions 21 to 27. M a n u a l fa l l ing and buck ing p r o d u c t i v i t y ( P R O F B , m 3 / h r ) : P R O F B = 5.684 + 6.955 L V - 0.715 L V 3 (21) where .3 m 3 < L V < 1.8 m 3 . H igh lead yarder p roduc t iv i t y ( P R O H L Y , m 3 / h r ) : P R O H L Y = [5.113 + In ( P L V + 1K23.625 - 0.0873 S) ] 1.1636 R (22) where P L V > , 5 m 3 R = 0.407 + 0.0908 In (V) V > 200 m 3 and S is the average s tand slope (96) s p e c i f i e d by the user; V is the vo lume harves ted ( m 3 / h a ) genera ted by the growth and y i e l d s imu la to r ; 1.1636 is a p roduc t iv i t y increase of 16.36 pe rcen t fo r "cherry p i c k i n g " . G r a p p l e yarder p r o d u c t i v i t y ( P R O G Y , m 3 / h r ) : P R O G Y = (4.479 + 24.727 In ( P L V + 1)) 1.1636*1.01 (23) where P L V > . 5 m 3 and 1.1636 is a p roduc t iv i t y increase o f 16.36 pe rcen t for "cherry p ick ing" ; 1.01 corresponds to an average te r ra in code of 2 for a modera te index of d i f f i c u l t y . Rubber t i red sk idder p r o d u c t i v i t y ( P R O R T S , m 3 / h r ) : P R O R T S = (9.141 + 7.421 P L V ) R (24) where .3 m 3 < P L V < 2.0 m 3 and the R value depends on the average stand s lope: Stand Slope R. 0-14.4% 1.148 14 .5-25 .4% 1.006 25.5%+ 0.864 Sof t t r a c k e d sk idder p roduc t iv i t y ( P R O S T S , m 3 / h r ) : P R O S T S = 1.102 + 16.165 P L V - 2.12 P L V 2 (25) where .3 m 3 < P L V < 2.0 m 3 . H e e l boom loader p roduc t iv i t y ( P R O H B L , m 3 / h r ) : P R O H B L = 1.5049 P R O Y (26) where P R O Y is the p roduc t iv i t y ( m 3 / h r ) of the s e l e c t e d yard ing s y s t e m , e s t i m a t e d wi th equat ion 22 or 23. F r o n t - e n d loader p roduc t iv i t y ( P R O F E L , m 3 / h r ) : P R O F E L = 3 P R O S (27) where P R O S is the p r o d u c t i v i t y ( m 3 / h r ) of the s e l e c t e d sk idding s y s t e m , e s t i m a t e d wi th equat ion 24 or 25, T h e d i rec t cost for e a c h of the three sub phases of the s e l e c t e d harvest ing sys tem is c a l c u l a t e d as: D i r e c t cost ( $ / m 3 ) = Hour ly cost ($/hr) (28) P r o d u c t i v i t y ( m 3 / h r ) where the e s t i m a t e d hour ly cost for e a c h s y s t e m is i n d i c a t e d in T a b l e VII. 38 Table VII. Hourly Cost by Harvesting Sub Phase* Sub Phase H o u r l y C o s t ($ /hr ) F a l l i n g and B u c k i n g 4 5 . 79 H igh L e a d Y a r d e r 171 . 29 G r a p p l e Y a r d e r 162. 25 Rubber T i r e d Skidder 52 . 56 Sof t T r a c k e d Skidder 4 8 . 45 H e e l B o o m L o a d e r 107. 85 F r o n t - E n d L o a d e r 6 1 . 36 These costs cor respond to a J u l y 1, 1983 cost base. The d i r e c t t r e e - t o - t r u c k cost at f ina l harvest wi th a cost base of J u l y 1, 1983 can now be e s t i m a t e d by s u m m i n g the d i rec t costs a s s o c i a t e d wi th the fa l l ing and buc k ing , ya rd ing or sk idd ing , and load ing a c t i v i t i e s . T h e resul t ing value is inc reased by a cost t rend a l lowance of 5.04 percent ( B C M o F 1985, 1986) to cor respond to the d i rec t t r e e - t o - t r u c k cost at f ina l harvest w i th the program's cost base of J u l y 1, 1985. 6.1.3 Other Operational Phases Th is s e c t i o n presents the equat ions used to s imu la te the rema in ing seven d i rec t cost components a s s o c i a t e d wi th e a c h harves t . Unless otherwise s t a t e d , these e q u a -tions are e x t r a c t e d f r o m the 1986 o f f i c i a l appra isa l manua l ( B C M o F 1986) and c o r -respond to a cost base of J u l y 1, 1984. In M I C R O S T A N D , values of these equat ions are inc reased by a cost t rend a l lowance of one percent ( B C M o F 1986) to cor respond to the program's cost base of J u l y 1, 1985. T r u c k haul cost ( T H C S T , $ / m 3 ) cor responds to the m o v e m e n t of logs f r o m the roadside or landing in the woods to the f ina l l o g d u m p . It is e s t i m a t e d as: T H C S T = 2.429 + 0.0845 H D (29) 39 where H D is the average o n e - w a y haul d is tance (km) s p e c i f i e d by the user . R o a d main tenance cost ( R M C S T , $ / m 3 ) is assoc ia ted wi th the operat ions r e -quired to keep the roads and br idges in opera t iona l cond i t ion for use by logging r e -l a t e d equ ipment . It is assumed to be d i r e c t l y re la ted to the road densi ty s p e c i f i e d by the user , as shown by equat ion 30 which was deve loped by the author: R M C S T = A R M C S T ( R D E N S / 0 . 0 5 ) (30) where A R M C S T is the average road ma in tenance cost for the C o a s t , e s t i m a t e d to be $ 1 . 7 2 / m 3 for f i na l harvest and $ 0 . 7 7 / m 3 for th inning^ 3 ) , and where ( R D E N S / 0 . 0 5 ) is a ra t io c a l c u l a t e d by d iv id ing the s p e c i f i e d road densi ty ( R D E N S , km/ha) by the e s t i m a t e d average road densi ty fo r logg ing operat ions on the C o a s t (0.05 k m / h a , R e f . S e c t i o n 6.1.1). D u m p , sor t , boom and sca le cost a l lowances are based on two genera l l o g t rans -port sys tems: $ 6 . 4 3 / m 3 for barg ing condi t ions $ 4 . 2 2 / m 3 for towing condi t ions $ 4 . 2 2 / m 3 when barg ing or towing are not requ i red where the water t ranspor ta t ion s y s t e m is s p e c i f i e d by the user . Barg ing or towing cost ( $ / m 3 ) is s p e c i f i e d by the user , wi th a cost base of J u l y 1, 1985. E s t i m a t i o n of towing and barg ing costs f r o m s p e c i f i c g e o g r a p h i c a l loca t ions are ava i lab le f r o m the o f f i c i a l appra isa l manua l ( B C M o F 1986, pp. 35, 36). C r e w t ranspor ta t ion ( C T C S T , $ / m 3 ) is e s t i m a t e d as: C T C S T = W R C S T + T R C S T (31) 3. These es t imates are der ived f r o m average values of the 1984 C o u n c i l o f Fores t Industries (COFI ) of Br i t i sh C o l u m b i a logging cost survey . In order to p ro tec t the c o n f i d e n t i a l i t y of this survey , these a p p r o x i m a t e values were suppl ied by M r . S . C o l e m a n of C O F I . where W R C S T = 0.158 + 0.753 In (HD + 1) (32) T R C S T = 0.00031 T R D (100 - P L C ) (33) and W R C S T is the woods run cost ( $ / m 3 ) for m o v i n g the crew f r o m the marshal l ing a rea to the work ing a r e a ; T R C S T is the town run cost ( $ / m 3 ) fo r mov ing the m e m b e r s of the c rew who c o m m u t e f r o m the marsha l l ing a r ea to the nearest c o m m u n i t y ; H D is the average o n e - w a y t ruck haul d is tance (km) s p e c i f i e d by the user for equat ion 29. In equat ion 32, this var iab le is an appr ox imat ion of the o f f i c i a l appra isa l manual 's " o n e - w a y d is tance f r o m the marsha l l ing a rea to the cent re o f work a rea" ; T R D is the o n e - w a y d is tance (km) f r o m the marsha l l ing a r ea to the nearest c o m m u n i t y as s p e c i f i e d by the user; P L C is the percen tage of the c rew l i v ing in the c a m p as s p e c i f i e d by the user . T h e t e r m (100 - P L C ) is an appr ox imat ion of "the percen tage of the crew that c o m m u t e s " in the o f f i c i a l appra isa l manua l . C a m p and cookhouse cost ( C K C S T , $ / m 3 ) is e s t i m a t e d as: C K C S T = 0.363 + 0.0355 P L C (34) E q u a t i o n 34 is s i m p l i f i e d f r o m the o f f i c i a l appra isa l manua l in that the percen tage of the crew l i v ing in the c a m p rep laces two de te rminants : the percentage of the crew l i v ing in c a m p single and mar r i ed quar ters and the percen tage of the crew l i v ing in m a r r i e d quar ters . Th is s i m p l i f i c a t i o n should not s ign i f i can t ly a f f e c t the c a m p and cookhouse cost e s t i m a t i o n . O v e r h e a d cost compr ises the admin is t ra t ion and superv is ion a c t i v i t i e s re la ted to logg ing . It is e s t i m a t e d to 8.85 dol lars per cub ic m e t r e , a value cor responding to t ree f a r m and forest l i c e n c e condi t ions . 6.2 Total Delivery Cost " C o s t a c c o u n t i n g norma l ly dist inguishes be tween opera t ing costs and c a p i t a l costs ; the f o r m e r re la t ing to the costs of inputs a c q u i r e d and consumed wi th in an a c c o u n t i n g per iod (usually a year) and the l a t t e r r e f e r r i n g to the costs of equ ipment and other assets that y i e l d a p roduc t ive se rv ice over s e v e r a l years" (Pearse et a l . 1974, 86). C a p i t a l costs c o m p r i s e deprec ia t ion (or c a p i t a l recovery ) and re turn on c a p i t a l . " C a p i t a l r e c o v e r y is usual ly cons idered as a ra te of d e p r e c i a t i o n appl ied against the amount inves ted , so that over the e s t i m a t e d l i fe of the assets the investor can r e c o v e r his c o s t . Re turns to c a p i t a l are t y p i c a l l y measured as a percen tage rate on the inves tment" (Pearse et a l . 1974, 79). A s prev ious ly s t a t e d , d i rec t costs e s t i m a t e d wi th the procedure descr ibed in Sec t ion 6.1 inc lude both opera t ing costs and d e p r e c i a t i o n . Th is s e c t i o n presents the method deve loped for M I C R O S T A N D to s imu la te the rema in ing two components of to ta l de l ive ry cost e s t i m a t e d at e a c h harves t , re turn on c a p i t a l and a s p e c i a l r isk a l l o w a n c e . R e t u r n on c a p i t a l is e s t i m a t e d as a d i rec t func t ion of deprec ia t ion through equat ion 35, de r ived as fo l lows: D E P ( $ / m 3 ) = INV ( $ / m 3 per year) L I F E (years) then INV ( $ / m 3 per year) = D E P ( $ / m 3 ) L I F E (years) R E T U R N ( $ / m 3 ) = INV ( $ / m 3 per year) R A T E ( /year) = D E P ( $ / m 3 ) L I F E (years) R A T E ( /year) (35) where D E P ( $ / m 3 ) is deprec ia t ion of the p h y s i c a l c a p i t a l c a l c u l a t e d wi th the "straight l ine" method that assumes that the deprec iab le assets are consumed in equal amounts throughout the i r l i f e (Leuschner 1984, 13). D E P is s p e c i f i e d by the user as a percen tage of to ta l d i rec t de l ivery cost ; INV ( $ / m 3 per year) is the average amount invested in the deprec iab le assets used for the de l ivery cost a c t i v i t i e s , here d iv ided by the average annual c a p a c i t y of these assets to obta in a per cub ic met re f igure ; L I F E (years) is the average l i f e of the deprec iab le assets as s p e c i f i e d by the user; R E T U R N ( $ / m 3 ) is the re turn on c a p i t a l c a l c u l a t e d with the "average i n v e s t -ment" method (Pearse et a l . 1974, 89); R A T E ( /year) is the rea l ra te of re turn on c a p i t a l as s p e c i f i e d by the user . T h e assumed deprec ia t ion is meant to cor respond to condi t ions e x p e r i e n c e d by an opera tor of average e f f i c i e n c y . It is s p e c i f i e d by the user because the o f f i c i a l appra isa l p rocedure does not separate deprec ia t ion f r o m opera t ing costs ( B C M o F 1985, 1986). T h e assumed ra te of re turn on c a p i t a l is "the m i n i m u m rate consis tent wi th main ta in ing a heal thy inves tment c l i m a t e " (Pearse et a l . 1974, 85). A s is the case fo r d i rec t c o s t s , re turn on c a p i t a l is a lso s ta ted in dol lars per h e c t a r e by mul t ip ly ing dol lars per c u b i c met re values of equat ion 35 by the vo lume per hec ta re r e m o v e d at e a c h harvest . T h e s p e c i a l r isk a l lowance is used to r e f l e c t p a r t i c u l a r l y uncer ta in cost e l e -ments that cannot be fu l ly r e f l e c t e d in an appra isa l based on average expec ta t ions . E x a m p l e s of such cost e lements are precar ious log t ransport s y s t e m s , the highly uncer ta in length of the logging season in c e r t a i n areas and e leva t ions , unpred ic tab le logging te r ra in cond i t ions , and risks assoc ia ted wi th ventures in new areas (Pearse et a l . 1974). T h e s p e c i a l r isk a l lowance is s p e c i f i e d for e a c h harvest as a percen tage on the s u m m a t i o n of d i rec t costs and re turn on c a p i t a l , o r , in equiva lent t e r m s , on the s u m m a t i o n of opera t ing and c a p i t a l cos ts . T h e second repor t of the task f o r c e on C r o w n t imber d isposal (Pearse et a l . 1974) suggests such a risk a l lowance ranging f r o m 2 to 10 p e r c e n t . T o t a l de l ive ry cost at e a c h harvest can now be e s t i m a t e d as the s u m m a t i o n of d i rec t c o s t s , re turn on c a p i t a l , and the s p e c i a l r isk a l l o w a n c e . T o t a l de l ivery cost is expressed in dol lars per cub ic met re and in dol lars per h e c t a r e . A s is the case for revenues , a u s e r - s p e c i f i e d average rea l ra te of change per year is a lso appl ied to de l ivery costs over the s imu la t ion pe r iod . In such a c a s e , the c a l c u l a t e d de l ive ry cost is mu l t ip l i ed by a c o m p o u n d i n g f a c t o r r e f l e c t i n g changes in cos ts . T h i s opt ion is fur ther deve loped in C h a p t e r 7. 6.3 Evaluation This sec t ions examines the st rengths and l im i ta t ions of the de l ive ry cost s i m u -la to r . Strengths Direct costs by operational phase E s t i m a t i o n of d i rec t costs fo r each of nine opera t iona l phases a l lows de ta i led sens i t iv i ty analysis on the e f f e c t of independent var iab les such as s tand slope and road densi ty . Such a mode l l ing approach also a l lows fo r e s t i m a t i o n of the re la t i ve propor t ion of t o t a l d i rec t costs assoc ia ted wi th e a c h of the opera t iona l phases. Cri t ica l cost determinants Wil l iams (1986a, b) ind ica tes eight key cost de te rminan ts of the road d e v e l o p -ment and t r e e - t o - t r u c k phases which encompass most of the d i rec t de l ivery costs assoc ia ted wi th an harvest . T h e s e var iab les are average s tand s lope , s e l e c t i o n of harvest ing equ ipment , average p iece s i z e , vo lume harves ted , road dens i ty , te r ra in roughness, and s ize and f requency of br idges and c u l v e r t s . With the excep t ion of the l a t te r three var iab les , the other f i ve var iab les c a n be d i r e c t l y or ind i rec t l y c o n -t ro l led by the user . T e r r a i n roughness and s ize and f r e q u e n c y of dra inage s t ruc tures are independent var iab les of the deve lopment cost s u b - m o d e l , but under the f o r m of f i xed average va lues . No te that the de l ive ry cost s imula tor a l lows the user to adjust road densi ty a c c o r d i n g to the s e l e c t e d harves t ing s y s t e m , which in turn can be re la ted to the s p e c i f i e d average stand s lope . In addi t ion to the d i rec t costs a s s o c i a t e d with road deve lopment and t r e e - t o -t ruck , s imu la t ion of the d i rec t costs assoc ia ted wi th the other opera t iona l phases is a lso based on c r i t i c a l de te rminan ts . E x a m p l e s are the average haul d is tance for t ruck haul cost and the se lec t ion of a l o g t ranspor ta t ion s y s t e m for the dump, sor t , boom and sca le c o s t . Provision for non-standard conditions T h e o f f i c i a l appra isa l p rocedure " re f l ec ts r e c e n t e x p e r i e n c e d costs and cur rent logging cond i t ions . C o n s e q u e n t l y , c e r t a i n cost phases - s p e c i f i c a l l y the t r e e - t o - t r u c k phase and deve lopment phase - are e s t i m a t e d wi thout much regard for n o n - s t a n d a r d cond i t ions , such as s m a l l logs and a l te rna t ive harves t ing s y s t e m s " (Wi l l iams 1986b, 45). Th inn ing is , o f course , a n o n - s t a n d a r d c o n d i t i o n , and consequent ly its cost is e s t i m a t e d wi th a s p e c i f i c s u b - m o d e l . T h e possib i l i ty to adjust the d i rec t road deve lopment cost through a s p e c i f i e d percentage is also re levant for th inning because in such a c a s e , a propor t ion of roads is l i ke ly to a l ready ex is t . Th is opt ion can a lso be used to r e c o g n i z e possible cost share a r rangements fo r roads serv ing other fores t operat ions as we l l as the genera l p u b l i c . Specific allowance for return on capital Under the o f f i c i a l appra isa l p r o c e d u r e , re turn on c a p i t a l is meant to be prov ided through a prof i t a l lowance main ly c a l c u l a t e d as a func t ion of d i r e c t de l ive ry cost components and se l l ing p r ice ( B C M o F 1985, 1986). Y e t , a c c o r d i n g to Pearse et a l . (1974), re turn on c a p i t a l should not be e s t i m a t e d as a func t ion of these two v a r i -ables to which it is not r e l a t e d , but should ra ther be re la ted d i r e c t l y to , and appl ied to , the c a p i t a l necessary for the forest opera t ions . T h e approach deve loped for M I C R O S T A N D to s imula te re turn on c a p i t a l respects this c r i t e r i o n . Specific allowance for special risks Under the o f f i c i a l appra isa l p r o c e d u r e , the incen t ive to incur the r isks invo lved in harvest ing is p rov ided for as part of a pro f i t and r isk a l lowance based large ly on se l l ing pr ice and d i rec t de l ive ry cost components ( B C M o F 1985, 1986). Such a procedure is inappropr ia te , main ly because the a l lowance is d i r e c t l y re la ted to se l l ing p r i c e . Indeed, "vu lnerabi l i ty to risk var ies widely in f o r m , but f r o m the o p e r a -tor's point of view the most consis tent measure of his l i ab i l i t y is the costs that he has i n c u r r e d in the forest opera t ion . Thus we r e c o m m e n d that s p e c i a l r isk be r e c o g -n i z e d as a percentage of appra ised costs" (Pearse et a l . 1974, 92). Th is is the p r o c e -dure adopted for M I C R O S T A N D . Note that the s imu la t ion of condi t ions e x p e r i e n c e d by a t y p i c a l e f f i c i e n t o p e r -a tor impl ies that it would be inappropr ia te to prov ide for a prof i t a l lowance as part of the de l ive ry cost at e a c h harves t . Indeed, prof i t or net i n c o m e depends main ly on fac to rs s p e c i f i c to e a c h l i c e n c e e , such as good l u c k , marke t power , and s p e c i a l en t repreneur ia l sk i l l (Pearse et a l . 1974). Limitations Determination of al l costs at the stand level C e r t a i n ca tegor ies of costs should not be a t t r ibu ted to the cost of logging a par t i cu la r c u t t i n g permi t because they are necessary for the e x t r a c t i o n of t imber over la rge areas . L o g g i n g camps as we l l as log dumps and sor t ing fac i l i t i es are n o r -mal ly of this k ind (Pearse et a l . 1974). A c c o r d i n g to the same s o u r c e , these costs should be e l ig ib le for w r i t e - o f f as c red i ts against s tumpage assessments . H o w e v e r , such an approach is i m p r a c t i c a b l e in the contex t o f a s tand appra isa l program where a l l costs must be a t t r ibu ted to a single s tand . 46 Unsophisticated method to simulate return on capital T h e method deve loped to s imu la te re turn on c a p i t a l at e a c h harvest can be cons idered unsophis t ica ted for three reasons. F i r s t , a single a l lowance for re turn on c a p i t a l is app l ied to to ta l d i rec t c o s t s , ra ther than s p e c i f i c a l lowances appl ied to e a c h d i rec t cost c o m p o n e n t . S e c o n d , es t ima t ion of the a l lowance is based on a percentage of d i rec t costs c o m p o s e d of d e p r e c i a t i o n , and on an average l i fe of the deprec iab le c a p i t a l ; both are more or less a rb i t ra r i l y s p e c i f i e d by the user . T h i r d , no prov is ion is made to generate a re turn on work ing c a p i t a l . In the appra isa l con tex t , work ing c a p i t a l can be de f ined as "the inves tment i t ems not a l lowed for e lsewhere in the appra isa l" , such as inves tments in inventor ies and other n o n - d e p r e -c iab le assets (Pearse et a l . 1974, 91). Y e t , the method used to genera te re turn on deprec iab le assets respects the cor responding e c o n o m i c concep ts and , in doing s o , exposes the p rogram user to these c o n c e p t s . In the contex t of the p r o g r a m , the chosen approach is d e e m e d pre fe rab le to adopt ing the prof i t and r isk a l lowance prov ided under the o f f i c i a l appra isa l p r o c e -dure because , as prev iously s t a t e d , such an a l lowance is not necessar i l y re la ted to the c a p i t a l base in c a u s e . 7. T H E F I N A N C I A L A N A L Y S I S S I M U L A T O R T h e revenue and cost es t imat ions descr ibed so fa r for e a c h scheduled harvest genera te values cor responding to a cost base of Ju ly 1, 1985. S e c t i o n 7.1 presents the procedure used in M I C R O S T A N D to al low for assumed changes in rea l costs and pr ices over the s imula t ion per iod^ 1 ) . Th is p rocedure a lso appl ies to the opt iona l s imula t ion of an annual ma in tenance cost be tween th inning and f ina l harvest . T h e resul t ing cash f low of rea l costs and revenues over the s imu la t ion per iod const i tues the basic input of the f i n a n c i a l analysis p rocedure descr ibed in S e c t i o n 7.2. Th is p rocedure is used to es t imate the value and the present va lue of s tanding t imber at e a c h harvest , as wel l as the net present va lue and the b e n e f i t - c o s t ra t io of the s imula t ion s c e n a r i o . T h e strengths and l im i ta t ions of the f i n a n c i a l analysis s imu la to r are examined in S e c t i o n 7.3. 7.1 Cash Flow and Real Costs and Revenues R e v e n u e s and costs can be changed in rea l t e rms dur ing a s imu la t ion per iod when the user spec i f i es a n o n - z e r o average rea l ra te of change in log pr ices or a v e r -age rea l ra te of change in cos ts . Th is opera t ion is r e a l i z e d through the genera l c o m -pounding f o r m u l a fo r s ingle payments : V n = V 0 (1 + r)n (36) where V n is the rea l va lue (of a cost or revenue) at yea r n of a s i m u l a t i o n ; V 0 is the va lue cor responding to year zero of a s imu la t ion pe r iod , wi th a cost base of J u l y 1, 1985; 1. A rea l change in p r ice occurs when a p r i c e increases or decreases re la t i ve to a l l o ther pr ices in the e c o n o m y , as measured by a genera l p r ice index (Leuschner 1984). T h e t e r m "pr ice" here re fe rs e i ther to a p r ice or a cos t . r is the average year ly rea l ra te of change (posit ive or negat ive) in costs or log p r i c e s , as s p e c i f i e d by the user . E q u a t i o n 36 is a lso used to es t imate fu ture rea l va lues when the user spec i f i es an annual road ma in tenance cost be tween th inning and f ina l harvest s ta ted in dol lars par k i lomet re of road ( A C S T 0 , $ /km) wi th a cost base of J u l y 1, 1985. But f i rs t , the A C S T 0 ($/km) value is t r a n s f o r m e d into a A C S T 0 ($/ha) va lue through the s p e c i -f i ed road densi ty at th inning ( T R D E N S , km/ha ) : A C S T 0 ($/ha) = A C S T 0 ($/km) T R D E N S (km/ha) (37) T h e n equat ion 36 is used to c a l c u l a t e (with the s p e c i f i e d rea l ra te of change in costs) the rea l road ma in tenance cost one year a f t e r th inning and the rea l road ma in tenance cost one year be fo re f ina l harves t . T h e s e two values cor respond to the range of annual road ma in tenance costs be tween the two harvests . 7.2 Financial Analysis F o r each scheduled harvest , the va lue of s tanding t imber is c a l c u l a t e d as the d i f f e r e n c e between the e s t i m a t e d value of the logs that can be r e c o v e r e d and the e s t i m a t e d costs for de l ive ry of the p r o d u c t . T h e cash f low of rea l va lues obta ined through the procedure descr ibed in S e c t i o n 7.1 prov ides the costs and revenues r e -quired for this c a l c u l a t i o n . A s is the case for its d e t e r m i n a n t s , the value of s tanding t imber is s ta ted in dol lars per cub ic met re and in dol lars per h e c t a r e . T h e present va lue of s tanding t i m b e r at e a c h harvest ( P V S T , $ / m 3 and $/ha) is c a l c u l a t e d through the genera l d iscount ing f o r m u l a for s ingle p a y m e n t s : P V S T = V S T n (38) (1 + i ) n where V S T n is the va lue of s tanding t i m b e r at yea r n of the s imu la t ion ; i is the r e a l d iscount ra te s p e c i f i e d by the user. When a ser ies of annual road ma in tenance costs between thinning and f ina l harvest is s p e c i f i e d , the present va lue ( P V A C S T , $/ha) is c a l c u l a t e d by equat ion 39 (the der iva t ion of which can be found in A p p e n d i x II): P V A C S T = A C S T [(1 + i)t - (1 + r)*] (39) A . . . T Y E A R + t , . . (1 + 0 (l - r) where t = F H Y E A R - T Y E A R - 1 and A C S T is the f i rs t annual road ma in tenance p a y m e n t ($/ha) at year T Y E A R + 1 c a l c u l a t e d f r o m equat ion 36 as i n d i c a t e d in S e c t i o n 7.1; r is the s p e c i f i e d year ly average r e a l ra te of change in cos ts ; i is the s p e c i f i e d rea l d iscount ra te ; t is the number of annual road ma in tenance p a y m e n t s ; F H Y E A R is the f ina l harvest s imu la t ion year s p e c i f i e d ind i rec t l y through the f ina l harvest age; T Y E A R is the th inning s imu la t ion year s p e c i f i e d ind i rec t l y through the thinning age . T h e annual road ma in tenance cost present va lue is also s ta ted in dol lars per cub ic met re by d iv id ing the P V A C S T ($/ha) va lue by the vo lume r e m o v e d at f ina l harvest ( m 3 / h a ) . In the unl ike ly case where the user s p e c i f i e s ze ro fo r both the average rea l ra te of change in costs and the rea l d iscount r a t e , equat ion 39 equals zero and , t h e r e -f o r e , cannot be used to c a l c u l a t e the annual road ma in tenance cost present va lue . In such a c a s e , the present va lue ( P V A C S T , $/ha) is c a l c u l a t e d by mul t ip ly ing the annual road ma in tenance payment ( A C S T 0 , $ /ha ; c a l c u l a t e d wi th equat ion 37) by the number of annual payments (t). T h e net present va lue of a s imu la t ion scenar io c a n now be c a l c u l a t e d by s u m -ming the present value of the s tanding t imber at each harvest and , i f r e q u i r e d , the present value of the annual road ma in tenance costs be tween thinning and f ina l h a r -vest . T h e net present value is expressed in dol lars per c u b i c met re and in dol lars per h e c t a r e , except for t w o - h a r v e s t scenar ios where it is s ta ted only in dol lars per h e c t a r e in order to a c c o m m o d a t e the d i f f e r e n c e in vo lume r e m o v e d at e a c h harvest . No te that when only one harvest is s i m u l a t e d , the net present va lue of the s imu la t ion scenar io is equiva lent to the present value of s tanding t i m b e r . T h e in te rna l ra te of re turn (IRR) of a s imu la t ion scenar io is a s p e c i a l case of net present va lue , in that IRR is the d iscount ra te that c a n c e l s out the present va lue of costs and revenues . T h e user can e s t i m a t e the IRR through an i t e ra t i ve process by mod i fy ing the rea l d iscount ra te unt i l the net present va lue of the s i m u l a -t ion scenar io approx imates z e r o . No te that the IRR can only be e s t i m a t e d for t w o -harvest scenar ios w i th , for e x a m p l e , a negat ive va lue of s tanding t imber at th inning and a posi t ive value of s tanding t imber at f ina l harves t . Indeed, o n e - h a r v e s t s c e -nar ios can generate e i ther posi t ive or negat ive net present values that wi l l approach ze ro a s y m p t o t i c a l l y . T h e b e n e f i t - c o s t ra t io of a s imu la t ion scenar io is a lso e s t i m a t e d f r o m the cash f low of r e a l costs and revenues obta ined through the procedure descr ibed in Sec t ion 7.1. T h e ra t io is c a l c u l a t e d as the sum of e a c h revenue's present value d i -v ided by the sum of e a c h cost 's present va lue . T h e present va lues are c a l c u l a t e d using the d iscount ing f a c t o r of equat ion 38 and , i f r e q u i r e d , equat ion 39 for annual road ma in tenance costs be tween two harvests . N o t e that for o n e - h a r v e s t scenar ios , the b e n e f i t - c o s t ra t io is independent of the rea l d iscount r a t e . Indeed, in such a case the revenues and costs o c c u r at the same year and , consequent ly , the d iscount ing f a c t o r of equat ion 38 is the same for both the revenue and the de l ivery cost c o m -ponents of the b e n e f i t - c o s t c a l c u l a t i o n . T h e net present value and the b e n e f i t - c o s t ra t io es t imat ions descr ibed above r e f e r to a b e f o r e - t a x procedure sui table for the publ ic sec to r (Leuschner 1984). A c c o r d i n g to the same s o u r c e , this p rocedure gives i d e n t i c a l results whether the ca lcu la t ions are made wi th rea l dol lars and a rea l d iscount ra te or cur ren t dol lars and a d iscount ra te that fu l ly compensa tes for the ra te of i n f l a t i o n . T h e r e a l - v a l u e approach is s i m p l e r , and consequent ly is used in M I C R O S T A N D to al low for assumed i n f l a t i o n . 7.3 Evaluation Th is s e c t i o n examines the strengths and l im i ta t ions of the f i n a n c i a l analysis s i m u l a t o r . Strengths Output values in dollars per cubic metre and dollars per hectare C e r t a i n output da ta such as the t r e e - t o - t r u c k cost are more easi ly ana lyzed in dol lars per cub ic met re uni ts , whereas others such as the road deve lopment cost are more easi ly a n a l y z e d in dol lars per h e c t a r e uni ts . C o n s e q u e n t l y , the genera t ion of cash f low and present va lue d a t a in both units prov ides the user wi th a f lex ib le output f o r m a t for de ta i l ed ana lys is . Annual road maintenance cost for two-harvest scenarios T h e opt iona l s imu la t ion of an annual road ma in tenance cost be tween th inning and f ina l harvest is c lose ly l inked to the s p e c i f i c a t i o n of a percen tage of fu l l road deve lopment cost for f ina l harvest (Ref . Sect ions 6.1.1 and 6.3). Indeed, road m a i n -tenance between thinning and f ina l harvest should reduce the necessary costs for road cons t ruc t ion at f ina l harvest . A s is the case for the percen tage of fu l l road deve lopment cos t , the annual road ma in tenance cost between harvests can also be used to r e c o g n i z e assumed cost share a r rangements for roads serv ing other forest operat ions as we l l as the genera l pub l ic . C o n s e q u e n t l y , the prov is ion for an annual road ma in tenance cost be tween thinning and f ina l harvest a l lows for add i t iona l s i m u -la t ion scenar ios in a contex t of in tensive and m u l t i p l e - u s e m a n a g e m e n t . Real changes in costs and revenues Simula t ion of rea l changes in costs and revenues over the s imu la t ion per iod al lows d i rec t compar isons be tween cash f low components o c c u r r i n g at d i f f e ren t y e a r s , such as road deve lopment costs at th inning and f ina l harvest . A s prev iously s t a t e d , this approach also s imp l i f i es the handl ing of i n f l a t i o n . Net present value and benefit-cost ratio of the simulation scenario Through their r e s p e c t i v e d iscount ing p rocedures , these two investment c r i t e r i a al low d i rec t compar isons between s imu la t ion scenar ios d i f f e r i n g e i ther in na ture , such as " th inning" and " f ina l harvest on ly" , or in the value of pa ramete rs such as the th inning age , the ro ta t ion age , or the u t i l i za t ion s tandard . Limitations No special adjustment for timber value minimum limits C o n t r a r y to m a x i m u m l i m i t s , there is some j u s t i f i c a t i o n to r e c o g n i z e m i n i m u m l imi ts for t imber values such as in the case of s o c i a l costs imposed by logging but not met by the l i c e n c e e (Pearse et a l . 1974). M I C R O S T A N D is not designed to r e v e a l parameters that can just i fy such m i n i m u m l i m i t s . In this c o n t e x t , prov is ion for m i n i m u m l imi ts would be unl ike ly to prov ide the user wi th usefu l insights into this s p e c i a l ad justment . No provision for changes in the relative prices of log grades A l t h o u g h trends over t ime in re la t i ve p r ices of l o g grades are not ev ident for c o a s t a l spec ies (Gasson and Wi l l iams 1986), prov is ion for such trends would appear to be a desirable fea ture for a s tumpage appra isa l l ea rn ing t o o l . P A R T n M I C R O S T A N D ; P R O G R A M M I N G A S P E C T S , C A S E S T U D Y , E V A L U A T I O N , A N D C O N C L U S I O N S 8. P R O G R A M M I N G A S P E C T S M I C R O S T A N D was deve loped to be used with vers ion 1A of the L o t u s 1 - 2 - 3 ™ m i c r o c o m p u t e r s o f t w a r e ^ ) . S e c t i o n 8.1 b r ie f l y presents 1 - 2 - 3 , based on L e B l o n d and C o b b (1983), and descr ibes the approach deve loped to p rogram M I C R O S T A N D . S e c t i o n 8.2 examines the advantages and l im i ta t ions of Lo tus 1 -2 -3 for designing a n a l y t i c a l sys tems such as M I C R O S T A N D . 8.1 Programming M I C R O S T A N D with Lotus 1-2-3 Lotus 1 -2 -3 combines an e l e c t r o n i c spreadsheet , a g raph ic s o f t w a r e , and a da ta manager into one in tegra ted so f tware p a c k a g e . T h e basic s t r u c t u r a l e lement of 1 -2 -3 is the e l e c t r o n i c spreadsheet c o m p o s e d of 2048 rows and 254 c o l -umns. E a c h row is assigned a number , e a c h c o l u m n a l e t t e r . T h e in te rcep t ion of the rows and co lumns are c a l l e d ce l ls and are iden t i f i ed by the i r r o w - c o l u m n c o o r -d inates . T h e s e ce l ls can be f i l l ed wi th numbers , m a t h e m a t i c a l f o r m u l a s , text , or m a c r o s . M a c r o s are a ser ies of key st rokes that can c o m m a n d the 1 -2 -3 sys tem to a u t o m a t i c a l l y p e r f o r m cer ta in operat ions on the cur ren t worksheet or on f i les saved on disk. L i k e f o r m u l a s , m a c r o s can inc lude some cond i t iona l funct ions with l o g i c a l operat ions such as equal to (=), less than or equa l to (<), l o g i c a l A N D , and l o g i c a l O R . A m o n g the operat ions that c a n be handled by m a c r o s are pr in t ing , c r e a -t ion and display of graphs, s imu la t ion p r o c e s s i n g , and i n t e r a c t i o n wi th the user through menus. A s w i l l be seen in the rest of this chapte r , m a c r o s were used e x t e n -s ive ly in the p r o g r a m m i n g of M I C R O S T A N D . M I C R O S T A N D ^is c o m p o s e d of 28 f i les (or worksheets) . T h e f i rs t f i l e , named 1. In order to s imp l i f y the text , the t e r m "vers ion 1A of the Lo tus 1 - 2 - 3 ™ s o f t -ware" w i l l be r e p l a c e d throughout the text by "Lo tus 1 -2 -3" or " 1 - 2 - 3 " . A U T 0 1 2 3 , is loaded a u t o m a t i c a l l y when the 1 -2 -3 spreadsheet p rogram is c a l l e d . Th is main f i le a c t i v a t e s a m a c r o that sets the program to an i n t e r a c t i v e mode through menu opt ions. O n c e an opt ion is s e l e c t e d , a cor responding m a c r o is a c t i v a t -ed which w i l l , fo r e x a m p l e , c a l l a s i m u l a t o r , c o n t r o l its opera t ions , present output d a t a , and provide the user wi th another menu for fur ther opera t ions . A l l operat ions p e r f o r m e d dur ing a s imu la t ion per iod are e x e c u t e d f r o m the main f i l e . T h e s imula tors and i n f o r m a t i o n notes are c o m b i n e d in the ma in f i le f r o m f i les saved on disk. S i m i l a r l y , graphs and da ta p r o d u c e d in the ma in f i le are t r a n s -f e r r e d to f i les on disk. T h e main f i le is p r inc ipa l l y c o m p o s e d of three sec t ions : an a rea fo r the s i m u l a -tors and their cor responding m a c r o s ; a s e c t i o n for the input and output da ta kept unt i l the end of a s imu la t ion per iod ; and a th i rd s e c t i o n for the a u t o m a t i c m a c r o that s tar ts the program and fo r other m a c r o s that ensure the l ink between d i f f e ren t s imu la tors . T h e operat ions re la ted to the product ion of graphs f r o m the growth and y ie ld tabular outputs are handled by a s p e c i a l m a c r o . A m a x i m u m of four teen d i f fe ren t graphs can be c r e a t e d , d isp layed , and saved on disk for fu ture pr in t ing . T h e p r in t -ing of graphs has to be d e f e r r e d because the 1 -2 -3 p rogram for pr in t ing graphs is not in tegra ted into the spreadsheet p r o g r a m . Graphs are norma l ly pr in ted at the end of a s imu la t ion p e r i o d ; pr in t ing ins t ruct ions can be d isp layed and pr in ted upon request . D u r i n g a g iven s imu la t ion s c e n a r i o , c e r t a i n input sequences are not c o n t r o l l e d through menu opt ions. T h e user is then p r o m p t e d to enter a ser ies of input data d i rec t l y into some c e l l s . In order to prevent some a c c i d e n t a l mod i f i ca t ions of p r o -g ram components dur ing these input phases, a l l spreadsheet ce l ls other than those s p e c i f i e d to r e c e i v e input da ta are p r o t e c t e d . A p r o t e c t e d c e l l cannot be erased or m o d i f i e d wi thout s p e c i f i c i n s t r u c t i o n . T h e p rogram also fea tures some m a c r o 57 rout ines designed to de tec t c o m m o n mistakes that can be made when users enter input da ta . 8.2 Evaluation of Lotus 1-2-3 Th is s e c t i o n examines the advantages and l im i ta t ions of Lo tus 1 -2 -3 for the deve lopment of i n t e r a c t i v e and u s e r - f r i e n d l y s tand management analysis p rograms . Advantages Software developed for IBM P C and compatible microcomputers Th is fea ture makes 1 -2 -3 c o m p a t i b l e wi th the major i ty of m i c r o c o m p u t e r s . N o t e that the U B C c o m p u t e r f ac i l i t i es inc lude IBM P C and c o m p a t i b l e m i c r o c o m p u t -ers . Comprehensive coding language and simple programming organization Lotus 1 -2 -3 can be used to p rogram c o m p l e x models in an i n t e r a c t i v e f o r m a t based on menus. Th is can be a c h i e v e d v i a a p r o g r a m m i n g approach c o m b i n i n g both 1-2-3 's m a c r o c o m m a n d s and a c o m p r e h e n s i v e set of m a t h e m a t i c a l func t ions . T h e p r o g r a m m i n g organ iza t ion is re la t i ve ly s imple for four reasons. F i r s t , the p r o g r a m m e r does not have to understand most of the mechan ics invo lved in the computer 's a c t i v i t i e s . F o r e x a m p l e , the system's c o m m a n d s are designed to be easi ly understandable through the i r r e s p e c t i v e names taken f r o m the c o m m o n Engl ish language. S e c o n d , c o m m a n d s are the same whether they are a c t i v a t e d in an i n t e r a c t i v e mode (through menus) or as e lements of m a c r o s . T h i r d , the p r o g r a m -ming organ iza t ion is based both on a conven t iona l l o g i c a l f r a m e w o r k and a spat ia l f r a m e w o r k , the l a t t e r cor responding to the l o c a t i o n of the ce l ls on a worksheet . T h e spat ia l f r a m e w o r k helps to v isua l i ze the program's s t r u c t u r e . F o u r t h , there is a p e r f e c t c o n f o r m i t y of "on s c r e e n " and pr in ted outputs . Th is fea ture s impl i f i es the conf igura t ion of m a t e r i a l to be p r in ted . Integration of graphics software Because graphics are an in tegra l part of the 1-2-3 's s y s t e m , da ta can be easi ly represented g r a p h i c a l l y . Limitations Coding complications A s is the case for a l l spreadsheet so f twares , 1 -2 -3 is not designed to process D O L O O P S . In M I C R O S T A N D , this l i m i t a t i o n is c i r c u m v e n t e d main ly through i t e r a -t ive processes invo lv ing the copy of a ser ies of equat ions a s p e c i f i e d number of t i m e s , where e a c h new ser ies of equat ions uses values of the prev ious ser ies as input d a t a . These processes are c o n t r o l l e d by m a c r o s , genera l ly through cond i t iona l funct ions using l o g i c a l opera t ions . Besides c o m p l i c a t i n g c o d i n g , the necess i ty to t ranspose D O L O O P S is a lso a f a c t o r that slows the process ing speed , as wi l l be seen below. A second cod ing c o m p l i c a t i o n wi th 1 -2 -3 is the absence of a u t o m a t i c ad just -ments fo r m a c r o s when the l o c a t i o n of ce l ls on a spreadsheet is changed dur ing p r o -g r a m m i n g . Indeed, unl ike equat ions, m a c r o s do not adjust in such a case unless their i n t e r a c t i o n wi th c e l l s , n o r m a l l y based on c e l l l o c a t i o n s , is r e p l a c e d by an in te rac t ion based on range n a m e s ^ ) . T h e s y s t e m a t i c use of range names in m a c r o s in order to ensure a u t o m a t i c ad justments c o m p l i c a t e s p r o g r a m m i n g , notably because this p recaut ion may requi re the c r e a t i o n and f o l l o w - u p of a very la rge number of ranges. A n o t h e r cod ing c o m p l i c a t i o n wi th 1 -2 -3 is the d i f f i c u l t y to read m a c r o s due to the coded f o r m of the i r c o m m a n d s . Indeed, m a c r o c o m m a n d s are only iden t i f i ed by their f i rs t l e t t e r . C e r t a i n m a c r o s ta tements requi r ing the use of cont iguous c o m -mands are par t i cu la r l y d i f f i c u l t to read for this reason . 2. In 1 - 2 - 3 , a range re fe rs to one or more ce l l s in a rec tangu la r group. 59 Possible slow processing speed "One of the p r i m a r y funct ions of a spreadsheet p rogram is to r e c a l c u l a t e a l l the ce l ls in a worksheet when a va lue or a f o r m u l a in one of the ce l ls changes" (LeB lond and C o b b 1983, 119). A l t h o u g h 1 -2 -3 is wr i t ten in assembly language and is we l l designed ( L e B l o n d and C o b b , 1983), the r e c a l c u l a t i o n of a large worksheet that involves many formulas may take some t i m e ^ ) . Some operat ions c o n t r o l l e d by macros and the i t e ra t i ve processes used to rep lace D O L O O P S involve the m o d i -f i c a t i o n of c e l l va lues , and , consequent ly , have a s lowing e f f e c t on the process ing speed . T h u s , it may take severa l minutes to process a c o m p l e x s imu la to r invo lv ing many c a l c u l a t i o n steps with 1 -2 -3 . No te that slow process ing is aggrava ted when the m i c r o c o m p u t e r hardware used does not inc lude fea tures such as a m a t h e m a t i c s c o - p r o c e s s o r , a hard disk, or a s u f f i c i e n t l y la rge random a c c e s s m e m o r y ( R A M ) . In this c o n t e x t , the author deve loped M I C R O S T A N D wi th p r o g r a m m i n g fea tures a i m e d at speeding up process ing t i m e . One of these fea tures is the convers ion of ranges c o m p o s e d of equat ion ce l ls into the i r values (numbers) as soon as these values are c a l c u l a t e d . U n f o r t u n a t e l y , this opera t ion also takes some t i m e , main ly because it has to be done by wr i t ing the equat ion values to a d i s k - f i l e , and by r e c o m b i n i n g these values into the ma in file<4). T h e p r o g r a m m e r has to judge i f the t i m e consumed by this opera t ion is saved dur ing the r e m a i n i n g process ing opera t ions . N o t e that the convers ion of equat ion ce l ls into the i r values is also requi red in order to keep the outputs of a s imu la to r a f te r its erasure f r o m the main p rogram f i l e . Indeed, the erasure of ce l ls cor responding to independent var iab les a u t o m a t i c a l -ly modi f ies (through reca lcu la t ion ) the va lue of the dependent var iab les . 3. T h e assembly language is the c losest language to the h e x a d e c i m a l numbers the c o m p u t e r uses. 4. In more recen t vers ions of Lo tus 1 - 2 - 3 , the convers ion of ranges of equat ion ce l ls into their values can be done d i r e c t l y on the main f i le thus s ign i f i can t ly a c c e l e r a t i n g the opera t ion . A n o t h e r a c c e l e r a t i n g fea ture used in M I C R O S T A N D is the b r e a k - u p of s i m u l a -tors into re la t i ve ly s m a l l f i les that can be rapid ly loaded and processed . H o w e v e r , this procedure c rea tes a c o m p l i c a t i o n s ince the equat ions on a f i le do not a u t o m a t -i ca l l y adjust when p r o g r a m m i n g changes are made on o ther f i les of the same s i m u l a -tor . Th is can be prevented only through an extensive use of range names such as in the case of m a c r o s . 61 C A S E S T U D Y USING M I C R O S T A N D T h e purpose of this chapter is to present the ma in in te rac t ions that take p lace between the user and M I C R O S T A N D dur ing a s imu la t ion pe r iod . T h e case study was s e l e c t e d to demonst ra te numerous M I C R O S T A N D features and not to m a x i m i z e possible f i n a n c i a l outputs . When the 1 -2 -3 spreadsheet p rogram is s e l e c t e d on the L o t u s system access menu, M I C R O S T A N D ' s ma in f i le is c a l l e d a u t o m a t i c a l l y and an in t roduct ion to the program is d isp layed on the s c r e e n . D i s p l a y e d in the c o n t r o l panel at the top of the s c r e e n are the opt ion c o m m a n d s of the in t roduc tory menu a long wi th their mean ing: Introductory Menu* 1) - Info: P rov ides i n f o r m a t i o n on the program s imu la to rs . - Continue: C h e c k s for graphs saved on disk, then ca l ls the growth and y ie ld inputs. T h e Info opt ion al lows the user to examine a br ie f descr ip t ion of any of the program s imu la to rs . Th is opt ion is also o f f e r e d a f te r c o m p l e t i o n of e a c h of the program's ma in s imu la t ion procedures . When the Continue opt ion is s e l e c t e d and growth and y ie ld graphs f r o m previous runs have been saved on disk, the user can e i ther erase the graph f i les or keep them for la te r p r in t ing . F o l l o w i n g one of these two opt ion c o m m a n d s , the user is p rompted to s p e c i f y a f i rs t ser ies of input da ta : the input da ta for the growth and y ie ld s i m u l a -tor . A s s u m e the s e l e c t i o n of va lues is as i l lus t ra ted on T a b l e VIII. 1. In order to s imp l i f y the tex t , some opt ion c o m m a n d s d e e m e d not essent ia l for the understanding of p rogram opera t ion are not l i s ted in the in t roductory menu nor in o ther menus r e f e r r e d to in this chapte r . f Table VUL Example of Input Data Selection for the Growth and Yield Simulator Species (1 = D o u g l a s - f i r ; 2 = C e d a r ; 3 = H e m l o c k ; 4 = Ba lsam) : 1 Si te index (m) : 32 D i a m e t e r l i m i t (cm) (7.5 17.5 22.5) : 17 .5 Stand age at beginning of s imu la t ion (yrs) : 30 Init ial basal a rea ( m 2 / h a ) (value or N A ) : 20 Th inn ing? (1 = y e s ; 0 = no) : 1 - th inning age (yrs) : 45 - percentage of s tand basal a rea r e m o v e d : 25 F i n a l harvest? (1 = y e s ; 0 = no) : 1 - harvest age (yrs) : 70 S imula t ion per iod (yrs) (1 10 20 30 . . . 100) : 40 T h e basic scenar io is a 4 0 - y e a r s imu la t ion wi th th inning fo l lowed by f ina l harvest . T h e 3 2 - m e t r e s i te index corresponds to a good qua l i ty s i te fo r D o u g l a s - f i r ( B C M o F 1983a) whereas the 1 7 . 5 - c e n t i m e t r e d i a m e t e r l im i t corresponds to one of the two c lose u t i l i za t ion in tens i t ies . T h e user a c t i v a t e s the growth and y ie ld s imu la to r by pressing two keys s i m u l -taneously , as ind ica ted at the top of the s c r e e n . When the s imula t ion procedure is c o m p l e t e , the growth and y ie ld values of T a b l e IX are d isp layed . A l s o d isp layed is the growth and y ie ld menu in the c o n t r o l panel at the top of the s c r e e n . Growth and Yield Menu - Timber-removed: D isp lays the t imber r e m o v e d tab le . - G r o w t h - & - Y i e l d : Re turns to the growth and y i e l d tab le . - Print: P r in ts G & Y input and output d a t a . - Graph: If more than one year s i m u l a t e d , opt ions: Create, View, Save and Print-steps. - Modify-inputs: Re turns to the G & Y inputs; repeats s i m u l a t i o n . - Info: P rov ides i n f o r m a t i o n on the program s imu la to rs . - Continue: C o n v e r t s the average harves ted t ree into logs . - Quit : T e r m i n a t e s the s imu la t ion sess ion . 63 Table IX. Example of Values for Growth and Yield Variables Estimated by M I C R O -S T A N D S i m u l a . Stand T o t a l M e a n N o . of B a s a l V o l u m e A n n u a l Mean Y e a r A g e He ight D B H S tems A r e a ( m 3 / h a ) Incre . A l (yrs) ( m ) ( c m ) ( /ha) ( m 2 / h a ) ( m 3 / h a ) ( m 3 / h a ) 0 30 21 .2 24 449 20 .0 150 .7 16 .0 5.0 1 31 21 .9 24 463 21 .5 167 .5 16 .7 5 .4 2 32 22 .5 25 475 23 .0 184 .9 17 .4 5.8 3 33 23 .2 25 487 24 .5 202.8 18 .0 6.1 4 34 23 .8 26 497 26.1 221 .3 18 .5 6 .5 5 35 24 .4 26 506 27 .6 240 .2 18 .9 6 .9 6 36 25 .0 27 514 29.1 259 .4 19 .2 7 .2 7 37 25.6 27 522 30.6 278 .9 19 .5 7 .5 8 38 26 .2 28 529 32.1 298 .6 19 .7 7 .9 9 39 26 .7 28 535 33 .5 318 .3 19 .8 8 .2 10 40 27 .3 29 541 34 .9 338.1 19 .8 8 .5 11 41 27 .8 29 546 36 .4 357 .9 19 .8 8 .7 12 42 28 .3 30 550 37 .7 377 .6 19 .7 9 .0 13 43 28 .8 30 554 39.1 397.1 19 .5 9 .2 14 44 29 .3 30 558 4 0 . 4 416 .4 19 .3 9 .5 15 45 29 .8 31 561 41 .7 435 .5 19.1 9 .7 16 46 30 .2 31 416 32.1 336 .0 20.1 7 .3 17 47 30 .7 32 421 33 .5 356.1 20.1 7.6 18 48 31.1 32 426 34 .9 376.2 20 .0 7.8 19 49 31 .6 33 430 36 .4 396.1 19 .9 8.1 20 50 32 .0 33 433 37 .7 415 .8 19 .7 8 .3 21 51 32 .4 34 436 39.1 435 .3 1 9 . 5 8 .5 22 52 32 .8 34 439 4 0 . 4 454 .6 19 .3 8.7 23 53 33 .2 35 442 41 .7 473 .6 18 .9 8 .9 24 54 33 .6 .35 444 43 .0 492 .2 18 .6 9.1 25 55 33 .9 36 446 44 .2 510 .4 18 .2 9 .3 26 56 34 .3 36 448 4 5 . 4 528 .3 17 .9 9 .4 27 57 34 .6 36 449 46 .6 545 .7 17 .5 9 .6 28 58 35 .0 37 450 47 .7 562.8 17 .0 9.7 29 59 35 .3 37 451 4 8 . 8 579 .3 16 .6 9 .8 30 60 35 .6 37 452 49 .9 595 .5 16.1 9 .9 31 61 35 .9 38 452 50 .9 611 .2 15 .7 10 .0 32 62 36 .2 38 452 51 .9 626 .4 15 .2 10.1 33 63 36 .5 39 453 52 .8 641 .2 14 .8 10 .2 34 64 36 .8 39 452 53 .8 655 .5 14 .3 10 .2 35 65 37.1 39 452 54 .7 669 .4 13 .9 10 .3 36 66 37 .4 40 452 55 .5 682 .8 13 .4 10 .3 37 67 37 .6 40 451 56 .3 695 .7 12 .9 10 .4 38 68 37 .9 40 450 57.1 708 .2 12 .5 10 .4 39 69 38.1 41 449 57 .9 720 .3 12.1 10 .4 40 70 38 .4 41 448 58 .6 731 .9 11 .6 10 .5 64 T h e t imber r e m o v e d values of T a b l e X are d isp layed by s e l e c t i n g the T imber -removed op t ion . Table X . Example of Values for Timber Removed Variables Estimated by M I C R O -S T A N D Harvest T y p e Th inn ing F i n a l S i m u l a t i o n Y e a r 15 40 Stand A g e (yrs) 45 70 M e a n D B H ( c m ) 31 41 T o t a l He ight ( m ) 29.8 38 .4 N o . of S tems ( /ha) 140 448 V o l u m e ( m 3 / h a ) 120 732 T h e Graph opt ion al lows the user to c r e a t e graphs f r o m the growth and y ie ld tab le . Independent var iab les can be the stand age or the s imula t ion y e a r . T h e other seven var iab les of the growth and y ie ld table can be s e l e c t e d as dependent var iab les . F i g u r e 4 shows four graphs that can be c r e a t e d f r o m the growth and y i e l d table and saved on disk fo r l a te r p r in t ing . Graphs A and D i l lus t ra te the assumed e f f e c t of th inning on the mean s tand d i a m e t e r and the annual vo lume i n c r e m e n t r e s p e c t i v e l y . N o t e that because the growth and y ie ld table produces only one dependent (Y) value cor respond ing to e a c h independent (X) va lue , the graphs do not display res idua l values a t the thinning age . R e s i d u a l va lues can be c a l c u l a t e d as the d i f f e r e n c e be tween the th inning year values of T a b l e IX and the cor responding th inning values of T a b l e X . T h e steps to pr int graphs saved on disk c a n be d isp layed and pr in ted by choosing the Print-steps opt ion of the graph s u b - m e n u . T h e Modify-inputs opt ion al lows m o d i f i c a t i o n of input da ta by re turn ing to the growth and y ie ld inputs in order to conduc t sens i t iv i ty ana lys is . A s is the case 65 Figure 4. Examples of Growth and Yield Graphs Produced by M I C R O S T A N D 41 40 39 35 37 36 35 E 34 u 33 I CD 32 O C 31 • V 30 S 29 28 27 28 25 24 23 - A -DBH as a funct ion of S tand Age (from the Growth 6c Yield Table) y' y y y * > 30 35 40 45 50 55 Stand age (yrs) 60 65 70 570 560 550 540 530 o _c 520 u V 510 CL n 500 £ u 490 tn 480 a 4-70 d z 460 450 +40 430 420 410 - B -S t e m s as a funct ion of S tand Age (from the Growth & Yield Table) / / / r y V 30 35 40 45 50 55 Stand age (yrs) 60 65 70 Figure 4 (Cohtd.) Examples of Growth and Yield Graphs Produced by M I C R O S T A N D - C -Volume as a funct ion of S tand Age (from the Growth & Yield Table) 800 - i , 1 , : , , — , , , 700 600 o ^ 500 V E 400 3 300 200 100 | i i • i | . i i • I i • i i | • i i i I i • i • | • • i • | i i i • I • i • • 30 35 40 45 50 55 80 65 70 Stand age (yrs) - D -Annual Incr. as a funct ion of S tand Age (from the Growth Ac Yield Table) 15 / \ / / \ \ \ \ \ 1 1 1 ) — 30 35 40 45 50 55 60 65 70 Stand age (yrs) for the Info op t ion , the Modify-inputs opt ion is also o f f e r e d a f ter c o m p l e t i o n o f e a c h of the program's main s imu la t ion p rocedures . T h e Continue opt ion a c t i v a t e s the t i m b e r - l o g convers ion s imula tor and the f i rs t step (highest possible grade per log) of the log grad ing s i m u l a t o r . When these s imula t ion procedures are c o m p l e t e , T a b l e XI is d isp layed a long with the t i m b e r - l o g convers ion and highest possible grade menu . Table XI. Example of Values for Log Variables of the Average Harvested Tree Estimated by M I C R O S T A N D Harvest T y p e Th inn ing L o g N o . 1 2 3 L e n g t h (m) 10 .0 10 .0 3 .5 T o p D I B * ( c m ) 21 .9 14 .2 10 .0 Highest G r a d e J J X L o g V o l . ( m 3 ) 0 .47 0.27 0 .04 Sum of L o g V o l . ( m 3 ) 0 .79 H a r v e s t T y p e F i n a l L o g N o . 1 2 3 4 L e n g t h ( m ) 10 .0 10 .0 10 .0 2 .4 T o p D I B * ( c m ) 29 .7 23 .7 1 3 . 4 10 .0 H ighest G r a d e H J J Y L o g V o l . ( m 3 ) 0 .83 0.58 0 .29 0 .03 Sum of L o g V o l . ( m 3 ) 1.72 DIB means d i a m e t e r inside b a r k . Timber- log Conversion and Highest Possible Grade Menu - Print: - Information: - Modify-inputs: - Continue: - Quit : Pr in ts the tab le . Prov ides i n f o r m a t i o n on the program s i m u l a t o r s . Re turns to the G & Y inputs; repeats s i m u l a t i o n . P r o m p t s s e l e c t i o n of l o g qual i ty to c o m p l e t e log grad ing . T e r m i n a t e s the s imula t ion sess ion . 68 T a b l e XI ind ica tes that the assumed highest possible grade is J Sawlog at th inning and H Sawlog at f ina l harvest . When the Continue opt ion is chosen , the user is p r o m p t e d to se lec t one of three log qual i t ies (good, med ium or low) fo r e a c h harves t . A s s u m e that the user s imula tes through thinning an i m p r o v e m e n t of the s tand s tem qual i ty by s e l e c t -ing med ium qual i ty for th inning and good qual i ty fo r f ina l harvest . When the log grad ing procedure is c o m p l e t e , the vo lume dist r ibut ions per grade of T a b l e XII are d isp layed together wi th the l o g grad ing menu . No te that the sums of vo lumes of T a b l e XII are i d e n t i c a l to the vo lumes r e m o v e d of T a b l e X . Table XII. Example of Volume Distributions by Grade Estimated by M I C R O S T A N D Harves t T y p e T h i n n i n g F i n a l S e l e c t e d Q u a l i t y M e d i u m G o o d G r a d e V o l u m e ( m 3 / h a ) ( m 3 / h a ) A P e e l e r 0 0 D L u m b e r 0 0 B P e e l e r 0 0 C P e e l e r 0 0 H S a w l o g 0 208 I S a w l o g 0 116 J S a w l o g 58 294 X U t i l i t y 48 92 Y C h i p p e r 13 20 R e j e c t s 1 1 Sum of V o l u m e s 120 732 Log Grading Menu - Print: - Information: Pr in ts the vo lume distr ibut ion(s) . P rov ides i n f o r m a t i o n on the p r o g r a m s imu la to rs . - Modify-inputs: Re turns to the l o g grad ing or the G & Y inputs; repeats s i m u l a -t i o n . - Continue: P r o m p t s inputs for the revenue , cos t , and f inanc ia l analysis s imu la tors . - Quit : T e r m i n a t e s the s imu la t ion sess ion . F o l l o w i n g the s e l e c t i o n of the Continue op t ion , the user is p r o m p t e d to s p e c i f y another ser ies of input da ta : part 1 of the input d a t a fo r the revenue , c o s t , and f inanc ia l analysis s imu la to rs . A s s u m e the s e l e c t i o n of values is as i l lus t ra ted in T a b l e XIII. Table XUi. Example of Input Data (Part 1) for the Revenue, Cost, and Financial Analysis Simulators R e a l d iscount ra te (%/yr) : 4 .0 A v e r a g e r e a l ra te of change in l o g pr ices (%/yr ) : 1.0 A v e r a g e r e a l ra te of change in d e l i v e r y costs (%/yr ) : - 1 . 0 A v e r a g e s tand s l o p e (posi t ive %) : 30 A v e r a g e o n e - w a y t ruck h a u l d is tance (km) : 10 Water t ranspor ta t ion for l o g s ? (1 = y e s ; 0 = no) : 1 - type (1 = towing; 2 = barging) : 1 - cost ( $ / m 3 ) : 1.50 D i s t a n c e m a r s h a l l i n g a rea to nearest c o m m u n i t y ( km) : 10 P e r c e n t of the c rew l i v i n g in the c a m p : 10 S P E C I F I C I N P U T D A T A F O R T H I N N I N G R o a d densi ty ( k m / h a ) : 0.06 P e r c e n t of the f u l l road d e v e l o p m e n t cost : 50 P e r c e n t of d i r e c t d e l i v e r y costs c o m p o s e d of d e p r e c i a t i o n : 10 A v e r a g e l i f e of the d e p r e c i a b l e assets (yrs) : 10 R e a l ra te of re turn on d e p r e c i a b l e c a p i t a l (%/yr ) : 7 S p e c i a l r isk a l l o w a n c e on d e l i v e r y costs (%) : 5 T h e f i rs t s e c t i o n of T a b l e XIII inc ludes inputs that are not s p e c i f i c for a p a r t i -cu lar type o f harvest whereas the second s e c t i o n inc ludes inputs that are s p e c i f i c for th inning. No te (1) the negat ive va lue for the average rea l ra te of change in de l ivery cos ts , and (2) the 50 percent value for the percen tage of the fu l l road deve lopment cost at th inn ing. Th is 50 percent value ind ica tes that a propor t ion of roads a l ready exists or that only part of the t ranspor ta t ion in f ras t ruc ture is charged against the i m m e d i a t e harvest . When a l l va lues of T a b l e XIII have been s e l e c t e d , the user presses two keys s imul taneous ly . A s a resul t , M I C R O S T A N D displays the harvest ing sys tem s e l e c t i o n menu c o m p o s e d of the four sk idding or yard ing systems that de te rmine the harvest ing sys tem for f ina l harvest^ 2 ) . Harvesting System Selection Menu - High-lead-yarder: H igh y ie ld yarder fo r f ina l ha rves t . - Grapple-yarder: G r a p p l e yarder for f ina l harves t . - Rubber-tired-skidder: Rubber t i red sk idder fo r f ina l harves t . - Soft-tracked-skidder: Sof t t r a c k e d skidder fo r f i n a l harves t . In addi t ion to the menu , M I C R O S T A N D displays F i g u r e 3 of Sect ion 6.1.2 that i l lust ra tes the four a l te rna t ive harves t ing s y s t e m s , and the p r e s e l e c t e d average s tand slope of T a b l e XIII that should be taken into a c c o u n t when s e l e c t i n g the har -vest ing s y s t e m . T h e harves t ing sys tem s e l e c t e d by the user is then shown as the yard ing and load ing sys tem entr ies of T a b l e X IV , and the user is p r o m p t e d to s p e c i f y a ser ies of input da ta s p e c i f i c for f ina l harvest : part 2 of the input data for the revenue , cos t , and f i n a n c i a l analysis s imu la to rs . A s s u m e the s e l e c t i o n is as i l lus t ra ted in T a b l e X IV . 2. A s ind ica ted in S e c t i o n 6.1.2, only the t r e e - t . o - t r u c k cost s u b - m o d e l fo r f ina l harvest incorpora tes the s p e c i f i c a t i o n o f a harves t ing s y s t e m . 71 Table XIV. Example of Input Data (Part 2) for the Revenue, Cost, and Financial Analysis Simulators S P E C I F I C I N P U T D A T A F O R F I N A L H A R V E S T S e l e c t e d yard ing s y s t e m : Soft t r a c k e d sk idder C o r r e s p o n d i n g l o a d i n g s y s t e m : F r o n t - e n d l o a d e r R o a d densi ty ( k m / h a ) : 0 .06 A n n u a l road ma in tenance cost be tween harvests ( $ / k m ) : 1000 P e r c e n t of the f u l l road d e v e l o p m e n t cost : 25 P e r c e n t of d i rec t d e l i v e r y costs c o m p o s e d of d e p r e c i a t i o n : 10 A v e r a g e l i f e of the d e p r e c i a b l e assets (yrs) : 10 R e a l ra te of re turn on d e p r e c i a b l e c a p i t a l (%/yr ) : 7 S p e c i a l r isk a l l o w a n c e on d e l i v e r y costs (96) : 5 No te that the harvest ing sys tem entr ies of T a b l e XIV should be taken into a c c o u n t when s p e c i f y i n g the road densi ty for f ina l harves t . F u r t h e r m o r e , the value s p e c i f i e d for the pe rcen tage of the fu l l road deve lopment cost at f ina l harvest should take into a c c o u n t the annual road ma in tenance cost be tween th inning and f ina l harvest . When a l l values of T a b l e XIV are s p e c i f i e d , the user a c t i v a t e s the revenue , cos t , and f i n a n c i a l analysis s imula tors by pressing two keys s imul taneous ly . A s a resul t , the cash f low of r e a l costs and revenues of T a b l e X V is d isp layed a long wi th the revenue , c o s t , and f i n a n c i a l analysis m e n u . 72 Table X V . Example of Cash Flow of Real Costs and Revenues Estimated by M I C R O -S T A N D Harvest T y p e Th inn ing F i n a l S i m u l a t i o n Y e a r 15 40 Item R e a l v a l u e R e a l v a l u e ( $ / m 3 ) ($ /ha ) ( $ /m 3 ) ($ /ha ) D I R E C T D E L I V E R Y C O S T S R o a d D e v e l o p m e n t 14 .36 1717 0 . 91 668 T r e e - t o - T r u c k 19 .72 2358 6 . 41 4688 T r u c k H a u l 2 .84 340 2. 21 1618 R o a d Ma in tenance 0 .80 96 1. 39 1020 D u m p , S o r t , B o o m & S c a l e 3 .67 438 2 . 85 2086 T o w i n g or Barg ing 1.29 154 1. 00 734 C r e w T r a n s p o r t a t i o n 1.95 233 1. 52 1109 C a m p & Cookhouse 0.62 75 0 . 49 355 O v e r h e a d 7 .69 919 5 . 98 4374 S u b - t o t a l 52 .94 6331 22 . 76 16652 R E T U R N O N C A P I T A L 3.71 443 1. 59 1166 S P E C I A L R ISK A L L O W A N C E 2 .83 339 1. 22 891 T O T A L C O S T S 59 .47 7113 25 . 57 18709 R E V E N U E S F R O M L O G S 30 .14 3604 6 1 . 39 44914 T I M B E R V A L U E - 2 9 . 3 4 -3509 3 5 . 82 26205 ( revenues - costs ) A N N U A L R O A D M A I N T E N A N C E C O S T B E T W E E N H A R V E S T S P e r i o d 24 yrs R a n g e 51 $ /ha to 41 $ /ha Revenue, Cost, and Financial Analysis Menu - Financial-return: D isp lays the f i n a n c i a l re turn analysis of cash f low. Re turns to the cash f low of rea l costs and revenues . Pr in ts revenue , cos t , and f i n a n c i a l analysis input data and output tab les . Returns to G & Y , log grad ing or last ser ies of inputs; repeats s i m u l a t i o n . - Cash-flow: - Print: - Modify-inputs: 73 - Log-prices: Displays, and p r i n t s upon request, the log prices used i n the program. - Info: Provides information on the program simulators. - Quit: Terminates the session. Table XV shows that the estimated value of the harvested timber i s negative at thinning and p o s i t i v e at f i n a l harvest, as r e f l e c t e d by both higher revenues and lower costs per cubic metre at f i n a l harvest. The f i n a n c i a l return analysis of cash flow of Table XVI i s displayed by s e l e c t i n g the Financial-return menu option. This table shows the present value f o r each operation together with the net present value and the benefit-cost r a t i o f o r the stand management scenario. Note that the net present value i s stated only i n d o l l a r s per hectare i n order to accommodate the d i f f e r e n c e i n volume removed at each harvest. Likewise, the benefit-cost r a t i o i s cal c u l a t e d from d o l l a r s per hectare values; Table XVI. Example of Financial Return Analysis of Cash Flow Estimated by MICROSTAND Operation Present Value ($/m3) ($/ha) Thinning F i n a l Harvest Road Maintenance Between Harvests Net Present Value -16.29 7.46 -0.54 * Benefit-Cost Ratio (from $/ha values) 1.378 -1948 5458 -393 3117 This value applies to the volume removed at f i n a l harvest. T h e Log-prices opt ion al lows the user to examine and print the log pr ices used by M I C R O S T A N D (c.f . T a b l e I in S e c t i o n 5.1). T h e Modify-inputs opt ion al lows the user to re turn to any prev ious input data step in order to conduc t sens i t iv i ty ana lys is . T h e fo l lowing examples show a few of the results that c a n be obta ined v i a a sens i t iv i ty analysis based on the case study: mod i fy ing the rea l d iscount ra te unt i l the net present value approaches zero shows that the in terna l ra te of re turn of the s imu la t ion scenar io is about 7.7 p e r c e n t ; using average rea l rates of change in log pr ices and de l ive ry costs equal to ze ro results in lower values of s tanding t imber ( $ / m 3 and $/ha) and c o n s e -quent ly lower net present va lue ($/ha) and b e n e f i t - c o s t ra t io of the stand management s c e n a r i o ; a s ingle harvest scenar io wi th f ina l harvest postponed by 10 years (in order to obta in s imi la r s t e m dimensions to the case study f ina l harvest) results in an a lmost i d e n t i c a l va lue of s tanding t i m b e r ( $ / m 3 ) at f i na l harves t , but in higher net present value ($/ha) and b e n e f i t - c o s t ra t io . No te that the m o d i -f ied scenar io uses the same l o g qua l i ty and percen tage of fu l l road deve lopment cost as the case study th inning o p e r a t i o n . a l l o ther condi t ions kept constan t , the 2 2 . 5 - c e n t i m e t r e d i a m e t e r l i m i t g ives the highest va lue of s tanding t imber ( $ / m 3 ) at f ina l harvest and the highest b e n e f i t - c o s t ra t io of the s imu la t ion scenar io whereas the 1 7 . 5 - c e n t i m e t r e d i a m e t e r l i m i t g ives the highest va lue of s tanding t i m b e r ( $ / m 3 ) at th inning and the highest net present va lue ($/ha). T h e lowest values are obta ined wi th the 7 . 5 - c e n t i m e t r e d i a m e t e r l i m i t wh ich corresponds to a whole s tem u t i l i za t ion s tandard . No te that the in i t i a l basal a rea used for the 7.5 and 2 2 . 5 - c e n t i m e t r e d i a m e t e r l im i t s imula t ions are 34 and 12 square metres per h e c t a r e r e s p e c t i v e l y . O n c e the s imula t ion session is c o m p l e t e , the user se lec ts the Quit opt ion in order to exi t f r o m the p rogram and to re turn to the Lo tus sys tem access menu f r o m which the Lo tus print graph sys tem can be loaded to print the graphs previously saved on disk. Us ing a convent iona l IBM P C m i c r o c o m p u t e r and the program on a f loppy disk, the execut ion t ime for the case study presented in this s e c t i o n is a p p r o x i m a t e -ly 8 min 30 s: 1 min 30 s for the growth and y ie ld s i m u l a t i o n , 5 min (2 min 30 s per harvest , w i th a log by log sequent ia l d isplay of va lues as soon as they are c a l c u -lated) for the t i m b e r - l o g convers ion and highest possible grade s i m u l a t i o n , 1 min 10 s (35 s per harvest) fo r the vo lume d is t r ibut ion per g r a d e , and 50 s for the revenue , cos t , and f i n a n c i a l analysis s i m u l a t i o n . T h e execut ion t ime for the growth and y ie ld s imu la t ion var ies wi th the length of the s imu la t ion per iod (ranging f r o m one year to 100 years) whereas the execu t ion t i m e for the t i m b e r - l o g convers ion and highest possible grade s imula t ion var ies wi th the number of logs that can be p roduced f r o m e a c h average harvested t ree . S i m i l a r l y , the execut ion t ime is s i g n i f i c a n t l y shor ter for o n e - h a r v e s t scenar ios than for t w o - h a r v e s t scenar ios . A s ind ica ted in S e c t i o n 8.2, the process ing speed of the p rogram can be increased s i g n i f i c a n t l y wi th hardware features such as a m a t h e m a t i c s c o - p r o c e s s o r or a hard disk. 76 10. PROGRAM EVALUATION This section examines the strengths and l i m i t a t i o n s of the program as a whole thus completing the evaluation of the i n d i v i d u a l simulators. Strengths Simulation of representative BC coastal conditions The program i s adapted to the c h a r a c t e r i s t i c s of both the f o r e s t resource and the u t i l i z a t i o n technology of the Coast. This i s achieved mainly through a simulation approach using the BC Forest Service's v a r i a b l e density y i e l d equations and d i r e c t d e l i v e r y cost estimation. Dser-friendly operation No previous experience with microcomputers i s required to use MICROSTAND; learning the e s s e n t i a l design of the program demands minimum e f f o r t from the user. Such u s e r - f r i e n d l y operation i s mainly due to four c h a r a c t e r i s t i c s of the program's design: simulation processing i s c o n t r o l l e d through menu options; information f i l e s can be displayed at d i f f e r e n t points of a simulation period; growth and y i e l d graphs f a c i l i t a t e the s e l e c t i o n of harvesting scenarios; and simulators are loaded sequentiall y i n a l o g i c a l manner that allows f o r a step-by-step introduction to the program. Note that t h i s t h e s i s and MICROSTAND's information f i l e s should provide enough support material f o r the program users. Therefore, i t was not deemed necessary to develop a user manual f or the program. C r i t i c a l appraisal determinants Although MICROSTAND does not include a l l the parameters that determine the value of timber, d i r e c t or i n d i r e c t c o n t r o l i s allowed on most of the c r i t i c a l a p p r a i s a l determinants. Among these determinants are u t i l i za t ion s tandard , harvested v o l u m e , average p iece s i z e , log qua l i ty , s tand s lope , harvest ing s y s t e m , road dens i ty , haul d i s t a n c e , and s p e c i a l r isks . No te that the program's design helps the user to r e c o g n i z e in terac t ions between var iab les: for e x a m p l e , the average stand slope in f luences the se lec t ion of the har -vest ing sys tem which in turn in f luences the s p e c i f i c a t i o n of the road densi ty . Detailed outputs T h e high resolut ion output f o r m a t of the p rogram includes i n f o r m a t i o n such as seven growth and y ie ld p a r a m e t e r s for e a c h year of the s imu la t ion p e r i o d , de l ivery cost for e a c h of nine opera t iona l phases, and cash f low and present value data e x -pressed in two d i f f e ren t units ( $ / m 3 and $/ha). Flexibility F l e x i b i l i t y is obta ined through a c o m b i n a t i o n of c h a r a c t e r i s t i c s inc lud ing a s imula t ion per iod ranging f r o m one year to 100 years ; four spec ies ; three basic har -vest ing scenar ios wi th numerous var ia t ions ; op t iona l s p e c i f i c a t i o n of both an annual road ma in tenance cost be tween harvests and a percen tage of fu l l road deve lopment cost at each harvest ; opt iona l s p e c i f i c a t i o n of a r e a l ra te of change in costs and revenues; and opt iona l re turn to prev ious s imula tors in order to mod i fy input d a t a . T h e opt iona l re turn c h a r a c t e r i s t i c f a c i l i t a t e s sens i t iv i ty analysis on appra isa l d e t e r -minants . Recognition of uncertainty T h e s i m p l i f i c a t i o n s requ i red fo r mode l l ing and the possible errors in pro jec t ing da ta over t i m e are two main sources of uncer ta in ty in t imber supply pro ject ions (Marshal l 1987). These same sources of uncer ta in ty apply to the processes and a c t i v i -t ies s imu la ted by M I C R O S T A N D . T h e res idua l nature of the value of s tanding t imber represents an ind i rec t source of uncer ta in ty : a s m a l l pe rcen tage er ror in es t imat ing the revenues f r o m logs or the costs requ i red to obta in these revenues may result in a large percen tage er ror in the res idua l value of s tanding t imber (Pearse et a l . 1974). No te that the magni tude of uncer ta in ty var ies wi th the s p e c i f i c c i r c u m s t a n c e s cons idered (Marsha l l 1987). T h e program's most obvious fea ture that a l lows for the recogn i t ion of u n c e r -ta inty is the s p e c i a l r isk a l lowance (spec i f ied for e a c h harvest as a percentage of appra ised costs) to r e f l e c t par t i cu la r ly uncer ta in costs e lements that cannot be ful ly r e f l e c t e d in an appra isa l based on average expec ta t ions . T w o other p rogram features that can be used to r e c o g n i z e uncer ta in ty are the opt iona l s p e c i f i c a t i o n of a rea l ra te of change in costs and revenues , and the opt iona l re turn to previous s imula tors in order to prov ide answers to a number of "what if" quest ions. No te that the possib i l i ty of con t ro l l ing the va lue of c r i t i c a l appra isa l de te rminants and the high resolut ion output f o r m a t of the p rogram prov ide a f lex ib le basis for assessing d i f fe ren t sources of uncer ta in ty through sens i t iv i ty ana lys is . Recognition of relevant economic concepts In addi t ion to the genera l c o n c e p t of s tumpage appra isa l , six re levant e c o n o m i c concepts are r e c o g n i z e d by the p r o g r a m : the "operator of average e f f i c i e n c y " c o n -cept through the es t ima t ion of average expec ta t ions fo r s p e c i f i c cond i t ions; the e c o n o m i c marg in of u t i l i za t ion through the d i a m e t e r l i m i t s e l e c t i o n ; the c o m m e r c i a l pa r t i a l cu t t ing concep t through the th inning op t ion ; the cost of c a p i t a l through the es t ima t ion of deprec ia t ion and return on c a p i t a l ; in f la t ion through the rea l rates of change in costs and revenues; and the t ime value of money through the rea l d i s -count rate and the ra te of re turn on deprec iab le c a p i t a l . Limitations Inclusion of unsophisticated and nonvalidated simulation procedures T h e reac t ions to th inn ing, the d is t r ibut ion of l o g vo lume a m o n g grades , and the return on c a p i t a l are genera ted by unsophis t ica ted and nonva l ida ted s imula t ion procedures . A s ind ica ted in Sect ions 3.3 and 6.3, the r e s p e c t i v e procedures used to s imula te the reac t ions to th inning and the re turn on c a p i t a l do not marked ly l i m i t the program for its in tended purpose. H o w e v e r , as i n d i c a t e d in S e c t i o n 5.2, the procedure used to d is t r ibute log vo lume a m o n g grades does not fu l ly r e c o g n i z e the var ia t ions of t ree s izes in a stand nor the consequent e f f e c t s of these var ia t ions on the revenues f r o m logs. T h i s does const i tu te a l i m i t a t i o n of the p rogram for its in tended learn ing purpose. Simulation of pure stands T h e s imula t ion of pure stands (composed of one of four species) represents a model l ing s i m p l i f i c a t i o n because pure stands are u n c o m m o n in the B C c o a s t a l con i fe rous forest ( U B C 1983). In the contex t of s tumpage appra isa l , this s i m p l i f i c a -t ion a f f e c t s the gross value of the t i m b e r but does not s ign i f i can t ly in f luence harves t -ing and other costs that must be s u b t r a c t e d f r o m the gross va lue to de te rmine a p -pra isa l pr ices (Pearse et a l . 1974). A c c o r d i n g to the same s o u r c e , it remains however appropr ia te to cons ider the proport ions of d i f fe ren t spec ies as one of a la rge number of qual i ty var iab les that de te rmine the gross value of a t i m b e r s tand . Because M I C R O S T A N D recogn izes such qua l i ty var iab les , notab ly through the l o g qual i ty s e l e c t i o n , the s imula t ion of pure stands does not appear a s ign i f i can t l i m i t a t i o n of the p r o g r a m . It should be noted that cont ra ry to the o f f i c i a l appra isa l p rocedure which is d i r e c t e d toward establ ishing the value of e a c h major spec ies of a cu t t ing unit ( B C M o F 1985, 1986), the appra isa l of pure stands with M I C R O S T A N D is equiva lent to a whole stand appra isa l a p p r o a c h . In whole stand appra isa l , the basis for the c a l c u l a -t ion of a l l revenues and costs of the appra isa l is "the whole stand approved for har -vest ing - not the ind iv idua l species conta ined in it" (Pearse et a l . 1974, 26). A c c o r d -ing to the same s o u r c e , whole s tand appra isa l is the appropr ia te t imber appra isa l approach f o r the C o a s t main ly b e c a u s e , as ment ioned above , the proport ions of d i f -80 ferent species i s merely one of a large number of q u a l i t y variables determining the gross value of a timber stand that must be harvested i n i t s e n t i r e t y . Slow processing speed Some c h a r a c t e r i s t i c s that Lotus 1-2-3 shares with a l l other spreadsheet programs have a slowing e f f e c t on the processing speed of simulators such as those used i n MICROSTAND. Thus, processing one of MICROSTAND's simulation procedures with a conventional IBM PC microcomputer takes a minimum of about 30 seconds, despite the f a c t that the program was developed with programming features aimed at speeding up the processing time. This i s r e l a t i v e l y slow for a program to be used as a learning t o o l . Note that the simulator with the longest processing time uses a complex i t e r a t i v e procedure to convert timber i n t o logs. As i n d i c a t e d i n Section 8.2, i t e r a t i v e procedures tend to slow the processing speed of models based on Lotus 1-2-3. Complex procedures to modify program's components As i s the case f o r a l l large, f l e x i b l e , and u s e r - f r i e n d l y programs, MICROSTAND's coding i s complex. Adding to t h i s complexity are the coding complications p a r t i c u l a r to 1-2-3 and the programming features aimed at speeding up the processing time. Therefore, possible attempts to modify the program's components could prove to be d i f f i c u l t . 11. C O N C L U S I O N S T h e main ob jec t ive of this thesis was to deve lop a c o m p u t e r i z e d stand m a n a g e -ment analysis p rogram based on the Lo tus 1 -2 -3 m i c r o c o m p u t e r sof tware that would be sui table for use as a s tumpage appra isa l l ea rn ing too l fo r U B C undergraduate fo res t ry e c o n o m i c s courses . A secondary ob jec t ive was to assess the appropr ia teness of Lo tus 1 -2 -3 for deve lop ing i n t e r a c t i v e and u s e r - f r i e n d l y stand management a n a l y -sis p rograms. T h e main ob jec t ive of the thesis is met by seven c h a r a c t e r i s t i c s of M I C R O -S T A N D : s imu la t ion of representa t ive B C c o a s t a l cond i t ions , u s e r - f r i e n d l y opera t ion , inc lus ion of c r i t i c a l appra isa l de te rminan ts , genera t ion of de ta i led outputs , f l e x i -b i l i ty , and recogn i t ion of both uncer ta in ty and re levant e c o n o m i c c o n c e p t s . T h e inc lus ion of unsophis t ica ted and nonva l ida ted s imu la t ion procedures proved not to be a s ign i f i can t source of p rogram l i m i t a t i o n s . Indeed, the quest ion of p rogram va l id i ty for i ts in tended app l ica t ion is r e d u c e d to M I C R O S T A N D ' s ab i l i ty to r e v e a l the nature and the in ter re la t ions of the ma in appra isa l p a r a m e t e r s . With the sole excep t ion of t ree s ize var ia t ions in a stand and the consequent e f f e c t s on l o g r e v e -nues, M I C R O S T A N D can e f f e c t i v e l y r e v e a l these p a r a m e t e r s and in te r re la t ions . A s ind ica ted in s e c t i o n 5.2, recogn i t ion of t ree s ize var ia t ions could be obta ined wi th a va luat ion procedure based on e m p i r i c a l da ta and regress ion techniques . M I C R O S T A N D ' s ab i l i ty to r e c o g n i z e re la t ionships a m o n g per t inent pa ramete rs wi l l not prevent c e r t a i n s imulat ions or combina t ions of s imula t ions f r o m occas iona l l y genera t ing unrea l is t ic p red ic t ions . Y e t , the c o m p l e x in te rac t ions between the p r o -gram's p a r a m e t e r s w i l l not ind ica te such possible b ias , i n a c c u r a c y , or i m p r e c i s i o n . Consequent ly , as suggested fo r the growth and y ie ld s i m u l a t o r , users should t ry to s imula te rea l is t i c condi t ions at e a c h input step and use the i r knowledge and judge-ment to d e t e c t possible unrea l is t ic p red ic t ions . F u r t h e r m o r e , it is r e c o m m e n d e d that program app l ica t ion should inc lude the d e t e c t i o n of l im i ta t ions and the c o n s i d e r -a t ion of model l ing i m p r o v e m e n t s . T h i s would encourage the students to deve lop a c r i t i c a l approach towards the use of models . Such an approach is an increas ingly impor tant a t t i tude in a f i e ld where c o m p u t e r i z e d s imu la to rs of a l l types are p r o l i f e r -a t ing . A l i m i t a t i o n of M I C R O S T A N D for its in tended purpose appears to be its r e l a -t ive ly slow process ing speed which is main ly due to two c h a r a c t e r i s t i c s that Lotus 1 -2 -3 shares with a l l o ther spreadsheet p rograms: the r e c a l c u l a t i o n of a l l the ce l ls in a worksheet when a value or a f o r m u l a in one of the ce l ls changes , and the n e c e s -s i ty to t ranspose D O L O O P S through i t e ra t i ve p rocedures . T w o fur ther c h a r a c t e r -is t ics of Lo tus 1 -2 -3 c o m p l i c a t e M I C R O S T A N D ' s cod ing and may c o m p l i c a t e possible mod i f i ca t ions to the program's components : the absence of a u t o m a t i c adjustments fo r macros when the l o c a t i o n of ce l ls in a worksheet is changed and the d i f f i c u l t y to read m a c r o s due to the coded f o r m of their c o m m a n d s . Desp i te these l im i ta t ions , Lo tus 1 -2 -3 appears to be an appropr ia te med ium for deve lop ing i n t e r a c t i v e and u s e r - f r i e n d l y s tand management analysis p rograms . Indeed, the p r o g r a m m i n g approach deve loped for M I C R O S T A N D (combin ing 1-2-3 's m a c r o c o m m a n d s , comprehens ive set of m a t h e m a t i c a l func t ions , and graph ic s o f t -ware) appears to be a f lex ib le f r a m e w o r k that cou ld be used for the deve lopment of a va r i e ty of i n t e r a c t i v e programs re la ted to forest management and o ther f ie lds . H o w e v e r , p rograms based on Lo tus 1 -2 -3 should re ly as much as possible on s imp le models in order to reduce the execu t ion t i m e , to prevent some p r o g r a m m i n g c o m p l i c a t i o n s par t i cu la r to 1 - 2 - 3 , and to f a c i l i t a t e possible p rogram m o d i f i c a t i o n s . No te that c o m p l e x models can o f ten be s i m p l i f i e d through regression techniques or through their adapta t ion for a s p e c i f i c purpose. T h i s is p a r t i c u l a r l y possible for programs deve loped for educa t iona l purposes because high degrees of p r e c i s i o n , a c c u r a c y , and l a c k of bias may not be requ i red in such cases . A n example of m o d e l -83 l ing s i m p l i f i c a t i o n a c h i e v e d through regression techniques is M I C R O S T A N D ' s road deve lopment cost s u b - m o d e l c o m p o s e d of three equat ions. M I C R O S T A N D in tegrates s e v e r a l b i o l o g i c a l , t e c h n i c a l , and e c o n o m i c p a r a -meters whose respec t ive mode l l ing procedures are genera l ly deve loped by spec ia l is ts of d isc ip l ines inc lud ing b i o m e t r i c s , ha rves t ing , and fores t ry e c o n o m i c s . F r o m the author's e x p e r i e n c e , such a pro ject cou ld benef i t f r o m the d i rec t input of spec ia l is ts f r o m e a c h d isc ip l ine in order to ensure g rea te r cons is tency in s imula tor qua l i ty , notably by eva lua t ing the mer i ts of a l te rna t ive models and by prov id ing expert o p i n -ion on the i m p a c t of mode l s i m p l i f i c a t i o n s . C o n s e q u e n t l y , the deve lopment of a s tumpage appra isa l program such as M I C R O S T A N D would be p re fe rab ly a c h i e v e d by a mul t id isc ip l inary t e a m . Such a t e a m would be c o m p o s e d of a pro ject c o o r d i -nator , s e v e r a l spec ia l is ts e a c h in charge of the deve lopment of a s p e c i f i c s imu la to r , and a p r o g r a m m e r to prov ide t e c h n i c a l suppor t . L I T E R A T U R E C I T E D Br i t i sh C o l u m b i a Min is t ry of F o r e s t s . 1976. M e t r i c D i a m e t e r C l a s s D e c a y , Waste  and Breakage F a c t o r s for A l l F o r e s t Inventory Zones . V i c t o r i a , B C . Br i t i sh C o l u m b i a Min is t ry of F o r e s t s . 1980. F o r e s t Serv ice C r u i s i n g Procedures  and C r u i s e C o m p i l a t i o n . V i c t o r i a , B C . Br i t ish C o l u m b i a M in is t ry of F o r e s t s . 1983a. Var iab le Dens i ty Y i e l d Pro jec t ion C o e f f i c i e n t s for Pure Stands in Br i t i sh C o l u m b i a . Inventory R e p o r t N o . 3. V i c t o r i a , B C . Br i t ish C o l u m b i a Min is t ry of F o r e s t s . 1983b. F o r e s t S e r v i c e Sca l ing M a n u a l . M a r c h 1983 A m e n d m e n t . V i c t o r i a , B C . Br i t i sh C o l u m b i a Min is t ry of F o r e s t s . 1985. C o a s t a l L o g Based A p p r a i s a l M a n u a l . January 1, 1985 V e r s i o n . V i c t o r i a , B C . Br i t i sh C o l u m b i a Min is t ry of F o r e s t s . 1986. C o a s t L o g - b a s e d A p p r a i s a l M a n u a l . January 1, 1986 V e r s i o n . V i c t o r i a , B C . C h a p p e l l e , D . E . 1969. A C o m p u t e r P r o g r a m for E v a l u a t i n g F o r e s t r y Oppor tun i t ies under T h r e e Investment C r i t e r i a . U S D A F o r e s t S e r v i c e R e s e a r c h Paper P N W -78. P o r t l a n d , O r e . : P a c i f i c Nor thwest F o r e s t and R a n g e E x p e r i m e n t S t a t i o n . C o o n e y , T . M . 1985. Spreadsheets: Versa t i l e P r o b l e m - s o l v i n g S o f t w a r e . J o u r n a l  of F o r e s t r y 83(4): 205-6 , 247. D a v i s , K . P . 1966. F o r e s t M a n a g e m e n t : R e g u l a t i o n and V a l u a t i o n . 2d e d . New Y o r k : M c G r a w - H i l l . D e m a e r s c h a l k , J . P . and A . K o z a k . 1977. T h e W h o l e - b o l e S y s t e m : A C o n d i t i o n e d D u a l - e q u a t i o n Sys tem for P r e c i s e P r e d i c t i o n of T r e e P r o f i l e s . C a n . J . F o r .  R e s . 7: 488 -97 . F i g h t , R . D . , J . M . C h i t t e s t e r , and G . W . C l e n d e n e n . 1984. D F S I M WITH E C O N O M I C S : A F i n a n c i a l A n a l y s i s O p t i o n for the D F S I M D o u g l a s - f i r S i m u l a t o r . U S D A F o r e s t Serv ice G e n e r a l T e c h n i c a l R e p o r t P N W - 1 7 5 . P o r t l a n d , O r e g . : P a c i f i c Nor thwest F o r e s t and R a n g e E x p e r i m e n t S t a t i o n . F o r e s t R e s o u r c e s Systems Inst i tute, n .d . Y i e l d 1.4: T i m b e r Y i e l d F o r e c a s t i n g  and P lann ing T o o l . T y p e s c r i p t . G a s s o n , R. and D . H . Wi l l i ams. 1986. A M e t h o d for E s t i m a t i n g the Va lue of T i m b e r Inventories of C o a s t a l Br i t i sh C o l u m b i a . 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Introduct ion to F o r e s t R e s o u r c e M a n a g e m e n t . New Y o r k : J o h n Wi ley & Sons. M a r s h a l l , P . L . 1987. Sources of U n c e r t a i n t y in T i m b e r Supply Pro jec t ions . T h e  F o r e s t r y C h r o n i c l e 63(3): 165-68. P e a r s e , P . H . 1976. T i m b e r R ights and F o r e s t P o l i c y . V o l . 1. R e p o r t of the R o y a l C o m m i s s i o n on F o r e s t R e s o u r c e s . V i c t o r i a , B C . P e a r s e , P . H . , A . V . B a c k m a n , and E . L . Y o u n g . 1974. T i m b e r A p p r a i s a l . Second R e p o r t of the T a s k F o r c e on C r o w n T i m b e r D i s p o s a l . V i c t o r i a : Br i t i sh C o l u m -bia M in is t ry of F o r e s t s . P ienaar , L . V . and K . J . T u r n b u l l . 1973. T h e C h a p m a n - R i c h a r d s G e n e r a l i z a t i o n of Von Ber ta lan f fy 's G r o w t h M o d e l fo r B a s a l A r e a G r o w t h and Y i e l d in E v e n -aged Stands. F o r e s t S c i e n c e 19(1): 2 -22 . R o g l e r , R . K . and H . O . C a n h a m . 1986. A n O p t i m a l L o g B u c k i n g P r o g r a m for M i c r o -c o m p u t e r s . T h e C o m p i l e r 4(2): 27, 30. T h o m p s o n , E . F . , R . C . M a n t i e , A . D . Su l l i van , and H . E . B u c k h a r t . 1973. E c o n o m i c Guide l ines fo r L o b l o l l y P ine M a n a g e m e n t in V i r g i n i a . P u b l i c a t i o n F W S - 4 - 7 3 . B l a c k s b u r g : V i r g i n i a P o l y t e c h n i c Institute and Sta te U n i v e r s i t y . T i t u s , S . J . and R . T . M o r t o n . 1985. F o r e s t Stand G r o w t h Mode ls : What for? T h e  F o r e s t r y C h r o n i c l e 61(1): 19 -22 . U n i v e r s i t y of Br i t i sh C o l u m b i a . 1983. F o r e s t r y Handbook for Br i t i sh C o l u m b i a . 4th ed . E d i t e d by S . B . Watts . V a n c o u v e r : U B C F o r e s t r y Undergradua te S o c i e t y . Wi l l i ams , D . H . 1986a. A M o d e l fo r S i m u l a t i n g D e v e l o p m e n t C o s t A l l o w a n c e s . In T h e E c o n o m i c Stock of T i m b e r in the C o a s t a l R e g i o n of Br i t i sh C o l u m b i a - T e c h n i c a l A p p e n d i c e s , e d . D . H . Wi l l i ams , 55 -65 . F E P A R e p o r t 86 -11 , V o l . II. V a n c o u v e r : F o r e s t E c o n o m i c s and P o l i c y A n a l y s i s P r o j e c t . U B C . Wi l l i ams, D . H . 1986b. A M o d e l fo r S i m u l a t i n g T r e e - t o - t r u c k C o s t A l l o w a n c e s . In T h e E c o n o m i c S tock of T i m b e r in the C o a s t a l R e g i o n of Br i t i sh C o l u m b i a - T e c h n i c a l A p p e n d i c e s , e d . D . H . Wi l l i ams , 45 -54 . F E P A R e p o r t 86 -11 , V o l . II. V a n c o u v e r : F o r e s t E c o n o m i c s and P o l i c y A n a l y s i s P r o j e c t . U B C . Wonnacot t , T . H . and R . J . Wonnacot t . 1984. In t roductory S ta t is t ics for Business  and E c o n o m i c s . 3rd ed . New Y o r k : J o h n Wi ley & Sons. Z u u r i n g , H . R . and E . G . Schuster . 1980. M T V E S T - A User 's M a n u a l . A C o m p u t e r  P r o g r a m to E v a l u a t e F o r e s t r y Investment Oppor tun i t i es . Bu l le t in 44. M i s -sou la : M o n t a n a F o r e s t and C o n s e r v a t i o n E x p e r i m e n t S ta t ion and U n i v e r s i t y of M o n t a n a . 86 A P P E N D I X I Input and Output Variables of the Program's Simulators Growth and Yield Simulator (G & Y) Input Var iab le Source Species (1 of 4) U s e r Si te index (m) U s e r D i a m e t e r l im i t (cm) (1 of 3) U s e r Stand age at beginning of s imu la t ion (years) U s e r Ini t ial basal a rea (m^/ha) (optional) User Th inn ing (optional) U s e r - th inning age (years) U s e r - percentage of s tand basal a rea r e m o v e d U s e r F i n a l harvest (optional) U s e r - harvest age (years) U s e r S imula t ion per iod (1 to 100 years) U s e r Output Var iab le For each year of the simulation period: Stand age (years) T o t a l s tand height (m) Q u a d r a t i c mean s tand d i a m e t e r at breast height (cm) N u m b e r of s tems ( /ha) M e a n stand basal a rea ( m 2 / h a ) Stand vo lume ( m 3 / h a ) A n n u a l vo lume i n c r e m e n t ( m 3 / h a per year) M e a n annual vo lume i n c r e m e n t ( m 3 / h a per year) A t each harvest: N u m b e r of s tems r e m o v e d ( /ha) Vo lume r e m o v e d (m^/ha) 87 Timber-log Conversion Simulator (Conv.) Input Var iab le Source Species (1 of 4) G & Y D i a m e t e r l i m i t (cm) (1 of 3) G & Y A t each harvest: Stand age (years) G & Y T o t a l s tand height (m) G & Y Q u a d r a t i c mean s tand d i a m e t e r at breast height (cm) G & Y Output Var iab le For each log of the average harvested tree: L e n g t h (m) T o p d i a m e t e r inside bark (cm) Gross vo lume inside bark ( m 3 ) Log Grading and Revenue Simulators (Rev.) Input Var iab le Spec ies A t each harvest: N u m b e r of s tems r e m o v e d ( /ha) Vo lume r e m o v e d ( m 3 / h a ) L o g qual i ty (1 of 3) For each log of the average harvested tree: L e n g t h (m) T o p d i a m e t e r inside bark (cm) Gross inside bark vo lume ( m 3 ) Output Var iab le A t each harvest: V o l u m e by grade ( m 3 / h a ) Revenues based on 1985 log pr ices ( $ / m 3 and $/ha) Source G & Y G & Y G & Y U s e r C o n v . C o n v . C o n v . 88 Delivery Cost Simulator (DELCST) Input Var iab le Source A v e r a g e stand slope (96) User A v e r a g e o n e - w a y t ruck haul d is tance (km) U s e r Water t ranspor ta t ion sys tem (optional) U s e r - type (1 of 2) U s e r - cos t , wi th a cost base of J u l y 1, 1985 ( $ / m 3 ) U s e r O n e - w a y d is tance (km) f r o m the marsha l l ing a r e a to the nearest U s e r c o m m u n i t y P e r c e n t a g e of the crew l iv ing in the c a m p User H a r v e s t i n g sys tem for f ina l harvest (1 of 4) U s e r A t each harvest: V o l u m e r e m o v e d ( m 3 / h a ) G & Y L e n g t h (m) of each l o g of the average t ree C o n v . Gross vo lume ( m 3 ) o f e a c h l o g of the average t ree C o n v . R o a d densi ty (km/ha) D e f a u l t or User P e r c e n t a g e of the fu l l road deve lopment cost U s e r P e r c e n t a g e of the d i rec t de l ivery cost c o m p o s e d of deprec ia t ion U s e r A v e r a g e l i f e of the deprec iab le assets (years) U s e r R e a l ra te of re turn on c a p i t a l ( / year ) U s e r S p e c i a l r isk a l lowance on de l ivery costs (%) U s e r Output Var iab le A t each harvest, with a July 1, 1985 cost base: D i r e c t de l ivery cost for e a c h of nine opera t iona l phases ( $ / m 3 and $/ha) T o t a l d i rec t de l ive ry cost ( $ / m 3 and $/ha) R e t u r n on c a p i t a l ( $ / m 3 and $/ha) S p e c i a l r isk a l lowance ( $ / m 3 and $/ha) T o t a l de l ivery cost ($/m* and $/ha) 89 Financial Analysis Simulator Input Var iab le R o a d densi ty at th inning (km/ha) A n n u a l road ma in tenance cost be tween harvests , wi th a cost base of J u l y 1, 1985 ($/km) (optional) A v e r a g e rea l ra te of change in costs ( / year ) A v e r a g e rea l ra te of change in log pr ices ( / year ) R e a l d iscount ra te ( / year ) A t each harvest, with a July 1, 1985 cost base: Revenue f r o m logs ( $ / m 3 and $/ha) D i r e c t de l ive ry cost for e a c h of nine opera t iona l phases ( $ / m 3 and $/ha) T o t a l d i rec t de l ivery cost ( $ / m 3 and $/ha) R e t u r n on c a p i t a l ( $ / m 3 and $/ha) S p e c i a l r isk a l lowance ( $ / m 3 and $/ha) T o t a l de l ivery cost ($ /m^ and $/ha) Output Var iab le A t each harvest, in real dollars: R e v e n u e f r o m logs ( $ / m 3 and $/ha) D i r e c t de l ivery cost for e a c h of nine opera t iona l phases ( $ / m a and $/ha) T o t a l d i rec t de l ivery cost ( $ / m 3 and $/ha) R e t u r n on c a p i t a l ( $ / m 3 and $/ha) S p e c i a l r isk a l lowance ( $ / m 3 and $/ha) T o t a l de l ivery cost ( $ / m 3 and $/ha) Va lue of s tanding t imber ( $ / m 3 and $/ha) Ne t present va lue of s tanding t imber ( $ / m 3 and $/ha) When an annual road maintenance cost between harvests is specified: N u m b e r of payments R a n g e of r e a l costs ($/ha) Net present va lue ( $ / m 3 and $/ha) For the simulation scenario: N e t present va lue ($ /ha and , except fo r t w o - h a r v e s t scenar ios , $ / m 3 ) B e n e f i t - c o s t ra t io Source D E L C S T User User U s e r U s e r R e v . D E L C S T D E L C S T D E L C S T D E L C S T D E L C S T A P P E N D I X H Derivation of Equation 39 Equat ion 39 o f S e c t i o n 7.2 is designed to d iscount a ser ies of annual road m a i n -tenance costs o c c u r r i n g between thinning and f ina l harves t . T h e s e costs can change in rea l te rms at a s p e c i f i e d average year ly ra te . T h e der iva t ion has two steps. Step 1 - Present value of a series of annual payments beginning at year zero and increasing at a real rate. A t ime l ine i l lust rates such a ser ies of payments . N u m b e r = 1 2 3 n n + 1 1 I I 1 ! Y e a r = 0 1 2 n - l n Solv ing for the present va lue (PV) of this ser ies of annual payments (AP) star ts wi th equat ion A l : P V = A P + A P ( l + r ) + A P ( i + r )2 + A P ( i + r )3 + . . . ( F T T ) (1 + i)2 (1 + i)3 + A P (1 + r ) n (1 + i ) n ( A l ) where r is the average year ly rea l ra te of change in c o s t s ; i is the r e a l d iscount ra te . E q u a t i o n A l can be t r a n s f o r m e d by mul t ip ly ing both sides by (1 + r) P V (1 + r) = A P (1 + r) + A P (1 + r ) 2 + A P (1 + r ) 3 + . . . (ITT) (1 + i) ( i + i)2 ( i + i)3 + A P (1 + r ) n + 1 (1 + i ) n + 1 (A2) subt rac t ing equat ion A 2 f r o m equat ion A l P V - P V ( 1 + r ) = A P - A P (1 + r ) n + 1 (TTi) (1 + i)n+l t r a n s f o r m i n g the l e f t - h a n d expression of equat ion A 3 91 (A3) P V - P V (1+r) = P V (T+T) = P V 1 - ( 1 + r ) T X + D 1 + i - 1 - r ] 1 +i J = P V (1 - r) (A4) (T+i) substituting the right-hand expression of equation A 4 for the left-hand expression of equation A 3 P V (1 - r) = A P - A P (1 + r ) n + 1 (1 + i) ( i + i)n+l (A5) mul t ip ly ing both sides by (1 + i) to obta in (i - r) P V = A P - A P (1 + r ) n + 1 (1 + i) (1 + i ) " + l (i - r) (A6) Step 2 - Generalization of equation A6 to allow for the first payment at a year other than year zero. Th inn ing does not necessar i l y o c c u r at year z e r o of a s imula t ion per iod , as shown by the f i rs t payment o f the fo l lowing t i m e l ine: N u m b e r Y e a r = 1 T Y E A R T Y E A R + 1 F H Y E A R - 1 F H Y E A R where t is the number of annual payments between the thinning year ( T Y E A R ) and the f ina l harvest year ( F H Y E A R ) , c a l c u l a t e d as: t = F H Y E A R - T Y E A R - 1 (A7) T h e rea l value of the f i rs t annual cost ( A C S T ) (or payment ) at year T Y E A R + 1 is c a l c u l a t e d as: A C S T = A C S T n (1 + r) T Y E A R + 1 (A8) where A C S T 0 is the annual cost s p e c i f i e d wi th year zero's cost base . Equat ion A 6 is designed to c a l c u l a t e P V wi th the f i rs t payment o c c u r r i n g at year z e r o . Now that the f i rst payment o c c u r s at year T Y E A R + 1, equat ion A 6 must be mod i f i ed by mul t ip ly ing it by „ A . / T Y E A R + 1 (1 + i) that ac ts as a d iscount f a c t o r f r o m year T Y E A R + 1 to year z e r o ; by r e p l a c i n g A P by A C S T (the rea l va lue of the f i rs t annual cost c a l c u l a t e d f r o m equat ion A8) ; and by r e p l a c i n g n + 1 ( represent ing the number of annual payments of the f i rst t ime line) by t (its equiva lent in the second t ime l ine) , to obta in P V A C S T - A C S T (1 + r ) 1 (1 + i)t (1 + i ) /• v i x - \ T Y E A R + 1 (l - r)( l + l) = A C S T 1 - (1 +r)t" (1 + i)t (1 + i ) /• wi ^ - \ T Y E A R + 1 (l - r)( l + l) = A C S T (1 + i)t - (1 + r)*' (1 + i)t (1 +0 (i - r)( l + i) T Y E A R + 1 P V = A C S T [(1 + i ) 1 - (1 + r)*] (1 + o T Y E A R + t ( i _ r ) (A9) Equat ion A 9 is equiva lent to equat ion 39 of S e c t i o n 7.2 

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