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Titles included in this collection are listed in the volumes published by the Comell University Press in the series The Literature of the Agricultural Sciences, 1991-1996, Wallace C. Olsen, series editor. FOREST VALUATION VOLUME II OF Michigan Manual of Forestry BY FILIBERT ROTH 1916 PUBLISHED BY THE AUTHOR ANN ARBOR, MICHIGAN CopyricHt, 1916 By Finrert Rorn 21017 TABLE OF CONTENTS FOREST VALUATION. PAGE Js: TNTRODUCTION’ sicisidGig dh ad oA aaa Aad ae ae ca I Ay JLiterature: wavexnciseurdsae wan tues as aerneae panes es I Bk. Scope and Application...........-......00 cece eee 2 T. (Genetal 4 pcceiuen sin dosiitsienedgs cage au ou genie 2 2. Valuation and Statics............ 00... eee eee 3 Be GAPPMCAHION: ..asienik ewiedeud ae eaacien come amet 4 ©. History of Valuation: cxescesexax eeenswewks ee sewn 7. II. ArirHMetic oF Forrest VALUATION... 0.0.0.0. 00 cee eee 10 as, Genétal g. esikescatiaantGesead oh aseae kale eee WAR 10 b. Prolongation, Discount and Rate................+-. II Stimmation of ‘Seriesic cans xc.acenchees sy vavataree II d:.. Present: WValtiG: Of SetieSicle den auada wun soa vate 13 e. Series of Periodic Payments.... ..........20000005 14 f. Sum of Infinite Series.......... 000-0 e ee eens 15 g. Change of Periodic to Yearly Payments............. 17 h. Table of Formulae............0....0:c cece eee eee 17 IIT. AppricaTion OF VALUATION... 0.20.00 000s cere eee eee 19 A. Timber Crop, its Nature and Value...............-. 19 By RRiske in: :Boresttyiaiek.couad goigedbra tected Sag icone nn gees 22 C. Interest Rate in Forestry........-...000-eeceeeeeee 24 D. Valuation of Land or Soil...................00005- 29 a. Cost, Sale—Income Value.............00000 00s 29 b. Cost and Sale—Value of Forest Land in United LACS) rcpt al lad testes. do oped esata baer ia erent 31 c. Income Value of Land in Forestry.............. 32 E. Valuation of Soil and Statics............ 00... e eee 36 a. Relation of Se and its Factors.. ............... 36 b. Values of Factors of Se and Variation in these PAClOTS, get eon eos gd oo argee lade one 38 ty “FheBinal Waeldvor Vira sop sovaise yeu iw 38 2. Thinnings: ascacucexgeca sasedicaines seaeaas 46 3. Cost of Reproduction, c................... 48 4. Current Expenses, €.............0000e ee ee 51 Bi ROtAT ONY. Bay cnais Ateer Shtecicole 4s Phan Besley 54 6. Interest Rate, p........- cece ee cee cence 55 IV FOREST VALUATION cy Actual Walties of Seuwies ea Skies Bieler ie tend d. Appreciation of Calculation of Se. ............ e. Se of the Copice Woods............... re suse scence f. Se in the Selection Forest.... ........... F. Value of Stand or Growing Stock in Even-aged Saath, a. Sale Value of Growing Stock...............0.6. b. Cost Value of Growing Stock.......0 .......05. c. xpectation Value of Growing Stock............ a, Which: Value tool s@ actors suki reuers a eeg spews e. Value of Land and Growing Stock together...... G. Value of Growing Stock of Regulated or Normal OP ESE: bee he ted ach, a tae eet iets alee aa cary a. The Regulated Forest.............0-.020 eee ee b. Expectation Value of Growing Stock of Regulated Normal Forest ..0¢54.¢:a0heewiesdi: cine ec. Cost Value of Growing Stock in Regulated or Notinal: Forest... 4.4062 se ceed aeetaae ews HH. Value of Growing Stock in the All-aged Forest. . a. In the Regulated Forest............ 0.0000 e ee b. In the Irregular Forest...............000055 IV RELATION oF CAPITAL AND INCOME IN ForesTRY.. 22... a. Nature of Income and Profit in Forestry... ......... b. Interest made by the Forest............ .. 2... eee. 1. Interest made by a Single Stand of Even-aged TROTESt. paiinaue $a alertnedn a adie ea alae ee os a. During a Short Period................005. b. During an Entire Rotation................. 2. Rate of Interest made by a Regulated Forest..... 3. Rate of Interest made in Forestry when starting with Bare Land as Capital.................. c. Comparison of Properties with Yearly and with Inter- mittent or Periodic Income....... ......... AS (ROUATON 0.22 0G bts dates ene eerie tae eel eeds a. Rotation for Largest Income................ 0.00008 b. Rotation for Largest Net Rental or Ilighest Rate of IntereSt sh v5 sexo re eek Heda eeeeta dae ow NSE NABI OE SU UMPAGE: Sonu. Gada igeed phoew la teed aici A. Cost Value of Stumpage............. 0.000.000 eee 13. Sale Value of Stumpage......... 0.0.0.0... 00 cee eee C. Expectation Value of Stumpage.................... YABLE OF CONTENTS Vv Vl. DApamer aa Tine ceva dccd waved Svassiee ieee 98 ae “olader Cree ges nichos sya as Seer se biead ale waa 98 b. Young Plantation of Forest ‘Trees.................. 99 @ Older Plantations. - ccc: etaning eee rel cae oe veeelallS 99 d. Ordinary Stand in Wild Woods................-04- 99 e. Young Stands of Wild Woods..................--- 101 f. The lumberman's Case............- 000. c cee eee 102 WILL. “EAXWTION OF RORESTS 4 cigs ca oicdewra reese bel 105 ay. INattire Of Taxation: accc eects aodeciled Gearete ele wacencs 105 b.. Assessment and Ratés..ssec cess dsosav tae eees aenws 105 c. Forest Tax Impersonal.........-........ ee re 108 d. Forest Taxation in Europe...............00eeeeeee 108 e. Forest Taxation in the United States................ 112 f. Recent Reforms in Forest ‘laxation................. 114 g. Basis-or New Tax Lawss ocd ieeesaveg eras eeee dials 115 h. Future in Forest Taxation...............00000e0e 119 TX. Fire Insurance IN FORESTRY. «0.2.0.0. cee eee eee ee 122 x. Ricut Use: oF LANDoc ce seneaanwaws oe eee tees SE OS 128 ae Natire of Wands sscuy deaneeaketinieou dundee ovens 128 by ‘Classification of Lands. :2.0s00500e944)0.e.0ceereee 128 c. Factors affecting the Use of Land................... 128 d. Use of Lands in the Old World.................... 130 e. Land Conditions in the United States................ 13 fa, AAerretltural MSS: icnssigs et aseie piandee uals eh doped oeeeete eae Bose 131 e@. Income)trom Land, suis. e.0dy diawore ee eee ee 133 1. Income from Farm Lands..............-.-..-. 135 2, Income from Forests... 0.5 0.05.-ce ene eres 138 3. Income from Range..............00.. paeeeranat 140 APPENDIX: cig eee Gide iaeles Oe Wie Ae wi eee eee OU eee on 143 A. Normal, Yield: Tables: .:.cigcnsause eee eee spe TAS B. Tables for Prolongation and Discount.............. 157 C. Suggestions for Problems for School use............ 167 FOREST VALUATION I. INTRODUCTION A. LITERATURE. Endres, Dr. Max. Lehrbuch der Waldwertrechnung und Forststatik, 2nd ed. 1911, published by Julius Springer, Berlin; 308 pp. Dr. Endres is Professor of Forestry at the University of Miinchen, and author of the great “Forst Politik,” one of the most instructive books in forestry literature. On pages 1-4 is given a full ‘list of the literature of the subject. In addition the literature and historic facts of interest are added to all important points in the treatise. An excellent set of tables of compound interest, etc., forms the appendix. As Dr. Endres says (p. 2), “Scientific forest valuation is based on the labors of Faustman, Pressler and Gustav Heyer,” and so it is but natural that this excellent and most complete treatise should follow the works of these three great men and represent what is accepted today as correct and scientific in forest valuation. Stoetzer, Dr. H. Waldwertrechnung und Forstliche Statik, Frankfurt, 1894; 4th ed. 1908. Dr. Stoetzer’s work as author, teacher and administrator, and also as editor of the great Handbuch, is well known. In Valuation and Statics he has stood and stands today one of the foremost authorities. Martin, Dr. H. Die Forstliche Statik, Berlin, 1905, Julius Springer, 361 pp. Dr. Martin is Professor of Forestry at Tharandt, formerly at Eberswalde, author of “Forsteinrichtung,’ a prolific writer, well known teacher and recognized authority. This book is entirely de- voted to Statics of Forestry; its position is defined in the sentence (p. 22), “As to the system and contents of this book, the author closely follows Hundeshagen.” In his introduction, one of the most interesting and instructive chapters ever published on Forest Valua- tion and Statics, he discusses the historic development and points out the fact that the useful study of Statics was opposed in practice 2 FOREST VALUATION chiefly because the writers clung too much to mathematics and formule. The chapter, “Choice between agriculture and forestry in the use of land,” to which thirty-five per cent of the book is devoted is one of the best discussions of this subject and particularly interesting at the present time to students of forestry and economics in the United States. Schlich, Dr. W. Manual of Forestry, vol. III, 1895, 4th ed. 1911. A brief chapter, fifty-nine pages in the first edition, following closely the treatment by German authors. Schenck, Dr. C. A. Forest Finance, published by Dr. Schenck, Biltmore, N. C., 1909. Chapman, H.'H. Forest Valuation, Wiley & Sons, New York, TQ15; 310 pp. Professor Chapman treats the subject from the American stand- point, and adds a number of topics not ordinarily treated in this connection, particularly, Appraisal of damages; Forest taxation; Stumpage values; Future values of forest products, and Risks. Convenient tables of the various formule, compound interest values and logarithms form the appendix. Fernow, Dr. B. E. Forest Economics and Forest History. Dr. Fernow, now Professor of Forestry at Toronto University, himself a student of Gustav Heyer, points out the historic develop- ment and the application of Forest Valuation and Statics. B. SCOPE AND APPLICATION OF FOREST VALUATION AND STATICS. 1. General. In Forestry, just as in farming and other lines of business, nearly every transaction involves expense and income and demands judgment of values. If a piece of land, the timber on the land, or a piece of forest (land and timber together) is bought, sold, rented, leased, or in any way contracted for, the first question concerns the value of the property under consideration. If a forester plants an acre of land to forest trees the owner wants to know what such work should cost and if under the particular conditions it may be expected to pay. Since it may take the crop fifty or more years to grow to useful size, the question as to whether it will pay or not involves the future and the owner must of necessity have faith in certain premises. He must believe that the trees will grow and VALUATION AND STATICS 3 thrive on the particular site, that a certain amount of expense will suffice to care for them, that they will reach a useful size in a cer- tain time, and finally, that they will have a definite value when cut. If he has no faith in any of these premises it is an inexcusable “gamble” for him to plant the trees. But to have faith in business premises is not peculiar to forestry; a man buying a farm believes that the land will produce certain crops, produce them in ten or twenty years just as now, and that the crops have a certain value, justifying his labor and expense. Some years a dry season, frost, hail or insects destroy most of his crops, but in the long run he main- tains a successful average. 2. Valuation and Statics. When the buyer estimates and examines a stand of timber which he intends to cut over at once, he merely determines the value for immediate use and the work is one of simple forest valuation. When a lumberman buys a body of timber with a view of supplying his business for the next twenty years, the case is less simple. He has to reckon with the future and with many uncer- tainties; the timber may be old and become defective before he is ready to cut; fire and insects may destroy; certain railway develop- ments which he expects may not take place; the prices of timber may not advance; taxes, interest, or other expense may eat up all the expected profits. It is a case of nice judgment in which the differ- ent factors and conditions are estimated, if possible, in money value and balanced to arrive at a final result. It is a case of weighing various conditions; weighing effort and expense against expected results. It is no longer simple valuation, but complex valuation with a heavy proportion of statics, of the science and art of weigh- ing cause and effect in our case, costs and results. When the owner of a piece of land decides to change from farm crop to forest, he does so because he has weighed the advan- tages and disadvantages of both lines and found that the forest will pay better. This weighing is Forest Statics. The “pay better” need not be in money at all. When a forester decides to give up natural reproduction and plant five year transplants of spruce, he does, or should do this only after careful weighing or calculation. His calculation should show clearly that he may expect a material gain by going to this greater expense of planting. In making his calculation he starts with the cost of planting. This he knows from experience. He figures on 4 FOREST VALUATION a more even stand, more rapid growth, earlier thinnings, more in- come from thinning and on an earlier final cut, saving him several years waiting, use of the land and interest on the value of the stand. Aside from the planting, all seems guess work. But this is not the case; he has the experience of centuries, of thousands of men, of many thousand acres of timber to guide him. He has faith in this experience and decides to plant. His process of weighing possi- bilities is Forest Statics. It computes extra costs and forecasts extra results. It is clear that Forest Valuation and Forest Statics are not sharply separated, that in most cases of valuation more or less statics is involved and for this reason the two are generally treated together in forestry, just as in other forms of valuation. In the above cases the lumberman or the forester might prefer not to go through any tedious process of reasoning, analysis or calculation, and simply “jump at” the conclusion that he could pay ten dollars per acre for the timber, or in the case of the forester that he could better afford to plant than to go on with natural repro- duction. No doubt much of this is done. Some gifted or lucky men succeed, most men lose. The gifted man has his own short method and his results are correct in proportion as he is clever. The aver- age man can not and does not jump at conclusions or guess results if he can avoid it. And it is to help the average man analyze a given case, weigh the various factors and combine them in a scientific and effective manner that modern forest valuation was developed. The importance of this development in forestry is emphasized by the fact that the forester commonly deals with large properties, not his own, where it becomes necessary to place the case before the owner or his agent in a perfectly clear and convincing form. At such a time every item must be clearly stated in a form capable of detailed discussion, the methods of analysis and calculation must be explained and stand the test of examination and trial. 3. Application of Valuation and Statics. As in every other business, so in forestry, the work of valua- tion or the determination of cost or value of property (land, timber, etc.,) or of operations (planting, thinning, protection, logging, etc.,) follows every line of work and is always in evidence. For example its application in a few of the most important branches of forest business : _ I. In purchase, sale and exchange of property, such as land timber, or forest (land and timber together) the necessity of ascer- APPLICATION OF VALUATION 5 taining the value of the property bought or sold is evident. This kind of work in the United States at the present time is very im- portant and will be more important in the future than it has been in the past. The mere cruise for merchantable timber will no longer satisfy men buying and selling forest properties. To sell a forest for the value of the merchantable stuff alone is equivalent to giving away over half the value in many localities and this condition is rapidly extending. 2. Holding of timber for future use is a common practice among lumbermen. In buying for ten or twenty years it is neces- sary to compute expenses, taxes, interest, protection, probable losses, and it requires an estimate or forecast of the price which may be obtained at the end of the period or at the time of cutting. Taxes and interest together with other current expenses come every year and accumulate with compound interest; the final value must be discounted to the present time. There is a right way of doing this and many wrong ways and some of our lumbermen in the Lake Region and elsewhere are finding today that it is not always easy to make a state tax commission see the right way of computing the true value of a lot of stumpage which can not possibly be cut before ten or twenty years. 3. Timber contracts, leases, rights of way. etc., are common and necessary. —. and not $50 + rest because the first income is larger by 15 than the established future incomes. TABLE OF FORMULAE 17 g. Change of Periodic to Yearly Payment. Where a forest property furnishes an income only every twenty years it may be desirable to convert this periodic income into a year- ly one. If this property, on account of the periodic income is worth, or has a safe income value of: $48000 48000 1.03"—17 180—1_ mee and the bank or trust company is willing to accept this as fact and pay the owner a yearly interest on the full $60,000 at 3% ; the owner of the forest would receive 0.03 X 60,000 = $1,800 per year. This may also be stated as follows: $48,000 __ 1800 1.03°—1I .03 Seem or the yearly income, 1800 = $48,000 (0.03) p ~ 1.03%—1 In general then: na Ss 4 OD (ort) “Copy gop" h. Table of Formulae. As above developed. No. ForMuLA. MEANING oF ForMULA. on a Prolongation of initial capital. C. for n years at 1. Cy = Co(1.0p") Pp per cent. ae ee Ca Discount of final capital C. for n years at p is I.0p" per cent. Bp RE hs Final capital C. divided by injtial capital C. to ‘Ge find interest rate p. a(t.op"—1) Sum. or end value of a series of payments a 4 G=$= aLop it coming every year continued for n years com- (1.0Pp—1) pounded at p per cent. Present value of a series of payments a com- a(t.op?—1) ing every year continued for n years com- ir ee PAY pounded at p per cent and discounted at the (1.0p — I) 1.0p same per cent, first payment to come in one year from now. 18 10. II. 12, Ci=$= (1.0p'—1) a(1.op"*—1) (1.0p‘—1) I.op"* Cm (1.0p'—1) rop"* a= = 0.0p A Ce (1.0p'—1) A .op'* Ce (1.0p'—1) A (o.0p) 1.0p'—1 a(1.op"'—1) a(1.op"*—1) 1.op'-* FOREST VALUATION End value or sum of a series of payments a coming every t years continued for n pay- ments “compounded at p per cent. Present value of a series of payments a com- ing every t years continued for n payments compounded at p per cent, discounted at same per cent, the first payment to come in t years. The same as No. 7 but with the first payment coming in x years so that the sum must be prolonged for t—x years. Where x is greater than t this becomes a discount. Income value of a property producing a net income a every year computed by capitalizing the income a at p per cent; or the present value of a series of payments a coming every year continued forever compounded and dis- counted at p per cent, the first payment to come in one year from now. Present value of a series of payments A com- ing every t years continuing forever com- pounded and discounted at p per cent, the first payment to come in t years from now. This is also the income value of a property furnishing a net income A every t years com- puted at p per cent. Same as No. ro but with the first payment coming in x years from now. Changing a periodic rental A coming every t years into a yearly rental a where the value of the property is computed by capitalizing the income at p per cent. Ill. APPLICATION OF VALUATION A. TIMBER CROP, ITS NATURE AND VALUE. Timber was not only important to man in the past, it was a necessity, a basic condition to every reasonable development. With the great progress in manufacture, extended use of iron and steel, especially with the introduction of cement the importance of wood seemed to decrease materially and it was commonly predicted that wood had really ceased to be a necessity. But the actual facts, the consumption per head, the great traffic, export and import of tim- ber, the intimate relation even dependence of many of our industries on a liberal use of wood and the unexpected rise in price of timber, the world over, all flatly contradict the common assertions and prophecy of the past years. (See Fernow, Economics.) The people of Europe use more wood today than formerly and pay higher prices. The timber import into Great Britain more than doubled be- tween 1850 and 1890 and is about seventy per cent greater now than in 1890, having exceeded one hundred and twenty millions. Germany, an exporter until 1860, is the second greatest timber importer in the world and this in spite of intensive forestry. France is a growing importer and is exceeded in its import by Italy. In the United States the consumption per head has increased from about three hundred and fiity feet b. m. of lumber in 1880 to over four hundred feet in 1910, in spite of the fact that stumpage and lumber have increased in price by about one hundred per cent. Our railways have not been able to free themselves from the wooden tie, the telegraph and telephone lines use wooden poles, as much lumber goes into ship building now as previously, charcoal iron is still a preferred product, pulp and paper industries demand more wood every year and nearly every new invention, even to the propeller of the aeroplane calls for wood. In keeping with this increased demand for wood prices have advanced for a century. While the price of rye, the stable bread- stuff, in Prussia decreased hy fifteen per cent, the price of timber increased by fifty-five per cent, between 1860 and 1903, and while the income from the field remained nearly stationary the income from forest, state forest, during the same period increased by one hundred and eighty per cent in Bavaria, one hundred and forty- 20 FOREST VALUATION seven per cent in Prussia and by over one hundred per cent for all Germany. Generally the demand is for lumber or larger sizes, and not ‘merely cordwood or quickly grown small stuff. The demand also is more for conifers than for hardwoods; in the United States the consumption of conifers to hardwoods being about three to one. Larger sizes require longer time to grow so that a forester of central Europe does not expect to cut his timber before it is eighty years old, the average rotations for conifers staying close to one hundred years. The forests of the world are limited, the really useful ones amount to about one acre for each human being. In the United States we now have about five acres of woods per head of popula- tion. The population increases and the forests decrease. Even under present conditions the people of the United States are depend- ent for the future on the growth of five acres per head. This growth at present is practically nothing. Even if cared for, it would prob- ably just suffice for the needs of the population as it is at present. This means that the future will demand reduction in consump- tion regardless of all human efforts. With this reduction will come further advance in price. In many localities this reduction has al- ready come, the supply of raw material for hundreds of mills is gone and from the state of Michigan alone industries with over sixty million dollars investment have disappeared in the past twenty years. The whole Lake Region, New York, Pennsylvania, parts of the South and parts of Canada share in this change. In many local- ities over large areas the change has been from industrial prosperity to utter desolation, so that towns have been deserted, railway lines taken up or abandoned. The forest crop has its peculiarities. Categorically stated: 1. The forest takes many years to grow. 2. It can use sand lands, cold, steep, rocky, even poorly drained lands, and so utilize large areas not useful otherwise. 3. The forest improves the land, and protects it against ero- — sion. 4. It is a much more certain crop than the field crops. 5. It is more independent of man, reproduces and grows very well without human effort wherever climate, chiefly moisture, is at all congenial to tree growth. 6. It requires not merely land but involves large investment in the growing stock. IMPORTANCE OF TIMBER 21 A forester with ten thousand acres of woods properly regulated so that he can cut every year, would cut about one hundred acres of ripe timber. The other ninety-nine hundred acres have timber from one to ninety-nine years old and this body of growing stock is worth about four or five times as much as the land on which it stands. In farming there is very little of this kind of investment, the orchard trees, bushes of smaller fruit and meadow grass resemble it. 7. The crop is not ripened in a week or even a year but may be cut when it is thirty, fifty or a hundred years old. 8. In case of accident, fire, insects, etc., a large part of the damaged timber can be used, providing there are means of getting it out, and a ready market. g. Timber after it is cut is not a perishable material like po- tatoes, fruits, etc., but is improved by seasoning. A body of sawed timber may make from three to five per cent on its value in this way. This gives independence in holding. 10. Timber crop requires further manufacture, sawmill, plan- ing mill, pulp, etc. It stimulates industries. 11. The forest furnishes more material for transportation per acre than the farm. The latter about two hundred and fifty pounds per acre, the forest about one thousand pounds. 12, The forest requires little help, therefore making larger net income. 13. From all ordinary and inferior lands the forest makes as large a gross income as does ordinary farming at present prices. 14. To the rural people the forest is a necessity to preserve sufficient independence with regard to fuel and building material. 15. The forest prevents erosion, agriculture leads to erosion. The forest is the only large agency at the disposal of man to influ- ence the flow of water in streams, safely, effectively and permanent- ly. In mountainous countries where the forest, because of the to- pography, covers seventy-five per cent of the land it is the greatest factor in water distribution. 16. Forest influences evaporation and rainfall, protects, locally, against drying wind. It encourages bird and insect life and tends to maintain a biological equilibrium, helpful to man, especially in agriculture. 17. The forest is the greatest and most important feature of the beauty of the earth. Thinking man will never wish to do with- out the forest wherever it can be made to grow. 22 FOREST VALUATION B. RISK IN FORESTRY. The following statement is made with an apology; it is not made because there is any special risk in forestry, or that forestry is less safe a business than farming or other industries. It is made because there is a very strong prejudice in the United States and because this prejudice is constantly being fostered and its arguments repeated in legislatures, among timber owners and others, as an excuse for not doing their simple duty to the country and the for- ests they control. The people of central Europe do not discuss the risks in forestry. They have practiced forestry for more than five hundred years. But many of the people of the United States who have never practiced forestry at all, who still prefer to let the native forests burn up rather than make any kind of adequate effort at protection, are fully convinced that forestry is not practicable be- cause forest fires can not be stopped. In speaking of risks, it is ustially the fire danger which is in the minds of the people. As is shown in detail in the chapter on fire insurance in forestry, this danger is universally overrated. For forty years the matter of forest fire insurance has been agitated abroad, but in spite of the fact that some good companies are ready to take up this insurance at $1.80 per $t,o00 property, the forester generally has not felt the need of insurance and at every meeting where this is discussed it is pointed out that the actual losses from fire, even in the pinery districts of North Germany do not amount to more than one-tenth the amount of this premium so there is no reason why large owners should spend their money in this direction. The statistical reports of Baden and Wiirttemberg do not find it necessary even to mention losses from fire, and Bavaria for years staid below four cents on the thousand dollars worth of woods. In the United States without any effort to prevent the fires and with many people eager to get rid of the forest, burning the forest intentionally, the losses from fire have been very great. The report of the United States Commission of Conservation in 1909 gives the estimated losses per year, since: 1870, at about fifty million dollars for saleable material. This is about ten cents per acre per year and therefore not far from the premium rate now demanded by the Ger- man insurance companies, so that it was as cheap to let the woods burn as it would have been to insure them in up to date companies, even if this could have been done. It is evident then that even in the United States in spite of all neglect, lack of law and law enforce- ment, in spite of land clearing, etc., which made burning necessary, the fire losses in the forest are relatively small. Had they been RISK IN FORESTRY 23 spread over all forests evenly instead of being concentrated at cer- tain points, there would not be the general fear of fire risk in for- estry. As a real menace to forestry insects and wood-destroying fungi are much more serious. Even in the best cared for forests of Ger- many, fungi, producing defects and decay in the timber, and even killing young trees, are a constant trouble. But this is true of the wild woods as it is of the cultivated forest and it is true of the farm crop more than of the woods. One of the greatest tasks of the United States Department of Agriculture and of all state experi- ment stations is to find remedies for the many plant enemies of our crops and fruits. Millions are spent every year by the farmer in spraying, etc., and millions more are lost for lack of effective treat- ment. The same is true with insects; scale, louse, moth, weevil, chinch bug, wheat fly, and potato beetle have, and do cost many millions every year. If the fly gets into wheat, the chinch bug into the corn or the boll weevil into cotton the loss is often complete. An attack of insects in timber, even if severe enough to kill, is only a partial loss, all large stuff can be used, wherever forestry has become a real business with means of utilization and a market. While the German forester is much more concerned about insects and fungi than about forest fires, it does not occur to anyone to think of these difficulties as a risk sufficient to discourage forestry as a business. Weber in the Handbuch and Endres in his Forst Politik made no effort to estimate these losses. Like those from fire in the United States they are great both here and abroad but they even up as they do in farming. To the small owner they are serious, in large hold- ings they form a regular trouble to figure with. Endres (p. 95) mentions the losses from wind, snow, ice and insects, (leaves out fire) and says that in all computation of averages these losses are inconspicuous—“IKommen nur wenig zum Ausdruck.” As regards the growth and reproduction of the crop itself which expresses more properly the certainty or success in crop production, the forest far excels the farm crop. From Michigan to the Gulf, the forest was practically unbroken, there were no large “burns” or other gaps. Nature had reproduced one crop after another, the crops had grown to old age, died and given way to new crops. Windstorms, insects and fungi had collected their toll but the forest was there and asked no help. In the most intensive forestry in Ger- many less than twenty per cent of the expenses are devoted to plant- ing, etc., to protection and care of the crop, about fifty per cent is spent in harvesting. Where the forest has not been abused and where the climate is good the new crop comes in without any help 24 FOREST VALUATION or delay, and even where planting is justified by better returns, this planting makes rarely more than ten per cent of the total expenses on a forestry property. The growth of the forest is quite secure, a dry season may produce less wood, but the next season makes up for it and the harvest of the year does not show the effects at all. Frost, hail, extremes of cold and heat, etc., all affect the forest, but only in a small degree and the cut of the year remains unchanged. Insects may partly defoliate a stand of oak and hurt it quite severe- ly ; but if the stand recovers, as is usually the case, the man who har- vests this stand will never know the difference and the effects of the injury are hardly felt or known by the business. In farming the time of ripening is a critical period; a few days of dry weather, dry hot winds, a hail storm, rain, etc., may largely destroy the season’s yield. Nothing of this kind exists in forestry. If a sixty-year-old stand is not growing well, if fungi have started their work and the stand begins to be defective it is cut and used and another put in its place. In a twenty-year average farming over large areas must be content with about sixty per cent full or normal crop, even in the great staples, wheat, corn, etc., while forestry, where properly prac- ticed at all, produces over seventy per cent of a full crop. In fruit farming it is doubtful if the average crop is twenty per cent of a regular full crop. From this sketch it is evident that the risk in forestry is small, smaller than in farming and much smaller than in most city business. It is this very security which has distinguished the state forests and forests of other large owners and which has made the forest the valuable and desirable property it is. Where the forest is neglected, stocked with poor species and handled by poor methods, coppice in France, for instance, and where mismanagement has left unmade suitable improvements, it is only natural that the value of the prop- erty is small, in keeping with low income. But even in these cases it is not risk but low income, due to neglect, which is the fault. C. THE INTEREST RATE IN FORESTRY. a. General. When a farmer who paid $6,000 for a 100-acre farm finds that for 10 years back he averaged $300 net income per year for his crops he naturally asks—what per cent is this on my investment? If he is satisfied with the 5% which it made he will be satisfied with farm INTEREST RATE 25 business, if he feels that he ought to make 10% on his money he will want to sell out. In this case it is a matter of experience and ae with $300 in- come 5% is what the farm made on $6,000 cost price. If now a man wishes to buy this farm and is shown that the farm made $300 net income per year he may say: the farm is good for $300 per year, is a safe property, I may as well put my money into this farm as keep it in the bank at three per cent. To him the income value of the _ $300 farm is: or $10,000 and he may be satisfied to pay this price. 0.03 To another man who values his money at 6% the farm is worth only half this amount. In this case the three per cent or six per cent are set by the man who wishes to buy the farm and judges its value by the income it makes and a per cent which he determines himself. In forestry, too, these two fundamental cases of determining interest rate occur and very commonly are both present in the same calculation. If a planted stand of pine sixty years old is ready to cut and worth $300 per acre the owner may want to know what per cent was made on the investment. He knows that it cost $10 to plant, that the land cost $20 per acre and that it cost 60 cents per acre each year to take care of the forest and pay taxes. The ten dollars for planting have been out at compotnd interest for fifty-nine years, and the question arises—at what per cent? Evidently it is for the man to choose this per cent. When the calculation is finished and he finds that all expenses for the sixty years amount to $180 per acre he can find the net income and real value of his business. The calculation of what interest rate a stand of timber actually makes or has made is comparatively simple and there is little dis- agreement as to method. But what per cent to assume or set in calculations of forest valuation is quite a different question, and the opinions often differ and have differed since valuation began. To choose a high rate, such as the current rate of interest paid by business men and farmers gives the calculation a business-like air and seems practical. But even the reasonable rate of five per cent will seem to prove most forestry a failure or lead to a demand for absurdly low rotations, etc. To choose a low rate, say two or three per cent, is unpopular, seems to discredit forestry, sounds theoretic and unpractical. But the choice must be made, forest valuation is impossible without it. The man who puts money into land and timber for for- 26 FOREST VALUATION estry must have some reasonable calculation to show what he ex- pects of the business. Tax commissions and legislatures will not change their methods unless shown convincing facts as argument. It is self-evident that the assumed interest rate and all calculations based on this rate have nothing at all to do with the growth of the timber and all these calculations can possibly do is to give a reason- able measure of what actually takes place and compare forestry as a business with other kinds of business. ‘I'he question is—is there a reasonable and acceptable basis for interest rate to set in forestry? b. Interest rates paid and made. In the United States today the ordinary loan pays about 5%, timberland owners and many industrials pay 6% and over, the far- mer pays about 6 % in the east and north, larger per cents in the south and west, so that it was reported in 1912 that the farmer of the United States borrows about 6,000 million dollars at an average rate of 8%. Large railroad companies. etc., pay four or five per cent. Cities and states pay about four per cent on their bonds, the United States Government can borrow at from two to two and a half per cent, and the savings banks with their enormous deposits pay generally three per cent, while millions of dollars are deposited in banks and draw no interest. In Germany mortgages pay about four or four and a half per cent, bonds about 3.4% to 3.8%. Interest rates are higher in new and undeveloped countries, the West pays higher than the East. In the fourteenth century the common rate in Germany was ten per cent, it sank to five per cent by the sixteenth century. After the Napoleonic wars it went up to eight per cent, then it sank to three per cent by 1870, rose again to five and then declined to present rates. 2. The fact that a man pays six per cent on his mortgage is no indication that the man makes six per cent in his business, what- ever that may be. This seems self-evident, and yet it is the most common fallacy in connection with this discussion to assume that because a certain per cent is paid by the men of a certain industry when in need of money this rate is also made or approximated by the industry. a. Since agriculture in the broad sense really includes forest- ry, it is fair to use farm business as a criterion and see what farm business pays. The data for the following analysis are taken from circular 132-A, 1913, of the United States Department of Agricul- ture, and based on the Census of 1910. INTEREST ON FARM 27 The average farm of the United States has 138 acres and is valued at $6,443, including stock and implements. The total or gross income is $980, leaving off cents, of which $860 is the value of the crop, including stuff fed. In the summary on page four of circular 132, the data are ar- ranged as follows: W Talal Sross COM sasore eevee ore eoustensacws $980 SE OFA: EXPENSES! wie) sete g ae se see Lew eee RoE eS 340 Net farint INCOME. «:ccccov.ohs 4d ch edadsaawioeceeeu ewes 640 Interest on investment 5%.......-.. cece e eee e eee 322 Labor income, including unpaid family labor and all the farm furnishes toward the family living except milk and cream. Does not include income from outside sources, and the amount paid for live stock bought must be deducted from this sum”........ 318 “Interest on mortgage, $1,715 at 6%. ..........048 $102 Available for live stock and for family living........ $537” These same data may be arranged as follows, where it is as- sumed that the farmer and his family should receive for their labor at least the wages of one farm laborer without board, since they board themselves, and that it takes $50 per year to replace teams and other live stock. Gross income per years ore evi eeeeseicaverarwienens $980 Expenses : LabO?™ 9.0.0 i-ghe Bild ea Soe ee fates htee sa $102 Fertilizer ssnns ccd cnains a tsi eioiewe dias ae 18 HOEG0 50st covesieche cond acted uses 47 To maintain buildings ................. 49 To maintain implements ............... 39 Taxes, at O69 10... ccc c cece ce eceetes 38 Miscellaneous sa:spvcwtenncoieeeeeawces 44 Salary of farmer and family............ 360 Replacement of live stock............... 50 $750 Netuncome: nce. cue ak er edbia ene kaa aden 4a $230 This $230 is three and a half per cent on the $6,443 capital. If the $102 interest on the mortgage is deducted there remains only two per cent interest actually made by the average farm of the United States in rgto. 28 FOREST VALUATION Since the average farmer with his family can not be engaged at less than $500 per vear and usually demand part or all the gro- ceries for the household paid by the employer it is evident that the above three and a half per cent is too high and it is doubtful if two per cent is actually made. This fully agrees with the findings of Cornell Agricultural Col- lege and with bulletin 41, United States Department of Agriculture, 1914, which shows that the interest made on selected farms in Indi- ana, Illinois and Iowa in 1917 was about three and a half per cent and in cash rent system less than three per cent. It is evident that many farmers make no interest at all and do not even make the com- mon farm hand wages. Whether this fact is explained by saying that farm products are sold too cheaply or that cost of production is too high is imma- terial, the fact remains that the rate actually made by the most im- portant industry of the country and the industry most closely re- lated to forestry is less than three per cent. In Germany farming paid about two per cent, in some provinces only one and a half, in 1899. b. What other kinds of business actually make is little known and much disguised. If the losses and gains of our stores, factories, railways, etc., could be known, and if the natural wealth, timber, coal, etc., could be deducted and also the entrepreneur’s risk and effort, if these could be ascertained, it is doubtful if the business of the country really makes one and a half per cent, even in good times like 1900-1910. Generally it is a fact that the current rate paid by the farmer is not made by the farm, it is equally certain that as an average it is not made by other business. To employ or set the current rate as measure, then, would discourage most of our ordinary industries. c. What rates a good forest business makes is well illustrated by the state forests of Saxony where the rate actually made has been 2.3 to 2.6% for over forty years. Since a great deal of forest prop- erty is assessed on a basis of income and an assumed rate of inter- est this interest rate in Germany frequently is an argument in circle. d. Germany today uses an interest rate of 3% or less, in Baden 2y4, in all calculations of values of land, timber or forest. e. In adopting an interest rate in forest valuation we have the choice and say: 1. Adopt a rate which the ordinary forest business can make, which encourages the improvements and methods necessary for a secure paying enterprise. ‘The best measure and basis is the farm business. VALUATION OF LAND "29 2. Adopt a rate which the business can not make, which tends to abandonment of land and great loss, which even under good con: ditions discourages all improvements and all better but more ex: pensive methods. Germany, Switzerland and Denmark have, unconsciously chosen the first, France and England the second, England has no forests, France little and mostly poor forests. See also Professor Kirkland’s article on the influence of the interest rate on timber production. Washington University Forestry Club Annual, rg15. D. VALUATION OF LAND OR SOIL. Generally, land is valuable in proportion as it produces rent. A city lot is valuable owing to its location, a field or forest land is valuable owing to the crop it can produce. The value of the crop is the measure of the value of the land. But even in the simplest case the matter is more or less complicated. The value of the crop does not depend only on the kind and amount of the crop, but also on the market and transportation and so on the location of field or forest. Again the same field may be used to raise wheat, corn, hay or timber and for each crop the same field may have a very different value. In farming, nature demands a change of crop and it is im- possible or at least unprofitable to raise wheat on the same area continuously. Generally the crop making the largest income is most trying to the land and succeeds only on good land and at reasonable intervals. Some crops, like tobacco, are very exhausting, while oth- ers like clover and timber tend to improve the land. a. Cost value, sale—and income—or expectation—value. 1. Ifa man bought a tract of land ten years ago for five thou- sand dollars and if the income from this land has paid expenses and interest it is evident that this tract today costs him the original five thousand. Generally however, the case is complicated, the income has been irregular, greater or less than expenses and interest, and so the cost value of a piece of land is not as clear or easily com- puted as it would seem. 2. The sale or market value of land seems to require no ex- planation. It is determined by sales actually made in the district, by supply and demand. It is interesting to see what conditions are most important in determining this sale value. The conditions may be divided as follows: 30 FOREST VALUATION a. Conditions affecting the Income: 1. Conditions which are part of the property itself; area and shape of the property, soil, topography, water supplies and drain- age, improvements. 2. Conditions which are not part of the property, or which extend beyond the property: climate, market, facilities for trans- portation, labor, taxation, character and business of the surround- ing people, and demand for properties. b. Conditions not affecting the income but important from the standpoint of sentiment: Beauty of the property and surroundings, social conditions, church, school, etc., family ties, habits, love of sport, “land hunger,” etc. With farmlands it is often more the second group of conditions, (b) which set the price, so that generally, the world over, farm lands are rated and paid for at a price higher than is warranted by income. But even in forestry it is frequently this second set of conditions which are decisive so that the majority of large estates held as for- est parks today in the United States are held more for love of scenery or sport than as properties for income. The sale value fluctuates greatly with demand for land and is easily affected by “booms.” Jt is an old experience in the United States to see a few land dealers, by means of shrewd advertising, succeed in a few sales at high prices. Whether always bona fide or not, such sales tend to raise the price of land for the entire district, in spite of the fact that there is no justification for this advance in larger crops or better prices. 2. The income value of the land, or expectation value de- pends on the crop, rent or income which the land produces and the interest rate which is assumed or is set by the individual making the valuation. As indicated before: net income = income value 0.0p ’ where p is the interest rate assumed and where the income is a yearly one as in farming. The income itself depends on the conditions enumerated under sale value and the ability of the owner. The interest rate usuall varies with: a. Outside conditions: Money market, location of property (old country as against newly settled districts), good and bad times, etc. COST-VALUE OF LAND 31 b. Conditions of property and business itself: Size of property, term of investment, regularity of income, safety of property and income. b. Cost-value and sale-value of land or soil in forest properties in the United States. Aside from the sales of small woodlots, etc., it is generally true that the land itself is not considered in sales of timber. In the past and even at the present time it is the common practice in buy- ing and selling timberlands to estimate the merchantable timber or the stuff now ready for ax and market and to set a price only on this marketable material leaving out of consideration both the land and the growing stock smaller than merchantable. In many cases even part of the large timber is considered non-merchantable and is not paid for. For instance, balsam, cedar and oak in California, hemlock and balsam in the northwest, Douglas fir and balsam in the northern Rockies, hardwoods in the northeast, gum and other hard- woods in the south. Generally, then, the cost value and the sale value of forest lands in the real forest districts of the United States is practically nothing. In the Great Lakes Region millions of acres were simply abandoned by the lumbermen after the timber had been cut and allowed to re- vert for non-payment of taxes. Of late these lands are turned over to some land company, often the same men, to sell to settlers. In the south millions of acres of cutover lands can be bought at less than three dollars per acre though there is a remnant of tree growth usually worth the price paid for the land. Michigan and Wisconsin and Ontario have sold millions of acres in the last twenty years at prices generally not over one dollar per acre and in these cases, too, the land was bought more for the remnants of timber than the land itself. New York bought over one and one-half million acres of land, over seventy-five per cent covered with timber, at about three dol- lars and sixty cents; Pennsylvania bought about a million acres at two dollars and twenty-seven cents; Pisgah forest of eighty thous- and acres was bought in 1914 at five dollars for land and timber and over thirty thousand acres in the White Mountains were bought at about four and a half dollars an acre, though in both cases nu- merous old abandoned farms were included, and the remaining tim- ber is worth the price paid. In 1915 a tract of over thirty-six thous- and acres in North Carolina was bought at one dollar and ninety cents an acre for land and timber. 32 FOREST VALUATION c. INCOME VALUE OF LAND OR SOIL IN FORESTRY. Expectation value of soil or Se. When a man buys land to raise timber and does this as a matter of business and not merely sentiment, for sport or summer home, etc., the case is one of investment and he values the land in propor- tion as it produces an income or crop. In business the income, here net income, which can be made from the land by raising a particu- lar crop, timber, is the only reliable measure of value. To the man who is in the business of raising the crop, whether farm crop or timber, this net income per acre is not only the correct measure of the value of the land but it is also a measure of the work or operation of raising the crop. A good farmer or forester who selects the right kinds of crop, best suited to the soil and climate, cares for the land, sows, tends and harvests well, gets a larger net income than a less competent man. Any mistake or neglect reduces the income and with this the income value of the soil or land. In this way the income value of the land becomes a measure of the value of land and the effectiveness of its management. 1. General method of calculation for Se. In the case of farm property where the income from each acre is a yearly one, the income value of a given acre of land is the net income capitalized. If an acre of land on a ten-year average can produce $10 net income and money is rated at 3% the income value 10 of this acre of land is or $33 330 0.03 Where an acre of land is planted to pine and the pine requires eighty years to grow to acceptable size, the income from this acre comes not yearly but every eighty years. It is a periodic income or _ rental which is assumed as in the case of a farm to come forever. The present value of these net incomes, coming every eighty years is the value of the acre of land. If the timber is worth $400 and it has cost $175 to raise it, the net income is $225 and the pres- ent value of all these net incomes, coming every eighty years, = A = 225 = 225 a (1op’—1) ~ (1.03°—1r) ~ (10.64—1 S a $23.40. which means that this particular acre of land is worth $23.40 when used to raise pine where this is allowed to grow to the age of eighty INCOME-VALUE OF LAND 33 years, where the expenses are $175 during the eighty years, and where the. final crop is worth $400 and money is rated at 3%. That the value of this acre may change if a different kind of timber is raised or if the pine is cut at sixty years, or expenses are lower or higher, or if a different rate of interest is set, is evident. It is clear too, that if the man pays $23.40 per acre for this land and uses it as outlined above, he makes three per cent on his investment and no more. This Se then, is rather the maximum price which he can actually pay. It is evident, also, that these same considerations hold in case of a piece of farmland. The same acre of land produces a larger income with sugar beets or potatoes than with wheat and more with wheat than hay, so that the same acre has different income value in different years owing to change in crops, vield, expenses, etc. Yet this income value is considered the safest measure of value and forms the basis of all farm valuation and assessment. 2. The usual case of Se. a. Premises: Area, 40 acres; method, clear cut, and plant. Rotation r, 80 years; interest rate p, 3%. Cost of planting c, $6 per acre. Yearly expenses, taxes and care, e, twenty-five cents per acre. Yield of timber eighty years old, or Yr, 30 M ft. at $10, $300 per acre. Thinning when stand is 20 years old, T.,, just pays expenses, hence no income. Thinning when stand is 4o years old, T,,, yields 5 cords at $3 or $15 per acre. Thinning when stand is 60 years old, T,,, vields 10 cords at $4.50 or $45 per acre. b. Gross income per acre at end of rotation: Final vield or cut 80 years old, Yr........... $300 Thinning when 20 years old, T2o........... to) Thinning when 40 years old, Tao, $15, with interest for 80-40 years Or SiG(OF")- adanogerwel veo hee teegecegaen 50.40 Thinning when 60 years old, T6o0, -$45 with interest for 80-60 years BF $45. (T03")> «asiarden gues Yo weg ogre 81 34 FOREST VALUATION c. Total expenses per acre at end of rotation. Cost of planting, c, $6 with interest for eighty years or 6 (1.03")...... $ 63.84 ‘Care, protection, and taxes, e, 0.25, coming every year with interest. 6.25 (1.03°—1) (1.03—1) Rotal: x pense 25 causa 36s avant $144.c9 d. The net income per acre at end of rotation: $431.40 144.09 $287.31 per acre. This net income of $287.31 per acre may be and is expected to come every 80 or r years and the value of all these net incomes or the value of the acre of land producing them is: value of land per acre, Se —<"—_ = $20.80 value of 40 acres: $1,192. In the above simple case it is assumed that the plantation suc- ceeds and that it does not require any filling in or cultivation, ete. If such work has to be done it is charged exactly like the plantation itself. Similarly, if there are more thinnings as there would be where intensive work is justified and also where there are other in- comes, such as grazing, turpentine, etc., these incomes are credited and prolonged exactly like the thinnings in the above simple case. It is evident from the above that this analysis is clear and logi- cal that it resembles computations made in other lines of business, requires only ordinary interest arithmetic and that there is no neces- sity for putting it into a formula which often seems to hinder rather than help. Nevertheless it is convenient and makes the matter much clearer and easier to discuss, and to understand the relation and influence of the various factors if it is arranged in a concise formula, and the usual arrangement follows closely the above sample case: e. Formula of Se: Yr + Ta(ropt-a)-+ Tb(ropr-b) + Te(1.0pt-¢)— ¢(1.0p")— ABT ees Se= (1op—1) (1.0p"—1) where Yr is the stumpage value of one acre of timber r years old: FORMULA FOR SE 35 Ta the stumpage value of the thinnings from one acre a years old, etc.; c the cost of planting, or otherwise reproducing, one acre; e the regular yearly expenses of tax and care for one acre of land; r_ the rotation; p the interest rate employed or assumed ; Se the expectation or income value of one acre of land or soil.* (1.0p" — 1) In the above formula the term e ——-———— may also be writ- (J.op — 1) e e ten ———__ (1.0p' — 1) == E(1.0p'--1) where E=—— = (1.0€p — 1) .Op capitalized so that E is a sum of money which will bear a yearly in- terest e at p per cent and therefore, if put out at interest will “take care” of the regular yearly expenses e. The formula then may also be written: _ Yr+Ta(t.op™*))+...... etc. — c(1.0p" )—FE (1.op"—1) Se (1.0p"—1) which may be and usually is simplified into: _ Y¥r+Ta(top'")+...... etc. — c(1op") — Ee (1.0p"—1) Se *lt is of great help to the student to use these terms or symbols con- sistently and use no more terms than are actually necessary. ‘lo use ¥ and Yr interchangeably or use Yr for one acre and for a given area of many acres. etc., soon confuses even able students. Where new cases come up, especially cases which are not really standard, but exceptional, it is much better to write out fully what each part means and use the full analysis, as in the above sample case, rather than try to force it into a formula. ** This formula is written by Endres as follows: _ Yr+Ta(top™")+........ etc. —c Se (1.op"—1) which means exactly the same but changes the order for c so that it confuses the beginner and the general student. As stated before, the average student will find it helpful to stay closely with the simple forms and write them out in full so that the formula shows clearly just how it was derived. 36 FOREST VALUATION E. VALUE OF SOIL AND STATICS. Just as in farming, so in forestry, the net income is larger on good land and with good management than on poor land or with less efficient work. Since the income value of the land is the net income capitalized at an arbitrary, accepted per cent this income value serves as a measure of land and management. With the ex- penses constant, or what may be assumed the same, with the same kind and quality of management, the income and with this the in- come value increases only with the quality of the soil; the better the land the greater its income value. Similarly, on the same acre of land the income and with this the income value of the land increases with the efficiency or quality and correctness of the work and man- agement. It is interesting to see how the income value of the soil differs with change in the various factors, what these several factors de- pend upon, and how they vary under ordinary conditions. a. Relation of Se and its Factors. 1. Increase of the final cut, Yr, increases the income and therefore the value of the land. -Since Yr is the value of one acre of timber r years old it is evident that everything which increases this Yr, such as good planting, right thinning, good prices, cheap logging, etc. also increases the net income and income value. 2. Thinnings not only increase the total income but as they come long before the final cut can be made, twenty to sixty years in ordinary cases, they help to bear expenses which are piling up at compound interest. A good thinning practice raises the quality of the final cut and so increases Yr; a very severe thinning practice may cut down the Yr in volume and if too early also in quality. 3. Cheap planting or small c means small expenses, for every dollar spent, even at three per cent, becomes nineteen dollars in a hundred year rotation. But if cheap planting means poor planting it may lead to a poor stand, reduce the income from thinnings and cut down the final cut or Yr. A large c, therefore may mean larger income. From the formula it is clear that whenever c (1.op") is larger than Yr-+ Ta (1.0p™4), etc., the term becomes negative, a condition which applies to practically all young stands. 4. The current yearly expenses for taxes, protection, etc., ac- cumulate with compound interest and reduce the income. They are FACTORS OF SE 37 generally small in forestry and their importance in the business is easily overrated. Where cheap protection means unreliable protection, the kind that fails in danger season, the saving in current expenses is the proverbial penny wisdom. As appears from the formula, the capital- ized expenses E affect the income or the income value of the soil uniformly; they are constant regardless of rotation and so do not cause the maximum of income value to come either earlier or later. A glance at the formula shows that whenever E is greater than Yr-+ Ta(1.0p"-*) etc. —c(1.0p") (1.0p"—1) the business is carried on at a loss and the income value of the soil becomes negative. 5. The rotation, r, affects the value of the crop and in this way the net income and income value. In spruce, pine, maple, etc., a five or ten year rotation would mean a final cut of mere brush of practically no value. Even a twenty year rotation would in most cases not even pay for the plantation. For these short rotations then, Se is negative regardless of quality of land or management. In the above cases the business would just about pay expenses at a thirty year rotation ; the income value would continue to increase and reach a maximum at about eighty years. After that the expenses, planting and current expenses, together with the discount would grow faster than the timber and Se would decrease, in spite of the fact that the final cut would be larger at one hundred years than at eighty years. The following figures for spruce site III (Endres, p. 275) illus- trate this: At three per cent Se is: Age, or rotation years 30 40 50 60 70 80 90 100 110 120 Income value of land per acre, Se..... $ ~—14 13 38 53 50 50 56 51 46 41 which shows that even in the German forest and at three per cent a rotation of thirty years leads to loss and negative value of Se of $14 per acre; that Se increases with increase in rotation up to sev- enty years, declines after eighty years and reaches a value of $41 with a 120 year rotation. 6. The interest rate, p, which is assumed in these calculations greatly affects the results. If in the sample case outlined above the 38 FOREST VALUATION interest rate of five per cent is set instead of three, the Se of $20.80 changes to a negative quantity ; i. e., the same land and management which gives to the land an income value of $29.80 per acre becomes a losing business to the man who values his money at five per cent. The same is illustrated by the following figures for spruce, site II (Endres, p. 274). The income value of the land, Se, with an 80 year rotation is at Be Gis ay eau ns nisin ro ee eae $105 per acre sas Teh ted iG a meadseyaestneen 9 ha de kak 173 per acre Doses arte ate cy sremeaatihale sin eats 285 per acre b. Values of the Factors of Se, and Variation in these Fac- tors under different conditions. 1. The final cut, Yr, depends on the growth to produce the crop and on market to pay for it. a. Both site and species affect the final cut. These possible variations are laid down in the yield tables for different species at least so far as volume and size or quality are concerned. In the more modern tables and for the settled conditions of the Old World they are commonly worked out for money values or made into mon- ey yield tables. The yield tables giving size and volume of timber per acre have been a matter of experience and growth. Even for the different districts of central Europe they are being improved continually and will be modified further with better methods of sil- viculture, added experience and more accurate and extended statis- tics. Nevertheless, for central Europe they are good now, quite the best we have; they are more reliable than farm yield tables and far surpass in safety the forecasting of ordinary business enterprises. In all new forest districts including the United States, data for yield tables are gradually accumulating. As a beginning the practice takes what it finds in the wild woods and the assumption is that what nature has produced unaided will be produced again on the same land and by the same species. Since the wild woods generally do not produce as much timber nor as good a quality, for ordinary rotations, the figures of yield and growth are conservative. This is doubly true of money vield tables. In fact money yield tables for most parts of the United States where they are based on present stumpage prices are conservative to the point of uselessness, as is clearly shown by comparing present stumpage prices with those of twenty-five years ago. VARIATION IN YR 39 b. The influence of site or quality of land, including climate, etc., is very great. Endres, (p. 94) using Lorey, Weise and Baur’s tables gives the following figures for the one hundred-year-old stand of timber fully stocked: Yield per acre.| Relative figures or per cent for different sites. On site I Cubic feet. I II Ill IV V PAnesasn eos 9200 100 7 61 48 38 Spruce .... 16000 100 81 64 49 35 White fir .. 17200 100 81 64 49 _— Beech ..... 10400 100 84 65 49 33 Since this classification itself is really based on arbitrary but generally accepted figures for the volume of timber per acre at a given age it may be said that the above figures are an argument in acircle. But the important fact is that in actual practice the forester deals with lands on which the yield at one hundred years differs as above. The figures clearly show therefore, the great influence of the site on the same kind of timber. That the influence of site is just as great in the United States as in central Europe is certain: the western yellow pine in the Black Hills makes a two or three log tree and yields about five or ten thousand feet per acre, while in parts of California and Oregon it is a six to eight log tree yielding forty thousand feet and over. The influence of site on the money value of the final cut, the Yr of the calculation, is even greater than on the volume, since the quality and price are largely matters of size and good land produces larger timber in the same time. Schwappach in his tables of 1902 gives the following for spruce, one hundred years old: Volume of site I per acre is 13800 cubic feet, its value $2,085 ; putting the val- ues for site I equal to 100, the relative figures for the different sites are: SiteS.cs sas eennawee cess I II III 1V Volume: weenie cegenesens 100 85 65 5D Value per acre......... 100 75 54 36 so that site IV produces half as much timber in volume, but only a little over one-third in value. In pine the average price per 100 40 FOREST VALUATION cubic feet of timber in the stand 120 vears old, in Prussia is given by Schwappach (pine, 1908, p. 144) as follows: DIE Ty casvecus atawitee earnna $12.00 per 100 cubic feet Site TM asad aiek assanne eta seeres 11.20 per 100 cubic feet Site TU «33.0 araswaees dae 9.10 per 100 cubic feet Site LW -suseess whee saves es 8.25 per 100 cubic feet Sites Vo Se Sains 6.60 per 100 cubic feet These figures well illustrate the effect of site on size, quality, and price of the material. The final cut in practice and for large areas involving a variety of sites is best illustrated by the cut in the German state forests. According to Endres’ Forst Politik, p. 96, in the year 1900 the cut for the state forests was set as follows: cubic feet of stuff three inches and over, per acre of forest area: Baden sancta cae aaeeiies aoe d 73 cubic feet Wiittemberg ........--.....5. 71 cubic feet SaXORV cud ac ceweoieuadmensed 70 cubic feet Bavaria; aisccaeaaaniea.iaeared 60 cubic feet Prussia aowawaewadaueeenenen 43 cubic feet Which means about sixty or sixty-five per cent of what the yield table calls for, on a basis of site III and the usual rotations. Since this condition is rapidly changing owing to the conservative cutting in the past, the later figures for Wtirttemberg are interest- ing. In the three years 1906-1908, the cut of the state forests aver- aged one hundred and three cubic feet per acre of woods. Of this about one-third is hardwoods, mostly beech. Using beech with one hundred and twenty year rotation and spruce with ninety year rota- tion, and assuming on an average forty per cent of area site II, and sixty per cent site ITI (very nearly the actual condition as reported by Graner) the cut according to Schwappach’s tables should be one hundred and forty cubic feet to be full or normal. Being one hun- dred and three cubic feet it is seventy-three per cent of normal, or in other words, the practice today in Wurttemberg is seventy- three per cent efficient, or successful. Since the cut is increasing in all states it is clear why the state forest authorities of Bavaria in their late instructions consider seventy-five or eighty per cent a pos- sible goal. VARIATION IN YR 41 c. The value of the final cut, Yr is greater for spruce than for pine, greater for pine than beech, etc. The following German fig- ures for site II, age one hundred years, ilustrate this: SPMUCE:, isiaranccwcnnewee wade aceon $1563 per acre Pin: ook Sheers cntse wees 627 per acre Oak: tiseaudeed wblessoesoses 377 per acre Be@Gh:. 2vawe eden s sna onsen 347 per acre While this comparison is not quite fair, since oak does not really develop quality until after one hundred vears, yet it bears out the general experience that the hardwoods do not make the values like conifers, and that tolerant conifers produce more value per acre than intolerants. When it is remembered that the land producing pine is generally poor sand, while oak land is good loam or clay, commonly fair agricultural land, the above comparison is even more impressive. d. The final cut depends on the methods of silviculture. A slow, long drawn out, natural restocking of the land wastes time and can not possibly produce the same volume and value of Yr which a good prompt reproduction does. Defective or imperfect cover at time of reproduction wastes space and leads to irregular stands where some trees have too much, others too little room and light. Very dense natural reproduction leads to dense stands, great com- petition, and if no thinning is practicable, leads to great loss of material by death and decay, loss of growth, and, besides producing less healthy and safe conditions, it leads to smaller timber, small volume and value of Yr. A good planting practice assures prompt reproduction, proper spacing, healthy growth, safe conditions, and with these, larger and better timber and larger Yr. A saving of five years in the rotation or what amounts to the same, a Yr five years. better in size, volume and value may be secured by good planting. Mixed stands have often been claimed to produce a larger cut per acre. The proof has never been furnished; the practice abroad does not believe it, the pure stand is gaining and not losing ground. Mayr was right in pointing out the poorer development of crown and waste of space on the line of contact between different species such as beech and spruce, etc. Clear cutting methods save in logging and so increase Yr. On good ground with proper improvements, roads, etc., the skidding is saved and buyers haul directly from the area. In parts of Ger- many this item alone offsets the cost of planting. Methods like the coppice produce small, cheap stuff, often difficult to market. The 42 FOREST VALUATION general experience of France with its non-paying coppice woods on relatively valuable sites clearly proves this. The regular timber forest with retations over sixty years alone makes a satisfactory Yr. e. Up to reasonable limits the final cut varies almost directly with the length of the rotation. German experience indicates that for pine, spruce, fir and beech a one hundred and forty year rotation produces as high a Yr as is likely to be produced by any higher rota- tion. The difficulty of keeping the stand intact and growing is very great and generally demands the cut before one hundred and forty. While the effects of the methods of treatment, silviculture, on Yr are quite well understood and fully recognized, their estimate in dollars and cents is not easy. This is especially true of the effects of thinning, and it is one of the important tasks of the forest ex- periment stations today, to gather reliable data based on careful ex- periment. Schwappach has made an effort to estimate the effects of thinnings in beech and spruce, and to a less extent in pine, but these efforts are still tentative. That a full and clear appreciation of these facts really constitutes the most important part of a for- ester’s judgment regarding his business, is self-evident. f. The market with its prices and grading determines the value of the crop when once it is produced. In the United States the market is irregular, uncertain and localized; it is excellent in New York, Boston, Chicago, etc., but poor in the forest districts. Most of the timber has to be transported over long distances and the price at the mill and in the forest is low as a result. Cypress goes from the Gulf to the northern states and east; red fir, sugar pine and red- wood are railroaded clear across the continent. A good telephone pole or a 1,000 fect of good pine retail for as much money in the towns of southern Michigan, Ohio or Indiana as they do in Germany. But an enormous supply of merchantable or mature stuff ready for the ax encourages destructive competi- tion among manufacturers so that while good quality pine is retailed in Michigan as high as one hundred dollars per thousand feet it may be sold by the manufacturer in California or Oregon for less than cost of production, leaving no Yr at all for the stand in the forest. These conditions are rapidly changing and the value of the stand in the United States as in Germany will be determined largely by the cost of growing the timber. As it is, the stumpage price or unit price of Yr has increased rapidly being now more than one hundred per cent greater than twenty-five vears ago. STUMPAGE IN EUROPE 43. In Europe timber prices have increased for one hundred years past, they have practically doubled between 1830 and 1890, but have remained rather constant since that time. The following figures from Endre’s Morst Politik, p. 120, will illustrate changes in price of timber sold from state forests in Ger- many. Average price in dollars per 100 cubic feet solid, paid in the state forests of! Average Prussia Bavaria Baden Pease for the All wood All wood All wood pee years $ per 100¢. ft.] $ per 100 c. ft.| $ per 100c. ft 5 anid Oat " $ per 100 c. ft. 1830-39 2.50 4.60 1840-49 3.00 ate acd 5.70 1850-59 3.20 3.50 4.10 6.40 1860-69 3.80 4.10 6.50 7 .QO 1870-79 4.40 5.20 7.90 9.20 1880-89 4.40 5.00 6.40 9.30 1890-99 4.90 5.80 7.60 10.20 1900 6.60 7.00 8.70 11.80 These prices were paid for the timber cut or cut and piled, in part at least, skidded to the road, i. e., in the form in which the tim- ber is usually sold by the authorities. Log timber is usually sold full length, cordwood is piled in the usual way. Prices for pine in eastern Prussia in sound clean sticks contain- ing thirty-five cubic feet or more according to Schwappach, 1908, p- 143, are $13 to $15.40 per 100 cubic feet solid, or about $16 to $19 per thousand feet b.m. actual stumpage. Tor spruce, Schwappach gives the folowing prices: Logs:class: I sive eiia vere $20.40 per M. feet bm. stumpage Logs class IT .............0- 19.20 per M. feet bm. stumpage Lows class: ITI cuiccscanes 18.80 per M, feet bm. stumpage For oak in Prussian state forests the same author gives prices as follow for logs cut and skidded: Logs over 24 inch diameter $42 per 100 cubic feet or $53 per M. feet bm. Logs 20-24 inch diameter 35 per 100 cubic feet or 44 per M. feet bm. Logs 16-20 inch diameter 28 per 100 cubic feet or 35 per M. feet bm. Logs 12-16 inch diameter 17 per 100 cubic feet or 22 per M. feet bm. . For beech saw timber Schwappach uses the average price of $7 per 100 cubic feet or $8.90 per M feet stumpage for north Germany 44 FOREST VALUATION and $2.10 to $4.90 per 100 cubic feet solid for cordwood and small timber, also on the stump. Average prices for log timber cut and usually peeled and skidded, i.e., ready to haul from the woods, in the state forests of Wurttemberg were as follows: Oak Conifers $ per 100 c.ft.| $per M. ft.bm.} $ per roo c.ft.|$ per M. ft..bm. 1880-84 17.70 22.25 9.00 II.50 1885-89 17.40 23.00 9.50 11.60 1890-94 24.00 30.00 10.50 13.20 1895-09 24.60 30.75 12.80 16.00 g. The cost of exploitation and transportation are intimately associated with market and greatly affect the value of the final cut. In the United States the cost of getting the timber cut, skidded and hauled to the railway, landing, etc., has not changed very much in spite of the great variety of conditions under which the work must be done. A cost of from four to six dollars per M feet of logs would probably include seventy-five per cent of all operations. Nor has this cost changed materially in the last twenty years. Generally the employment of machinery and the utter disregard for the safe- ty and condition of the forest have enabled forest utilization to keep down the expenses of logging or immediate exploitation. Timber exploitation in Europe works with cheaper labor, less equipment and less efficiency. In districts with good and ample road systems it is cheaper than the work in the United States, in all difficult situations and whenever it works over long distances as is the rule in the United States, it is not cheaper and often eats up the larger part of the value of the cut. The cost of exploitation, (Werbung's Kosten), for all timber in the state forests was as follows in 1900: Prussia ...... Psat: $0.98 per 100 cubic feet, or about $1.25 per M. feet bm. Saxony .........05 1.26 per 100 cubic feet, or about 1.55 per M. feet bm. Wiirttemberg ...... 1.33 per 100 cubic feet, or about 1.65 per M. feet bm. But these figures are not readily comparable to logging costs in the United States. The stuff includes cordwood, poles, ties, mine- props, etc. Moreover the material is commonly not skidded, and even if skidded, it is so only for a very short distance, generally less than two hundred yards. TRANSPORTATION AND YR 45 The logging costs in the German states have increased in keep- ing with better wages; this increase is over fifty per cent since 1870 and the increase continues. Usually the costs vary but little from year to year and so may be estimated very closely. Transportation of logs to mill and of timber and lumber to markets affects Yr very seriously everywhere. In the United States the transportation of logs to mill formerly meant long drives, costly improvements, much loss by “sinkers” and a great deal of risk. Today it involves costly railway construction where the one cut must pay for all improve- ment in this way subtracting heavily from the value of the standing material. Transportation to market in the United States is normally long distance haul. The average haul in the United States for cypress and southern pine may be assumed to be over six hundred miles be- tween mill and customer; for western timber over fifteen hundred miles, and even for Lake states’ stuff over three hundred miles, and this practically all by rail. In Europe too the influence of transportation costs on the price of timber is evident in spite of shorter railway haul and more exten- sive use of waterways. The same kind of timber in east Prussia and Poland sells for fifty to one hundred per cent less than it does in the industrial Rhine districts. The influence of a good system of roads is well illustrated in the Black Forest, while the utter lack of roads in parts of the Alps pre- vents many villages from having any material income from the for- est properties. h. The volume, quality and value of the final cut depends on the care and protection of the stand and the presence or absence of injurious agencies like storm, fire, insects, fungi, drought, snow, sleet, etc. On every large property some of these enemies are at work at different times and it is the rare exception that a stand of timber passes through its entire life of one hundred years or more without suffering more, or less injury. Ftngi and insects are always present and need only suitable conditions to multiply into regular epidemics. Often these enemies are assisted through the mistakes of the for- ester in selecting the wrong species for the site in question, by keep- ing too dense a stand, etc. It is due to these enemies and injurious conditions that most stands of timber, especially intolerants, “break,” or open up long before the end of the rotation and often compel earlier cutting or underplanting, and on poor sites, adoption of shorter rotation. 46 FOREST VALUATION Much of the trouble, particularly from fire, can be averted by proper protection and much can be done hy prompt and frequent thinning and underplanting of older stands on poor, sandy sites. For this reason a saving in current expenses or in caring for the stand may prove false economy by reducing the final cut. 2. Thinnings. The incomes from.thinnings are set down in most modern yield tables for the important species and the several sites and have of late been expressed as money tables. ‘I‘hese tables for thinnings are not as fully developed as the tables for the final yield because of the great difference in the practice of thinnings. Different practicing foresters still disagree within rather wide limits in their views regarding the proper degree of thinning. In addi- tion the market, income, labor, etc., may enable one forester to thin early and often and compel another to postpone thinnings, and to come only at long intervals. Modern practice in good intensive work expects a thinning every ten years and in young stands of oak on good sites five vears is considered a long interval. Like the final cut, Yr, the thinnings vary in volume and value income with species, site and practice. a. Fora stand one hundred years old, on site I, as per Schwap- pach, the sum of all thinnings taken out during the life of the stand and the volume and value of the main stand one hundred years old are as follows for wood of all sizes per acre: Thinnings taken out Main stand Ioo years old i > during life of stand Volume cu. ft.| $per acre} Volume cu. ft.}| $peracre Pine ..... 6550 627 6100 303 Spruce ... II500 2028 10800 450 Oak, oo... 6150 798 7800 535 Beech ... 9200 431 5720 193 Arranging these values of thinnings as per cents of the volume and value of the final cut gives the following interesting compari- son: Thinnings expressed as per cent of main stand or final cut of stand one hundred years old, site J In volume In value Oaks cucesinrn are weedy 126% 67% PING sveceveeenaseseasean8 94% 57% DOPHUCE aeiasa has acceded 04% 22% BeGGH? conn vanes ee awiasdared 62% 459% VALUE OF THINNINGS 47 In oak and pine thinning out of a large volume is necessary, in spruce and beech it is not necessary bit it is possible and desirable. The smaler value of thinnings is due to inferior quality, is most conspicuous in spruce and least in beech where even the final cut is largely firewood. The tendency at present is for heavier thinnings and a larger return from this source. In pine (Schwappach, p. 5) the thinnings in 1889 made about thirty-five per cent of the total growth while in 1908 they made about fifty per cent and the same change is apparent in the treatment of other species. The influence of site on thinnings is ilustrated in the following figures for the stand of pine one hundred and twenty years old: Main or final cut, Sum of thinnings during 120 years old. life of stand. Volume cu. ft. $ per acre Volume cu. ft. $ per acre Site I 6860 774 7540 505 Site IT 5640 600 6650 365 Site III 4550 368 5340 284 Site 1V 3620 268 3940 203 Site V 2760 153 2800 136 From the foregoing figures it is apparent that site greatly af- fects the volume and value of thinnings and also that the difference for different sites corresponds closely to that of the final stand. b. The influence of the method of treatment or silviculture extends beyond the mere practice of thinning itself. A dense repro- duction like good stands of natural reproduction, or dense seeding and planting, call for early thinning. In many localities even in central Europe such a thinning is made at a loss. Thinnings of oak ten years old from usual seeding, also thinnings of beech and even pine and spruce, comie under this description. Here the method, if artificial, by wider spacing may save money in seeds and plants and again save the expense of early thinnings, besides producing larger material in the same period of time. The mixed forest, especially mixture of hardwoods and con- ifers, introduces disadvantages as well as advantages, with the for- mer still prevailing. Thinnings of mixed stands require more judg- ment and care and generally increase the difficulty of selling the material. In hardwoods like ash, hickory, maple, where small sec- ond growth stuff is valuable the mixture may prove an advantage. As stated before, the greatest differences in the income from thin- nings rest with the thinning practice itself. Fifty and more years 48 FOREST VALUATION ago many foresters still believed in the dense stand, removed only dead and dying trees. This did practically nothing to stimulate the growth of the stand, either in volume or quality, and did not relieve the stand of the struggle between individual trees. This method furnished very little of value in thinnings and tended to produce smaller timber for the final cut. As indicated by Schwappach’s tables the modern practice is now taking out as much volume in thinnings as is expected in the final cut and the tendency is for further increase. With a closer utilization and better prices for small stuff it seems a possibility to increase the income from thinnings and in pine, oak and many hard- woods, make it approach closely the money value of the final cut. 3. The cost of reproduction, c of the formula, varies with site species and methods and is greatly affected by enemies, fungi, in- sects, rodents, also by season, storm, frost, or conditions which may not be classed, ordinarily, with site. From a business point of view. as expressed in the income value of the land, it is not enough that reproduction may be accomplished but it is necessary that a new stand be established with certaintv and safety, and in reasonable time. Generally natural reproduction is considered cheaper than planting. In many cases this is true. But if a stand of beech is opened in the shelterwood plan and has perhaps a growth of less than one per cent in value with only about one-half cover it is poor economy to wait ten years and more, as has actually been done even of late years, for natural re-seeding. In some cases where this was observed in 1910 the land readily produces from four to seven dol- lars worth of timber per acre and year so that the expense of ten years waiting would plant up the area several times. a. Artificial reproduction. Schwappach in his tables for pine uses ten dollars per acre as cost of planting on site I and V, the best and poorest lands. For sites II to IV he uses eight dollars per acre. The higher price for site I is due to the troublesome weeds and brush which come into clear cut areas on good land and usually require extra work to keep down. Endres, “Valuation,” uses twelve dollars per acre and Schwap- pach ten for all sites in spruce, for white fir Endres uses ten dollars but evidently he has in mind that much of this is reproduced nat- urally. For pine Endres follows Schwappach and uses ten dollars, but does so for site ITI as well as I. For beech, where again arti- ficial and natural reproduction are both employed and figures for costs are mixed, he uses five dollars per acre. Reproduction of oak COST OF ARTIFICIAL REPRODUCTION 49 in Germany is rather costly since a great deal of protective work, fencing, etc., must be done to prevent damage from game. Yet in oak, as in beech the cost varies from almost nothing in good natural reproduction to expensive planting of large transplants. The great- er part of. oak is started artificially by very dense seeding. Schwap- pach therefore puts reproduction costs in oak at fifteen dollars per acre. For the state forests of Wiirttemberg, nearly five inundred thousand acres, with sixty-nine per cent conifers and forty per cent occupied by beech and white fir where natural reproduction prevails, the official costs of reproduction include: drainage, seeding, whether in the open or to assist natural reproduction, planting of all kinds as well as maintenance of nurseries and purchase of seeds and plants. But it does not include the extra expenses in logging due to methods of natural reproduction, an item which would require estimate from one piece of work to the next and so far is never introduced in forest statistics. The following is taken from Graner, for 1908: Total expense for reproduction $129,000, or 26 cents per acre of forest, of this total there was for (round numbers) : Ty CDitching? teisntend cunts sewed. cere de ae aeaAnet ah Weveeeeaaas $ 1100 2. Seeding, new, 150 acres, corrections 40 acres, cost per acre $1030," GOlal) setcudeage sa Sew oe gens Reis esc hitademieas tele Sek weiss 2000 « 3. Planting, new plantations 4430 acres, corrections 1130, cost per acre $10.03, cost per 1000 plants set out, $3.30, total.... 55800 4. ‘Maintenance of nurseries, 500 acreS .........-.2-00e eee y 49100 Cost of restocking lands or reproduction forms only seven per cent of all expenses as against 12 per cent spent for roads in 1908. The high cost of seeding is due to the large proportion of oak. In thé pineries of Prussia reproduction by artificial seeding has been revived by Splettst6sser and the cost in some cases is less than a dollar and a half anacre. But in dry years this method fails and the cost of successful reproduction by seeding is still uncertain and greater than is usually assumed. For the state forests of Prussia reproduction costs in 1900 were about twenty-seven cents per acre of forest. These expenses have increased from about nine cents in 1870. In the Saxony state forests the average costs for restocking were about twenty cents per acre of forest, including ditching work, having approximately doubled since 1870. 50 FOREST VALUATION In the United States the cost of planting and seeding is very variable. In the eastern states for conifers and most native hard- woods it may be figured approximately : Cost of raising plants: three year seedlings—$1 per 1,000; four year transplants, or 2-2 plants, $3 per 1,000; to set out either coni- fers or hardwoods about $4 per I1.c00. Since 1,000 per acre is quite sufficient, the cost per acre is $5 to $7. To this must be added thirty to fifty per cent for mishaps, bringing the cost per acre to $7—$10, or about the same as the cost in Europe, where, however, much denser planting is practiced. For oak and beech about two to five bushels of seed per acre is used. \Vith acorns at a dollar and a half, a common price, the seeding costs about $10 or $12 per acre. These figures vary with site, lahor, cost of seed, etc., and will be high wherever conditions are adverse to forest growth and call for extra effort. The experience of the United States Forest Ser- vice though the most extensive in this country can not well be used here, since the conditions under which most of this work has been done so far are very difficult, particularly as regards site, accessi- bility, cost of labor, and, in many lacalities, the work of seeding suffered excessively through rodents, which make this method al- most useless. Experience in district 1, Montana, etc., indicates that even here the cost of “effective” or successful planting is now close to $11 per acre, and that much planting is done at about $7 per acre, and seeding at about $2.50 per acre in conifers. But it should be added here that seeding has generally been a failure in these western forests and is largely abandoned. b. Natural reproduction. The cost of natural reproduction is assumed to be zero. This is not true in most cases. If natural reproduction is slow it wastes valuable time, years of rent are lost. If it produces a stand in which a portion of the trees are of poor species and not wanted and this condition requires the cutting out of material at a loss, this expense may very well be charged to the form of reproduction. And even where the natural reproduction is perfect as to species and tiine, but produces dense thickets of stuff which cause extra expense by early thinning or involve years of struggle and consequent loss of growth, the method is certainly not without cost to the owner of the forest. Unfortunately statistics on these points are still too im- perfect to base general statements on. The universal adoption of clear cutting and planting in pine and spruce in German and other forests is the best wholesale evidence that natural reproduction in- volves expense, or, what is the same thing, that artificial reproduc- COST OF NATURAI, REPRODUCTION 51 tion saves money. Similarly, when the best Danish foresters find it to their advantage to spend fifteen or twenty dollars in tilling, liming and artificial seeding to assist so-called natural reproduction, we have here artificial seeding and the old stand is useful only as shelter. In good coppice on good sites the expense of cleaning out use- less sprouts and useless species is small and if need be can be neg- lected. But such saving is poor business on excellent site which should produce from ten to twelve dollars worth of good material per acre and year. In selection forest of our ordinary hardwoods natural repro- duction is quite certain, fairly prompt, but often made up of the less desirable species and either means a loss in the vield or an expense for cutting out this material. In situations where a dry climate, lack of seed, etc., prevent prompt reproduction, the waste by having a part of the land unused for years may be a very considerable expense, as pointed out above. In nearly all cases, except coppice, natural reproduction in- creases the cost of logging. In many cases in central Europe today this amounts to more than twice the cost of planting and should be charged to reproduction and not deducted from the final yield as is always done. In remote mountainous districts where the cold climate retards growth and the site at best produces but a small yield, lodge pole, Engelman spruce, tamarack in swamp, jack pine, etc., the cost of artificial reproduction may not be warranted except perhaps as a starter on burned over districts, and here the natural reproduction in spite of its loss in time and rent may still be the only economical method. And even on better sites in our unsettled districts, western yellow pine, etc., with enormous masses of excellent but unsalable material, natural reproduction may be indicated. But to leave large areas of these better sites entirely bare for many years would be a mistake. This is recognized so that even now planting is being started in many localities. 4. Current expenses, e, usually consist of administration and protection, improvements and taxes. a. Taxes are beyond the control of the owner; they are known and remain fairly constant for large rural properties for many years. In the United States under ordinary settled conditions rural property pays about six. or eight dollars on the thousand dollars worth of property or about twelve dollars on a two-thirds valuation. 52 FOREST VALUATION This will no doubt remain so whether forest taxation continues on the present plan or changes to a yield tax or single tax, for in the end the income or the income value of the forest determines the ability of the owner to pay. b. Administration and protection are usually given together in recent statistics. Endres, “laluation,” p. 38, quotes the following for the state forests of Germany: Prussia, Bavaria and Alsace- Lorain about seventy cents per acre; Baden eighty-six cents, Wiirt- temberg one dollar and five cents and Saxony one dollar and thirty- five cents per acre. Usually about sixty per cent of this goes for administration proper and the rest for protection. Since so much of the under-forester’s or ranger’s time is spent in work where pro- tection and supervision is combined it is impracticable to separate the two. It is doubtful, however, if protection proper is done for less than twenty cents per acre in any of these state forests. Ac- cording to Schwappach, the larger private estates in south Germany spend about forty-five or sixty-five cents per acre and year for ad- ministration and protection. In the United States there are no satisfactory, comparable fig- ures on this point. The total appropriation for the care of approx- imately one hundred and sixty million acres of national forests is only about five million dollars or three cents per acre, a figure which can not be considered here for it does not even indicate a reasonable interest in the property. Of this three cents it is assumed that about two cents an acre are devoted to administration and protection. But everything is new; a large amount of labor is absolutely necessary to survey, locate, map and describe or record things, to enable any administration to be carried on at all, and in addition much work is necessary to attend to the orderly disposition of timber, grazing, etc., so that it is doubtful if much more than one cent an acre is actually devoted to protection and supervision. It is difficult, as yet, to estimate what will constitute a satisfac- factory figure for administration and protection in our extensive enterprises. Recent experience would indicate that protection of the kind that will really protect can not be furnished under ten cents an acre; about half this sum should be allowed for administration if the property is to be properly regulated, inspected and its busi- ness recorded. Undue economy in either direction is costly. c. Improvements in forest properties consist chiefly in roads and besides these in buildings for foresters and rangers, and in tele- phone lines. Occasionally special improvements like chutes, flumes, etc., are provided, but they may well be charged to exploitation and deducted from the gross yield. CURRENT EXPENSES 53 For the most part improvements are developed gradually and the expense for improvement is fitted to the income, and may there- fore remain fairly constant for a long term of years. In the state forests of Europe the construction and maintenance of roads is usually the only item quoted in the reports. In the state forests of Wurttemberg road work in the five years ending 1908, averaged about forty cents per acre of forest and of this twenty-four cents was for maintenance. Ever since 1875 the roads have received over twenty-five cents per acre and year, and while new construction will become less in time the item of roads will always amount to over thirty cents per acre and year. In the United States there is as yet little experience in this mat- ter outside the United States Forest Service and as stated, the Ser- vice has had too little support to do more than make a beginning. On a good forest property with satisfactory market, etc., a suitable road system is a necessity and it is reasonable to suppose that this will cost here what it does abroad. Combining the factors of current expenses for our conditions the following estimate will suit a large part of our forests: Tax€S 2474 dnaimvande ees 15 cents per acre Protection ............+-- Io cents per acre Administration .......... 5 cents per acre Improvements ........... 1o cents per acre Total chen s¢euedas yee 40 cents per acre This should be regarded rather as minimum than average for good, intensive work. That these expenses must be suited to the income or the value of the crop which any tract can produce is evident. From the for- mula it is apparent that: Yr-+ Ta (1.op™@) must be greater than c (1.0p") + E (1.0p*— 1). If we take the value of the thinnings, prolonged, to be equal to one half Yr or the final cut, and use ten dollars for planting and forty cents for current expenses, eighty years as rotation and figure with three per cent, then the final cut must be worth more than one hundred and seventy-five dollars to produce any rent on the land. In jack pine, tamarack, or high mountain timber where the final cut can not be expected to be worth over fifty dollars and in the moun- tain forest requires perhaps one hundred and fifty years to grow, 54 FOREST VALUATION it is evident that planting should be avoided and the current expenses cut to one half or less of the above estimate. 5. The rotation is largey a matter of species, site and market and also of treatment. The first condition is to produce material which can be sold at fair price and in large quantities. Generally, then, the market determines the size and quality while site, species and method determine the time required to produce the demanded size and quality. In central Europe oak requires over one hundred and fifty years, pine saw timber and beech over one hundred and twenty, while spruce and balsam are now commonly cut at about one hundred years. The following figures of age, class, conditions for the timber forests of all Germany are instructive in this connection: Area in 1,000 acres of different age classes in 1900. Over 109 | 80-100 | 60-80 |40-60 |20-40 | to 20} bare years. Oak 244 147 181 | 208 250] 272] 25 Beech 792 823 937 | 816 657] SII} 20 Pine 975 |1133 |1801 2859 | 3319 | 3383] 53 Spruce 403 548 875 |IIQI 517 | 1517 | 17 White fir 150 118 120 | 108 122] 16] 15 Larch 0.3 1.6 5 8 of 9.| — From a financial standpoint the temptation is to set a rotation producing the largest Se or largest interest rate on the business. For spruce in Saxony state forests according to Schulze, the following is true with present prices: Rotation 50-60 years, rate made 5 % 60-70 3.7% 70-80 3.2% 80-90 2.6% 9Qo-100 2.2% But if a rotation of fifty to sixty years was attempted on all Saxon state forest lands the price of smaller sizes would drop and the result would be a failure. Again, for large areas of poor sites, IV and V, such a rotation would not produce marketable stuff at all. INFLUENCE OF INTEREST RATE 55 In fact, according to the same author, a rotation of fifty-five or sixty-five years is most profitable, even with present prices, on only eleven per cent of all forests, while the rest require, owing to slower growth, rotations of over sixty-five and as high as one hun- dred. With better machinery, manufacture of pulp and extensive use of timber in mining, etc., the use of smaller sizes has been increased. In conifers timber ten to fourteen inches d.b.h. with bark can be sold at good price and in largest quantities. In addition the modern practice of thinning gives more space to each tree, stimulates growth and so produces these sizes in shorter time. Accordingly, there is a tendency toward shorter rotations in all timber except oak, where satisfactory quality requires trees over eighteen inches d.b.h. In the United States the timber industries are rapidly adapting them- selves to the use of smaller sizes so that, locally, at least, as small stuff is sawed and worked up as in Furope. In the handling of de- fective stuff the United States methods far excell those of the old world. It is reasonable, therefore, to assume that the conditions de- termining the rotation will be the same here as abroad. With warm- er climate and better growth, shorter rotations such as fifty years even for saw timber are anticipated, established or accepted in legis- lation, in Massachusetts and Connecticut. In loblolly pine, hard- woods in river bottoms, etc.. no doubt this will apply, but in all cases the quality of “grain,” fine or broad rings, will also be considered by the market and may call for denser stands and longer time. 6. The interest rate, p, has been discussed before. Its effect on calculation of the income value of the land and of the success of the forest business is very great. The interest rate actually made in the forest business in the state forests of Germany varies from two to three per cent on the sale value of the property. An interest rate of five per cent will probably prove ninety per cent of European forestry a failure. In the United States at present and for some time to come the unsettled conditions of values in timber and tim- ber lands will make it possible to acquire lands at prices which will assure higher rates. In time the real value of land and timber will approach the true income value and the interest rate made in the business will be normal just as it is in agriculture and other lines of business. ‘To make these calculations reasonable, comparable and useful it would be well if a uniform rate could be adopted and since three per cent has been used extensively in European works it com- mends itself for adoption here. 56 FOREST VALUATION c. Actual values of Se. The following figures are taken from Endres’ Valuation, and Schwappach’s Tables of Growth. The interest rate is three per cent. Income or expectation value of land per acre for different spe- cies and rotations. Spruce White fir Pine Beech Rotation on sites on sites on sites on sites years I II Ill I Ill I III} 1 Ill dollars per acre 30 51 10 ig || ==10 ==30 | 43 —3| 4 —I9 40 100 47 13 67 —5 | 59 7| 25 —4 50 139 77 38 134 25 | 66 13] 32 6 6o 159 98 53 156 38 | 67 13} 35 7 70 166 105 59 156 44 | 64 13 | 35 7 80 161 105 59 145 44 | 59 18] 34 4 a0 I5I 99 56 130 AI 53 8) 31 2 100 138 QI 51 TI4 36 48 5 | 27 2 110 126 83 46 99 30 43 4] 24 —2 120 117 75 41 &6 25 40 2] 21 —4 For white oak in Germany two per cent, the values are as fol- lows for Se: Rotation, years Site I Site II Site III 100 $262 $131 $56 120 272 133 63 140 260 134 60 160 236 124 53 180 215 113 49 200 201 101 44 The above figures are based on normal yield tables of Schwap- pach for spruce, pine and oak, Fichorn, 1902, for white fir, and Grundner, 1904, for beech. They asume cost of reproduction twelve dollars per acre for spruce, ten for fir and pine, five for beech and fifteen for oak. The current expenses are taken at ninety cents per acre and year for all but oak where sixty cents is used. Since the above values are based on normal yield tables, assuming full and sat- isfactory stands, the values require reduction in practice by at least APPRECIATION OF SE 57 the amount by which the practice now fails to keep the forest in fully stocked good growing condition. This for the state forests of Wiirttemberg would be less than thirty per cent, and for most state forests would vary from thirty to forty per cent. An examination of values for Se at three and two per cent re- veals the interesting fact that the maximum for Se comes too early at three per cent, and of course still earlier at higher rates, for a safe technical rotation which works for the sizes most demanded by the present market. On a basis of two per cent the maximum Se and the best technical rotation fairly coincide for all species ex- cept oak where even two per cent brings maximum Se too early by at least forty years. This seems to indicate clearly that the true value growth of the forest is about two per cent for pine and spruce and below two per cent or about one and one-half for white oak in the German forest and present conditions of market. On the other hand a two per cent rate makes forest lands gen- erally more valuable than farm lands of far better quality for all species except oak. In oak even a two per cent rate gives to the land no higher value than the same land would have for farming. d. Appreciation of the calculation of the income value of the land. According to Endres, von Zanthier's articles in Stahl’s Forst- magasin, 1764, may be considered the earliest satisfactory efforts to develop money yield tables and a calculation by which different methods may be compared. The first calculation of the income value of the soil was pub- lished by Konig in his -inleitung zur Holztavation, 1813. His for- mula agrees with the present except that he used c in place of c (1.0p") (1.op* — és. The formula as now used was first developed by Faustman in 1849 in the Allgemeine Forst und Jagdzeitung, under the title Wald- bodenrentenformel, formula of soil rent in forest. The formula has been and is still being attacked in spite of the fact that the basis for the calculation, final cut and thinnings, cost of planting and current expenses are well known, the values, yield tables, etc., constantly used, and universally accepted as the best there is, and as being as reliable as any similar compilations in other 58 FOREST VALUATION lines of business. The calculation itself as a simple problem in arith- metic is no longer discussed. Usually the criticism is one of the three following: a. Forest valuation, in Germany, does not ordinarily start with bare land but with a forest business fairly regulated fer a long timie. There is no deed of any compound interest calculation. This argu- ment seems convincing but is not true. In modern forest practice, excepting selection forest, every acre of forest is cut once in each rotation. Whether this is done in clear cutting in a single year or in shelterwood in several years, the land is cleared of the old timber and a new stand is started. To start this stand and care for it dur- ing eighty or a hundred years costs money and when the stand is ripe, the question is: what has it cost to produce? Since the money spest in planting, protection, administration, taxes, etc., has not paid any interest it is proper that this interest be compounded yearly and charged to the cost of producing the stand exactly as is done in the above calculation for Se. b. The second criticism is that the values for final yield and thinnings are useless, since timber prices advance so rapidly that they may double and more during one rotation. This argument is valid but it does not affect the case at all. If a man examines two farms with a view to buying, he is apt to judge on a basis of present prices and if one farm produces thirty bushels of corn per acre and the other fifty bushels he will consider that the latter is worth more than the former. And he will be right regardless of any change in the price of corn. Exactly the same thing is true in forestry. If Faustman applied his calculation to two tracts of forestland sixty years ago and found one of them worth twice as much as the other the important point in his calculation is still valid in spite of the fact that timber has doubled in value during this time. And even the ab- solute value was, for his purpose, entirely right, for no one is willing to buy a farm or forest on the assumption that in one hundred years the crops will be worth double the price. Occasionally there are cases where an advance in price is practically certain and may well be introduced even in calculation of the business. For instance a plantation of pine set out today in the eastern United States may take eighty years to mature and will then certainly not be sold at present stumpage prices. Dut even in such a case it is not necessary or desirable to assume uncertain advances in prices and most men’ would prefer to estimate the value of their enterprise on the basis of present prices, using, no doubt, maximum rather than average fig- ures. CRITICISM OF SE 59 c. The third criticism is that the calculation is a failure as soon as “reasonable” or “current” rates of interest are employed. This point has been discussed under “Rates of interest.’ As pointed out, current rates of interest are normally far above what large in- dustries and business actually make. On the basis of six per cent farming in the United States is a losing business, though the farmer pays this as a current rate. The forests and their growth depend on natural laws and have nothing to do with interest rates. The only use of an interest rate in the study of these forests and their growth is to serve as a measure. We can use five per cent and have all values of Se negative and still secure a very good comparison between different tracts of land, between different species and meth- ods of treatment. But these negative values while making possible this comparison will give a distorted picture of things: they will tell the truth and yet mislead. ‘The absolute values will be correct so far as the five per cent basis goes but they will show a good safe business bringing in millions and giving paying employment to thousands as being a losing enterprise. This same criticism was amplified by pointing out that this form of calculation on a basis of ordinary interest rates would lead to a ridiculous and disastrous shortening of rotation. In part this was provoked by enthusiasts in mathematics who actually argued for such shortening of rotation. That shorter rotations were needed most authorities agreed but rotations of forty or fifty vears in spruce, etc., were evidently wrong and the practitioner saw this. The mis- take was one of judgment in establishing the value of timber. Ag stated under rotation, the maximum Se for Saxon spruce with pres- ent prices would come at about fifty years. At present the great body of timber offered to the market is larger than is produced in fifty years and the prices of the smaller, less useful stuff are pur- posely kept up by not offering too much of this kind of material. If the Saxon state forest should go to a fifty year rotation this small stuff would at once become a drug on the market and what seemed profitable would prove a loss. But this merely proves that in deciding on the proper rotatiou and consequent final yield, it is necessary to use some judgment and consider the demands of the market. Good material, clean stuff, fourteen inches in spruce, etc., necd not fear depression in prices. Its market is practically unlimited in central Europe and therefore the rotation is set to produce this ma- terial. The calculation of the income value of the land devoted to for- est is not mere formula, in fact the formula may well be dispensed 60 FOREST VALUATION with, it is an analysis of value such as is used in other lines of bus- iness. The estimate of value or the assessment of every farm in- volves this same analysis and the only difference lies in the time cie-- ment, a peculiarity of the forest business. Just as the forester uses vield tables, expenses of starting the crop, caring for this crop, taxes, improvements, etc., so the farmer has acecpted standard figures for costs of plowing, seeding, culti- vating, his “stock figures” or yield tables, and finally his average prices which guide him in setting a value on the land, on different crops and methods. e. The Se in coppice woods. Since in ordinary coppice the crop is cut clean and the ground cleared there is a temptation to use the calculation for Se without any allowance and put cost of reproduction equal to zero. ‘This is not correct for a piece of coppice woods recently cut is not bare land, but bare land plus living stumps. These stumps are the equivalent of a good plantation safely established and so have value. f. The Se in the selection forest. Here the crop is never entirely removed. Where the forest has been in use for a long time and satisfactory records of growth have been established the stumpage value of the material removed during one rotation and properly prolonged may be substituted for Yr + = Ta (1.op™?) in the usual calculation. In most cases it is simpler to estimate the Yr, etc., from the size, quality and growth of the timber found upon the land at any time and make up a new case. F. VALUE OF STAND OF TIMBER OR THE GROWING STOCK IN THE EVEN-AGED STAND. A stand of white pine now fifty years old may be sold without the land to a man who intends cutting the timber at once. In a neighborhood in New Hampshire where many such stands are cut every year, this kind of a stand will have a fairly definite market- or sale value. Stands of white pine in this same vicinity but less than thirty years old would probably have no ready market and there would be no established or accepted sale value, while there would be ready sale value for any stand over fifty years old. Under ordinary con- ditions stands not yet ready for use, non-merchantable or immature, VALUE OF GROWING STOCK 61 have no regular sale value and this is true even of stands abroad, for the sale of such stands is not sufficiently common, even there. The same stand may be sold to a man who wants to keep it until it is seventy vears old and of better size and quality. He would have considerable expense holding the stand; interest on the monev he has to pay for the stand, rent to the owner of the land , care and protection for twenty vears and taxes for this period. To determine what he could pay for the stand he would assume a certain value which the stand is expected to have at seventy vears, deduct all ex- penses and find what he may expect to get at the end of twenty years when the stand is cut. He would discount this to present date and get the present value of the stand on the basis of his expecta- tions. This would be the expectation value of the stand. The owner who wishes to sell the stand would set the price first of all by the amount which it has cost to produce the stand, by the cost value of the stand. This cost value of an even-aged, plant- ed stand he can determine exactly as the farmer finds the cost of producing an acre of corn. He charges the expense of planting, the rent on the land, taxes and care. But unlike the farmer he has to charge and compound these sums for the whole fifty years or the age of the stand. Any stand of timber regardless of age or size has the usual three values, cost, sale and expectation, with the sale value rather indefinite for non-merchantable stands. a. Sale value of growing stock. Since this is largely a matter of stumpage of marketable stuit either for immediate use or to hold for future use, and since in the United States this is important chiefly in connection with our wild woods, it is discussed under stumpage value in chapter VI. b. Cost value of growing stock. The usual case for an even-aged stand of timber is as follows: 1. Area of stand, 80 acres; age, m, 45 years, interest rate, p, 2%. : Premises per acre: Cost value of land, Sc, $5, therefore rent Se (.op) is ten cents. Cost of planting, c, $8. Current expenses yearly, e, 50 cents. Income from thinnings: Thinning at age of 20 years, Ta, costs $3, negative income, 30 Tb, just paid for cutting, 40 Tc, 5 cords of wood worth $10. 62 FOREST VALUATION 2. Expenses incurred to produce the stand or grow it to the age of 45 years: ‘Cost of planting prolonged, ¢ (1.0p"), OF 8: CHOS Nn aiGaliGgaagschacarninchene arta nea $ 19.40 Current yearly expenses e with interest. e(1op"—I te _—_ & ovr a E(10p"—1) where E= Op and yearly rent of land with interest, (1.0op"—1) I.op—i rent = Sc(1.0p"—1), simplifying (E+Sc) (1.0p"—1) or (5-e 5) (re2" 1). aces bc amvackwdias dusnGors ss eahe $ 43.13 Thinning at age of 20 years, cost with interest. Parop JS 3 ChO2F > S asaenania ee od pad oe ehaasunte 4.92 Total expenses per Acre ...........0-e cee ee eee $ 67.45 3. Income per acre obtained from the stand during the 45 years, Thinning at 30 (just paid expense)..............00- $ 0 Thinning at 40, $10 with interest for five years....... IT .04 Lotal, IMCONIE: acacia aietovdesdesimevadgn eaten $11.04 4. Net cost per acre: ; $67.45 — $11.04 = $56.41 and cost value of the stand of 80 acres, $4,512. 5. This calculation is usually expressed in a formula as fol- lows: ™Ge = c(10p")+(Se + E) (1.0_p"—1)—(Ta(1.0p" ")+ Tb etc.) when Ta is made at a loss or is a negative quantity, —Ta, is de- ducted from costs as —(—Ta) as in the sample case above. In the formula "Gc means: the cost value of one acre of the growing stock, m years old. 6. The above case fully illustrates the usual calculation. If natural reproduction replaces planting, c may be zero. Similarly, if there are expenses of clearing the land, as on a burn, of cultivat- ing the plantation, of filling fail places, etc., these expenses are charged and prolonged exactly as planting, c. EXPECTATION VALUE OF STAND 63 7. In the above case the cost value Sc of the land was used. In most cases it is but natural that this should be sc. But where the cost value is practically zero, quite common where the land and timber were bought together and only the merchantable timber con- sidered in the price, the cost value is misleading, the land may read- ily be worth five or ten dollars an acre and so have an accepted sale value. In such cases the sale value, Ss, is used. Occasionally the land has neither cost nor sale value which could be agreed upon, for in- stance, state and national lands, remote mountain or non-agricultural land. Here the temptation is to ignore the value of the land entirely. This is wrong since any land which can and does, or. actually has produced a crop of timber having value, has value itself. Incon- sistency here is liable to lead to trouble for sooner or later the value of these very lands may come in question. In such cases, the Se properly based and discounted should be substituted as S: To employ Se without deductions is hardly advisable since Se is rather the maximum value of the land for the particular purpose and to employ a maximum price in these calculations is hardly safe or satisfactory. c. Expectation value of growing stock. Ordinary case: Spruce, clear cut, and plant; rotation, ninety years; area, eighty acres; age of stand, forty-five years, p, two per cent. 1. Premises per acre: Tang! Vales Se siaciataiecucna ed ade Anas etheantoniene ia.e Mia wie ak oe $ 20 Yearly current expense €....... 0.0.0. cece eee eee eee 0.50 Final yield, Yr, stumpage value, 40 M. feet at $10 or.... 400 Thinning at 50 years, stumpage................0c00e eee 30 Thinning at 70 years, stumpage ...............0.0e00ee 60 2. Gross income per acre at end of rotation: Pinal yield: 2.4. 4ioweacacasn eared wei Sencdiees Wag Reaaens $400 Thinning at 50 and interest for 40 years............... 66 Thinning at 70 and interest for 20 years .............. 8&9 Total. vvgresccus yom ewes os anh ad SANs Mie a $555 3. Expenses per acre to end of rotation: Rent of land and current expenses treated as in case of cost value, (Sc +E) (1.0p'-"—1) = (20 +- 25) (1.02%—1) ....$64. 64 FOREST VALUATION 4. Net income per acre at end of rotation or net value of the stand then, $555 — $64 or $491. 5. Present value of the stand on basis of expected income: Final value discounted to date, or I Value of the stand on 80 acres == $16.160. 6. This calculation may be put in a general formula: _ Yr-+ Ta(1opra)+ Tb(1opr-b) ete. — (Sc E) (top-"—1) "Ge aaa where ™Ge means the expectation value of one acre of growing stock, m years old. 7. It is evident that proper allowances must be made in esti- mating future incomes, i.e., that these values must be reasonably conservative. It also appears that if, in the above case, $202 per acre is paid and the values are secured as per estimate, the buver does not make anything over and above his two per cent on all in- vestment. Evidently then, the full expectation value is the maxi- mum which can be paid for the stand. Where risks of injury from fire, etc., are great, such risks are allowed for in the calculation by proper deduction from the values of the final yield and thinnings. d. Which value to use. In selling and buying a house the owner first considers the cost value or what the property cost him. The buyer cares little or noth- ing about this cost value but considers the market or sale value or else the value which he may make on the property. So in the valua- tion of the stand of timber. The buyer does not care whether the cost of planting was high or low, and how much expense the owner had in care, protection, taxes, etc., he merely cares about the values which he can make out of the timber, the sale or expectation value. This situation is complicated by the uncertainties of a living crop. Commonly the age and condition of the stand decide. If a stand of pine ten years old is injured or destroyed the question almost naturally is—what did it cost to reproduce or grow it, what will it cost to replace the stand, i. e., what is the cost value? In older stands it is the sale value which determines. But in many cases, especially in new districts, as in the far west, it often happens that even a fine, mature stand of timber has no sale value VALUE OF STOCK IN NORMAL FOREST 65 at all, but is certain to have a value as soon as a certain railway is finished. Similarly a stand of lodge pole may be nearly mature and yet be a few inches below the marketable size; here evidently the stand has a future value or expectation value, though neither sale value nor an accepted cost value exist. In the courts the sale value has always been accepted. Of late, since these matters have been more carefully considered and the evidence has been sufficient and clear, both cost and expectation value have been admitted. For young stands, less than half rota- tion, the cost value or cost of replacing is the more satisfactory. e. Value of land and growing stock, together, i, e., value of forest with even age stands. This is merely a matter of addition of the values of land and timber. In adding, the question arises as to the use of cost, sale or expectation value of both land and timber. As stated before, this depends on the viewpoint of the person making the valuation. The owner of a tract of timber is apt to use cost values for both land and timber, the buyer will use sale values as far as possible. If the stand is young, he too is apt to employ cost value for the stand, but is quite certain to use the sale value of the land, for it would be use- less to employ cost values where this is zero or at least uncertain. Both buyer and seller should work out the expectation value to get a fair measure and check on all sale value estimates. Since the growing stock is expected to pay rent on the land, the value of the land is not changed by the fact that the stand must remain for twen- ty or more years on the land before removal and so prevents use of the land for other purposes. G. VALUE OF THE GROWING STOCK OF A REGU- LATED OR NORMAL FOREST. When the State of Michigan starts out to establish a million acres of state forest it must determine: how much capital is to be tied up in this property and how much of it in land and how much in perishable growing stock or trees of all ages from the seedling to mature timber. The same is true of any owner or buyer who con- siders selling, buying or developing a real forest business. The im- portance of the growing stock in such a business is great since it usually makes from sixty to eighty per cent of the entire value of the property. 66 FOREST VALUATION a. The regulated or normal forest. 1. Premises: Area, 16,000 acres. Method, clear cut, and plant, even age stands. Rotation, 80 years. Thinnings every 10 years, beginning when the stand is ten years old, the last at seventy years. 2. Condition of forest in spring just after planting: Two hundred acres just planted, growing stock o years old. Two hundred acres growing stock 1 year old, etc. Two hundred acres 79 years old, or r-1 years old. 3. Yearly work, expense and income on this forest: Two hundred acres are cut. income 200x Yr. Fourteen hundred acres thinned, income T,, (200), T.) (200), Ty (200), etc. Two hundred acres are planted, 200 xc. Sixteen thousand-acres protected and cared for in road building and other improvements, taxes paid, cost 16,000 x e. Sixteen thousand acres growing stock pay rent of land 16,000 x Sc (.op). 4. A proper sample of this regulated forest would contain 80 acres, one acre just planted, one acre with one vear old stuff, cne acre two years old, etc. to one acre 79 years old, taken from the oldest stands. Whatever is true as to the average value of this sample of eighty acres applies to the whole forest of 16,000 acres so that if the growing stock on the sample eighty acres is worth fifty dolars an acre on the average, the growing stock on the 16,000 is worth fifty dollars an acre average. b. Expectation value of the growing stock of the regulated or normal forest. For sake of simplicity the rotation is assumed to be only ten years so that the sample of the regulated forest contains ten acres. Diagram, Fig. 1, illustrates this 10-acre sample and indicates the present value of yields, Yr, and thinnings, which are to be obtained. The yearly work and expense and income on this to-acre sam- ple are: One acre cut, income Yr. One acre thinned, when stand is 4 years old, income T,. One acre planted, costs c. Ten acres protected, cared for, taxes paid, expenses Ioxe. Ten acres of growing stock pay rent on the Io acres of land, cost 10 x Sc (.op). GE IN NORMAI, FOREST 67 2. Adding the values of the growing stock of the 10 acres gives the value of the growing stock for the entire sample of 10 acres and dividing this sum gives the average value per acre for the sample, and also of the regulated forest. Chops By.) Ty] o-y: Oo. AY) Sry Bayt Vay} Ov. -5 = 4) Ye | Mee] ee | Y-b | Y-7 | ¥-8 | ¥-9 | 7-10 Mr Ms Se | be Me] be We | Wr Yr Wr \OP | LOR | V.0— | vom | LOR | OP | V.0— | VOM | vot] Lop? \ Q ar S Q if \ : cw Value r Kann as expec ed uot) Laos tS one : 0. 0. 0 0 ust NOM" Loh | Lop | vop® exipecle . removed Fig. 1. Diagram representing Io acres (r acres), a sample of a forest regulated on a to year rotation, indicating the age of the growing stock on each acre; the present value of the final yield (Yr) from each, and the present value of the thinnings expected from each acre. Since Yr on the acre of 7 year old stuff is to be cut in 3 years, its final value, or stumpage value is discounted for 3 years. On the several acres 4, or more years old, no further thinning is to be expected, but the stand 3 years old will furnish a thinning next year, and hence the value of this is discounted for one year, etc. Since the general formula for expectation value of growing stock reads: Yr + Ta(1.op"-")—(Se 4- E) (1.0p?-"--1) I.op*-" ™Ge= the value of the several acres beginning with the oldest stand may be written: _ Yr-+o—(Se+E) (1.0p"*--1) *Ge 5 | 1.0p Note:—The thinning from this acre has been taken and no further thinning is expected. 68 FOREST VALUATION =: Yr +o—(Se+ E) (1.0p"*—1) "Ge TLS etc. I.0p Ge — LEAT. G.op")—(Se + E) C.op"™*—11 <2 r3 1.0p and Ge ps Yr + Ts (1.0p'*)—(Se + E) (1.0p™°—1)* I.op™”’ To get a common denominator for 3 Ta, treat in this manner: Ta(1.0pa—1) Lopra Ta(1.opt-a) (1.0pa—1) Top2 (1.0p-—1 Lopra —— I.opt (1.0p—1 adding we have: ie pee (Yr+ E+ Sc) (1.0pt—1r)-+ Ta(t.opr-a) (1.0pa—r) 7 (1.op") (1.0p—1) —r(Sc-|- E) as the expectation value of the growing stock on the ten-acre, or r acre sample. Dividing this by r the average value of the growing stock per acre is obtained and the formula reads: °-("-4)Ge average per acre= (Yr+E-+ Sc) (1.0pr—r)-+ Ta(1.0pr-a) (1.0pa—1? r(z.0p") (1.0p—1) —(Sc+ E) 3. To illustrate: Assume an area 16,000; clear cut, and plant, P, 2%. Rotation, 80 years. Premises per acre: final yield or Yr, stumpage value per acre, $400. Thinning at 20 years, no income. Thinning at 40 years, $10 stumpage. Thinning at 60 years, $20 stumpage. 1.50 Current expenses $1.50, hence E—=——.,, or $75. .02 Cost value of land, Sc, $10. * For the class it is helpful to write these out as follows: ees Yr i Ta(1.0p"-") af (‘Sc + E) r.0p"-™ (Sce-+ E) = I.op"-"™ I.op"-™ I.op*-™ 1.op"-™ this makes addition of Yr, =Ta, etc., much easier and clearer. THE SIMPLE FORMULA 69 The average value per acre of the growing stock on this forest is: (400 + 75 + 10) (1.02%—1)+10(1.02") (1.02°—1)-+ 20(1.02”) (1.02%—1) 80 (1.02) (1.02—1) —(75 +10) = 253 — 85 = $168 per acre, or about $2,688,000 for the property. This case closely resembles a fair case in spruce in Germany, site II, except that the cost value of the land is taken rather low. The calculation indicates that the growth produced by this growing stock will pay two per cent on the capital invested in the property and composed of $160,000 for land and $2,688,000 in growing stock. 4. Simplifying the above formula by substituting Se, or its value for Sc, results as follows and gives a very useful form: sinceSe —- Yi-+ Ta(1.opr-a)— c(1.0pr)— E(1.0pt—1) (1.0p"—1) Se (1.0p‘ —1) may replace Sc (1.0p"—1) in the above for- mula as follows: °-(")Ge per acre= Yr(1.ept—1)-+ E(1.opr—1)-++ Yr + Ta(1.0pt-4)—c (1.0pt) —E (1.0p'—1) + r(L.opt) (1.0p—1) Ta(t.opt-a) (1.0pa—1 r(1.opt) (1.0p—1) )_ (E+ Se) which simplifies into: Yr+Ta—c r(I.op—1) Yr + Ta—c—re r(1.0p—1) In this last form the formula clearly shows the work, expense and income of the r acre sample, of the regulated forest. The yearly income is Yr and Ta; the yearly expenses are c and re, the differ- ence is the net income from the r acres. This net income divided by r is‘the net income per acre, and this capitalized gives the income value of the forest, i.e., land and timber together, so that the value of the growing stock is this income value of property minus the value of the land. Using the premises set before and putting c= $10 and replac- ing Sc with Se at $28 we have: —(E+Se)= sie 400 +10 + 20 —10 —120 80(.02) In this particular case the result, $159, compares closely enough with $168 as obtained by the ordinary formula. In any case it is Value of growing stock per acre — 28 = $159. 70 FOREST VALUATION necessary to keep in mind that this simple formula depends on sub- stituting Se for other values of soil, Sc or Ss. c. Cost value of the growing stock of a regulated forest. In this case the value of the growing stock of the ten-acre sam- ple is obtained by adding the values of the ten acres, writing the value of each by the general formula as developed before: "Ge = c(1.0p™)+(E-+ Sc) (1.0p"—1)— Ta (1.0p™-") where again m is the age of any one stand. 1. This leads to the formula: (c-+ E+ Sc) (1.0p'r—1)— Ta(1.opt-a—1) r(1.op —1) *-(-1)Ge per acre= —(Se +E) 2. To illustrate: forest of 16,000 acres, clear cut, and plant; rotation, 80 years ; p, 2% ; premises per acre: Cost value of land, $10. Cost of planting, $10. Current expense, $i.50, hence FE, $75. Thinning at 20 years, no income. Thinning at 40 years, $ro. Thinning at 60 vears, $20. Then the average cost value of growing stock per acre: (10 + 75 +10) (1.02%°—1)—10( 1.02"°—1)— 20(1.02"—1) 80(1.02 —1) —(75+ 10)= $131 and for 16,000 acres about $2,096,000. 3. Simplification of this formula by substituting Se(1.op" — 1) for Sc(1.op'—1) results in the same form found for °%")Ge so that: o-(r-1)Ge = 0-(r-1) Ge when Se is employed as the value of the land in place of Sc, or Ss. H. VALUE OF THE GROWING STOCK IN THE ALL- AGED OR MANY-AGED FOREST. Two cases arise: the regulated and the irregular forest. a. The stand is truly all-aged and regular as in the case of a well managed selection forest. Here old and young are in proper proportion, all age classes are represented and occupy equal areas. The difference between the growing stock of this forest and that of a forest of even aged stands is merely in the distribution of old VALUE OF ALL-AGED STAND Fi and young on the ground. Theoretically at least, the following holds: if the rotation is 120 years, the area 3,600 acres, the period of return 20 years, so that each year 180 acres are cut over, each rotation one of the 180 acre lots contains six age classes, —————, and on return the 3,600 acres all age classes, from 1-—120 vear old stuff, are repre- sented, provided reproduction is secured promptly, as is here as- sumed. On each 18o0-acre lot the trees of the six age classes would occupy the same amount of ground, 30 acres, not in separated areas, but mixed, so that every acre would have old. young and middle aged stuff, i.e., trees of all six age classes. If this forest were cut over every ten years, each lot would have twelve age classes, and if cut over every year every lot should contain every age class from one to one hundred and twenty years old. The work, expenses and income from this regulated forest of many-aged stands would be similar to that on the regulated forest of even aged stands. Every year there is: a. A cut of 180 acres, (but not clear cut), which takes: 1. The mature, 120-year-old stuff, theoretically occupying 30 acres, but scattered all over the 180 acres. 2. Thinnings, and stuff cut to improve the woods on the 186 acres, really from 150 acres. b. The entire 3,600 acres are protected and cared for in im- provements, etc., and have taxes paid on them. c. The growing stock must pay rent on the 3,600 acres of land. To illustrate the computation: The yearly income is the stuff cut from the 180 acres, or 30 Yr + 150 acres thinnings, say, $10,000 ; the expenses $5,500 per year; net income $4,500 per year: cap- italizing this at 3% gives the forest an income value or expectation 4500 value of or $150,000 for land and timber together. 03 To find the value of the growing stock on this forest the value of the land is deducted. This value of the land may be cost value or sale value or expectation value, according to the object of the cal- culation or viewpoint of the person making this valuation. If the land cost $10 per acre and this value appears satisfactory to use, the growing stock on this forest is worth $114,000, or about $31.60 per acre, on the basis of the yearly income it can produce and is ex- pected to produce. 72 FOREST VALUATION b. The irregular forest of many-aged stands requires a val- uation from stand to stand and no general calculation can apply. Such a forest can not possibly yield a uniform income, steadily until it is changed by systematic regulation. In our wild woods the fol- lowing three forms or conditions are common: 1. The stand is generally mature, the merchantable timher makes up seventy-five per cent and more of all growing stock. Such stands have little value beyond that of the merchantable timber, for usually the rest is stunted and is injured during the removal of the old stuff. This, then, is a case of stumpage values. 2. The stand is largely middle age stuff, which may be ex- pected to be merchantable in a certain number of years, as seen by growth studies. Here it is simply a case of ™Ge, as developed before. 3. The stand is mostly young stuff, such as reproduction on burns, windfall, etc. In these cases the cost value, ™Gc, should pre- vail. Where such reproduction comes in with open, mature, or over mature stands, the area of the young stand is estimated; its cost value and the stumpage value of the old stuff are determined sep- arately. IV. RELATION OF CAPITAL AND INCOME IN FORESTRY A. NATURE OF INCOME AND PROFIT IN FORESTRY. 1. General notion of profit. a. If an article for a store is bought at one dollar and sold at a dollar and a quarter there is twenty-five cents profit, or the profit is 25%. b. If a house, bought at $1,000, is sold within two months at $1,200, the profit is $200, or 20%. c. An office building in a small town cost $150,000, there is little demand for this and the income after paying taxes, running expenses and upkeep is about $3,000 per year. There is this net in- come but no one considers the building a profitable one. To the contrary it is well known as a “losing proposition.” Savings banks and the best commercial papers would pay twice this income. In figuring the loss it is asumed that the capital of $150,000 should have been invested at 4%, the income therfore, $6,000, that the yearly loss is $3,000, or 2% on the money; and if the building had to be sold this would mean a total loss of $75,000. We have income here but certainly no profit. d. A house is bought at $1,000 and current rate of interest is 5%, the true net income from this house is $80 per year. Evident- ly the new owner makes 8% on his money and the house nets him 3% more than the current interest rate. In this case there is a profit, even though the owner does not sell, and this profit is 3% and not 8%. In this way the net income from the house divides itself into two parts, a reasonable regular income on the capital invested, i.e., the 5% on the $1,000, and a 3% profit. Since on this point authors vary, some putting the net income as synonymous or at least interchangeable with profit, the position taken in these discussions is here stated. e. A farm is bought at $5,000, the new owner borrows $2,000 additional at 5% as a working capital to buy teams, tools, etc. He produces a net income of $700 or 10% on all the money put into the enterprise. He pays his creditor $i00 yearly interest and retains $600. This $600 makes 12% on the farmer’s own money so that he has his regular 5% income and 7% profit in this business. But even 74 FOREST VALUATION here there is a doubt as to whether part of this seven per cent profit is not a personal matter. These few cases suffice to show that the matter of profit is not as simple as it seems; a great variety of combinations necessarily arise, there may be profit even though there is no sale of property, and also there are various viewpoints possible. f. A man buys a house for $5,000, he borrows the entire sum, giving the house as security. In one month he sells the house at $7,500, and returns teh cash with a few dollars interest. The profit is practically $2,500 and is not made on any real investment on his part. It is usually stated that his credit is used, etc., but in many cases this is not true at all; the capitalist does not trust the man but considers the house good for the money. It is neither ordinary profit nor wages but a special form of profit paying him for his enterprise, shrewdness or more often his good luck, exactly as in gambling. 2. Profit from income producing properties. a. Incase under 1, c, a house is bought at $1,000, the interest rate is 5%, the net income $80 or 8% on the money invested, the yearly profit is $30 or 3%. The cost value of the house, He is $1,000, 80 income value He is —-— or $1,600, the total profit is $1,600 —.$1,009 05 or $600 and may be stated as He — He. b. A forest property is bought at $250,000, it produces $10,000 per year or 4% on the investment, net income. Whether this would be regarded a profitable investment or not depends on the purchaser, chances for investment, the current rate of interest, etc. In central Europe it would be considered an excellent property, in the United States at present, it would be considered poor, in the west, barely paying in the middle states, fair in the east. Any one who could easily get five per cent on his money would not buy this property. and would certainly not speak of a profit in this case. Assume now that the property yields $20,000 per year or 8%, then the case is similar to that of the house, i. e., Cost value of forest, $250,000. 20,000 Income value - - OF 400,000. .05 WHAT IS PROFIT 75 The yearly profit is $20,000 — $12,500 or $7,500, or expressed in per cent it is 8%-—5% or 3%; and expressed as a total it is $400,000 — $250,000 or $150,000 which may he stated as: profit = Fe — Fc. That the same reasoning applies to land which is to be used for forest is evident and leads to the statement: Profit = Se — Sc. 3. Profit from a forest not producing regular yearly income. Usual case: A tract of 40 acres of timber is bought at $5,000, the owner is not ready to cut the timber, it is not to be sold, or else no offer is made; in many cases of this kind in the more remote districts, it might be impossible at times to get a buyer even at half the real value of the timber: there is neither loss nor profit here actually es- tablished until the timber is cut or some sale is made. As a fore- cast, however, it may he possible and worth while to work out an expectation value in the manner outlined before, and then the prob- able or expected profit is equal to the expectation value of this 40 acres minus the cost value, in this case $5,000. From the foregoing illustration, it is evident that the term profit is clear and that it is consistently employed in the ordinary store, and in ordinary sale of property. But when employed in connection with the regular income from a house, farm or forest, factory, etc., it is not clear, being confused, commonly, with gross, or net incomes and largely loses its usefulness. B. INTEREST MADE BY THE FOREST. In forestry the question frequently comes up—what rate of in- terest is made by the growth of timber on a given tract. Three cases may be distinguished : a. The growth of a single stand such as a 4o-acre stand of even aged timber. b. The growth of a regulated forest, or more precisely, of a working section with perfect age class conditions. c. The growth of timber which may be produced on an area of land which is bare to start with. 1. The interest made by a single even aged stand of timber. Here the usual case considers the growth for only a short period, say 10 years, but frequently, however, it demands the interest made by the growth for an entire rotation. 76 FOREST VALUATION a. Interest made by the growth of a stand during a short period or part of a rotation: If the cost value of the land is $10 per acre and the cost value of the stand, now 30 years old, is $80, then the amount invested in this enterprise is $90 per acre. Evi- dently the only increase in value of this piece of forest is due to the growth of the timber. If the growth in volume, quality and mar- ket price amounts to $20 in 5 years then this $20 represents the in- terest for 5 years on the $90 invested, and approximately the rate of 20 X 100 : interest is: ————— or 4.4%. While this calculation is a fair ap- 5 X 90 proximation it requires modification for larger enterprises, and bet- ter analysis. The following illustrates the ustial modification. Area, 40 acres; stand, even aged 50 years old at beginning of period, and 55 at end; p, 2%; land, $10 per acre; yearly expenses, e or E is $50; the value of the stand at Cn 50 years is $250 and at 55 is $300. The reasoning then is: 1.op" = —. Co e, $1 per acre; therfore Ae The initial capital, Co, is made up of stand at 50 years, land, and E, the final capital, Cn, of stand at 55, plus land and E, and we may set: 5. Y"+S+E — $300+10+50 op! YL SE $250 +-10 + 50 = 1.16 and hence p= 3%. This per cent made by the current growth of the stand may be term- ed “forest per cent,” or P;, and is the “Weiser” per cent of the Ger- man authors. The formula as written by Endres is: wom (SEES: ) or in our terms, pain (EEE ) which readily changes into the above simple form. This form of analysis was used by Pressler and Heyer over fifty years ago. It is useful in determinig whether a given stand should be cut or left standing, the usual assumption is that if the FOREST PER CENT 77 per cent drops below 3% or whatever per cent may reasonably be demanded by the owner, the stand is no longer worth holding. While the calculation is quite simple the actual determination in the woods is not easy and is never more than an estimate rein- forced by measuring the outer rings of a few trees. From these measurements the Pv or growth in volume in per cent is determined by Schneider’s formula; the per cent growth in quality is estimated on a basis of diameter at beginning and end of the period, and the per cent increase in market price is a figure worked out for several years in any given district. Having this, the growth of the stand is expressed in per cent for the three lines and Pressler conceived the idea of simply using these as follows: assum- Ym ing the actual growth in value per year is: (Py + Pq + Ps) 100 and that this growth is made on a capital Ym + Se. ; Ym ) 4 Ym Then pt =(pv + pa-4-Ds) ao =(eP PsP) Goo ee To illustrate: If the stand is worth $250 and land $10 per acre and py =1.3% pa =I ps =1 250 or 3.1%. then pr=(1.3 TH oe 6 Since this method or inquiry is usually applied only to older stands where the value of the timber is very large as compared with Yin the value of the land, the value of —--_—— may be put = 1 and for Yu + Se ordinary purposes, therfore, it is quite sufficient to state: Pi:—=Pv+Pa+Ps; in the above case pp=1.3 +1+1=3.3%, a very convenient form. In the United States where at present the value of timber is usually by M. ft. b.m. on rather uniform price per M. feet, the case of working out the data for p; may take the following form: Assume stand of pine, pure, even aged, 80 years old; volume table exists for species and district; from borings or felling the diameter growth of the timber is ascertained, the stand is calipered 78 FOREST VALUATION and volume known; stumpage $10 per M. feet ; assume that the stand now, 80 vears old, contains 250 M. feet. Value of this 250 X 10= 2,500. From growth study it appears that the stand 10 years ago con- tained 200 MM. feet, valued at $2,000. Then the growth in value, be- side increase in market price, is $500 in 10 years. Expressed as per cent: 2500 L.0px°= tose 1.25 Ps= 2.3%. This p, or 2.3% includes both the growth in volume and the growth in quality as it finds expression in our present day practice of scaling timber so that we may state: 2.3% —=p,—=py + py, and this requires merely the addition of p, or the growth in market price to state the total growth in value. b. Rate of interest made by the growth of an even aged stand during the entire rotation, i.e., from the time of planting to time of cutting. Here again it is convenient to apply the fundamental form of reasoning that Cr _ Capital or values at end of rotation Co™~ Capital or values at beginning opr The initial capital Co is made up of: land, Sc; cost of planting, c, or the value of young growth; capital E, to take care of the stand, pay taxes, protection, etc. While this capital, E, is not really on hand, the results are the same, the owner must provide from some source, an amount equal to the interest on E at p per cent. At the end, or time of cutting the final capital, Cr, into which Co has grown, is made up of: land, Sc; capital for expenses, E, stand of ripe timber, Yr, and the state- ment becomes: stand + land + expense capital _ Yr+Se+E land + expense capital + cost of planting c+tSe+E T.opr.= Concrete case: Jand $15 per acre, p== 2%, e— $1, hence E 1.00 —— = $50; Yr, $400; c, $12; r, 80 years; then: .02 ip EE ae a gy I2+154+50 77 and from tables: p; = 2.3%. FOREST PER CEN? 79 The above formula may also be written: 1-0 (EE ) which is nothing more than the old form of the Weiser per cent, where the period includes the entire rotation, c the cost of planting represents the value of the stand just planted or at the beginning, and Yr is the value of the stand at the end of the period. Whether the value of the land is taken at cost, sale or expecta- tion value is optional. Certainly the introduction of Se means the use of a maximum which is not to be recommended. Since the val- ues of land are apt to change very decidedly during a period of eighty years it is not only permissible but even proper to set a higher value for S in the numerator, i.e., in the final capital, than in the denominator or initial capital. In some recent publications the formula is written in a modified form as: Y S— . : op’— l.op’= eae and E; is equivalent to e a or merely the end value of all expenses during this one rotation com- pounded at ordinary interest rate, the assumption being that money is borrowed (actually or not) at ordinary rates for this purpose of paying taxes, protection, etc. Jt is evident that this, as well as many other forms, is possible and that some uniformity in the use of the letters and writing of these formulz will greatly help all concerned. Where thinnings are made, and this must be assumed as the normal condition in forestry, the above formula is incomplete and must be modified to take care of the receipts from thinnings. This may be done as follows: eS Yr+ 2 Ta(topr-9)+ Sc4-E : e+Sc+E z. Rate of interest made by a regulated forest, or one pro- ducing a regular yearly income. Since the yearly net income is in the nature of interest on the capital invested in the forest and since this income is known, it is necessary only to determine the value of the property, stand, and land. But as this may be cost, sale, or expectation value of either land or stand, a variety of conditions are possible. Where the forest has been purchased in recent time, where the income so far received has paid all expenses including an acceptable rate of interest, and where the management has prevented any de- 80 FOREST VALUATION terioration of the forest, the cost price is evidently the capital in- vested, and the rate of interest made by this forest is: vearly net income pr — cost value of forest xX 100 If the man bought the forest at $250,000 and receives $10,000 per year net income, he evidently makes 4%. If this same man paid $250,000 ten years ago and has “put back” $50,000 to develop a better road system then evidently the for- est costs him more nearly $300,000 and the Sto,000 income is about 3% on the cost value of the property. Similarly, if instead of get- ting $10,000 net income he has saved with a view to improving the growing stock on the property and has secured only $5,000 per year net income, the $5,000 reduction of cut is an investment and in- creases the cost value. Again, the forest may be part of an old estate or it may have been bought twenty years ago at a “bargain” so that the present cost value is not clear and certainly not equal to the present sale value of the property. In this case the income is not referred to the cost value but to the sale value. With properties which are not common objects of sale like state forests, national forests, etc., the value of the property itself is based on the very income made from it together with an assumed interest rate. The forest producing $10,000 per year net income would be valued by capitalizing the $10,000 at, say, 3%, and the 10,000 capital value would be ——— or $333,000. 03 If this capitalization is now accepted it may serve as a measure to find the forest per cent for future years. For the present, how- ever, this value of the forest must be regarded as arbitrary, for it would have been just as fair to use two or four as the per cent of capitalization, and for the present, therefore, the per cent or interest rate which this forest makes can not be determined for lack of ac- ceptable basis, the value of the property on which the $10,000 were made. In determining the rate of interest made by any property pro- ducing regular yearly income there enters the notion or custom of “watering stock.”” In the above case, for instance, the owner would at once set a much higher sale value in place of the 250,000 cost value and in this way bring down not the income but the apparent rate of interest. Practically all state forests of Germany never cost INTEREST ON LAND 81 the states any money, they were simply taken charge of by the gov- ernments, paid their way and all improvements to the present day. And yet their value is set so high that the splendid net income bare- ly makes 3%, in most cases not that. The strange part is that this high value is not a fictitious one but a very real thing and that these properties could readily be sold at these high prices. We have the same situation in the case of farm properties in Europe as well as in our country. 3. Rate of interest made in a forestry enterprise starting with bare land. Under this head come the ordinary plantations, where no forest exists, where the bare land is considered as the real capital, where the money for planting, etc., is or may be borrowed at the interest rate used in the calculation. In this case then: __ yearly income X_100__ yearly income X 100 __ a X 100 = capital ™ cost value of land ~ Sc Since the income here is not a yearly one but a periodic one, every r years, the value of the equivalent yearly income may be found by the formula: == Ap oP I.0p"—I The periodic‘income is: A= Yr- Ta(t1.opt-a)— C(1.0pr)— E(1.0pr—1) and the above calculation for yearly income is then: os (Yr + Ta(1.0pt-2)— C(1.0pr)— E(1.0pt—1) .op T.0pT—1 = Se(.op), and: _aXt00_ Se.op 100 _ Se aes Sc 7 Se = Se? Pp To illustrate: If the land costs $10 per acre, the accepted rate, p, is 3%, and the forest enterprise is such that it pays 3% on $30, i. e., makes the land worth $30, then evidently the man makes on his cost value of land on the $10, not 3% but 9%, or, as per formula: 30 px = — X 3 0r9. Io This is an interesting statement and has value especially in the United States where cost values of forest lands are still very low. 82 FOREST VALUATION To illustrate: Cut over lands in the southern states may be bought at $2 per acre. The Se even on a very conservative basis is $20 per acre. To a company financially able to hold and develop such lands as forest properties the enterprise would make: 20 px = — 3 = 30 % on the cost value of the land. 2 It should be noted that p in this case should be the p employed in calculation of Se, and also that the p,, the 30% in the above case, is the interest made only on the cost value of the land, on Sc, and that the other parts of the investment, costs of planting, taxes, pro- tection, etc., produce simply p the accepted rate of interest, usually 3% in these studies. ; C. COMPARISON OF PROPERTIES WITH YEARLY AND WITH INTERMITTENT INCOME. The great advantage of having any kind of business in a condi- tion of producing approximately equal and yearly incomes is quite evident. Ordinarily an enterprise is not considered a business at all until it does produce a yearly income at least balancing expenses. In most cases it is difficult to interest and enlist financial support or purchasers unless there is an assured yearly return at least equal toa conservative rate of interest, except in cases where a body of nat- ural wealth is in view, as in standing timber, coal] veins, etc., or else in cases of great possibilities or probabilities where the element of lottery or gamble enters. Financial concerns under public control are generally forbidden to lend on securities of this kind. The reg- ular yearly income has been, therefore, one of the aims in forest business and forms one of the principal tasks of forest regulation. Merely to emphasize and illustrate this fact the following concrete case is here considered. Assume two properties of 1,000 acres each; rotation 80 years; p, 3%; Yr, $400; Sc, $10; average growth of ripe stuff per acre, one cord per year, value per cord, $4; cost of planting, c, $10; cur- rent expenses, e, $1 per acre. Thinnings left out for sake of sim- plicity. YEARLY AND INTERMITTENT 83 Comparison of yearly and intermittent working. Property with yearly Property with a cut cut and yearly income.jand income every 80 years. 1. Growing stock at] 40,000 cords. None. beginning. 2. Growth of ripe stuff} 80,000 cords. 80,000 cords. during the 80 years. 3. Growing stock at end of 80 years. 4. Value of property at beginning. 5. Income during the 80 years. 6. Income at 80, i. e, in last year. 7. Condition at end of first twenty years: 40,000 cords. $10,000 for land and about $60,000 for grow- ing stock. $320,000 plus interest. $4,000. Has Earned: Per year: Income: 4000. Expenses : Rent 335. Tax and care 1000. Planting 125. Total expense 1460. Net income per year, $2540. Net income for 20 years (1.03%—1) 2540 or about 1.03—I $67,700. 8c,000 cords. $10,000 for land noth- ing for growing stock; might enter plantation. None, thinnings not considered. $320,000. In Debt: Expenses per year: Rent 335. Tax and care 1000. Total 1335. For 20 years’ expenses: (1.03"—1) 1335 or 1.03—I $35,600. For planting 10,000. Plus interest or 10,000 (1.03”)= 18,000. Total expenses for 20 years: $53,600. This simple case of a comparatively small property brings out the great disadvantages of the intermittent working of a forest prop- erty. The man who owns 1,000 acres of land and sees before him 84 FOREST VALUATION the piling up of over $50,000 expenses in only one-fourth of the ro- tation is not very much encouraged to go into the forest business. It also illustrates why in common sense and fairness the owner of such a property is not able to pay taxes like the owner of a regu- lated forest who has a net income every year. It also illustrates the fairness, in fact the necessity, of deferring the taxes to the time when the timber is cut and an income secured, such taxes to stand as a lien against the property.* *Read: “The Need of Working Plans on National Forests and the Policies Which Should be Embodied in Them,” by Professor Burt P. Kirk- land, in Proceedings of the Society of American Foresters, Oct. 1915. This article shows clearly the necessity of working for a sustained yearly cut in the forests, and the principles laid down in this article apply in all real forestry work the world over. V. ROTATION In planning a forest business it becomes necessary to decide upon a rotation. To do this is one of the most important tasks of forest regulation and requires a most careful consideration of all conditions and factors concerned. Among these the most impor- tant are the market, site, species and treatment. The market sets its requirements as to species, size and quality which must be raised, and it is useless to discuss rotations which fail to raise timber of the required size. Site, species, and treatment, particularly practice of planting and thinning decide the length of time in which the desired size and quality of timber can be raised. Being largely a weighing of conditions and factors, the setting of the rotation is primarily a problem in statics and perhaps the most important task of statics in forestry. In so far as the conditions and results require expression in dollars and cents, the basis for the study of a proper rotation is sup- plied by forest valuation. In any ordinary forest business the aim is to keep the forest and land in best possible condition and at the same time make the largest income. Assuming the silvicultural conditions cared for, the best rota- tion is the one furnishing the best income for the longest time. There are two distinct ways of judging this income: 1. We may demand the largest net income per acre of estab- lished forest ; 2. We may wish to secure the largest per cent on the money invested in the forest or the largest net rental on the soil, the max- imum Se. These two viewpoints have for many years divided the foresters of central Europe into two schools, the division still exists and prom- ises to continue for a long time. a. Rotation for largest net income per acre of forest. The assumption here is that we start with a forest and not merely bare land; that this forest is more or less regulated and able to produce a yearly income. All of these conditions actually apply to the majority of forest properties of central Europe. The following case illustrates the calculation: Area of forest, 16,000 acres; rotation, 80 years; age classes fairly regular. From this forest we can select an 80 acres sample 86 FOREST VALUATION with stands of all ages from 1-80 years. From this sample we would get each year: One acre of ripe stuff to cut or Yr, Several acres of thinnings, or =Tq, And we should have expenses of one acre to plant, or c, and 80 acres to pay taxes, protection, etc., or re, which may be put into the following form: average net income per acre = Yr+<=T.-—c—re r or according to the following table for spruce site II, for a rotation of 583+ 7I1—12—54 60 years = $ 9.80 60 98o -+- 232 — 12 — 72 80 years = $14.10 80 Spruce site II, Germany, Endres, after Schwappach, gross in- come, expenses, net income and Se for different rotations from 30 to 120 years for use in formula. Average net income per acre Yr+=T,—C—re T Gross Income. Expenses. Net Income. re Se Yr or | 2Tq/] Total current} Total | Total on basis Reus final }sum of{income}| ¢ |expenselexpense| from of 3% a cut thin- | from r | plant-+tax,pro| forr | racres |Average| rental ears. | per | nings | acres | ing off tection| acres of per | value acre |from r of one jetc., for] of normal] acre. |oneacre t years| acres. }normal | acre.| racres}| normal | forest. bare old. forest. e $0.90 | forest. land $ $ $ $ $ $ $ $ $ 30 87 a 87 12 27 30 48 1.60 10 40 203 7 210 12 36 48 163 4.00 47 50 371 31 402 12 45 57 354 6.99 77 60 583 71 654 12 54 66 588 9.80 98 70 786 137 923 12 63 75 848 | 1210 | 105 80 98o 232 1212 12 72 84 1129 14.10 105 90 1123 351 1474 12 81 93 1382 15.30 99 100 1222 488 I710 12 90 102 1609 16.00 91 110 1281 683 I9IQ I2 99 III 1808 16.40 83 120 1206 791 2087 12 | 108 120 1967 | 16.30 75 FINANCIAL ROTATION 87 From the foregoing table it appears that the average net in- come with spruce site IT and present prices, is but $1.60 per acre for a rotation of thirty years, rises rapidly and steadily to $15.30 for a ninety year rotation and passes a maximum of $16.40 at a rota- tion of about IIo years. b. Rotation for largest net rental on land, maximum Se, and with this of highest per cent interest on the investment. See also chapter on Se. The assumption is that the bare land is the real capital and that by using it to raise timber this land is made to pay a rental and the object is to decide upon a rotation which will secure the highest net rental per acre. i.e., the highest Se. That a forest producing the largest Se also pays the Jargest rate of interest or p is evident from a previous study into p where it is shown that: Se px = — p, the rate of p on Sc. Sc Since Sc or the cost value of the land is fixed and p is the accepted rate of interest which is also fixed, it is evident that p, increases directly with Se. This calculation applies to every stand or every acre in the forest and therfore to the entire property. Generally longer rotation means larger and hetter timber, larger growing stock, larger capital, larger net income per acre of property. As seen from the table for spruce, site II, and from discussion of Se it means a larger Se and better rate of interest. But this reaches a maximum after which the Se and with it the rate of interest made by the forest decreases. Formerly unduly long rotations and large timber were the rule and in most forest districts there was no regard to the relation of this rotation with the capital invested and the in- come secured. It was against this kind of luxury in forest manage- ment that Pressler and Heyer raised their voices and used the math- ematics of forest valuation and statics. And it was the fundamen- tal formula for Se first developed by Faustman which served to make clear the mistakes of very long rotations. At first the current rates of interest, four and five per cent, were employed. But as seen from discussion of Se these higher rates not only reduce Se but bring the maximum Se very early and so suggest or demand too short rotations. ‘That there must be a limit to shortening of rotation and that good marketable timber must be raised regardless of any formule was evident to every good practitioner. Unneces- sary stress on mathematical formule on the one side and common sense with an aversion for formule, especially for bringing in com- 88 FOREST VALUATION pound interest discussions into the business of raising timber, on the other, have prevented the two schools from coming together. Of late there is a better understanding, it is evident to all that the forest must produce good marketable stuff, and that if the for- est can not make more than 3% in doing this, there is little use of introducing 5% in the formule. On the other hand it is clear that the planting of small saplings at $50 per acre and holding old stands which have not earned 1% for a quarter of a century are mistakes to be avoided. With an interest rate of 2%, the rotation of highest Se, the financial rotation coincides closely with the technical rotation or that producing the timber most in demand and now in actual use. A few figures may serve to illustrate this: Ordinary rotations for regular timber forest in central Eurupe run about as follows: Pine and spruce.............2.00: 80 to I00 years Balsam and beech................. 100 to 120 years Qalksc: toidasans e's cadate's Wine cine ataninetete ee 150 to 200 years For spruce in Germany as seen from the tables under discussion of Se, the maximum Se, and therfore p,, for site I-IV, on a basis of 2% comes at 70-80 vears, at a 3% basis in 60-70 years. For pine in Germany on sites I-IV, on a basis of 2% as well as 3% the maximum Se comes at 60-70 years. For balsam in Germany according to Lorey, maximum Se for sites II-III on a basis of 214% comes at 100-110 years, which ac- cording to Lorey is also the preferable age from the standpoint of silviculture. For oak in Germany, according to Schwappach, a rate of 2% puts the maximum Se at 120-130 years, but here the modern tech- nical requirements demand a rotation of 160 or over. For beech in Germany the maximum Se on 2% basis for sites I-IV comes at about 80 years, a rotation which does not produce satisfactory saw timber and similar goods. Poor sites such as poor sands in the pinery of north Germany are unable with any rotation to make a 3% income under the ordi- nary conditions of German management, and barely work out 2% for land and costs. That the rotation can be shortened by planting good transplants and by an energetic practice of thinning is evi- dent. In addition, the modern means of manufacture have made it possible to use smaller sizes and so work toward shorter rotations in the forest. VI. VALUE OF STUMPAGE Under present conditions in the United States timber is gen- erally bought and sold as standing timber or on the stump, and usually goes with the land, so that in most cases it is really a sale of the forest, i.e., land together with the entire growing stock and not merely a sale of the timber. In these ordinary sales of timber or forest, the price paid is determined merely by the value of the merchantable timber and the rest of the growing stock as well as the land is left out of consid- eration, thrown into the bargain. Of late, especially on the national forests larger sales have been made where the value of the merchant- able timber alone was concerned. In some cases, timber, whether forest or timber alone, is bought for immediate use or cutting, in other cases the timber is bought years ahead with a view of supplying a regular lumber or timber business, or else just for speculation, when it has to be held for years before any return is secured from the money invested. In this way a great variety of cases arise, each having its own peculiar con- ditions as to time, location, market, cost of exploitation, etc. But all of these cases have a few fundamental conditions in common and these only can here be considered. Timber, here only merchantable timber, like other property has three forms of value: cost, sale, and expectation value. A. Cost value of stumpage. 1. Where timber is raised the cost value of the merchantable timber can be determined in the ways before described. But gen- erally the time between planting and harvest is so long, that this cost value is rarely considered, and mature timber even in central Europe is estimated by sale, rather than cost value. But it is well to keep in mind that with present prices of timber from twelve to twenty dollars per M. feet b.m. and cut into logs for spruce and pine, the per cent made in the forest business is generally three per cent or less, so that present prices may be regarded as cost prices with three per cent and no profit, in spite of the fact that forestry pays a larger net rent per acre than farming. 2. Where timber is bought for immediate use, as is much of the timber purchased on national forests, etc., the price paid is the cost value. 90 FOREST VALUATION But where timber was bought years ago, in advance of cutting, the present cost value involves: price paid; interest, compound, us- ually 5-6% in the United States; taxes with compound interest ; care of property, of late some money for fire protection, with interest ; losses by fire, theft, insects, windfall, etc. Part of these losses is made up by growth, but in most cases it is not safe to figure on any material growth. On large areas the growth is usually balanced by decay, on smaller areas, the decay or loss may far outrun growth, as in timber infested by insects, etc. In these cases only a detailed examination determines the true status. Leaving out this very uncertain element of losses by fire, etc., the cost value results in a case approximately like the following: Area, 2,000 acres; price paid 10 years ago, $40,000 ; Present value of this 40,000 (1.05°) == $65,160; Taxes at 114% on half cost price, $300 per year; Care of property by some local agent, lawyer, etc., together with expenses of fire control and occasional visit by cruiser, etc., $200 per year. These two items with interest: (1.05°—1) (300 + 200) ————— = $6,200, 1.05—I Total cost, $71,360, or nearly double the original cost price. This explains a common phrase among timber owners in the United States—that the value of a property must double every ten years if there is to be no loss. B. Sale value of stumpage. This may be considered under two heads: The ordinary market price of stumpage as determined by actual sales. The stumpage value for immediate se as determined by an an- alysis of the various factors entering into, or affecting this value. 1. The ordinary market price of stumpage should approxi- mate: value of lumber at mill—cost of logging and milling, where a proper profit, etc., forms part of costs. But so far the market price of stumpage has not been deter- mined in this way. Probably more than ninety per cent of all stump- age bought during the past twenty-five years was paid at prices quite independent of the prices of lumber and cost of logging, and deter- mined chiefly ‘by the activity of large buyers. A number of causes contributed to this peculiar condition. Large quantities, thousands of acres of fine stumpage were secured without pay from the United STUMPAGE AND DISCOUNT gt States government under the homestead act, large areas were alien- ated at the nominal price of two dollars and a half per acre under the Timber and Stone act and by Commutation of homesteads, large areas were given as land grants to railways, etc. Several of our states, Florida, Oregon, Idaho, New Mexico and others sold lands, given them by the government under various acts, at prices in no way graded by the price of lumber. Even our lake states sold tim- ber at give-away prices. In this way Michigan sold 114 million acres of land in the ten years ending 1910, at prices usually below two dollars per acre and most of it helow a dollar and a quarter, and most of this land was bought for the timber. Large areas of timberlands have been held by small owners, or owners financially unable to exploit and market the material and in many cases, a lack of market, transportation facilities, etc., prevented the owners from doing anything with the timber. Aside from these personal factors there has always been the great balance of demand and supply. Even today with more than fifty years cut in sight, of timber already ma- tured, it is useless to estimate the value on a basis of immediate ex- ploitation and present prices. To illustrate: assuming prices of lumber, mill run, to stay at about $15 per M. feet, and cost of logging and milling to average $10 per M. feet. Then the true value of stumpage should be $5 per M. feet average. But this is not true. The first year’s cut is worth the $5, but the second, third, etc. year’s cut is not worth it. The stumpage cut in the tenth, twentieth or thirtieth vear, at five per cent discount is 5.00 5.00 5.00 worth only ’ : . or $3.10, $1.89 and $1.15 per M. feet. 1.62 2.65 4.32 In keeping with these peculiar and unsettled conditions of stumpage prices stumpage of pine in Minnesota brought $12 while in the same year millions of better stumpage was bought in Oregon for less than $1 per M. feet. The man in Minnesota could use it at once and make money, the man in Oregon bought it to hold and he had to hold, and may lose money at it. Stumpage prices today vary not only for species but vary with locality, with market, railway facilities, habit of the people of the district, etc. Average figures for stumpage have little value, they vary chiefly between $3 and $7, go as high as $20 and as low as $1, and generally make from to to 30% of the value of the lumber at the mill. g2 FOREST VALUATION In central Europe most of the timber is cut, or cut and skidded to the road and sold not really as stumpage but as logs ready for hauling. Here the prices have gradually settled to a fairly exact condition, the value of the logs depending on mill or market value, and cost of transportation. The prices vary little from year to year, have risen steadily for many years, about doubled, in Germany in the last sixty years. The timber is bought at auction, the bids usually naming a per cent of the price set by the forest office. In pine and spruce the timber is classified by the cubic contents of the stem, i. e., the number of cubic feet per stem. The following figures illustrate: Spruce, logs cut full length, ready to haul: Stem Class: Contents : Price per c. ft. Price M. ft. bm. Class I | 100 ¢. ft. or over 14 cts. per c. ft. $20 Class II 70-100 c. ft. 13 cts. per c. ft. $19 Class III 35- 70 c. ft. II cts. perc. ft. $17 Class IV 18- 35 c. ft. Io cts. per c. ft. $15 Pine, stems cut full length, ready to haul: Stem Class: Contents: Price per c. ft. | Price M. ft. bm. Class I 70 c. ft. or over 15 cts. $22 Class II 35-70 c. ft. 13 cts. $19 ‘Class ITI 18-35 c. ft. 9 cts $13 Class IV below 18 c. ft. 7 cts. $10 Cordwood: 4 cts. solid, or $3.60 per cord. White oak, classification by middle diameter of stem: Stem Class: Middle Diameter:] Price per c. ft. | Price M. ft. bm. Class I 24 inches and over 42 cts. $60 Class II 20-24 35 cts. $50 Class III 16-20 28 cts. $40 ‘Class IV 12-16 17 cts. $20 ‘Class V under 12 10 cts. $10 SALE VALUE OF STUMPAGE 93 Beech usually sells at 4-7 cents per cubic foot and most of it, even clear logs 12 inches diameter and better go as cordwood. This cordwood is commonly sold from $3-$4 per cord. Table of size and value of average tree, all for site I: Age Pine. Spruce Oak Beech Diam. ”| Value | Dbh. ”| Value | Dbh. ” | Value | Dbh. ”| Value 60 9.5 $1.10 9.0 2.35 8 0.85 8 “55 80 12 2.90 12.6 4.50 12 3 10.8 1.30 100 14 4.50 15.8 8.30 16 9.80 13 2.25 120 16 6.80 18.4 11.40 18 22.50 I5 3-25 140 17.2 9.60 21.5 | 2 16.8 4.29 160 23 34 180 24.5 | 48 200 26 52 The above prices are for straight, well-cleaned, sound timber. They clearly indicate that prices in parts of the United States are rapidly approaching and in many cases have fully reached those paid in the forests of south Germany and other European countries. In fact it is doubtful if the same grade of large stems could be bought for the same prices in Ohio or Indiana and several other states. 2. Sale value of stumpage, determined by consideration of the. various factors. Here the calculation attempts to show: price of lumber at mill; cost of logging and milling ; the assumption being that the stumpage price should be the dif- ference between these two, i.e., if the lumber is worth $15 and it costs $10 to log and mill then the stumpage should be $5. a. Price of lumber at mill. Where the lumber is sold “mill run” this value is easily obtained providing the sale of the lumber is bona fide and under normal con- ditions. Where lumber is graded at mill and sold by grades to various dealers, attempts are made to get at the true average price by learn- ing the per cent each grade makes of the cut and the price of each grade. In some cases this is quite simple, in most it is not. Any change in the quality of the timber in the woods affects the per cent of 94 FOREST VALUATION grades. Where several species are logged together such as hemlock, maple and beech, etc., the proportion as well as the quality vary from one tract to another. To use the general prices of the district and agree on some pro- portion of kinds and grades is usually as far as the analysis can go. b. Cost of milling. This also involves various considerations differing radically for different cases.. In one case the logs go to an established mill, the particular body of timber is only one of several or many which are cut at this mill. The large mills along, or at the mouths of the rivers in Michigan and Wisconsin are of this order. In this case the cost of milling is quite simple, there is a regular market value of this milling toll which is fairly well established. In other cases the mill is established to cut the particular body of timber and no more, it must be torn down and moved away, is largely a loss and with it also a number of other buildings, quarters for men, boarding houses, office, store, shops, etc. In such a case the cost of milling involves: 1. Labor, material and repairs; 2. Depreciation of all buildings and machinery ; 3. Interest, taxes, insurance, supervision and profits. Generally the direct cost of labor and materials is fairly well known, varies within narrow limits, mostly between $1.50 and $3 per M. feet b.m. The depreciation of mill and machinery and buildings may be treated as follows: Mill and buildings may be assumed to last throughout the job, the different machines may and may not need separate treatment. Suppose the amount of stumpage sufficient to furnish Io years cut- ting. Let the mill and other buildings, including those machines which are fairly certain to last the ten years he worth $150,000 and let the interest rate be 5%. Then this outfit together with interest costs at the end of the ten years: 150,000 (1.05*°)—-the wrecking value of the outfit. If the latter is $10,000, then the end value is 240,000 — 10,000 or $230,000. Usually we desire to know what yearly sum will take care of this $230,000 and from this derive the cost of the depreciation per M. feet of lumber. To get this we may set for the above case: (Log =F} 1.05 —I yearly cost of depreciation = X and X == $230,000, and from this X == $18,400. COST OF LUMBER 95 If the yearly cut is 20 million the depreciation is 92 cents per M. feet. It should be noted that this 92 cents pays for this part of the outfit including all interests. c. The cost of logging. Logging is a very simple kind of business but the conditions under which it is done are variable and many, and tend to complicate matters. Size and quantity of timber per acre, mixture of species, mixture of large and small stuff, distances, topography, surface, rocks, brush, swamp, weather, snow, etc., all exert their influence. The men are scattered over a large area and not easily supervised. Where the timber is large as in the Pacific coast ccuntry or located in swamps as cypress so that heavy machinery must be employed the matter is made still more difficult. Nevertheless the cost of logging like milling varies within nar- row limits, the good parts of the job making up for the bad. Us- ually it may be said that the cost of logging varies from 4 to 6 dol- lars per M. feet b.m., rarely going below 4, occasionally going up to 8 in mountain country. For eastern United States it runs per M. feet logs about as follows: Felling and cutting into logs...............2 000 eee $ .75 Skidding and swamping................e eee cece ee eeee 1.25 Hauling to landing or railway.........0.... 0000 cee aee 1.50 Ratlway hati, OF dfivé.s.cs cis cacexsoewnesnmeed eons wa 1.00 Overhead charges of supervision replacement of equip- ment, teams, camps, roadS............ cee sees eee 1.50 $6.00 In these items the profit is included with each item. For large timber on the Pacific coast: Felling and cutting into logs...............eceeee eee $ .60 Yarding and loading ..c0 i605 pe8 secede ies eee cheats 1.00 Hauling: to) milli, 2). ds censcuers ves veg xx a antares ws base 1.50 Booming, scaling, etc... .... ccc cece cece nee ee eee .40 DIF ECEMCOSIS: 20. Mcweumn yearend Auatetenhls aes $3.50 Depreciation of machinery and wire cables on basis of the time they last and how many millions they handle, also railway track and rolling stock, etc....$2.00 Taxes, insurance, interest on money invested, super- Niston: and: profits ws qieceaw od eos ge0r4444 Senda ease 1.50 96 FOREST VALUATION Usually logging is cheaper in the Great Lakes country and South than in East and West. But these general average figures are little more than guide marks, each job has its own peculiarities and it is not easy to standardize where considerations are so varia- ble and where the human element is so very impcrtant. Logging as done in the United States is the work of a transition period, many of the methods will disappear, simpler methods under more uniform conditions will take their place. When that time comes the cost of logging in the United States as is now the case in many of the forest districts of Europe, may be predicted within very close limits. , Where the sale of stumpage involves large amounts of timber, requiring ten or more years to remove, though cutting begins at once, the case of sale value grades into the expectation value, and demands special consideration. On the national forests large bodies of timber are sold, the timber is paid for as it is cut, the buyer does not really own the stumpage, he takes no risks in case of fire or other injury, except so far as the injury affects his camps, equipment and the use of his outfit or investments. In this case he not only can pay full stumpage value as calculated above but can pay higher prices for stumpage as the prices of lumber increase. For this rea- son provision is made in these contracts to review or re-arrange the price scale at fixed intervals or on a particular scale. C. Expectation value of stumpage. Leaving out the question of timberland speculation there still arise many cases where this value is involved. In buying a large lumber business, mill, railway equipment and body of timber, the first question is: what is the timber worth? Suppose the concern has four hundred million feet or twenty years’ supply of stumpage, the present value of stumpage for immediate use being five dollars per M. feet. Evidently it would be a mistake to pay for the four hundred million at the rate of five dollars per M. feet unless the buyer is very certain that the increase in value of lumber warrants this. How much increase would this mean? If he pays $5 per M. feet, or 2 million dollars for the 400 mil- lion feet, and if money is worth 5%, then this sum grows to 2 mil- lion X (1.05°) or $5,300,000 in round numbers. The lumber val- ues do not rise year by year but rise by groups of years usually, and with this rises the value of stumpage. Assume that the stumpage stays at $5 for the first 10 years and then rises to a constant figure 3 ec To years, how much must this be? About $13 per . Teet. EXPECTATION VALUE OF STUMPAGE 97 If he pays $5 and stumpage does not rise he loses upwards of two million dollars in the twenty years. What can he pay if he expects stumpage to stay at $5? About $3.10 per M. feet. In these calculations no attention is paid to expenses, taxes, pro- tection, etc., which the owner has to incur in holding these forest lands. The way of computing these was indicated under cost value of stumpage and in other connections. From what has been said about stumpage valuation it is evi- dent that in most cases it is a matter of business judgment and inti- mate knowledge of conditions which guides the investor. This knowledge is largely one of forest utilization. The methods of cal- culation or arrangement of data present nothing new but follow the general lines of forest valuation. The traffic in stumpage as it has existed in the United States up to the present time will be modified in time and take more and more the form of timber sale now in use on the national forests and in the more settled districts change to the form of timber disposal now in use in central Europe. Good silviculture will press steadily for full control of the timber cutting. VII. DAMAGES IN TIMBER Here belong a great variety of cases, from gas injury of shade trees in the town to the burning of Jarge bodies of timber by fires started by a railway locomotive. And it is not merely the cases where someone is liable or supposed to be so, but the numberless additional cases where it is part of the forest business to ascertain damages done by fire, storm, insects, etc. Normally, the damage is only to the live, growing trees, but at times there is added damage, since it may cost considerable sums to put the land in shape for a new crop. Commonly these cases are complicated. A fire running through a stand of hardwoods may kill half the trees and leave the rest in an injured condition so that a few survive staying alive for twenty years, while most of them die during the first five years. In such cases it is anvthing but easy to determine the exact facts, or condition. Such cases are usually complicated still further by the fact that parts or all of the timber could be used if cut at once, but that various circumstances prevent the owner from cutting, so it may be several years before he gets to all of the lands burned over and in this way loses nearly all of the timber. How far conditions compel him and how far he is at fault himself is usually impossible to ascertain accu- rately. Only a few sample cases may he considered here: a. The shade tree in town. A tree forty years old, satisfactory in every way, is destroyed by a gas leak. What is the true value destroyed? The owner guid- ed by his feelings would probably place the value at several hun- dred, the person responsible for the leak would value it as fire wood. The following calculation may be helpful and approach a just settlement as nearly as possible: Cost of establishing a good tree, $15; interest at 5% ; 25 years before the tree is really serving its purpose, after that the tree pays its way, pays by its service as shade tree interest on the cost of es- tablishing it. The value of the tree is then 15 (1.05%) = $51.80 and this val- ue remains as long as the tree is in good condition. Cost of caring for the tree, etc., might also be added. DAMAGE ESTIMATES 99 b. Young plantation of forest trees. Spruce twenty-five years old destroyed by fire; evidently the stuff is of little use save as inferior fre wood. Assuming the cost value of the stand to be forty-five dollars and the value of the dam- aged wood to be ten dollars per acre the real damage is clearly thir- ty-five dollars. li the wood is of no value and the man spends ten dollars per acre to get the land cleared sufficiently to plant another crop, the loss to him is fifty-five dollars. In the past the courts in the United States judged the value of the timber solely as sale value. Since the timber on this plantation has no sale value and since the man actually incurred these losses it is only fair that he should receive pay accordingly. To ask damages in proportion to an expectation value of this stand, on assumption that at the age of eighty vears, or fifty-five years hence, the stand may be worth five hundred dollars an acre, while perfectly reasonable, would not appeal to any court of justice. c. Older plantation of pine. Fifty-year-old stand completely destroyed, sale value is only one hundred and twenty dollars an acre, but the expectation value on an eighty year rotation is two hundred dollars. Which should be al- lowed? Evidently the latter, or at least a compromise between sale and expectation value. In this case the costs of establishing the stand are remote; it ray have been natural reproduction on non- agricultural land, etc., and might be less than fifty dollars. So it would not be fair to restrict the price to this cost value. On the other hand, expensive planting on costly land and much extra care, cultivating, etc., might bring the cost value to two hundred and fifty dollars, which in all probability would not be allowed. d. Ordinary Stand of wild woods. Timber on forty acres of hardwoods and hemlock is largely destroyed by fire. History and conditions of the forty acres of forest: bought 12 years ago at $800; interest rate 5%; ready to cut 7 years from now; timber 400 M. feet, present stumpage price $5 per M. feet; land now worth Sro per acre when cut over; expect stumpage to go to $6 in the next 7 years. Value of timber after fire, $500; tax and care for the 40, $30 per vear. 100 FOREST VALUATION Estimate of the damage may be set in one of three ways: 1. By cost value: ‘Value before fire: $800 (1.057) ....... 0... cece eee eeee $ 1434 30 (1.05"°—1) Tax and care...... cece 480 (1.05—1) ED Otalls eeeasoeag GaKe 400 Total gross value in 7 years.......... $2800 Expenses during 7 years: 30(1.05'—1) 1.03—1 2556 Present vale —— ..............008- 1817 Value after fire, $900; damage, $917. In cases of this kind the value of the young stuff, i. e., the non- merchantable part of the growing stock is usually left out of the calculation, though frequently it has a greater value than the mer- chantable stuff. ESTIMATE BY AVERAGE YEARLY GROWTH IOL e. Young Stands in Wild Woods. In the more remote districts of the United States the value of the land, and the value of young, or non-merchantable timber is de- batable. The determination of the cost of production of such a stand, with calculations of compound interest, rent, charge of pro- tection, etc., is not well understood, and not well received, and the same is even more true with regard to the expectation value. For such cases it has been suggested to use a method strongly advocated for years by Frey in Germany (See Zeitschirft fir F. and J., 1915, p. 284), and employ the sale value exclusively as the basis of estimate. Ordinarily this would work out about as follows: The ripe stand, 120 years old, is worth $300. -A stand 40 years 300 X 40 old is worth ————-. Generally, then, the value of any stand is 120 based on the average yearly growth in value, in the above case: 300 == $2.50 per acre and year. Due allowance is made for de- 120 gree of stocking or condition of the stand. The advantage of this method lies in its simplicity ; it expects the trespasser to pay only for the wood actually on the ground and destroyed. For stands older than one-half the rotation this method is satisfactory; for young stands it does not quite do justice to the owner. Thus if a plantation is destroyed 4 years after being estab- lished the $2.50 per acre and year (in above case) would hardly clean the ground and replant, and the owner would have nothing for the four years’ growth and expenses. To charge the cost of planting and protection, etc., to the $10.00 actual value per acre, in this case, is really to ask pay for the stand twice, once, its actual value, and once on basis of cost of production, or at least a large part of this. Where natural reproduction is assumed to require 10-20 years time, this period of reproduction is made part of the rotation; i.e., the rotation includes the entire time from one harvest to the next. For the above case the crop worth $300 is produced in 120 years. If an additional 16 years is required for natural reproduction the 300 average yearly growth is: ————— = $2.20 per acre and year. In 120 ++ 16 the usual case of natural reproduction a stand of trees with an aver- age of 20 years may contain trees from about 12 to 28 years old; 102 FOREST VALUATION the land has been occupied and used for 28 years, and the question arises: should the trespasser pav for a stand 20 years old or one 28 vears old? Evidently the latter, at least in all cases of clear. cutting. In the shelter-woods where an old stand shares in the growth dur- ing the 16 years in which the new stand is established, it may suffice to charge for 20 years’ growth. It is evident that this method of computing the value of the stand lacks analvsis and must always be defective especially with young stands, where the computation of the regular cost value of stand is much more satisfactory. f. The lumberman'’s case. Two years after the fire, claimedly caused by the locomotive of a railway company, the lumber company sues the railway com- pany and claims: Lumber company bought, merely as “permit” or “license,” from the Canadian province, 460 million feet stumpage, it had cut three years and still owned 400 million feet, it has the right to continue lumbering on the “timber limit” as long as there is any timber ; it pays 50 cents per MM. feet “rovalty,” or stumpage; it in- vested $200,000 in mill, railway and equipment, and aimed to cut the timber in next 20 vears; was making a profit of $2 per M. feet in the business. The fire destroyed 200 million and so reduced the cut by nearly Io years, since most of the timber destroyed is not vet accessible. The particular claim set forth: 1. Lump sum to cover loss in manufacture of lumber and for increased cost of logging due to reduction of total stand available for the plant. 2. Value of stumpage actually destroyed. 3. Value of equipment, camps, railway bridges, etc., de- stroyed. 4. Logs and ties burned up. 5. Value of young timber. not yet merchantable, destroyed. Among the questions which came up were the following: 1. Is all dead timber on the area killed by the particular fire? 2. Is all dead timber actually a loss, and if not how much has been saved, how much could be saved, and at what gain? 3. What is the company’s basis for claiming that it can make $2 per M. feet, and how is this affected by future logging from more remote portions of the tract? 4. What effort did the company make to protect its logs and equipment ? LUMBERMAN’S CASE 103 5. What right has the company to claim pay for immature stuff when the forest belongs to the province and the company pays stumpage as it cuts? 6. Is not the province the real owner of the stumpage and the one entitled to pay for stumpage destroyed? 7. What rate of interest should be used in calculation of damages? Other complications came up but need no mention here. Evi- dently claim numbers five and two for young stuff and stumpage re- quires a court decision as to rights of a “limit holder.” If favorable, then the expectation value or Ge should be established on basis of growth study, and cruise. Claims three and four are clearly right, if properly substan- tiated. Claims one and two are not easily separated since one depends on two. The simplest calculation is offered hy establishing the in- come or expectation value of the whole business before the fire and the same value after the fire and the difference should be the loss. Expectation value before the fire: the cut is 20 million feet per year with profit, (evidently net income and profit), $2 per M. feet, or a total of $40,000 per year; interest at 3% ; since this would have continued for 20 years the present value of these 20 years income is: (1.03"—1) (1.03—1) 1.03% $591,000 40,000 plus the provable wrecking value of the outfit at end of 20 years, discounted to present time; let this be 10,000, then the total is $601,000. The expectation value after the fire on basis of only $1.50 profit, due to extra work of logging. (1.03.—1) 1.03—I 1.03” = $257,000 plus the wrecking value at end of ten years, discounted to present time; if this is $50,000, then the present value is $307,000, and the loss due to fire is about $294,000. Another way of attacking. this problem is to ascertain the value of the stumpage on a liberal basis. Good stumpage is sold at $2 in this district. Assume that 200 million feet are destroyed, that this timber would have formed a uniform part of the cut during the 20 years. Then its present value is as follows: 104 FOREST VALUATION Every year 10 million would have been cut, valued at $20,000 ; (1.03°° --- 1) —-——_—-—— = $296,000. total present value: 20,000 (1.03 —1) 103”° In questions of this kind there is still some uncertainty as to how far a company or person should be held responsible in cases of fire. In the city the owner ofa burning building is generally not held liable for harm which comes to other properties from the burn- ing of his. In any case the public and both parties to the suit are more or less closely bound together and should suffer together. This case sufficiently illustrates efforts at determining damage. It is evident that it is chiefly a matter of accurate examination into all the facts and the establishment of a reasonable basis which is needed. Detail knowledge of the business and honest dealing should solve these problems outside the courts. VIII. TAXATION OF FORESTS The subject of forest taxation is primarily one of public policy ; the attitude of government toward the forest business. But since the basis of equitable taxation of forests must be supplied by forest valuation a brief treatment of this subject is necessary. a. Taxation is for public good, to collect money for public expenses. There are three fundamental principles apparent in all taxation except punitive forms which have no place here: 1. All people are asked to share in proportion as they are able to pay. 2. Taxation should be no more irksome or offensive than is necessary, indirect taxation, revenue, tariff, etc. 3. Taxation should not interfere or injure useful or necessary business. While rarely expressed in just this way, the many modi- fications of the methods of taxation to suit different kinds of busi- ness were based on this principle fully as much as on the difficulty of finding a satisfactory basis. Even in the United States we have taxes of various kinds: or- dinary property tax for house, farm, valuables, etc.; income tax, national, and also for railwavs by states, poll tax or head tax, “road tax” to be worked out or paid for, tariff duties, internal revenues, licenses to do business, special taxes, like present war tax, and other forms. Taxes are gathered by United States authorities for the na- tional government and by local authorities for town, county and state. b. In ordinary taxation of real estate in the United States we have to distinguish between assessment and rate. 1. The assessment sets a value on the property. It usually takes the ordinary sale or market value, it may take the entire value or only a certain, more or less uncertain fraction. This latter con- dition is not always fixed by law and even where it is, it is com- monly modified in practice and gives the assessor a chance to favor certain persons or properties. It is clear that this local agent, an ordinary elective officer, without special training, experience or other qualities, can modify the amount of taxes paid on any particular property and in this way he becomes the most important part in the entire tax system. 106 FOREST VALUATION That this is not easily overcome by law is well illustrated in the report of the State I'ax Commission of Michigan where it is shown that about one half of the state, in 1914, was assessed at nearly full value, (ninety-seven per cent), and the other half at only sixty-nine per cent, in spite of the law which requires assessment at full cash value, and in spite of the efforts of past tax commissioners. As late as 1911 the assessment for the whole state was about sixty-one per cent of the full value. Assessment is not always simple. A 16c-acre farm with ordi- nary buildings may make a good net income and yet sell for only $50 an acre while a similar farm with fine brick buildings, etc., may not pay expenses and yet sell for $100 an acre. Fundamentally the owner of the first farm is better able to pay. In practice the second farmer pays double the taxes. A store or factory doing poor business may not be worth the land and buildings, or visible property, one doing a good business may be worth five times the sale value of the visible property. Of two railways from Detroit to Chicago the shorter one is the best paying and most valuable but the longer route cost more money to build and maintain, etc. 2. The rate of taxation is set to meet the expenses necessary or supposed to be necessary by state, county and town. The total taxes, state, county, town, including road, school, etc., for Michigan have been about fifteen to eighteen per thousand dollars worth of property. Of $16.55 total taxes in 1902, $12.26 were for local taxes, town, school, roads, etc., $2.41 for county and only $1.88 for state. Naturally the local taxes vary most, and vary from one school dis- trict to another, even in the same township. The great range for different counties in the same state is apparent from the following: for 1901 the average tax rate for the different counties in Michigan was as follows: Over $ 50 per $1000 property in 1 county 40-49 5 30-39 13 20-29 30 15-19 18 10-14 15 Below 10 dollars I It is apparent that in any county where timber is assessed at full value and taxed at forty dollars per thousand of value, the inter- est and taxes eat up the property every six or ten years. Since this rate is an arbitrary affair without limits and left to local politicians, UNITED STATES TAX RATES 107 it is quite common that the tax rate and not the tax assessment is the more dreaded phase of taxation. Good, old settled, rural dis- tricts in southern Michigan commonly fall below ten dollars per thousand of property while poorly settled, new, districts are normally high in their tax rates, in fact one of the most sparsely settled coun- ties in 1901 had an average tax rate of over sixty-three dollars per thousand of property. It is doubtful if rural taxes should be al- lowed to go much above ten dollars per thousand. In this connection the following table is interesting: Tax Rate Per Thousand Dollars of Assessed Valuation, according to bulletin 109, Department of Commerce and Labor, 1910, p. 849: 1902 1899 1880 1870 1860 Continental United States..... $20.50 $18.50 $18.30 $19.80 $ 7.80 North Atlantic, Maine-Penna... 18.30 16.40 17.70 18.70 9.70 South Atlantic, Delaware- Florida .sccsedax els aeeuien 16.00 14.40 12.70 14.10 3.80 North Central, Ohio-Wisconsin- Kansas-Minnesota ..... ste B4IO: 23-70 20.90 24.40 11.70 South Central, Kentucky-Arkan- sas-Alabama-Texas ....... 17.30 14.30 16.30 18.00 "4.10 Western, including Pacific Coast 25.50 19.90 22.30 25.50 17.70 Ohio: gesweesce ices ye seemsounee 23.80 19.10 16.80 20.10 10.09 MnGiana ses taleshscussgaeeeganie 19.70 18.20 16.40 16.30 9.00 THOS, ai esveedh eae ia Oernlececans 51.50 40.90 31.30 45.20 15.70 Michigan, << +s «smdeveenoavackons 16.60 16.10 16.70 19.99 10.80 New Yiothk: ¢o:.44 fava aewdumccee 22.20 19.80 21.30 24.70 II.00 Pennsylvania ................. 14.90 14.00 17.10 18.70 12.10 Massachusetts ................ 15.80 14.60 15.40 15.70 9.60 Wisconsin ............ aegaoaute 13.60 22.90 18.70 16.20 12.50 The above table indicates that Michigan, in this, as many other matters is very nearly average and also that for the entire Union fifteen to twenty dollars per thousand is considered a reasonable rate. The tendency to increase in rate may be expected to give way to a tendency to decrease with about twelve dollars per thousand as the proper minimum for the state and about six dollars for rural property. In circular 132, A, United States Department of Agri- culture, 1913, this rate of six dollars per thousand, of farm property, is accepted as average for farm property in the United States. As 108 FOREST VALUATION pointed out, property is not assessed at full value and even in states where the law demands this it is not done consistently. In most states the assessment is at about 2/3 value for rural property and varies from twenty-five to one hundred per cent in city property with large amounts escaping taxation altogether. c. When farm taxes were gathered as “tithes,” or one-tenth of the crop, not in money but in grain, etc., the tax was clearly'a personal tax and of the nature of income tax, on gross income. When this changed to a fixed money tax, based on the value of the farm and this latter based on the fertility of the farm, it lost the character of a personal tax though still of the nature of a tax on an implied or estimated income. ‘ Today in the United States the farm or forest is assessed at its sale value; the tax books are based on the property, it is the prop- erty which is taxed regardless of ownership. If the owner neglects to pay, it is not the owner who is looked up and addressed, but the property itself which is at once taken charge of and sold for taxes, etc. The property tax as it applies to real estate, farm and forest, then, is no longer a personal tax, it ignores the owner and condi- tion of ownership, is not concerned whether the owner is able finan- cially, or poor and in debt, whether or not he makes any income from this property. d. In Europe forests are taxed in various ways. Usually the forest property is so regulated that a yearly income is secured and the ordinary forest property resembles the farm and the ability of the owner to pay is much more easily determined. The three forms of forest taxation most generally applied in central Europe are: ground tax; income tax; property tax. 1. The ground Tax, “Grundsteuer,” or “Ertragsteuer,” of the Germans is a tax on the soil, based on its estimated income or else on an official estimate of the productivity, ‘““Kataster,” and is used exactly like the ordinary tax on farm property or real estate in the United States; where the farm is largely assessed according to the crop it produces. 2. The property tax of European states is a regulator in cases where the property does not produce an income in keeping with its value. An empty lot in the city is only an expense to the owner but it has a sale value. Similarly a farm in the outskirts of a city may be worth a thousand dollars an acre and yet as a farm may not make as large a net income as another farm three miles away and valued INCOME TAX IN FOREST 109 at only one hundred an acre. Private parks, summer homes, etc., belong in this class. In these cases the sale value of the property is taken in the assessment. 3. Income tax is a personal tax and takes a certain part, say one-tenth, of the net income. The income is taken as an average of three or five years and all expenses are deducted. In these expenses are included also the interest which the owner of the property is paying on debt. The following case illustrates: Area of property, 10,000 acres; Forest of spruce, all one site; Clear cut and plant, rotation, 100 years; Yr, $500, yearly cut, 100 acres, worth $50,000 ; Yearly expenses, $1.50 an acre, or $15,000 total; Tax rate, one-tenth of net income. The taxes are: 0.10 X (50,000 — 15,000) or $3,500. This amount is seven per cent of the stumpage value of the ripe timber cut during the vear so that a yield tax of seven per cent in this typical case is equivalent to ten per cent on net income. If in the above case there was a mortgage of $200,000 at 4% on the property the $8,000 of interest would he added to the expenses and the taxes reduced to $2,700. 4. Where the forest is not regulated it does not produce a yearly income but produces an income only at long intervals, (inter- mittent working of Schlich), as for instance a single plantation, all one age and kind where, if we neglect thinnings, no income is se- cured from time of planting till the stand is ripe. In such cases the method of taxation by income tax is not readily applicable and vari- ous modifications are employed. The simplest of these and most nearly in keeping with the principle of income tax is the postponing of payment until the timber is ripe and then paying a sufficient sum in keeping with the large income at that time. In other cases the value of the intermittent income is calculated and converted into a yearly income by the formula: periodic income __ yearly income I.op"—I I.op—t periodic income .. yearly income = y y I.op"—I But this means practically a return to the ground tax system which in these cases no doubt deserves preference. IIo FOREST VALUATION 5. The state and local taxes in Germany are not always com- puted by the same methods, in fact it is common for state taxes to be levied as income tax and local taxes as ground or property tax. Since the state forests pay local taxes, corresponding to county, town, highway, etc., taxes with us, and since these local taxes repre- sent probably not less than seventy-five per cent of all taxes paid, the following figures are of interest, doubly so because they affect a large proportion of all forests of the several states. Local taxes paid on the state forests of Wtrttemberg on a total area of about 490,000 acres: wale Local taxes paid by state. ° forest or Yearly met net Tax Years. | income | income Tax Tax Pls capital- per Total Per on as % of ot ized acre: $1000. ee iad ae stump- at 10 %. $ property.| income, | "oo $ per $ % % acre, » 1880-89 26 $2.69 80.9 .16 6.10 6 4.3 1890-99] 38 3.86 105 al 3.50 5.4 4:3 1900 50 5-07 117 i2g 4.60 4.5 3.7 IQOL 54 5.41 119 24 4.45 4.4 Bich 1902 47 4.73 126 +25 5.30 5.2 4.1 1903 51 5.10 128 26 5.10 5.1 3.9 1904 57 5.79 105 21 3.69 3.6 2.9 1905 61 6.10 167 34 5.55 5.6 293 1906 67 6.78 178 .36 5-35 5-3 4.1 1907 74 7.47 188 . 38 5.10 5.1 4.1 1908 65 6.50 200 mar 6.30 6.3 4.9 Assuming these local taxes to be seventy-five per cent of total taxes the forests of Wiirttemberg were taxed in 1908 on a basis of about $8.40 per $1,000; or 8.4 of net income, or 6.5 stumpage tax, or 54 cents an acre. The following figures represent the same con- dition for the state forests of Baden for the year 1902, arranged by the political districts: TAX RATES IN EUROPE III Local taxes paid by the state forests of Baden in 1902: Value of Local Taxes. Area Net ost et Tax Tax Le of yearly | pasis $1000 as Jo as Jo District. | forests,] income of pret of of 1009 per net Total Per erty. |. net stump- acres; | “acte: |ineome| yooo. | dere. * |income.| age. and 10 %. $ $ $ $ $ %o Jo I 13 8.48 &4 3.5 27 3.20 3.2 omg 2 4s 3.52 35 8 18 5.10 Sak 4. 3 110 5.98 59 | 32.5 29 | 4.90 4.9 355 4 50 5.92 59 | 23.7 47 | 8.00 8. 6.1 5 46 6.19 61 4-5 09 1.48 1.4 2.1 6 8 4.13 41 3.2 40 9.80 9.8 a. ay, 14 2.04 20 33 22 | I1.00 II GF. ti as 248 S78 | Se | 78 29 | 3.10) for 44 The great variation in the local taxation as it appears in this table is, no doubt, due to the fact that so many villages and towns in parts of Baden have large communal properties which relieve local taxation very materially. On previous assumption of loca] taxes representing seventy- five per cent of total taxes the Baden forests were taxed in 1902 about thirty-eight cents an acre; six dollars and eighty cents per thousand dollars worth of property ; six and eight-tenths per cent of net income; or five and eight-tenths per cent of stumpage cut per year. In Prussia with about 6,540,000 acres of state forest the local taxes for many years varied between three and a half and four and a half per cent of total expenses. Taking the year 1892-93 as basis of income and expenses, the following results: Total iricomeé (per AChE: so % aces ckmarwre oees vex cede s as $ 2.66 Total. expenses Per aCrciidvceecwednne deed ones eames 1.38 Net inCOMe Per ACKC.. 2.2 cccncke dade dev ete chasse ane 1.27 Value of forest per acre on 10% basis............... 12.70 Local taxes at 4% of expenses per acre: 5.2 cents, Local taxes per $1000 property. ........ eee eee eeeee 4.20 As per cent of net income .......... ccc sense eee eee ee 4.2% As per cent of stumpage.......... 00. e cere cece eens 2.3% 112 FOREST VALUATION Assuming again the local taxes to be seventy-five per cent cf total taxes these forests appear taxed at about seven cents per acre; or five dollars and sixty cents per thousand; five and six-tenths of net income, or three per cent of value of stumpage. 6. The general tendency in forest taxation in Europe is toward some form of income tax but it is doubtful if ground tax and property tax will ever be entirely dispensed with. An important and interesting fact is that forestry as a business is not only possi- ble but thrives under a variety of methods of taxation and that in the best forest districts, Wiirttemberg, Saxony and Baden, the old- est form of ground tax is still employed. This clearly proves that it is not so much a matter of method of taxation as it is an understanding of ferestry as a business and a sense of justice which is needed, here, as in many other lines of taxation. The application of some one simple method by one au- thority, as is done today in the United States for farm property, would certainly be preferable to the irregular variety of taxation, in method, rate and authority of most European countries. e. Forest taxation in the United States. 1. Forests are taxed in all states of the Union as real estate, the timber and the land, or crop and land being taxed together. The taxation is not uniform; in one county the forest may be assessed low as wild land, in another the timber is carefully estimated and its value added. Non-resident owners and therefore a large part of the forest owners usually fare worse than residents of the township or county. A common mistake is to assess stumpage which can not possibly come into use for years, as if it were ready to cut at once. For instance—a lumber company has twenty years’ supply of stump- age; its mill is the most important enterprise in the county, furnishes opportunity for labor, market for produce and a supply of cheap building material. Stumpage is worth six dollars per M. feet. At a recent revision an effort was made to assess the twenty years sup- ply at this rate. It was shown that by doing so with the prevailing tax rate of three per cent, the taxes and interest would eat up the value of a large part of this stumpage long before the timber could be used at the mill. The complaint usually is that the present methods of taxation” force the owners to cut and thereby discourage the holding of for- ests. 2. In actual forestry practice, the present method of assessing the stand at full sale value and taxing it at a rate of three per cent would prove prohibitory. To illustrate: a plantation of white pine INFLUENCE OF TAX RATES II3 costs ten dollars an acre and is located on land worth ten dollars more. It is assessed at twenty dollars and pays taxes at three per cent for thirty years. So far the owner has had no income but has paid sixty cents per year for taxes alone. This together with inter- est at three per cent makes thirty vears holding of the plantation cost $28.54 for taxes. If now the value of the stand AC 30° VARS IS: — Ge Sauunvac awe eat muladgaieanlaieaes $100 WACS5O Years IS oven cee edces sass eeadias sean gne: 250 AL 96 Yeats AS: ance nrt news eaeewncaGi tesa s 400 and if the assessment is raised, as it should be according to law in some states, to these values at thirty and at fifty years the case is as follows: Taxes and interest between 30-50 years......... $ 80 Taxes and interest between 50-70 years......... 200 and the growth in value of the stand between fifty and seventy years fails by as much as fifty dollars to make good the expense of taxes. In addition to taxes there is a charge of $39.14 between 30 and 50 and a charge of $70.68 between 50 and 70 on the original invest- ment of land and plantation. The above case presents no special peculiarities, the rotation of seventy years is below the ordinary and the value of the stand at seventy is liberal. It is evident therefore that with present methods of assessment and rates, forestry, even at such favorable conditions as in the above case, must be carried on at a large loss. The fundamental fallacy of this method lies in the fact that the same year’s growth is taxed over and over again, for seventy years, in the above case. This is never done in taxation of farm property. 3. From the standpoint of the state or people the following is true: To the state the taxes on standing timber are only of mod- erate importance; in the Lake states and east of very little import- ance. On the other hand the secondary benefit through manufac- ture of timber is of great value to the state. With the counties this varies. In well settled farm counties the taxes from woodlots are unimportant and there is no reason why woodlots should not be treated like the rest of the farm land, i.e., the value of the timber left out of consideration. In sparsely settled forested counties the taxes from timber are important and there is usually clamor for large sums and also for a steady income, to enable development. 114 FOREST VALUATION In some localities this is justified, in most places it is not, for usually the sawmill, etc., are worth more to the counties than any direct taxes. Lack of state control and the unreasonable insistence on high local taxes have repeated the story of the goose of the golden egg a great many times in all our forest districts. The claims of the local people are usually of this order: the forests were not raised by their present owners but given away by the people at nominal prices to encourage the timber business and general development. The owners are not in the forestry business and have no intention of perpetuating the forest. There is no reason why a man should not pay taxes on a hundred thousand dollars which he invests in timber exactly as if he had invested it in other property. The holding of large areas of forest is a form of land monopoly and generally inimical to settlement and development. f. Reform in forest taxation in the United States. 1. For about forty years efforts have been made to encourage forestry either by modifying taxation or by actual bonus. Among the earliest of these efforts was the Timber Culture Act of 1873, giving United States lands on condition of establishment of a stand of forest trees. Since that time different states have enacted a variety of laws. Usually the aim was to encourage planting of woods in small tracts. In some cases the plantation was exempt entirely or partially, in others only the land was taxed and assessed at nominal value, etc. In most cases these laws, excepting the United States Timber Cul- ture Act, produced no results whatever. In the last five vears, Con- necticut, Massachusetts, New York and Pennsylvania have enacted well planned laws. In recent legislation the following three essential points in our transition stages of forestry in the United States are considered: The requirement of the local people of a continuous income is met by a yearly tax on the land, either on its sale value, or a nominal value. Lack of income from plantations and immature stands is con- sidered by deferring the tax on the timber to the time of cutting, i. e., making it a harvest or yield tax. The variable and peculiar condition of merchantable timber is taken care of by varying the amount of the yield tax. In the Connecticut law of 1913 the following provisions are made: 1. The application of the new tax law is optional with the owner. NEW TAX LAWS II5 2. Land worth twenty-five dollars or more is not considered forest land and does not come under the provisions of the act. 3. An existing forest placed under the new law pays not over ten per mill on actual value of the forest as a yearly tax, and when the timber is cut it pays a vield tax which is varied as follows: If cut in first ten years, yield tax.... 2% of stumpage value and 3% of stumpage value 3rd 4% of stumpage value 4th 5% of stumpage value 5th 6% of stumpage value after 5th 7% of stumpage value 4. New plantations are not exempt, but pay: a. Yearly tax on the assessed value of the land alone at not over ten per mill; b. Yield tax of ten per cent of the stumpage value of the ma- terial removed, to be paid when the timber is cut. In the Pennsylvania law of 1913 the harvest or yield tax is also set at ten per cent of the stumpage value, the land is assessed at one dollar per acre and the state pays the yearly land tax and the owner of forests is free to avail himself of the law. g. Basis of new tax laws. 1. The various efforts at some reform in forest taxation clear- ly show a lack of uniformity in the basis for such tax law. Even with regard to the land we have: Lands worth over twenty-five dollars excluded ; Lands assessed at sale value; Lands assessed at one dollar, in Pennsylvania, and assessment at five dollars recommended by Massachusetts. A reasonable sale value should be employed, and there is no reason why even fifty dollar land should be excluded. Efforts at tax dodging would be taken care of by the sale value assessment. 2. The greatest amount of uncertainty, however, was involved in finding a proper rate for the yield tax. Should it be five or ten per cent, should it be ten per cent of the stumpage, of logs at land- ing, at mill, etc.? 116 FOREST VALUATION Pennsylvania and Connecticut employed ten per cent without apparently attempting to develop a reasonable basis or giving an explanation. The Massachusetts Commission, see Senate document number 426, 1914, made an effort which preves instructive. Its premises are: Rotation, 50 years, also assumed by Connecticut and Vermont in recent acts (setting a general rotation is of very doubtful value and certainly 50 years will not raise proper sizes for general mar- ket) ; Tax rate, $17.39 per $1,000 worth of property; Yield at 50 years, $240; value of land, $5 per acre; interest rate for total tax, 8% ; for land tax, 5%. The plan is to pay a yearly tax on the land and pay a yield tax at the time of cutting the timber. The reasoning is this: the income from this property consists in the timber cut. The tax on this in- come or timber is the tax for the whole property, timber and land. The land tax is paid to furnish a yearly income for the local government but should be deducted from the yield tax which is the principal tax which the property should pay. Computation of vield tax or principal tax: The present value of Yr pays taxes every year at rate of $17.39 per $1,000, and this is to be compounded at 8%, so that for $1 of Yr we have: I 17.29 f 1.08°—1 1.08" “* tooo \ 1.08—1 ) = vied tax for each $1 Yr, or $0.212. Of this 21 cents only 2/3 is taken, since it is customary in Massa- chusetts to tax rural property on a 2/3 valuation. The yield tax then is 14 cents for each dollar of final yield or thirty-three dollars and sixty cents an acre, if $240 worth of timber is cut per acre. The land tax is computed as follows: 17.39 {1.05 —1 5X 7:39 5 ) tooo \ 1.05—1 or $19.11 an acre, which makes about 12 cents per $1 of final yield. Again taking only 2/3 of this, or 8 cents and subtracting this from the 14 cents yield tax leaves a final yield tax of 6 cents per dollar of stumpage, to be paid at the end of the rotation or when the tirn- ber is cut. In this way the commission decided that a yield tax of six per cent is a proper tax to charge. BASIS OF TAX RATES 117 An attempt to use the Massachusetts plan on other rotations gives, even with a uniform land price of five dollars an acre, the following yield tax: Rotation: 50) VeaTsiesdccs edad Oi weuw nav nea 6% Rs waved deeds quidem nee bess 3% TOO «= «pate s Eedee sas, Siceeanccoswmmabees —10% so that the state would be rebating as soon as reasonable rotations are employed. : 3. In seeking a proper basis for any tax rate the following may be assumed: The most important point of all is that the tax rate on forests should be no higher than that on other rural property. If farm property generally pays less than twelve per thousand in practically all parts of the United States then forest property should pay the same, but certainly not more. This principle is recognized in the Massachusetts plan. Again if the value of farm property universally is judged by the income which it can produce the same measure is fair for forest property. A yield tax should be fair not only for one rotation but for all reasonable rotations. In judging the value of a farm or forest for taxation by capital- izing the net income the interest rate should be fairly high, since the owner takes all risks and the state takes none. This also seems rec- ognized by the Massachusetts commission, and it is common practice in valuation of real estate. If a yield tax is fair for one stand of timber it is fair for any other stand regardless of methods and regulation, and the proper rate may, therefore, be found by a study of the regulated forest. That a regulated forest property would pay more taxes, even at the same yield tax rate than a property worked on the intermit- tent plan, is self-evident. The following case brings out the relations of property tax at 12 per 1,000 and the yield tax for the stands of a regulated forest at different rotations. Premises: Yr is taken at about half the normal yield in spruce, site II, as per Schwappach, Wer-at §0 years: v.eckesiessndsadisiesdeawcvede s $200 Wir Bt 275, Yeats” i iinwikage cee ernbinui olenaulas 400 Wie cat 100: years...owedeiecwasee oases 600 land, $5 per acre, p—10% to capitalize net income and find income value of the property, 118 FOREST VALUATION Current yearly expenses $1 per acre; cost of planting, $10 per acre. Tax rate, 12 per 1,000 as being about average for rural prop- erty in the United States. Relation of property tax at 12 per 1,000 and yield tax in regu- lated forest. Rotation, years. 50 73 109 Minimum number of acres in regulated forest, Be Cry FE ACHES -nyeecarte ties ean dsalesow ines 50 75 100 Yearly gross income from r acres, neglect CHINHINES crananicasce dvd dana Sin elem uren $ 200 $ 400 $ 600 Yearly expenses on r acres, current and plant- WTAE Siacouneern ee sateapt ami Captentes ee icreioSaccnseng Hane $ 60 $ 85 $ 110 Yearly net income from r acres.............. $ 140 $ 315 $ 490 Value of the r acres regulated forest, i. e., net income capitalized at ten per cent........ $1400 $3150 $4900 Taxes, as property tax at rate of 12 per 1000 Of -FACres: -seweanmsacs hse s he a N NN go0o ef oe H4a_ seis DhAI Ron P 8000 > So H g0— 7000 Db he” 6000 7 Fig. 4. Spruce; Middle and. North Germany; Sites I-V; Normal Yield of Main Stand in cubic ft. per acre. Also the points indicating at what age the average tree attains a diameter of 8”, 10” and 12”, and a height of 4o ft. 50 ft., etc. Only wood 3” and over is here considered. 153 50 60 70 80 90 00 WO A qe /4000 oft. D.b+e, a oo /3000 8 ae Hi0o fa = te /2000 /O0000 /0 000 Fig. 5. White Fir; South Germany; Sites I-IV; Normal Yield of Main Stand in cubic feet per acre. Also the points indicating at what age the average tree attains a diameter of 8”, 10”, etc., and a height of 60 ft., 70 ft., etc. Only wood 3” and over is here considered. 154 70 80 90 100 HO 20 130 [40 150 160 170 180 1/90 Age 8000 cr /000 eft /000 70 80 90 /00 //0 /20 130 /40 /50 460 _/70 /80 /90 Fig. 6. White Oak; N. Germany; Sites I-III; Normal Yield of Main Stand in cubic feet per acre. Also points indicating at what age the average tree attains a diameter of 12’, 16” 24”, and a height of 60 ft., 7o ft., etc. Only wood 3” and over is here considered. 155 , 506090 §0 GO 100 “0 /20 730 Age 8000 oft. 70 80 90 /00 0 120 /30 Fig. 7. Beech; N. Germany; Sites I-V; Normal Yield of Main Stand in cubic ft. per acre. Also points indicating at what age the average tree attains a diameter of 8”, 10”, etc, and a height of so ft., 60 ft. etc. Only wood 3” and over is here considered. 156 APPENDIX A 157 B. Tables of prolongation and discount. The following tables follow Kraft’s in his “Zuwachsrechnun- gen.” Their use is best illustrated by a few examples: 1. To find capital, Cn. A stand of timber has now 5,500 cubic feet per acre; a growth study determines that it is growing at 2.5%. What will this stand contain in 15 years, growth being assumed to continue at present rate? Under 2.5% find figure 1.448 opposite 15 years; multiply 5,500 by 1.448, result is the volume per acre in 15 years. The figure 1.448 is 1.025). 2. To find the initial capital Co. Same stand during the last IO years grew at rate of 3%. What was the volume Io years ago? Find in column of 3% the figure 1.343 opposite Io years. Divide 5,500 by 1.343, result is the volume 10 vears ago. 3. To find the growth in per cent. A stand now 50 years old can be sold at $6.10 per 100 cubic feet. From a growth study it is evident that if kept until 70 years old the stand would bring $10 per 100 cubic feet. What is the per cent growth in quality these 20 Cn 10 is 1.0p" we have I.op?° == —— == Co 6.10 years? Keeping in mind that 1.638 and p the rate of growth, 2.%. In teresting and convenient to use in this connection is the fact that the capital growing at com- 7a pound interest doubles, approximately, every — years. To illus- P trate, one dollar, or one cubic foot grows into two dollars or two 72 cubic feet at 3% in — = 24 years. 3 158 FOREST VALUATION Short Table of Years Values of 1.0p", where p — n 2 2,5 3 3,5 4 4,5 5 10 121 1,28 1,34 1,41 1,48 1,55 1,62 20 1,48 1,63 1,80 1,98 2,19 2,41 2,65 30 1,81 2,09 2,42 2,80 3,24 3,74 4,32 40 2,20 2,68 3,26 3,95 4,80 5,81 7,04 50 2,69 3,43 4,38 5,58 7,10 9,03 11,46 60 3,28 4,39 5,89 7,87 10,51 14,02 18,67 70 3,99 5,63 7,91 11,11 15,57 21,78 30,42 80 4,87 7,20 10,64 15,67 23,04 33,93 49,56 90 5,94 9,22 14,30 22,11 34,11 52,53 80,73 100 7,24 11,81 19,21 31,19 50,50 81,58 131,5 110 8,83 15,12 25,82 43,99 74,75 126,7 214,2 120 10,76 19,35 34,71 62,06 110,6 196,7 348,9 130 13,12 24,78 46,64 87,54 163,8 305,5 568.3 140 15,99 31,72 62,69 123,4 242,4 474,5 925,7 150 19,49 40,60 84,25 174,2 358,9 736,9 1507 160 23,76 51,97 113,2 245,7 531,2 —— — 170 28,97 66,53 152,1 346,6 786,4 —— — 180 35,32 85,17 204,5 488,9 1164 —. — 190 43,05 109,0 274,8 689,7 1723 —— — 200 52,48 139,5 369.3 972,9 2550 —- — APPENDIX 159 Years Values of 1.0p”, where p = n 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,0 1 1201 1,002 1,003 1,004 1,005 1,006 1,007 1,008 1,009 1,010 2 1,002 1,004 1,006 1,008 1,010 1,012 1,014 1,016 1,018 1,020 3 1,003 1,006 1,009 1,012 1,015 1,018 1,021 1,024 1,027 1,030 4 1,004 2008 1,012 1,016 1,020 1,024 1,028 1,032 1,036 1,041 5 1,005 1,010 1,015 1,020 1,025 1,030 1,035 1,041 1,046 1,051 6 1,006 1,012 1,018 1.024 1,030 1,037 1,048 1,049 1,055 1,062 7 1,007 1,014 1,021 1,028 1,036 1,043 1,050 1,057 1,065 1,072 8 1,008 1,016 1,024 1,082 1,041 1,049 1,057 1,066 1,074 1,083 9 1,009 1,018 1,027 1,037 1,046 1,055 1,065 1,074 1,084 1,094 10 1,010 1,020 1,030 1,041 1,051 1,062 1,072 1,083 1,094 1,105 11 1,011 1,022 1,033 1,045 1,056 1,068 1,080 1,092 1,104 1,116 12 1,012 1,024 1,037 1,049 1,062 1,074 1,087 1,100 1,114 1,127 13 1,013 1,026 1,040 1,053 1,067 1,081 1.095 1,109 1,124 1,138 14 1,014 1,028 1,043 1,057 1,072 1,087 1,103 1,118 1,134 1,149 15 1,015 1,030 1,046 1,062 1,078 1,094 1,110 1,127 1,144 1,161 16 1,016 1,032 1,049 1,066 1,088 1,100 1,118 1,186 1,154 1,173 17 1,017 1,035 1,052 1,070 1,088 1,107 1.126 1,145 1,165 1,184 18 1,018 1,037 1,055 1,075 1,094 1,113 1,134 1,154 1,175 1,196 19 1,019 1.039 1,059 1,079 1,099 1,120 1,142 1,163 1,186 1,208 20 1,020 1,041 1,062 1,083 1,105 1,127 1,150 1,173 1,196 1,220 21 1,021 1,048 1,065 1.087 1,110 1,134 1,158 1,182 1,207 1,232 22 1,022 1,045 1,068 1,092 1,116 1,141 1,166 1,192 1,218 1,245 é 1,023 1,047 1,071 1,096 1,122 1,148 1,174 1,201 1,229 1,257 24 1,024 1,049 1,075 1,101 1,127 1,154 1,182 1,211 1,240 1,270 25 1,025 1,051 1,078 1,105 1,183 1.161 1,190 1,220 1,251 1,282 26 1,026 1,053 1,081 1,109 1,188 1,168 1,199 1,280 1,262 1,295 27 1,027 1,055 1,084 1,114 1,144 1,175 1,207 1,240 1,274 1,308 28 1,028 1,058 1,087 1,118 1,150 1,182 1,216 1,250 1,285 1,321 29 1,029 1,060 1,091 1,123 1,156 1,189 1,224 1,260 1,297 1,334 30 1,020 1,062 1,094 1,127 1,161 1,197 1,283 1,270 1,308 1,348 35 1,086 1,072 1,111 1,150 1,191 1,233 1,277 1,822 1,368 1,417 40 1,041 1,083 1,127 1,173 1,221 1,270 1,822 1,875 1,431 1,489 45 1,046 1,094 1,144 1,197 1,252 1,309 1,869 1,481 1,497 1,565 50 1,051 1,105 1,162 1,221 1,283 1,349 1,417 1,490 1,565 1,645 55 1,057 1,116 1,179 1,246 1,316 1,390 1,468 1,550 1,637 1,729 60 1,062 1,127 1,197 1,271 1,349 1,432 1,520 1,613 1,712 1,817 65 1,067 1,139 1,215 1,296 1,383 1,475 1,574 1,679 1,790 1,909 10 1,072 1,150 1,233 1,322 1,418 1,520 1,630 1,747 1,872 2,007 75 1,078 1,162 1,252 1349 1,454 1,566 1.687 1,818 1,958 2,109 80 1,083 1,173 1,271 1,376 1,490 1,614 1,747 1,892 2,048 2,217 85 1,089 1,185 1,290 1,404 1528 1,668 1,809 1,969 2,142 2,330 90 1,094 1,197 1,309 1,432 1,567 1,713 1,874 2,049 2,240 2,449 95 1,100 1,209 1,829 1,461 1,606 1,765 1,940 2,132 2,842 2,574 100 1,105 1,221 1,349 1,491 1,647 1,819 2,009 2,219 2,450 2,705 110 1,116 1,246 1,390 1,551 1,731 1,981 2,154 2,402 2,680 2,988 120 1,127 1,271 1,483 1,615 1,819 2,050 2,310 2,602 2,931 3,300 FOREST VALUATION Years Values of 1.0p", where p = n eI 1,2 1,3 1,4 1,5 1,6 1,7 1,8 1,9 2,0 1 1,011 1,012 1,013 1,014 1,015 1,016 1,017 1,018 1,019 1,020 2 1,022 1,024 1,026 1,028 1,030 1,032 1,034 1,086 1,038 1,040 3 1,033 1,036 1,040 1,048 1,046 1,049 1,052 1,055 1,058 1,061 4 1,04F~.1,049 1,053 1,057 1,061 1,066 1,070 1,074 1,078 1,082 5 1,056 1,061 1,067 1,072 1,077 1,083 1,088 1,093 1,099 1,104 € 1,068 1,074 1,081 1,087 1,093 1,100 1,107 1,118 1,120 1,126 q 1,080 1,087 1,095 1,102 1,110 1,118 1,125 1,133 1,141 1,149 8 1,091 1,100 1,109 1,118 1,126 1,185 1,144 1,153 1,168 1,172 9 1,103 1,118 1,123 1,183 1,143 1,154 1.164 1,174 1,185 1,195 10 1,116 1,127 1,188 1,149 1,161 1,172 1,184 1,195 1,207 1,219 11 1,128 1,140 1,153 1,165 1,178 1,191 1,204 1,217 1,230 1,243 12 1,140 1,154 1,168 1,182 1,196 1,210 1,224 1,239 1,254 1,268 13 1,153 1,168 1,188 1,198 1,214 1,229 1,245 1,261 1,277 1,294 14 1,166 1,182 1,198 1,215 1,232 1,249 1,266 1,284 1,302 1,319 15 1,178 1,196 1,214 1,232 1,250 1,269 1,288 1,307 1,826 1,346 16 1,191 1,210 1,230 1,249 1,269 1,289 1,810 1,330 1,352 1,373 At 1,204 1,225 1,246 1,267 1,288 1,810 1,332 1,354 1,877 1,400 18 1,218 1,240 1,262 1,284 1,307 1,381 1,855 1,379 1,403 1,428 19 1,281 4,254 1,278 1,802 1,827 1,352 1,878 1,404 1,480 1,457 20 1,245 1,269 1,295 1,821 1,847 1,874 1,401 1,429 1,457 1,486 21 1,258 1,285 1,312 1,839 1,867 1,896 1,425 1,455 1,485 1,516 23 1,272 1,300 1,329 1,358 1,888 1,418 1,449 1,481 1,513 1,546 28 1,286 1,316 1,346 1,377 1,408 1,441 1,474 1,507 1,542 1,577 24 1,300 1,331 1,363 1,396 1,429 1,464 1,499 1,585 1,571 1,608 25 1.3815 1,347 1,881 1,416 1,451 1,487 1,524 1,562 1,601 1,641 26 1,329 1,864 1,399 1,485 1,473 1,511 1,550 1,590 1,681 1,673 27 1,343 1,380 1,417 1,456 1,495 1,585 1,576 1,619 1,662 1,707 28 1,858 1,397 1,436 1,476 1,517 1,560 1,603 1,648 1,694 1,741 29 1,873 1,418 1,454 1,497 1,540 1,585 1,631 1,678 1,726 1,776 30 1,388 1,430 1,473 1,518 1,563 1,610 1,658 1,708 1,759 1,811 35 1,467 1,518 1,572 1,627 1,684 1,748 1,804 1,867 1,932 2,000 40 1,549 1,611 1,676 1,744 1,814 1,887 1,963 2,041 2,123 2,208 45 1,636 1,710 1,788 1,869 1,954 2,043 2,185 2,232 2,333 2,438 50 1,728 1,816 1,908 2,004 2,105 2,211 2,823 2,440 2,563 2,692 ay 1,825 1,927 2,035 2,148 2,268 2,394 2,527 2,668 2,816 2,972 60 1,928 2,046 2,171 2,303 2,448 2,592 2,750 2,917 3,094 3,281 65 2,036 2,171 2,315 2.469 2,682 2,806 2,991 3,189 3,399 3,623 70 2,151 2,805 2,470 2,646 2,835 3,038 3,254 3,486 3,734 4,000 75 2,272 2,446 2,685 2,887 3,055 3,289 3,541 8,811 4,103 4,416 80 2,399 2,597 2,810 3,041 3,291 3,560 3,852 4,167 4,508 4,875 85 2,534 2,756 2,998 3,260 3,545 38,854 4,191 4,556: 4,952 5,383 90 2,677 2,926 3,198 3,495 3,819 4,173 4,559 4,981 5,441 5,948 95 2,827 3.106 3,411 3,746 4,114 4,518 4,960 5,446 5,978 6,562 100 2,986 3,296 3,639 4,016 4,482 4,891 5,396 5,954 6,568 17,245 110 3,331 3,714 4,140 4,615 5,144 5,782 6,387 7,116 7,928 8,831 120 3,717 4,185 4,711 5,303 5,969 6,718 7,560 8,506 9,570 10,77 APPENDIX 161 Years Values of 1.0p", where p = n 2.1. 2.2 2:3 2,4 2,5 2,6 2,7 2,8 2,9 3,0 1 1,021 1,022 1,023 1,024 1.025 1,026 1,027 1,028 1,029 1,030 2 1,043 1,045 1,047 1,049 1.051 1,053 1,055 1,057 1,059 1,061 3 1,064 1,068 1,071 1,074 1,077 1,080 1,083 1,086 1,090 1,093 4 1,087 1,091 1,095 1.100 1,104 1,108 1.118 1,117 1,121 1,126 5 1,110 1,115 1,120 1,126 1,131 1,137 1,140 1,148 1,154 1,159 6 1,183 1140 1,146 1,153 1,160 1,167 1,173 1,180 1,187 1,194 it 1,157 1,165 1,173 1,181 1,189 1,197 1,205 1,213 1,222 1,230 8 1,181 1,190 1,200 1,209 1,218 1,228 1,238 1,247 1,257 1,267 9 1,206 1,216 1,227 1,238 1,249 1,260 1,271 1,282 1,293 1,305 10 1,231 1.2438 1,255 1,268 1.280 1,293 1,305 1,318 1,831 1,344 11 1,257 1,271 1,284 1,297 1,312 1,826 1,341 1,355 1,370 1,384 12 1,283 1,299 1,314 1329 1,345 1,361 1,377 1,893 1,409 1,426 13 1,310 1,827 1,844 1,361 1,379 1,396 1,414 1,432 1,450 1,468 14 1,338 1356 1,375 1,394 1.413 1,433 1,453 1,472 1,492 1,513 15 1,366 1,886 1,407 1,427 1,448 1,470 1,492 1,518 1,536 1,558 16 1,395 1,417 1,439 1.462 1,485 1,508 1532 1,556 1,580 1,605 17 1,424 1,448 1,472 1497 1,522 1,547 1,573 1,599 1,626 1,653 18 1454 1,480 1,506 1,533 1.569 1,587 1,615 1,644 1,673 1,702 19 1,484 1,512 1,541 1,569 1,599 1,629 1,659 1,690 1,721 1,753 20 1,515 1,545 1,576 1.607 1,639 1,671 1,704 1,737 1,771 1,806 21 1,547 1,579 1,612 1,646 1,680 1,714 1,750 1,786 1,823 1,860 22 1,580 1614 1,649 1,685 1.722 1,759 1,797 1,836 1,876 1,916 23 1,613 1,650 1,687 1,726 1,765 1,805 1,846 1,887 1,930 1,974 24 1,647 1,686 1,726 1,767 *.809 1,852 1,895 1.940 1,986 2,033 25 1,681 1,723 1,766 1,809 1,254 1,900 1,947 1,995 2,044 2.094 26 1,717 1,761 1.806 1,853 1,900 1,949 1,999 2,050 2.103 2,157 27 1,753 1,800. 1,848 1,897 1,948 2,000 2,053 2,108 2,164 2.221 28 1,790 1,839 1,890 1,943 1,997 2,052 2,109 2,167 2.227 2,288 29 1,827 1,880 1,934 1,989 2,046 2,105 2,165 2,227 2,291 2.357 30 1,865 1,921 1.978 2,037 2,098 2,160 2,224 2,290 2.358 2,427° 35 2,070 2,142 2,216 2,294 2,373 2,456 2,541 2,629 2,720 2.814 40 2,296 2,388 2,483 2,581 2,685 2.792 2,908 3,017 3,138 3,362 45 2,548 2,663 2,782 2,907 3,038 3,174 3,316 3,465 3,620 3,782 50 2,827 2,969 3.117 3,274 3,487 3,609 3.789 3,978 4.176 4,384 55 53,126 3,310 3,493 3,686 3,889 4,103 4,329 4,567 4,818 5,082 60 3,480 38,690 3,913 4,150 4,400 4,665 4.946 5,243 5,558 5,892 65 3,861 4,115 4,385 4,672 4,978 5,304 5,650 6,019 6,412 6,830 70 4,284 4.587 4,912 5,260 5,632 6,030 6,455 6,911 7.397 7,918 75 4,758 5,115 5,504 5,923 6,372 6,856 7,375 7,934 8.534 9,179 80 5,273 5,703 6,167 6,668 7,210 7,795 8,426 9,109 9,845 10,64 85 5,850 6,358 6,909 7,508 8,157 8,862 9,627 10,46 11.35 12,34 90 6,491 7,089 7,741 8.452 9,229 10,06 11,00 12,01 138,10 14.30 95 7,702 7,904 8,673 9,517 10,44 11,46 12,57 13,78 15,12 16,58 100 7,991 8,812 9,718 10,72 11,81 13,02 14.26 15,82 17,44 19.22 110 9,836 10,83 12,20 13,58 15,12 16,60 18,74 20,86 23.21 25,83 120 12,11 13,62 15,31 17,21 19,86 21,76 24,46 27,49 30,89 34,71 FOREST VALUATION Years Values of 1.0p", where p = Mw 3,1 3,2 3,3 3,4 3,5 3,6 3,7 3,8 3,9 4,0 1 1,031 1,032 1,033 1,034 1,035 1,036 1.037 1,038 1,039 1,040 2 1,063 1,065 1,067 1,070 1,071 1,073 1,075 1,077 1,080 1,082 3 1,096 1.100 1,102 1,106 1,109 1,112 1,115 1,118 1,122 1,125 4 1,130 1,184 1,139 1,143 1,148 1,152 1,157 1,161 1,165 1,170 5 1,165 1,171 1,176 1.182 1,188 1,194 1199 1,205 1,211 1,217 6 1,201 1,208 1,215 1,222 1,229 1,286 1,244 1,251 1,258 1,265 7 1,238 1.247 1,255 1,264 1,272 1,281 1,290 1,298 1,307 1,316 8 1,277 1,287 1,297 1,807 1,817 1,327 1,837 1,348 1,358 1,369 9 1,316 1,328 1,889 1,851 1,363 1,375 1,887 1,399 1,411 1,423 10 1,357 1,370 1,384 1,397 1,411 1,424 1,488 1,452 1,466 1,480 11. 1,399 1,414 1,429 1,445 1,460 1,476 1,491 1,507 1,523 1,539 12 1,443 1,459 1,476 1,494 1,511 1,529 1,547 1,565 1,583 1,601 13 1,487 1,506 1,525 1,545 1,564 1,584 1,604 1,624 1,644 1,665 14 1,533 1,554 1,576 1,597 1,619 1,641 1,663 1,686 1,709 1,732 15 1,581 1,604 1,628 1,651 1,675 1,700 1,725 1,750 1,775 1,801 16 1,630 1,655 1,681 1,707 1,734 1.761 1,788 1,816 1,844 1,873 17 1,680 1,798 1,737 1,766 1,795 1.824 1,855 1,885 1,916 1,948 18 1,738 1,763 1,794 1,826° 1,857 1,890 1.924 1,957 1,991 -2,026 19 L786 1,819 1,853 1,888 1,928 1,958 1.994 2,031 2,069 2,107 20 1,842 1,878 1,915 1,952 1,990 2,029 2,068 2,108 2,149 2,191 21 1,899 1938 1,978 2,018 2,059 2.102 2,145 2,189 2,233 2,279 22 1,958 2,000 2,043 2,087 2,182 2,177 2,224 2,272 2,320 2,370 23 2,018 2,064 2,110 2,158 2,206 2,256 4,306 2,358 2,411 2,465 24 2,081 2,130 2,180 2,231 2,283 2,837 2,392 2,448 2,505 2,563 25 2,145 2,198 2,252 2,807 2,863 2,421 2,480 2,541 2,603 2,666 26 2,212 2,268 2,326 2,385 2,446 2,508 2,572 2,637 2,704 2,772 27 2,280 2,341 2,403 2,467 2,532 2,599 2,667 2,737 2,810 2,883 28 2,351 2,416 2,482 2,550 2,620 2,692 2,766 2,841 2,919 2,999 29 2,424 2,493 2,564 2,637 2,712 2.789 2.868 2,949 3,033 3,119 30 2,499 2,573 2,649 2,727 2,807 2,889 2,974 3,061 3,151 3,248 85 2,911 3,012 3.115 38,223 3,334 3,448 93,567 3,689 3,815 3,946 40 3,391 3,525 3,664 3,809 3,959 4,115 4,277 4,445 4,620 4,801 45 8,951 4,127 4,310 4,502 4,702 4,911 5,129 5,357 5,594 5,841 50 4,602 4,830 5,070 5,321 5,585 5,861 6,151 6,455 6,776 7,107 55 5,361 5,654 5,964 6,290 6,633 6,995 7.376 7,778 8,201 8,646 60 6,245 6,619 7,015 7,484 7,878 8,848 8846 9,373 9,930 10,52 65 7,275 7,748 8,251 8,784 9,857 9.963 10,61 11,29 12,02 12,80 70 8,473 9,069 9,706 10,39 11,11 11,89 12,78 138,59 14,56 15,57 75 9,872 10,62 11,42 12,28 18,20 14,19 15.26 16,40 17,63 18,95 80 11,50 12,43 13,48 14,51 15,68 16,94 18,29 19,76 21,34 23,05 85 18,40 14,56 15,80 17,15 18,62 20,21 21,94 23,81 25,84 28,04 90 15,61 17,03 18,58 20,27 22,11 24,12 26,31 28,69 31,29 34,12 95 18,18 19,93 21.85 23,96 26,26 28,79 31.55 34,58 37,89 41,51 100 21,16 28,33 25,71 28.32 31,19 34,36 37,88 41,66 45,87 50,50 110 28,74 -31,97 35,57 39,56 44,00 48.93 54,41 60,50 67,25 74,76 120 39,00 43,81 49,21 55,27 62,06 69,69 78,25 87,84 9859 110,7 APPENDIX Years Values of 1.0p", where p = n 41 4,2 4,3 4,4 4.5 4.6 4,7 4,8 4,9 5,0 all 1,041 1,042 1,043 1,044 1,045 1,046 1,047 1,048 1,049 1,050 2 1,083 1,086 L088 1,090 1,092 1,094 1.096 1,098 1,100 1,103 3 1,128 1,181 1,135 1,188 1,141 1,145 1,148 1,151 1,154 1,158 4 1,174 1.179 1,184 1,188 1,193 1197 1,202 1,206 1,211 1,216 S 1,223 1,228 1,284 1,240 1,246 1,252 1,258 1,264 1,270 1,27 6 1,273 1,280 1,287 1,295 1,302 1,810 1.317 1,325 1,333 1,340 7 1,325 1,334 1,843 1,852 1,361 1,370 1,379 1,389 1,398 1,407 8 1,379 1.890 1,401 1,411 1,422 1,483 1,444 1,455 1,466 1,478 9 1,486 1.448 1,461 1,473 1,486 1,499 1,512 1,532 1,539 1,551 10 1,495 1,509 1,524 1,589 1,553 1,568 1.583 1,598 1,614 1,629 11 1,556 1,573 1,589 1,610 1,623 1,640 1,657 1,675 1,693 1,710 12 1,620 1.638 1,657 1,677 1,696 1,716 1,735 1,755 1,776 1,796 13 1,686 1,707 1,729 1,750 1,772 1,794 1,817 1,840 1,863 1,886 14 1,755 1,779 1.803 1,827 1,852 1,877 1,902 1,928 1,954 1,980 16 1,827 1,854 1,881 1,908 1,985 1,963 1,992 2,020 2,050 2,079 16 1,902 1.932 1,961 1,992 2,022 2,054 2,085 2,117 2,150 2,183 17 1,980 2,013 2,046 2,079 2,113 2,148 2,183 2,219 2,255 2,292 18 2,061 2,097 2,184 2,171 2,208 2,247 2,286 2,326 2,366 2,407 19 2,146 2,185 2,225 2,266 2,308 2,350 2,393 2,437 2,482 2,527 20 2,284 2.277 2,321 2,366 2,412 2,458 2,506 2,554 2,603 2,653 21. 2,325 2,873 2,421 2,459 2,520 2,571 2,624 2,677 2,731 2,786 22 2,421 2,472 2,525 2.579 2,634 2,690 2,747 2,805 2,865 2,925 23 2,520 2,576 2,684 2,692 2,752 2,813 2,876 2,940 3,005 3,072 24 2,623 2.684 2,747 2,811 2,876 2.943 3,011 3,081 3,152 3,225 25 2,731 2.797 2,865 2,934 3,005 23,078 3,153 3,229 3,307 3,386 26 2,843 2,915 2,988 3,064 3,141 3,220 3.301 3,384 3,469 3,556 ae 2,959 3,037 3,117 3,198 3,282 3,368 3,456. 3,546 3,639 3,733 28 3,081 3$.164 3,251 3,339 3,430 3.523 3,618 3,716 3,817 3,920 29 8,207 3,297 3,390 3,486 3.584 3,685 3,788 3,895 4,004 4,116 30 3,338 3,436 93.536 3,640 3,745 3,854 3,967 4,082 4,200 4,322 35 4,081 4,221 4,365 4,514 4,667 4,826 4,990 5,160 5,335 5,516 40 4,989 5,185 5,887 5,598 5,816 6,043 6,279 6,523 6,777 7,040 45 6,099 6,369 6,650 6,948 7,248 7,567 7,900 8,246 8,608 8,985 50 7,257 7,823 8.208 8,611 9,033 9,475 9,939 10,43 10,93 11,47 55 9,116 9,610 10,13 10,68 11,26 11,87 12,51 18,18 13,89 14,64 60 11,15 11,81 12,51 13.25 14,03 14,86 15,73 16,66 17,64 18,68 65 13,62 14,50 15,44 16,43 17,48 18,60 19,79 21,06 22,41 23,84 70 16,66 17,81 19,05 20,37 21,78 23,29 2490 26,63 28,46 30,43 75 20,36 21,88 238,52 25,27 27,15 29,17 31,33 33,66 36,16 38,83 80 24,84 26.88 29,03 31.34 33,93 36,52 39,42 42,55 45,93 49,56 85 30,43 33,02 35,82 38,86 42,16 45,73 49,60 538,79 58,33 63,25 90 37,20 40,56 44,22 48,20 52,54 57,26 62,41 68,00 74,10 80,73 95 45,48 4982 54,58 59,78 65,47 71,70 78,51 85,97 94,12 103,0 100 55,60 61,20 67,37 74,14 81,59 89.78 98,78 108,7 119,6 131,5 110 83,10 92,35 1026 114,0 126,7 140,8 1564 173,7 192,9 214,2 120 124,2 1894 1564 175,4 196,8 220,7 247,5 277,5 311.2 348,9 FOREST VALUATION Years Values of 1.0p", where p = n 5,1 5,2 5,3 5,4 5,5 5.6 5,7 5,8 5,9 6,0 1 1,051 1,052 1,058 1,054 1,055 1,056 1,057 1,058 1,059 1,060 2 1,105 1,107 1109 1,111 1,113 1,115 1,117 1,119 1,122 1,124 3 1,161 1,164 1,168 1,171 1,174 1,178 1,181 1,184 1,188 1,191 4 1,220 1,226 1,230 1,234 1,239 1,244 1.248 1,253 1,258 1,262 5 1,282 1,289 1,295 1,301 1,307 1,813 1,319 1,326 1,332 1,338 6 1,348 1.3856 1,363 1,371 1,379 1,387 1,395 1,403 1,411 1,419 vi 1,417 1,423 1,486 1,445 1,455 1,464 1,474 1,484 1,494 1,504 8 1,489 1,500 1,512 1,523 1,585 1,547 1,558 1,570 1,582 1,594 9 1,565 1,578 1,592 1,604 1,619 1,683 1,647 1,661 1,675 1,689 10 1,645 1,660 1,676 1,692 1,708 1,724 1,741 1,757 1,774 1,791 li 1,729 1,747 1,765 1,783 1,802 1,821 1,840 1,859 1,879 1,898 12 1,817 1,837 1,859 1,880 1,901 1,923 1.945 1,967 1,990 2,012 13 1,909 1,933 1,957 1,981 2,006 2,031 2,056 2,081 2,107 2,133 14 2,007 2.083 2,061 2,088 2,116 2,144 2,173 2,202 2,231 2,261 15 2.109 2.139 2,170 2,201 2,233 2,265 2,297 2,330 2,363 2,397 16 2,216 2,250 2,285 2,820 2,355 2,891 2.428 2,465 2,502 2,540 17 2,329 2,867 2,406 2,445 2,485 2,525 2566 2,608 2,650 2,693 18 2,448 2491 2,534 2,577 2,621 2,667 2,712 2,759 2,806 2,854 19 2,573 2,620 2,668 2,716 2,766 2,815 2,867 2,919 2,972 3,026 20 2,704 2,756 2,809 2,863 2,918 2,974 3.030 3,088 3,147 3,207 21 2,842 2,900 2,958 3,018 3,078 3,140 3.203 3,267 3,383 3,400 22 2,987 3050 3,115 3,181 3,248 3,316 3,386 3,457 3,530 3,604 23 3,136 3,209 3,280 3,352 3,426 3,502 3,579 3,657 3,738 3,829 24 3.300 3,876 3,454 3,533 3,615 3,698 3.783 3,870 3,958 4,049 25 $8,468 3.551 3,637 38,724 3,813 38,905 3,998 4,094 4,192 4,292 26 3,645 3,736 3,830 3,925 4,023 4,124 4,226 4,832 4,439 4,550 27 3,831 3,930- 4.033 4,187 4,245 4,854 4,467 4583 4,701 4,822 28 4,026 4,185 4,246 4,361 4,478 4,598 4,722 4,850 4,978 5,112 29 4,231 4.350 4.471 4,596 4,724 4,856 4,993 5,130 5,272 5,418 30 4,447 4.576 4,708 4,844 4,984 5,128 5,275 5,427 5,583 5,744 35 5.703 5,896 6,095 6,301 6,514 6.734 6.960 7,195 7,486 17,686 40 7,313 7,596 7,891 8,197 8,513 8,842 9,184 9.537 9,905 10,29 45 9378 9.788 10,22 10,66 11,13 11,61 12,12 12,64 13,19 13,77 50 12.03 12,61 18,23 18,87 14,54 15,25 15,99 16,76 17,57 18,42 55 15,42 16,25 17,02 18,04 19,01 20,02 21.09 22,23 23,40 24,65 60 19,78 20,94 22,17 23,47 24,84 26,29 27,83 29,45 31,17 32,99 65 25,86 26.98 28,70 30,52 32,46 34,53 36,72 39,05 41,52 44,14 70 32,52 34,76 37,15 39,71 42,43 45,34 48,15 51,76 55,30 59,08 75 41,71 44,79 48,10 51,65 55,46 59,54 63,92 68,62 73,66 79,06 80 53,48 57,71 62,27 67,18 72,48 78,18 84,38 90,96 98,10 105,8 85 68,59 74.36 80,62 87,38 94,73 102,7 111,38 120,6 130,6 141,6 90 87,95 95,81 104,4 118,7 123,8 134,8 146,8 159,9 174,0 189,5 95 112,8 123,4 135,1 147,9 161,8 177,0 193,7 211,9 231,8 253,5 100 144,6 159,1 174,9 192,83 211,5 232,5 249,8 280,9 305,8 339,38 110 237,9 264.1 293,2 325,4 361,2 400,9 4449 493,7 547,7 607,6 120 391,1 438,4 491,4 550,7 617,0 691,38 488,7 867,5 971,7 1088 APPENDIX Years Values of 1.0p*, where p = H 6,2 6,4 6,6 6,8 7,0 G2 T4 7.6 7,8 8,0 1 1.062 1,064 1,066 1,068 1,070 1,072 1,074 1,076 1,078 1,080 2 1127 1.132 1,186 1,141 1.145 1,149 1,154 1,158 1,162 1,166 3 1.198 1,205 1,211 1,218 1,225 1,232 1,239 1,246 1,253 1,260 4 1,272 1,282 1,291 1,301 1,811 1,321 1331 1,341 1,851 1,361 5 1,351 1,864 1,377 1,390 1,403 1,416 1,429 1442 1,456 1,469 6 1,435 1451 1,467 1,484 1.501 1,518 1,535 1,552 1,569 1,587 T, 4.524 1,544 1,564 1,585 1,606 1,627 1,648 1.670 1,692 1.714 8 1,618 1,643 1,668 1,693 1,718 1,744 1.770 1,797 1,824 1,851 9 1.718 1,748 1,778 1,808 1,839 1,870 1,901 1.933 1,966 1,999 10 71.825 1.860 1,895 1,931 1,967 2,004 2,042 2,080 2,119 2,159 11 1.938 1,979 2,020 2,062 2,105 2,149 2,193 2,238 2,285 2,326 12 2,058 2,105 2,153 2,202 2,252 2,303 2.355 2,409 2,463 2,518 13 2,186 2,240 2,295 2,352 2,407 2,469 2,530 2.592 2,655 2.720 14 2.321 2.383 2,447 2,512 2,579 2,647 2.716 2,789 2,862 2,938 15 2465 2,535 2,608 2,683 2,759 2,838 2,918 3,001 3,085 3,172 16 2,618 2,698 2,781 2,865 2,952 3,042 3.133 3,229 3,326 3,426 lv 2,781 2,870 2,964 3,060 3,159 3,261 3,366 3.474 3,585 3,700 18 2,953 3,055 3,160 3.268 3,380 3,496 3,615 3,738 3,865 3,996 19 2.1386 3,250 3,368 3,490 3,617 3,747 3,882 4,022 4,166 4,316 20 3,330 3,458 3,590 3.728 3,870 4,017 4.170 4,328 4,491 4,661 21 3.5387 3,679 3,827 3,981 4,141 4,306 4,478 4.657 4,842 5,034 22 8,756 3.915 4,080 4,252 4,431 4,616 4,810 5,010 5,219 5,437 23 2,989 4,165 4,849 4,541 4,741 4,949 5,165 5,391 5,627 5,872 24 4,236 4.432 4,686 4,850 5.072 5,305 5.548 5,801 6,065 6,341 25 4.499 4.716 4,942 5,180 5,428 5,687 5.958 6.213 6,538 6,849 26 4,778 5.018 5,269 5,532 5.897 6,096 6,399 6,716 17,048 7.396 om 5074 5,339 5,616 5,908 6,214 6,535 6,873 7,227 7,598 7,988 28 5,389 5,680 5,987 6,310 6,649 7,005 7.381 7,776 8,191 8,627 29 5.723 6,044 6,382 6,739 6,794 7,510 17,927 8,367 8,830 9,317 30 6.078 6.431 6,803 7,197 7,612 8,051 8,514 9,003 9,518 10,06 35 §.210 8,769 9,365 10,00 10,68 11,40 12.17 12,99 13,86 14,79 40 11,909 11,96 12,89 13,90 14,98 16,14 17.89 18,73 20,17 21,73 45 14,98 16,31 17,75 19,31 21,00 22,85 24,84 27,01 29,37 31,92 50 20,24 22.24 24,43 26,82 29,46 32,34 35,50 38,96 42,75 46,90 55 27.84 30,33 33,62 37,28 41,82 45,79 50,73 56,19 62,24 68,92 60 36,94 41,35 46,29 51,79 57,95 64,82 72,49 81,05 90,60 101,3 65 49,90 56,39 63,71 71,97 81.27 91,76 103,5 1164 131,9 149,1 ff 67,41 76,90 87,70 100,0 114,0 129,9 148,0 1686 1920 2186 75 91,06 104,9 120,7 139,0 159,9 183,9 211.5 243.2 2795 321.2 80 123,0 148,0 166,2 193,1 224.2 260,4 302.2 350,7 406,9 472.0 85 166.2 195,0 2288 2683 314.5 368.6 431,9 505,8 592.4 693,5 90 224,5 265,9 314.9 372.8 441,1 521,8 617,1 729,6 862,4 1019 95 302.3 362.6 433,5 517,9 618,7 738,8 881.9 1052 1256 1497 100 409.7 4945 596,7 867,7 1046 1260 1518 1828 2200 FOREST VALUATION Years Values of 1.0p", where p= 1 8,2 8,4 8,6 8,8 9,0 9,2 9,4 9,6 9,8 10 1 1,082 1,084 1,086 1,088 1.090 1,092 1,094 1,096 1,098 1,100 2 1,171 1,175 1,179 1,184 1,188 1,193 1,197 1,201 1,206 1,210 3 1,267 1,274 1,281 1,288 1,295 1,302 1,309 1,317 1,824 1,331 4 1,871 1,381 1,891 1,401 1,412 1,422 1,482 1,443 1,454 1,464 5 1,483 1,497 1,510 1,525 1.589 1,552 1,567 1,582 1,596 1,611 6 1,605 1,623 1,641 1,659 1,677 1,696 1,714 1,783 1,752 1.772 7 1,736 1,759 1.782 1,805 1,828 1,852 1,876 1.900 1,924 1,949 8 1,878 1,907 1,985 1,964 1,998 2,022 2,052 2,082 2,113 2,144 9 2.083 2,067 2,101 2,136 2,172 2.208 2,245 2,282 2,320 2,358 10 2,199 2,240 2,282 2,324 2,367 2,411 2,456 2,501 2,547 2,594 11 2,380 2,429 2,478 2,529 2,581 2,633 2,687 2,741 2,797 2,853 12 2.575 2,632 2,691 2,751 2,813 2.875 2,989 3,004 3,071 3,139 13 2,786 2,854 2,923 2,994 3,066 3,133 3,215 3,298 3,872 3,452 14 3,014 3,098 3174 3,257 3,337 3,429 3,518 3.609 38,702 3,798 15 3,262 3,353 3,447 3,544 3,643 3,744 3,848 3,955 4,065 4,177 16 3.529 3,655 3,744 3,855 3,970 4.089 4,210 4,334 4,463 4,595 17 3,818 3,940 4,066 4,195 4,328 4,465 4,606 4,751 4,901 5,055 18 4,131 4,271 4.415 4,564 4,417 4,875 5.088 5,207 5,381 5,560 19 4,470 4,630 4,795 4,965 5,142 5,324 5,512 5,707 5,908 6,116 20 4,837 5,019 5,207 5,402 5,605 5,814 6,030 6,254 6,487 6,728 21 5,233 5,440 5,655 5,878 6,109 6,349 6,597 6,855 7,123 7,400 22 5,662 5,897 6.141 6,395 6,659 6,933 7.217 7,513 7,821 8,140 23 6,127 6,393 6,669 6,958 7,258 7,571 7,896 8,235 8,587 8,954 24 6.629 6,930 7,248 7,570 7,911 8,267 8,638 9,025 9,429 9.850 25 7,173 7,512 7,866 8,236 8,623 9,028 9,450 9,892 10,35 10,84 26 7,761 8,143 8,542 8.961 9,399 9,858 10,34 10.84 11,37 11,92 27 8,397 8,827 9,277 9,750 10,25 10,77 11,81 11,88 12.48 13,11 28 9,086 9,568 10,08 10,61 11.17 11,76 12,37 13,02 138.71 14,42 29 9,831 10,37 10,94 11,54 12,17 12,84 13,54 14,27 15,05 15,86 30 10,64 11,24 11,88 12.56 13,27 14,03 14,81 15,64 16,52 17,45 35 15,78 16,83 17,95 19,14 20,41 21,77 238,21 24,73 26,37 28,10 40 23,39 25,19 27,11 29,19 31.41 33,80 386,37 39,12 42,08 45,26 45 34,69 37,70 40,96 44,49 48,33 52,48 56,99 61,87 67,16 72,89 50 51,45 56,43 61,87 67.83 74,36 81,50 89.30 97,84 107.2 117,4 55 76,30 84,45 98,46 103,4 1144 126,6 140,0 154,7 171,1 189,1 60 113.2 1264 141,2 157.7 1760 196,5 219,383 244,7 273.0 304,5 65 167,8 189,2 2133 240,4 270,8 305,1 348,7 887,0 435,7 490,4 70 248,8 288,2 322,2 366.5 416,7 473,8 588.5 612,0 695.3 789,8 15 369,0 423,8 486,7 558,7 641,2 735,7 843,9 967,8 1110 1272 80 547,3 634,4 735.2 851,8 986,6 1142 1323 1531 {771 2048 APPENDIX 167 C. Suggestions for problems for use in teaching. The following problems are offered here merely as suggestions. Some practice in the use of the analyses and formulae has been found necessary to fix these matters in the minds of the students. 1. Capital Co=S50, p=3%; what does this capital grow into in 7, 19, 37, and 83 years? 2. Capital now is $500; has been out at 274% compound in- terest ; what was it worth 17, 43, and 120 years ago? , 3. S140 grew into $190 in 17 years; what is 1.op** and what is pP 4. A tree contains 430 cubic feet; it is growing at 1.2% ; what is the growth for 5 years in cubic feet? 5.