UC-NRLF B 3 sag am x . - 1' 01 esuy • -Mui 73 '2 • . FOREST VALUATION, VOLUME II OF Michigan Manual of Forestry BY FILIBERT ROTH 1916 )/ PUBLISHED BY THE AUTHOR ANN ARBOR, MICHIGAN I/ Ni * COPYRIGHT, 1916 BY FII^IB^RT ROTH TABLE OF CONTENTS FOREST VALUATION. PAGE; I. INTRODUCTION i A. Literature I B. Scope and Application 2 1 . General 2 2. Valuation and Statics 3 3. Application 4 C. History of Valuation 7 II. ARITHMETIC OF FOREST VALUATION 10 a. General 10 b. Prolongation, Discount and Rate n c. Summation of Series 1 1 d. Present Value of Series 13 e. Series of Periodic Payments 14 f . Sum of Infinite Series 15 g. Change of Periodic to Yearly Payments 17 h. Table of Formulae 17 III. APPLICATION OF VALUATION 19 A. Timber Crop, its Nature and Value 19 B. Risk in Forestry . 22 C. Interest Rate in Forestry 24 D. Valuation of Land or Soil 29 a. Cost, Sale — Income Value 29 b. Cost and Sale — Value of Forest Land in United States 31 c. Income Value of Land in Forestry 32 E. Valuation of Soil and Statics 36 a. Relation of Se and its Factors 36 b. Values of Factors of Se and Variation in these Factors 38 1. The Final Yield or Yr 38 2. Thinnings 46 3. Cost of Reproduction, c 48 4. Current Expenses, e 51 5. Rotation, r 54 6. Interest Rate, p 55 333963 IV FOREST VALUATION c. Actual Values of Se 56 d. Appreciation of Calculation of Se 57 e. Se of the Copice Woods '. . . . 60 f. Se in the Selection Forest. 60 F. Value of Stand or Growing Stock in Even-aged Stand. 60 a. Sale Value of Growing Stock 61 b. Cost Value of Growing Stock 61 c. Expectation Value of Growing Stock. . . . , 63 d. Which Value to Use 64 e. Value of Land and Growing Stock together 65 G. Value of Growing Stock of Regulated or Normal Forest 65 a. The Regulated Forest 66 b. Expectation Value of Growing Stock of Regulated Normal Forest 66 €. Cost Value of Growing Stock in Regulated or Normal Forest 70 H. Value of Growing Stock in the All-aged Forest 70 a. In the Regulated Forest 70 b. In the Irregular Forest. . . 72 IV. RELATION OF CAPITAL AND INCOME: IN FORESTRY 73 a; Nature of Income and Profit in Forestry. . 73 b. Interest made by the Forest 75 1. Interest made by a Single Stand of Even-aged Forest 75 a. During a Short Period 76 b. During an Entire Rotation 78 2. Rate of Interest made by a Regulated Forest 79 3. Rate of Interest made in Forestry when starting with Bare Land as Capital 81 c. Comparison of Properties with Yearly and with Inter- mittent or Periodic Income 82 V. ROTATION 85 a. Rotation for Largest Income 85 b. Rotation for Largest Net Rental or Highest Rate of Interest 87 VI. VALUE OF STUMPAGE 89 A. Cost Value of Stumpage 89 B. Sale Value of Stumpage 90 C. Expectation Value of Stumpage 96 otf CONTENTS v VII. DAMAGE IN TIMBER 98 a. Shade Tree 98 b. Young Plantation of Forest Trees 99 c. Older Plantations 99 d. Ordinary Stand in Wild Woods 99 e. Young Stands of Wild Woods 101 f. The Lumberman's Case 102 VIII. TAXATION otf FORESTS 105 a. Nature of Taxation 105 b. Assessment and Rate 105 c. Forest Tax Impersonal 108 d. Forest Taxation in Europe 108 e. Forest Taxation in the United States 112 f. Recent Reforms in Forest Taxation 114 g. Basis of New Tax Laws • 115 h. Future in Forest Taxation 119 IX. FIRE INSURANCE IN FORESTRY 122 X. RIGHT USE OF LAND 128 a. Nature of Land .- 128 b. Classification of Lands 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 131 f. Agricultural Use 131 g. Income from Land 133 1. Income from Farm Lands. . 135 2. Income from Forests 138 3. Income from Range 140 APPENDIX , 143 A. Normal Yield Tables 143 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 formulae. 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. Ill, 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, 1915; 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 formulae, 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. i. 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- APPU CATION Otf 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. A long time contract for hemlock in a hemlock and hardwood forest may become a very difficult and troublesome affair. To draw up such a contract requires a forester's judgment; to settle it equitably involves forest valuation and statics. 4. Damage in timber, usually trespass or fire, is very com- mon. In the past it was impossible for the courts to administer justice: these cases were among the most unsatisfactory; the evi- dence was neither clear nor convincing, the methods of calculation could not be explained, they were never agreed upon ; it was a battle of unproved assertion backed by a pretence of experience and authority. As a result the courts granted nothing beyond a simple provable loss of material actually saleable at the time of destruction. Since modern forest valuation has found its way into the woods business this situation has been relieved very materially and the courts are glad to be able to grant real justice based upon an orderly, intelligent method of determining the values. In fact the applica- tion of modern forest valuation in the United States had its first tests in damage cases. 5. Taxation requires assessment of the true value of the property. As long as it was a fight with local assessors the old 6 FOREST VALUATION methods alone were effective. Since the state tax commission takes a hand in the assessment it becomes necessary to apply forest valua- tion to show that if hemlock is worth five dollars per M. feet on the stump for immediate use that the stuff to be cut in ten years from now is not worth five dollars unless it doubles in value during the ten years, which it has not done in the last ten years and will not in the next. Similarly in our efforts at tax reform. Several states, notably Pennsylvania, New York, Massachusetts and Connecticut have initiated change of laws regarding taxation of forest property. In all cases a "yield tax" was introduced and the taxation of the land was modified. But what is a reasonable tax on stumpage? Is it ten per cent as in Pennsylvania, or six per cent as in Massachusetts and what basis has either state for its estimate? Guessing and juggling a few figures will not give any permanent, satisfactory relief ; it will require modern forest valuation to supply a basis. 6. The right use of land is one of the most important economic questions in two-thirds of the United States. Is it wise to try to farm all lands in Michigan, New York and Pennsylvania ; should part be devoted to forest and if so what part, in what amount; what will be the economic result if these lands are used to raise timber; how may we determine which of the two, forest or field should have preference in a given case ? Booster oratory or decision by the man in the office may deceive some people for a time but it will lead to great losses in the end. Pennsylvania, the Lake Region and other districts today have millions of acres of idle, unused lands entailing a loss of millions of dollars. The chief obstacle to any improve- ment in this situation is the land boomer and his friends who con- tinue to convince the legislatures that all land is farm land. The loss is great and has accumulated for years. Nothing but the application of sound methods of valuation and the recognition of this valuation by the legislatures will prepare for the remedy and change great money loss to income for the people. 7. The Management of the forest is and must always be the most important subject of forest valuation and statics. As stated before, every time an acre of land is planted to trees the question arises — does it pay — should a different kind of tree, cheaper plant stock, cheaper methods of planting be used. Later on — does it pay to thin, should the thinning be light or heavy, and how often can we afford to thin in this stand. All along there is expense for protec- tion— should it be cheap, less than five cents per acre, will it pay to go as high as ten cents, is it better to use many men or depend on outfit, etc. In the end comes the question — is it more profitable to HISTORY OF VALUATION 7 cut the stuff at the age of fifty, eighty or a hundred years. These and many other questions must be studied and answered for each stand, for each neighborhood, not merely once but repeatedly because the answer varies with the premises, with success of silviculture, market, transportation, cost of logging, labor in general, and many other conditions. It is evident that in management the. wrork of valuation is largely a matter of weighing or statics, though a great deal of simple valuation also enters. Every year dozens of stands must be estimated and millions of feet of timber appraised as to their proper stumpage value. C. HISTORY. Forest valuation is old. Timber was an object of traffic with the ancients, and traffic is unthinkable without valuation or the setting of a price on the object bought or sold. When timber was shipped or rafted, forests sold or exchanged, or mortgaged as is recorded as early as the days of Charlemagne, an important part of the transaction was the determination of the value of the forest or timber. Even the more modern conception of forest valuation the com- parison of the growing stock to a capital increasing at a certain per cent, the influence of the rotation or long interval between planting and harvest, and finally the application of an orderly mathematical analysis to discover the proper rotation and to compare different kinds of forest, beech, spruce, etc., date back one hundred and fifty years and more. According to Endres (p. 183) the Forest Order of the princi- pality of Neuburg, Bavaria, of the year 1577 makes it clear that the yield from the forest is in the nature of interest on a capital and that the person in possession has no right to cut more than the growth or proper yield, being entitled only to the interest. As early as 1623 the English economist Culpepper explained that the forest could not produce a large interest rate. In 1721 Reaumur pointed out that too long a rotation meant real money loss, and in 1742 Buffon in his "Memoirs sur la culture des forets" discussed the same subject and pointed out the accumulation of ex- penses in growing a forest crop. In 1764 the great von Zanthier, first to establish a "Meister- schule" for foresters, used compound interest calculations in forest valuation ; worked out a comparison for different rotations in beech, a comparison of beech, spruce and oak in which all expenses 8 FOREST VALUATION are prolonged to the end of the rotation. He also prepared the first money yield tables. Endres says of these calculations that they were satisfactory (zweckentsprechend) so that we have here a perfectly up-to-date piece of valuation and statics one hundred and fifty years old. In 1765 a writer in Stahl's Forstmagazin discusses a proper interest rate to use in forest valuation and brings up the same argu- ments used to this day to show that the ordinary commercial rate, then four per cent, was too high. With the rapid development of forest regulation and literature about the end of the eighteenth century came considerable discus- sion of forest valuation, for it now became necessary to promulgate regular instructions to guide the practicing forest officials. G. L. Hartig, Cotta, Konig and Pfeil all busied themselves with this subject. Konig in 1813 first expressed clearly the value of using the net rental on the land which might be secured in forestry as proper measure not only of the value of the land but of the success of the operation in silviculture, protection and utilization. In 1823 Hundeshagen first uses the term forest statics and defines it as the ''art of measuring the productive forces and results in forestry." About the same time Konig in his "Forstmathematik" discusses the profitableness of forestry and introduces the idea of the profit of undertaking (unternehmergewinn) and that of the per cent at which a given forest works. In 1849 Faustman, more or less inde- pendently, worked out the expectation or income value of the soil, first expressed by Konig, and gave to forest valuation this analysis in a formula — Se— which has never been changed or even modified materially since, and which is recognized as the most important analysis in forest statics. He showed that this analysis is applicable alike to forests cut over at intervals (intermittent) and to regulated properties with yearly cut. In 1858 Pressler began publishing his works "Rationelle Wald- wirt" and "Waldan des hochsten Ertrags" which really form the beginning of a new epoch in forest valuation. In 1865 Gustav Heyer published the first complete treatise on valuation and followed this up in 1871 by the first treatise on forest statics. Lehr worked over the subject for the Handbuch in 1887, and Kraft, in 1882, distinguished himself in his efforts to determine correct methods of measuring the value-growth in the forest, in his "Zuwachsrechnungen." The practice, as usual, was reluctant to accept everything. Yield tables and every kindred means of helping the forester to know the HISTORY Otf VALUATION 9 volume and value of the stand and the growth in time found no difficulty in adoption by the practice. But when it came to formulae with compound interest and especially when these formulae seemed to be wrong as soon as five per cent, the current interest rate, was used and when they seemed to lead to wholesale reduction of rota- tions, the practicing forester ceased to have faith and refused to accept. Common sense and experience showed the forester that it required at least eighty years (in a given case) to grow marketable sizes of spruce, that smaller stuff was drug on the market. When Pressler's and Heyer's calculations and formulae demanded a "finan- cial" rotation of fifty years it was clear to the forester that some- thing was radically wrong and even good men like Borggreve, Urich, Bose and Baur denounced the whole method. Some discussion is still going on, but the truth is gradually becoming evident to all, that all these calculations have nothing to do with the raising of timber, that this is left to silviculture and regulation as guided by growth on one hand and market on the other, and that these calculations merely try to supply a correct measure, a reasonable, orderly, acceptable analysis to show exactly what forestry is doing and wrhat it can do in any given case. If then the growth of timber is so slow that the crop increases only at the rate of two per cent compound, there is no amount of calcula- tion and no juggling of methods and figures which will change the plain fact and only one question remains — will we keep on raising timber or quit? If the timber is needed and the land will not grow any other crops or do better it is quite certain that forestry will continue regardless of the rate per cent which it makes on the capital. At the same time it is becoming evident to all that valuation is necessary. As pointed out before, the owner wants to know what is actually made, what the land is worth if used to raise timber, whether expensive planting of transplants is actually better than cheap natural reproduction, etc. And he is not willing to take the forester's mere word for it, he wants to see by what method of calculation and upon what premises the recommendation is based. In the efforts of bringing correct forest valuation and statics into the forest business the labors of Judeich, master of forest regulation, stand out conspicuously. In his long and successful career at the head of the Saxon forests, he not only recommended but introduced everything of value into the practice and he may well be regarded as the most powerful exponent of modern forest statics and especially of the general usefulness of Se. II. ARITHMETIC OF FOREST VALUATION a. General. A stand of timber fifty years old after planting may be worth two hundred dollars per acre. If this stand is to remain and con- tinue to grow until it is eighty years old, it is right for the owner to ask — at what rate is the stand, now fifty years old, growing, what per cent is this growth on the two hundred dollars which the stand is now worth, etc. Since the stand does not pay or give up any interest, the two hundred dollars or the value of the fifty year old stand is evidently like a capital out at interest, where the interest remains unpaid, but is added to the capital every year. In other words, the stand of timber grows like capital out at compound interest. If the owner wishes to know what this stand has cost to pro- duce or grow to the age of fifty years he adds up the various items, cost of planting, care and taxes during the fifty years, and the rent on the land. The ten dollars per acre spent in planting have been out for fifty years without drawing any interest, they have grown, there- fore, at compound interest for fifty years. The expense of taxes and care comes every year, the sum paid out the first year has been out for forty-nine years, the sum paid the second year has been out forty-eight years, etc., for none of this interest has been paid. If the owner wishes to forecast or estimate what this stand is worth to him today if it is to continue to grow until it is eighty years old, he must first decide that when eighty years old the stand will bring, say, five hundred dollars per acre and then discount the five hundred dollars to the present day, i. e., for thirty years. From this it is evident that forest valuation works a good deal with the arithmetic of interest, with discount and with the summa- tion of series, usually geometric series, the geometrical progressions of many writers. The following are the more common forms of interest here.1 1The elementary treatment of these simple problems in literal arithmetic has been fully justified by fifteen years experience in University teaching. The student will do well not only to go over this ground very thoroughly, work out all formulae on paper and repeat often, but also to speak aloud the true meaning of each formula and learn to state, as in geometry, exactly what each formula means. DISCOUNT AND PROLONGATION I I b. Discount, Prolongation and Rate. If $75 is put out at 4% compound interest for eight years, the capital and interest to be paid at the end of the period, the $75 capital grows as follows : at the start, C0 = $75; at the end of first year, Ct— 75 -f- interest for one year = 75 +75 (.04) = 75 (i +.04)= 75 (1.04); second year, C2 = 75 (1.04) -f- interest = 75 (1.04) (1.04) = 75(1.04')! third year, C3 = 75 (1.04*) (1.04) —75 (i.O43) ; eighth year, C8 = 75 (i.O4T) (1.04) =75 (l.Qf); or, in general, Cn=^C0 (i.opn) ; that is: the final capital equals the initial capital multiplied by i.opn. Cn From the above : - - = C0 or, the initial capital equals the final i.opn capital divided by i.opn, or it is equal to the final capital discounted for n years at p per cent. c. Also : — = i.opn, or i.op" equals the final capital divided by the Co initial capital. Since the numerical value of i.opn may be found in the table, the value of p, or the interest rate is readily determined. C0 (i.opn) signifies that the initial capital C0 is prolonged at p Cn per cent for n years. — signifies that the final capital Cn is dis- i.opn counted at p per cent, n years.2 c. Summation of Geometrical Seriez. If the yearly expenses on a property are $500, and these con- tinue for fifty years and money is worth 3%, what will these ex- penses amount to? Evidently the first $500 is out at compound interest for 49 years, the second for 48 years, etc., and it is desira- ble to find a short way of computing these various amounts. 2 The word capital is used here in a rather loose way, perhaps, but not more so than .in ordinary conversation, etc., and it is a very helpful term to employ in these explanations. 12 FOKF.ST VALUATION 1. Fundamentally this series is: sum, S = a -j- ar -j- ar2 + ar3 + ar4 and Sr — ar + ar2 -f ar3 + ar4 + ar5 subtracting the upper from the lower, Sr— S — ar5 — a or S(r-i)=a(r5-i) when 0 a(r5-!) : (r-i) since 5 is the number of terms in the series, or n, and this form is perfectly general, it may be written : a (rn— i) :77^7T In this series a is the regular payment, and r is the ratio between ar2 any two consecutive terms, as : ->=-•= r. ar 2. Applying this to the above case of a yearly or current ex- pense of $500 at 3%. sum, S = 500 (i-0349) + 500 (I.0348) + +500 S (1.03) = 500 (i.035°) + 500 (i.0349) -f etc + 500 (1.03) here 1.03 is the ratio, i. e., 5oo(i.Q349) ._ 500 (I.0348) ~ r'°3 subtracting : S (1.03—1) =5oo(i.o350— i) SOP (I.0350— i) (1.03 -i) By looking up I.O350 in the tables (see Appendix), the compu- tation becomes perfectly simple and requires little time. 3. Since this same process applies to any similar case it may be written as a general formula : a(i.opn— i) 1 d.op-i) which may be expressed: The sum of a series of payments a coming every year, contin- ued for n years and compounded at p per cent. PRESENT VALUE OF SERIES 13 Since this sum represents the value of all these payments at the end of the period, it may be termed the end value of the series.3 500 (i.o350— i) Query : Is the sum - - the same whether it begins (1.03—1) in 1902 or in 1925, whether it begins in ten years from now, or has run for fifteen years? d. Present Value of the Series. A farmer or forester may be able to get $500 rent per year from a certain property. He may wish to know the value of twenty years rent of this property with a view to raising money or selling the twenty years' rent. i. The end value or sum of the twenty years' rent is found as above and is expressed : 500(1.03"— i) sum or end value =: - 1.03—1 But what is the value of this sum today? Keeping in mind that -i.opn and that Cn is the above sum or end value of the series : CM 500 (l.032° — • i) present value, Co = — ^ = / - — N - i 1.03" (1.03—1) 1.03" Expressed in words : The present value of a series of payments of $500 coming every year, continued twenty years, compounded at 3% and discounted at the same per cent, the first payment coming a year from now, in general, a (i.op" — i ) present value of series = -, - ^r-7 - ^ (i.op— i) (i.opn) 2. Assuming that the above series runs for twenty years and suppose that it has already run for seven years, what is its present value ? Evidently the owner is seven years to the good, he does not 8 The student will do well to write these formulae exactly as he has learned to develop them. The temptation is to write, for instance, a (i.opn — i — . This is correct, but it loses the connection, the student for- .op gets how he came by it. In solving ordinary problems write out the general formula and keep this before you. This will avoid many mistakes. 14 FOREST VALUATION need to discount it for twenty years but only for twenty less seven or thirteen, and the case may be written : 500 (I.0320— i) present value = ^— — y—^ 500 (i.Q320 — O i.Q37 (1.03—1) i.of this latter having the advantage that it keeps the whole story clearly before the student. If in the above case the series does not begin until fifteen years from today, evidently the discount to present time must be longer by these fifteen years, and the case may be written : 500 (i.032°— i) present value = — ; rr-p- (1.03—1) I.03**1 or to make it more clear, 500 (i.Q329 — 1), (1.03-1) (i.o320) (i.o315) e. Series of Periodic Payments. If a forest property can be cut over every fifteen years and at •each return the cut nets $500 it may become of interest to determine what the value of ten cuts of the forest is. Assuming that the property has just been cut over so that the next cut comes in fifteen years and the last cut in one hundred and fifty years, the end value or the value of the sum of these cuts is : i. End value or sum : S = 500 (I.03150-15) + 500 (i.o3150-30) 500 S (i.o315) = 500 (i.o3150) + 500 (I.03150-15) 500 (i.o315) (Note that the ratio here is I.O315.) Subtracting : S (i.o315— i)=5oo(i.o315c— i) 500 (i.Q3150— i) (i.o315-i) If in the above case we let fifteen years = t, and 10, the num- ber of cuts = n, then 150 — nt, and we may write the general form : a (i.opnt — i) 1 d.op4-!) Note: The student will recognize these periodic cases by the -exponent t in the denominator. INFINITE; SKRIES . 15 Expressed in words : The end value or sum of a series of pay- ments of $500 each coming every fifteen years continued for ten payments compounded at 3% and the first payment to be made in fifteen years. r^c-v^*— Query : Will the above sum or end value be greater or smaller if the first cut comes in five years instead of fifteen years? 2. Present value of the sum of a series of periodic payments. The case is the same as under d — I and 2. Present value is : a (i.opDt— i) (i.op* — i) i.opnt and is modified according to the time when the series begins, or, in the above case, when the first cut is made by writing it: a (iopnt — i) ioptj*~- (i.op1 — i) i.opnt where x is the number of years before the first cut or payment. .f. Sum of Infinite Series. When a farmer buys a farm he really buys the yearly income or rent of the farm for all time, at least there is no set limit. In practice about fifty years' rent is worth as much as the farm, but this fact does not alter the nature of the bargain. i. Using the formula as developed under c — 2 and 3, and tak- ing its present value as under d — i, present value: a(i.opn— i) (i.op — i) i.opn and letting n infinity or oo the formula becomes: a (i.op00 — i) present value = (iQp_ j} ^ „ and since i.opcc — i -— i.opc/o : present value a a (i.op — -i) i.op00 ~~ i.op— i ~~ .op If a is the rental per year or $500, and p = 5, then the present 500 value of all the rentals from this farm forever are worth - or •05 $10,000, which simply means that the farm is worth $10,000 if it brings a net income of $500 and the buyer is willing to take 5% on 1 6 FOREST VALUATION his money. The $10,000 is the income value of the farm at 5%, and is equal to the net income capitalized at 5%. 2. If the income is periodic, comes every fifteen years, as in the case of the forest cut over every fifteen years, the foregoing is modified as follows : 500 (1.03 °° 15— i) present value = 500 (l,03 i.0315— i (1.03 500 or in general : (i.op'-i) where A is the periodic rent or money income at each cut in the above case. If in the above case the first cut comes in six years instead of fifteen the owner is fifteen less six or nine years to the good and this may be expressed as follows : value of property : 500 1.03" ~(i.0315-i) That is, the sum is prolonged at 3% for nine years, or in general, A i.op1-* -(i.op'-i) where x is the number of years before the first payment is due. Note: Care must be taken to see that the sum A is really the sum in every case. To illustrate : A forest of 100 acres can be cut over every 20 years for $50 worth of timber (stumpage value) per acre. The yearly expenses for the 20 years sum up to $15 per acre so that the net income A is 50-15 or $35. ]f now the first cut may be made at once the value of this property is : income value = $50 + M—I, and not ' ^ Q^ __ I because the first income is larger by 15 than the established future incomes. 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 —2-^ = -g = $60,000 1.03 — i i. 80 — i 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 . I.03'-"0 — i ~ .03 or the yearly income, _ $48,000 (0.03) loOO — .YI 1-03 — i In general then : A a A (.op) (i.op* — i) (.op)' i.op* — i h. Table of Formulae. As above developed. No. FORMULA. MEANING OF FORMULA. £ _ £ (I0nn) Prolongation of initial capital C0 for n years at p per cent. 2 ro__ 'CQ Discount of final capital Cn for n years at p i.opn per cent. 3. Cn _ n Final capital Cn divided by initial capital Co to Co ~ find interest rate p. ofTon11— T") Sum. or end value of a series of payments a 4. Cn = S = ( v ^- coming every year continued for n years com- (i.op — i) pounded at p per cent. Present value of a series of payments a com- / n_,>> ing every year continued for n years com- 5. Co = - —^ pounded at" p per cent and discounted _at the (i.op — i) i. op same per cent, first payment to come in one year from now. 1 8 FOREST VALUATION a(iopnt j^ Rnd value or sum of a series of payments a 6. €n = S = ( ' t_ ' coming every t years continued for n pay- ments compounded at p per cent. Present value of a series of payments a com- - P _ a(i.opp — i) ing every t years continued for n payments (i.pp* — i) i.oput 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 g £ — a^I-°P" — *) i-Qpt~x coming in x years so that the sum must be (i.op* — i) ioprt 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 a the income a at p per cent; or the present 9. Co— 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 10. Co — -, 't 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. jj Co = — I-°P "x Same as No. 10 but with the first payment (i.op* — i) coming in x years from now. Changing a periodic rental A coming every A (o.op) t years into a yearly rental a where the value i. op1 — i of the property is computed by capitalizing the income at p per cent. III. 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 fifty 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 by 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. 9. 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 usually 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,OOO 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 Handb-uch 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 — "Kommen 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 loo-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 fact, 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 compound 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. The 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 I32-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 : "Total gross income .$980 Total expenses 340 Net farm income 640 Interest on investment 5% 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% $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 year $980 Expenses : Labor $102 Fertilizer 18 Feed 47 To maintain buildings 49 To maintain implements 39 Taxes, at 0.6% 38 Miscellaneous .' 44 Salary of farmer and family 360 Replacement of live stock 50 $750 Net income . $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 1910. 28 FOREST VALUATION Since the average farmer with his family can not be engaged at less than $500 per year 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 1911 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 2^, 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 : I. 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, 1915. 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. If a 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." It 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, o.op wrhere 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. i. 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 $33^3^ 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, Se = (i. op1— i) == (i.o3S(t— i) = (10.64—1) = 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-VAIAJE) OF I.AND 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, yield, 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, T20, just pays expenses, hence no income. Thinning when stand is 40 years old, T4o, yields 5 cords at $3 or $15 per acre. Thinning when stand is 60 years old, T60, yields 10 cords at $4.50 or $45 per acre. b. Gross 'income per acre at end .of rotation : Final yield or cut 80 years old, Yr $300 Thinning when 20 years old, Tzo o Thinning when 40 years old, T4O, $15, with interest for 80-40 years or $15(1. 0340) 50.40 Thinning when 60 years old, T6o, $45 with interest for 80-60 years or $45(1.03") 81 Total $43140 34 FOREST VALUATION c. Total expenses per acre at end of rotation. Cost of planting, c, $6 with interest for eighty years or 6 (i.O3s<)) ...... $ 63.84 Care, protection, and taxes, e, 0.25, coming every year with interest. Total expense .................. $144.09 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 2*7-3i — = $2980 (i.o;f— i) 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, etc. 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 : f Tc(.I.OPr-c)_c(l.Opr)— - ... be = _ . _ (lop — i ) (i.opp— i) where Yr is the stumpage value of one acre of timber r years old : FORMULA FOR SD 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.* (i.opr— i) In the above formula the term^ - - may also be writ- (i.op— i) e e ten - - ( i .opr — i ) — E ( i .opr — i ) where E = — = e (i.op— i) .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 : Yr4-Ta(i.opr-a)) + ...... etc. — cd.opr)— E(i.opr— i) which may be and usually is simplified into : Yr + Ta(i.opr-")-f ...... etc. — c(iopr) (i.op'-i) * It is of great help to the student to use these terms or symbols con- sistently and use no more terms than are actually necessary. To use Y 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 fprmula is written by Emdres as follows : 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 ftfrd 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. vSince 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 (i.opr) is larger than Yr + Ta (i.opr'a), 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 Ta(i.opr-a) etc.— c(i.opr) (i.opr— i) 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 go 100 no 120 Income value of land per acre, Se ..... $ —14 13 38 53 59 59 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 1 20 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 3§ FOREST VALUATION interest rate of five per cent is set instead of three, the Se of $29.80 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 3 % $105 per acre 2l/2% 173 per acre 2 % 285 per acre b. Values of the Factors of Se, and Variation in these Fac- tors under different conditions. i. 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. Asa 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 yield 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 fullv stocked : Yield per acre. Relative figures or per cent for different sites. On site I Cubic feet. I II III IV V Pine 9200 100 78 61 48 38 Spruce 16000 100 81 64 49 35 White fir ... 17200 100 Si 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 a circle. 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 I II III IV Volume 100 "85 65 50 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 4° FOREST VALUATION cubic feet of timber in the stand 120 years old, in Prussia is given by Schwappach (pine, 1908, p. 144) as follows: Site I $12.00 per 100 cubic feet Site II 1 1.20 per 100 cubic feet Site III 9.10 per 100 cubic feet 'Site IV 8.25 per TOO cubic feet Site V 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 73 cubic feet Wiittemberg 71 cubic feet Saxony 70 cubic feet Bavaria 60 cubic feet Prussia 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 Wurttemberg 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 III (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, ilnstrate this : Spruce $1563 per acre Pine 627 per acre Oak 377 per acre Beech 347 per acre While this comparison is not quite fair, since oak does not really develop quality until after one hundred years, 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 rotations 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 feet 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 years ago. STUM PAGE; 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 Forst 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 for the • years Prussia All wood $ per 100 c. ft. Bavaria All wood $ per loo c. ft. Baden All wood $per looc. ft Saxony Only wood 3" and over $ per loo c. ft. 1830-39 2.50 .... .... 4.60 1840-49 3.00 .... .... 5-70 1850-59 3.20 3-50 4.10 6.40 1860-69 3-80 4.10 6.50 7-90 1870-79 4.40 5.20 7.90 9.20 1880-89 4.40 5-oo 6.40 9.30 1890-99 4.90 5.8o 7.60 10. 2O 1900 6 . fio 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 $1540 per TOO cubic feet solid, or about $16 to $19 per thousand feet b.m. actual stumpage. For spruce, Schwappach gives the folowtng prices: Logs class I $20.40 per M. feet bm. stumpage Logs class IT 19.20 per M. feet bm. stumpage Logs class III iS.Soper Mk 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 100 c.ft. $ per M. ft. bm. 1880-84 1885-89 1890-94 1895-99 17.70 17.40 24.00 24.60 22.25 23.00 30.00 30.75 9.00 9.50 10.50 12.80 11.50 ii.6o 13.20 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 $0.98 per 100 cubic feet, or about $1.25 per M. feet bm. Saxony 1.26 per 100 cubic feet, or about 1.55 per M. c) (i.op™ — i) or (25 + 5) (i.0245— i) $ 43. 13 Thinning at age of 20 years, cost with interest. Ta(i.op'"-a) = 3(i-0225) 4-92 Total expenses per acre $ 67.45 3. Income per acre obtained from the stand during the 45 years, Thinning at 30 (just paid expense) $ o Thinning at 40, $10 with interest for five years 11.04 Total income $11.04 4. Net cost per acre: $67.45 — $11. 04 = $56.41 and cost value of the stand of 80 acres, $4,5.12. 5. This calculation is usually expressed in a formula as fol- lows : mGc — c(i.opin)-f- (Sc + E) (i.op111— i>^(Ta(i.opm--a)+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 so. 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. ~ /a^l 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: Land value Sc $20 Yearly current expense e 0.50 Final yield, Yr, stumpage value, 40 M. feet at $10 or. ... 400 Thinning at 50 years, stumpage 30 Thinning at 70 years, stumpage , 60 2. Gross income per acre at end of rotation : Final yield '. $400 Thinning at 50 and interest for 40 years 66 Thinning at 70 and interest for 20 years 89 Total $555 3. Expenses per acre to end of rotation : Rent of land and current expenses treated as in case of cost value, (SC + E) (l.0pr-m-l)=r- (20 + 25) (I.0245— 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.02 Value of the stand on 80 acres — $16.160. 6. This calculation may be put in a general formula : mG _YT-4-Ta(i.opr-a)4-Tb(i.opr-b) etc.— (Sc + E) (i.opr-m— i) i.opr-m where mGe 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 buyer 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 Otf 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 FORF,ST 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 I year old, etc. Two hundred acres 79 years old, or r-i years old. 3. Yearly work, expense and income on this forest: Two hundred acres are cut. income 200 x Yr. Fourteen hundred acres thinned, income T10 (200), T20 (200), T30 (200), etc. Two hundred acres are planted, 200 x c. 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 year old stuff, one 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. I, illustrates this lo-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 lo-acre sam- ple are: One acre cut, income Yr. One acre thinned, when stand is 4 years old, income T4. One acre planted, costs c. Ten acres protected, cared for, taxes paid, expenses 10 x e. Ten acres of growing stock pay rent on the 10 acres of land, cost ipXSc(.op). IN NORMAI, 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. T-\ Jalue dalive o^ oxve o. H \ \\ T-5 \x\xv\\\as ex T-b 0- 0 T-l X-8 T-\0 \.op'° Fig. i. Diagram representing 10 acres (r acres), a sample of a forest regulated on a year rotation, indicating the age of the growing stock on each acre; the present value of e final yield (Fr) from each, and the present value of the thinnings expected from each .re. Since Yr on the acre of 7 year old stuff is to be cut in 3 years, its final value, or umpage value is discounted for 3 years. On the several acres 4, or more years old, no rther thinning is to be expecte^, but the stand 3 years old will furnish a thinning next jar, and hence the value of this is discounted for one year, etc. Since the general formula for expectation value of growing stock reads: mGe = Yr + Ta(i.opr-a) — (Sc -I- E) (i.opr-m— i) i.opr-m the value of the several acres beginning with the oldest stand may be written : op _Yr-f o— (Sc + E) (i.opr-9— i) °Ge=: i.opr NOTE: — The thinning from this acre has been taken •and no. further thinning is expected. 68 FOREST VALUATION «Ge = Yr-f-o — (Sc-f E) (i.opr-8-i) * sOe __ Yr + T4(i.op'--4) — (Sc 4- E) (i.opr-3— i » i. op1"-3 and °Ge = Yr + T4(l-°Pr~4)— (S'C 4- E) (i.opr-°— i)* To get a common denominator for S Ta, treat in this manner : Ta(l.0pa— i) I.ppr-a __ Ta(l.Opr-a) (i.ppa— .T) I0pa(i.op— I v I.Opr-a ' I.0pr(l.0p— I adding we have : q.(r-i?C (Yr + E + Sc) (l.Opr— l)+Ta(l.Opr-a) (i.opa-i) _ ( (I.0pr) (l.Op— I) 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: °-(r-1)Ge average per acre = (Yr + E+Sc) (l.0pr— - 1)+ Ta(l.opr-a) (l.ppa— i] r(i.opr) (i.op-i) 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: Yr Ta(i.opr-a) _ QSc 4- E) i.opr-m ~ i.opr-m i.opr-m i.opr-m i.ppr this makes addition of SYr, 2Ta, 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) (1.02s0— I ) +10(1.02**) (l.024°— l)+20(l.02a>) (I.0260— I) 80(I.02S°) (1.02— I) -(75+io) — 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 = Yr + Ta(i.opr-a)— c( i.opr)— £( i.opr— i) (i.opi— i) Se (i.opr — i) may replace Sc (i.opr — i) in the above for- mula as follows : --e per acre = Yr(i.opr— i)4-E(i.opr— i).f Yr + Ta(i.opr-a)— c(i.opr)— E(i.opr— r( i.opi-) (i.op— i) ) Ci.0pa— i) T(l.Opr) (I.op-l) which simplifies into : ,p Yr + Ta— c Yr + Ta — c — re E--Se -Se 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 = $io and replac- ing Sc with Se at $28 we have : 400 +10 4- 20 —TO —120 Q ^ Value of growing stock per acre— — g, Q^ — —20 = ^159. In this particular case the result, $159, compares closely enough with $ 1 68 as obtained by the ordinary formula. In any case it is 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 : mGc — c(i.opm) + (E + Sc) (i.op171— i)— Ta(i.opm-a) where again m is the age of any one stand. i. This leads to the formula: per acre= 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, $1.50, hence E, $75. Thinning at 20 years, no income. Thinning at 40 years, $10. Thinning at 60 years, $20. Then the average cost value of growing stock per acre : (10 + 7=; + 10) (l.02S° — i) — IO(I.024° — l) — •2O(l.O22° — i) , 80(1.02-1) -(75 + io)= $131 and for 16,000 acres about $2,096,000. 3. Simplification of this formula by substituting Se(i.opr — i) for Sc(i.opr — i) results in the same form found for Q-^-^Ge so that: 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 Y-\IYUE OI- ALL-AGED STAND 7 1 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 I — 120 year old stuff, are repre- sented, provided reproduction is secured promptly, as is here as- sumed. On each i8o-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, I2o-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 180 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 timber 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 mGe, as developed before. 3. The stand is mostly young stuff, such as reproduction on burns, windfall, etc. In these cases the cost value, mGc, 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. i. 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 $i>ooo 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 $100 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. In case under i, 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 — $1,000 •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 or 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 be 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 be 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. i. 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 interest is: — —or 4.4%. While this calculation is a fair ap- 5X90 proximation it requires modification for larger enterprises, and bet- ter analysis. The following illustrates the usual 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 e, $i per acre; therfore — - or E is $50; the value of the stand at .02 Cn 50 years is $250 and at 55 is $300. The reasoning then is : i.opn = — . Co 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: Y53 4- S -f E $300 4-io 4- 50 i. op = ' = ^ - • - f-*- — 1.16 and hence p = 3%. Y°° 4- S -j- E $250 -f 10 4- 50 This per cent made by the current growth of the stand may be term- ed "forest per cent," or Pf, and is the "Weiser" per cent of the Ger- man authors. The formula as written bv Endres is : w AH-B4-V or in our terms, /„ lYx+n 4- S -I- E " = ""(>/ Y. + SI-E - 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 : (Pv + Pq + Ps) and that this growth is made on a capital Ym -f- Se. 100 Then pf = (pv -f- pq ~j-ps) IOQ (Ym+ Se) = ^pv ~^ P<1 ~'r ps^ Ym -Tse To illustrate : If the stand is worth $250 and land $10 per acre and pv=i.; pq=I ps— I or 3-'i%. Since this method or inquiry is usually applied only to older stands where the value of the timber is very large as compared with Ym the value of the land, the value of may be put = I and for Ym + Se ordinary purposes, therf ore, it is quite sufficient to state : Pf = Pv + Pq + Ps ; in the above case pf = 1.3 + I + I = 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 pf 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 7 8 FOREST VALUATION and volume known ; stumpage $10 per M. feet ; assume that the stand now, 80 years 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 M. 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: I.OPx10= — = 1.25 Px= 2.3%. This px 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% — px = Pv + pq, and this requires merely the addition of ps 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 r Cr Capital or values at end of rotation Co ~~ Capital or values at 'beginning 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 : r_ stand + land + expense capital _ Yr + Sc + E ~ land + expense capital + cost of planting c + Sc + E Concrete case: Land $15 per acre, p — 2%, e = $i, hence E I. 00 _ = $50 ; Yr, $400 ; c, $12 ; r, 80 years ; then : 465 ,. = TT = 6.04 12 + 15 + 50 77 and from tables : pf = 2.3%. FOREST PER CENT 79 The above formula may also be written : p= ic 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 : Yr 4- S — Ex i.opr— T i.opr= 0 , „ — and Ei is equivalent to e I. op— i 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. It 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 formulae 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 : 2. 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 : yearly net income X loo , co&t value of forest 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 $10,000 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. Practicallv all state forests of Germany never cost INTEREST ON LAND 8 1 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 ioo _ yearly income X ioo a X ioo 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 : A .( The periodic income is : A = Yr + Ta(i.opr-a)— - C(i.opr) — E(i.opr— i) and the above calculation for yearly income is then: (Yr -j- Ta(i.opr'a) — C(i.opr) — 'E(i.opr — i) .op ^ _ a X ioo Se .op X ioo _ Se . 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 P* = — X 3 or 9. 10 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 P* = — 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 px, 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 to a 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, $i per acre. Thinnings left out for sake of sim- plicity. AND INTERMITTENT Comparison of yearly and intermittent working. Property with yearly cut and yearly income. Property with a cut and income every 80 years. 1. Growing stock at beginning. 2. Growth of ripe stuff 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. 80,000 cords. 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 (i.03M— i) 2540 — — or about i .01 — i $67,700. None. 80,000 cords. 80,000 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 33-5. Tax and care 1000. Total I335- For 20 years' expenses : (I.0329— i) 1335 - or 1.03—1 $35,6oo. For planting 10,000. Plus interest or 1 0,000 ( i .0320 ) — 1 8,000. 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 ST 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 3Tq, 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 = re or according to the following table for spruce site II, for a rotation of 583+ 71 — 12 — 54 60 years = $ 9.80 60 980 + 232 — 12 — 72 80 years = $14.10 80 Spruce site II, Germany, Endres, after Schwappach, gross in- come, expenses, net income and Se for different rotations from 30 to 1 20 years for use in formula. Average net income per acre Gross Income. Expenses. Net Income. re Se Yr or 2Tq m Total current Total Total on basis Rotation Years. final cut per sum of thin- nings income from r acres c plant- ing of expense tax, pro- tection expense forr acres from r acres of \verage per of 3% rental value acre from r of one etc., for of normal acre. one acre r years acres. normal acre. r acres normal forest. bare old. forest. e$o.9o forest. land $ $ $ $ $ $ $ $ $ 30 87 87 12 27 39 48 1. 00 10 40 203 7 210 12 36 48 163 4.00 47 50 371 3i 402 12 45 57 354 6.90 77 60 583 7i 654 12 54 66 588 9.80 98 70 786 137 .923 12 63 75 848 12.10 105 80 980 232 1212 12 72 84 1129 14^10 105 90 1123 35i 1474 12 s7 93 1382 15-30 99 100 1222 488 I7IO 12 90 102 1609 16.00 91 no I28l 683 1919 12 99 III 1808 16.40 83 120 I2Q6 791 2087 12 108 1 2O 1967 16.30 75 FINANCIAL ROTATION 87 From the foregoing table it appears that the average net in- come with spruce site II 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 no 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 largest 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 arid p is the accepted rate of interest which is also fixed, it is evident that px 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 better 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- ematics1 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 formulae was evident to every good practitioner. Unneces- sary stress on mathematical formulae on the one side and common sense with an aversion for formulae, especially for bringing in com- 88 FdREST 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 formulae. 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 i% 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 Europe run about as follows : Pine and spruce 80 to 100 years Balsam and beech TOO to 120 years Oak 150 to 200 years For spruce in Germany as seen from the tables under discussion of Se, the maximum Se, and therfore pf, for site I-IV, on a basis of 2% comes at 70-80 years, 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 2l/2% comes at loo-no 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 lass 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 (i.o510) =$65,160; Taxes at i%% 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 : (300 -f- 200) — — = $6,200, 1.05—1 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 use as determined by an an- alysis of the various factors entering into, or affecting this value. i. 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 STUMPAGK AND DISCOUNT gi 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 il/2 million acres of land in the ten years ending 1910, at prices usually below two dollars per acre and most of it below 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 materia.1 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 year, 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 $i 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 $i, and generally make from 10 to 30% of the value of the lumber at the mill. 92 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 c. 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. per c. ft. $17 Class IV 18- 35 c. ft. 10 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 III 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 VALUE; OF STUM PAGE: 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 4-5<> 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 15 3-25 140 17.2 9.60 21.5 28 16.8 4.20 160 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 10 years cut- ting. Let the mill and other buildings, including those machines which are fairly certain to last the ten years be 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 (i.O510) — 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: (i.o510— i) yearly cost of depreciation = X and X = $230,000, and 1.05—1 from this X = $18,400. COST OF DUMBER 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 country 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 $ .75 Skidding and swamping i .25 Hauling to landing or railway 1 .50 Railway haul or drive I . oo Overhead charges of supervision replacement of equip- ment, teams, camps, roads 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 $ .60 Yarding and loading 1 .00 Hauling to mill i . 50 Booming, scaling, etc 40 Direct costs $3-5o 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- vision and profit i . 50 $7.00 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 important. 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 (J-OS20) °r $5>3OO>OO° m 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 for the second TO years, how much must this be? About $13 per 'M. feet 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 large 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 anything 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 be 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 (i.O523) =$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 fire 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. If 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 years, 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 may 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 $10 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 year. 100 FOREST VALUATION Estimate of the damage may be set in one of three ways : I. By cost value: Value before fire : $800 (i.os12) $ 1434 30 (i. OS12— 0 Tax and care — — 480 (1.05—1) Total $ 1914 Value after fire: Land $400 Timber 500 Total - $900 damage, $1,014. 2. By sale value : Value before fire : land $400 Timber 400 X 5 2000 Total $2400 damage, $1,500. In this case it must be shown that the sale value could actually be obtained without delay. The fact that timber is worth $5 stump- age in the particular district is not sufficient evidence. 3. By expectation value : Expectation value of the 40 before fire : Value of timber 400 X 6 $2400 Value of land 400 Total gross value in 7 years. $2800 Expenses during 7 years: 3o(i.o57— i) .$ 244 1.05—1 2556 Present value 1817 i.o57 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 ioi 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 fur 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 300X40 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 -h 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 pay for a stand 20 years old or one 28 years 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 analysis 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 M. feet "royalty," or stumpage ; it in- vested $200,000 in mill, railway and equipment, and aimed to cut the timber in next 20 years ; was making a profit of $2 per M. feet in the business. The fire destroyed 200 million and so reduced the cut by nearly 10 years, since most of the timber destroyed is not yet 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 by 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 : 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. 30000 i.o3-i 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 ; (i.o320 — i) total present value : 20,000 — - = $296,000. (1.03 — 1) I.0320- 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 of a 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 arid 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 railways 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. i. 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 Tax 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 i6o-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 $TCO 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 I 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 : 1890 $18.50 16.40 14.40 23.70 1880 $18.30 17.70 12.70 20.90 1870 $19.80 18.70 14.10 24.00 1860 $7-80 9.70 11.70 1002 Continental United States $20.50 North Atlantic, Maine- Penna.. . 18.30 South Atlantic, Delaware- Florida 16.00 North Central, Ohio-Wisconsin- Kansas-Mirmesota 24.70 South Central, Kentucky-Arkan- sas-Alabama-Texas J7-3O Western, including Pacific Coast 25.50 Ohio 23.80 Indiana 19.70 Illinois 5.1.50 Michigan 16.60 New York 22.20 Pennsylvania 14.90 Massachusetts 15.80 Wisconsin 13.60 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 14.30 16.30 18.00 4.10 19.90 22.30 25-50 17.70 19.10 16.80 20. IO IO.OO 18.20 16.40 16.30 9.00 40.90 31-30 45.20 15.70 16.10 16.70 19.90 10.80 19.80 21.30 24.70 11.00 14.00 17.10 18.70 12.10 14.60 15.40 1570 9.6O 22.90 18.70 16.20 12.50 108 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 : o.ioX (50,000 — 15,000) or $3,500. This amount is seven per cent of the stumpage value of the ripe timber cut during the year 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 be 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.opr — i i. op — i periodic income . . yearly income = ; .op. i. op1— i But this means practically a return to the ground tax system which in these cases no doubt deserves preference. I IO 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 Wiirttemberg on a total area of about 490,000 acres : Value Local taxes paid by state. of forest or Yearly Years. net income capital- ized at 10%. net income per acre. Total $1000. Per acre. $ Tax on IOOO property. Tax as % of net income. Tax as% of stump- age. $per $ % acre. 1880-89 26 $2.69 80.9 .16 6.10 6 4.2 1890-99 38 3-86 105 .21 5-50 5-4 4-3 1900 5er. ce_nt or more of the value of the forest property, fire danger is serious. For the owner of a small forest, from forty to one hundred acres, who may lose in one fire the greater part of all he owns, this is no doubt true. Generally the danger is overrated. The burning of a few plantations on a large forest property is not a serious mat- ter ; they must be replaced and this adds to the current expense but it does not affect the regular income for years to come. In stands over fifty years old, the fire-injured or fire-killed timber is not a total loss, in fact, it may be utilized often up to eighty or ninety per cent of its full value. Here the fire may disturb the plans and or- derly business of the forest but does not cause a serious loss. In wild woods the case has been different. In the United States fires have done enormous damage and even today are the greatest factor preventing action in forestry. According to the report of the Na- tional Conservation Commission of1 1909, the fire losses in the United States may be estimated at about fifty million dollars per year for merchantable timber alone. To this the report adds a much larger sum for destruction of stuff below merchantable size and -usually a total loss. Leaving out the latter, yearly fire losses of merchant- able stuff for the last fifty years in the United States have been at least ten cents per acre of forest area, and if the average value of forest is twenty dollars an acre, the loss amounts to five dollars per thousand dollars worth of forest, or about seventy per cent of what good forests should pay in taxes. The difficulty here has been a lack_oL^rgtecjiDJi_and lack of market and roads to enable immediate use of the stuff injured or killed. It has been the rule rather than the exception that timber killed byjires in the United States has been a total loss. This is all changing now and will change a great deal more even in the near future. It may be expected that in fifty years conditions FIRES IN EUROPE: 123 in the United States except perhaps in the high mountain country of the west, will resemble those of Europe. Here the fire danger is no longer considered a serious difficulty in forestry and all large owners, state and private, do not even feel the necessity of fire insurance. The following figures will illustrate : DAMAGE FROM FOREST FIRES :* Prussia. Bavaria Austria All forests. 1881-1894 State forests. 1881-1912 state forests. 1877-1902 not Hungary. 1881-1895 Total area of forest, million acres. .. 20.4 6.2 2.07 24.27 Total gross' income, million dollars. . 50$ 15-5 6 30$ Net income per acre, approximate $. 1.25$ 1-25 2 0.30$ Value of forests on basis of 3% and net income, million dollars 810 250 120 24O Damage from forest fires $1000 93 4 ACfft* 35 For each 100,000 acres of forest the fires burned over acres 25 21 10 I/* For every $1000 gross income fire *"j **ff damage is in dollars I QO .66 1.16 For every million dollars worth of j. • y^ forest damage is $. . 117 , •3? 17? Average number of fires per year. . . A A / 388 26 OO 91 *o/ Average area burned over each year, acres •4955 1500 200 3420 In the statistical works for Wiirttemberg and Baden the damage by forest fires is not even mentioned. While it is evident from the foregoing that large f^restjDwners have little reason to seek insur- ance, the case is different for the great number of small owners. For this reason forest^fire insurance was discussed and planned as early as 1877 by Burckhardt and the matter agitated from that time tcTthis. Insurance by the state, by cooperation of forest owners and by commercial concerns, all have been discussed. * See Endres Forst Politik, also Forstliche Verhaltnisse Preussens Wurttem'burg, etc. ± May be a little high since it is based on income in state forests and iveraged for a number of years. 124 FORF.ST VALUATION So far only commercial organizations have worked extensively in this field. Of these a department of the Gladbacher jfire insurance company, starting in 1895 is the oldest and most important. In 1903 this company had more than 300,000 acres of forest covered by insurance, mostly in the densely settled Rhine province where the forest is in small tracts. The average rate has been about $1.80 perJjSipocLof property. Since then the Bayerische Hypoteken und Wechselbank, the Provincial Fire Insurance Institute of the Rheinprovinz and others have taken up this work. The^rates usually run from one to five dollars per thousand- dollars worth of property. Usually it is demanded that the insurance continue for at least ten years, that the owner insure all his holdings in one company, and that he give to his property such protection as is customary in the district, this point being stipulated rather in detail. The rate of premium varies with the kind of timber and age, formerly the rates increased with age up to thirty years, this appears to have been given up and the rate^ starts with a maximum and decreases. Regular published tables of yield and methods of assessing damage are provided, the cost^ and sale value of the stand prevail, the expectation value is permissible only under certain exceptional conditions, the payment is to cover only actual damage, any income from material salvaged is deducted, the interest rate for any calcu- lation of values is three _per cent. The following figures f rom, Vorster, director of the Provincial Fire 'insurance Institute of the Rheinprovinz, published in Zeit- schrift fur Forst und Jagdwesen, 1908, p. 797, etc., will illustrate what is today good forest fire insurance as to rates, and change in these. v j r »• u • Premium per $1000 Kind of timber insured. , * of property, 1. Pure 'hardwoods, coppice or timber $0.25 — .80 2. Mixed 'hardwoods and conifers in timber forest 60 — 1 . 50 3. Coppice mixed with conifers 90 — 3 .00 4. Pure conifers: Up to 8 years old 3.00 — 4.00 8-15 2.50—4.00 15-40 i . 50— 2 .co over 40 50 — 1.50 The following illustrates how a small forest of pine, site IV, of Schwappach, properly regulated, with present prices for timber, fares in this insurance. Figures of the Rhenish Institute are com- pared with those of the Gladbach Fire Insurance company. FIRE: INSURANCE) IN EUROPE; 125 For simplicity, the lower rates only are here considered for both "»a TTIP>C companies. Cost < acres, rotation 60 years. panics. Cost of insurance for a regulated forest of pine, site IV, 60 Rhein Province Glad-bach Institute. Insurance Co. Area. Acres. Age of Stand. Years. Value of Stand per Acre $. Premium. Premium. Rate per $1000. Cost for 10 Acres $. Rate per $1000. Cost for 10 Acres $. 10 10 28 2.50 .70 4 I. 12- 10 20 52 1.50 .78 3-40 1.76 10 30 9i 1.50 1-37 2.80 2.56 10 40 133 i,5o 2.OO 2. 2O 2-93 10 50 165 .50 .82 1.50 2.48 10 60 197 • 50 •98 1. 00 1.97 Total 6.67 Total 12.84 Per acre .11 .21 Per $1000 worth of woods i.oo 1.94 Assuming the yearly gross income from this sixty acres to be $225, Yr + Tq, and the total expense c -f e, $75, the insurance would take 4.4% in one, or 8.5% in the other, of the net income of this forest. From each $1,000 of gross income this insurance takes $30 in one, $57 in the other company. Comparing this to the actual yearly losses in Prussia, $1.90, and Bavaria $0.66, as seen in the foregoing table, it is easy to see why the state forests are not insured. So far the forest fire insurance has not been a success, the com- panies have not made any money in this line of insurance and the proportion of forest insured is still insignificant. Compulsory jstate insurance would no doubt readily solye this^rjroblem and reduce the rate to nearly the actual average loss and so reduce it to less than twenty per cent of the present rates. In this connection the comparison of cost of insurance and cost of good fire protection is interesting.: For a regulated forest of pine with a rotation of only sixty years the lowest premium is eleven cents per acre for a hundred year rotation of the same kind of woods, pine, it amounts to twenty-seven cents. But with any large property and any kind of system of protection tenjcents an acre goes a long way toward preventing fire entirely and certainly can well reduce the damage to the insignificant minimum now secured in 126 FOREST VALUATION Germany. In the national forests an expenditure of only about t\vo cents an acre has reduced fire losses from an estimated ten cents per acre to less than one cent per acre. By an expenditure of ten cents an acre it is to be expected that this loss will be reduced still further, and what is more important, this protection will protect with a certainty regardless of conditions, and so prevent any of the great forest fires which from time to time have completely devas- tated many thousands of acres in a single season. So far forest fire insurance has not really been tried in the United States. All financial concerns, including insurance com- panies have been afraid of forest properties ; some of the reasons for this attitude are found in the following conditions : The values are badly distributed and scattered in a forest ; there is a large area for a relatively small amount of money. This is less true in the well-cared for forest with good market than with the wild woods ; and it is less true of the heavy stands of timber in the Pacific coast states, but generally the fact remains. In the city,, property on one acre is worth many thousands, in^the forests of the eastern half of the United States it is worth about twenty dollars. The value of wild woods is hard to ascertain with any degree of accuracy. The insurance company's agent can not simply inspect and verify; it takes a regular cruise and involves expense. The amount of damage by a forest fire is very hard to ascertain. A lot of hardwood timber run over by fire may all leaf out and ap- pear practically uninjured and yet half the stuff may die and start to decay before five years are past. Two estimators would often fail to agree with regard to the same tree before them. Much of our timber is owned in separated and often^videjv scattered bodies. The owners of timber are only holding stumpage; it is a spec- ulative affair, and does not inspire confidence. The owners do not practice forestry, the forest is left without improvements, roads, etc., and there is no real care and protection. The community, state and county. do_jj.othjng, as yet, to_niake forest property reasonably secure. Public opinion and habit has no regard for forest property and is quite generally inimical to the owners of forests. This attitude finds expression in the behavior of young and old in the forest, in legislation and in the enforcement of law. What the future will bring is doubtful. For large owners of forest, who practice real forestry, there is no object in insuring, as FUTURE; IN INSURANCE; 127 is evident from the experience on the national forests today. For the small holding, especially the wqqdlot on the farm, insurance would be beneficial and may even become necessary if these valuable woods are to be preserve'd. For commercial companies these wood- lots are not inviting as objects to insure, the difficulties in appraisal of damage alone being sufficient to discourage any company. It will require mutual insurance as now exists in many counties, or state insurance will have to supply security. X. THE RIGHT USE OF LAND FORESTRY VS. AGRICULTURE AND RANGE. a. Nature of land. Since the area of land can not be increased and since land can not be moved from place to place, the occupancy of land, as by a farmer, is monopolistic, and the right use of the land is important, in fact, fundamental to the welfare of any people. That a farmer should have a duty, not only to himself, but to the people or state, and that the state authorities have a duty in seeing" that the land of the state is put to its best use for present and future, are modern conceptions, rapidly developing and becoming influential in public economy. Even in the past, the state felt justified in taxing the shiftless owner of a good piece of land, farm or city lot, not in keeping with what it produced but according to what it should pro- duce. Today all civilized states are spending money to devise ways and means of making the land more productive. In this effort to maintain and better the land it is of as much importance to select the right crop as it is to give the proper care, and it is here where the choice between forest and field crop asserts itself. b. Lands may roughly be divided into : agricultural, forest, range and waste lands ; but the lines between these four classes are rarely very sharp. On the agricultural lands, including the garden and truck lands, the crop is to furnish food for people or animals. The forest crop, on the other hand, serves two very distinct purposes ; it may merely maintain a necessary cover on mountain lands and be useful as a protective forest, or it may serve solely to produce timber and other products. The importance of the forest as protective cover is so great and has of late been so well recognized by the governments of civilized countries that Martin in his Statik classifies lands into those used to raise products and those requiring a protective cover. In the following paragraphs the protective forest is considered as occupying absolute forest soil. c. The factors which determine or limit the use of land are chiefly: climate, (temperature and moisture,) soil, topography and population. In mountain countries small patches of valley or bench land may be excellent farm land and yet not desirable for this WHAT DETERMINES USE OE LAND 1 29 use because of their location and size, a condition which applies, however, only to a very small per cent of our lands. i. Climate is invariably the principal factor. More than half of N. America and Asia is too cold for agriculture; more than 35% of North America, more than sixty per cent of Asia and Africa, and more than eighty per cent of Australia are too dry for farming. About forty degrees Fahrenheit average yearly temperature limits good farming; about 30° F. ends the useful forest, except pro- tective woods. In the United States about twenty-five inches of rainfall for the year limits the natural forest ; about fifteen inches sets a limit to dry farming or farming without irrigation ; at ten inches of rainfall the prairie changes to desert. In countries with an average yearly temperature less than fifty degrees Fahrenheit and with dry summers and low relative humid- ity all lean sandy lands have failed in maintaining satisfactory agri- culture. Topography affects agriculture ; generally a five per cent slope washes as soon as plowed ; a ten per cent slope gullies and is ruined. Usually steep lands become stony and lean and millions of acres of farm lands have been abandoned in Europe because of topography. Dense population commonly stimulates the use of land for farming. In the United States millions of acres of good land are not used or poorly used for lack of labor and demand. But while it is generally true that dense population leads to the use of lands for agriculture, this is no longer true to the same extent that it was fifty or more years ago. Formerly the majority of the people lived on the farm, today over sixty per cent of the people of the United States live in town. The people do not flock to the country, they leave the country and move to town. It is the town which furnishes employment and a safe and comfortable living. This is as true of Europe as it is of the United States. The result is that millions of acres of land even in the better populated parts of the United States and the most densely populated states of Europe are not tilled, and large areas have been abandoned to deteriorate into waste lands. Dense population today, means cities, manufacture and commerce, good wages and living in the city, higher wages and less farm labor for the farm; and intensive use of good farm lands which justify labor and machinery ; and abandonment of poor farm lands. In Europe this situation has shifted the use of lands from agriculture to forestry for large areas ; it has led to regular appropriations by the states and the development in this direction is more rapid today 130 FOREST VALUATION than ever before. Lands worth up to fifty dollars an acre are today being converted from field into forest in southern Germany. England has had a special commission to work on this problem. In its report this body cites the case of a tract of land of twelve thousand acres, bought at ten dollars an acre, which for years had brought only about thirty cents per acre rental, and it recommends extensive purchase of lands and reforestation in densely populated England. d. The countries of the Old World are interesting in this connection: of Scandinavia less than 8% is tilled, about 50% is waste land; Spain and Italy are about 33% tilled and more than 25% is g°at and sheep range which will be regarded waste land as soon as industrial conditions are such as to give the people a 50 cent per day wage. Russia in Europe is claimed to be about 26% tilled and 37% forest, leaving 37% as waste land, with an uncertain portion of range lands. Turkey in Asia tills about 3% of its 580 million acres, the rest being mostly waste land with various combinations of rock waste, desert and range lands. India, China and Japan, with about half the human race as population, till probably less than 20% of their land. Use of land in highly developed states : Cities Highways Meadow and waste Fields. and Forest. including Pasture. some range. Germany 48 19 26 6 France 55 14 18 13 30 31 3 36* Both in France and Germany the tilled land is not on the in- crease. Prices of land are not advancing and the rents or income from farms is not materially better than fifty years ago. * Includes considerable heather land. LAND CONDITIONS e. Land conditions in the United States. 13* Area Per Cent. Region by States. million acres. Improved land. Forest. Rest is Atlantic, Maine to Georgia. . . . Gulf, Florida to Louisiana Texas 225 126 167 35%. 18 12 45% 65 25 cut over land cut over land prairie Lake States, including Ohio, Indiana and Illinois 207 51 31 cut over land East Central, West Virginia to Arkansas 146 41 40 cut over land West Central, Oklahoma to Dakota 250 40 4 prairie Rocky Mountain C4Q I C 20 prairie desert Pacific, California to Washington 20^ Q 4O brush and waste prairie, desert, brush and waste Total United States IpOO 25 26 Apparently over 900 million acres are neither forest nor field, largely too dry and therefore prairie or desert. About 300 million acres are wild woods on absolute forest soils, the lands being un- suited to farming by reason of climate, cold mountain country, to- pography, all large mountain ranges, and to a lesser extent, poor soil, South and Lake states and the East. What these conditions may be even in an old settled state is well seen from the following figures for Michigan : State. S. Half. N. Half. Total area million acres 36.8 17 19.8 Per cent improved .35% 64% 6% f. Agricultural use. Generally the agricultural possibilities of any district finally de- cide its use. Any good tract of agricultural land as large as an ordi- nary county will become farm settlement in our country. This fact, based on large experience has helped to fix in the minds of most 132 FORKST VALUATION people, and especially the so-called representative men who are in duty bound to "boost" and to "believe in the country," the assump- tion that all lands are agricultural lands. That this is practically true of Iowa and Illinois no one doubts, but that it is true of very few other states every one who cares to can see for himself. Formerly the policy of the states was to get people and settle the country. Usually this policy was forcefully emphasized by the land boomer and other people who had, or believed they had a mon- etary interest in rapidly populating the state. Of late the author- ities agree that the state wants : 1. Not merely many people biit rather good and prosperous people. 2. To the state, any kind of "pauper'' industry or industry in which the people can not make fair wages and a fair living is an injury. Of these pauper industries the farming of non-agricultural lands is one of the worst. 3. The state needs manufacture as well as farming, and that even the best farming districts may lose in population and business because of the one-industry condition. Consider Missouri and Iowa, and some of the best farm counties of several of our states. 4. The state wants to have its people supplied with raw ma- terial and manufactured goods by the state itself and so be as inde- pendent of import as possible. This applies as much to timber as to grain. 5. Every acre of land should raise the best possible crop and make the largest return in permanent use. 6. Labor conditions should be carefully balanced, so that labor is steadily employed and all work is well done. The great wheat districts, though excellent farm country, waste grain for lack of help in the harvest season, and fail to give employment all the rest of the year. 7. Regulation of stream flow, protection from erosion and winds and the beauty of the landscape are important and in many cases decide the choice between field and forest. In our country public policy regarding the proper use of land is largely controlled by the views and wishes of the farmer and it is interesting to see how he is affected by the choice. i. The farmer wants not merely good crops but good prices. A good home market is the only means of liberating the farmer FARMER'S VIEWPOINT 133 from the speculator and the manipulator of the world markets. Two good sawmills where twenty per cent of the land is tilled in a county of the Great Lakes district, are worth more to these farmers of the county than a condition of sixty per cent of the land cleared, com- petition trebled and the local market spoiled for lack of manufac- tures. This competition is especially painful in one-crop districts, potato, fruit, etc., and it is doubly bad where the average farmer is poor and compelled to sell for what he can get. 2. The farmer needs labor, cheap and convenient, usually for short periods. Without other business a district can not keep itself supplied. 3. The farmer needs railways. The farm furnishes about two hundred and fifty pounds of freight per acre and year, the forest about one thousand and the manufacturer exceeds them both. 4. The farmer wants good roads and schools and yet low taxes. The state taxes, and these in the long run determine school and road, are not paid by the farmer. In the United States the farmer owns less than one-third of the property, is assessed at about sixty per cent of its value and usually pays about sixty or seventy- five per cent of the average tax rate for the state, so he contributes less than twenty per cent to the state tax burden. It is evident that to the farmer there is very little inducement to urge agricultural use of lands wherever this brings competition and reduces manufacture and local market. In the past this phase of the question was clouded because, most farmers were as much spec- ulators as they were farmers ; they wanted to feel that their farm was increasing in value and that they would make money by selling out if they chose to do so. The utter fallacy of this reasoning to the real farmer is apparent ; all he gained by the boost was a larger tax assessent, for his crop, and his income was not increased by it. A few boost sales in a county frequently upset farm assessment though they did not add a cent to the income of ninety-nine per cent of the farmers. g. The income from the land has always been regarded as an important criterion of its use. A century ago before railway and modern manufacture, wood was cheap, over large areas it had no value at all, while food was a necessity and measured by a day's wage was high in price everywhere. Accordingly, the incomes from forests were very small and even foresters like Hundeshagen and Cotta felt that only the state could afford forestry on anything like 134 FOREST VALUATION fair land. Today these conditions have changed, and agriculture is called on to explain its smaller net income from better lands. In this discussion it is well to keep in mind the following : 1. Timber is a necessity to modern civilization. All substi- tutes have not been able to reduce the per capita consumption and in Europe any state with fair industrial development becomes, a timber importer as soon as its forest area drops below thirty per cent. 2. The forest crop is safe and certain wherever forest is native and even on prairies the forest once established modifies its own local climate. On all lean and difficult, stony, rough, etc., lands the forest is far more certain than any field crop. The forest crop takes care of the land, the field crop drains it. 3. The forest crop is durable, unlike potatoes, fruit, etc. A few years seasoning increases the value of timber. 4. Prices of forest products have gone up steadily for a cen- tury and have more than doubled in half a century ; prices of field crops in Europe and the United States have not changed materially for the last half century. See Endres, Forst Politlk, p. 119, etc. Rye, the great bread stuff, was cheaper in Prussia in 1893-1903 than it was in 1860-1890. For the United States, see United States Dept. Agri. Farmer's bulletin, 645, 1914, p. 23, the value per acre of the ten most important farm crops was $15.74 in 1871, then declined rapidly and did not regain this value until 1908. 5. Forest statistics of necessity are averages since it requires many seasons to grow a crop of timber. To be comparable at all the figures for farm income therefore must be ,taken as averages. This is commonly overlooked and accidental maximum figures are constantly quoted and repeated. "Great money in clover-seed," "$400 per acre in cherries," etc., are repeated in journals and by booster orators until the average person is completely misled. It is one of the most useful works of the United States Department of Agriculture and the Experiment Stations to gather truthful statis- tics of the farm. So long as the booster succeeds in making the people believe that there is big money in sand farms, so long the public is reluctant to pay even a decent cost price for farm products. 6. Forest statistics as used here describe large averages of incomes not from the good lands but from inferior, largely non-agri- cultural lands. It is doubtful if more than thirty per cent of all German forest lands could be farmed continuously and successfully. If all lands of Germany were arranged in five classes of equal area, INCOME FROM FARMLANDS 135 the forest lands would take practically all of number five and about half of number four with very little of class I-III. For this reason it is quite safe to say that for the same use, the lands now in fields, etc., should by virtue of their fertility produce a much larger return than the forest lands. This as will be seen, they do only for the gross income in which a large per cent is labor, but they fail to do this for net income, clearly proving the superiority, at present prices, of the forest uses when judged by net income. i. Income from field and farm land in the United States. For over thirty years the United States Census authorities have gathered farm statistics. Of late the United States Department of Agriculture and also some of our Agricultural Experiment Stations have checked, verified and amplified this work and have generally proven the accuracy of the work of the Census.* In discussing the income from land used in farming it is neces- sary to keep separate the income from the crop and that from the animals, etc., which represent a separate investment. The total value of the farm crops in the United States, includ- ing the value of the material fed to live stock, was reported in cir- cular 132, as taken from the Census of 1910, at 5,487 million dollars, or $860 per farm. The average farm has 138 acres, of which 75 acres are improved land. Allowing only 50% for cost of produc- tion, exclusive of rent of land, the 138 acres of farm land produce a gross crop income of $6.24 per acre, or a net crop income of $3.12. Even if referred to the 75 acres of improved land only the gross crop income is $11.40 and net $5.70 an acre. United States Bulletin 645, 1914, p. 23, gives the "Yearly value per acre of ten crops combined." The crops are corn, wheat, oats, * See United States Crop Reporter for 1911 for cost of producing wheat, oats and potatoes in the United States. Ohio Agricultural Experiment Station bulletin 266 cost of producing corn in Ohio, 1913. United States Farmers' Bulletin 641, 1914, cost of producing cotton. United States Farmers' Bulletin 635, what the farm contributes directly to the farmer's living, 1914. United States Farmers' Bulletin 645, Agricultural Outlook, 1914, p. 23, yearly value per acre of the ten most important crops combined for 1866-1914. Bulletin 41, United States Department of Agriculture, 1914, farm manage- ment survey of three representative areas in Indiana, Illinois and Iowa. Farmers' Bulletin 665, 1915, Agricultural Outlook for farm wages in the United States; Farmers' Bulletin 570, 1913, and circular I3^-A, 1913, which discuss the farmers' income, using Census of 1910. 136 • FOREST VALUATION barley, rye, cotton, potatoes, hay, tobacco and buckwheat. The data are presented in the following diagram. /6 /5 $14 &3 $12 A7 z V L Fig. 2. Chart showing the value per acre of 10 crops combined (corn, wheat, oats, barley, rye, buckwheat, potatoes, hay, tobacco, and cotton), rep- resenting about 90% of the total cultivated area of the United States. These figures present the gross income per acre of fields and meadows, actually tilled that year, and show that even at present prices this gross income is only about $16 an acre and that for more than 25 years prior to 1904 it was usually below $12 an acre of fields and meadows. These fields contained 47 acres per farm, or made only 34% of the farm itself. The following table indicates the rel- ative importance of the principal crops, and presents some figures on the cost of production of farm crops in the United States, 1909. Cost of Total area million Total Value million Yield per Value per acre. production per acre exclusive acres. dollars. acre. $ of rent. $ Corn 10^ i=;2O 32 bu. 10 8.52 Wheat 4Q ccc 17 bu. 17 7.85 Oats -ty 4.C2 W bu. 14 7.13 Cotton T.J 825 240 Ibs. 3,0 16.70 Potatoes 3.6 212 iiSbu. 35 25 Hay AT. 856 1.2 tons 14 Barley and rye 9-7 135 22 bu. ii about like oats. CROP AND EXPANSES ON FARM 137 Bulletin 645, 1914, states that the thirteen principal crops occupied three hundred million acres, and had a value at the farm of 4,919 million dollars, or about $16.38 an acre. Another reliable measure of farm-crop income is the rent act- ually paid to owners of farms. While in a few localities the rent has been boosted up to as high as $8, the general average of cash rent seems to be close to $3, closely agreeing with the average net crop income. Even this $3 rent per acre and year is not a net in- come to the owner since taxes and repair of buildings, etc., must still be deducted. It is also quite generally conceded that the farm is rarely well kept up in the cash rent system. The following figures describe the crop income conditions in Germany. They are taken from Helferich "Deuts Maud's Wohl- stand',' and represent average yields for 1909-1913, valued at cur- rent prices. Rye $14-56 per acre Wheat 21.50 Barley 13 Potatoes 19-20 Oats 11.80 Hay 12 Which would indicate a general average close to $16 or the same as the present average for the United States. Since less machinery is used in Germany and the fields are gen- erally too small for economical farming, the cost of production is higher in spite of cheaper labor. The "Schlesische Landschaft," see Martin, Statik, p. 259, estimates the cost of producing the crop as follows : on lands of Class i cost is 55-65% of value of crop 2 57-6; 3 60-70 4 65-75 5 72-82 Taking land of class 3 as average and using the above $16 aver- age for crop, the net income even from these fields and meadows in Germany is only $5.60 or about the same as from the improved land in the United States. As regards the regularity of income the figures of the United States Department of Agriculture, see Farmer's bulletins 629, 641, 645, indicate that in hay even, the average is below seventy per cent of a fair stand. As stated in part one, the state forests of Wurttem- berg today cut about seventy-three per cent of normal, are still im- 138 FOREST VALUATION proving and may be expected to be eighty per cent normal in their yield before another twenty years. 2. Income from the forest. Since there are no forests in the. United States in a regulated business condition, it is necessary to consider European results. Even in Europe it is only the state forests and the holdings of other large owners, cities, etc., which can be considered as properly taken care of in a way at all comparable to the farmer's fields. The following table represents large averages and the figures are reliable. The great difference between Prussia on one hand and Wurttemberg and Saxony on the other is due to soil, sand, and climate, and in part, market ; the smaller income in Bavaria is large- ly due to topography, mountain woods, and to a lack of develop- ment. In Bavaria and Prussia a further development, road build- ing, etc., will continue to absorb much of the yield. Later on, in twenty-five or fifty years, this will cease and then the net income will be a much larger part of the total income. Incomes from state forests in Germanv:* Area. Wurttemberg 1908. Saxony 1911. Bavaria 1912. Prussia 1912. Acres. 490,000 431,000 2,330,000 6,796,000 Total yearly $4,906,000 $4,015,000 $16,156,000 $38,490,000 income. Years. Income per acre. Income per acre. Income per acre. Income per acre. Gross. Net. Gross. Net. Gross. Net Gross. Net. 1850-59 $ 3-6o $ 2.1 1 $ 3-03 $ 1-94 • $ -97 $ -54 1860-69 4-73- 2.89 4.46 3.21 $ 2.32 $ 1.35 1-43 .83 1870-79 5-77 3-45 5.76 3-92 2.95 1.66 1.98 .97 1880-89 4-99 2.70 6.47 4-33 2.64 1.30 2.2O I.OI 1890-99 6.35 3-87 7-13 4-50 3-73 1.81 2.68 1.29 1905 9.20 6.10 8-44 5-39 4-5-5 2. 2O 4.26 2.42 1906 10.05 6.78 8.28 5-o8 4-95 2.55 4.27 2.27 1907 10.90 7-47 9.60 6.17 4.90 2.55 4-54 2.51 1908 10.00 6.50 9.22 5.58 5-50 2.95 445 2.21 1909 9.90 6.35 8.96 5-24 6.30 3-30 4-53 2.O2 1910 . 9-15 5.36 4.22 1-93 1911 • 9.20 6.03 5-19 2.98 * See Endres, Forst Politik ; Verhaltnisse Wiirttembergs ; Tharander Forstliches Jahrbuch und Zeitschrift fur Forst und Jagdwesen. Figures round. FARM OR FOREST 139 From the preceding it appears : 1. The gross income per acre in the well kept forests of Wurt- temberg and Saxony with present prices of timber is larger than the gross income from the field and meadow when the quality of soil is considered ; and that it is about sixty per cent of crop income even if no allowance is made for the difference of soil. In Prussia the gross income from forest is about thirty per cent of the gross income from the fields, a difference fully accounted for by the poor quality of the pinery sands devoted to forestry. 2. The net income from forests in Wiirttemberg, Baden, Sax- ony, etc., state forests, is as large and often larger than the net income from farm lands in the same districts. This, of course, is chiefly due to the smaller cost of production since this cost is nor- mally below7 fifty per cent of the value of the crop in forestry and above sixty-five per cent in farming. 3. The gross crop income and net crop income from farmland in the United States is smaller than that obtained from the state forests of Wiirttemberg, Baden, Saxony, etc., and is but. little higher than that from the poor pinery forests of Prussia. Even if only the improved lands of our farms are considered, the gross income is little higher than that of the state forests of Wurttemberg and Saxony and the net income is even lower. To some extent this condition is due, no doubt, to the fact that farm products in the United States and abroad are not paid for at a proper price in keeping with the value of soil and the cost of pro- duction. If correctly adjusted the field with its better soil and large amount of labor should produce at least twice the gross income ob- tained from the forest. But the fact remains that the growth pro- duced in the forest is very large and also that the forest, owing to the large crop-capital in the form of growing stock is entitled to a correspondingly large net income. Summing up: 1. The forest can utilize colder, frostier sites. 2. It can use rough, steep, stony and poorly drained land. 3. It can use poor soils, especially sands. 4. It maintains the fertility of the soil and therefore is a much surer crop than any farm crop. 5.- Bad seasons are averaged up in forestry, an excellent stand harvested in 1914 may have been through many poor seasons but their effect is no longer seen. 6. Its products are enduring and generally gain in value by storage. 140 FOREST VALUATION 7. The crop is not ripened in a few days or even months, but can be cut at any time from the age of fifty to one hundred and fifty years. 8. It requires less labor than the farm crop. Agricultural use on the other hand : 1. Is possible or practicable on probably less than fifty per cent of the land area of the United States. 2. It is the most important use of land. 3. It uses more unskilled labor than forestry. 4. It furnishes greater values only from better lands. 5. It furnishes less material per acre for transportation and further manufacture. 6. It encourages erosion, rapid run off of water and so injures land and disturbs water distribution. 3. Use of land for range. Real range lands occur chiefly in dry districts, prairie and des- ert, and mountain countries where the forest can not hold its own on account of conditions of temperature, or moisture, or both. On better prairies of the West the range has given way to the farm. On poor soils in forest districts like the southern pinery and the sands of the Great Lake region the forage plants are readily crowded out by more frugal but useless plants, so that grazing on these lands is of very little value, and can not be compared with the use of these same lands for forest. The poor jack pine lands will grow fifty cents worth of jack pine and scrub oak per acre and year, but they will never be worth ten cents per acre and year continuously as range. The following general averages describe the range conditions in western United States : Number of head of range live stock and their equivalent in sheep. United States. West. Equivalent in sheep West of plains. in the West. Cattle 61 million 9 million, or 15% 50 million Horses 24 million 2.5 million, or 10% 20 million Sheep 52 million 28 million, or 54% 28 million Assuming that the feed of a sheep is worth sixty cents per year and that the four million acres of tilled agricultural land in the west furnish one-third of all the feed, the range lands, approximately RANGE: is WASTE: 141 four hundred million acres furnish about forty million dollars worth of feed or ten cents per acre and year. Where range lands are leased as by the state of Texas and oth- ers, or where stock is grazed at fixed rate per head as by the United States Indian Office and the United States Department of Agricul- ture, the price is generally below five cents per acre and year, or season. From these few figures it is clear that where land can be used for forestry or for farming the use as range is an inexcusable waste. APPENDIX. A. Normal Yield Tables. These tables will prove useful in giving actual reliable data con- cerning forestry as a business. They will be helpful in preparing problems for class use. American yield tables are still deficient ; practically all data come from wild woods ; the growth of the individual tree is usually determined on dominant trees only, the yields per acre on stands far beyond a justifiable rotation; the effects of man's care in thinning are yet to be learned. None of these data are as yet accepted by a representative body of men. Under these conditions it seemed best to use the German tables as worked out in connection with the forest experiment stations and compiled by Professor Doctor Adam Schwappach, the foremost authority in this line of study. The division into five sites was agreed to by the Experiment Stations in 1888, and bases the division on the total volume of the main stand and provides for the stand one hundred years old the following relations: Site. Pine. Spruce and fir. Beech. I 100 100 100 II 78 82 80 III 60 66 64 IV 43 • 50 49 V 29 36 35 In Schwappach's tables this relation is fairly adhered to as is apparent from the following: total volume of the pure fully stocked normal stand one hundred years old is : Site. Pine. Spruce. Oak. Beech. I I II III IV V 6600 c. ft. 11600 6200 IOIOO 100 100 IOO ICO 85 83 79 80 69 66 58 64 55 5i — 49 43 36 — 35 144 FOREST VALUATION Since these German tables can not be used in the United States without modification, it seemed unnecessary to tabulate for all rive sites, and only the figures for site II as nearly a good average, are here reproduced. Most of the figures are rounded off. The graphs, figures 3-8, follow Schwappach's as given in his admirable "Fvrtrag- stafeln d. wichtigeren Holzarten," 1912. How far these tables may serve to guide and check in our work in the United States is yet to be learned. It seems reasonable, how- ever, that for trees of similar habits, tolerance and soil requirements, etc., the yield per acre is well indicated by height growth, and that as a provisional check we may assume that if spruce in a certain district in the United States has # height growth equal to that of spruce site III in Germany, the yield per acre will also approximate that of site III, etc. MONEY YIELD TABI& FOR SPRUCE, SITE II. Middle and N. Germany : Sdhwappach ; 1902. Only wood 3" and over (Derbholz) considered. Age. Main Stand. Price Value Thin- nings added. Total value. Main stand and Average Tree Main Stand. of TreVs per total Value thin- Diam per 100 per per nings Height b.h. Vol- Value acre. c. ft. acre. acre. per o.b. ume acre. $ $ . '$ $ ft. inch. c. ft. $ 30 1800 4.80 56 56 27 3-2 0.5 0.03 40 1 020 6.70 172 10 182 4i 4-8 2-5 0.17 50 680 8.60 366 4i 407 56 6.4 6. 0-54 60 485 9-30 54i 104 645 67 8. 12.8 i. n 70 372 1 1. 60 803 207 IOIO 76 9-5 >i8.8 2.15 80 295 12.60 9/2 336 1308 83 10.8 26.5 3-28 90 239 13-25 1092 483 1575 90 12. 1 34-5 4-50 100 198 13-80 1183 648 1831 96 13-3 44- 5-9^ no 167 14.40 1260 814 2074 101 14-3 53- 7-50 120 140 14.80 T305 969 2274 105 15-6 64- 9-25 APPENDIX 145 MONEY YIELD TABLE FOR PINE, SITE II. In N. Germany, Schwappach, Kiefer, 1908. Only for wood 3" and over (Derbholz). Main Stand. Thin- nings Total value. Main stand Average Tree of Main Stand. Age. Price Value added. and Trees per total Value thin- Height Diam. Vol- Value per IOO per per nings ulme acre. c. ft. acre. acre. per acre. $ $ $ $ ft. inch. c. ft. $ 30 1560 5.8o 133 17 150 33 3-7 .0.9 0.08 40 840 6.10 201 55 ,256 43 5-3 3- 0.24 50 550 6.40 267 98 365 52 6-7 6. 0.48 60 400 6.70 333 143 476 59 8.0 9-5 0.83 70 290 7.10 423 190 613 65 9-2 14. 1-45 80 240 7.70 499 242 74i 7i 10.5 19. 2.05 90 200 8.40 567 299 866 75 n-5 24-5 2.83 IOO 160 9.20 623 36o 983 79 12.5 32. 3-90 no 140 IO.20 700 428 1128 83 13-5 37- 5-00 120 120 II. 2O 770 501 1271 85 145 44- 6.40 130 105 I2.OO 838 574 1412 87 15-2 50. 8.00 140 96 12.80 859 639 1498 89 15-6 54- 8.90 146 VALUATION MONEY YIELD TABLE FOR OAK, SITE II. In N. Germany, Schwappach, 1905. Only the Yield of Stuff 3" and over (Derbholz). Main Stand. Price Value Thin- nings added. Total value. Main stand and Average Tree of Main Stand. Age. Trees per total Value thin- per 100 per per nings Height Diam. Vol- Value acre. c. ft. acre. acre. per ume acre. $* $ $ $ ft. inch. c. ft. $ 30 2650 7.85 39 39 26 2. O.OI 40 1240 7.85 82 27 109 35 3- — 0.06 50 610 7.85 no 86 196 43 4-9 2.5 0.18 60 370 7.85 150 155 305 51 7- 6. 0.40 70 260 7-85 202 222 424 59 8.5 10.5 0.77 80 195 7.85 244 28l 525 64 10. 17-5 1.25 90 145 7-85 295 332 627 69 11.5 27. 2.06 100 125 8.60 373 374 747 73 13- 36. 3.00 no no IO.OO 476 410 886 76 15- 44- 4-34 120 96 11.50 584 442 1026 79 16. 54- 6.05 130 86 13.60 735 472 1207 82 17. 64- 8.50 140 78 15.80 895 503 1398 85 18. 74- 11.40 150 7i 17.20 I02O 535 1555 . 88 19. 86. 14.30 160 65 18.00 IIOO 564 1664 00 19.7 97- 16.90 I/O 60 18.60 1177 645 1822 92 20.5 108. 19.60 180 55 19.40 1242 690 1932 94 21.2 120. 22.50 190 5i 19.40 1277 736 2013 96 22, 130. 25.00 200 48 19.40 I206 786 2082 97 22.6 I4O. 27.00 *For the Stand below looy the value of n Mark pro. F. m. was used as the nearest average. APPENDIX MONEY YIELD TABLE FOR BEECH, SITE II. N. Germany; Schwappach; ion. Only wood 3" and over (Derbholz). Heavy Thinning (Lockerer Schluss). Main Stand. Price Value Thin- nings added. Total value. Main stand and Average Tree of Main Stand. Age. Trees per total Value- thin- Diam per 100 per per nings Height b.h. Vol- Value acre. c. ft. acre. acre. per o.b. ume acre. $ $ $ $ ft. inch. c.ft. $ 30 2900 28 2. 40 2IOO 3-10 4i i 42 4i 2.8 0.6 O.O2 50 1360 3-8o 88 19 107 52 3-8 i-7 O.O6 60 780 4-15 127 57 184 62 5-i 4.0 0.16 70 430 4-50 166 103 269 72 6.8 8-5 0.38 So 260 4-90 205 154 359 78 8-5 15-6 0.79 90 187 5-30 248 208 456 85 10.4 23- 1.30 100 153 5-6o 292 267 559 9i II.2 3i. 1.90 no 131 5-90 34i 328 669 96 12.2 39- 2.60 120 112 6.30 388 393 78i IOI 13.2 47- 3-45 130 93 6.60 428 460 888 105 14-3 59- 4.60 140 76 7.00 458- 529 987 109 15-8 70. 6.00 148 FOREST VALUATION !£*§ 's * U»S ^^S5 ON Tf ON NO co co 04 04 CO M MOO 04 04 04 M tx\O Tf co 8 dill .si * «5S o^«|^ co ol 8 ON ^K«^ ssa8 & ^ o t— t M HH 04 04 04 04 *04 04 ^4 >—* 0 03 0, a *rt £ t— i co tO^O OO O *•" ' 04 S%9^ ON O 04 01 Tf to to to aoo? rd f 1 | ! ^ O CO 'I'Sh u xt" to CO CO to to 01 VO ON O ON ON to co ON tx ON ONOOOO CO Q tx to 00 00 tx tx 03 3_, | ||^| ^ r^-\O O COVO ON 04 M 1-1 M t-i O4 W8RS VOOO O 04 •CO co ^t r^- ?^i O O O 00 04 04 co •^f^O ^4 O co M OO ^^4 co 04 w M 04 VH 04 to NO to Tj- CO R^saa ^2^2-^ K-s «^03 M d 26 . g ^ tOOlvoOO vO^J-040 00 to 04 00 to M tx co VO CO OVO w ^ -^-^ "• ~* e 04 CO co ^f tovd txOO" 00 ON O O 1-1 04 04 CO CO '•sf' to to rt | Q-0 ° — < CO Q .s >•§ ^ QtX-rJ-M ONtOOllX 04 04 CO ^T Tt- tO\O ^O 01 \O O co tx txOOOO 00 ON ON O\ ON I-H co to ON O O O W i— i K c ,1 s §1 « OO ON 1-1 Ol co ^ tovt5 r^-QQ C>1 tO txOO ON ON 00000005 VQ to Tf 04 00 00 00 00 NORMA1 O'M-I S *-" ^ OQOO olOOOto toOO co O 00 NO to "^" co 04 O to Ol tx co ON •rf- co CO 04 10 ON txoo VC co •-" ON 01 tx co O 00 VC to Tf HH l-i M M 1 to O to O 10 O 'O O 04 co co ^f ^f to toNO to O to Q \O lx txOO S&S| to O «-o p O >-i M 01 APPENDIX 149 O bJ3J^-£ rt u. > gSl Q C^ 'rt £ %Z o n o '•8*">S rt^ £ 1|§ C pH ^ ^ j3 S L.'O > ^ o-r: ^ ft ^ loll ^ u « u ft ° ^_i Cu II ^t ^^ ^ oq vq co to d tx to xt- co co oi 01 04* ^t- co 04 M q _;_;_;_; w p o" o ON to 04 tx co ON Tf O OO 00 00 tx txvovovo Qs co M co co co ON ON ON ON co to IOVQ vo vo vO vo vo vO rf ON rt-OO 01 toOO O Ol rf o^ co" coo? ^- rj- CO CO 0^ CO rj- to to to VO co O VO -sT- O to O T}- O\ Tt- O ^00 01 •-< 04 co fO^toto VOVOVOtx OOOOOOCy. tOOO M Tf-tXON^ lOtxONI-l COCO^ ^t^fTtlO tOlO tOVO go ooo^ oop co vo ix ON ON O1. 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CT5 O O O O vo Q O i-i co §• M VO vo 04 vo ^- O 00 txVO vovo M h-l H< ^-CO ., ri -M 1-1 °1 || TJ- O vooO' O H< HH 04 CO^ "^•"^ vovo vovo O 04 co vo vO ^^ ON 04 0404 0404 O4O4 O4CO vovo vovo vovo vovo vo tx cO cO vo vo O ^ ft^-, ft v, go visits CO vo ON vo 04 OO ^^ O vo O\ 04 VOOO >-> CO vovo T^- vo vo vO vO vO ^O vO ^ < " S o « 04 ON vo vo VO vo T3* c^ ^ ^ >• »C 04CO ^txOOd MCO vovo 1^x00 O^ O O I~H O4- 04 s § 5^°' < ^ +-> w ^-» •? . 1— 1 c • »^ ^"co 3£ v^vB" v^r^ "RR 0000 §8 S\ ONOS "SNO ^ i » VOON ^f04 O ^Q ^Q ^0 *~* ^-^ Q *^ w ON oo rx t^*O ^o 10 uo^- ^ °H ^^ vrjO^ vOcO 04Hi i-Ht-i bo ^^ 05 Ro &S 00 00 O^ ,0^ QN O •^ hH M IH APPENDIX c ^"5 S vSRRR RRRR RRRR R£&& OlcO"^"tO totOlOio tOtOtoiO lOlOtOiototototo ;tO010J t-i-rfi-iVO lOOlOli-i M M M CO CO 01 O< M M ON O O\ ONOO 00 2- S^ nit ia§s im Tf tO to to to to to IO O\OO tx to T|- ^00 01 tx 01 tx 01 tx CO p 00_ IOVC5 txOO' O^OO1-^ MOioico cO^toio rf co (N i-i - QtoO tootoO toOtoO 100*00 CO co Tf rf to to\O \O IX IXOO OO O\ O O SO 60 10 80 r- ». 1 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 X091 1,123 1,156 1,189 1,224 1,260 1,297 1,334 30 1,030 1,062 1,094 1,127 1,161 1,197 1,233 1,270 1,308 1,348 35 1,036 1,072 1,111 1,150 1,191 1,233 1,277 1,322 1,368 1,417 40 1,041 1,083 1,127 1,173 1,221 1,270 1,322 1,375 1,431 1,489 45 1,046 1,094 1,144 1,197 1£52 1,309 1,369 1,431 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 €0 1,062 1,1-27 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 70 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 1.349 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 1,528 1,663 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 1,329 1,461 1,606 1,765 1,940 2,132 2,342 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 1,931 2,154 2,402 2,680 2,988 120 1,127 1,271 1,433 1,615 1,819 2,050 2,310 2,602 2,931 3,300 i6o FOREST VALUATION Years n 1,1 1,2 Values of 1.0pn, where p 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 1,036 1,038 1,040 3 1,033 1,036 1,040 1,043 1,046 1,049 1,052 1,055 1,058 1,061 4 1,045 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 6 1,068 1,074 1,081 1,087 1,093 1,100 1,107 1,113 1,120 1,126 7 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 1,135 1,144 1,153 1,163 1,172 9 1,103 1,113 1,123 1,133 1,143 1,154 1.164 1,174 1,185 1,195 10 1,116 1,127 1,138 1,149 1,161 1,172 1,184 1,195 1,207 1,219 11 1,128 1U40 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 1,183 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 1,326 1,346 16 1,191 1,210 1,230 1,249 1,269 1,289 1,310 1,330 1,352 1,373 17 1,204 1,225 1,246 1,267 1,288 1,310 1,332 1,354 1,377 1,400 18 1,218 1,240 1,262 1,284 1,307 1,331 1,355 1,379 1,403 1,428 19 1,231 1,254 1,278 1,302 1,327 1,352 1,378 1,404 1,430 1,457 20 1,245 1,269 1,295 1,321 1,347 1,374 1,401 1,429 1,457 1,486 21 1,258 1,285 1,312 1,339 1,367 1,396 1,425 1,455 1,485 1,516 22 1,272 1,300 1,329 1,358 1,388 1,418 1,449 1,481 1,513 1,546 23 1,286 11,316 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 1,535 1,571 1,608 25 1,315 1,347 1,381 1,416 1,451 1,487 1,524 1,562 1,601 1,641 26 1,329 1,364 1,399 1,435 1,473 1,511 1,550 1,590 1,631 1,673 27 1,343 1,380 1,417 1,456 1,495 1,535 1,576 1,619 1,662 1,707 28 1,358 1,397 1,436 1,476 1,517 1,560 1.603 1,648 1,694 1,741 29 1,373 1,413 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 1,743 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 2,135 2,232 2,333 2,438 50 1,728 1,816 1,908 2,004 2,105 2,211 2,323 2,440 2,563 2,692 55 1,825 li,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 2,443 2,592 2,750 2,917 3,094 3,281 65 2,036 2,171 2,315 2.469 2,632 2,806 2,991 3,189 3,399 3,623 70 2,151 2,305 2,470 2,646 2,835 3,038 3,254 3,486 3,734 4,000 75 2,272 2,446 2,635 2,837 3,055 3,289 3,541 3,811 4,103 4,416 80 2,399 2,597 2,810 3,041 3,291 3,560 3,852 4,167 4,508 to* 85 2,534 2,756 2,998 3.260 3,545 3,854 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 5,943 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 4,432 4,891 5,396 5,954 6,568 7,245 110 3,331 3,714 4,140 4,615 5,144 5,732 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 n 2,1 2,2 Values of 1.0pn, where p 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 1,113 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 1,133 1,140 1,146 1,153 1,160 1,167 1,173 1,180 1,187 1,194 7 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 1,243 1,255 1,268 1..280 1,293 1,305 1,318 1,331 1,344 11 1,257 1,271 1,284 1,297 1,312 1,326 1,341 1,355 1,370 1,384 12 1,283 1,299 1,314 1.329 1,345 1,361 1,377 1,393 1,409 1,426 13 1,310 1,327 1,344 1,361 1,379 1.396 1,414 1,432 1,450 1,468 14 1,338 1.356 1,375 1,394 1,413" 1,433 1,453 1,472 1,492 1,513 15 1,366 1,386 1,407 1,427 1,448 1,470 1,492 . 1,513 1,536 1,558 16 1,395 1,417 1,439 1.462 1,485 1,508 1,532 1,556 1,580 1,605 17 1,424 1,448 1,472 1,497 1,522 1,547 1,573 1,599 1,626 1,653 18 1,454 1,480 1,506 1,533 1.560 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 1.614 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 1,809 1,852 1,895 1,940 1,986 2,033 25 1,681 1,723 1,766 1,809 1,854 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 2,903 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 3y782 50 2,827 2,969 3.117 3,274 3,437 3,609 3,789 3,978 4,176 4,384 55 3,136 3,310 3,493 3,686 3,889 4,103 4,329 4,567 4,818 5,082 60 3,480 3,690 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 4,753 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 13,10 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 14.36 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 19,36 21,76 24,46 27,49 30,89 34,71 162 FOREST VALUATION Years n 3,1 3,2 Values of 1 3,3 3,4 ..Opn, where p 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 1,134 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 1,236 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 1,307 1,317 1,327 1,337 1,348 1,358 1,369 9 1,316 1,328 1,339 1,351 1,363 1,375 1.387 1,399 1,411 1,423 10 1,357 1,370 1,384 1,397 1,411 1,424 1,438 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 1,708 1,737 1,766 1,795 1.824 1,855 1,885 1,916 1,948 18 1,733 1,763 1,794 1,826 1,857 1,890 1,924 1,957 1,991 2,026 19 1.786 1,819 1.853 1,888 1,923 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 2,191f 21 1,899 1,938 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 2,132 2,177 2,224 2,272 2,320 2,370 23 2,018 2,064 2,110 2,158 2,206 2,256 2,306 2,358 2,411 2,465 24 2,081 2,130 2,180 2,231 2,283 2,337 2,392 2,448 2,505 2,563 25 2,145 2,198 2,252 2,307 2,363 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 3,243 35 2,911 3,012 3.115 3,223 3,334 3,448 3,567 3,689 3,815 3,94£ 40 3,391 3,525 3,664 3,809 3,959 4,115 4,277 4,445 4,620 4,801 45 3,951 4,127 4,310 4,50,2 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 7,434 7,878 8,348 8,846 9,373 9,930 10,52 65 7,275 7,748 8,251 8,784 9,357 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 13,59 14,56 15,57 75 9,872 10,62 11.42 12,28 13,20 14,19 15.26 16,40 17,63 18,95 80 11,50 12,43 13,43 14,51 15,68 16,94 18,29 19,76 21,34 23,05 85 13,40 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 23,33 25,71 • 28,32 31,19 34,36 37,83 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 98,59 110,7 APPENDIX 163 Years n 4,1 4.2 Values of l.Op", where p 4,3 4,4 4,5 4,6 4,7 4,8 4,9 5,0 1 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 1/088 1,090 1,092 1,094 1,096 1,098 1,100 1,103 3 1,128 1,131 1,135 1,138 1,141 1,145 1,148 1,151 1,154 1,158 4 1,174 1.179 1,184 1,188 1,193 L,197 1,202 1,206 1,211 1,216 5 1,223 1,228 1,234 1,240 1,246 1,252 1,258 1,264 1,270 1,276 6 1,273 1,280 1.287 1,295 1,302 1,310 1.317 1,325 1,333 1,340 7 1,325 1,334 1,343 1,352 1,361 1,370 1,379 1,389 1,398 1,407 8 1,379 1,390 1,401 1,411 1,422 1,433 1,444 1,455 1,466 1,478 9 1,436 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 1,539 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 1,6-93 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 1,989 15 1,827 1,854 1,881 1,908 1,935 1,963 1,992 2,020 2,050 2,079 16 1.902 1932 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 2,134 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 2,234 2,277 2,321 2,366 2,412 2,458 2,506 2,554 2,603 2,653 21 2,325 2,373 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 2,634 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 3,078 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 27 2,959 3,037 3,117 3,198 3,282 3,368 3,456 3,546 3,639 3,733 28 3,081 S.164 3,251 3.339 3,430 3.523 3,618 3,716 3,817 3,920 29 3,207 3,297 3,390 3,486 3,584 3,685 3,788 3,895 4,004 4,116 30 3,338 3,436 3.536 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 5.1S5 5,387 5,598 5,816 6,043 6,279 6,523 6,777 7,040 45 6,099 6,369 6,650 6,943 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 13,18 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 24. ,90 26,63 28,46 30,43 75 20,36 21,88 23,52 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 53,79 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 92,35 102,6 114,0 126,7 140,8 156,4 1*73,7 192,9 214,2 120 1-24,2 139.4 156,4 175,4 196,8 220,7 247,5 277,5 311,2 348,9 1 64 ST VALUATION Years H 1,1 5,2 Values of l.Op", where p 5,3 5,4 5,5 5,6 5,7 5,8 5,9 6,0 1 1,051 1,052 1,053 1,054 1,055 1,056 1,057 1,058 1,059 1,060 2 1,105 1,107 1,109 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 1,313 1,319 1,326 1,332 1,338 6 1,348 1.356 1,363 1,371 1,379 1,387 1,395 1,403 1,411 1,419 7 1,417 1,423 1,436 1,445 1,455 1,464 1,474 1,484 1,494 1,504 8 1,489 1,500 1,512 1,523 1,535 1,547 1.558 1,570 1,582 1,594 9 1,565 1,578 1,592 1,604 1,619 1,633 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 11 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 2,033 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 2,320 2,355 2,391 2,428 2,465 2,502 2,540 17 2,329 2,367 2,406 2,445 2,485 2,525 2,566 2,608 2,650 2,693 18 2,448 2.491 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 3,050 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 3,376 3,454 3,533 3,615 3,698 3.783 3,870 3,958 4,049 25 3,468 3,551 3,637 3,724 3,813 3,905 3,998 4,094 4,192 4,292 26 3,645 3>,V36 3,830 3,925 4,023 4,124 4,226 4,332 4,439 4,550 27 3,831 3,930 4.033 4,137 4,245 4,354 4,467 4,583 4,701 4,822 28 4,026 4,135 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 7,436 7,686 40 7,313 7,596 7,891 8,197 8,513 8,842 9,184 9,537 9,905 10,29 45 9,378 9,788 10,22 10,66 11,13 11,61 12,12 12,64 13,19 13,77 50 12,03 12,61 13,23 13,87 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 25,36 26..9S 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 84,33 90,96 98,10 105,8 85 68,59 74,36 80,62 87,38 94,73 102,7 111,3 120,6 130,6 141,6 90 87,95 95,81 104,4 113,7 123,8 134,8 146,8 159,9 174,0 189,5 95 112,8 123,4 135,1 147,9 161,8 177,0 193,7 211,9 231,8 253,5 100 144,6 159,1 174,9 192,3 211,5 232,5 249,8 280,9 305,8 339,3 110 237,9 264.1 293,2 325,4 361,2 400,9 444,9 493,7 547,7 607,6 120 391,1 438,4 491,4 550,7 617,0 691,3 488,7 867,5 971,7 1088 APPENDIX 165 Years ft 6,2 6,4 Values of 1.0pn, where p 6,6 6,8 7,0 7,2 7,4 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 1,127 1,132 1,136 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 1,311 1,321 1.331 1,341 1,351 1,361 5 1,351 1,364 1,377 1,390 1,403 1,416 1,429 1,442 1,456 1,469 6 1,435 1,451 1,467 1,484 1,501 1,518 1,535 1,552 1,569 1,587 n i 1.524 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 1,825 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 2,465 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 17 2,781 2,870 2,964 3,060 3,159 3,261 3,366 3i,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 3,136 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 3,537 3,679 3,827 3,981 4,141 4,306 4,478 4,657 4,842 5,034 22 3,756 3,915 4,080 4,252 4,431 4,616 4,810 5,010 5,219 5,437 23 3.989 4,165 4,349 4,541 4,741 4,949 5,165 5,391 5,627 5,872 24 4,236 4.432 4,636 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 5,807 6,096 6,399 6,716 7,048 7,396 27 5.074 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 7,927 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 8.210 8,769 9,365 10,00 10,68 11,40 12,17 12,99 13,86 14,79 40 11,09 11,96 12,89 13,90 14,98 16,14 17.39 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 27,34 30,33 33,62 37,28 41,32 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 91,76 103,5 116,4 131,9 149,1 70 67,41 76,90 87,70 100,0 114,0 129,9 148,0 168,6 192,0 218,6 75 91,06 104,9 120,7 139,0 159,9 183,9 211,5 243.2 279,5 321,2 80 123,0 143,Q 166,2 193,1 224,2 260,4 302,2 350,7 406',9 472rO 85 166.2 195,0 228,8 268,3 314,5 368,6 431,9 505,8 592,4 693,5 90 224,5 265,9 314,9 372,8 441,1 521,8 617,1 729,6 862,4 1019 95 303,3 362.6 433,5 517,9 618,7 738,8 881,9 1052 1256 1497 100 409,7 494,5 596,7 719,7 867,7 1046 1260 1518 1828 2200 i66 FOREST VALUATION Years n 8,2 8,4 Values of l.Op", where p 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 1.324 1,331 4 1,371 1,381 1,391 1,401 1,412 1,422 1,432 1,443 1,454 1,464 5 1,483 1,497 1,510 1,525 1.539 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 1,733 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 1,935 1,964 1,993 2,022 2,052 2,082 2,113 2,144 9 2.033 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 2,939 3,004 3,071 3,139 13 2,786 2,854 2,923 2,994 3,066 3,133 3,215 3,293 3,372 3,452 14 3,014 3,093 3,174 3,257 3,337 3,429 3,518 3,609 3,702 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 3,635 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 5,038 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 7,243 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 11,31 11,88 12,48 13,11 28 9,086 9,568 10,08 10,61 11.17 11,76 12,37 13,02 13,71 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 23,21 24,73 26,37 28,10 40 231.39 25,19 27,11 29,19 31.41 33,80 36,37 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 93,46 103,4 114,4 126,6 140,0 154,7 171,1 189,1 60 113x2 126,4 141,2 157,7 176,0 196,5 219,3 244,7 273,0 304,5 65 167,8 189,2 213,3 240,4 270,8 305,1 343,7 387,0 435,7 490,4 70 248,8 283,2 322,2 366.5 416,7 473,8 538.5 612,0 695,3 789,8 75 369,0 423,8 486.7 558,7 641,2 735,7 843,9 967,8 1110 1272 80 '547,3 634,4 735,2 851,8 986,6 1142 1323 1531 1771 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 = $50, p = 3%; what does this capital grow into in 7, 19, 37, and 83 years? 2. Capital now is $500; has been out at 2l/2% compound in- terest; what was it worth 17, 43, and 120 years ago? 3. $140 grew into $190 in 17 years; what is i.op17 and what is p? 4. - A tree contains 430 cubic feet ; it is growing at 1.2% ; what is the growth for 5 years in cubic feet ? 5. A tree now has 430 cubic feet ; 23 years ago it had 375 ; at what p did it grow, wThat is i.opn in this case? 400 6. Schneider's formula says: pv=- for older timber (D nD being dbh and n the number of rings in outer one inch). Suppose stand of timber has 40,000 cubic feet; average D 21 inches, and n 12 ; at what rate is this stand growing, what is the value of five years growth at 7 cents per cubic foot ? 7. A locomotive sets fire to a stand of pine planted 25 years ago ; it cost 10 dollars an acre to plant ; what is the loss if only planting expense and interest at 3% is counted? 8. A stand is now 35 years old. We expect it to be worth $350 when 80 years old; what is its present value; p — 3%, and no expenses figured. 9. A farm rents at 100 dollars, clear, over and above expenses. Rate per cent 3% and also 2%. What is the value of the farm and what is the value of 25 years use of it? 10. A forest property is worth $10,000, based on income, but it can not be sold until 15 years from now ; the property is used and no change is expected. What is its value today at 2% and at 4% ? 11. A note for $500 at 4% is due in 7 years; it has run 3 years ; all interest and capital to be paid in at end of 7 years. What is the note worth now to a man who is willing to take 3% on his money ? 12. A stand of timber contains 550 cords ; it contained 470, 10 years ago; what was pv for this time? If this timber now brings $4.50 per 100 cubic feet but brought only $3.75 per 100 cubic feet, 10 years ago, what is pq, quality growth, in per cent? If there is no price growth, what is pf, i. e., the growth in value of this stand? 1 68 FOREST VALUATION, 13. What is the growth, in quality in' per cent, for each decade which will keep the growth in value constant between the ages 40 and 100 years in spruce, site II, as in Schwappach tables? 14. Eight hundred acres of timber is cut over every 10 years and nets $12 per acre at each cut. Expenses per acre: taxes 15 cents, protection 10 cents. What is the value of the forest at 2% and at 3% ? What is 100 years lease worth if the last cut came 6 years ago? 15. One hundred acres of land may be farmed. At farming it brings 75 cents per acre net. If planted to pine and r = 80 years ; Yr=6o cords at $3; C — $10; €==25 cents; p = 4, 3, and 2% — which use is more profitable? 1 6. Six thousand acres of North Carolina pinery cut over lands bought at $5 per acre ; expenses per acre : taxes 10 cents, protection 5 cents, p = 3% ; what is Fc in 25 years? If timber is $6 per M. feet, how much must one get to make interest and expenses, and leave the forest as good as when bought? 17. Mountain lands in Pennsylvania; can return every 15 years for 6 cords of hardwood stuff, mostly coppice, worth $2 per cord on stump. Taxes 5 cents per acre ; no other charges ; what is the value of the woods at 3% ? 18. A farmer has 60 acres inferior lands ; he paid $18 an acre. He has rented this at $i per acre for pasture. Expenses per acre: taxes 15 cents, fences 10 cents, p = 3%. He plants up 30 acres to hardwoods. C — $10, first cut when 15 years old. How much must he cut if income is to be as good as at pasture use, if he values stuff at $2 per cord? 19. One hundred acres coppice ; non-agricultural land, can be cut every 20 years for 15 cords of stuff, last cut 9 years ago, stump- age now $i per cord. Expected rise in market price 20 cents per cord for each of the next 5 rotations ; after this constant. What is this woods worth at 3% ? Y 20. Four thousand acres of pine woods in North Carolina can ^ Y be cut over every 15 years for 5 M. feet." Last cut 7 years ago. What yearly payment or annuity can a trust company pay if they rate money at 3% ? 21. One thousand acres of coppice woods in Pennsylvania have cut 15 cards every 25 years for iron furnace; stumpage $1.50. Plan is to concert into spruce for pulp on 50 year rotation. If Yr = 3O cords at %;t£=$io; thin. = o; taxes in first case 15 cents, in new case i6% of stumpage as yield tax ; protection and care = 10 cents ; pz^3%. How do the two compare? APPENDIX J 69 22. Spruce forest. a. Present practice : Natural reproduction, takes 10 years, requires no artificial help ; rotation 90 years, i. e., 90 from end of one reproduction to end of next; thinning needed early, 15 years after reproduction is started, costs $5 an acre. Second thinning costs $2 per acre at age of 25. Third thinning at 40 years brings $5 net. Fourth thinning at 60 years brings $20 net. Fifth thinning at 80 years brings $40 net. Yr at 90 years would be $600 but owing to extra cost of logging is only $560. e is $i per acre and year, including taxes; p = 3%. What is Sehere? b. Plan is now to change this as follows : Plant 5 year transplants space 6x6; plants cost $3 per M, set- ting costs $5 per M. First thinning at 20 years pays expense. Second thinning at 40 years pays $20. Third thinning at 60 years pays $40. Fourth thinning at 80 years pays $iop. Yr should be $600 but heavy thinning reduces volume but raises quality so that we still have $540, saving $40 on cost of logging. e and p same as before. What is the new Se, and how does this compare to the old plan? 23. Beech forest, site II, is not satisfactory as to income. Make concrete case from Schwappach to show how this would work out if changed to spruce and to pine. Put p — 3 %, e = $i, C = $10. 24. State of Michigan has been selling land inclusive of some growing stock at $i per acre. If put in pine, C = $10, e = 50 cents, p = 2% and r^=8o years, how much pine must the state cut per acre to beat the $i, with stumpage at $10 per M? 25. Work out Se at 2, 4 and 5% for spruce, pine and oak, all for site II; C = $io, e = $i, and r = 4O, 60, 80, 100 and 120 years. Yr and thinnings as by Schwappach. Tabulate. 26. What is Se in coppice, rotation 25 years ; Yr 20 cords at $2 ; thinnings cover expenses and taxes, planting costs $2 in each- rotation, i. e., at each cut; p — 3%. Is this really Se? 27. Fe, pine in North Carolina ready to cut over* n&w, for 10 M. feet at $6, can return every 20 years ; e — 50 cents, soil = $5, = . Find Fe. 1 70 FOREST VALUATION 28. What is °-Gc and °-