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Interest rates in the German forest valuation literature of the early nineteenth century
Forest Policy and Economics 30 (2013) 1–5
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Review
Interest rates in the German forest valuation literature of the early nineteenth century
Martin Moog, Matthias Bösch ⁎
Technische Universität München, Institute of Forest Economics, Hans-Carl-von-Carlowitz-Platz 2, D-85354 Freising, Germany
a r t i c l e
i n f o
Article history: Received 19 September 2012 Received in revised form 27 March 2013 Accepted 28 March 2013 Available online 23 April 2013 Keywords: Forest valuation Present value Interest rate Germany
a b s t r a c t Valuation with the help of the present value method can be traced back to at least medieval times. In forest literature the scientific achievement of calculating the present value of forestland is predominantly attributed to Martin Faustmann, whose 1849 publication is truly considered pioneering. However, without cheapening Faustmann's intellectual effort, this paper points to some earlier and relatively unknown German authors. By doing so, it presents the state of knowledge on forest valuation in the early nineteenth century, which is a very interesting and lively period of time with respect to the choice of the interest rate. It is revealed that already at that time publications on forest valuation showed a tendency towards an interest rate that yields a desired result. © 2013 Elsevier B.V. All rights reserved.
1. Introduction Valuation with the help of the present value method can be traced back to at least medieval times. At the end of the fifteenth century, Luca Pacioli (1494) cited interest tables and was able to solve mathematical questions involving compound interest. Important successive milestones in the application of discounting to financial contracts mainly occurred in the major banking centers of Italy, France and Flanders (Smith, 1967). The first discount tables were published by Simon Stevin in 1582. Where modern accountants prefer to use the term “present value”, Stevin used ghereedt ghelt, which means “ready money”, to denote values derived from discount tables (Scorgie, 1996). In 1613 (Witt, 1613), Richard Witt presented 124 examples involving cash inflows and outflows that were solved with the help of discount tables and compound interest. The same author also made an important step towards the application of the present value concept to semi-monetary resources, namely to property. In 1730, John Richards, an Exonian surveyor and accountant, extended the use of discounting to the valuation of forests in his book The Gentlemen's Steward and Tenants of Manors Instructed. Richards (1730, pp. 85 ff.) discussed the valuation of a coppice and used the term “present value” to denote the discounted values that he calculated. Richards' application of discounting to forest valuation does not appear to have been extended by other English writers in the eighteenth and the early nineteenth century (Scorgie, 1996). In the German as well as in the Anglo-Saxon and the Scandinavian forest literature the scientific achievement of calculating the present value of forests and bare forest land is predominantly attributed to
⁎ Corresponding author. Tel.: +49 8161 71 4636; fax: +49 8161 71 4631. E-mail address: [email protected] (M. Bösch). 1389-9341/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.forpol.2013.03.004
Martin Faustmann (1849), who was most likely unaware of Richards' calculations. Faustmann surely is one of the most frequently cited authors in the field of forestry and his 1849 publication is truly considered pioneering. 1 However, without cheapening Faustmann's intellectual effort, our purpose is to direct attention to some earlier German publications on forest valuation and their authors, most of whom are relatively unknown or who even wished to remain anonymous. By doing so, this paper presents the state of knowledge on forest valuation in the early nineteenth century. This period of time is very lively in particular with respect to the choice of the interest rate. Thus, our research focus is on the question of what were the significant steps in the evolution of the choice of the interest rate for valuating forestland. The methodology required an extensive literature search of papers and monographs in German. Some of the authors whose work we will explore are strongly associated with forestry schools and forestry academies (Table 1). This is especially true for Friedrich August Ludwig von Burgsdorf, Heinrich Cotta, Georg Ludwig Hartig, Gottlob König and Wilhelm Hossfeld. On the other hand, Joseph Ritter von Jordan, Julius Simon von Nördlinger, Georg Friedrich Krause, Carl Montanus and Claus Kröncke can rather be considered as public servants. 2. Chronological evolution 2.1. Von Burgsdorf Proceeding chronologically, one has to mention first Friedrich August Ludwig von Burgsdorf (1747–1802). Von Burgsdorf, son of a 1 The status of the “Faustmann condition” or “Faustmann rule” has been compared to Hotelling's rule in non-renewable resource economics (e.g., Hanley et al., 1997; Brazee, 2006).
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professional huntsman, first pursued a military career path. After an accident, he changed to forestry, completed a hunting apprenticeship and bought the position of an invalid forestry commissioner. 2 The focus of his scientific work was in the field of botany. In 1787, he became head of the Berlin forestry academy and in 1789 he became a member of the Prussian Academy of Sciences. One chapter of von Burgsdorf's (1796) two-volume textbook is devoted to the topic of forest valuation. In it he complains about insufficiency in the practice of forest valuation and identifies the major shortcoming as being the insufficient consideration of constraints to valuation. Correspondingly, he structures his elaborations according to factors to be taken into consideration when it comes to valuation (von Burgsdorf, 1796, pp. 243 ff.). The valuation calculation in the publication by von Burgsdorf is a simple present value which corresponds to the so-called “Waldrentierungswert” (net income from forestry) in present-day literature on forest valuation (von Burgsdorf, 1796, pp. 258 ff.). The annual net income is capitalized by an interest rate; thus, the formula represents the present value of an annual perpetuity. Von Burgsdorf demonstrates his valuation calculation with the help of two simple arithmetic examples. For instance, when the annual net income is 1000 thaler and the calculatory interest rate corresponds to 6%, one obtains a forest value of 16,666.66 thaler (1.000 / 0.06 = 16,666.66). Thus, the calculation used by von Burgsdorf corresponds to the calculation of the present value known from present-day Business Administration (capitalization of the sustainable income). The methodologically most interesting part of von Burgsdorf's paper deals with risk. The author considers forest management as being risky and yields as being uncertain (von Burgsdorf, 1796, pp. 255 ff.). For him, the problem consists of comparing a forest investment entailing opportunities and risks with a secure interest rate. In his opinion, opportunities and risks may level each other out in many cases. Nevertheless, he argues for the use of an interest rate that is higher than the market interest rate (a ratio of 3/2). Von Burgsdorf motivates his suggestion by arguing that it is the forest buyers' main concern to invest their capital more profitably than they could on the financial market (von Burgsdorf, 1796, pp. 257–258). Thus, von Burgsdorf proposes a higher interest rate not due to an unequal distribution of opportunities and risks. Rather, he sees the need to give forest buyers an adequate profit, because they make significantly larger effort to manage their capital than “normal” financial investors. 2.2. Von Jordan Only a few years after the publication of the second volume of von Burgsdorf's textbook, Joseph Ritter von Jordan (1800) published a book in which forest valuation is dealt with on some 50 pages (134–184). It thus takes a significant part of the total 266 pages. Relatively little is known about this author (von Wurzbach, 1863, p. 265). Von Jordan worked as a civil servant in Bohemia and published another book on the Bohemian civil law. 3 Von Jordan, who refers explicitly to the part on forest valuation in von Burgsdorf's textbook, first presents a calculation of the felling value (in the sense of a liquidation value). He later discards this procedure for most cases and prefers a present value calculation where the average annual net income is capitalized (von Jordan, 1800, pp. 159–160). Because he does not want to estimate future incomes, von Jordan chooses the average volume increment from the time of planting as the basis for estimation. Because the valuation calculation 2 Paying in order to obtain a civil servant position was a relatively common occurrence in many European countries between the sixteenth and the early nineteenth century. 3 Joseph Ritter von Jordan is sometimes confused with Peter Jordan (1751–1827), who studied medicine and other subjects in Göttingen (today Lower Saxony) and who is considered to be the founder of agronomy in Austria (cf. for example Gerber, 2004, p. 336).
Table 1 Foundations of forestry schools and forestry academies in Germany at the turn of the nineteenth century. Year
Founder and/or head
Location
Present-day federal state
1786
Cotta
Thuringia
1786 1787 1801 1805a
Hartig von Burgsdorf Bechstein, Hossfeld König
Zillbach (from 1811 on in Tharandt) Hungen Berlin Dreissigacker Ruhla
a
Hesse Berlin Thuringia Thuringia
Officially recognized in 1813.
corresponds fairly well to the one used by von Burgsdorf and thus to the so-called “Waldrentierungswert” (net income from forestry), it is justified to speak of a present value calculation. Similar to von Burgsdorf, von Jordan also argues for the use of an interest rate that lies slightly above the customary one (von Jordan, 1800, p. 31 ff.). He sets the markup to one percentage point and justifies this choice with the fact that there are a number of risks involved in forestry. Moreover, he also sees the need for realizing a profit that is higher than the costs of financing. When the forest is debt financed, something which is common according to his remarks, the customary interest rate is to be applied. 2.3. Cotta A few years later, in 1804, Johann Heinrich Cotta (1763–1844) published a textbook entitled Systematische Anleitung zur Taxation der Waldungen (Systematic Guide for the Assessment of Forests). Cotta did a forest apprenticeship and studied mathematics, natural sciences and cameralism at the University of Jena (today Thuringia). In 1786, he started to hold forestry classes in Zillbach near Wasungen (about 130 km southeast of Jena) together with his father, who managed a forest district in this region. In 1811, Cotta became head of the forest surveying office in Dresden (today Saxony). He established a forestry school in Tharandt (approximately 12 km southwest of Dresden), which would later be known as the Royal Saxon Forestry Academy and is today part of the Dresden University of Technology (Richter, 2010; Hess, 1876). While the main subject of Cotta's two-part textbook is forest planning, which attracted a lot of interest at that time due to emerging concerns about sustainable use of timber, one chapter of the book is devoted to forest valuation (Cotta, 1804, pp. 141–186). As with von Burgsdorf, the forest valuation calculation is simply presented as the capitalization of the sustainable net income. Of particular interest from an economic point of view are Cotta's reflections about the choice of the interest rate. 4 Cotta questions the assumption of a perfect capital market (Cotta, 1804, p. 151). In his opinion, one has to consider that interest debts are not always paid on time and that creditors are not always able to reinvest their interest income immediately and completely. Thus, he argues that it is justified to use an interest rate that is slightly below the market interest rate when calculating the present value. Even though this argument is possibly only brought up to back up the estimation of higher forest values, in principle its conclusiveness cannot be denied. As opposed to von Burgsdorf and von Jordan, Cotta does not deal with the balancing of risks through an interest rate markup. In the same year that Cotta's textbook appeared, the Prussian forestry engineers Bein and Eyber (1804) published an essay which appeared in the journal Diana at the forestry academy in Dreissigacker (today town of Meiningen, Thuringia). While the two authors do not make any methodological propositions about the question of forest valuation, they point to a number of circumstances that should be considered 4
This aspect is also critically discussed by Kröncke (see below).
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when valuating forest, especially the problem that returns of a forest arise irregularly over time.
represents the oldest use of this calculation that we have been able to find so far in German forestry literature.
2.4. Von Nördlinger
2.6. König
One year later, in 1805, Julius Simon von Nördlinger (1771–1860) published in the same journal a paper that picked up on the points mentioned by Bein and Eyber with the intention of assisting practitioners both with the concept of a valuation calculation and arithmetic examples. Von Nördlinger grew up in very poor circumstances in Tübingen (about 40 km south of Stuttgart). After completing an apprenticeship he was hired by the forestry commission in Tübingen. There, he quickly proved to be very talented and was granted a traveling scholarship by Frederick I of Württemberg. Therefore, he traveled through different Central European countries between 1804 and 1806 and came in contact with several forestry schools (Hess, 1887). 5 Von Nördlinger's (1805) approach to dealing with irregularly arising returns over time consists of distinguishing between ordinary and extraordinary income and expenditure, respectively. He made this division first of all due to computational reasons: for valuating ordinary items that accrue regularly and by the same amount (e.g., thinning), one can use the formula for the present value of a perpetuity (net income from forestry). On the other hand, for the valuation of extraordinary income and expenditure that is to be expected only once (e.g., placing boundary stones), von Nördlinger simply calculates their present values. Therefore, his calculation extends over an infinite time horizon. Moreover, one does not have to care about valuating the land. Even more interesting from an economic point of view are von Nördlinger's elaborations on opportunities and risks in forestry and the choice of an interest rate. His thoughts imply the use of a risk-equivalent forestry interest rate, which lies somewhere between the one associated with the less risky field and the one of the more risky financial market. He explains convincingly that calamities should not be overvalued, as their present value is low if they occur in the far-distant future. For von Nördlinger, it is a matter of course to consider the uncertainty of future incomes. His formulation of opportunities and risks almost reminds one of the present-day option pricing theory (von Nördlinger, 1805, p. 373).
Deviating somewhat from the chronological order, it should be noted here that in 1813 (König, 1813) Gottlob König (1779–1849) published a booklet with the title Anleitung zur Holztaxation (Guide for the Assessment of Forest). König was educated by Heinrich Cotta and hired by his forestry school as a geometry instructor. In 1805 he became a forester in Ruhla (some 50 km west of Erfurt, today Thuringia), where he instructed junior foresters. After Cotta had moved his forestry school to Tharandt in 1811, König established a private forestry institute in 1813, which was meant to replace Cotta's school in Zillbach. In 1821 he became head of the newly-built forestry taxation commission of the Grand Duchy of Saxe-Weimar-Eisenach and in 1829 a member of the supreme forestry district Eisenach, to which he moved one year later together with his forestry school. His institute was officially recognized and became a state forestry school as the Eisenach Grand Ducal-Saxon Academy of Forestry, which König led until his death. In recognition of his excellent work, König was promoted to a supreme forestry commissioner in 1837 and given the honorary doctor of the University of Jena in 1840 (Hess, 1882; Schwartz, 1999; Pacher, 1979). König's booklet includes an arithmetic example that deals with the valuation of a piece of land that is to be cultivated with trees. König's calculation has an infinite time horizon using the formula for the present value of a periodic perpetuity, with the length of one period equaling to one rotation. Compared to the example of the anonymous author (see above), König goes somewhat more into formal details. It is remarkable from an economic point of view that König understood his present value of land as a “decision value” or marginal price. In another publication, he uses a very similar example, which does not add anything new in terms of content (König, 1835, pp. 118–119). It should be emphasized that König's arithmetic examples correspond nearly to Faustmann's famous land expectation formula. The only difference is that the former, as opposed to the latter, employs planting costs only once — at the establishment of the stand. It seems that König implicitly assumes natural regeneration of the stand, whereas Faustmann assumes reiterating planting costs.
2.5. Montanus
2.7. Krause
Two years later, in 1807, Carl Montanus, a forester from Gengenbach (about 100 km southwest of Stuttgart in the Black Forest), published an article, in which he proposes a calculation for the valuation of stocked forest properties (Montanus, 1807). Montanus sets a time horizon that goes up to the final cutting of the standing timber and valuates the forest property with the help of two items, the first being the present value of all net timber yields of the forest up to its final cutting. The second item is the discounted value of the land that is expected at the time of the final cutting. For this second item, Montanus inserts a random amount of money into his arithmetic example. Thereby, he deals somewhat more elegantly with the problem of the irregularly arising returns over time. Moreover, Montanus provides practitioners with a structure of present value calculation that is easy to handle. In the same year and in the same journal, an anonymous author criticized Montanus' arbitrarily assumed land value (Anonymous, 1807). This author discusses the question of how to calculate a land value for forestry. Like Montanus, he argues with an arithmetic example. From this, one can see that this author uses the formula for the present value of a periodic perpetuity, which will later form the core of Faustmann's famous calculation. The article by this anonymous author
Going back to the chronological order, one has to mention a book that was published in 1812 by Georg Friedrich Krause (1768–1836), an author that is relatively unknown in forestry (Krause, 1812). Krause grew up in Berlin and became an artillery officer in the Prussian army. He studied mathematics, cartography, forestry and political science. After his military service, he became a supreme forestry commissioner and head of the forest map department in Berlin (Hilger, 1979). In his book, Krause also calculates the present value of forest, using an age-class composition of the forest and Montanus' approach for the valuation of a forest property (present value of all net timber yields of the forest up to its final cutting plus discounted land value at the time of the final cutting). The calculated land value represents utilizations in later rotation periods. Krause uses compound interest for discounting and is apparently familiar with the idea of a risk markup to the interest rate. 6 The most interesting aspect of Krause's book with regard to forest valuation is his suggestion to simply valuate forest of different ages in relation to the felling value of a mature stand. This suggestion is not operationalized but it already carries the
5 Due to von Nördlinger's publication in the journal Diana one can speculate that he also visited the forestry academy in Dreissigacker and encountered Johann Wilhelm Hossfeld, who was a teacher there.
6 At the beginning of the nineteenth century there were no consistent standards for citing other authors. This may explain why Krause did not refer explicitly to Hartig's paper that was published in the same year (see below). However, it can be presumed that Krause was familiar with the approach proposed by Hartig. Moreover, it is likely that Krause's elaborations on the use of compound interest are an indirect criticism of Hartig's approach.
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idea of the so-called value reduction factors — the predominant heuristic procedure today in the German practice of forest valuation. 2.8. Hartig In 1812 Georg Ludwig Hartig (1764–1837) published a paper dealing with forest valuation, which was meant as a supplement to his 1795 (Hartig, 1795) textbook on forest management. Hartig is probably the best-known German forestry scientist. After completing a forest apprenticeship and his studies in forestry at the University of Giessen (today Hesse), he entered the service of the Prince of SolmsBraunfels. In 1791 he founded a forestry school in Hungen (about 20 km southeast of Giessen) and in 1811 became head of the Prussian State Forestry Commission in Berlin. In 1821 he established a chair for forestry at the University in Berlin, out of which the forestry academy in Eberswalde (today Brandenburg) emerged (today University for Applied Sciences) (Hess, 1879; Weimann, 1990). Hartig's paper contains a rather unconventional valuation calculation. Like Krause, Hartig divides the forest into age-classes and calculates present values for each age-class. However, he does not calculate with compound interest but with simple interest because, as he argues, most forest owners would consume their interest incomes annually (or periodically) (Hartig, 1812, p. 11). Similar to von Burgsdorf and von Jordan, Hartig argues for an interest rate that lies above the market interest rate. Basically, Hartig mentions two reasons for a markup on the market interest rate. First, forestry involves risk and second, capital that is tied up in the forest is not as easily available as “normal” capital (Hartig, 1812, p. 10). Especially interesting is Hartig's proposition to discount those net incomes that lie further in the future by greater interest rates due to higher risk. He suggests to take an interest rate of 6% as the initial value and to increase it by half a percentage point for every age-class (usually 20 years). Thus, Hartig's proposition consists of a stepwise risk markup on the interest rate. 2.9. Kröncke Already in the following year (1813), Claus Kröncke (1771–1843) published a paper in the journal Allgemeiner Kameral-Korrespondent. Kröncke was a professor of water engineering, road construction and accounting at the University of Giessen. In 1802 he became a building inspector and tax commissioner in Darmstadt, where he earned great merits for the regulation of the Rhine River. Kröncke's paper deals with the question of how forest is to be valuated in the context of wealth tax collection. He discusses both Cotta's (1804) and Hartig's (1812) methods for valuating forests with special regard to the chosen interest rate. As seen above, Hartig favored the use of simple interest. Kröncke (1813, sections 16–21) judges this proposal quite harshly. With the help of an example, he shows that independent of the investor's objective (i.e., asset accumulation or income generation) only the calculation with compound interest yields plausible results. Kröncke thus refutes Hartig's argument that the objective of income generation and the associated consumption of returns should be restricted to simple interest. 7 In section 24 of his paper, Kröncke elaborates on Cotta's proposal for an interest rate that is slightly below the market interest rate due to imperfect capital markets. First, Kröncke shows that the effect of a simple markdown, for example lowering the interest rate from 5% to 3%, depends heavily on the discount period. Thus, Kröncke does not consider this method appropriate. He rightly describes the most 7 Another striking argumentation was given by Hossfeld (1820). He shows that a valuation of future periodic incomes of the same amount with simple interest leads to a higher figure than the capitalization as yearly perpetuity. This shows the inconsistency of the suggestions given by Hartig and Cotta, the latter of who later (Cotta, 1818) favored average interest rates.
important characteristic of a perfect capital market, namely the opportunity for complete and immediate reinvestment of the returns at a given interest rate. He observes that in real-world situations such a complete and immediate reinvestment of the capital is often not feasible. Kröncke (1813, section 28) then proposes a method for estimating the magnitude of capital market imperfections with the help of an arithmetic example. In his example (present value of 40,000 florins, 20 years, 5% interest rate) he assumes a time lag of one year and a fixed amount of 100 florins which cannot be reinvested and thus bears no interest. He argues that greater amounts of money could be reinvested at any time. Kröncke's present value (PV) is calculated as follows: PV ¼
39; 900 þ 100 ¼ 15; 598: 1:0519 þ 0:05 1:05
ð1Þ
The present value in a perfect capital market is given as: PV ¼
40; 000 ¼ 15; 076: 1:0520
ð2Þ
Thus, Kröncke's present value of 15,598 florins is only 522 florins or about 3% higher. 3. Concluding remarks Martin Faustmann (1849) has been credited with the scientific achievement of calculating the present value of forests and bare forest land, but in this paper we have shown that already at the turn of the nineteenth century the same principles of valuation were discussed by German forestry scientists and (forestry) civil servants in a very qualified way (for an overview see Table 2). Because forests increasingly became a considerable source of income for various German states and principalities, it is conjecturable that foresters were induced to come up with more sophisticated methods for estimating the value of forest land as well as with exact inventory methods for forest resources. Therefore, many foresters developed detailed plans for timber harvesting and reforestation; some forest management plans were even extended far into the twenty-first century (Viitala, 2006). It is interesting to see that there were close relations among many of the leading forestry scholars of that time. Even though none of these authors had an in-depth education in the field of economics nor was dealing full-time with economic questions, their writings were quite likely influenced by the leading political economists of that time, in particular Ricardo (1817) and von Thünen (1826). The approaches presented in this paper had some clear parallels to the methods used in presentday business valuation. Von Jordan's (1800) book can even be considered a manual for valuating agricultural enterprises. However, there are also aspects that are missing in this early literature, such as the impact of income taxes on the value of forest. Still today, the debate on the choice of an adequate interest rate for valuating has not yet come to an end. Already the early German publications on forest valuation presented in this paper showed a tendency towards an interest rate that yields a desired result. This use (or misuse) of the interest rate generally tends to be even more pronounced in more recent literatures on forest valuation, as well as in literatures on valuation of (agricultural) real estate and enterprises. The suggestions to use lower interest rates or to use simple interest instead of compound interest reveal two things. First, already 200 years ago there was a significant discrepancy between the actual purchase price for forest and the present value of the forest calculated with market interest rates, current timber prices and costs. Second, already at that time methods were not immune to “valuation tricks” that narrow the gap between the estimated value and the purchase price in order to achieve higher
M. Moog, M. Bösch / Forest Policy and Economics 30 (2013) 1–5 Table 2 Overview of the proposals on modification of the interest rate in the early German forest valuation literature. Year
Author
Modification of the interest rate
1796 Von Burgsdorf 1800 Von Jordan
Markup of 1/2 (e.g., 6% instead of 4%), because forest buyers need an adequate profit (and forestry involves risk) Markup of one percentage point first of all due to risk in forestry, but also because there is a need for realizing a positive profit. 1804 Cotta Markdown due to capital market imperfections 1805 Von Risk-equivalent forestry interest rate that lies somewhere Nördlinger between the one of the less risky field and the capital market interest rate. 1812 Hartig Stepwise markup of half a percentage point per age-class (20 years)
acceptance. This phenomenon, however, was not restricted to Germany. In England, for example, it started even earlier. Even though the English debate of the seventeenth century mainly concerned the level of interest rate in the whole economy, Sir Thomas Culpeper the elder showed already in 1621 (Culpeper, 1621) that he understood the deleterious impact of a high interest rate on the evaluation of investment projects such as forestry and land improvements. In his opinion, the wealth of England was not being developed because the interest rate was too high in comparison to that of other nations. Culpeper (1668) followed his father's example and sought a further reduction in the interest rate (a reduction from 6% to 4%). In his opinion, “many Gentlemen” would preserve their young timber trees and plant new groves for prosperity if interest rates were lower. References Anonymous, 1807. Bemerkungen zu dem Aufsatze in Nro. 35 dieses Journals: über die Abschätzung kleiner Stücke Hochwaldungen, die zu verkaufen sind. Journal für das Forst- Jagd- und Fischereiwesen 44, 689–695. Bein, Eyber, 1804. 2. Verschiedene, die Bestimmung des Werthes eines zu veräußernden Waldes betreffende Bedenklichkeiten. Diana 2, 127–144. Brazee, R.J., 2006. The Faustmann face of optimal forest harvesting. Tietenberg, T., Folmer, H. (Eds.), The International Yearbook of Environmental and Resource Economics 2006/2007: A Survey of Current Issues. Edward Elgar, Cheltenham and Northampton. Cotta, H., 1804. Systematische Anleitung zur Taxation der Waldungen. J. D. Sander, Berlin. Cotta, H., 1818. Entwurf einer Anweisung zur Waldwerthberechnung. Arnoldische Buchhandlung, Dresden. Culpeper, T., 1621. A tract against usurie. (the elder) Walter Burre, London (reprinted Theatrum Orbis Terrarum, Amsterdam 1974). Culpeper, T., 1668. A Discourse Showing the Many Advantages Which Will Accrue to this Kingdom by the Abatement of Usury Together with the Absolute Necessity of Reducing Interest of Money to the Lowest Rate It Bears in Other Countries, That, At Least, We May Trade with Our Neighbours Upon Equal Terms. (the younger) Christopher Wilkinsion, London. Faustmann, M., 1849. Berechnung des Wertes welchen Waldboden sowie noch nicht haubare Holzbestände für die Waldwirtschaft besitzen. Allgemeine Forst- und Jagdzeitung 12, 441–455. Gerber, T., 2004. Persönlichkeiten aus Land- und Forstwirtschaft, Gartenbau und Veterinärmedizin — Biographisches Lexikon, Band 1. Nora, Berlin.
5
Hanley, N., Shogren, J.F., White, B., 1997. Environmental Economics in Theory and Practice. Macmillan, London. Hartig, G.L., 1795. Anweisung zur Taxation der Forste oder zur Bestimmung des Holzertrags der Wälder. Heyer, Giessen. Hartig, G.L., 1812. Anleitung zur Berechnung des Geldwerthes eines, in Betreff seines Naturalertrages, schon taxierten Forstes. Friedrich Maurer, Berlin. Hess, R., 1876. Cotta, Johann Heinrich, In: Allgemeine Deutsche Biographie, 4, pp. 521–526 (available at: http://www.deutsche-biographie.de/sfz69596.html). Hess, R., 1879. Hartig, Georg Ludwig, In: Allgemeine Deutsche Biographie, 10, pp. 659–665 (available at: http://www.deutsche-biographie.de/sfz26168.html). Hess, R., 1882. König, Gottlob, In: Allgemeine Deutsche Biographie, 16, pp. 509–512 (available at: http://www.deutsche-biographie.de/sfz43778.html). Hess, R., 1887. Nördlinger, Julius Simon von, In: Allgemeine Deutsche Biographie, 24, pp. 11–14 (available at: http://www.deutsche-biographie.de/sfz72259.html). Hilger, M.-E., 1979. Krause, Georg Friedrich, In: Allgemeine Deutsche Biographie, 12, pp. 698–699 (available at: http://www.deutsche-biographie.de/sfz44941.html). Hossfeld, J.W., 1820. Reformation der Forstwissenschaft. Kesselringsche Buchhandlung, Hildburghausen. König, G., 1813. Anleitung zur Holztaxazion. Becker, Gotha. König, G., 1835. Die Forst-Mathematik mit Anweisung zur Holzvermessung, Holzschätzung und Waldwerthberechnung nebst Hülfstafeln für die Forstschätzer. Becker, Gotha. Krause, G.F., 1812. Anleitung zur Abschätzung und Berechnung des Geldwerths der Forstgrundstücke theils zum Behuf der Veräußerung, theils zur Begründung der Anleihen. Köchly, Leipzig. Kröncke, C., 1813. Betrachtungen über den Kapithalwert eines Waldes, dessen Naturalertrag ausgemittelt ist, vorzüglich in Hinsicht der Veranschlagung desselben zur Versteuerung. Allgemeiner Kameral-Korrespondent 55, 241–243. Montanus, C., 1807. Über die Abschätzung kleiner Stücke Hochwaldungen, die zu verkaufen sind. Journal für das Forst- Jagd- und Fischereiwesen 35, 545–553. Pacher, J., 1979. König, Gottlob, In: Allgemeine Deutsche Biographie, 12, pp. 338–339 (available at: http://www.deutsche-biographie.de/sfz43778.html). Pacioli, L., 1494. Summa de arithmetica, geometria, proportioni e proportionalita. Paganinus de Paganinis, Venice (reprinted Abrizzi, Venice 1994). Ricardo, D., 1817. On the principles of political economy and taxation. John Murray, London. Richards, J., 1730. Annuities on Lives, and for Limited Terms of Years, Considered: Being Observations on What Hath Been Lately Advanced by Divers Authors, Tending to Depreciate the Value of Estates on Those Tenures. J. Osborn, London. Richter, A., 2010. Heinrich Cotta — Leben und Werk eines deutschen Forstmannes, 3rd ed. Neumann-Neudamm, Melsungen. Schwartz, E., 1999. Gottlob König, 1779–1849; ein Leben für Wald und Landschaft. Kessel, Erfurt. Scorgie, M.E., 1996. Evolution of the application of present value to valuation of nonmonetary resources. Accounting and Business Research 26, 237–248. Smith, G.W., 1967. A brief history of interest calculations. Journal of Industrial Engineering 18, 569–574. Viitala, E.-J., 2006. An early contribution of Martin Faustmann to natural resource economics. Journal of Forest Economics 12, 131–144. von Burgsdorf, F.A.L., 1796. Forsthandbuch — Allgemeiner theoretisch-praktischer Lehrbegriff der höheren Forstwissenschaften, zweiter Theil. Selbstverlag, Berlin. von Jordan, J.R., 1800. Grundsätze über die Abschätzung der Landgüter. K. Widtmann, Prague. von Nördlinger, J.S., 1805. Versuch den Werth der Waldungen zu bestimmen, mit Rücksicht auf die in Diana II. S. 127 geäußerten Bedenklichkeiten. Diana 3, 363–400. von Thünen, J.H., 1826. Der isolierte Staat in Beziehung auf Landwirtschaft und Nationalökonomie (Reprinted by Wissenschaftliche Buchgesellschaft, Darmstadt 1966). von Wurzbach, C., 1863. Biographisches Lexikon des Kaiserthums Oesterreich, Zehnter Theil. Kaiserlich-königliche Hof- und Staatsdruckerei, Vienna. Weimann, H.-J., 1990. Hartigiana — Kurze Lebens- und Familieneschichte des Staatsrathes und Ober-Landforstmeisters Georg Ludwig Hartig und dessen Gattin Theodore, geborene Klipstein. Selbstverlag, Biebertal. Witt, R., 1613. Arithmeticall Questions Touching the Buying or Exchange of Annuities; Taking of Leases for Fines, or Yearly Rent; Purchase of Fee Simples; Dealing for Present or Future Possessions; and Other Bargains and Accounts, Wherein Allowance for Disbursing or Forbearance of Money Is Intended; Briefly Resolved, by Means of Certain Breviats. R. Redmer, London.
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Review
Interest rates in the German forest valuation literature of the early nineteenth century
Martin Moog, Matthias Bösch ⁎
Technische Universität München, Institute of Forest Economics, Hans-Carl-von-Carlowitz-Platz 2, D-85354 Freising, Germany
a r t i c l e
i n f o
Article history: Received 19 September 2012 Received in revised form 27 March 2013 Accepted 28 March 2013 Available online 23 April 2013 Keywords: Forest valuation Present value Interest rate Germany
a b s t r a c t Valuation with the help of the present value method can be traced back to at least medieval times. In forest literature the scientific achievement of calculating the present value of forestland is predominantly attributed to Martin Faustmann, whose 1849 publication is truly considered pioneering. However, without cheapening Faustmann's intellectual effort, this paper points to some earlier and relatively unknown German authors. By doing so, it presents the state of knowledge on forest valuation in the early nineteenth century, which is a very interesting and lively period of time with respect to the choice of the interest rate. It is revealed that already at that time publications on forest valuation showed a tendency towards an interest rate that yields a desired result. © 2013 Elsevier B.V. All rights reserved.
1. Introduction Valuation with the help of the present value method can be traced back to at least medieval times. At the end of the fifteenth century, Luca Pacioli (1494) cited interest tables and was able to solve mathematical questions involving compound interest. Important successive milestones in the application of discounting to financial contracts mainly occurred in the major banking centers of Italy, France and Flanders (Smith, 1967). The first discount tables were published by Simon Stevin in 1582. Where modern accountants prefer to use the term “present value”, Stevin used ghereedt ghelt, which means “ready money”, to denote values derived from discount tables (Scorgie, 1996). In 1613 (Witt, 1613), Richard Witt presented 124 examples involving cash inflows and outflows that were solved with the help of discount tables and compound interest. The same author also made an important step towards the application of the present value concept to semi-monetary resources, namely to property. In 1730, John Richards, an Exonian surveyor and accountant, extended the use of discounting to the valuation of forests in his book The Gentlemen's Steward and Tenants of Manors Instructed. Richards (1730, pp. 85 ff.) discussed the valuation of a coppice and used the term “present value” to denote the discounted values that he calculated. Richards' application of discounting to forest valuation does not appear to have been extended by other English writers in the eighteenth and the early nineteenth century (Scorgie, 1996). In the German as well as in the Anglo-Saxon and the Scandinavian forest literature the scientific achievement of calculating the present value of forests and bare forest land is predominantly attributed to
⁎ Corresponding author. Tel.: +49 8161 71 4636; fax: +49 8161 71 4631. E-mail address: [email protected] (M. Bösch). 1389-9341/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.forpol.2013.03.004
Martin Faustmann (1849), who was most likely unaware of Richards' calculations. Faustmann surely is one of the most frequently cited authors in the field of forestry and his 1849 publication is truly considered pioneering. 1 However, without cheapening Faustmann's intellectual effort, our purpose is to direct attention to some earlier German publications on forest valuation and their authors, most of whom are relatively unknown or who even wished to remain anonymous. By doing so, this paper presents the state of knowledge on forest valuation in the early nineteenth century. This period of time is very lively in particular with respect to the choice of the interest rate. Thus, our research focus is on the question of what were the significant steps in the evolution of the choice of the interest rate for valuating forestland. The methodology required an extensive literature search of papers and monographs in German. Some of the authors whose work we will explore are strongly associated with forestry schools and forestry academies (Table 1). This is especially true for Friedrich August Ludwig von Burgsdorf, Heinrich Cotta, Georg Ludwig Hartig, Gottlob König and Wilhelm Hossfeld. On the other hand, Joseph Ritter von Jordan, Julius Simon von Nördlinger, Georg Friedrich Krause, Carl Montanus and Claus Kröncke can rather be considered as public servants. 2. Chronological evolution 2.1. Von Burgsdorf Proceeding chronologically, one has to mention first Friedrich August Ludwig von Burgsdorf (1747–1802). Von Burgsdorf, son of a 1 The status of the “Faustmann condition” or “Faustmann rule” has been compared to Hotelling's rule in non-renewable resource economics (e.g., Hanley et al., 1997; Brazee, 2006).
2
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professional huntsman, first pursued a military career path. After an accident, he changed to forestry, completed a hunting apprenticeship and bought the position of an invalid forestry commissioner. 2 The focus of his scientific work was in the field of botany. In 1787, he became head of the Berlin forestry academy and in 1789 he became a member of the Prussian Academy of Sciences. One chapter of von Burgsdorf's (1796) two-volume textbook is devoted to the topic of forest valuation. In it he complains about insufficiency in the practice of forest valuation and identifies the major shortcoming as being the insufficient consideration of constraints to valuation. Correspondingly, he structures his elaborations according to factors to be taken into consideration when it comes to valuation (von Burgsdorf, 1796, pp. 243 ff.). The valuation calculation in the publication by von Burgsdorf is a simple present value which corresponds to the so-called “Waldrentierungswert” (net income from forestry) in present-day literature on forest valuation (von Burgsdorf, 1796, pp. 258 ff.). The annual net income is capitalized by an interest rate; thus, the formula represents the present value of an annual perpetuity. Von Burgsdorf demonstrates his valuation calculation with the help of two simple arithmetic examples. For instance, when the annual net income is 1000 thaler and the calculatory interest rate corresponds to 6%, one obtains a forest value of 16,666.66 thaler (1.000 / 0.06 = 16,666.66). Thus, the calculation used by von Burgsdorf corresponds to the calculation of the present value known from present-day Business Administration (capitalization of the sustainable income). The methodologically most interesting part of von Burgsdorf's paper deals with risk. The author considers forest management as being risky and yields as being uncertain (von Burgsdorf, 1796, pp. 255 ff.). For him, the problem consists of comparing a forest investment entailing opportunities and risks with a secure interest rate. In his opinion, opportunities and risks may level each other out in many cases. Nevertheless, he argues for the use of an interest rate that is higher than the market interest rate (a ratio of 3/2). Von Burgsdorf motivates his suggestion by arguing that it is the forest buyers' main concern to invest their capital more profitably than they could on the financial market (von Burgsdorf, 1796, pp. 257–258). Thus, von Burgsdorf proposes a higher interest rate not due to an unequal distribution of opportunities and risks. Rather, he sees the need to give forest buyers an adequate profit, because they make significantly larger effort to manage their capital than “normal” financial investors. 2.2. Von Jordan Only a few years after the publication of the second volume of von Burgsdorf's textbook, Joseph Ritter von Jordan (1800) published a book in which forest valuation is dealt with on some 50 pages (134–184). It thus takes a significant part of the total 266 pages. Relatively little is known about this author (von Wurzbach, 1863, p. 265). Von Jordan worked as a civil servant in Bohemia and published another book on the Bohemian civil law. 3 Von Jordan, who refers explicitly to the part on forest valuation in von Burgsdorf's textbook, first presents a calculation of the felling value (in the sense of a liquidation value). He later discards this procedure for most cases and prefers a present value calculation where the average annual net income is capitalized (von Jordan, 1800, pp. 159–160). Because he does not want to estimate future incomes, von Jordan chooses the average volume increment from the time of planting as the basis for estimation. Because the valuation calculation 2 Paying in order to obtain a civil servant position was a relatively common occurrence in many European countries between the sixteenth and the early nineteenth century. 3 Joseph Ritter von Jordan is sometimes confused with Peter Jordan (1751–1827), who studied medicine and other subjects in Göttingen (today Lower Saxony) and who is considered to be the founder of agronomy in Austria (cf. for example Gerber, 2004, p. 336).
Table 1 Foundations of forestry schools and forestry academies in Germany at the turn of the nineteenth century. Year
Founder and/or head
Location
Present-day federal state
1786
Cotta
Thuringia
1786 1787 1801 1805a
Hartig von Burgsdorf Bechstein, Hossfeld König
Zillbach (from 1811 on in Tharandt) Hungen Berlin Dreissigacker Ruhla
a
Hesse Berlin Thuringia Thuringia
Officially recognized in 1813.
corresponds fairly well to the one used by von Burgsdorf and thus to the so-called “Waldrentierungswert” (net income from forestry), it is justified to speak of a present value calculation. Similar to von Burgsdorf, von Jordan also argues for the use of an interest rate that lies slightly above the customary one (von Jordan, 1800, p. 31 ff.). He sets the markup to one percentage point and justifies this choice with the fact that there are a number of risks involved in forestry. Moreover, he also sees the need for realizing a profit that is higher than the costs of financing. When the forest is debt financed, something which is common according to his remarks, the customary interest rate is to be applied. 2.3. Cotta A few years later, in 1804, Johann Heinrich Cotta (1763–1844) published a textbook entitled Systematische Anleitung zur Taxation der Waldungen (Systematic Guide for the Assessment of Forests). Cotta did a forest apprenticeship and studied mathematics, natural sciences and cameralism at the University of Jena (today Thuringia). In 1786, he started to hold forestry classes in Zillbach near Wasungen (about 130 km southeast of Jena) together with his father, who managed a forest district in this region. In 1811, Cotta became head of the forest surveying office in Dresden (today Saxony). He established a forestry school in Tharandt (approximately 12 km southwest of Dresden), which would later be known as the Royal Saxon Forestry Academy and is today part of the Dresden University of Technology (Richter, 2010; Hess, 1876). While the main subject of Cotta's two-part textbook is forest planning, which attracted a lot of interest at that time due to emerging concerns about sustainable use of timber, one chapter of the book is devoted to forest valuation (Cotta, 1804, pp. 141–186). As with von Burgsdorf, the forest valuation calculation is simply presented as the capitalization of the sustainable net income. Of particular interest from an economic point of view are Cotta's reflections about the choice of the interest rate. 4 Cotta questions the assumption of a perfect capital market (Cotta, 1804, p. 151). In his opinion, one has to consider that interest debts are not always paid on time and that creditors are not always able to reinvest their interest income immediately and completely. Thus, he argues that it is justified to use an interest rate that is slightly below the market interest rate when calculating the present value. Even though this argument is possibly only brought up to back up the estimation of higher forest values, in principle its conclusiveness cannot be denied. As opposed to von Burgsdorf and von Jordan, Cotta does not deal with the balancing of risks through an interest rate markup. In the same year that Cotta's textbook appeared, the Prussian forestry engineers Bein and Eyber (1804) published an essay which appeared in the journal Diana at the forestry academy in Dreissigacker (today town of Meiningen, Thuringia). While the two authors do not make any methodological propositions about the question of forest valuation, they point to a number of circumstances that should be considered 4
This aspect is also critically discussed by Kröncke (see below).
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3
when valuating forest, especially the problem that returns of a forest arise irregularly over time.
represents the oldest use of this calculation that we have been able to find so far in German forestry literature.
2.4. Von Nördlinger
2.6. König
One year later, in 1805, Julius Simon von Nördlinger (1771–1860) published in the same journal a paper that picked up on the points mentioned by Bein and Eyber with the intention of assisting practitioners both with the concept of a valuation calculation and arithmetic examples. Von Nördlinger grew up in very poor circumstances in Tübingen (about 40 km south of Stuttgart). After completing an apprenticeship he was hired by the forestry commission in Tübingen. There, he quickly proved to be very talented and was granted a traveling scholarship by Frederick I of Württemberg. Therefore, he traveled through different Central European countries between 1804 and 1806 and came in contact with several forestry schools (Hess, 1887). 5 Von Nördlinger's (1805) approach to dealing with irregularly arising returns over time consists of distinguishing between ordinary and extraordinary income and expenditure, respectively. He made this division first of all due to computational reasons: for valuating ordinary items that accrue regularly and by the same amount (e.g., thinning), one can use the formula for the present value of a perpetuity (net income from forestry). On the other hand, for the valuation of extraordinary income and expenditure that is to be expected only once (e.g., placing boundary stones), von Nördlinger simply calculates their present values. Therefore, his calculation extends over an infinite time horizon. Moreover, one does not have to care about valuating the land. Even more interesting from an economic point of view are von Nördlinger's elaborations on opportunities and risks in forestry and the choice of an interest rate. His thoughts imply the use of a risk-equivalent forestry interest rate, which lies somewhere between the one associated with the less risky field and the one of the more risky financial market. He explains convincingly that calamities should not be overvalued, as their present value is low if they occur in the far-distant future. For von Nördlinger, it is a matter of course to consider the uncertainty of future incomes. His formulation of opportunities and risks almost reminds one of the present-day option pricing theory (von Nördlinger, 1805, p. 373).
Deviating somewhat from the chronological order, it should be noted here that in 1813 (König, 1813) Gottlob König (1779–1849) published a booklet with the title Anleitung zur Holztaxation (Guide for the Assessment of Forest). König was educated by Heinrich Cotta and hired by his forestry school as a geometry instructor. In 1805 he became a forester in Ruhla (some 50 km west of Erfurt, today Thuringia), where he instructed junior foresters. After Cotta had moved his forestry school to Tharandt in 1811, König established a private forestry institute in 1813, which was meant to replace Cotta's school in Zillbach. In 1821 he became head of the newly-built forestry taxation commission of the Grand Duchy of Saxe-Weimar-Eisenach and in 1829 a member of the supreme forestry district Eisenach, to which he moved one year later together with his forestry school. His institute was officially recognized and became a state forestry school as the Eisenach Grand Ducal-Saxon Academy of Forestry, which König led until his death. In recognition of his excellent work, König was promoted to a supreme forestry commissioner in 1837 and given the honorary doctor of the University of Jena in 1840 (Hess, 1882; Schwartz, 1999; Pacher, 1979). König's booklet includes an arithmetic example that deals with the valuation of a piece of land that is to be cultivated with trees. König's calculation has an infinite time horizon using the formula for the present value of a periodic perpetuity, with the length of one period equaling to one rotation. Compared to the example of the anonymous author (see above), König goes somewhat more into formal details. It is remarkable from an economic point of view that König understood his present value of land as a “decision value” or marginal price. In another publication, he uses a very similar example, which does not add anything new in terms of content (König, 1835, pp. 118–119). It should be emphasized that König's arithmetic examples correspond nearly to Faustmann's famous land expectation formula. The only difference is that the former, as opposed to the latter, employs planting costs only once — at the establishment of the stand. It seems that König implicitly assumes natural regeneration of the stand, whereas Faustmann assumes reiterating planting costs.
2.5. Montanus
2.7. Krause
Two years later, in 1807, Carl Montanus, a forester from Gengenbach (about 100 km southwest of Stuttgart in the Black Forest), published an article, in which he proposes a calculation for the valuation of stocked forest properties (Montanus, 1807). Montanus sets a time horizon that goes up to the final cutting of the standing timber and valuates the forest property with the help of two items, the first being the present value of all net timber yields of the forest up to its final cutting. The second item is the discounted value of the land that is expected at the time of the final cutting. For this second item, Montanus inserts a random amount of money into his arithmetic example. Thereby, he deals somewhat more elegantly with the problem of the irregularly arising returns over time. Moreover, Montanus provides practitioners with a structure of present value calculation that is easy to handle. In the same year and in the same journal, an anonymous author criticized Montanus' arbitrarily assumed land value (Anonymous, 1807). This author discusses the question of how to calculate a land value for forestry. Like Montanus, he argues with an arithmetic example. From this, one can see that this author uses the formula for the present value of a periodic perpetuity, which will later form the core of Faustmann's famous calculation. The article by this anonymous author
Going back to the chronological order, one has to mention a book that was published in 1812 by Georg Friedrich Krause (1768–1836), an author that is relatively unknown in forestry (Krause, 1812). Krause grew up in Berlin and became an artillery officer in the Prussian army. He studied mathematics, cartography, forestry and political science. After his military service, he became a supreme forestry commissioner and head of the forest map department in Berlin (Hilger, 1979). In his book, Krause also calculates the present value of forest, using an age-class composition of the forest and Montanus' approach for the valuation of a forest property (present value of all net timber yields of the forest up to its final cutting plus discounted land value at the time of the final cutting). The calculated land value represents utilizations in later rotation periods. Krause uses compound interest for discounting and is apparently familiar with the idea of a risk markup to the interest rate. 6 The most interesting aspect of Krause's book with regard to forest valuation is his suggestion to simply valuate forest of different ages in relation to the felling value of a mature stand. This suggestion is not operationalized but it already carries the
5 Due to von Nördlinger's publication in the journal Diana one can speculate that he also visited the forestry academy in Dreissigacker and encountered Johann Wilhelm Hossfeld, who was a teacher there.
6 At the beginning of the nineteenth century there were no consistent standards for citing other authors. This may explain why Krause did not refer explicitly to Hartig's paper that was published in the same year (see below). However, it can be presumed that Krause was familiar with the approach proposed by Hartig. Moreover, it is likely that Krause's elaborations on the use of compound interest are an indirect criticism of Hartig's approach.
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idea of the so-called value reduction factors — the predominant heuristic procedure today in the German practice of forest valuation. 2.8. Hartig In 1812 Georg Ludwig Hartig (1764–1837) published a paper dealing with forest valuation, which was meant as a supplement to his 1795 (Hartig, 1795) textbook on forest management. Hartig is probably the best-known German forestry scientist. After completing a forest apprenticeship and his studies in forestry at the University of Giessen (today Hesse), he entered the service of the Prince of SolmsBraunfels. In 1791 he founded a forestry school in Hungen (about 20 km southeast of Giessen) and in 1811 became head of the Prussian State Forestry Commission in Berlin. In 1821 he established a chair for forestry at the University in Berlin, out of which the forestry academy in Eberswalde (today Brandenburg) emerged (today University for Applied Sciences) (Hess, 1879; Weimann, 1990). Hartig's paper contains a rather unconventional valuation calculation. Like Krause, Hartig divides the forest into age-classes and calculates present values for each age-class. However, he does not calculate with compound interest but with simple interest because, as he argues, most forest owners would consume their interest incomes annually (or periodically) (Hartig, 1812, p. 11). Similar to von Burgsdorf and von Jordan, Hartig argues for an interest rate that lies above the market interest rate. Basically, Hartig mentions two reasons for a markup on the market interest rate. First, forestry involves risk and second, capital that is tied up in the forest is not as easily available as “normal” capital (Hartig, 1812, p. 10). Especially interesting is Hartig's proposition to discount those net incomes that lie further in the future by greater interest rates due to higher risk. He suggests to take an interest rate of 6% as the initial value and to increase it by half a percentage point for every age-class (usually 20 years). Thus, Hartig's proposition consists of a stepwise risk markup on the interest rate. 2.9. Kröncke Already in the following year (1813), Claus Kröncke (1771–1843) published a paper in the journal Allgemeiner Kameral-Korrespondent. Kröncke was a professor of water engineering, road construction and accounting at the University of Giessen. In 1802 he became a building inspector and tax commissioner in Darmstadt, where he earned great merits for the regulation of the Rhine River. Kröncke's paper deals with the question of how forest is to be valuated in the context of wealth tax collection. He discusses both Cotta's (1804) and Hartig's (1812) methods for valuating forests with special regard to the chosen interest rate. As seen above, Hartig favored the use of simple interest. Kröncke (1813, sections 16–21) judges this proposal quite harshly. With the help of an example, he shows that independent of the investor's objective (i.e., asset accumulation or income generation) only the calculation with compound interest yields plausible results. Kröncke thus refutes Hartig's argument that the objective of income generation and the associated consumption of returns should be restricted to simple interest. 7 In section 24 of his paper, Kröncke elaborates on Cotta's proposal for an interest rate that is slightly below the market interest rate due to imperfect capital markets. First, Kröncke shows that the effect of a simple markdown, for example lowering the interest rate from 5% to 3%, depends heavily on the discount period. Thus, Kröncke does not consider this method appropriate. He rightly describes the most 7 Another striking argumentation was given by Hossfeld (1820). He shows that a valuation of future periodic incomes of the same amount with simple interest leads to a higher figure than the capitalization as yearly perpetuity. This shows the inconsistency of the suggestions given by Hartig and Cotta, the latter of who later (Cotta, 1818) favored average interest rates.
important characteristic of a perfect capital market, namely the opportunity for complete and immediate reinvestment of the returns at a given interest rate. He observes that in real-world situations such a complete and immediate reinvestment of the capital is often not feasible. Kröncke (1813, section 28) then proposes a method for estimating the magnitude of capital market imperfections with the help of an arithmetic example. In his example (present value of 40,000 florins, 20 years, 5% interest rate) he assumes a time lag of one year and a fixed amount of 100 florins which cannot be reinvested and thus bears no interest. He argues that greater amounts of money could be reinvested at any time. Kröncke's present value (PV) is calculated as follows: PV ¼
39; 900 þ 100 ¼ 15; 598: 1:0519 þ 0:05 1:05
ð1Þ
The present value in a perfect capital market is given as: PV ¼
40; 000 ¼ 15; 076: 1:0520
ð2Þ
Thus, Kröncke's present value of 15,598 florins is only 522 florins or about 3% higher. 3. Concluding remarks Martin Faustmann (1849) has been credited with the scientific achievement of calculating the present value of forests and bare forest land, but in this paper we have shown that already at the turn of the nineteenth century the same principles of valuation were discussed by German forestry scientists and (forestry) civil servants in a very qualified way (for an overview see Table 2). Because forests increasingly became a considerable source of income for various German states and principalities, it is conjecturable that foresters were induced to come up with more sophisticated methods for estimating the value of forest land as well as with exact inventory methods for forest resources. Therefore, many foresters developed detailed plans for timber harvesting and reforestation; some forest management plans were even extended far into the twenty-first century (Viitala, 2006). It is interesting to see that there were close relations among many of the leading forestry scholars of that time. Even though none of these authors had an in-depth education in the field of economics nor was dealing full-time with economic questions, their writings were quite likely influenced by the leading political economists of that time, in particular Ricardo (1817) and von Thünen (1826). The approaches presented in this paper had some clear parallels to the methods used in presentday business valuation. Von Jordan's (1800) book can even be considered a manual for valuating agricultural enterprises. However, there are also aspects that are missing in this early literature, such as the impact of income taxes on the value of forest. Still today, the debate on the choice of an adequate interest rate for valuating has not yet come to an end. Already the early German publications on forest valuation presented in this paper showed a tendency towards an interest rate that yields a desired result. This use (or misuse) of the interest rate generally tends to be even more pronounced in more recent literatures on forest valuation, as well as in literatures on valuation of (agricultural) real estate and enterprises. The suggestions to use lower interest rates or to use simple interest instead of compound interest reveal two things. First, already 200 years ago there was a significant discrepancy between the actual purchase price for forest and the present value of the forest calculated with market interest rates, current timber prices and costs. Second, already at that time methods were not immune to “valuation tricks” that narrow the gap between the estimated value and the purchase price in order to achieve higher
M. Moog, M. Bösch / Forest Policy and Economics 30 (2013) 1–5 Table 2 Overview of the proposals on modification of the interest rate in the early German forest valuation literature. Year
Author
Modification of the interest rate
1796 Von Burgsdorf 1800 Von Jordan
Markup of 1/2 (e.g., 6% instead of 4%), because forest buyers need an adequate profit (and forestry involves risk) Markup of one percentage point first of all due to risk in forestry, but also because there is a need for realizing a positive profit. 1804 Cotta Markdown due to capital market imperfections 1805 Von Risk-equivalent forestry interest rate that lies somewhere Nördlinger between the one of the less risky field and the capital market interest rate. 1812 Hartig Stepwise markup of half a percentage point per age-class (20 years)
acceptance. This phenomenon, however, was not restricted to Germany. In England, for example, it started even earlier. Even though the English debate of the seventeenth century mainly concerned the level of interest rate in the whole economy, Sir Thomas Culpeper the elder showed already in 1621 (Culpeper, 1621) that he understood the deleterious impact of a high interest rate on the evaluation of investment projects such as forestry and land improvements. In his opinion, the wealth of England was not being developed because the interest rate was too high in comparison to that of other nations. Culpeper (1668) followed his father's example and sought a further reduction in the interest rate (a reduction from 6% to 4%). In his opinion, “many Gentlemen” would preserve their young timber trees and plant new groves for prosperity if interest rates were lower. References Anonymous, 1807. Bemerkungen zu dem Aufsatze in Nro. 35 dieses Journals: über die Abschätzung kleiner Stücke Hochwaldungen, die zu verkaufen sind. Journal für das Forst- Jagd- und Fischereiwesen 44, 689–695. Bein, Eyber, 1804. 2. Verschiedene, die Bestimmung des Werthes eines zu veräußernden Waldes betreffende Bedenklichkeiten. Diana 2, 127–144. Brazee, R.J., 2006. The Faustmann face of optimal forest harvesting. Tietenberg, T., Folmer, H. (Eds.), The International Yearbook of Environmental and Resource Economics 2006/2007: A Survey of Current Issues. Edward Elgar, Cheltenham and Northampton. Cotta, H., 1804. Systematische Anleitung zur Taxation der Waldungen. J. D. Sander, Berlin. Cotta, H., 1818. Entwurf einer Anweisung zur Waldwerthberechnung. Arnoldische Buchhandlung, Dresden. Culpeper, T., 1621. A tract against usurie. (the elder) Walter Burre, London (reprinted Theatrum Orbis Terrarum, Amsterdam 1974). Culpeper, T., 1668. A Discourse Showing the Many Advantages Which Will Accrue to this Kingdom by the Abatement of Usury Together with the Absolute Necessity of Reducing Interest of Money to the Lowest Rate It Bears in Other Countries, That, At Least, We May Trade with Our Neighbours Upon Equal Terms. (the younger) Christopher Wilkinsion, London. Faustmann, M., 1849. Berechnung des Wertes welchen Waldboden sowie noch nicht haubare Holzbestände für die Waldwirtschaft besitzen. Allgemeine Forst- und Jagdzeitung 12, 441–455. Gerber, T., 2004. Persönlichkeiten aus Land- und Forstwirtschaft, Gartenbau und Veterinärmedizin — Biographisches Lexikon, Band 1. Nora, Berlin.
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