value of the land and the growing-stock is raised, so long as such thinnings do not affect the final return from the mature fall of timber; but, otherwise, such early returns may perhaps only be obtained at the cost of subsequent loss-as is now the case in many British woodlands. With a knowledge of the local market and rates for the small material yielded by early thinnings it is, however, easy to calculate whether it will be most profitable to plant so close as 3×3 ft., or at 4×4 ft., or 4×4 ft. in forming new plantations, and to see how the financial position, as to net cost up to date, of each given crop would thereby be affected at, say, 25 or 30 years of age, in consequence of the thinnings obtainable meanwhile. (4) The Valuation of a Growing Crop of Wood.1-If of marketable size, the present market value of single trees and of the whole crop in any compartment may easily be determined by measurement, as already described in Chap. II. If only immature and comparatively young crops of wood, it will usually be most convenient to estimate the value, for such purposes as sale or transfer, according to their cost up to the present, care being taken, however, to discriminate between the actual cost of sowing, planting, &c., and any outlay in the way of fencing against rabbits-all charges of the latter nature being debitable to the game account, and not to the timber-crops. But in either of these cases a deduction must be made on account of the rental value of the land, and of general annual charges, in order to arrive at the true value of the timber-crop alone. Otherwise, the present value of the crop may also be estimated according to its productivity or prospective value, much in the same way as shown in the previous section with regard to the productivity of the land. Fa 1·0p" m Here the present value, at the age m, of the net returns from the mature fall, F, harvested at n years of age, is=. (Formula II.); while the various thinnings Ta, Tò, . . . Tq, at a, b, and 9 years of age, are, if prolonged to n, so as to give them the same denominator as Fn, and any minor produce is similarly calculable. Against these receipts certain charges are, however, debitable for rent of land, r, and general charges, g, which will be incurred during the years n-m. These amount respectively to -1) r(1·0 pm - (Formula VII.) and to 9(10pm —. ]). = 0.0p 1·0pn 1 Subtracting these debits from the prospective returns from the crop, we therefore have the Present Capital Value of the Timber Crop == [F2 + (Ta × 1·0p"-a) + (Tò × 1·0μ” ̄) + . . . + (T ̧ × 1·0p"-")] - [~ + (1·0pm-1)]. Example. What is the present value per acre of a 40-year-old crop of Larch, forming part of a working-circle worked with a rotation of 80 years, if the mature fall may be estimated at £250 an acre, and thinnings are probably obtainable having a net worth of £8 at 50 years of age, £10 at 60, and £12 at 70, the rental value of the land being 10s. 1 Where ornamental trees and groups of trees have to be valued, estimates must of course be made on some such basis as what they have actually cost, or at what they are worth as timber plus something extra for their ornamental effect, according to the given circumstances. an acre, general annual charges amounting to 5s. an acre, and the rate of interest being 3 per cent? The Present Value of Crop is here 0.5+0.25 [250 + (8 × 1·033) + (10 × 1·032o) + (12 × 1·031o)] − [ = 1.0340 0.03 [250+(8 × 2·4273) + (10 × 1·8061) + (12 x 1·3439)] – (25 × 2.2620) One weak point of this method (e.g., when applied to valuations for expropriation) is that the value thus shown may vary considerably according to the age at which the crop is intended to be felled, whereas the true intrinsic value of a timbercrop per se ought, one might think, to be capable of being fixed at something definite and irrespective of the future use made of it. This does not suit the nature of the investment, however; and the value of the crop in such cases must be taken to be that shown if the timber be utilised at its most profitable age. In fixing the latter, the above formula can be used quite as well as that for determining the productivity of the land. If the rental value of the land be estimated too low, the apparent value of the timber-crop will work out too high, and vice versâ. But the rotation which indicates the maximum productivity of the land will also indicate the highest present value of the timber-crop, so long as the returns and expenses correspond in both cases, because in either calculation the most profitable age for felling the crop is when the difference between receipts and expenditure is greatest. 5. The Valuation of the Normal Capital in Wood throughout a Working-Circle. If the woods forming a working-circle are in a normal condition, capable of yielding a regular annual fall of equal amount, then it is essential that there should be a regular gradation of age-classes normally distributed throughout the woodlands and varying from 1 to n years (just before the annual fall) or from 0 to n-1 years of age (just after the fall), n being the rotation with which the woods are worked. It is therefore of advantage to estimate the monetary value of the normal capital in wood so as to be able to reckon the rate of interest yielded by the working-circle. Whether this be done by means of long, intricate calculations regarding either the productivity of such normal capital in wood, or what it has cost (or would cost) to produce it, the result in each case works out so as to correspond identically with the present capitalised value of the regularly sustained annual returns from the woodlands, less the capital value of the land itself. If the annual income from woodlands in a "normal condition "-an ideal standard never attained in actual practice—be capitalised (C), this amount consists partly ... of the capital value of the land and partly of that of the normal capital in wood. If worked with a rotation of n years, the annual income from a working-circle of n acres (or other unit of area) is = Fn+(Ta+Tv+ Tạ) − (c +gx n). Capitalising this annual income, we have the Normal Capital in Wood + Capital Value of the Land Fn+ (Ta+Tv+ . . . + Tq) − (c + g×n) 0'Op Hence, for the whole working-circle, the Normal Capital in Wood Fn+(Ta+To+...+T,) - (c+gXn) and for the acre (or other unit of area) - Capital Value of the Land, Fn + (Ta + T8 + . . . + Tq) − (c + g× n) – Capital Value of Land per acre (or other unit of area). n x 0.0p Or, expressed in words, the value of the Normal Capital in Wood throughout a normal working-circle is equal to the capitalised value of the normal annual income, less the capital value of the land. Example.-Say the normal annual returns from a working-circle of 800 acres in normal condition, worked with a rotation of 80 years, consist of £2400 for the mature fall of timber, and £300 from thinnings in woods of different ages, that each year the cost of planting the area cleared is £40, and that the gross general charges amount annually to £160; what is the present value of the Normal Capital in Wood, if the annual rental value of the land is 10s. an acre, and the rate of interest be 3 per cent? Here the net 2500 receipts are 2700 - 200= £2500, and their capitalised value is = £83,333. The rental 0.03 400 0.03 = value of the land being £400 a year, its capital value is =£13,333. Hence the capital value of the Normal Capital in Wood is 83,333 -13,333} = £70,000. The "normal condition" being always a mere ideal, when a valuation of woodlands is made it must necessarily be that of the actual growing-stock or capital in wood. It is only by making such a valuation that the actual rate of interest obtained on the capital invested in the woodlands can be ascertained. To satisfy the requirements of the Succession Duty Act, the custom in England has generally been to value all the timber and other wood, and to take 3 per cent of this as a fair annual return under good management. This income is then treated as an annuity, aud succession duty has to be paid upon it on a scale laid down in tables annexed to the Act. Thus, if the life-tenant were 40 years of age on entering into succession, and the annual income from the woods were estimated at £500 a year, this annuity would be considered as having a capital value of £7437 assessable to duty (and not as £500÷00·3= £16,666). If it be desired to estimate the whole capital value of woodlands (i.e., land plus growing-stock of wood) by means of detailed calculations regarding productivity and prospective value, then this must be done by reckoning each of these separately by the formulæ already given and adding the results together. This is rather a cumbersome method, because the value of the land has to be fixed according to the crop which may show the greatest productivity. If, however, it be desired to contrast the present productivity with that of some other method of treatment, then the value of the land must in this latter case be calculated according to the new returns anticipated. The same practical difficulty is found in trying to estimate the capital value by means of calculating what the land and the growing-stock have actually cost up to the present. In either case it is very difficult to estimate the productivity, and therefrom the value of the land, with correctness; and unless this, as well as the rate of interest at which the calculation is made, be correct, the estimate cannot be reliable. Hence the advantage of using the simple direct formula, capital value annual net income of woodlands (land and growing-stock)= wherever the manage" rate of interest ment is sufficiently regular to permit of this method being applied. In copse and coppice yielding only intermittent returns, their annual rental value can be found for this purpose by permuting the former into the latter. As the monetary returns from woodlands are seldom or never so regular as to produce the same income year by year, it is desirable to introduce such a scheme of management as will tend to give a more regular annual return during fixed periods of ten or twenty years; and from these the capital value of the woodlands can in course of time be estimated with a fairly close approach to accuracy. In such cases, however, the estimated capital value can only be for the system of treatment adopted under the given circumstances. A different system of working might often indicate a higher capital value for the woodlands, even if the growing-stock or capital in wood represented a smaller monetary capital than that necessary under the present method of working. This paradox seems absurd; yet the statement is quite correct. For example, if 6000 acres of woodlands are stocked with hardwoods and worked with a rotation of 100 to 120 years, their annual fall will be 50 to 60 acres. But if the area were stocked with mixed Conifers worked with a rotation of 60 to 70 years, the annual fall would be from 86 to 100 acres. And in the latter case it is almost certain that the net annual income would be considerably larger than in the former, although the monetary value of the capital in growing-stock would be very much greater in the case of the hardwoods than of the Conifers, because the capital value of the land, de facto, varies so much according to its productivity, as determined by the specific nature of the timber-crop and the treatment under which this is. Hence it follows that, consequent on injudicious treatment in the past with regard to the formation and the general management of the timber-crops, the British woodlands have a present value of probably only about one-third to one-half of what they might otherwise have been estimated at. In some rare cases it may perhaps be possible to determine in an apparently more direct, but really equally circumstantial, manner the capital value of woodlands for purposes of sale or of raising a loan on their security. Say, for example, that a scheme of management has been drawn up for their treatment on commercial principles, and that the following financial estimate seems justified : : what is their present capital value, the rate of interest being 3 per cent? Here, after varying periodical rentals for the first four periods of 20 years each, the estimated income becomes a fixed annual return from 1980 onwards. The summarised present value of these is therefore for I. Period (see Appendix, Table V.), 900 x 14.8775 = £13,389.75 from 1980 onwards a perpetual rental of £750, with a capital 750 value of =25,000, the present value of which is 25,000 0.03 × 0.094. = £2,350.00 The present capital value of the woodlands therefore amounts to £24,061·48 = £24,061·9·7. 6. Estimating the Income derivable from Woodlands.-Besides being necessary in order to determine the capital value of woodlands, definite knowledge as to the net income or rental they yield is desirable so as to be able to draw correct comparisons between forestry and arable or pastural utilisation of the land. With a regularly sustained annual yield under a sound system of management the woods forming a working-circle of n acres give an annual return, in the mature fall (F) and thinnings (T) at various ages, as also in minor produce, less cost of reproduction and of general charges, = F2+ (Ta+To+ + T1) − (c + g× n), so that the net annual income As this includes the net income from the capital in growing-stock as well as that of the land, the result thus obtained cannot be used in comparing the profit of forestry with that of agriculture. It shows the net income merely, but it gives no indication as to this being as profitable as it ought to be for the given land. In this the productivity of the land, as calculated by Faustmann's formula, is the only safe basis of comparison. As copses and coppices only give a periodical return, R, this can be permuted into an annual rental, r, which gives (Formula XII.) for a rotation of n years, as the rental value of the land and the coppice-stools r= R 7. The Application of Actuarial Methods to Forestry is, despite the obvious difficulties about the assessment of the different factors used in making calculations, the only correct way of estimating the financial position of timber-crops as a commercial investment. It is only thus that any profit connected with Forestry under given local circumstances can be measured or forecast, so as to enable a correct comparison to be made between timber production on the one hand, and arable occupation, pasturage, deer-forests or grouse-moors, on the other. It is only thus, too, that such important questions can be decided as relate to the selection of particular kinds of timber-crops from among several perhaps suitable for any given soil, situation, and local market, or to the choice of the method and details of formation, the general system of treatment, and the most profitable time of reproduction. As special reference has already been made to these matters, and more particularly to the financial maturity of timber-crops, in explaining the theoretical principles of woodland management in Chap. II., it is unnecessary to repeat, or to add anything to, what has already been said on pp. 239 to 241. |