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Forestry Commission

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Investment appraisalj f / - n K / ^ o t **\ / with particular reference I I I l U i a O L I y to conifers in Britain

by R J N B usby and A J G ra y so n F orestry C o m m iss io n

London: H e r M ajes ty ’s S ta tio n e ry O ffice.

© Crown copyright 1981 First published 1981

ODC No. 651:652:67

Enquiries relating to this publication should be addressed to the Publications O fficer, Forestry C om m ission Research Station, A lice H olt Lodge, W recclesham, Farnham, Surrey, G U 10 4LH .

ISBN 0 11 710190 7

Printed in England for Her Majesty’s Stationery Office by Hobbs the Printers o f Southampton (1638) Dd0696970 K24 3/81 G327

Contents

Pagev Summary

vi Acknowledgements

1 I, The Principles of Investment Appraisal

1 Introduction2 Discounting3 The measurement o f relevant costs and returns4 Inflation4 Non-market costs and benefits5 Choice o f discount rate5 Risk, uncertainty and sensitivity analysis

7 II, The Assumptions

7 Revenues7 Yields8 Prices9 Costs

12 Effect o f taxation and grants on costs and returns

13 III, Applications

13 Land purchase16 Choice o f species18 Fertilisation22 Beating up, weeding and cleaning23 Protection

272833

36

384446487282

8490

iv

RoadingThinningTiming of felling and crop replacement

References and Further Reading

Appendices

1 Compound interest tables at 3, 5 and 7%2 Price-size schedule for conifers3 Factors for adjusting for inflation4 Discounted revenues calculated to year of planting at 3, 5 and 1%5 Discounted volumes at 3, 5 and 7%6 Discounted revenue for different thinning regimes in Sitka

spruce7 Optimum felling ages at 3, 5 and 7°7o8 Age of first thinning as specified in the management tables

Summary

The purpose o f investment appraisal is to show the relative profitability of alternative courses of action. The measure of profit used is net discounted revenue at a chosen discount rate. A ttention is concentrated on conifers in pure stands. The assumptions adopted in preparing tables o f discounted revenue at 3, 5 and l°7o are the predictions o f Forestry Commission yield tables. A generalised curve relating standing tree values with diameter at breast height is assumed. Discounted revenues for the m ajor conifer species by yield classes are tabulated in the appendices. Illustrative examples of their use are presented for appraisal of land purchase, choice of species, fertilisation, beating up, weeding and cleaning, crop protection, roading, thinning, timing of felling and crop replacement. Taxes and grants often affect costs and returns to the private or corporate owner and thus influence commercial decisions which should be based on post-tax and post-grant costs and revenues.

v

Acknowledgements

The authors wish to acknowledge the help given by colleagues in both the Forestry Commission and private forestry who suggested many improve­ments to an early draft of the text.

Thanks are also due to past and present members o f the Planning and Econ­omics Division of the Forestry Commission, whose work has been used as the basis for some of the sections in this Booklet, and in particular to Jim Dewar, Mike G arforth and John Morgan; and especially to Bob Cochrane who carried out all the programming and com puter work.

I. The Principles o f Investment Appraisal

Introduction

The purposes of this Booklet are to outline the basic concepts o f investment appraisal as they apply to forestry, to provide tables of use in appraisal and to illustrate their application to a variety o f cases in forestry.

The Appendices and Tables relate only to the common conifers. Broad- leaves have not been covered owing to the difficulty o f nominating plausible and generally acceptable assumptions on the value o f broadleaved trees of different sizes. Their exclusion should not be taken to imply that manage­ment of broadleaved woodlands does not merit the same treatment of appraising options as arises with conifers. Indeed, the range of options may well be wider. As with commercial coniferous woodlands, the purpose of appraisal may not be simply to discover the course o f action likely to yield the highest profit but rather to determine the cost of departing from it in order to satisfy some non-commercial objective.

The economic justification of a project lies in the belief that the cost of carrying out the project will be more than covered by the income generated by it. Where there is a significant lapse of time between the start of costs being incurred and the end of the period in which all costs and benefits arise the original expenditure is considered to be an investment. An investment is thus any action which incurs costs now and gives returns in the future.

Because o f the time lag between incurring costs and receiving returns, especially in forestry, it is not always easy to evaluate the costs and returns. In particular, difficulties arise in predicting future inputs and outputs in physical terms (e.g. m an-hours, cubic metres), assessing the future value of these inputs and outputs and comparing the value of the costs and returns arising at different times. Because o f these difficulties it is often not immediately apparent that a particular investment is worth doing or which is the best investment to choose from among several alternatives. This is,

1

however, no excuse for not attempting to make any appraisal of the invest­ment but emphasises the need for such appraisals rather than relying on intuition.

Discounting

Investm ent appraisal entails quantifying future costs and returns, evalu­ating in terms of a common measure, namely £s, and weighting these values to take account of their timing by the process of discounting. The concept of discounting for time is based on the premise that, in general, people pre­fer to receive benefits sooner rather than later. If offered £1 now or in a year’s time (and leaving aside at this stage the question of inflation) most people would have it now. If they have it now they can either buy some goods which bring them current satisfaction or they can invest the money so that at the end of, say, one year it brings returns in excess of the original amount invested. Thus £1 received now is considered by most people to be of greater value than £1 at some future date. Just how much depends on the individual’s attitude to time. Some people may value £110 next year as equivalent to £100 now, while others may value £105 as equivalent.

Just as compound interest is applied to show how an investment grows to some point in the future, so one can discount in order to bring some future am ount back to the present. As a m atter o f convention it is usually assumed that the discount rate remains constant through time. By this means all costs and returns can be increased or decreased by a set factor each year in order to make them comparable with other costs and returns which arise at differ­ent points in time. Where values are increased to make them comparable with a value at a later date, this is known as com pounding and when values are reduced to make them comparable with values at an earlier date this is known as discounting. The compounding and discounting formulae and factors for a range of rates are shown in Appendix 1. The following examples illustrate the calculation o f the present value (that is the value dis­counted or compounded to the present) of various sums:

5% com pound or discount factor

Present value at 5% , £

£70 4 years ago 1.216 85.1£100 now 1.0 100.0£250 in 10 years 0.614 153.5£500 in 15 years 0.481 240.5

2

The terms discounted expenditure and discounted revenue relate to the present values of either individual sums of money or sets o f sums expended or received. Thus the discounted revenue at 5% from revenues of £250 received 10 years hence and £500 received 15 years hence equals £153.5 plus £240.5, or £394.0. N et discounted revenue (NDR) is equal to the difference between discounted revenue (DR) and discounted expenditure (DE). If the DR for a particular project is estimated at £160 and the DE at £100 the NDR is £60. The common point to which all cash flo w s are usually related is either the present or the starting year of the investment under consideration. Once all cash flows have been brought to the same point in time it is possible to rank them in order of present value and identify the one with the highest net present value (i.e. NDR).

The Measurement of Relevant Costs and Returns

The first question that arises is which costs and revenues are to be included in an investment appraisal. Where an item of revenue or expenditure in a particular year remains the same whether or not the investment is under­taken, such an item may be omitted from the appraisal. For instance, there are costs associated with an enterprise which are unlikely to change whether a particular investment is undertaken or not. Examples o f this might arise in appraising a fertiliser programme for a forest. Some foresters’ time will be involved in the operation but it is unlikely that there will be any additional payment o f salaries as a result of going ahead with the programme or any reduction in the total salary bill if the programme is not undertaken. In such circumstances these costs are therefore f ix ed costs which do not vary with the investment and thus can be excluded from the appraisal. Most overhead costs come into this category although some costs which are often con­sidered as overheads, such as labour oncost (wet time, holidays, travelling etc.) are usually not independent of the investment and so need to be taken into account.

In contrast to fixed costs are the variable costs. These do need to be con­sidered in an appraisal because the costs will vary depending on whether the investment is undertaken or not. There is no sharp dividing line between fixed costs and variable costs but the further into the future a cost is incurred the more likely it is to be variable.

A similar sort o f consideration arises where an appraisal is being made of an investment in harvesting roads in an area due for first thinning and there is an existing pre-planting road. In these circumstances, the original cost of

3

the pre-planting road can be ignored as the money has already been spent and will be unaffected by any decision regarding the harvesting roads.

Inflation

It might be thought that future inflation must cause difficulties in estimat­ing future costs and returns. In practice, the inclusion of an assumption about future inflation is relevant only where loans are concerned and repay­ment is due in money regardless o f how the purchasing power o f the £ has changed over time. Otherwise the best way to handle inflation expected in the future is to ignore it. By removing the effects o f inflation one deals with values expressed in real terms. This does not mean, however, that one necessarily assumes that all costs and prices will move in harmony in the future. The prices of some goods and services will rise relative to others, that is they show an increase in relative (or real) price. If they do the relative price of others must fall. For example, it is likely that with increased stan­dards of living real earnings and the price of services, for example haircuts, will rise while the real price of most m anufactured goods may fall.

Such trends in real price, if confidently predicted, should be included in any appraisal. This can most simply be done by converting the trend in real costs or prices into a compound interest percentage and then discounting. For example, suppose that the chosen discount rate is 5% but that there is good evidence to suggest that prices are going to increase in real terms, i.e. rela­tive to other goods and services, at 2% per annum . In this case, the costs will continue to be discounted at 5% but the prices will rise at 2% and then be discounted at 5% . This means that prices unadjusted for their predicted real increase can be discounted at 3% (5% - 2%), the approxim ation being satisfactory for most purposes at low rates o f interest, to find their present value in real terms.

Non-Market Costs and Benefits

The money values of costs and revenues based directly on m arket measures may not always reflect the social costs and benefits o f a particular invest­ment. Differences between m arket and social values may arise because resources may be priced above or below their real value to society, or because there is no m arket in goods and services produced or consumed, for example landscape or clean water.

4

Normally cost-benefit analysis incorporating measures in social terms of the various inputs and outputs is undertaken by Government bodies, but not by private owners. There may, of course, be non-m arket costs or benefits of a course of action taken by a private owner either to himself or to his heirs (e.g. gain in amenity) but, in this case, the owner himself is in the best pos­ition to make a subjective choice having considered the results of the financial appraisal.

Choice of Discount Rate

The level of the discount rate is of param ount im portance in forestry owing to the large effects a small change in rate has when used to discount values over long periods of time. The discount rate used in the public sector gener­ally is related to the rate of return on capital in the private sector of the industry and commerce. The test discount rate is currently set at a minimum of 5% applied to costs and returns expressed in real terms (Cmnd 7131 April 1978 and H ansard, House of Commons, 5 April 1978).

However, the economic environment o f the private sector differs from that in the public sector, for example because of taxes or different valuations of non-m arket costs and benefits, and as a result there will be differences in discount rate. In this account, discount rates of 3, 5 and 7% have been employed in an attem pt to cover the range of real rates of return likely to be available from alternative investments open to private investors in forestry. Where an investor is uncertain which rate is most appropriate in his circum­stances, he can separately discount his cash flows at each o f these rates and thereby determine the internal rate of return (the rate at which NDR is zero) by either interpolation or extrapolation. An example of this calculation is given on pages 17 and 18. The investor must then decide whether he con­siders this rate o f return to be satisfactory.

Risk, Uncertainty and Sensitivity Analysis

Uncertainty obviously has a bearing when considering future events. Very often in investment appraisal it is assumed that cash flows can be predicted with certainty. Where there are a number of possible outcomes resulting from an investment it may be possible to measure the risk involved by con­sidering what has happened in the past. It may then be possible to allocate probabilities to each possible outcome. For example, it may be estimated that on average over the long-term there is a 30 per cent (i.e. 0.3) chance

5

that a crop will be blown down when it reaches a top height o f 16 m, a 40 per cent chance o f this happening at 17 m and a 30 per cent chance o f it remaining until the designated height o f felling of 18 m. The DR for each event is multiplied by its probability and the sum of the products used as the expected DR having taken into account the risk (note that the probabilities of all possible events must sum to unity):

Expected DR = 0.3 (DR: 16 m) + 0.4 (DR: 17 m) + 0.3 (DR: 18 m)

Very often in forestry such probabilities will have to be estimated subjec­tively.

Whether or not it is possible to assign probabilities to different outcomes it may well be useful to carry out a sensitivity analysis. This looks at the variation in the results of an appraisal when some of the assumptions are changed. Sensitivity analysis, as its name implies, indicates to which assumption the results are most sensitive. For example, it may be helpful to show the consequences of a particular course o f action in terms o f net dis­counted revenue at a variety o f discount rates indicating the sensitivity of the results to the choice of discount rate.

In the absence of any guidance on the likely range of values of the various factors the analysis has to be conducted on the basis of determining the sensitivity of the results to a given percentage change (say 10 per cent) in each o f the factors. Examples o f sensitivity analysis are given on pages 18 and 21.

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II. The Assumptions

Revenues

The forest yields a number of benefits in addition to timber. Some have a m arket value, such as sporting lettings, while others such as amenity and conservation are more difficult, if not impossible, to value in money terms. In this account we shall only be considering the revenues derived from the yield o f wood. If there are additional sources o f money income which can be foreseen, for example the sale of foliage and sporting rentals, these should be included.

Yields

The yield data used in computing the tables and appendices that are given in this Booklet are based on those given in the metric version of the Forest M anagement Tables (Hamilton and Christie, 1971) and on more recent work carried out by the Commission’s M ensuration Section, such as that described in the Bulletin entitled Influence o f Spacing on Crop Character­istics and Yield, also by Hamilton and Christie (1974).

British yield tables have related to pure even-aged crops only, but if tables for mixtures or uneven-aged stands were available there would be no differ­ence in the principles o f conversion from yield to discounted revenue. Yield models being published by the Forestry Commission will include the Forest M anagement Tables (out o f print as Booklet 34) and will show the changes in yield associated with changes in initial spacing, line-thinning and delays in thinning (see p. 36).

Spacing

The initial crop spacings assumed for the discounted revenue (DR) tables are those that were current in the 1950s and early 60s because the available

7

yield tables were set up for forecasting production from such stands. In the 1960s wider spacings o f 1.7 m to 1.8 m came into vogue, subsequently extending as far as 2.1 m. These are economically m ore attractive in that they reduce establishment costs while not markedly affecting production other than decreasing the number of stems and increasing average stem diameter and volume at the time of first thinning. Despite these changes in practice, the tabulated DRs may also be employed for wider spaced crops in the knowledge that spacings of the order of 2 to 2.5 m will not markedly change the revenue values.

Stocking

Forestry Commission yield tables assume full stocking and the figures must be adjusted to allow for gaps resulting from crop failures o f one form or another and for reduction in area resulting from roads, streams, buildings etc. This reduction factor varies with conditions, but 15 per cent has been assumed in the calculations of the DR tables here.

Felling and Thinning Regimes

The tables in Appendix 4 cover two possible management regimes: thinning in accordance with the M anagement Tables and no thinning. The timing of first thinnings (see Appendix 8) is the first age at which the stand can be thinned such that the volume increment will allow subsequent thinning on a 5 year cycle at the intensity stipulated in the M anagement Tables. The econ­omically optimal age o f first thinning may be somewhat later than this under certain circumstances and P art III sets out the type o f calculation required to determine this age.

Wind

The effect o f wind may be taken into account in a num ber of ways and is dealt with specifically in Part III, where questions of timing o f thinning and clear felling are considered.

Prices

The prices used in the com putations correspond to standing tree prices (i.e. m arketing overheads are not included). These prices are based on average

8

values obtained by the Forestry Commission over the decade 1967 -7 7 con­verted into £s o f 76/77 value (average for April 1976 to March 1977). This price-size relationship which is shown graphically in Figure 1 and as a schedule in Appendix 2 is used in the revenue calculations which follow on the assumption that in the longer term average price levels for wood will not be different in real terms from those obtained over the decade 1967-77 .

For analyses involving revenues to be obtained from early thinning or in the near future it may well be more realistic to use current local prices and allowance is made for this in Part III. Discounted volumes (DV) are equiv­alent to discounted revenues with the price per cubic metre taken as unity. If it is felt that the general price assumptions are, say, too low by £2 per cu m over all sizes then the tabulated DRs can be adjusted to take account of this by multiplying the appropriate DV (see Appendix 5) by £2 and adding this product to the original DR. If, on the other hand, it is felt that prices should be say 30 per cent higher than shown in Appendix 2 then an amended DR can be calculated by multiplying the tabulated figure by 1.30.

Where it is felt that the shape of the price-size curve shown in Figure 1 is inappropriate then the appraiser can use his own price-size relationship to generate DRs using full DV tables. These tables show volumes o f thinnings and of main crop before thinning and their respective discounted volumes at a number o f discount rates. Each element o f DV can be multiplied by the price for the particular tree size to yield a DR element which summed give DR0 to a given age. An example o f a layout is shown in Figure 2. When DV tables are not available the DV can be calculated quite easily by multiplying the volume given in a yield model appropriate to age and treatm ent by the factor (Appendix 1) for the period o f discounting.

As noted above the prices used in computing the tabulated DR values are in £(76/77). It is im portant when comparing costs with revenues or when cal- lating NDRs that both costs and revenues are assessed in £s o f the same value. This means either deflating current costs back to 1976/77 levels if using the DRs given or inflating revenues to current £s. Indices for making these adjustments are contained in Appendix 3 and an example o f their use is given in P art III, p 19.

Costs

Overhead costs (local supervision, office expenses etc.) should be included in the appraisal if a full assessment o f the financial implications o f a course

9

12-

£ per cu m (over bark)

Figure 1 The price-size curve from data given in Appendix 2 and used in the example calcu­lations. The negative values m ake allowance for harvesting costs being in excess o f revenue.

of action is required. They should also be included if they are expected to differ between alternative projects. Otherwise it is suggested that the costs considered should be up to the level o f wages, materials, machinery and labour overheads (sick pay, holidays, transport o f workers etc.).

It is desirable to consider cost levels in recent years as well as the present in order to establish whether current costs are appropriate (for example, they may be abnormal as a result of unusual weather) and also whether there is any significant trend, either up or down. To do this it is necessary to inflate the unit costs of previous years into current £s using the factors given in Appendix 3.

10

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Effect of Taxation and Grants on Costs and Returns

Although these calculations show costs, revenues and net revenues as if they were exclusive o f taxes, tax allowances and grants, it will usually be the case that a private individual or company is most interested in the cash flows, and their present value, after taxes and grants have been taken into account. Indeed, the only sensible method of appraisal of investments affected by taxation and grants is to compare costs net of tax allowances and grants with revenues after tax.

The main problem in estimating the position after tax and after grant con­cerns the identification of the investor and the beneficiary of the investment under appraisal. In most cases of plantation investment, the same individual will not receive the revenues flowing from the original outlay. This question of the treatm ent of future returns can be handled in one of two ways. The first is to consider the period of occupation of the woodland by one person. This creates its own problem, however, because a value has to be attached to a given stand before its planned life is complete. The second is to create the fiction of a continuing owner or occupier whose tax position may, if necessary, be supposed to alter favourably as a result of changes in ownership or occupation of a particular woodland. Although the case is hypothetical, it appears to be the most direct way o f approaching the problem of appraisal for investments covering the bulk, or whole, of a crop’s life.

Thus, for woodlands assessed under Schedule D, the required adjustm ent of costs to be incurred in the near future will not be difficult to calculate. If the marginal income tax rate applicable expressed as a fraction is t, the cost of allowable expenditure, assuming this does not exceed the am ount in the tax band covered by t, is cost, net of any grants, times (1 - t ) . For costs which are likely to be incurred some time into the future, such as pole-stage fertilisation or the cutting o f inspection racks, a judgem ent must be made about whether these are likely to be relieved through Schedule D income tax or not because the woodland concerned may then be assumed to be taxed under Schedule B. In relation to revenues from thinnings and felling, the simplifying assumption of Schedule B income tax may be made.

In the case of capital taxation, it is suggested that for working purposes a judgem ent must be made on the effective rate of tax arising which, applied to revenues from the class of stand under consideration, is equivalent to the expected Capital Transfer Tax liability arising from a transfer at death.

12

III. Applications

The following examples cover the main sorts of appraisal that may be carried out during the life of a tree crop starting with land acquisition and finishing with the timing of clear felling. These examples follow the prin­ciples outlined in Part I and include assumptions detailed in Part II. If the particular decision area the reader is interested in is not covered in these examples it is hoped that sufficient guidance is given to enable him to undertake the appraisal from first principles.

Land Purchase

The value o f a parcel of land for forestry depends on the cost o f establishing and maintaining the tree crop and the value o f the receipts expected from the produce. Total revenues minus total costs discounted back to the time of purchasing the land, which may be a year or two before the time of plant­ing, represents the expectation value o f the crop at whatever discount rate is deemed appropriate by the prospective purchaser. Assuming this expec­tation value, or net present value, is positive then this is the sum which the purchaser can afford to pay for the land and make a profit in real terms equal to the rate of discount used. If the expectation value is lower than the m arket price or worse still is negative (DE is greater than DR) then the land is only worth purchasing if:

i. the prospective owner expects additional non-m arket benefits (e.g. amenity and recreation) not included in the appraisal—tax benefits, grants and net revenues from sporting should have been included in the appraisal; or

ii. the purchaser expects the value of the land to increase in real terms (although this can be included explicitly in the appraisal).

The question o f choice o f species and management regime will be discussed in subsequent sections. The Forest site yield guide to Upland Britain

13

(Busby, 1974) may be of some help in this context. In the example below, the following assumptions are made:

species to be planted: Sitka spruce 50% of area \ both crops toJapanese larch 50% of area J be thinned,

expected yield class : SS YC 12JL YC 10

rate of discount 5%

The costs per hectare are set out below and their discounted value at the chosen discount rate o f 5% shown in the right hand column.

£(78/79)<a> Year Discounting factor D iscounted value

£preplanting road 10 - 1 1.05 10.5Wfencing 20 0 1.0 20.0ploughing 40 0 1.0 40.0planting 40 0 1.0 40.0beating up 15 1 0.952 14.3weeding 25 2 0.907 22.7fertilising 35 10 0.614 21.5roading<b> 50 16W 0.458 22.9protection and

m aintenance 4.5 p /a 1 - 50<d> 18.26 82.2

274.1

N otes(a) These costs exclude overheads.(b) Including upgrading o f preplanting road.(c) JL to be first thinned at 17 years.(d) Felling age o f m aximum DR at 5% from Appendix 7:

SS = 55 years "IJL = 45 y e a r s ) (av^ g e = 50 years)

(e) Costs com pounded forward one year to time o f planting.

Revenues per Hectare

Using the tables in Appendix 4, which give values in £(76/77), we find the discounted revenue at 50 years for SS YC 12 (thinned) to be £385 per ha and for JL YC 10 (thinned) £390, which as the species are to be planted in equal proportions gives an average of £387.5.

14

Using the inflation factors from Appendix 3 it is evident that the net dis­counted revenue (NDR) of the crop in £(78/79) is (£387.5 x 1.2363)- £274.1 =£205.0, but this does not take into account:

i. the value of a successor crop, if the area is to continue in forestry;

ii. the value of the land at the end of the rotation for other purposes;

iii. the value of any other fixed assets such as roads and buildings left after the felling.

Assumptions about the value of successor crops or fixed assets 50 years hence can be no more than conjecture. However such matters do affect the calculation of the land value and there are two ways of dealing with this. The first is to assume that the area will be planted with the same species and hence produce a similar NDR, only differing because subsequent expendi­ture on roads is unlikely to be the same as in the life of the first crop. The other, equivalent, way is to ascribe a value to the land at the end of the first crop’s life equal to that at the beginning. There may of course be other fixed assets remaining after the first crop has been cleared. It is assumed that roads are the only assets other than the land and that these are conserva­tively valued at one half their original cost, that is 1/2(50) or £25 per ha. The expectation value of the land, LV, is then calculated thus:

LV = 205 + (25 x 0.087) + (LV x 0.087) Note: 0.087 is the discount factor for 50years at 5%.

Crop Discounted Discounted N D R Residual Residual

Road Value Land Value

LV(1 - 0.087) = 205 + 2 .2 = 207.2

207.2Therefore LV = -------------

1 -0 .0 8 7 = £227 per ha

Any expected increase in land values in real terms would be included by adjusting the land value on the right hand side of the equation.

The sum of £227 represents the expectation value o f the land per hectare at the time of planting. If there is to be a lapse of a year or two between pur­chase and planting this figure must be further discounted to account for that period. If the investor buys the land at this price, then on the stated assumptions the investment will make 5% in real terms.

It should be noted that LV depends on the felling age adopted. The land value determined in Lhis calculation is close to the maximum since the felling

15

ages assumed for the com ponent crops are those which are likely to give the maximum DR at the chosen discount rate.

The investor may wish to do this calculation using the actual expectedmarket price of land in order to determine the internal rate o f return hemight expect if he decides to go ahead with the investment. To do this he has to put the land value on the right hand side of the above equations and thereby determine the net present value (NPV) of the whole investment. The initial equation now becomes:

N PV = C ro p + Discounted + Discounted - Cost N D R Residual Residual o f

Road Value Land Value Land

If the expected m arket price of the land is £300 per ha and acquisition expenses are assumed to be £10 per ha, then the net present value at 5% in the above example is:

N PV = 205 + (25 x 0.087) + (300 x 0.087) - 310 = - 7 6 .7

Repeating this calculation at 3% and at 7% and plotting the results would show that with the price of the land at £300 the net present value would be zero at 4Zi°Ia and this is therefore the internal rate of return for the investment.

Choice of species

Site factors such as soil, vegetation and climate affect the choice o f which species to plant. As the site factors become more adverse to tree growth so the choice of species becomes restricted. It is, of course, possible to ameliorate the adverse characteristics of the soil and ground vegetation by ploughing, draining and use of fertilisers.

On some sites the decision boils down to a choice between a high yielding species such as Sitka spruce requiring a fairly intensive establishment regime and a lower yielding but less exacting species such as Lodgepole pine which can be established and maintained at considerably less expense. Elsewhere, as on the more fertile sites, there may be a choice between larch with its short establishment period and early yields and, say, Douglas fir costing much more to establish but promising a much higher yield of timber.

16

The appraisal then reduces to the comparison of the alternative levels of expenditure and consequential returns. Take, for example, the Sitka/ Lodgepole choice on an unflushed peat at an elevation of 300 m in the Scottish Borders. Table 1 shows the fertiliser/herbicide regimes expected to be required to grow Sitka Yield Class 11 (SS YC 11) or Lodgepole Yield Class 8 (LP YC 8). The initial formation (application of a PK fertiliser, ploughing, draining and planting) is expected to be the same for both species and can therefore be ignored as can the cost of roading which, in practice, is unlikely to be significantly different either in density or timing for these two options. This leaves the comparison between the additional cost of the more intensive Sitka spruce fertiliser/herbicide regime and the gain in DR for SS YC 11 as against LP YC 8. The calculation is shown in Table 2.

Table I Expenditure on alternative herbicide and fertiliser regimes for SS and LP on unflushed peats

£ per ha

Operation Sitka spruce Lodgepole pine

Discounted DiscountedYear Expenditure Expenditure Year Expenditure Expenditure

3 % 5 °7o 7% 3% 5% 1%

Apply 2,4-D 5 25 21.6 19.6 17.8 — — _ _ _PK 5 45 38.8 35.3 32.1 5 45 38.8 35.3 32.1PK 10 45 33.5 27.6 22.9 - - - - -

P - - - - 15 25 16.0 12.0 9.1N 15 40 25.7 19.2 14.5 - - - - -NP 20 60 33.2 22.6 15.5 - -

Totals 215 152.8 124.3 102.8 70 54.8 47.3 41.2

N o te: initial applications o f fertiliser before year 5 are the sam e for both species and have therefore been ignored.

Assuming both crops are to be thinned and will be felled at the age of maxi­mum DR, the DR gain can be determined from Appendix 4 and compared with the additional DE, as shown in Table 2, ensuring that both expendi­tures and revenues are in £s o f the same value. For example at 5% the gain in DR0 = Vi (385 + 2 7 0 )- 155 = £172.5.

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Table 2 Com parison o f net g a in /lo ss from choosing SS (YC 11) as against LP (YC 8)

D iscount Rate

3% 5% 7%

A dditional D E 0 98.0 77.0 61.6(from Table 1)

Gain in D R 0 402.5 172.5 77.5(from Appendix 4)

N et ga in /loss + 304.5 + 95.5 + 15.9

These results suggest that the choice of the high input regime with SS is more profitable than the low input LP at all three interest rates implying an internal rate o f return of just over 7% at which point DE = DR. However, the long-term response to a fertiliser regime in forestry cannot be defined with any certainty and in such circumstances it is essential to undertake a sensitivity analysis to determine the effect of changes in assumption about the yields from the two regimes. For example, suppose the yield class of the SS is expected to lie between 10 and 12 and that for LP between 7 and 9. As the above analysis indicates that the SS high input regime is the more profit­able, it is desirable to look at the sensitivity of the result to the lowest prob­able yield for SS (i.e. YC10) in comparison with the highest probable yield of LP (i.e. YC9). The DR0 gain, at say 5% , resulting from the use o f SS instead of LP, becomes 2 7 0 - Vi (155 + 255) = £65. This produces a net loss because the additional cost of the SS high input regime is £77 at 5% (see Table 2). This illustrates that in this appraisal the result is fairly sensitive to assumptions on yield class.

Fertilisation

Until further evidence is available on response to fertilisation in terms of volume and wood quality it is reasonable to make the assumption that the revenue gained by treatm ent can be found by reference to increase in top height over the life of the treated crop. Given an assessment o f this total increase to rotation age, it is possible to assess the change in yield class over the life o f the crop and hence the DR increase. For example the M anagement Tables show for Sitka spruce at a felling age o f say 55 years, top heights of 20.2 m for YC 10 and 22.7 m for YC 12. Hence if an increase in top height of 2.5 m is expected as a result of treatment the gain in DR can

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be assessed by comparing the DR values for YC 12 and 10. The Booklet on fertilisers in the establishment of conifers in Wales and Southern England (Everard, 1974) gives guidance on the use of fertilisers.

Appraisal o f Single Applications

Tables 3 and 4 apply only to unthinned stands, that is either pre-first thinning or non-thin regimes. For appraisal of crops already thinned it should be possible to measure the enhanced growth in terms of added volume, attribute a value to this and compare this value, suitably dis­counted to the time of the application of the fertiliser, with the cost of the applications. However, as the experimental evidence for the response to fertiliser application in pole stage and older crops is very limited, the fol­lowing discussion is confined to the appraisal of the treatm ent of younger crops.

Table 3 Gain in D R 0 per 10 cm increase in top height at age o f maximum DR

£(76/77) per ha

Yield Class 6 8 10 12 14 16

Discount Rate % 3 5 7 3 5 7 3 5 7 3 5 7 3 5 7 3 5 7

Crops to be

SS 7 3 1 9 4 2 11 5 2 13 6 3 14 7 4 15 8 5

th inned LP 6 2 1 7 3 2 8 4 3 10 5 3 11 6 4

Crop to SS 6 3 :1 7 3 2 8 4 2 9 4 3 10 5 3 11 6 4be leftun­thinned LP 5 2 11 5 3 2 6 4 2 7 4 3 8 5 3

Table 3 sets out the gain in DR at year u associated with a 10 cm increase in top height at the end of the crop’s life. For example, suppose a single appli­cation of phosphate (P) applied to SS YC 10 at age 5 is expected to lead to an increase in top height over the succeeding say 10 years, and hence over the crop’s life, o f 75 cm. Then the gain in DR0 at 5% for a thinned crop is £5 x 75/10 = £(76/77) 37.5 per ha. This figure £37.5 has to be compounded 5 years and inflated into £s of the same value as the expenditure. The DR compounded 5 years by a factor of 1.276 (from Appendix 1) and adjusted for inflation from 76/77 to 78/79 by a factor of 1.2363 (from

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Appendix 3) yields a result of 37.5 x 1.276 x 1.2363 = £(78/79)59. This compared with a cost of treatment of say £(78/79) 30 indicates that if the increase in height is achieved the investment will be profitable at 5%.

Allowance fo r Advancem ent in A ge o f First Thinning or o f Felling

Increases in growth will affect the time of certain expenditures, and hence DE. Thus in crops which are to be thinned, the age of first thinning and hence roading and brashing may well have to be brought forward. In non- thin crops the felling age may be brought forward and hence roading costs may be incurred earlier.

For thinned crops the effect on DE will be limited to the influence of res­ponses achieved before the age of first thinning. Table 4 sets out the period by which first thinning age is brought forward as a result of fertiliser res­ponses obtained by that time, or the age of felling is brought forward for non-thin crops. For example, in the case quoted above, suppose the combined cost o f roading is £200 per ha and the planned age of first thinning is 30 years (that is 4 years delay from the age indicated in the Management Tables). Then the roads element o f DE at say 5% to year 5

Table 4 Reduction in age o f first th inning/felling per 10 cm increase in top height o f Sitka spruce and Lodgepole pine

Years

Yield class 6 8 10 12 14 16

Crops to be thinned<a) .3 .2 .2 .2 .2 .2

Crops(b)3% .5 .4 .4 .3 .3 .3

to be left

5% .4 .4 .3 .3 .2 .2

unthinned 7% .4 .3 .3 .2 .2 .2

N otes: (a) Assessed by reference to responses achieved by tim e o f first thinning. These figures are independent o f discount rate because the M anagem ent Table age o f first thinning is specific to the yield class and is determined m ensurationally.(b) D iscount rate. These figures have been assessed by reference to responses over the w hole life o f the crop. The figures vary with discount rate because the age o f clear cutting (non-thin crops) is defined in this paper as the age o f m axim um D R and is therefore a function o f the rate o f discount used.

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(when the fertiliser is to be applied) amounts to £200x0.295 (discounting factor for 25 years) or £59. For a height response of 75 cm the advancement is roughly 2 years (7.5 x 0.2 from Table 4) that is from year 30 to year 28. The roads and brashing element of DE5 is £200 x 0.326 (discounting factor for 23 years) or £65. Thus the increase in DE is 6 5 -59 = £6 which therefore reduces the gain in DR5 from £(78/79) 59 to £(78/79) 53. This value still exceeds the cost of fertilising.

Where m ajor increases in growth are obtained by fertilisation, there will be cases where it is profitable to thin a crop which would otherwise be left unthinned. The appraisal is broken down into two stages. The first is to decide whether, for the Yield Class expected over the crop’s life as a result o f fertilising, thinning or no thinning is optimal, taking into consideration the main factors of bringing forward roading costs and possible changed liability to wind damage. The section on thinning (page 28) gives guidance on this point. Once the optimum thinning regime has been decided it is then simply a m atter of calculating the difference between DR net of discounted roading and comparing this difference with the discounted cost of fertilising.

Appraisal o f M ultiple Applications

The appraisal of multiple applications of fertilisers is carried out in basically the same way as for single applications. The total height gain for the set of treatments has to be predicted and expenditure on each treatment is discounted to a common point in time and summed. In practice it is desirable during the course of a crop’s life to reassess the economics of additional treatments in the light of local experience.

Sensitivity Analysis

As with the appraisal on choice of species, the results o f this calculation are likely to be sensitive to assumptions on the yield responses to fertiliser applications and therefore sensitivity analysis is desirable. For example, suppose there is a possibility o f the cost of treatment rising to £35 per ha and that the increment in top height as a result o f treatm ent might be only 50 cm over the crop’s life. The DR gain at 5% then falls below the cost of application and the investment is no longer viable at this rate of interest.

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Beating up, Weeding and Cleaning

Recent work on the pre-tax financial implications of different spacings indicates that in most circumstances planting at 2 to 2Vi m is desirable. Possibly on upland sites suffering from severe exposure the maximum spacing necessary to ensure speedy establishment may be a little less than this (Low, 1974), but in general the planting of more than 2,500 trees per hectare rarely appears to be justified.

Financial appraisal of the timing of first thinning at a range of discount rates indicates an optimum age some 5 years later than indicated in the Management Tables, except where windthrow is a significant risk (see section on thinning pp 28-32). Both the economics of the timing of first thinning and of spacing suggest that there should not be too much concern over scattered losses in a young crop providing the stocking at first thinning age is o f the order of 1,500 stems per hectare (excluding roads and rides, etc.).

Where the losses are grouped such that there will be a gap in the canopy that will endure for a large part of the life of the crop, then an appraisal of whether to beat up (or weed or clean to prevent such losses) is desirable. The loss in discounted revenue can readily be calculated from the tables in Appendix 4. In the example below the question of whether to beat up or not is considered. The appraisal of weeding or cleaning and indeed, protection, follows the same basic principles.

Assume a crop of Sitka spruce YC14 is to be appraised 2 years after planting to determine the loss in DR as a result of large gaps in the crop estimated to cover 30 per cent of the area planted. The D R0, at say 5% , expected for a thinned crop is £510 per hectare. Because the edge trees around the gap will grow more vigorously than if they had been within the stand the loss in DR will not be as high as 30 per cent. As a rough rule of thum b, a figure o f two- thirds the initial percentage is probably a satisfactory guide. Thus in this example 20 per cent of the DR0 value is £102 and this represents the loss per planted hectare at year 0. It might be thought that this figure should be com pounded forward, in this example to year 2, but this would only be appropriate if the beaten up plants were to grow faster than the initial planting and so make up for lost time (by not compounding forward some allowance is being made for the likely actual growth). In the case o f weeding or cleaning, the DR0 should be com pounded forward to the year of operation concerned.

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In order to compare the estimated DR loss with the current cost of beating up (or weeding or cleaning) the former has to be brought into £s of the same year using the appropriate factor from Appendix 3. When estimating the costs involved it must not be forgotten that beating up may lengthen the period of establishment and additional weeding costs, suitably discounted, may also have to be allowed for.

Protection

In most examples of investment appraisal presented so far the physical consequences of a given course of action are more or less readily predictable, the volume yields, tree sizes and other features being assessed from sample plots and experiments. In the case of protection from animals, insects, fungi and man, the degree of damage by a particular agent is liable to be peculiar to the locality and crop and to be sporadic. Estimation of the probable damage for a given crop, degree of protection and external cir­cumstances is the m ajor difficulty in appraisal. A great deal depends, therefore, on the experience of the local maifager, and the role o f judgement in deciding the most favoured level of protection is far greater than in many other fields of applied forest economics.

The aim o f maximising NDR means that it is worth spending up to the point when an extra £1 of expenditure produces only £ l ’s worth of benefit. In the case o f protection, the benefit is the reduction in losses. The rate of reduction in the value of losses just equals the rate of increase in expenditure at a point when the sum of the losses plus the expenditure is at a minimum. This concept of minimising the sum of costs plus losses is the basis for the first example below. The examples illustrate appraisal techniques where the value of loss is confined to reduction in wood revenue. There will, however, be cases in which values over and above wood production are considered im portant, in which case these should be incorporated in the appraisal.

One of the simplest ways of arriving at an approximate optimum level of expenditure is to consider a number of options (for example, a complete deer fence, or a full-time stalker, or regular shoots) and to estimate the probable level of damage associated with each option. This is easier said than done, but experience should enable plausible estimates to be made of the range o f damage that might be expected to result from a particular course o f action.

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These levels of damage must be converted into loss in DR. This can be done with some precision by, for example, determining the likely number o f trees which will be damaged and converting this into terms of loss of thinning yield and thence to revenue and DR. An easier and probably just as accurate method is to assess the damage in terms of delay in establishment an d /o r as the percentage o f the crop lost over the life of the stand and to convert these into a reduction in DR by reference to the figures in Appendix 4. Having established the costs and losses associated with various options, which should always include the possibility of doing nothing, it is then only necessary to determine which option minimises the sum of the costs plus losses.

Suppose, for example, that within a 500 hectare block o f conifers that has just moved into the thinning stage, 50 hectares o f m ature Sitka spruce have been clear felled and this area is to be replanted with SS with an expected yield class o f 12. The ring fence round the whole block is in reasonable condition but there are a few breaks and deer are known to be in the block but not doing any damage to the pole stage crop. However, it is expected that they would almost certainly damage any restocking. Four options might be considered:

A. No action—only 80 per cent of area established and then only after a delay of 10 years;

B. Employ contract stalker when deer causing damage, at a cost of £500 per annum (net of any income from sale of venison etc.) and leave Vi hectare unplanted as a deer lawn—only 49 'A hectare planted, 10 per cent of which fails to become established;

C. Deer fence 50 hectare block at cost of £5,000 plus £50 per annum for maintenance for 10 years—5 per cent o f area lost;

D. Repair and maintain existing fence around 500 hectare block at an initial cost of £500 plus £200 per annum maintenance for the next 10 years (in practice the fence would be repaired intermittently) and employ part-tim e stalker for 4 months a year at a total cost (net of any income) of £1,300 per annum —full crop established.

From Appendix 4, DR0 values for SS YC12 are £1,005, 385 and 170 at 3, 5 and 7°7o respectively. The costs plus losses of the four options are set out in Table 5.

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Table 5 Com parison o f four wildlife protection options

£

Option A B C D

C osts Year 0 5000 500

1 -1 0 — 500 50 1500

D E 0 at 3% — 4265 5427 • 13295

5% — 3861 5386 12083

7% — 3512 5351 11035

L osses 20% D R plus 10 years delay

10% DR plus '/2 ha unplanted

5% DR —

D R 0 at 3% 5 0 x 1005x [1 - (0 .8 x 0 .7 7 4 ) ] = 19135

491/2 (1 0 0 5 x 0 .1 )

= 5477

50 (1 0 0 5 x 0 .0 5 )

= 2513

5% 5 0 x 385 x [1 - (0 .8 x 0 .6 1 4 )1 = 9794

491/2 (3 8 5 x 0 .1 )

= 2098

50 (3 8 5 x 0 .0 5 )

= 962

7% 50 x 170x [1 - (0 .8 x 0 .5 0 8 )1 = 5046

491/2 (1 7 0 x 0 .1 )

= 927

50 (1 7 0 x 0 .0 5 )

= 425

C osts p lu s lossesN P V 0 at 3% 19135 9742 7940 13295

5% 9794 5959 6348 12083

7% 6975 4439 5776 11035

N ote: Figures in b o ld typ e indicate the least (cost + loss) at each test d iscount rate.

As might be expected the choice of option varies to some extent with the dis­count rate; it will of course be desirable to test the sensitivity of the choice to both the cost and loss assumptions.

The same concept of minimising costs plus losses applies equally to fire protection, but there is then the added complication that if the area burnt is sufficiently large it may warrant immediate replanting. It may even reopen the question of desirable land use, but in most circumstances a change in land use as a result o f fire is unlikely. Assuming that the area burnt will be replanted then the cost of damage can be calculated as:

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The revenue loss through postponem ent of yield as a result o f having to replant, plus the initial restocking cost, less costs of operations no longer required (for example, fencing) less postponem ent of expenditures not now required until later as a result of having to replant (for. example, roading) less value of salvage.

In symbols, the value of loss equalsp [D R0 (k" - 1) + DEo-n - X - DEn-r (1 - k 'n) - S]

DR foregone Restocking Postponem ent Valuen years costs less o f later o f any

+ operations — expenditures — salvageno longer n yearsrequired

where p = probability o f the plantation being burnt at year nn = average age o f plantation likely to burnf = felling ageD E 0-n = initial expenditure until time that plantation is burnt X = discounted cost to year 0 o f operations no longer required in the estab­

lishment o f a new crop DEn-r = expenditure that would have been incurred from age n to time o f felling k = com pounding factor for n years to bring D R 0 to D R nS = salvage value o f burnt crop (if any)

Multiplying the value of loss at any given age by the probability of loss gives expected average loss. The cost of operations such as fire patrols, road building and provision of water tanks has then to be assessed together with the associated probabilities of damage. Thus the relationship might be as shown in Table 6.

Table 6 Com parison o f five fire protection options

Option A B C D E

(a) protection expenditure £/h ectare/p er annum

0 0.25 0.50 0.75 1.00

(b) probability o f losing plantation by fire in an average year

.010 .002 .001 .0007 .0005

(c) value o f loss,say £500 per hectare times probability (b)

5.00 1.00 0.50 0.35 0.25

(d) Total cost plus loss (a + c)

5.00 1.25 1.00 1.10 1.25

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These results suggest that, in this example, expenditure in the region of 50p a year per hectare results in minimising costs plus losses. However, this is only an illustration and the figures should not be given any more credence than that. The m ajor problem is the derivation of the probabilities related to the different levels of expenditure. Only experience can help here and even then it is specific to the vegetation and locality (the hazard and risk) of the area in question.

Roading

The subjects of road standard and road spacing are discussed in Rowan (1976) with illustrations of the method of appraising different lengths and types of road in a given block. The calculations on harvesting roads refer to roading just before the start of thinning but there is no reason why the appraisal should not relate to different times of road construction such as the time of establishment. It is assumed that the aim is to minimise the sum of road construction and discounted maintenance costs plus the discounted costs of loading, moving and unloading the trees harvested over the crop’s life. In order to simplify the calculation, an average cost of extraction per cubic metre is nominated for the removal of all thinnings and the final felling. Then instead of calculating the relevant extraction costs for each and every cut, discounting these to the time of roading and summing them, the short-cut procedure is adopted of multiplying the nominated extraction cost by discounted volume (DV). The tables in Appendix 5 show discounted volume for thinned stands (after a 15 per cent reduction for gaps, roads etc.) calculated at 3, 5 and 7% to year 0. For any later year of roading up to the age of first thinning, the figures should be compounded using the factors in Appendix 1. If roading is delayed until after first thinning, the discounted volume is influenced by the am ount of thinning already carried out, and for working purposes the discounted volume from remaining thinnings and final crop can be estimated sufficiently accurately by inter­polation between the DV calculated to the year of first thinning and the final crop yield. Thus for Sitka spruce YC14, first thinning and roading are planned in, say, year 22, DV0 at 5% =77 (from Appendix 5) which com­pounded forward 22 years equals 225. The final crop yield at age 50 from the M anagement Tables, is 371 (main crop) plus 45 (thinnings) or 416 cu m per ha; and after adjustm ent for 15 per cent gaps, equals 354 cu m per ha. If roading is being appraised at age 35, 13 years after the Management Table age o f first thinning, the discounted volume equals 225 + 13/28 x (354-225) = 285 cu m per ha. The fraction 13/28 represents the period from the Management Table age o f first thinning to the time of

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roading (assuming thinning has gone on in the interim period) divided by the interval between first thinning and clearfelling.

M ost woodlands contain a range of yield classes and ages and there is usually more than one species. An adequate measure of discounted volume can be found by averaging yield class (a worked example is provided by Rowan) and planting year and then referring to the discounted volume table for the dom inant species and compounding up for the average age of the block.

Thinning

Thinning practice has long been the subject of fierce debate and will no doubt continue to be so. If crops are to be thinned, and that may well be the issue to be resolved, there are choices to be made on the age of first thinning, the intensity of thinning, the thinning cycle, the type of thinning (selective, namely crown or low, or systematic) and the age at which thinning should cease. The answers to each of these will depend on such fac­tors as the owner’s objectives, the markets available at the time and likely to be available in the future, the quality of the stand, its liability to wind damage and the implication of the terrain for harvesting methods and hence cost. This account is not intended as a treatise on these and other aspects of thinning that may concern the woodland owner but instead is intended to serve as a guide to the m ajor issue of whether to thin and, if so, when. The Forestry Commission’s M anagement Tables* (1971, Part II) discusses thinning policy in terms of intensity, cycle (and hence weight) and type. The intensity o f thinning, or annual am ount removed per hectare, is set in the Tables at 70 per cent of the yield class. This rate has been calculated to be on the slightly conservative side of the optimum if the aim is to maximise NDR at discount rates of between 3 and 5% . A higher intensity may be favoured if the owner is impatient to gain more revenue in the near future, but such cutting runs the risk of reducing the growing stock to a point at which less than full volume increment is produced. The following discussion therefore assumes the M anagement Table intensity and concentrates on the issue of time o f thinning.

’ These Tables will be reproduced by the Forestry Com m ission during 1981 in a new form at— Y ield M o d e ls f o r F orest M anagem ent.

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Inspection of the figures for DR0 in Appendix 4 shows that at lower yield classes in all the main conifer species, the discounted revenue expected from a stand first thinned at the age noted in the M anagement Tables is less than that of an unthinned crop, allowance for mortality having been made in the yield tables on which these DR results are based. This is because small early thinnings are assumed to be unprofitable (see price-size schedule in Appendix 2). The tables of Appendix 4 are intended as a guide for com­parisons between species, taking account of broad differences between dis­counted revenues from thinning and no-thinning, at the time of planting. They do not however provide guidance on the optimum timing of thinning. Recently produced yield models for the main conifer species covering line thinning o f crops with thinning at Management Tables time (MTT), 5 years later than these ages (MT plus 5) and 10 years later (MT plus 10) show that with the price-size curve o f Figure 1 higher values of DR can often be obtained with some delay in the start of thinning.

This effect would be offset if higher prices (of the order o f £2 to 5 per cu m depending on yield class) were obtained for trees of around 0.04 cu m (Figure 1 assumes a net loss of £1 per cu m for trees of this size). Conversely lower prices for small trees make a later start to thinning relatively more profitable assuming that the risk of windthrow is not such as to make a delay in first thinning unacceptable. Further, where crops are unroaded, delay in installing roads is attractive and when the costs of roading are taken into account the maximum DR net of road costs and, where applicable, brashing costs, arises at later ages than apply in crops which are already roaded. Because of the variety of thinning regimes that can be applied, differences in the price of thinnings of various sizes from place to place, and differences in the costs of access and risk of windthrow, it is difficult to make general rules about the course of management which is likely to pro­duce maximum net discounted revenue. However, given some assumptions about these factors and with the aid o f some generalised tables, it is possible to calculate the most profitable course of action.

Figure 3 shows the general relationship of thinning regimes to yield class and to windthrow hazard (Booth, 1977) whilst Appendix 6 sets out values of discounted revenue for Sitka spruce calculated to the age of first thinning of the M anagement Tables for the three discount rates 3, 5 and 7% assuming the price-size curve o f Figure 1. The time to which values are discounted has no relative effect on the results as long as it is the same for all the regimes being compared. However, as appraisal will normally be carried out towards the M anagement Table time (MTT) o f first thinning (see Appendix 8), it is sensible to use this as the point to which values are discounted.

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Figure 3 Relationship o f thinning regime to yield class and windthrow hazard

M TT = M anagement Table time o f first thinning MT + 5 = Delay first thinning 5 years M T + 10== Delay first thinning 10 years.

The example in Table 7 calculates the optimum time for first thinning at a discount rate of 5% for an unroaded area of SS YC 12 in which the total cost of roading is £150 per hectare and road m aintenance is expected to am ount to £1.5 per hectare per year thereafter.

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Table 7 Determination o f optimum time o f first thinning for Sitka spruce Y C 12

M anagem ent regime option

SITKA SPR U C E YC 12 A ge at first thinning A ge at felling

D iscount rate 5% Time o f roadingYears o f road maintenance

MTT

24552431

M T + 5 yrs

29552926

M T + 10 yrs

34553421

Non-thin

4545

A . Discounted revenue to M anagem ent Table age o f first thinning (24 years) from Appendix 6

(a)1230 1295 1280

(a)1090

B. Calculation o f discounted expenditure^) per ha (to MT age o f first thinning)

1. Capital road cost per ha 150 150 150 150

2. Capitalised road maintenance annual cost o f £1.5 per ha from time o f first thinning to time o f clear felling 23 22 19 0

3. D elay (X years) o f roading compared with MT age o f first thinning 0 5 10 21

4. D iscount factor for X years 1 0.784 0.614 0.359

5. Total capitalised road cost discounted to MT age o f first thin [(1 + 2 ) x 4] = variable DE 173 135 104 54

C. N D R = (A -B 5 ) 1057 1160 1176 1036

N o te: (a) These figures differ slightly from the Appendix 4 D R 0 values com pounded for­ward 24 years, because the results in Appendix 6 have been sm oothed across yield classes.(b) Brashing costs are assumed to be zero since the DRs are derived from yield models which assume the first thinning is a line thinning.

In the example, maximum NDR occurs with thinning starting 5 to 10 years later (MT + 5 to 10) than the age of 24 implied by the Management Tables.

Appraisal of the decision on timing o f thinning is often complicated by the presence in a block of a number of different species, ages of plantation and yield classes. In most cases it is adequate to adopt a single calculation based on a weighted average assumption for age of first thinning, yield class and hence DR, using area of each crop as the weight.

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A llow ing fo r W indthrow R isk

The values in row A o f the calculation will be significantly different where the hazard of windthrow is high. Objective knowledge o f how windthrow risk changes with the age o f a stand and with different heights and kinds of first thinning is at present almost entirely restricted to Sitka spruce. For this species, estimates have been made of the height at which windthrow may on average be expected to start in a crop of a given W indthrow H azard Class (Booth 1977). In addition, assessments of the rate of progress o f wind damage with different treatments has been made which allow the ‘terminal height’ to be estimated. This is the height at which it is judged such signifi­cant damage has occurred that felling of the crop is justified. A loss of about one-third o f the growing stock appears to be a reasonable measure of this point. Table 8 sets out some broad estimates of term inal heights for Sitka spruce.

Table 8 Provisional estimates o f terminal heights for M T age o f thinning and for non-thin: Sitka spruce

W indthrow Hazard Class III IV V VI

Onset height, metresTerminal height, metres: M T A ge o f First

19 16 13 10

Thinning 24 20 16 12Terminal height, metres: Non-thin 27 23 19 15

Given assumptions on terminal height it is a simple m atter to find the ages implied in different yield classes and to calculate the expected discounted revenues to these ages. Using the lay-out of Table 8, it is then possible to make an objective decision, for Sitka spruce at least, about the best thinning practice in areas subject to windthrow. It must be added however that these figures are based on limited evidence from silvicultural experiments and should be regarded as only indicative.

The type of first thinning (selective or systematic) has an effect on DR apart from changed liability to wind damage (Ham ilton, 1980). When allowance is m ade for the reduced harvesting costs in line-thinned crops and the lower cost o f access through inspection racks as opposed to brashing, available inform ation on yields indicates that where the risk of windthrow is negligible or slight, line thinning is more profitable in Sitka spruce, Norway spruce and Douglas fir, that line thinning or low thinning are about equally profitable in Scots pine and Corsican pine and that low thinning is favoured

32

in Lodgepole pine and Japanese larch. Where there is risk of windthrow the desirable treatm ent is less clear cut and no general guidance is possible at present.

Timing of Felling and Crop Replacement

The optimum felling age is defined here as the age when the net discounted revenue from the existing and successor crops combined is maximised. The implication of fixing felling age by reference to maximum NDR at a given discount rate is that the current rate of return on capital, represented by growing stock and land, equals the chosen interest rate at that age.

The curve o f NDR against felling age is fairly flat near the point of culmin­ation and therefore the value of NDR is insensitive to changes in felling age within a range o f plus or minus 5 years or so. Local marketing opportunities should influence the actual timing of the felling, higher than normal prices advancing the timing and a short-term m arket recession delaying it. Other considerations such as taxation, sporting and landscaping may well have an overriding effect on the timing of clear felling.

Where the successor crop NDR (including allowance for land value) is 0, that is the successor crop makes a return just equal to the discount rate, then the felling ages are as shown in Appendix 7. When the successor crop is expected to make a large positive NDR then some degree of advancement of felling age is justified on economic grounds.

The general rule is that a positive successor crop of NDR of up to £200 per ha will not advance the economic optimum felling age shown in Appendix 7 by more than 5 years and it is not until the successor crop NDR is more than £500 per ha that the felling age of the existing crop is advanced by between 5 and 10 years. The actual values vary with species, yield class and discount rate and can be specifically determined using the data in Appendix 4.

A sufficiently close estimate o f the successor crop NDR can be found by deducting from the DR value shown in Appendix 4 the sum of the undis­counted form ation costs. Fixed costs, such as protection and forest and road maintenance expenditure which apply whether the current crop is felled now or at some future date, can be ignored. There may be some post­establishment costs such as those of cleaning and brashing. These have only a small effect on optimum replacement ages and can normally also be ignored. The form ation costs used should be those locally applicable, including preparation of ground, redraining, planting, beating-up and

33

weeding, inclusive of labour oncost. For example, if the successor crop is Corsican pine YC14 (thinned), reference to Appendix 4 shows that the DR at say 5% is £505 per ha. Assuming total form ation costs are £250 per ha, the successor crop NDR is £255 per ha, implying that the existing crop should be felled some 5 years earlier than the age given in Appendix 7.

Frequently the clearfelling of one stand has to be linked with that of a neighbour, whether for reasons of extraction or to reduce windthrow risk. In such cases the NDR for the whole felling coupe should be calculated for a series of felling ages in order to obtain the optimum. However, a reasonable approxim ation may be calculated by taking a weighted average (using area) o f the individual felling ages.

Replacement o f Unsatisfactory Crops

It does not follow that because a crop is judged to be unsatisfactory on silvicultural grounds, for example, poorly stocked, unhealthy or of lower growth rate than an alternative species, it should be replaced at the earliest opportunity. Unless considerations of forest hygiene demand the early removal of a source of potential infection it will often be more profitable to keep an unsatisfactory crop on the ground than to clearfell and replace it at an early stage. Once past the establishment phase, quite poor crops will often be capable of growth in value which places them at an advantage compared with replacement crops requiring new investment before they can produce any greater contributions to revenue. This point applies equally to broadleaves (where these are not being retained for amenity reasons alone) or when considering whether to accept natural regeneration or to replace it by planting another species or provenance.

Further, of two stands which are growing at different rates, it will not necessarily be true that the slower growing one should be replaced first. It may well be that the faster growing crop occupies a better site on which an alternative species would be relatively much more profitable than the alternative species on the poorer site.

Premature Felling in Anticipation o f Windthrow

In some parts of the country there is a high risk of crops being blown down before they reach the age of economic maturity. Because of the costs associ­

34

ated with windthrow it is often considered desirable to fell crops prema­turely before they become too vulnerable. The problem is to determine how vulnerable a crop needs to be before it is worth considering premature fel­ling given various assumptions on the cost of windthrow.

Allowing windthrow to happen rather than felling prematurely has two potential disadvantages:

i. the volume recovered after windthrow may be less than the amount expected if the crop had remained standing, either through snapping of the stems or through a loss of production pending clearance of the site;

ii. the surplus value per cubic metre may be reduced because of increased harvesting costs and, in the case of large windthrows, owing to depressed prices in m arkets, increased transport costs and the managerial costs of reorganising harvesting and marketing.

These effects can be expressed as a percentage reduction in volume har­vested and as a penalty in pence per cubic metre, the latter being a com­bination of the reduction in timber value and increased harvesting costs.

On the other hand, premature felling can result in a considerable reduction in revenue, depending upon the age of the crop. It is not worth felling prematurely unless the cost o f windthrow times the probability of wind­throw actually happening exceeds the revenue foregone as a result of prema­ture felling. It is therefore necessary to compare the revenue foregone from felling prematurely by a number of years, with the cost of windthrow. As windthrow is not a certainty this latter cost must be multiplied by the probability (which must lie between 0 and 100 per cent) of windthrow actually occurring during that period.

Appraisals have been undertaken on Sitka spruce, assuming reductions in volume harvested of up to 10 per cent and harvesting cost and timber value penalties o f up to £1 per cubic metre, to assess the magnitude of the probability required to warrant premature felling. At a discount rate of 5% , the results show that premature felling 5 years earlier than the age shown in Appendix 7 requires a probability of windthrow of the order of 20 to 50 per cent during the next 5 years o f the crop’s life, depending on the loss of volume and increase in harvesting costs etc. expected as a result of wind­throw. Prem ature felling by as much as 10 years requires a probability of windthrow in the next 5 years of more than 50 per cent. A 3% discount rate would increase the required probability and a 7% rate would reduce it. As

35

the assessment of the probability o f windthrow is highly subjective, precise calculations o f predicted loss of volume, additional harvesting costs and reduction in timber values, and hence the probability required to advance felling age, are hardly justified, but some working rules such as those indi­cated may be useful.

References

Booth, J C (1977) Windthrow hazard classification Forestry Commission Research Inform ation Note 22/77/SILN .

Busby, R J N (1974) Forest site yield guide to Upland Britain Forestry Commission Forest Record 97, HMSO, London.

Edwards, P N and Christie, J M (1981) Yield models fo r fo rest man­agement Forestry Commission Booklet 48, Forestry Commission, Edinburgh.

Everard, J E (1974) Fertilisers in the establishment o f conifers in Wales and Southern England Forestry Commission Booklet 41, HMSO, London.

Ham ilton, G J (1980) Line thinning Forestry Commission Leaflet 77, HM SO, London.

H am ilton, G J and Christie, J M (1971) Forest management tables (metric) Forestry Commission Booklet 34, HM SO, London.

H am ilton, G J and Christie, J M (1974) Influence o f spacing on crop characteristics and yield Forestry Commission Bulletin 52, HMSO, London.

Low, A J (1974) Initial spacing in relation to establishment and early growth o f conifer plantations Research and Development Paper 110, Forestry Commission.

Rowan, A A (1976) Forest road planning Forestry Commission Booklet 43, HM SO, London.

Further reading

Blatchford, O N (Editor) (1978) Forestry practice 9th Edition, Forestry Commission Bulletin 14, HMSO, London.

36

G arforth, M F (1979) Mixtures of Sitka spruce and Lodgepole pine in South Scotland: history and future management Scottish Forestry 33(1).

H art, C E (1979) Private Woodlands: a guide to British timber prices and forestry costings H art, Coleford.

H am ilton, G J (1976) Aspects o f thinning, Forestry Commission Bulletin 55, HMSO, London.

Johnston, D R, Grayson, A J and Bradley R T (1967) Forest planning Faber, London.

M cIntosh, R (1978) Response of Sitka spruce to remedial fertilisation in Galloway Scottish Forestry 32(4).

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Forestry Commission Booklet 47 £3.75

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