0209-B1

A Method of Estimating the most Profitable Thinning Degree

Mikael Grut^[1]

Abstract

It is suggested that if a reduction in the grade of an individual thinning results in an increase in the value of the stand immediately before the next cutting, and if that increase is big enough to yield a rate of return on the forfeited thinning revenue which is greater than the alternative rate of return that the forest owner can get on other investments of comparable risk, then the thinning degree should be thus reduced; otherwise not. This marginal analysis method can be incorporated in computer programmes that assist in the preparation of forest management plans.

1. Introduction

1.1 Before the computer age, an optimal thinning regime was generally estimated for each forest type, region and site quality by - at best - calculating the profitability in terms of rate of return or net discounted revenue for various regimes which seemed reasonable from a silvicultural or other point of view, and then selecting the most profitable of those regimes. This had several disadvantages. First, there are hundreds of regimes which are acceptable from the silvicultural and other points of view, and the likelihood that the economically optimal regime would be found with the above hit-or-miss approach is remote. Secondly, to have a “one size fits all” thinning regime for a certain forest type, site quality and region, from forest to forest and from year to year, that is a strait-jacket. Today, with the advent of cheap computing power, we can do better. Below, one method of calculating the economically optimal degree for each individual thinning is described.

2. The Method

2.1 As we consider different degrees for a particular thinning, beginning with the heaviest one which we judge permissible (too heavy thinnings encourage weed growth and windthrow), each lighter degree will entail some loss of thinning revenue. This loss should be weighed against the change in the stand value immediately before the next thinning, or before the clearfelling if no further thinnings are planned. If the estimated future stand value increases when we move to a lighter thinning degree, and if the increase exceeds the thinning revenue loss compounded to the same future point in time at the rate which we can obtain for alternative investments of comparable risk, then the lighter of the two thinning degrees is more profitable. That degree is then compared with the next lighter one etc., until one is found beyond which further reduction of the thinning degree is not profitable.

2.2 The example in Table 1 below illustrates this method. In that example it is assumed that the thinning degree is expressed in percentage of trees removed; that the heaviest permissible thinning degree is considered to be 50%, and the lightest acceptable degree 20%; that the alternative rate of return is 8% p.a., and that the next thinning is expected to take place in 10 years’ time.

2.3 In Table 1, if the thinning degree is reduced from 50 to 40 per cent, the thinning revenue is reduced from €660 to €420 per hectare, i.e. by €240 (per ha). This can be regarded as an investment. The benefit resulting from that investment is that the value of the stand immediately before the next thinning in 10 years’ time is expected to be €600 greater than it would be with a 50% thinning. An investment of €240 which results in a benefit of €600 ten years’ later has a rate of return of 9.6%, which is higher than we could get in a comparable investment elsewhere. So it is worth reducing the thinning grade from 50 to 40 per cent. In the table this is shown by giving the value of the forfeited thinning revenue (Column 3) compounded by 8% over 10 years (Col. 4), and showing (Col. 7) that it is smaller than the resulting increase in the stand value (Col. 6).

Table 1: Estimating the most profitable thinning degree

2.4 However, when we reduce the thinning degree further from 40 to 30 per cent, the future estimated stand value (in this example) goes down, so we have a lose-lose situation, and it is obvious that this reduction in the thinning degree is not profitable. This conclusion is quantified in Col. 7 in which it is shown that the change in the stand value (-€100) plus the compounded loss of thinning revenue (-€389) has gone from positive (€82/ha) when the thinning degree was reduced from 50 to 40 per cent, to negative (-€489/ha) when the thinning degree was reduced a further step from 40 to 30 per cent. So, of the thinning degrees investigated in Table 1, 40% is obviously the most profitable, whether by that we mean that it yields the highest marginal rate of return, or that it yields the highest compounded money profit.

2.5 If - deviating for a moment from Table 1 - the reduction in the thinning degree from 40 to 30 per cent had resulted in an increased future stand value of €5000/ha, the figures in Columns 6 and 7 would have been respectively €400 and €11, and the thinning degree reduction would have been profitable in the sense that the rate of return on the investment would still have exceeded 8%. It is true that the marginal profit per hectare of the last thinning degree reduction would have decreased from €82 (Col.7) to €11, but even this last step would add something to the total money profit. If, however, we seek to maximise the rate of return, not the money profit (“net compounded revenue” or “net discounted revenue”), we should select the 40% thinning, because that is where the rate of return is maximised: reducing the thinning degree from 50 to 40 per cent yields a rate of return of 9.6% (see para 2.3 above), whereas reducing the thinning degree further from 40 to 30 per cent yields - even if the future stand value increases by €400 as assumed in this deviation from Table 1 - a rate of return of “only” 8.3% (€180 x 1.0831¹⁰ = €400).

2.6 There is a voluminous literature on whether we should maximise the rate of return or the money profit. Here it will be assumed that the forest owner will want to maximise the money profit, because we cannot “use” percentages. In that case, we should go on reducing the thinning degree as long as each reduction yields a benefit which is higher than the compounded cost, as shown above, especially in Column 7. Another way of saying the same thing is that we should maximise the sum of the stand value and the compounded thinning revenue (Col. 8). In Table 1 this sum reaches a maximum of €5507 with a 40% thinning. In the deviation from Table 1 discussed in para 2.5 above, the sum reaches a maximum of €5518 with a 30% thinning, which is thus in that case the degree which should be selected. The fact that a 50% thinning is associated with a value of €5425 in Col. 8 of Table 1, whereas a 40% thinning is associated with a value of €5507, means that by reducing the thinning degree from 50 to 40 per cent, we make a profit of €5507 - €5425 = €82 per hectare, i.e. the value shown in Col.7.

2.7 If we want to determine the thinning degree in more detail, we can of course do the calculation for intervals of 5% or even 1%. In practice we will often find that when we reduce the thinning grade below the heaviest allowable one, the estimated value of the stand before the next thinning does not increase at all, or the increase is not enough to yield an acceptable rate of return on the thinning revenue loss. I.e., we will often find that the heaviest allowable thinning grade is the most profitable one. That does not mean that there is something wrong with the method, it means that the heaviest allowable thinning grades generally are the most profitable ones.

3. Testing the method

3.1 It seems logical to maximise the profit from each thinning in the above way. But can we be sure that this stepwise approach will always maximise profits over the whole rotation? Is it not possible that we can sometimes gain a bigger overall profit if we sacrifice some profit along the way? (Though it may be risky to make such sacrifices, considering how much costs and prices may change later during the rotation period.) The method was therefore tested for 727 different combinations of site index, interest rate (8, 10 and 12 per cent), planting espacement, costs and timber values; for plantations of Pinus radiata in South Africa, for which a computerised yield model is available. For each of the 727 combinations the most profitable thinning programme was first calculated step by step for the whole rotation in the above-mentioned way. Then the net discounted revenue was calculated for each combination with just about every conceivable reasonable thinning programme, and the programme yielding the highest net discounted revenue was considered to be the most profitable one.

3.2 Altogether the net discounted revenue was calculated for some 364,000 different thinning programmes, i.e. about 500 programmes for each combination. This was thus a trial-or-error approach, requiring an enormous amount of computing time. It was found that the average of the 727 net discounted revenues calculated by means of the systematic step-wise method described in this article was 97.5% of the average of the 727 best net discounted revenues calculated by means of the trial-or-error “method”. Not only does the hit-or-miss approach require enormously much more computing time than the systematic step-wise method, but it is also much less flexible because it applies to the whole thinning programme, from the first thinning to the last one; during that long time prices and costs can change radically, requiring modifications of the overall programme, and the step-wise method can cope more easily with that.

4. Applicability of the method

4.1 Before the computer era this method would only have been of academic interest. To estimate the rates of return of the thinning revenue losses resulting from successive reductions of the thinning degree, would have been unthinkably time-consuming. Today, however, this method can be incorporated in computer programmes assisting in the preparation of forest management plans (working plans), provided these computer programmes contain yield models for the different species or species mixtures in the management plan area. For every forest management plan, the required costs, prices, alternative interest rate, proposed thinning ages, and thinning degree intervals to be tested (e.g. 5 or 10 per cent) would be entered as inputs.

4.2 The optimal degree of each individual thinning is of course dependent not only on its profitability, but also on the maximum allowable annual volume yield from the management plan area, on the minimum volume required by industries and in contracts, and by considerations of weed growth, windthrow, fire risk, stem form, wood quality and other factors. However, these considerations can also be incorporated in the computer model. The fact that the considerations are many is no reason for “copping out” and not even trying to including any of them. These computer models, like the medieval cathedrals, take a long time to build; in fact longer, because the models are never finished, but will always need further tinkering and improvement.