3. The economic model

#### 3.1 The objective

We assume that an investor has a capital that can be invested in a forest and that the required conditions (commitment to good management over 30 years) are then

Assessment of the Impacts of an Inheritance Taxation Relief on the Profitability… DOI: http://dx.doi.org/10.5772/intechopen.101380

satisfied to benefit from the 75% deduction for inheritance tax. This capital can also be used for an alternative investment (forest without the commitment of good management, finance, real estate, etc.). To facilitate the understanding of the analysis, we assume that the investments provide the same return without this inheritance tax. Our objective is to quantify this benefit of the partial exemption from this tax in terms of additional profitability, depending on the general inheritance tax rate, the time horizon, and the current age of the investor.

#### 3.2 Assumptions on tax rates and wealth growth

We use here the current (2021) inheritance tax rates in France. The practical details have been simplified over the last 30 years (see [15]) since the marginal tax rates are now the same for the transmissions between (a) parents and children, (b) parents and grandchildren, and (c) parents and great-grandchildren. On the other hand, an exemption from inheritance tax applies for the first euros according to the degree of parenthood (respectively (a) €100,000, (b) €31,865, and (c) €5,310). Depending on the total value of the inherited wealth, this exemption is likely to change the marginal tax rate of the forest, but for simplicity, we assume that this is not the case (otherwise, the numerical results are only slightly changed, since the difference between these marginal rates is relatively small, 5% or 10%).

The tax rates, after the aforementioned partial exemption, are presented in Table 1 (source: e.g., Le Particulier, 1183, July–August 2021). We will use these different marginal tax rates in the following sections.

To simplify the presentation of the results, we assume that these rates will remain the same in the future. We also assume that the overall value of the estate held by the heir(s) concerned by the forest may change in the future, but without involving a change in these marginal tax rates, so that successive heirs face the same marginal tax rates.

We will assume that the annual return on capital invested in and out of the forest, regardless of inheritance tax, is constant and equal to r. The annual returns are capitalized (added to the capital) and the value of the capital, therefore, grows regularly at the rate of r, except in the case of payment of inheritance tax, in which case the tax is deducted from the capital transmitted. Furthermore, the nature of the investment (forest or non-forest) is assumed not to change in the future.


#### Table 1.

Marginal tax rate according to the amount of wealth transferred to the heir under consideration, after exemption of the first euros (see text).

Future values are discounted at a constant rate of a. To simplify the interpretation of the results, and thus assuming that forest owners are perfect altruists, we do not change the discount rate when an inheritance occurs. Numerically, if we take a = r, this leads to a present value of capital that is constant excluding inheritance taxes. Numerically, we use r = 4% (for the forest this corresponds to the results of [18] and a = 4% (see e.g., [25–27]).

#### 3.3 The importance of the inheritance tax

The model of the evolution of the wealth subject to inheritance tax is presented in more detail in Appendix 2. The results make it possible to construct Figure 7, in which we present the percentage of the wealth that will be used to pay this inheritance tax over the next 20 years, depending on the marginal tax rate and whether or not the partial allowance is obtained.

We can then deduce the additional profitability induced by this partial inheritance tax relief, which we express in terms of additional annual growth of the capital invested (Figures 8 and 9). Obviously, this interest in the allowance is closely linked to the marginal tax rate, i.e., indirectly, to the capital transmitted to each heir. It is also closely linked to the age of the current owner (Figure 8) and to the considered time horizon (Figure 9).

The rate is higher when the current owner is older (the transmission is closer, so the benefit obtained from this abatement is relatively greater, due to discounting). In the case of a relatively old investor, it is more important when the horizon of the calculation is not very distant, as we see in the Figure 9.

Whatever the tax rate, Figure 9 shows that this exemption first increases, then decreases according to the time horizon considered, taking a maximum between 25 and 30 years, for an owner who is 70 years old: for a short time horizon, he/she has little probability of dying before this time horizon, and the advantage provided by this abatement is not very significant. For a long time horizon, the successive transmissions are smoothed out over a longer period of time, and likewise the advantage provided by this abatement.

#### Figure 7.

On the x-axis, the age of the owner (of the forest or of the investment); on the y-axis, the share of this wealth represented by the inheritance tax to be paid over the next 20 years. Curves with squares: without tax abatement. Curves with triangles: with partial tax abatement (Monichon). Solid curve: marginal tax rate: 45%; dashed: 30%; dotted: 15%.

Assessment of the Impacts of an Inheritance Taxation Relief on the Profitability… DOI: http://dx.doi.org/10.5772/intechopen.101380

#### Figure 8.

For a time horizon of 20 years: on the x-axis, the age of the owner; on the y-axis, the equivalent investment performance increase (in yield points; 1 = 1% more return) due to the partial abatement (Monichon), depending on the tax rate: solid curve: marginal tax rate: 45%; dashed: 30%; dotted: 15%.

#### Figure 9.

For a 70-year-old owner, on the x-axis, the time horizon of the computation; on the y-axis, the equivalent performance increase of the investment (in yield points; 1 = 1% more return) due to the partial abatement (Monichon), depending on the tax rate, for the tax payable in the coming years up to the horizon of the calculations. Solid curve: marginal tax rate: 45%; dashed: 30%; dotted: 15%.

### 4. Conclusion

Our results concerning the age structure of French forest owners confirm that forests are most often inherited, conserved and managed, and then are passed on to heirs. Furthermore, we have a better understanding of why older forest owners generally cut fewer trees than younger ones, as noted, for example, in [22]. This is not without consequence on the production of biomass.

Some of the reasons could be that at the age of inheritance, in a country where longevity is relatively high, and different means (pension system, different forms of financial savings … ) may be sufficient to meet the current needs of retirees, forests are kept in the portfolio firstly for philosophical reasons and motives other than financial (feeling of stability provided by trees, various amenities). Secondly, forests are also seen more as precautionary savings (in case of major temporary difficulties) than as a source of income. Finally, they are a means of transmitting a heritage marked for the following generations by the personal investments and forest management decisions of the owner. All this encourages the retention of standing trees and the delaying of harvesting.

And from an economic point of view, as we have seen, inheritance tax relief is not an incentive for the owner to sell his/her forest or cut down his/her trees, but rather to pass on his/her heritage in the form of woodland.

We have also seen that the older the owner, the more he/she has an interest in doing so, and in particular in postponing the age at which trees are cut, but also in investing in silviculture (pruning, maintenance, etc.) to give more value to his/her forests. In doing so, forest owners create externalities that benefit society as a whole, most of which are positive: more biodiversity (cf. [28]), more carbon storage, more attractive forests for walkers, etc. Tax relief on forests, of the type studied here, can thus be a very useful tool for public authorities to obtain such externalities at a low cost. It can also be used to guide the short- or long-term commercialization of the biomass produced.

However, in France, these effects may be partly counterbalanced, for certain estates, by the tax on forest assets (named IFI: Impôt sur la Fortune Immobilière). If one compares forest investments that are subject to this tax (also with an abatement of three-quarters of the value of the forest, under the same conditions of commitment as the tax on inheritance studied here) with financial investments that are not subject to this burden, this IFI encourages cutting down trees and passing on financial assets. The calculation of this incentive remains to be done, and for the forests that are subject to it, the synthesis of the two effects to be calculated, both on the biomass production and on the externalities; it is a new research to be undertaken.

Finally, it should be remembered that the quantitative results presented here are based on average parameter values for the demographic and economic models, and are not a substitute for an expert appraisal, which is the only way to advise a particular forest owner or individual investor.

### Acknowledgements

This study has been carried out with financial support from the French National Research Agency (ANR) in the frame of the Investments for the Future Program, within the Cluster of Excellence COTE (ANR-10-LABX45), thanks to the LUCAS Project.

### A. Appendix 1: additional information on the demographic model

We consider that the evolution of the population of owners of the assets considered (forest, financial portfolio … ) can be entirely deduced from its current state. Consequently, a Markov model can be used [29]. We still have to implement it.

For simplicity, and in the absence of any other realistic hypothesis, we assume in the following that the demographic parameters (life expectancy, etc.) do not change. We use Insee data (see [23], data for the year 2019, before the COVID-19 pandemic).

In the model, time, denoted by t, is discrete, the unit being a year; t = 1 is the present. Suppose that in year n, the owner of the forest (or of any other property or

#### Assessment of the Impacts of an Inheritance Taxation Relief on the Profitability… DOI: http://dx.doi.org/10.5772/intechopen.101380

portfolio considered) has the age of a. Insee [23] tells us directly the probability that he/she will not die in year n. Otherwise, there is inheritance.

The publication [23] also provides us with the age of the mother for every birth in France (for fathers, there is no data; perhaps a problem of uncertainties … ); we deduce the probability distribution of the age gap between a generation (between mothers and children).

If the owner (generation G) dies in year n, we thus have the probability distribution of the age of the heir child (generation G + 1). But he/she himself may have died (we know the probability, since [23] directly mentions the survival rate at a given age). In this case, the forest is passed on to the descendant of this heir, who is already deceased. This descendant (generation G + 2) himself may be already deceased, and in the calculation, we take this possibility into account by integrating the fact that the forest can be transmitted directly from generation G to G + 3. This consideration is important because the age of the heir, second or even third rank, does not follow the same probability distribution as in the case of a parent-child transmission.

In the (unlikely) case that the heir at G + 3 is also deceased, we assume that the forest is transmitted to another "branch" of the family, and we return to G + 1, to repeat the same calculations. We also suppose that the considered part of the inheritance is never divided, until the time horizon of the calculations. This is a weak assumption because if it were not the case, one can imagine that the calculation relates in fact only to one of the parts, after the partition.

For practical purposes, we consider a maximum age of 104 years: we assume that at this age, the owner voluntarily passes on his/her property to his/her heirs, under the same tax conditions.

We then define the real vector Xt(104,1) with coordinates Xt(i), each equal to the probability that the owner of the asset under consideration is i years old in year t.

We then define the Markov matrix M(104,104): M(i,j) is the probability that the assets owned by an owner aged j years in year t are owned by an owner aged i years in year t + 1. M(i,j) is calculated using the data presented in the text.

The evolution of Xt is given by:

$$\mathbf{X}\_{t+1} = \mathbf{M} \cdot \mathbf{X}\_t \tag{1}$$

### B. Appendix 2: additional information on the economic model

We start with an asset belonging to an owner of any age (less than 104 years). After a sufficiently long period of time, the after-tax value of this asset will depend on the past sequences of transfers, which also depends the present value of the taxes that will have to be paid.

We introduce Vtð Þ<sup>i</sup> <sup>∈</sup> <sup>ℜ</sup><sup>∗</sup> 104, where i is the age of the owner at time t: If t <sup>&</sup>gt; 1, Vt(i) is the undiscounted after-tax value at time t of the investment if the owner is i years old, multiplied by the probability that the owner is that age. V1(i) is the initial value of the capital under consideration, with i the current age of the investor.

Since we assume that the tax rates do not change in the future, we are dealing with a Markov process.

In the case where there is no partial tax relief, we can define N, a 104 � 104 matrix of real coefficients, as follows:

$$\mathbf{V}\_{t+1} = \mathbf{N} \cdot \mathbf{V}\_t, \forall t \ge 1; \tag{2}$$

N is calculated in a similar way to M, but the coefficients corresponding to a transmission are multiplied by a coefficient (1 � F) representing the loss in value of the part of the estate in question due to taxation. The model takes into account the fact that the transmission may take place via one or more generation gaps: for example, the transmission of capital to an heir 40 years younger may involve either a direct transmission (parent-child) or a transmission with a generation skip (with a child 20 years younger but previously deceased, and a grandchild heir 40 years younger than the grandparent).

In the case where a partial tax relief ('Monichon') is obtained for a capital invested in forest, we define a new matrix N<sup>0</sup> in the same way. The only difference with N is due to the use of the tax parameters F<sup>0</sup> taking into account this abatement instead of the parameters F:

$$\mathbf{V\_{t+1}} = \mathbf{N'} \cdot \mathbf{V\_t} \tag{3}$$

#### B.1 Expected present value of inheritance tax

We are now able to calculate E(t) (resp. E<sup>0</sup> (t)), the present value of the capital at time t, in the case of an investment not benefiting from the abatement (resp. a forestry investment benefiting from it), a being the discount rate:

$$\mathbf{E}(t) = \frac{\sum\_{\mathbf{k}=1}^{104} \mathbf{V}\_{\mathbf{t}}(\mathbf{k})}{\left(\mathbf{1} + a\right)^{\mathbf{t}}} \tag{4}$$

We then define the discounted portion of the value of the estate that will be used in the future to pay inheritance taxes as follows

$$\mathbf{V\_{1}(i)} - \mathbf{E(t)} \left(\mathbf{resp.V\_{1}(i)} - \mathbf{E'(t)}\right) \tag{5}$$

with i the current age of the owner of the capital.

The numerical values of r (the annual return on the invested capital) and a (the discount rate) have both been taken to be equal to 4% per year, in real terms (zero inflation is assumed in the future, which does not affect the results presented in the text but simplifies their presentation).

#### B.2 Additional rate of return induced by the tax abatement

Finally, we define the additional rate of return s due to the partial estate tax abatement as the additional rate at which the non-forestry investment would have to grow to yield an expected value equal to the expected value of a forestry investment benefiting from the allowance, at the given time horizon t.

This additional rate s is defined by:

$$\mathbf{V\_1(i)} \cdot (\mathbf{1} + \mathbf{r} + \mathbf{s})^\mathbf{t} = \mathbf{V\_1(i)} \cdot (\mathbf{1} + \mathbf{r})^\mathbf{t} + (\mathbf{E'(t)} - \mathbf{E(t)}) \cdot (\mathbf{1} + \mathbf{r})^\mathbf{t} \tag{6}$$

Assessment of the Impacts of an Inheritance Taxation Relief on the Profitability… DOI: http://dx.doi.org/10.5772/intechopen.101380
