# Two Sets of Boundary Conditions in Cyclical Systems with Goodwill in Capitalization

## Abstract

**:**

## 1. Introduction

## 2. Mathematical Analysis

## 3. Example Data

## 4. Results of the Example Cases

## 5. Discussion

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**The expected value of capital return rate on the pine (Pinus sylvestris) stands of different initial sapling densities, as a function of rotation age, when the growth model is applied as early as applicable, along with the Real Estate strategy (Equation (8)) and the Timber Sales strategy (Equation (7)).

**Figure 2.**The expected value of capital return rate on spruce (Picea Abies) stands of different initial sapling densities, as a function of rotation age, when the growth model is applied as early as applicable, along with the Real Estate strategy (Equation (8)) and the Timber Sales strategy (Equation (7)).

**Figure 3.**The expected value of capital return rate on birch (Betula pendula) stands of different initial sapling densities, as a function of rotation age, when the growth model is applied as early as applicable, along with the Real Estate strategy (Equation (8)) and the Timber Sales strategy (Equation (7)).

**Figure 4.**The expected value of capital return rate, as a function of rotation age, when the growth model is applied to seven observed wooded stands, along with the Real estate strategy (Equation (8)). Thinnings do not enter. The numbers in legends identify stands and observation plots.

**Figure 5.**The expected value of capital return rate, as a function of rotation age, when the growth model is applied to seven observed wooded stands, along with the Timber Strategy (Equation (7)). Thinnings do enter in all cases. The numbers in legends identify stands and observation plots.

**Figure 6.**The expected value of capital return rate on pine (Pinus sylvestris) stands of different initial sapling densities, as a function of rotation age, when the growth model is applied as early as applicable, along with the Real Estate strategy (Equation (8)) and the Timber Sales strategy (Equation (7)). Thinnings have been introduced into the RE strategy to extend the feasible rotations by 20 years.

**Figure 7.**The expected value of capital return rate on spruce (Picea Abies) stands of different initial sapling densities, as a function of rotation age, when the growth model is applied as early as applicable, along with the Real Estate strategy (Equation (8)) and the Timber Sales strategy (Equation (7)). Thinnings have been introduced into the RE strategy to extend the feasible rotations by 20 years.

**Figure 8.**The expected value of capital return rate on birch (Betula pendula) stands of different initial sapling densities, as a function of rotation age, when the growth model is applied as early as applicable, along with the Real Estate strategy (Equation (8)) and the Timber Sales strategy (Equation (7)). Thinnings have been introduced into the RE strategy to extend the feasible rotations by 20 years.

**Figure 9.**The expected value of capital return rate, as a function of rotation age, when the growth model is applied to seven observed wooded stands, along with the Real Estate strategy (Equation (8)). The numbers in legends identify stands and observation plots. Thinnings have been introduced into the RE strategy to extend the feasible rotations by 20 years.

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**MDPI and ACS Style**

Kärenlampi, P.P.
Two Sets of Boundary Conditions in Cyclical Systems with Goodwill in Capitalization. *Foundations* **2024**, *4*, 3-13.
https://doi.org/10.3390/foundations4010002

**AMA Style**

Kärenlampi PP.
Two Sets of Boundary Conditions in Cyclical Systems with Goodwill in Capitalization. *Foundations*. 2024; 4(1):3-13.
https://doi.org/10.3390/foundations4010002

**Chicago/Turabian Style**

Kärenlampi, Petri P.
2024. "Two Sets of Boundary Conditions in Cyclical Systems with Goodwill in Capitalization" *Foundations* 4, no. 1: 3-13.
https://doi.org/10.3390/foundations4010002