Abstract
A capital return rate function for growth processes is introduced and applied to financial considerations in periodically growing multiannual plants. The capital return rate function is composed of a momentary capital return function, a probability density function in the time domain, and their integration over time or age. It is shown that the expected value of capital return rate within a single stand equals momentary capital return rate within an estate, integrated over an even distribution of stand ages. We distribute the capitalization to operative and non-operative capitalization. In the case of a low non-operative capitalization, financially sound operations favor relatively small amount of operative capital. In the case of a high, but constant non-operative capitalization, optimal practices correspond to those resulting in maximum sustainable yield. Appreciating non-operative capitalization favors small operative capitalization. Optimal rotation and operative capitalization are weak functions of increasing level of non-operative capitalization, even if they are strong functions of its increment rate. It is argued that large but non-appreciating non-operative capitalization, favoring practices corresponding to maximum sustainable yield, would not appear frequently. In summary, it is found that appreciation of non-operative capitalization dominates financially sustainable management practices.
Highlights
In businesses involved in growing multiannual plants, sustainability may refer to maintenance of growing stock, maintenance of growth, or maintenance of productive area (Kuusela, 1961; Posavec et al, 2012)
Comparing Eqs. (3), (4) and (5), we find that the probability density function of capital return rate in the time domain is pðr; tÞ 1⁄4 ZKτðtÞ
We have introduced a momentary capital return rate function, the expected value of capital return rate, as well as the expected value of capital return rate in time-age domain
Summary
An obvious reason for this is that a discounting interest rate is taken externally, were as optimization of capital return rate should be based on the features of any production process Such results have been gained in the case of stationary rotation forestry (K€arenlampi, 2019a). Maximization of the net present value of future proceeds becomes similar to the IRR, provided the discounting interest rate is calibrated to yield a realistic bare land value (K€arenlampi, 2019a). Another interesting development regards financial performance of continuous-cover forestry (K€arenlampi, 2018). A significant appreciation rate on non-operative capitalization requires a small volume of standing trees, corresponding to a low cutting limit diameter (K€arenlampi, 2018). The methods introduced could be used to any growth process, provided a yield function can be approximated
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