最適輪伐期之分析─實質選擇權之應用

Abstract

一般傳統上決定森林輪伐期的方法包括最大木材永續收穫法、最大淨現值法以及最大土地期望值法，此三種方法均在外生價格為確定下求解最適輪伐期。然而，實際上地主在造林時，包括林木價格以及二氧化碳價格均為不確定型態，故使用上述方法來計算最適輪伐期可能會錯估真正的造林淨現值。據此，本研究引入Chladna（2007）之實質選擇權模型，考慮木材價格及二氧化碳價格不確定下，建立我國森林最適輪伐期之理論模型，進一步以台灣杉木作為代表樹種進行實證模擬分析，估算台灣地主在面對價格不確定下之杉木最適輪伐期。本研究之主要實證結果如下：（1）杉木價格與二氧化碳價格固定時，則我國杉木之最適輪伐期為21年，而考慮任一價格隨機變動時，其輪伐期均會比價格固定下之輪伐期長，其中以杉木價格變動造成輪伐期增加之影響較為顯著。例如考慮杉木價格變動，則輪伐期增加為29年；考慮二氧化碳價格變動，則輪伐期增加為24年；考慮兩種價格均隨機變動下，則輪伐期增加為25年。（2）當考慮折現率變動下，則無論杉木價格與二氧化碳價格變動與否，折現率越高，則輪伐期均會愈短。（3）考慮杉木價格隨機變動而二氧化碳價格固定時，則當折現率為3％以上時，碳釋放比例愈小，則輪伐期愈短。（4）當杉木價格與二氧化碳價格均隨機變動時，則隨著碳釋放比例愈小，輪伐期亦愈短。

Traditionally, the approaches of deciding the optional forest rotation period include the maximum sustainable yield, the maximum land expected value, and the maximum net present value. All these approaches are seeking to solve the optimal rotation period under an exogenously determined price of timber. However, in reality, when a landowner decides to afforest, both the prices of timber and carbon dioxide are not certain. Therefore, the above mentioned methods may not properly assess the net present value of afforestation. By assuming the uncertainty of prices of timber and carbon dioxide, based on the real option model of Chladna(2007), this study develops a theoretical model of optimal forest rotation period in Taiwan. Furthermore, under the assumption of timber price uncertainty, an empirical study is conducted to simulate and analyze the optimal rotation period of cunnignhania lancelata of landowner in Taiwan. The empirical results are summarized as follows: (1) When the prices of cunnignhania lancelata and carbon dioxide are fixed, the optimal rotation period of cunnignhania lancelata in Taiwan is 21 years. When either one of the prices of timber and carbon dioxide fluctuates randomly, the optimal rotation period will become longer than that of fix-priced one. For example, if only the price of cunnignhania lancelata fluctuates randomly, the optimal rotation period will increase to 29 years; if only the price of carbon dioxide fluctuates randomly, the optimal rotation period will increase to 24 years; if both prices fluctuate randomly, the optimal rotation period will increase to 25 years. (2) If the discount rate increases, the optimal rotation period will become shorter, whether the prices of cunnignhania lancelata and carbon fluctuate randomly or not. (3) When the price of cunnignhania lancelata fluctuates randomly and the price of carbon dioxide fixed, while the discount rate is above 3%, if the carbon release proportion becomes lower, the optimal rotation period will become shorter. (4) When both the prices of cunnignhania lancelata and carbon dioxide fluctuate randomly, the optimal rotation period will become shorter if the carbon release proportion becomes lower.