以模糊理論分析BOT計畫自償率之研究

Abstract

以模糊理論分析BOT計畫自償率之研究 研究生：羅文聖 指導教授：馮正民 教授 康照宗 教授 國立交通大學交通運輸研究所 摘 要 在BOT計畫中，自償率是政府推動公共建設民營化重要指標之一，其意義是BOT計畫營運期收入與興建期成本之比。自償率高低除顯示公共建設計畫之財務自償性與非自償性外，其作用亦在區別建設資金籌措之來源與顯示政府出資比例與權利金之間的關係，其重要性不可言喻。 長久以來，相關研究報告分析營運收入與工程支出等相關變數，皆假設某固定值或以某一固定比率進行資金估算，而此種作法，所得到之B/C或自償率仍然屬單一值。然而，考量實際環境裡，由於BOT計畫具備計畫時間長，不確定性因素很多，決策者受限於資訊之不確定性因素，很難有效且精確掌握未來之投資效益、收入及成本變數之資料。因此，在諸多假設條件下，目前BOT計畫自償率是無法真實反應實際計畫投資評估決策環境，決策者對於自償率存在譬如「70%∼80%」之區間概念；如此一來，財務上之成本效益分析或自償率不再是固定值。 因此，本研究目的以模糊理論觀點分析自償率，改善傳統BOT計畫自償率單一值之特性。本研究首先將影響自償率之營運收入與工程支出之相關變數，利用模糊理論予以模糊化，進而修正自償率公式，推導模糊自償率公式，得此式之模糊區間值。同時，為改善模糊自償率無客觀機率值之比較缺失，本研究亦以蒙地卡羅模擬機率與自償率之間的關係，此有助於瞭解模糊自償率與機率自償率之差別。另外，考量政府、民間企業乃至於融資機構在實際資源有限之情況下，本研究以政府觀點，構建模糊自償率數學規劃模式。 在此研究架構基礎上，本研究中發展出七種模式進行分析與比較，並以『台北港貨櫃儲運中心BOT計畫』為例，驗證本研究所發展之模式可用性。經本研究實例分析，估計結果顯示法定自償率為1.16，廣義自償率為0.82，法定模糊自償率為(0.59, 1.16, 1.98)，廣義模糊自償率為（0.48，0.82，1.59）。若以蒙地卡羅法模擬自償率(機率自償率)，法定自償率介於0.71至1.77之間，廣義自償率則為0.43至1.01之間。若考量資源有限情形，模糊自償率(模糊數學規劃模式)為(1.67, 1.76, 1.84)，此模式能有效預測財務變動之自償率區間值。 關鍵字：BOT計畫、權利金、模糊理論、蒙地卡羅法、模糊數學規劃模式。

Applying Fuzzy Set Theory to Analyze Self-Liquidation Ratio of BOT Projects Student：Wen-Shen Lo Advisors：Dr. Cheng-Min Feng Dr.Chao-Chung Kang Institute of Traffic & Transportation National Chiao Tung University ABSTRACT The Self-Liquidation Ratio (SLR) is an important financial indicator that can be used to justify the ability of private sectors to participate in BOT projects. SLR means the ratio of net operation revenues in operation period to construction cost in the construction period. In the past, the SLR or Benefit/cost analysis (BCA) in financial analysis was a single value in some studies. However, decision makers cannot capture full and précised information about costs and revenues due to the characters of the huge cost, long term period, many risks associated with BOT projects. That is why the SLR cannot be used to justify investment by decision-makers appropriately. The purpose of this study is to correct drawbacks of SLR for BOT projects by using fuzzy sets theory. Firstly, we used concept of fuzzy theory to de-fuzzy key cost or revenue variables of BOT projects, and developed the fuzzy SLR index. Secondly, this paper used Monte Carlo Simulation to simulate the possible probability density function (p.d.f.) of SLR in order to correct the defects of fuzzy SLR and to compare the difference between possibility model and probability model. Thirdly, this study employs the fuzzy mathematical programming model under the limited resource of governments, private sectors, and bank sponsors. By integrating fuzzy sets theory and SLR, this study develops seven models, including (1) SLR in law; (2) generalized SLR; (3) fuzzy SLR in law; (4) fuzzy generalized SLR; (5) probability SLR; (6) probability generalized SLR, and (7) fuzzy linear programming SLR. This study also makes an empirically study with “Taipei Container Port BOT Project” to find the solutions of these models. The results of the empirical study show that (1) SLR in law is 1.16; (2) generalized SLR is 0.82; (3) fuzzy SLR in law is [0.59,1.16,1.98]; (4) fuzzy generalized SLR is [0.48,0.82,1.59]; (5) probability SLR in law is 0.71-1.77; (6) probability generalized SLR is 0.43-1.01; and (7) fuzzy linear programming SLR is [1.67, 1.76,1.84]]. Our models could be used to calculate interval of SLR under real decision-making environment. Keywords: BOT projects, fuzzy set theory, Monte Carlo simulation, fuzzy linear programming model.