傳統資金管理的成效有賴於對未來現金流量預測之準確性，然而在金融風暴蔓延與貨幣戰爭激烈的不確定年代，產品價格、利率與匯率等風險深深影響公司獲利的穩定性。基於傳統財務管理理論未能充分將企業經營的不確定性納入考量，本論文將價格與利率的不確定性整合至公司理財與投資決策模型中，提出一個在延遲付款下的公司價值評價模型，並進而推導出公司價值的封閉解。接著將公司價值的動態，以隨機動態規劃法與蒙地卡羅模擬法，分別推導出在風險環境下具有延遲支付貨款權益的公司之實質選擇權價值。
本論文整合Merton在1973年所發表的隨機利率模型與常見於金融衍生性商品評價的幾何布朗運動隨機價格模型，將其應用在具有交易信用的公司評價與實質選擇權評價模型之建立。在模型的建構過程中，本論文考慮以下諸參數：隨機價格與隨機利率的漂移項與波動性、銷貨成本率、需求的價格彈性、產品的市場占有率、信用期間的長短等。以上諸因素對公司價值與實質選擇權價值的影響程度不一，依其重要性排序，可提供經營管理者投資決策與風險控管之依據。在本文中，風險性與隨機性的源頭來自於價格與利率的動態過程，這與日常管理實務上的經驗不謀而合，而公司營運活動的營收與盈餘受到這兩股具有高度不確定性的因子影響，未來現金流量亦呈現隨機波動之現象，乃至於公司價值亦是一個隨機漂移的過程。本文將管理實務上常見的交易信用制度整合至隨機模型中，使得模型本身更具備有管理上的意涵與貢獻。

In the world surrounded by uncertainties ranging from financial crisis to currency war, the volatility of commodity price, interest rate and foreign exchange rate significantly affects the stability of corporate earnings. However, many frameworks of corporate valuation did not explicitly take into account risk factors, which the thesis intends to incorporate in a valuation model for a firm with trade credit under price and interest rate uncertainties. Analytical solutions for corporate value under uncertainties are derived and used as the basis of further formulation for the real option value, representing the investment profits for such a firm with trade credit under uncertainties. The stochastic dynamic programming and Monte Carlo simulation approaches are employed to derive the real option value.
This thesis integrates the stochastic interest rate model of Merton (1973) and the geometric Brownian motion model of price into a framework for corporate valuation when a firm facing both the price and the interest rate risks. The risks are propagated from the price, the interest rate, the future cash flows to the corporate value. The supplier allows the firm to defer its merchandise payments due to the trade credit terms. To obtain more earnings, the firm has an opportunity to invest the deferred payment amounts in interest-bearing financial instruments. Other factors considered in this framework include the cost rate, the market share, the price elasticity of demand, and the time length of credit period. The analytical solution for corporate value is derived. Subsequently, the analytical and numerical solutions for the investment threshold and the real option value are obtained. The sensitivity analyses of the corporate value, the investment threshold, and the real option value are performed in illustrations. The managerial implications provide an insight into the investment strategy for the firm under uncertainties.

目錄  I
表目錄  III
圖目錄  IV
通用符號─覽表  VI
                     
第一章  緒論  1
  1.1研究動機與目的  1
  1.2文獻探討  3
  1.3本文結構  13
第二章 利率為常數的公司評價模型  14
  2.1符號及假設  14
  2.2模型之建立  15
  2.3模型之求解  18
  2.4模型之敏感度分析  22
  2.5小結  26
第三章 利率為隨機過程的公司評價模型  28
  3.1符號及假設  28
  3.2模型之建立  29
  3.3模型之求解  32
  3.4模型之敏感度分析  44
  3.5小結  47
第四章 實質選擇權的評價模型  49
  4.1符號及假設  49
  4.2常數利率下的實質選擇權評價  50
  4.3隨機利率下的實質選擇權評價  62
  4.4數值範例  65
  4.5模型應用  71
  4.6小結  73
第五章 結論  75
  5.1研究結論  75
  5.2管理意涵  78
  5.3未來研究方向  79
參考文獻  81

表目錄
表 1-1  本文相關研究的內容分析對照表  12
表 4-1  實質選擇權價值的數值範例：在10,000條樣本路徑、價格動態下跌趨勢與參數組合δ= 1 week、ρ= 0.12、P0= 0.008、r0= 0.065、αr = -0.005、σr = 0.015下的蒙地卡羅模擬結果	 67
表 4-2  實質選擇權價值的數值範例：在10,000條樣本路徑、價格動態下跌趨勢與參數組合δ= 1 week、ρ= 0.12、P0= 0.008、r0= 0.065、αr = +0.005、σr = 0.015下的蒙地卡羅模擬結果	 67
表 4-3  實質選擇權價值的數值範例：在10,000條樣本路徑、價格動態上漲趨勢與參數組合δ= 1 week、ρ= 0.12、P0= 0.008、r0= 0.065、αr = -0.005、σr = 0.015下的蒙地卡羅模擬結果	 68
表 4-4  實質選擇權價值的數值範例：在10,000條樣本路徑、價格動態上漲趨勢與參數組合δ= 1 week、ρ= 0.12、P0= 0.008、r0= 0.065、αr = +0.005、σr = 0.015下的蒙地卡羅模擬結果	 68
表 4-5  實質選擇權價值的數值範例：在10,000條樣本路徑、利率動態下跌趨勢與參數組合δ= 1 week、ρ= 0.12、P0= 0.008、r0= 0.065、αp = -0.01、σp= 0.05下的蒙地卡羅模擬結果  69
表 4-6  實質選擇權價值的數值範例：在10,000條樣本路徑、利率動態下跌趨勢與參數組合δ= 1 week、ρ= 0.12、P0= 0.008、r0= 0.065、αp = +0.01、σp= 0.05下的蒙地卡羅模擬結果  69
表 4-7  實質選擇權價值的數值範例：在10,000條樣本路徑、利率動態上漲趨勢與參數組合δ= 1 week、ρ= 0.12、P0= 0.008、r0= 0.065、αp = -0.01、σp = 0.05下的蒙地卡羅模擬結果  70
表 4-8  實質選擇權價值的數值範例：在10,000條樣本路徑、利率動態上漲趨勢與參數組合δ= 1 week、ρ= 0.12、P0= 0.008、r0= 0.065、αp = +0.01、σp = 0.05下的蒙地卡羅模擬結果  70

圖目錄
圖 1-1  2001至2010年間，LCD零組件的每月價格與出貨量的動態過程  10
圖 1-2  2001至2010年間，三個月期國庫券的殖利率的動態過程  10
圖 2-1  在不同的常數利率下，公司價值對價格動態起始值之敏感度分析  24
圖 2-2  常數利率下，公司價值對價格動態的漂移項與波動性之敏感度分析  24
圖 2-3  常數利率下，公司價值對銷貨成本率與需求的價格彈性之敏感度分析  25
圖 2-4  常數利率下，公司價值對銷貨成本率與產品市占率之敏感度分析  25
圖 2-5  常數利率下，公司價值對交易時間間隔與延遲付款期數之敏感度分析  26
圖 3-1  隨機利率下，公司價值對利率動態的漂移項與波動性之敏感度分析  45
圖 3-2  隨機利率下，公司價值對價格動態的漂移項與波動性之敏感度分析  45
圖 3-3  隨機利率下，公司價值對銷貨成本率與需求的價格彈性之敏感度分析  46
圖 3-4  隨機利率下，公司價值對銷貨成本率與產品市占率之敏感度分析  46
圖 3-5  隨機利率下，公司價值對交易時間間隔與延遲付款期數之敏感度分析  47
圖 3-6  隨機利率下，公司價值對價格動態與利率動態起始值之敏感度分析  47
圖 4-1  不同常數利率下，投資門檻對價格動態的起始值之敏感度分析  58
圖 4-2  常數利率下，投資門檻對價格動態的漂移項與波動性之敏感度分析  58
圖 4-3  常數利率下投資門檻對需求的價格彈性與銷貨成本率之敏感度分析  58
圖 4-4  常數利率下，投資門檻對產品市占率與銷貨成本率之敏感度分析  58
圖 4-5  常數利率下，投資門檻對交易時間間隔與延遲付款期數之敏感度分析  58
圖 4-6  不同常數利率下，實質選擇權價值對價格動態的起始值之敏感度分析  60
圖 4-7  常數利率下，實質選擇權價值對價格動態漂移項與波動性之敏感度分析  60
圖 4-8  常數利率下，實質選擇權價值對需求的價格彈性與銷貨成本率之敏感度分析  61
圖 4-9  常數利率下，實質選擇權價值對產品市占率與銷貨成本率之敏感度分析  61
圖 4-10 常數利率下，實質選擇權價值對交易時間間隔與延遲付款期數之敏感度分析  61
圖 4-11  隨機利率的蒙地卡羅模擬之樣本路徑  64
圖 4-12  隨機價格的蒙地卡羅模擬之樣本路徑  64
圖 4-13  公司價值動態的蒙地卡羅模擬之樣本路徑  64
圖 4-14  投資效益(Vt-I)折現值的蒙地卡羅模擬之樣本路徑  64
圖 4-15  應用本隨機模型進行交易信用公司之投資決策步驟  72

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