都市更新計畫的選擇權評價

Abstract

於過去的文獻中，都市更新計畫案主要是利用折現現金流量模型（discounted cash flow model）來做評價以及可行性評估。然而，都市更新投資相當複雜且市場不確定性極高，而折現現金流量法無法充分解釋市場不確定性所造成的投資彈性與我國都市更新法令與機制推動所賦予之延長期限權利。因此，本研究以私部門的開發商為實施者，針對多階段都市更新獨特的開發流程特性，利用實質選擇權概念，運用序列複合銷售者可展延選擇權評價模型，用以分析都市更新流程之延期彈性所造成的經濟價值變化。 本研究利用臺北市信義區都市更新計畫案做為實際案例以驗證序列複合銷售者可展延買權評價模型之實用性。一般而言，計畫總體時間長度與計畫價值成反比，亦即若時間成本增加，將會導致計畫價值減少。因此，若將計畫案之延長期限完全考慮而計算所得之淨現值將會低於未考慮延長期限計算出之淨現值。但本研究之案例結果顯示根據銷售者可展延買權模型所計算出之價值不僅高於考慮延長期限之淨現值，甚至也高於未考慮之淨現值。因此，本研究證明此模型可以實際考量到我國都市更新流程之延期彈性所產生的計畫價值。另外，一般歐式買權，無風險利率變動與價值成正比，資產價值報酬變異數變動亦同，而本研究由敏感度分析中發現無風險利率變動與資產價值報酬變異數變動皆讓買權價值無規則可言，但此特性與銷售者可展延買權定價公式之偏微分結果相符。綜上所述，此評價模型優於目前所常用之折現現金流量模型，故此模型未來可望成為嶄新的都市更新計畫之評估工具。

In early researches, the discounted cash flow (DCF) model is usually used for valuation of urban regeneration. However, the DCF model is not able to quantify the opportunities for investors to choose to postpone the deadline or to abandon the next stage of the investment. To evaluate this flexibility of investment, a sequential compound writer-extendible option approach is developed for the valuation of urban regeneration using real option theory in this research. This research tests the valuation model by an empirical study with a case of the urban regeneration project of Xinyi District in Taipei City. Generally the value of a project is a decrease function of time. Therefore, the net present value with a postponed deadline is lower than the net present value without postponement. However, the value of the case using sequential compound writer-extendible option approach is higher than both of them, which proves that the sequential compound writer-extendible valuation model is able to evaluate the option value of the investor. Besides, the sensitivity analysis shows that there is no significant relationship between risk-free interest rate and the underlying asset volatility, which is different from most types of call option. However, the results satisfy the partial derivative of the writer-extendible call pricing formula. In conclusion, the sequential compound writer-extendible valuation model has the potential to be the new valuation tool of urban regeneration plans.