本計畫以實質選擇權法 (real options approach) 的概念，將新創公司 (start-ups) 所擁有的選擇權特性 (遞延選擇權、擴張選擇權與放棄選擇權) 納入公司價值的評鑑。根據這些選擇權之間的順序關係，利用最小平方蒙地卡羅模擬法 (least squares Monte Carlo simulation) 依序計算出其價值。同時，本文在定價新創公司的過程中，同時考量下列五個重要的因子：(1) 市場的競爭狀況，(2) 等待的機會成本，(3) 潛在競爭者進入的頻率，(4) 未來研發成功的機會，和 (5) 不同營運模式的影響。在考量上述選擇權與五個重要因子下，同時以實質選擇權法與傳統現金流量折現法 (DCF method) 來評價新創公司的價值。
本研究的貢獻有五：首先，我們建議一個評價新創公司的模型，除了考量新創公司三種選擇權的性質外，還納入上述五個市場競爭性與策略性的因子。第二， 提供資訊給公司創辦人做合理的決策，如併購或股票公開上市 (IPO)。第三，模擬的結果，對於具有選擇權性質的無形資產或管理決策的價值能有所闡述，並且舒緩新創公司與資本提供者間資訊不對稱的現象。第四，探討在何種情境下，淨現值法將無異於實質選擇權法。最後，在特定的參數設定下，我們陳列出每一種選擇權的會被執行的機率。這些預測，在設計具有選擇權特性之契約時，可以做為參考的依據。
我們所評價的新創公司，是一家在台創立，且正與一S&P500公司商談相關策略聯盟或併購事宜。經由模擬分析的結果得知，涵蓋五種因子所建構的完整模型 (full model)，相對於其他形式的模型穩健 (robust)。由敏感度分析結果來看，期初營收、期初成長率、平均回復速度、新競爭者進入的影響與未來研發成功的可能性都是相對關鍵的參數。以這些參數做不同的情境模擬時，當期初營收、期初成長率都在悲觀的設定狀態下，選擇權價值會接近零。不過在中立的情況下，實質選擇權法所估測出的新創公司價值會比一般淨現值法高約44 % ~ 61 %左右。

This paper exploits real options approach to evaluate start-ups with three option-like features embedded: options to defer, expand, and abandon. Based on the sequence and interactions among those options, we use the Least Squares Monte Carlo Simulation to price the options accordingly. Meanwhile, five key factors are considered simultaneously: (1) market competition, (2) opportunity cost of waiting, (3) potential competitors’ entrance, (4) growth opportunity of further and related research, and (5) the impact of different business models chosen by the entrepreneur. Given all possible combinations of option types and five factors mentioned above, we evaluate a start-up in Taiwan by both real option approach and traditional DCF method.
The contribution is fivefold. First, we propose a valuation model for start-ups while considering not only three options embedded but also five key factors regarding market competition and strategic considerations. Second, we provide information for entrepreneurs to make rational decisions in a case of merger, acquisition, or IPO (initial public offering). Third, our simulation results shed light on valuation of intangible assets and/or managerial decisions with option-like features and on the information asymmetry between entrepreneurs and fund providers. Fourth, we provide predictions about the conditions under which traditional DCF method is as good as real options approach. Finally, under certain parameter settings, we specify the probability that each of the three options will be exercised. These predictions can be used for designing an option-based contract with a predetermined strike price. To verify these predictions will be an interesting empirical exercise.
We initiate this project upon an invitation by a start-up in Taiwan, who is negotiating with an S&P 500 firm in a case of strategic alliance or acquisition. Our results show that the full model which incorporates five factors mentioned above is more robust than others. From sensitivity analysis, we find that key parameters are initial revenue, initial growth rate, mean-reversion speed, the effect of new entrants (competitors), and the likelihood of success in further and related research. From a scenario simulation of those key parameters, the option premium is seemingly worthless if initial revenue and growth rate are both under pessimistic settings. But in general cases, start-ups are more valuable (44% to 61% higher) under real options approach than under traditional NPV method.

一、中文文獻
王健安，1998年12月，「資本投資計畫評核術的新觀念─實質選擇權之理論與實證方法的文獻回顧」，《臺灣土地金融季刊》 第35卷第4期 (No. 138)，頁 75-99。
伍忠賢，2002年8月，《公司鑑價》 初版，臺北市：三民書局。
張傳章、鍾炫城、林秋發，2001年12月，「同時考慮R&D與市場需求不確定下之高科技產業投資方案評估分析」，《管理學報》 第18卷第4期，頁 589-616。
游李興，2002年7月，《2002 半導體工業年鑑》 初版，財團法人工業技術研究院 產業經濟與資訊服務中心。
顏錫銘、吳明政，2001年4月，「創業投資公司投資案價值的評估─採用多重實質選擇權評價方法」，《科技管理學刊》 第6卷第1期，頁 103-130。
林家帆、陳威光、郭維裕，2002年7月，「高科技產業股票之評價─實質選擇權評價法」，《管理評論》 第21卷第3期，頁 97-113。

二、英文文獻
Arnold, T., and T. F. Crack, 2000, “Option pricing in the real world: a generalized binomial model with applications to real options,” Working Paper, University of Richmond.
Bakshi, G., and Z. Chen, 1997, “An alternative model for contingent claims,” Journal of Financial Economics, Vol. 44, pp. 123-165.
Barraquand, J., and D. Martineau, 1995, “Numerical valuation of high dimensional multivariate American securities,” Journal of Financial and Quantitative Analysis, Vol. 30, No. 3, pp. 383-405.
Bares, D. S., 1996, “Jumps and stochastic volatility: exchange rate process implicit in Deutsche mark options,” Review of Financial Studies, Vol. 9, pp. 69-107.
Baz, J., and R. Strong, 1997, “The bias in delta as an indicator of the actual likelihood of option exercise,” Finance Practice and Education, Vol. 7, pp. 91-94.
Beaver, W. H., and G. Parker, 1995, Risk Management: Problems & Solutions, New York: McGraw-Hill, pp. 239.
Berger, P. G., E. Ofek, and I. Swarv, 1996, “Investor valuation of the abandonment option,” Journal of Financial Economics, Vol. 42, pp. 257-287.
Bhide, A., 1996, “The road well travelled: a note on the journeys of HBS entrepreneurs,” HBS publication.
Bollen, N., 1999, “Real option and product life cycles,” Management Science, Vol. 45, No. 5, pp. 670-684.
Brennan, M., and E. Schwartz, 1985, “Evaluating natural resource investments,” Journal of Business, Vol. 58, pp. 135-157.
Broadie, M., and P. Glasserman, 1997, “Pricing American-style securities using simulation,” Journal of Economics Dynamics and Control, Vol. 21, pp. 1323-1352.
Broadie, M., P. Glasserman, and G. Jain, 1997, “Enhanced Monte Carlo estimates for American option prices,” Journal of Derivatives.
Cassiman, B., and M. Ueda, 2002, “Optimal project rejection and new firm start-ups,” CEPR Discussion Paper No. 3429.
Christensen, C., 1997, “The innovator’s dilemma: when new technologies cause great firms to fail,” Harvard Business School Press.
Clement, E., D. Lamberton, and P. Protter, 2001, “An analysis of the Longstaff-Schwartz algorithm for American options,” Working Paper.
Constantinides, G., 1978, “Market risk adjustment in project valuation,” Journal of Finance, Vol. 33, No. 2, pp. 603-616.
Cortazar, G., 2000, “Simulation and numerical methods in real options valuation,” Working Paper, Pontifical Catholic University of Chile.
Cox, C., J. E. Ingersoll, and S. A. Ross, 1985, “An intertemporal general equilibrium model of asset prices,” Econometrica, Vol. 53, pp. 363-384.
Dixit, A. K., and R. S. Pindyck, 1994, Investment under Uncertainty, New Jersey: Princeton University Press.
Dixit, A. K., and R. S. Pindyck, 1995, “The option approach to capital investment,” Harvard Business Review, Vol. 73, pp. 105-115.
Gamba, A., 2002, “Real options valuation: a Monte Carlo simulation approach,” Working Paper, University of Verona, Italy.
Gamba, A., and L. Trigerogis, 2002a, “A log-transformed binomial lattice extension for multi-dimensional option problems,” The Fifth Annual Conference on Real Options, UCLA.
Gamba, A., and L. Trigerogis, 2002b, “A modular approach to capital budgeting problems with many real options,” Working Paper, University of Verona, Italy.
Gompers, P., and J. Lerner, 1999, The venture capital cycle, Cambridge Massachusetts: MIT Press.
Gompers, P., and J. Lerner, 2000, “Money chasing deals? The impact of fund inflows on private equity valuation,” Journal of Financial Economics, Vol. 55, pp. 281-325.
Grenadier, S., and A. Weiss, 1997, “Investment in technological innovations: an option pricing approach,” Journal of Financial Economics, Vol. 44, pp. 397-416.
Hayes, R., and D. Garvin, 1982, “Managing as if tomorrow mattered,” Harvard Business Review, Vol. 60, pp. 71-79.
He, H., and R. S. Pindyck, 1992, “Investment in flexible production capacity,” Journal of Economic Dynamic and Control, Vol. 13, No. 4, pp. 575-599.
Hull, J. C., 2003, Options, Futures, and Other Derivatives, fifth edition, Prentice-Hall Press.
Hull, J. C., and A. White, 1987, “The pricing of options on assets with stochastic volatilities,” Journal of Finance, Vol. 42, pp. 281-300.
Hull, J. C., and A. White, 1988, “An overview of contingent claims pricing,” Canadian Journal of Administrative Sciences, pp. 55-61.
Ingersoll, J., and S. Ross, 1992, “Waiting to invest: Investment and uncertainty,” Journal of Business, Vol. 65, pp. 1-29.
Jansen, P., and E. Perotti, 2002, “Valuation of internet companies: a survey of the evidence,” Working Paper.
Kester, C., 1984, “Today’s options for tomorrow’s growth,” Harvard Business Review, Vol. 62, pp. 105-115.
Kulatilaka, N., and G. Wang, 1996, “A real option framework for evaluating infrastructure investments,” Journal of Financial Studies, Vol. 4, No. 2, pp. 1-19.
Kulatilaka, N., and L. Trigeorgis, 1994, “The general flexibility to switch: real option revisited,” International Journal of Finance, Vol. 6, No. 2, pp. 778-798.
Lee, T. S., H. C. Tsai, and H. D. Chen, 2002, “Pricing patents under knowledge-based economy: real option approach,” Working Paper, National Taiwan University.
Lerner, J., 2002, “Boom and bust in the venture capital industry and the impact on innovation,” mimeo., Harvard University.
Longstaff, F. A., and E. S. Schwartz, 2001, “Valuing American options by simulation: a simple least-squares approach,” Review of Financial Studies, Vol. 14, No. 1, pp. 113-147.
Luehrman, T.A., 1995, “Capital projects as real options: an introduction,” Harvard Business School Press, 9-295-074.
Luehrman, T.A., 1998, “Investment opportunities as real options: getting started on the numbers,” Harvard Business Review, Vol. 76, pp. 51-67.
McDonald, R., and D. Siegel, 1984, “Option pricing when the underlying asset earns a below-equilibrium rate of return: a note,” Journal of Finance, Vol. 39, No. 1, pp. 261-265.
McDonald, R., and D. Siegel, 1985, “Investment and the valuation of firms when there is an option to shut down,” International Economic Review, Vol. 26, No. 2, pp. 331-349.
Merton, R. C., 1976, “Option pricing when underlying stock returns are discontinuous,” Journal of Financial Economics, Vol. 3, pp. 125-144.
Milne, A., and A. E. Whalley, 2000, “Time to build, option value and investment decisions: a comment,” Journal of Financial Economics, Vol. 56, pp. 325-332.
Moreno, M., and J. F. Navas, 2001, “On the robustness of least-squares Monte Carlo (LSM) for pricing American derivatives,” Working Paper, Universitat Pompeu Fabra.
Moretto, M., P. Panteghini, and C. Scarpa, 2003, “Investment size and firm’s value under profit sharing regulation,” FEEM Working Paper No. 80.
Moriarty, R. T., and T. J. Kosnik, 1989, “High-tech marketing: concept, continuity and change,” Sloan Management Review, Vol. 30, pp. 7-17.
Mueller, H. M., and R. Inderst, 2002, “The effect of capital market characteristics on the value of start-up firms,” Working Paper, New York University.
Myers, S. C., and S. Majd, 1990, “Abandonment value and project life,” Advances in Futures and Options Research, Vol. 4, pp. 1-21.
Myers, S. C., 1977, “Determinants of corporate borrowing,” Journal of Financial Economics, Vol. 5, No. 2, pp. 147-176.
Naik, E., and M. Lee, 1990, “General equilibrium pricing of options on the market portfolio with discontinuous returns,” Review of Financial Studies, Vol. 3, pp. 493-521.
Ottoo, R., 1998, “Valuation of internal growth opportunities: the case of biotechnology company,” The Quarterly Review and Finance, Vol. 38, pp. 615-633.
Palacios, F., S. Payo, and D. Camino, 2002, “Growth option valuation models: an integrated approach of human information processing methods and simulation,” European Financial Management Association, Annual Meeting.
Raymar, S., and M. Zwecher, 1997, “Monte Carlo valuation of American call options on the maximum of several stocks,” Journal of Derivatives, pp. 7-23.
Scherer, F. M., 1980, Industrial market structure and economic performance, second edition, Boston: Houghton Mifflin.
Scherlis, D. R., and W. A. Sahlman, 1989, “A method for valuing high-risk, long-term investments,” Harvard Business School Press, 9-288-006.
Schwartz, E. S., and M. Moon, 2000, “Rational pricing of internet companies,” Financial Analysts Journal, Vol. 56, pp. 62-75.
Schwartz, E. S., and M. Moon, 2001, “Rational pricing of internet companies revisited,” The Fifth Annual Conference on Real Options, UCLA.
Scott, L. O., 1987, “Option pricing when the variance changes randomly: theory, estimation, and an application,” Journal of Financial and Quantitative Analysis, Vol. 22, pp. 419-438.
Scott, L. O., 1997, “Pricing stock options in a jump-diffusion model with stochastic volatility and interest rates: application of Fourier inversion method,” Mathematical Finance, Vol. 7, pp. 413-426.
Shackleton, M. B., A. E. Tsekrekos, and R. Wojakowski, 2002, “Entry, exit and activation probability in a two-player real options game,” Working Paper, Lancaster University.
Trigeorgis, L., and S. P. Mason, 1987, “Valuing managerial flexibility,” Midland Corporate Finance Journal, Vol. 5, pp. 14-21.
Trigeorgis, L., 1993, “The nature of option interactions and the valuation of investments with multiple real options,” Journal of Financial and quantitative analysis, Vol. 28, No. 1, pp. 1-20.
Trigeorgis, L., 1999, Real Options: Managerial Flexibility and Strategy in Resource Allocation, fourth edition, Cambridge Massachusetts: MIT Press.
Wiggins, J. B., 1987, “Option values under stochastic volatility,” Journal of Financial Economics, Vol. 19, pp.