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A game options approach to the investment problem with convertible debt financing

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  • Egami, Masahiko
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    Abstract

    We consider a firm that operates a single plant and has an expansion option to invest in a new plant with convertible debt financing. This conversion feature introduces another complication not only because of the added conversion timing problem (by the bond holder) but also because the equity holder needs to take future conversion into account when evaluating her expansion/financing decision. We have two main objectives here. We use game options techniques to analyze optimal strategies involved in this convertible debt financed expansion problem. The first goal is to provide a comprehensive framework and procedure for solving the problem in a mathematically tractable way. Secondly, we illustrate our solution method through a concrete example with economic analysis. This includes a comparison with straight bond financing and comparative statics with respect to price volatility and conversion ratio. In this regard, we attempt to clarify how the conversion feature affects the equity holder's investment decisions. Throughout the paper, we study expansion options by viewing a firm's existing operation, bankruptcy threat, conversion decisions and financing decisions all together.

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    File URL: http://www.sciencedirect.com/science/article/pii/S0165-1889(10)00071-0
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    Article provided by Elsevier in its journal Journal of Economic Dynamics and Control.

    Volume (Year): 34 (2010)
    Issue (Month): 8 (August)
    Pages: 1456-1470

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    Handle: RePEc:eee:dyncon:v:34:y:2010:i:8:p:1456-1470
    Contact details of provider: Web page: http://www.elsevier.com/locate/jedc

    Keywords: Convertible bond Investment decision Optimal stopping Game options;

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    1. Kyoko Yagi & Ryuta Takashima & Hiroshi Takamori & Katsushige Sawaki, 2008. "Timing of Convertible Debt Financing and Investment," CARF F-Series CARF-F-131, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    2. Egami, Masahiko, 2009. "A framework for the study of expansion options, loan commitments and agency costs," Journal of Corporate Finance, Elsevier, vol. 15(3), pages 345-357, June.
    3. Mauer, David C. & Sarkar, Sudipto, 2005. "Real options, agency conflicts, and optimal capital structure," Journal of Banking & Finance, Elsevier, vol. 29(6), pages 1405-1428, June.
    4. Christopher A. Hennessy, 2004. "Tobin's "Q", Debt Overhang, and Investment," Journal of Finance, American Finance Association, vol. 59(4), pages 1717-1742, 08.
    5. Childs, Paul D. & Mauer, David C. & Ott, Steven H., 2005. "Interactions of corporate financing and investment decisions: The effects of agency conflicts," Journal of Financial Economics, Elsevier, vol. 76(3), pages 667-690, June.
    6. Gong, Pu & He, Zhiwei & Zhu, Song-Ping, 2006. "Pricing convertible bonds based on a multi-stage compound-option model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 366(C), pages 449-462.
    7. Mello, Antonio S & Parsons, John E, 1992. " Measuring the Agency Cost of Debt," Journal of Finance, American Finance Association, vol. 47(5), pages 1887-1904, December.
    8. Sarkar, Sudipto, 2003. "Early and late calls of convertible bonds: Theory and evidence," Journal of Banking & Finance, Elsevier, vol. 27(7), pages 1349-1374, July.
    9. Yuri Kifer, 2000. "Game options," Finance and Stochastics, Springer, vol. 4(4), pages 443-463.
    10. Hennessy, Christopher A. & Tserlukevich, Yuri, 2008. "Taxation, agency conflicts, and the choice between callable and convertible debt," Journal of Economic Theory, Elsevier, vol. 143(1), pages 374-404, November.
    11. Dayanik, Savas & Karatzas, Ioannis, 2003. "On the optimal stopping problem for one-dimensional diffusions," Stochastic Processes and their Applications, Elsevier, vol. 107(2), pages 173-212, October.
    12. Korkeamaki, Timo & Moore, William T., 2004. "Capital investment timing and convertible debt financing," International Review of Economics & Finance, Elsevier, vol. 13(1), pages 75-85.
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    Cited by:

    1. Yagi, Kyoko & Takashima, Ryuta, 2012. "The impact of convertible debt financing on investment timing," Economic Modelling, Elsevier, vol. 29(6), pages 2407-2416.
    2. Di Corato, Luca & Moretto, Michele & Rossini, Gianpaolo, 2017. "Financing flexibility: The case of outsourcing," Journal of Economic Dynamics and Control, Elsevier, vol. 76(C), pages 35-65.
    3. Lyandres, Evgeny & Zhdanov, Alexei, 2014. "Convertible debt and investment timing," Journal of Corporate Finance, Elsevier, vol. 24(C), pages 21-37.
    4. Lim, Dongjae & Li, Lingfei & Linetsky, Vadim, 2012. "Evaluating callable and putable bonds: An eigenfunction expansion approach," Journal of Economic Dynamics and Control, Elsevier, vol. 36(12), pages 1888-1908.

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