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A valuation model for firms with stochastic earnings

  • Steven Li
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    A model is proposed to value a firm with stochastic earnings. It is assumed that the earnings of the firm follow a time-varying mean reverting stochastic process. It is shown that the value of the firm satisfies a boundary value problem of a second-order partial differential equation, which can be solved numerically. Some special cases are discussed. An analytic solution is found for one special case. Moreover, it is shown that the analytic solution is consistent with a previous result obtained by other researchers. Numerical solutions are obtained for the other special cases. Finally, the model is also applied to value the debt issued by the firm.

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    Article provided by Taylor & Francis Journals in its journal Applied Mathematical Finance.

    Volume (Year): 10 (2003)
    Issue (Month): 3 ()
    Pages: 229-243

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    Handle: RePEc:taf:apmtfi:v:10:y:2003:i:3:p:229-243
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    1. Merton, Robert C, 1974. "On the Pricing of Corporate Debt: The Risk Structure of Interest Rates," Journal of Finance, American Finance Association, vol. 29(2), pages 449-70, May.
    2. Robert J. Shiller, 1980. "Do Stock Prices Move Too Much to be Justified by Subsequent Changes in Dividends?," NBER Working Papers 0456, National Bureau of Economic Research, Inc.
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    4. Marsh, Terry A & Merton, Robert C, 1987. "Dividend Behavior for the Aggregate Stock Market," The Journal of Business, University of Chicago Press, vol. 60(1), pages 1-40, January.
    5. Black, Fischer & Cox, John C, 1976. "Valuing Corporate Securities: Some Effects of Bond Indenture Provisions," Journal of Finance, American Finance Association, vol. 31(2), pages 351-67, May.
    6. Raymond Chiang & Ian Davidson & John Okunev, 1996. "Some Further Theoretical and Empirical Implications Regarding the Relationship between Earnings, Dividends and Stock Prices," Working Paper Series 60, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
    7. Epstein, D. & Mayor, N. & Schonbucher, P. & Whalley, A. E. & Wilmott, P., 1998. "The valuation of a firm advertising optimally," The Quarterly Review of Economics and Finance, Elsevier, vol. 38(2), pages 149-166.
    8. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
    9. Fama, Eugene F. & French, Kenneth R., 1988. "Dividend yields and expected stock returns," Journal of Financial Economics, Elsevier, vol. 22(1), pages 3-25, October.
    10. Merton H. Miller & Franco Modigliani, 1961. "Dividend Policy, Growth, and the Valuation of Shares," The Journal of Business, University of Chicago Press, vol. 34, pages 411.
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