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Mathematical Model of Optimal Payouts under Non-linear Demand Curve  

Won, Chaehwan (Department of Business Administration Sejong University)
Publication Information
Management Science and Financial Engineering / v.10, no.2, 2004 , pp. 53-71 More about this Journal
Abstract
In this study, a mathematical model that shows the optimal payout policy is developed. The model is new and unique in the sense that not only continuous-time framework is used, but also both partial differential equation (PDE) and real-option approach are utilized in the derivation of optimal payouts for the first time. In the model building, non-linear demand curve for dividend payouts in the competitive capital markets is assumed. From the sensitivity analysis using traditional comparative static analysis, some useful managerial implications which are consistent with famous previous studies are derived under realistic conditions. All results in this study, however, are valid under the assumption that the opportunity costs follow geometric Brownian motion, which is widely used in economic science and finance literature.
Keywords
Dividend payout; Geometric Brownian motion; Equilibrium model;
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1 Rozeff, Robert S., 'Growth. Beta and agency costs as determinants of dividend payout ratios,' Journal of Financial Research (Fall 1982), 249-259
2 Rubinstein, Mark, 'Derivative Assets Analysis,' Journal of Economic Perspectivese 1 (1987), 73-94
3 Shiller, R. J., 'Do stock prices move too much to be justified by subsequent changes in dividends?,' American Economic Review 71, 3 (1981), 421-436
4 Benartzi, Shlomo, Rini Michaely, and Richard Thaler, 'Do changes in dividends signal the future or the past?,' Journal of Finance 52 (1997), 1007-1034   DOI
5 Bhattacharya, S., 'Imperfect Information, dividend policy, and the 'Bird-in-the-Hand' fallacy,' Bell Journal of Economics and Management Science, (1979), 259-270
6 Capozza D. and Yuming Li, 'The Intensity and Timing of Investment: The Case of Land,' American Economic Review 84 (1994), 889-904
7 Hansen, Robert S., Raman Kumar and Dilip K. Shome, 'Dividend policy and corporate monitoring: Evidence from the regulated electric utility industry,' Financial Management 23 (Spring 1994), 16-22   DOI
8 Dhillon, U. S. and H. Johnson, 'The effect of Dividend changes on stock and bond prices,' Journal of Finance 49 (March 1994), 281-289   DOI
9 Gordon, M. J., 'dividends, earnings and stock prices,' Review of Economics and Statistics 41 (May 1959), 99-105   DOI   ScienceOn
10 Gordon, M. J., 'The savings, investment and valuation of corporation,' Review of Economics and Statistics 44 (Feb 1962), 37-51   DOI   ScienceOn
11 Hess, P. J., 'Tests for tax effects in the pricing of financial asserts,' Journal of Business 56, 4 (1983), 537-554   DOI   ScienceOn
12 John, K. and A. Kalay, 1982, 'Costly contracting and optimal payout constraints,' Journal of Finance 37 (May 2000), 457-479   DOI
13 Kester, W. Carl, 'Today's Options for Tomorrow's Growth,' Harvard Business Review (1984), 153-160   DOI
14 Lowellen, W., K. L. Stanley, R. C. Lease and G. G. Schlarbaum, 'Some direct evidence on the dividend clientele phenomenon,' Journal of Finance 33 (Dec. 1978)
15 McDonald, R. L. and D. R. Siegel, 'Investment and the valuation of firms there is an option to shut down,' International Economics Review 26 (June 1985), 331-349   DOI   ScienceOn
16 Miller, M. H. and F. Modigliani, 'Dividend policy, growth and valuation of shares,' Journal of Business 34 (Oct. 1961), 411-433   DOI   ScienceOn
17 Pindyck, R. S., 'Irreversibility, uncertainty, and investment,' Journal of Economic Literature 29 (1991), 1110-1148
18 Shimko, D. C., Finance in Continuous Time: A Primer, Miami, Kolb Publishing Co., 1992
19 Dixit, A. and R. Pindyck, Investment under Uncertainty, Princeton, NJ., 1994
20 Boyd, J. H. and R. Jagannathan, 'Ex-dividend price behavior of common stocks,' Review of Financial Studies 7, 4 (1994), 711-741   DOI   ScienceOn
21 Miller, M. H. and M. S. Scholes, 'Dividends and taxes,' Journal of Financial Economics 6 (1978), 633-664
22 Hess, P. J., 'The ex-dividend day behavior of stock returns: Further evidence on tax effects,' Journal of Finance 37 (May 1982), 445-456   DOI
23 Black, F. and M. S. Scholes, 'The effects of dividend yield and dividend policyon common stock prices and returns,' Journal of Financial Economics 1 (May 1974), 1-22   DOI   ScienceOn
24 Easterbrook, F. H., 'Two agency cost explanations of dividends,' American Economics Review 74, 4 (1984), 650-659
25 McDonald, R. L. and D. R. Siegel, 'The Value of Waiting Investment,' Quarterly Journal of Economics, (1986),707-727   DOI   ScienceOn
26 De Angelo, H. and L. De Angelo, 'Dividend policy and financial distress: An empirical investigation of troubled NYSE firms,' Journal of Finance 45 (Dec. 1990), 1415-1431   DOI
27 Brealey, R. A. and S. C. Myers, Principles of Corporate Finance, 4th ed., N.Y.; McGraw-Hill, 1991
28 Fama, E., 'The empirical relationship between the dividend investment decision of firms,' American Economic Review 64, 3 (1974), 304-318
29 Litzenberger, R. H. and K. Ramaswamy, 'The effect of personal taxes and dividends on capital asset prices,' Journal of Financial Economics 7 (1979), 163-195   DOI   ScienceOn
30 Brennan, M. J., 'A note on Dividend Irrelevance and the Gordon valuation model,' Journal of Finance 26 (Dec. 1971), 1115-1122   DOI
31 Schwartz, E. and C. Zozaya, 'Valuation of Investment Technology Investments as Real Options,' Working paper, University of California, LA., 2000
32 Litzenberger, R. H. and K. Ramaswamy, 'The effects of dividends on common stock prces: Tax effects or information effects?,' Journal of Finance 37 (May 1982), 429-443   DOI
33 Eades, K. M, P. J. Hess and E. H. Kim, 'Time-series variation in dividend pricing,' Journal of Finance 49 (Dec. 1994), 1671-1638   DOI
34 Grenadier, S. R., 'Valuing lease contracts: A real-options approach,' Journal of Financial Economics 38 (1995), 297-331   DOI   ScienceOn
35 Jarrow, Robert and Andrew Rudd, Option Pricing, Homewood, IL.: Irwin., 1983
36 Merton, R. C., 'Theory of rational option pricing,' Bell Journal of Economics and Management Science 4 (Spring 1973), 141-183   DOI   ScienceOn
37 Nissim, Doran, and Amir Ziv, 'Dividend changes and future profitability,' Journal of Finance 56 (Dec. 2001), 2111-2133   DOI   ScienceOn
38 Hakansson, N., 'To pay or not to pay dividends,' Journal of Finance 37 (May 1982), 415-428   DOI   ScienceOn
39 Miller, M. H. and K. Rock, 'Dividend policy under asymmetric information,' Journal of Finance 40 (Sept. 1985), 1031-1051   DOI
40 Ackert, L. F. and B. F Smith, Stock volatility, ordinary dividends, and other cash flows to share-holders, Journal of Finance 48 (Sept. 1993), 1147-1160   DOI
41 Brennan, M. J. and E. Schwartz, 'Evaluating natural resource investments,' Journal of Business 58 (1985), 135-157   DOI   ScienceOn
42 De Angelo, H., L. De Angelo and Douglas J. Skinner, 'Reversal of fortune: Dividend signaling and the disappearance of sustained earnings growth,' Journal of Financial Economics 40 (1996), 341-371   DOI   ScienceOn
43 Eades, K. M., P. J. Hess and E. H. Kim, 'On interpreting security returns during the ex-dividend period,' Journal of Financial Economics 13, 1 (1984), 3-34   DOI   ScienceOn
44 Kao, C. and C. Wu, 'Tests of dividend signaling using the Marsh-Merton model: A generalized friction approach,' Journal of Business 67, 1 (1994), 45-68   DOI   ScienceOn
45 Lintner, J., 'Dividends, earnings, leverage, stock prices and the supply of capital to corporations,' Review of Economics and Statistics 64, 3 (1962), 243-269   DOI   ScienceOn
46 Miller, M. H. and M. S. Scholes, 'Dividends and taxes: Some empirical evidences,' Journal of Political Economy 90 (1982), 1118-1142   DOI   ScienceOn
47 Marsh, T. A. and R. C. Merton, 'Dividend Behavior for the Aggregate stock market,' Journal of Business 60, 1 (1987), 1-40   DOI   ScienceOn
48 Dixit, A., 'Entry and exit decisions under uncertainty', Journal of Political Economy 97 (1989), 620-638   DOI   ScienceOn