The valuation of a firm advertising optimally

In this paper we model the value of a firm based on its current earnings and cash balances. The value is modelled on the assumption that earnings follow a mean-reverting process. The effect of advertising on earnings is modelled, and the condition for optimal advertising derived. The value of the firm is derived as the solution to a partial differential equation. The way in which this value depends on the legal structure and banking arrangements of the firm is discussed.

[1]  P. Wilmott,et al.  A model for the value of a business, some optimization problems in its operating procedures and the valuation of its debt , 1997 .

[2]  Alan G. White,et al.  The Pricing of Options on Assets with Stochastic Volatilities , 1987 .

[3]  Eduardo S. Schwartz,et al.  Evaluating Natural Resource Investments , 1985 .

[4]  F. Black,et al.  VALUING CORPORATE SECURITIES: SOME EFFECTS OF BOND INDENTURE PROVISIONS , 1976 .

[5]  Alan W. Pearson,et al.  Application of option pricing theory to R&D , 1994 .

[6]  Avinash Dixit,et al.  Options, the Value of Capital, and Investment , 1995 .

[7]  F. Black,et al.  The Pricing of Options and Corporate Liabilities , 1973, Journal of Political Economy.

[8]  J. Hull.  Options, futures, and other derivative securities , 1989 .

[9]  A. C. Chiang.  Fundamental methods of mathematical economics , 1974 .

[10]  Eduardo S. Schwartz,et al.  Investment Under Uncertainty. , 1994 .

[11]  A. Bensoussan,et al.  Stochastic equity volatility and the capital structure of the firm , 1994, Philosophical Transactions of the Royal Society of London. Series A: Physical and Engineering Sciences.

[12]  Darrell Duffie,et al.  Implementing Arrow-Debreu equilbria by continuous trading of a few long-lived securities , 1985 .

[13]  R. C. Merton,et al.  On the Pricing of Corporate Debt: The Risk Structure of Interest Rates , 1974, World Scientific Reference on Contingent Claims Analysis in Corporate Finance.

[14]  R. McDonald,et al.  Investment and the Valuation of Firms When There Is an Option to Shut Down , 1985 .

[15]  P. Wilmott,et al.  Option pricing: Mathematical models and computation , 1994 .

[16]  Alistair Milne,et al.  Firm behaviour under the threat of liquidation , 1996 .

[17]  Eduardo S. Schwartz,et al.  A Simple Approach to Valuing Risky Fixed and Floating Rate Debt , 1995 .

[18]  R. C. Merton,et al.  Continuous-Time Finance , 1990 .

[19]  Ian A. Cooper,et al.  The Default Risk of Swaps , 1991, World Scientific Reference on Contingent Claims Analysis in Corporate Finance.

[20]  Spanning with Short‐Selling Restrictions , 1993 .

[21]  S. Dreyfus.  Dynamic Programming and the Calculus of Variations , 1960 .