When are Capital Structure Decisions Nonseparable from Production Planning? The Case of Generalized Royalty-Based Hybrid Finance

Kaivanto, Kim and Zinober, Alan (2015): When are Capital Structure Decisions Nonseparable from Production Planning? The Case of Generalized Royalty-Based Hybrid Finance.

Abstract

The well-known result that capital structure is irrelevant for firm value follows from a set of assumptions conducive to theoretical analysis. In this note we explore the implications of relaxing one of these assumptions: the independence of cash flows from capital structure. Unlike debt and equity, funding that is accompanied by a royalty payment obligation has the effect of increasing marginal cost, to which a profit-maximizing firm responds by reducing output, violating the independence assumption. We study the effect on optimal production plans of generalized royalty payment obligations in which the royalty rate need not be constant across partitions of cumulative output, resulting in piece-wise linear cumulative royalty schedules that are not everywhere differentiable. The associated optimization problem for intertemporal production planning is nonstandard as it is not time separable. Here we solve this nonstandard problem by formulating an equivalent problem that in turn can be solved by the Pontryagin Maximum Principle using numerical techniques. When generalized royalty-based finance is included in the financing mix, the optimal production plan is non-trivially related to capital structure and capital structure is relevant to firm value. Unless the financing mix is restricted to debt and equity, financing decisions and production planning decisions cannot be undertaken independently in general.

• Item Type: MPRA Paper
• Language: English
• Keywords: capital structure, separability, Pontryagin maximum principle, numerical methods, royalty-based finance, hybrid instruments
• Subjects: L - Industrial Organization > L2 - Firm Objectives, Organization, and Behavior > L23 - Organization of Production

References

Aivazian, V.A., Booth, L., S. Cleary. 2006. Dividend smoothing and debt ratings. Journal of Financial and Quantitative Analysis 41(2) 439--453.

Cabral, L.M., M.H. Riordan. 1994. The learning curve, market dominance, and predatory pricing. Econometrica 62(5) 1115--1140.

Dada, M., K.N. Srikanth. 1990. Monopolistic pricing and the learning curve: An algorithmic approach. Operations Research 38(4) 656--666.

Damodaran, A. 1999. Financing innovations and capital structure choices. Journal of Applied Corporate Finance 12(1) 28--39.

Kaivanto, K., P. Stoneman. 2004. Risk shifting, technology policy and sales contingent claims: when is Launch Aid to the aerospace industry a subsidy? CEPR Discussion Paper no 4798, Centre for Economic Policy Research, London.

Kaivanto, K., P. Stoneman. 2007. Public provision of sales contingent claims backed finance to SMEs: A policy alternative. Research Policy 36(5) 637--651.

Lintner, J. 1956. Distribution of incomes of corporations among dividends, retained earnings, and taxes. American Economic Review 46(2) 97--113.

Mazzola, J.B., K.F. McCarle. 1997. The stochastic learning curve: Optimal production in the presence of learning-curve uncertainty. Operations Research 45(3) 440--450.

Modigliani, F., M. Miller. The cost of capital, corporation finance and the theory of investment. American Economic Review 48(3) 261-–297.

Press, W.H., Teukolsky, S.A., Vetterling, W.T., B.P. Flannery. 2007. Numerical Recipes: The Art of Scientific Computing, 3rd edition. Cambridge University Press, Cambridge.

Sethi, S.P, G.L. Thompson. 2008. Optimal Control Theory: Applications to Management Science and Economics. Springer, Heidelberg.

Spence, M. 1981. The learning curve and competition. Bell Journal of Economics 12(1) 49--70.

Wright, T.P. 1936. Factors affecting the cost of airplanes. Journal of the Aeronautical Society 3(4) 122--128.

Yelle, L.E. 1979. The learning Curve: Historical review and comprehensive survey. Decision Sciences 10(2) 302--328.