Generalization of the Modigliani–Miller Theory for the Case of Variable Profit

Peter Brusov,George Lin,Veniamin Kulik,She-I Chang,Tatiana Filatova,Natali Orekhova

doi:10.3390/math9111286

Abstract

For the first time we have generalized the world-famous theory by Nobel Prize winners Modigliani and Miller for the case of variable profit, which significantly extends the application of the theory in practice, specifically in business valuation, ratings, corporate finance, etc. We demonstrate that all the theorems, statements and formulae of Modigliani and Miller are changed significantly. We combine theoretical and numerical (by MS Excel) considerations. The following results are obtained: (1) Discount rate for leverage company changes from the weighted average cost of capital, WACC, to WACC–g (where g is growing rate), for a financially independent company from k0 to k0–g. This means that WACC and k0 are no longer the discount rates as it takes place in case of classical Modigliani–Miller theory with constant profit. WACC grows with g, while real discount rates WACC–g and k0–g decrease with g. This leads to an increase of company capitalization with g. (2) The tilt angle of the equity cost ke(L) grows with g. This should change the dividend policy of the company, because the economically justified value of dividends is equal to equity cost. (3) A qualitatively new effect in corporate finance has been discovered: at rate g < g* the slope of the curve ke(L) turns out to be negative, which could significantly alter the principles of the company’s dividend policy.

Highlights

Within the new Generalized Modigliani–Miller theory (GMM theory), we study the dependence of the weighted average cost of capital, WACC, the equity cost, ke, the discount rate, i, and the capitalization of the company, V, on leverage level L
The discount rate for a leveraged company changes from the weighted average cost of capital, WACC, to WACC–g, for an unleveraged company from k0 to k0 –g. This means that WACC and k0 are no longer the discount rates they are in the case of classical Modigliani–Miller theory with constant profit
Discount rate for the leverage company change from the weighted average cost of capital, WACC, to WACC–g, for a financially independent company from k0 to k0 –g. This means that WACC and k0 are no longer the discount rates as it takes place in case of the classical Modigliani–Miller theory with constant profit

Summary

Introduction

The original theory by Nobel Prize Winners Modigliani and Miller [1,2,3] has been modified by many authors and we shortly discuss some of these. A few important modifications have been done by the authors of this paper [4,5,6], who created the general theory of capital cost and capital structure, the Brusov–Filatova–Orekhova (BFO) theory, which generalized the Modigliani–Miller theory for the case of companies of arbitrary age (and arbitrary lifetime), as well as for the case of advance payments of tax on profit [6], for rating needs [5,6] as well as for variable debt cost. Note that a stochastic extension of the Miller–Modigliani theory has been created by some authors [7,8]

Objectives

Results

Conclusion