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2022 | Buch

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Generalized Modigliani–Miller Theory

Applications in Corporate Finance, Investments, Taxation and Ratings

verfasst von: Prof. Dr. Peter Brusov, Prof. Tatiana Filatova, Prof. Natali Orekhova

Verlag: Springer International Publishing

Buchreihe : Contributions to Finance and Accounting

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Wirtschaft"

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Über dieses Buch

The original theory of capital cost and capital structure put forward by Nobel Prize Winners Modigliani and Miller has since been modified by many authors, and this book discusses some of them. The book’s authors have created general theory of capital cost and capital structure – the Brusov–Filatova–Orekhova (BFO) theory, which generalizes the Modigliani–Miller theory to encompass companies of an arbitrary age (and arbitrary lifetime). Despite the availability of this more general theory, the classical Modigliani–Miller theory is still widely used in practice. In this book, the authors for the first time generalize it for cases of practical relevance: for the case of variable profit; for the case of advance tax-on-profit payments and interest on debt payments; for the case of several tax-on-profit and interest on debt payments per period; and for the combination of all three effects. These generalizations lead to valuable theoretical results as well as significantly widen of practical application this theory in practice and increase of the quality of finance management of the company. As well, the book investigates the applications of said results in corporate finance, investments, taxation and ratings, where employing a generalized Modigliani–Miller theory can be very fruitful.

Inhaltsverzeichnis

Frontmatter

Chapter 1. Introduction

Abstract

In modern conditions, as we mentioned in Preface, the requirements for the quality of the company’s financial management, for the efficiency of corporate finance management, for improving the quality of assessing the effectiveness of investments, for improving the taxation and tax control system, for developing an adequate system of business assessment, for increasing the objectivity of ratings are increasing. In the financial management of a company, the management of the cost of raising capital and the structure of the company’s capital plays a fundamental role. Historically, the first quantitative theory of the capital structure of a company—the theory of Nobel laureates Modigliani and Miller, due to a large number of limitations of this theory, had a very distant relationship to economic practice. Since the creation of the theory of Modigliani and Miller, numerous attempts have been made to modify it, the analysis of which is given in the monograph. Of all the modifications, we mention the two most important ones that brought the theory closer to economic practice: accounting for corporate and individual taxes (carried out by the authors Modigliani and Miller themselves) and generalization to the case of companies of arbitrary age and arbitrary lifetime, performed by the authors of this monograph, who created the Brusov–Filatova–Orekhova (BFO) theory. The rest of the modifications, although some of them are interesting from a theoretical point of view, have little effect on the possibility of the practical application of the Modigliani–Miller theory. Note that the importance of the Modigliani–Miller theory is determined by the fact that, despite its many limitations (the most significant of which is the perpetuity of companies), it is still widely used in practice, and also by the fact that it is, due to its simplicity and that it is the perpetuity limit of the BFO theory, serves as a good testing ground for new modifications, which, after verifying their significance for practical application, are then used in the BFO theory.

Peter Brusov, Tatiana Filatova, Natali Orekhova

Modigliani–Miller Theory in Corporate Finance

Frontmatter

Chapter 2. Capital Structure: Modigliani–Miller Theory

Abstract

One of the two main theories of capital cost and capital structure is the theory of Nobel Prize winners Modigliani and Miller (Am Econ Rev 48:261–297, 1958, Am Econ Rev 53:147–175, 1963, Am Econ Rev 56:333–391, 1966). In this chapter, we describe the main results of this theory.

Under the capital structure, one understands the relationship between equity and debt capital of the company. Does capital structure affect the company’s main settings, such as the cost of capital, profit, value of the company, and the others, and, if it affects, how? Choice of an optimal capital structure, i.e., a capital structure, which minimizes the weighted average cost of capital, WACC, and maximizes the value of the company, V, is one of the most important tasks solved by a financial manager and by the management of a company. The first serious study (and first quantitative study) of the influence of capital structure of the company on its indicators of activities was the work by Modigliani and Miller (Am Econ Rev 48:261–297, 1958, Am Econ Rev 53:147–175, 1963, Am Econ Rev 56:333–391, 1966). Until this study, the approach existed (let us call it traditional), which was based on empirical data analysis.

Peter Brusov, Tatiana Filatova, Natali Orekhova

Chapter 3. Modern Theory of Capital Cost and Capital Structure: Brusov–Filatova–Orekhova Theory (BFO Theory)

Abstract

The most significant generalization of Modigliani–Miller theory has been done by Brusov, Filatova, and Orekhova in 2008 (Filatova et al., Bull FU 48:68–77, 2008). The Brusov, Filatova, and Orekhova theory (BFO theory) has replaced the famous theory of capital cost and capital structure by Nobel laureates Modigliani and Miller, making latter one the perpetuity limit of BFO theory. The authors have moved from the assumption of Modigliani–Miller concerning the perpetuity (infinite time of life) of companies and further elaborated quantitative theory of valuation of key parameters of financial activities of companies with arbitrary time of life (of arbitrary age). Results of modern BFO theory turn out to be quite different from those of Modigliani–Miller theory. They show that the latter, via its perpetuity, underestimates the assessment of weighted average cost of capital, WACC, and the equity cost of the company and substantially overestimates the assessment of the capitalization of the company. Such an incorrect assessment of key performance indicators of financial activities of companies has led to an underestimation of risks involved, and impossibility, or serious difficulties in adequate managerial decision-making, which was one of the implicit reasons of the global financial crisis in 2008.

As we discussed in Chap. 2, one of the serious limitations of the Modigliani–Miller theory is the suggestion about perpetuity of the companies. In 2008, Brusov–Filatova–Orekhova (Filatova et al., Bull FU 48:68–77, 2008) have lifted up this limitation and have shown that the accounting of the finite lifetime (or finite age) of the company leads to significant changes of all Modigliani–Miller results (Modigliani and Miller, Am Econ Rev 48:261–297, 1958; Am Econ Rev 53:147–175, 1963; Am Econ Rev 56:333–391, 1966): capitalization of the company is changed, as well as the equity cost, k_e, and the weighted average cost of capital, WACC, in the presence of corporative taxes. Besides, a number of qualitatively new effects in corporate finance, obtained in Brusov–Filatova–Orekhova theory (Brusov, J Rev Glob Econ 7:i–vi, 2018a; J Rev Glob Econ 7:i–v, 2018b; Brusov et al., Modern corporate finance, investments and taxation. Springer, 2015; Modern corporate finance, investments, taxation and ratings. Springer, 2018a; Modern corporate finance and investments. Monograph. Knorus Publishing House, 2018b; J Rev Glob Econ 7:37–62, 2018c; J Rev Glob Econ 7:63–87, 2018e; Rev Glob Econ 7:104–122, 2018f; J Rev Glob Econ 7:360–376, 2018g; J Rev Glob Econ 8:437–448, 2019; J Rev Glob Econ 9:257–268, 2020; Filatova et al. 2018; Brusov and Filatova, Finance Credit 435:2–8, 2011; Brusov et al., Appl Financ Econ 21(11):815–824, 2011a; Res J Econ Bus ICT 2:16–21, 2011b; Res J Econ Bus ICT (UK) 2:11–15, 2011c; Appl Financ Econ 22(13):1043–1052, 2012a; J Rev Global Econ 1:106–111, 2012b; Rev Global Econ 2:94–116, 2013a; J Rev Global Econ 2:183–193, 2013b; Cogent Econ Finance 2:1–13, 2014a; Rev Global Econ 3:175–185, 2014b), are absent in Modigliani–Miller theory.

Only in the absence of corporate taxes, we give a rigorous proof of the Brusov–Filatova–Orekhova theorem that equity cost, k_e, as well as its weighted average cost, WACC, does not depend on the lifetime (or age) of the company, so the Modigliani–Miller theory could be generalized for arbitrary lifetime (arbitrary age) companies.

Until recently (before 2008, when the first paper by Brusov–Filatova–Orekhova [Filatova et al. (Bull FU 48:68–77, 2008)] has appeared), the basic theory (and the first quantitative one) of the cost of capital and capital structure of companies was the theory by Nobel Prize winners Modigliani and Miller (Am Econ Rev 48:261–297, 1958; Am Econ Rev 53:147–175, 1963; Am Econ Rev 56:333–391, 1966). One of the serious limitations of the Modigliani–Miller theory is the suggestion about perpetuity of the companies. We lift up this limitation and show that the accounting of the finite lifetime (finite age) of the company leads to change in the equity cost, k_e, as well as of the weighted average cost of capital, WACC, in the presence of corporate taxes. The effect of leverage on the cost of equity capital of the company, k_e, with an arbitrary lifetime, and its weighted average cost of WACC is investigated. We give a rigorous proof of the Brusov–Filatova–Orekhova theorem that in the absence of corporate taxes, cost of company equity, k_e, as well as its weighted average cost, WACC, does not depend on the age (lifetime) of the company.

Peter Brusov, Tatiana Filatova, Natali Orekhova

Chapter 4. Optimal Capital Structure of the Company: Its Absence in Modigliani–Miller Theory with Risky Debt Capital

Abstract

In this chapter, we discuss the problem of optimal capital structure of the company. Choosing of optimal capital structure of the company, i.e., proportion of debt and equity, which minimizes the weighted average cost of capital, WACC, and maximizes the company capitalization, V, is one of the most important tasks of financial manager and the management of a company. The search for an optimal capital structure, like the search for a “golden fleece,” attracts attention of economists and financiers for many tens of years. And it is clear why: one can, nothing making, but only by changing the proportion between the values of equity capital and debt one of the company, significantly enhance the company capitalization, by other words to fulfill the primary task, to reach critical goal of the business management. Spend a little less of your own, loan slightly more (or vice versa), and company capitalization reaches a maximum. In the classical Modigliani–Miller theory [Modigliani and Miller (Am Econ Rev 48:261–297, 1958], there is no optimal capital structure: an increase in the share of borrowed capital reduces the cost of raising capital, WACC, and increases the capitalization of company V up to infinite leverage level L values. We show here that in Modigliani–Miller theory [Modigliani and Miller (Am Econ Rev 48:261–297, 1958; Am Econ Rev 53:147–175, 1963] modified by us by taking off the suggestion about riskless of debt capital, the optimal capital structure is still absent as well as in the famous trade-off theory.

Peter Brusov, Tatiana Filatova, Natali Orekhova

Chapter 5. The Equity Cost in the Modigliani–Miller Theory

Abstract

The cost of equity is very important in finance because the economically justified cost of dividends is equal to the cost of equity. Thus, knowledge of the cost of equity capital helps the company’s management to formulate an adequate dividend policy for the company.

But calculation of the cost of equity capital is one of the most difficult tasks of company management. This could be done correctly only within the modern capital structure theory—Brusov–Filatova–Orekhova theory (BFO theory) (Filatova et al., Bullet FU 48:68–77, 2008; Brusov et al., Appl Financ Econ 21:815–824, 2011a, Res J Econ Bus ICT 2:16–21, 2011b, Res J Econ Bus ICT 2:11–15, 2011c, Appl Financ Econ 22(13):1043–1052, 2012a, J Rev Glob Econ 1:106–111, 2012b, J Rev Glob Econ 2:94–116, 2013a, J Rev Glob Econ 2:183–193, 2013b, Cogent Econ Finance 2:1–13, 2014a, J Rev Glob Econ 3:175–185, 2014b; Brusova, Financ Anal Probl Solutions 34:36–42, 2011) and within its perpetuity limit Modigliani–Miller theory (Modigliani and Miller, Am Econ Rev 48:261–297, 1958, Am Econ Rev 53:147–175, 1963, Am Econ Rev 56:333–391, 1966).

In this chapter, we consider the value of the cost of equity k_e in the theory of Modigliani and Miller, its dependence on leverage level L and tax on profit rate T. We study the dependence of cost of equity on leverage level L at different tax on profit rates T and the dependence of cost of equity on tax on profit rates T at different leverage level L and show that in this perpetuity limit the cost of equity k_e is always growing with leverage (for any tax on profit rate T).

Note, that within the modern Brusоv–Filаtоvа–Orekhоvа theory for companies of arbitrary (finite) age or with finite lifetime a qualitatively new effect takes place: decreasing of the cost of equity with the leverage. The effect takes place at tax on profit rate T, exceeding a cutoff value T*.

In Chaps. 9 and 10 we will study the influence of frequency of payments of tax on profit rate T on equity cost k_e and on its dependence on leverage level L and on tax on profit rate T.

Peter Brusov, Tatiana Filatova, Natali Orekhova

Chapter 6. The Role of Taxing and Leverage in Evaluation of Capital Cost and Capitalization of the Company

Abstract

In this chapter, the role of tax shield, taxes, and leverage in the Modigliani–Miller theory is investigated. It is shown that the equity cost as well as the weighted average cost of capital decrease with the tax rate, while the capitalization increases. A detailed investigation of the dependence of the weighted average cost of capital WACC and the equity cost k_e on the tax rate at fix leverage level L (at debt capital fraction w_d) and on the leverage level at fix tax rate is made. We have introduced the concept of tax operation leverage.

Peter Brusov, Tatiana Filatova, Natali Orekhova

Chapter 7. Inflation in Modigliani–Miller Theory

Abstract

In this chapter, the influence of inflation on capital cost and capitalization of the company within Modigliani–Miller theory (Мodigliani and Мiller Am Econ Rev 48: 261–297, 1958, Am Econ Rev 53: 147–175, 1963, Am Econ Rev 56: 333–391, 1966) is investigated. By direct incorporation of inflation into Modigliani–Miller theory, it is shown for the first time that inflation not only increases the equity cost and the weighted average cost of capital but as well it changes their dependence on leverage (Brusov et al. J Rev Global Econ 3:175–185, 2014b). In particular, it increases the growing rate of equity cost with leverage. Capitalization of the company is decreased under the accounting of inflation.

Peter Brusov, Tatiana Filatova, Natali Orekhova

Chapter 8. Modification of the Modigliani–Miller Theory for the Case of Advance Tax on Profit Payments

Abstract

The Modigliani–Miller theory, discussed in Chap. 2, has a lot of limitations. One of the most important and serious assumptions of the Modigliani–Miller theory is that all financial flows as well as all companies are perpetuity. This limitation was lifted out by Brusov–Filatova–Orekhova in 2008 (Filatova et al. Bull FU 48:68–77, 2008), who have created BFO theory—modern theory of capital cost and capital structure for companies of arbitrary age (Brusov et al. 2018, Modern corporate finance, investments, taxation and ratings, Springer Nature Publishing, Cham, 2018a, J Rev Global Econ, 7:360–376, 2018b, J Rev Global Econ, 7:37–62, 2018c, J Rev Global Econ, 7:88–103, 2018d, J Rev Global Econ, 7:63–87, 2018e, J Rev Global Econ, 7:104–122, 2018f, Modern corporate finance and investments, monograph, Knorus Publishing House, Moscow, 517, 2018g, h, j, k, J Rev Global Econ, 8: 437–448, 2019, J Rev Global Econ, 9:257–268, 2020; Filatova et al. Bull FU 48:68–77, 2008, J Rev Global Econ, 7:645–661, 2018). Despite the fact that the Modigliani–Miller theory is currently a particular case of the general theory of capital cost and capital structure—Brusov–Filatova–Orekhova (BFO) theory—it is still widely used in practice.

In the current chapter, we discuss one more limitation of Modigliani–Miller theory: a method of tax on profit payments. Modigliani–Miller theory accounts for these payments as annuity-immediate while in practice these payments are often made in advance and thus should be accounted as annuity-due. We generalize the Modigliani–Miller theory for the case of advance tax on profit payments, which is widely used in practice and show that this leads to some important consequences, which change seriously all the main statements by Modigliani and Miller (Brusov et al. J Rev Global Econ, 9:257–268, 2020). The modified Modigliani–Miller theory (MMM theory) is the second of the three main theories which consist of the base for conducting of modification of existing rating methodologies. In this chapter, we describe the main results of MMM theory.

Peter Brusov, Tatiana Filatova, Natali Orekhova

Chapter 9. The Modigliani–Miller Theory with Arbitrary Frequency of Payment of Tax on Profit

Abstract

The tax shield plays a crucial role in both main capital structure theories: Brusov–Filatova–Orekhova (BFO theory) and its perpetuity limit Modigliani–Miller theory. How it is formed influences the results of both theories. To study this problem, we modify for the first time the Modigliani–Miller theory for the case of arbitrary frequency of payment of tax on profit. Combining the theoretical consideration with numerical calculations within MS Excel, we show that: (1) all Modigliani–Miller theorems, statements and all formulas change; (2) all main financial indicators, such as the weighted average cost of capital, WACC, company value, V, and equity cost, k_e, depend on the frequency of tax on profit payments. This allows to company manage WACC, V, k_e, etc. by choosing the number of payments of tax of profit p per year; (3) in case of income tax payments more than once per year (at p ≠ 1), as it takes place in practice, the weighted average cost of capital, WACC, company value, V and equity cost, k_e start depend on k_d, while in ordinary (classical) Modigliani–Miller theory all these values DO NOT depend on k_d; (4) the tilt angle of the curve of equity cost, k_e (L), decreases with the number of payments of tax of profit p, this modifies the dividend policy of the company, because the economically justified value of dividends is equal to equity cost; (5) obtained results allow to company choose the number of payments of tax of profit per year, as many, as it is profitable to it (of course, within actual tax legislation): more frequent payments of income tax are beneficial for both parties: for the company and for the tax regulator.

Peter Brusov, Tatiana Filatova, Natali Orekhova

Chapter 10. How Frequently Should Companies Pay Tax on Profit

Abstract

Two main capital structure theories: Brusov–Filatova–Orekhova (BFO theory) and its perpetuity limit—Modigliani–Miller theory—describe the case of annual payments of tax of profit at the end of periods, but in practice, these payments (1) are made more frequent: semiannually, quarterly, monthly; (2) could be made in advance. To study the influence of these two effects on main financial indicators of the company, such as the weighted average cost of capital, WACC, company value, V, and equity cost, k_e, we modify the Modigliani–Miller theory for the case of arbitrary frequency of payments of tax on profit: for payments at the end of periods as well as for advanced payments. Account of two these effects leads to very important consequences. We show that:

All Modigliani–Miller theorems, statements, and all formulas change.

All main financial indicators, WACC, V, and k_e depend on the frequency of tax on profit payments and start depend on debt cost k_d, while in ordinary (classical) Modigliani–Miller theory all these indicators DO NOT depend on k_d.

The tilt angle of the curve of equity cost, k_e (L), changes with the frequency of payments of tax of profit p, this modifies the dividend policy of the company, because the economically justified value of dividends is equal to equity cost.

For payments of tax of profit at the end of periods more frequent payments of income tax are beneficial for both parties: for the company and for the tax regulator: (1) for the company, this leads to decrease of the cost of attracting capital, WACC, and thus to an increase in the value of the company, V, and (2) for the tax regulator, more frequent payments are beneficial due to the time value of money.

For payments of tax of profit in advance more frequent payments of income tax are NOT beneficial for the company: this leads to increase of the cost of attracting capital, WACC, and thus to decrease in the value of the company, V, but for the tax regulator it remains beneficial: earlier payments are beneficial due to the time value of money.

All these allow company to choose the method of payments of tax of profit(at the end of period or in advance) and number of payments of tax of profit per year, as many, as it is profitable to it (of course, within actual tax legislation).

Peter Brusov, Tatiana Filatova, Natali Orekhova

Chapter 11. Generalization of the Modigliani–Miller Theory for the Case of Variable Profit

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:

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.

The tilt angle of the equity cost k_e(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.

A qualitatively new effect in corporate finance has been discovered: at rate g < g* the slope of the curve k_e(L) turns out to be negative, which could significantly alter the principles of the company’s dividend policy.

Peter Brusov, Tatiana Filatova, Natali Orekhova

Applications of the Modigliani–Miller Theory in Investments

Frontmatter

Chapter 12. Investment Models with Debt Repayment at the End of the Project and their Application

Abstract

In this and next chapter, we describe the modern investment models, created by the authors and well tested in the real economy. These models used by us for investigation of different problems of investments, such as influence of debt financing, leverage level, taxing, project duration, method of financing, and some other parameters on efficiency of investments and other problems. But we use them in Chap. 18 for modification of methodology of project ratings. In this chapter we consider the investment models with debt repayment at the end of the project and their application, while in Chap. 13, we consider the investment models with uniform debt repayment and their application.

Peter Brusov, Tatiana Filatova, Natali Orekhova

Chapter 13. Investment Models with Uniform Debt Repayment and Their Application

Abstract

In the previous сhapter, we have established investment models with debt repayment at the end of the project, well proven in the analysis of real investment projects. In practice, however, a scheme of uniform debt repayment during the duration of the project is more extended. In this chapter, we describe new investment models with uniform debt repayment during the duration of the investment project, quite adequately describing real investment projects. Within these models, it is possible, in particular, to analyze the dependence of effectiveness of investment projects on debt financing and taxation. We will work on the modern theory of capital cost and capital structure developed by Brusov–Filatova–Orekhova (Brusov and Filatova 2011; Brusov et al. 2011a, b, c, 2012a, b, 2013a, b, 2014a, b; Filatova et al. (Bull FU 48:68–77, 2008); Brusova 2011) as well as on perpetuity limit [Мodigliani and Мiller (Am Econ Rev 48:261–297, 1958; Am Econ Rev 53:147–175, 1963; Am Econ Rev 56:333–391, 1966)].

In this chapter, we consider the application of the investment models with uniform debt repayment to rating methodology.

Peter Brusov, Tatiana Filatova, Natali Orekhova

Chapter 14. Innovative Investment Models with Debt Repayment at the End of the Project

Abstract

New modern investment models are created that are as close as possible to real investment conditions. We consider the long-term as well as arbitrary duration models with payments of interest on debt and of tax on income a few times per year (semiannually, quarterly, monthly), which could be applied in real economic practice. Their verification will lead to the creation of a comprehensive system of adequate and correct assessment of the effectiveness of the company’s investment program and its investment strategy. One of the most important elements of calculating the effectiveness of investment projects is the assessment of the discount rate, the calculation methods of which are generalized for the real conditions of the implementation of investment projects. We consider the effectiveness of the investment project from two points of view: the equity owners and the owners of equity and debt. NPV for each of these cases is calculated by two different methods: with the separation of credit and investment flows (and thus discounting of the flows using two different rates) and without such separation (with discounted of both flows using the same rate, and WACC can be chosen as rate). Numerical calculations, conducted for four investment models (without flow separation) show, that: (1) in case of considering of the effectiveness of investment project for owners of equity capital, the increase of number of payments of tax on income and of interest on debt p leads to decrease of NPV: this means that the effectiveness of investment project decreases with p; (2) in case of considering of the effectiveness of investment project for owners of equity and debt capital, the increase of number of payments of tax on income and of interest on debt p leads to increase of NPV: this means that the effectiveness of investment project increases with p. In the former case, companies should pay tax on profit and interest on debt once per year, while in the latter case, more frequent payments are profitable for the effectiveness of investment. Eight innovative investment models created in this paper can assist decision-makers in the optimal design, planning, and control in company investments and development of company investment strategy.

Peter Brusov, Tatiana Filatova, Natali Orekhova

Chapter 15. Investment Models with Advance Frequent Payments of Tax on Profit and of Interest on Debt

Abstract

Recently [Brusov et al. (Mathematics 9(13):1491, 2021)] new modern investment models have been created by us to be as close as possible to real investment conditions. We developed long-term as well as arbitrary duration models with payments of interest on debt and of tax on income a few times per year (semiannually, quarterly, and monthly), which could be applied in real economic practice.

We considered the effectiveness of the investment project from two points of view: the equity owners and the owners of equity and debt. NPV for each of these cases was calculated by two different methods: with the separation of credit and investment flows (and thus discounting the flows using two different rates) and without such separation (with discounting of both flows using the same rate, and the weighted average cost of capital, WACC, can be chosen as the rate). Numerical calculations, conducted for four investment models (without flow separation) showed that: (1) WACC decreases with p; (2) in the case of considering the effectiveness of an investment project for owners of equity capital, the increase in the number of payments of tax on income and of interest on debt p leads to a decrease in NPV: this means that the effectiveness of an investment project decreases with p; (3) in the case of considering the effectiveness of an investment project for owners of equity and debt capital, the increase in the number of payments of tax on income and of interest on debt p leads to an increase in NPV: this means that the effectiveness of an investment project increases with p. In the former case, companies should pay tax on profit and interest on debt once per year, while in the latter case, more frequent payments are profitable for the effectiveness of investment.

But in practice payments of tax on profit and of interest on debt could be made in advance. In the current Chapter, we develop the innovative investment models with frequent advance payments of tax on profit and of interest on debt and study the effectiveness of investment projects within them [Filatova et al. (Mathematics 10(4):666, 2022)].

Numerical calculations carried out for four investment models (without split flows) showed that in the case of advance payments of income tax and interest on debt, all the results related to the effect of the number of payments of income tax and interest on debt on the effectiveness of the investment projects are opposite to the results in the case of payments at the end of the periods obtained by us in the previous article: (1) WACC increases with p; (2) in the case of considering the effectiveness of an investment project for owners of equity capital, the increase in the number of payments of tax on income and of interest on debt p leads to an increase in NPV: this means that the effectiveness of an investment project increases with p; (3) in the case of considering the effectiveness of an investment project for owners of equity and debt capital, the increase in the number of payments of tax on income and of interest on debt p leads to the decrease in NPV: this means that the effectiveness of an investment project decreases with p. In the latter case, companies should pay tax on profit and interest on debt once per year, while in the former case, more frequent payments are profitable for the effectiveness of investment.

Thus, this means that method of payments of tax on income and of interest on debt (in advance or in the ends of periods) changes drastically the effect of the number of payments of income tax and interest on debt on the effectiveness of investments. Depending on the relationship between the investor and the lender, the investor can choose (within the framework of tax legislation):

The frequency of payment of income tax
Scheme for payment of income tax (in advance or at the end of periods)

The verification of developed by us the innovative investment models with frequent advance payments of tax on profit and of interest on debt will lead to the creation of a comprehensive system of adequate and correct assessment of the effectiveness of the company’s investment program and its investment strategy for both schemes for payment of income tax (in advance or at the end of periods).

One of the most important elements of calculating the effectiveness of investment projects is the assessment of the discount rate, the calculation methods of which are generalized for the real conditions of the implementation of investment projects. Eight innovative investment models with advance payments of tax on profit and of interest on debt created in this paper can assist decision-makers in the optimal design, planning, and control of company investments and the development of a company’s investment strategy.

The results obtained in the current chapter and papers [Brusov et al. (Mathematics 9(13):1491, 2021); Filatova et al. (Mathematics 10(4): 666, 2022)] help tax regulator (Finance Ministry) understand the influence of the number of payments of tax on income and to credit regulator (Central Bank) understand the influence of the number of payments of interest on debt on the effectiveness of investment projects. These allow both regulators to modify and improve tax legislation and credit policy, respectively.

Peter Brusov, Tatiana Filatova, Natali Orekhova

Applications of the Modigliani–Miller Theory Ratings and Rating Methodologies

Frontmatter

Chapter 16. Application of the Modigliani–Miller Theory in Rating Methodology

Abstract

This chapter, Chaps. 17 and 18 suggest a new approach to rating methodology. This chapter and Chap. 17 are devoted to rating of nonfinancial issuers, while Chap. 18 is devoted to long-term project rating. The key factors of a new approach are: (1) The adequate use of discounting of financial flows virtually not used in existing rating methodologies, (2) The incorporation of rating parameters (financial “ratios”) into perpetuity limit [Modigliani and Miller (Am Econ Rev 48:261–297, 1958; Am Econ Rev 53:147–175, 1693; Am Econ Rev 56:333–391, 1966), Myers (J Econ Perspect 15(2):81–102, 2001)] of the modern theory of capital structure (Brusov–Filatova–Orekhova (BFO) theory) [Brusov et al. (Modern corporate finance, investments and taxation. Springer International, 2015; Modern corporate finance, investments, taxation and ratings. Springer Nature, 2018a; Modern corporate finance and investments. Knorus Publishing House, 2018b; J Rev Glob Econ 7:37–62, 2018c; J Rev Glob Econ 7:88–103, 2018d; J Rev Glob Econ 7:63–87, 2018e; J Rev Glob Econ 7:104–122, 2018f; J Rev Glob Econ 7:360–376, 2018g; J Rev Glob Econ 8:437–448, 2019; Ratings: critical analysis and new approaches of quantitative and qualitative methodology. Springer Nature, 2020a); Brusov (J Rev Glob Econ 7:i–vi, 2018a; J Rev Glob Econ 7:i–v, 2018b); Filatova et al. (J Rev Glob Econ 7:645–661, 2018)]. This, on the one hand, allows the use of the powerful tools of this theory in the rating, and on the other hand, it ensures the correct discount rates when discounting financial flows. We discuss also the interplay between rating ratios and leverage level which can be quite important in rating. All these create a new base for rating methodologies. New approach to ratings and rating methodologies allows to issue more correct ratings of issuers, making the rating methodologies more understandable and transparent.

Peter Brusov, Tatiana Filatova, Natali Orekhova

Chapter 17. Application of the Modigliani–Miller Theory, Modified for the Case of Advance Payments of Tax on Profit, in Rating Methodologies

Abstract

Recently we have modified the theory of Nobel Prize winners Modigliani and Miller (MM theory), which is a perpetuity limit case of the general theory of capital cost and capital structure—Brusov–Filatova–Orekhova theory (BFO theory), into two ways: we apply it for rating methodologies needs and later we generalized it for the case of advance payments of tax on profit, which is widely used in practice (MMM theory) (Brusov et al. (Mathematics 9(11):1286 (WoS Q1), 2021b). In current chapter, we use the Modified Modigliani–Miller theory (MMM theory) and apply it for rating methodologies needs. The financial “ratios” (main rating parameters) were introduced into MMM theory. The dependence of the weighted average cost of capital (WACC), which plays the role of discount rate in financial flows discounting in rating methodologies, on coverage and leverage ratios, is analyzed. Obtained results will help improve the existing rating methodologies. During a couple of years, we have suggested a new approach to rating methodology of nonfinancial issuers, as well for project rating (for long-term projects as well as for projects of arbitrary duration) [Brusov et al. (Modern corporate finance, investments, taxation and ratings. Springer Nature, 2018a; Modern corporate finance and investments. Knorus Publishing House, 2018b; J Rev Glob Econ 7:37–62, 2018c; J Rev Glob Econ 7:88–103, 2018d; J Rev Glob Econ 7:63–87, 2018e; J Rev Glob Econ 7:104–122, 2018f; J Rev Glob Econ 7:360–376, 2018g; J Rev Glob Econ 8:437–448, 2019; J Rev Glob Econ 9:257–267, 2020c); Brusov (J Rev Glob Econ 7:i–vi, 2018a; J Rev Glob Econ 7:i–v, 2018b); Filatova et al. (J Rev Glob Econ 7:645–661, 2018). The key factors of a new approach are: (1) The adequate use of discounting of financial flows virtually not used in existing rating methodologies, (2) The incorporation of rating parameters (financial “ratios”) into the modern theory of capital structure (Brusov–Filatova–Orekhova (BFO) theory) [Brusov et al. 2011, 2014, (Modern corporate finance, investments and taxation. Springer International, 2015; Modern corporate finance, investments, taxation and ratings. Springer Nature, 2018a; Modern corporate finance and investments. Knorus Publishing House, 2018b; J Rev Glob Econ 7:37–62, 2018c; J Rev Glob Econ 7:88–103, 2018d; J Rev Glob Econ 7:63–87, 2018e; J Rev Glob Econ 7:104–122, 2018f; J Rev Glob Econ 7:360–376, 2018g; J Rev Glob Econ 8:437–448, 2019); Brusov (J Rev Glob Econ 7:i–vi, 2018a; J Rev Glob Econ 7:i–v, 2018b); Filatova et al. (J Rev Glob Econ 7:645–661, 2018)] and into its perpetuity limit.

Recently we have generalized the Modigliani and Miller theory for a more realistic method of payments of tax on profit payments: for the case of advance payments of tax on profit, which is widely used in practice [Brusov et al. (J Rev Glob Econ 9:282–292, 2020b)]. Modigliani–Miller theory accounts these tax payments as annuity-immediate, while in practice, these payments are making in advance and thus should be accounting as annuity-due. We have shown that this generalization leads to some important consequences, which change seriously all the main statements by Modigliani and Miller.

In current chapter, we use the modified Modigliani–Miller theory (MMM theory) and apply it for rating methodologies needs. A serious modification of MMM theory in order to use it in rating procedure has been required. The financial “ratios” (main rating parameters) were introduced into MMM theory. The necessity of an appropriate use of financial flows discounting in rating methodologies is discussed. The dependence of the weighted average cost of capital (WACC), which plays the role of discount rate, on coverage and leverage ratios is analyzed.

Obtained results make it possible to use the power of this theory in the rating and create a new base for rating methodologies, by other words, this allows to develop a new approach to methodology of rating, requiring a serious modification of existing rating methodologies.

Peter Brusov, Tatiana Filatova, Natali Orekhova

Chapter 18. A New Approach to Project Ratings

Abstract

The chapter continues to create a new approach to rating methodology: in addition to two previous chapters, which have considered the creditworthiness of the nonfinance issuers (Brusov et al. J Rev Global Econ 7:88–103, 2018c, J Rev Global Econ 7:63–87, 2018d), we develop here a new approach to project rating. We work within investment models created by authors. One of them describes the effectiveness of investment project from the perspective of equity capital owners, while the other model describes the effectiveness of investment project from the perspective of equity capital and debt capital owners. The important features of current consideration as well as in previous studies are: (1) The adequate use of discounting of financial flows virtually not used in existing rating methodologies, (2) The incorporation of rating parameters (financial “ratios”), used in project rating, into considered modern investment models. Analyzing within these investment models with incorporated rating parameters the dependence of NPV on rating parameters (financial “ratios”) at different values of equity cost k₀, at different values of credit rates k_d as well as at different values of on leverage level L we come to a very important conclusion, that NPV in units of NOI (\( \frac{\mathrm{NPV}}{\mathrm{NOI}} \)) (as well as NPV in units of D (\( \frac{\mathrm{NPV}}{D} \))) depends only on equity cost k₀, on credit rates k_d, on leverage level L as well as on one of the leverage ratios l_j (on one of the coverage ratios i_j) and does not depend on equity value S, debt value D and NOI. This means that obtained results on the dependence of NPV (in units of NOI) (\( \frac{\mathrm{NPV}}{\mathrm{NOI}} \)) on leverage ratios l_j (as well as on the dependence of NPV (in units of D) (\( \frac{\mathrm{NPV}}{D} \)) on coverage ratios i_j) at different equity costs k₀, at different credit rates k_d, at different leverage levels L carry the universal character: these dependencies remain valid for investment projects with any equity value S, debt value D and NOI.

Peter Brusov, Tatiana Filatova, Natali Orekhova

Chapter 19. Conclusions

Abstract

In monograph, the Modigliani–Miller theory, which is the perpetuity limit of the BFO theory and nevertheless widely used in practice, is generalized taking into account the conditions for the actual functioning of companies: for the case of variable company income, for the case of income tax payments with an arbitrary frequency (monthly, quarterly, semiannual, or annual payments), as for advance tax payments for profit, and for payments at the end of the period, as well as other conditions.

Peter Brusov, Tatiana Filatova, Natali Orekhova

Titel: Generalized Modigliani–Miller Theory
verfasst von: Prof. Dr. Peter Brusov
Prof. Tatiana Filatova
Prof. Natali Orekhova
Verlag: Springer International Publishing
Electronic ISBN: 978-3-030-93893-2
Print ISBN: 978-3-030-93892-5
DOI: https://doi.org/10.1007/978-3-030-93893-2