Benefits of Advance Payments of Tax on Profit: Consideration within the Brusov–Filatova–Orekhova (BFO) Theory

Abstract

The modern capital cost and capital structure theory—the Brusov–Filatova–Orekhova (BFO) theory and its perpetuity limit, the Modigliani–Miller theory—describe the case of the payments of income tax at the end of the year. However, in practice, companies could make these payments in advance. Recently, the Modigliani–Miller theory has been modified for the case of advanced payments of income tax and has shown that the obtained results are quite different from ones in the “classical” Modigliani–Miller theory. In the current paper, for the first time, we modify the Brusov–Filatova–Orekhova (BFO) theory for the case of advanced payments of income tax and show that the impact of the transition to advance payments is much more significant than in the case of a perpetuity limit (the MM theory) and even leads to a qualitatively new effect in the dependence of equity cost on leverage. An important conclusion drawn in this paper is that the tax shield is very important, and the way it is formed (payments at the end of the year or in advance) leads to very important consequences, changing all the financial indicators of the company, such as the cost of raising capital and company value and radically changing the company’s dividend policy.

1. Introduction

The structure of the manuscript is as follows.

In the Introduction, we discuss the importance of consideration of upfront pay-ments (Section 1.1) and give a literature review on the evolution of the theory of the cost of capital and the capital structure (Section 1.2).

In Section 2, we consider modification of the Brusov–Filatova–Orekhova (BFO) theory for companies with frequent advance payments of tax on income, deriving formulas for the tax shield (Section 2.1), for the company value (Section 2.2), for the weighted average cost of capital, WACC (Section 2.3) and for the equity cost.

In Section 3, we make numerical calculations of the dependence of the weighted average cost of capital, WACC, capital value, V, equity cost, k_e, on leverage level L for three-year (Section 3.1) and six-year (Section 3.2) companies, using Microsoft Excel. We consider two types of payments of income tax: (1) at the end of the year and (2) in advance.

In Section 4, the comparison of results for three-year and six-year companies is made.

Section 5 is devoted to discussion and conclusions.

In back matter part, we describe author contributions.

1.1. The Importance of Consideration of Upfront Payments

Most financiers believe that companies should pay income tax at the end of the year. This is a widely held belief based on the time value of money. However, this does not take into account some of the competitive mechanisms described in this innovative article. These competitive mechanisms are (1) the influence of the tax shield and (2) the influence of the methods of its formation. As shown in the article, advance income tax payments are beneficial to both parties: to the companies, as they lead to a decrease in the cost of raising capital and an increase in the value of companies; to the regulator, since earlier budget replenishment ensures an increase in the stability of budget revenues. Thus, the regulator should expand the practice of early payment of taxes by companies, which is currently used in some countries (India, Russia and others). This determines the practical significance of the article. With regard to upfront payments, a company can pay tax payments in advance with subsequent adjustment if it receives a stable and predictable income.

With regard to upfront payments, a company can pay tax payments in advance with subsequent adjustment if it receives a stable and predictable income.

The importance of study of a methodology and impact of upfront payments rests on two points: (1) for companies they lead to a decrease in the cost of raising capital and an increase in the value of companies; (2) the development of a methodology for advance payments allows the regulator to expand this practice, which ensures an increase in the stability of budget revenues. As the results of this work show, advance income tax payments are very important for both parties: for companies and for the regulator.

The novelty of the current consideration lies in the recommendations to the regulator to expand the practice of advance payments on income tax, with a clear understanding by the regulator that such a practice is beneficial to both parties: companies and the state.

1.2. A Literature Review on the Evolution of the Theory of the Cost of Capital and the Capital Structure

We give below the short review of evolution of the theory of capital cost and capital structure.

(1)

The Modigliani–Miller (MM) theory, created by Nobel Prize winners in 1958 [1], was the first quantitative theory of capital structure. It was based on many restrictions, the main of which were the absence of taxes and the perpetual nature of all financial flows and companies. The first limitation was removed by the MMs themselves [2,3], and the following formulas were obtained:

For tax shield, TS:

TS = DT;

(1)

For company value, V (financially independent company V₀, leverage company, V:

$$V_0=CF/k_0 \mathrm{and}\hspace{1em}V=CF/WACC.$$

(2)

For weighted average cost of capital, WACC:

$$WACC=k_0\cdot \left(1-w_{d}t\right)$$

(3)

For equity cost, k_e:

$$k_e=k_0+L\left(k_e-k_d\right)\cdot (1-t)$$

(4)

(2)

In 1969, Hamada [4] derived the following formula for the leveraged company equity cost, accounting both financial and business risk of company, and united the Modigliani–Miller theory with the Capital Asset Pricing Model (CAPM):

$$k_e=k_{\mathrm{F}}+\left(k_{\mathrm{M}}-k_{\mathrm{F}}\right)b_{\mathrm{U}}+\left(k_{\mathrm{M}}-k_{\mathrm{F}}\right)b_{\mathrm{U}}\frac{D}{S}\left(1-T\right),$$

(5)

where b_U is the β-coefficient of the company of the same group of business risk, that the considering company, but with L = 0.

(3)

Merton Miller in 1977 [5] took into account the corporate and individual taxes. He got for the capitalization of the financially independent company the following formula:

$$V=V_0+\left[1-\frac{\left(1-T_C\right)\left(1-T_S\right)}{\left(1-T_D\right)}\right]\cdot D$$

(6)

Here, T_C–the tax on corporate income rate, T_S–the tax rate on income of an individual investor from his ownership by corporation stock, T_D–tax rate on interest income from the provision of investor–individuals of credits to other investors and companies.

(4)

In [6,7,8,9], the following formula for the WACC has been derived [6]:

$$WACC=k_0\left(1-w_{d}t\right)-k_d{w}_{d}t+k_{TS}t{w}_d$$

(7)

which is more general than the Modigliani–Miller (MM) formula for WACC.

Here, k₀, k_d, and k_TS are the expected returns, respectively, on the unlevered company, the debt and the tax shield, V is the capitalization of the levered company, VTS is the tax shield value, D is the debt value, and T_C is the rate of corporate tax.

Formula (7) is derived from the balance identity and the WACC definition (Berk and De Marzo, 2007 [8]). While Equation (15) is more general than the Modigliani–Miller (MM) formula, for its practical applicability some additional conditions are required. If, as it is stated in [6], the WACC is constant over time, the financially dependent company capitalization can be found by discounting with the WACC for the financially independent company cash flows. The formulas for this special cases, where the WACC is constant, could be found in textbooks [8,9].

In 1963, Modigliani and Miller [2] assumed that the debt level D is constant. As the expected after-tax cash flow of the unlevered company is fixed, V₀ is also constant. By assumption, k_TS = k_d and the tax shield value is TS = tD. Thus, for the levered company value, V, one gets the classical Modigliani–Miller (MM) formula for WACC instead of formula (7):

$$WACC=k_0\left(1-w_{d}t\right)$$

(8)

Our opinion is that the “classical” Modigliani–Miller (MM) theory, suggesting the equality of the expected returns on the debt k_d and of the tax shield k_TS (because both of them have debt nature), is much more reasonable and, namely, the “classical” Modigliani–Miller (MM) theory was modified by us in [10].

(5)

The problem of tax pressure is actual in most countries. The article [11] was the first empirical study of the impact of tax pressure on the financial equilibrium of energy companies. The obtained results showed that tax pressure has stronger impacts on the equilibrium (both the short- and long-term) of oil and electricity companies than of gas companies. The research could be useful to energy companies managers underestimating the equilibrium state evolution of the company considering different possible financial crises.

(6)

Batrancea [12] used econometric models with two-stage least squares (2SLS) panel and panel generalized method of moments (GMM) to study how financial liquidity and financial solvency impact the performance of healthcare companies. It follows from an empirical evidence that such financial parameters as current liquidity ratio, quick liquidity ratio, and financial leverage significantly influenced company performance measured by return on assets, gross margin ratio, operating margin ratio, taxes, earnings before interest, amortization and depreciation. Based on liquidity and solvency insights, the strategies were also addressed with the intention to improve business performance.

(7)

In 2008, Brusov, Filatova, and Orekhova [13] lifted up the limitation concerning the perpetuity of flows and companies and created the modern theory of capital cost and capital structure—the BFO theory—which describes the companies of arbitrary age (and arbitrary lifetime). The generalization of the MM theory for the companies of arbitrary age (and arbitrary lifetime) required the modification of the valuation of the tax shield TS, as well as of the valuation of the company capitalization: financially independent, V₀, as well as financially dependent, V.

The following formulas were obtained: for the tax shield, TS, company value, V, and for weighted average cost of capital WACC:

$$\begin{gathered} TS=k_{d}DT{\displaystyle \sum _{t=1}^n{\left(1+k_d\right)}^{-t}}=DT\left[1-{\left(1+k_d\right)}^{-n}\right]. \\ {V}_0=CF\left[1-{\left(1+k_0\right)}^{-n}\right]/k_0;\hspace{1em}V=CF\left[1-{\left(1+WACC\right)}^{-n}\right]/WACC. \\ \frac{1-{\left(1+WACC\right)}^{-n}}{WACC}=\frac{1-{\left(1+k_0\right)}^{-n}}{k_0\left[1-{\omega }_{d}T\left(1-{\left(1+k_d\right)}^{-n}\right)\right]}. \end{gathered}$$

(9)

Here, S—the value of equity capital of the company, $w_d=\frac{D}{D+S}$—the share of debt capital, $k_e,w_e=\frac{S}{D+S}$—the cost and the share of the equity capital of the company, and $L=D/S$—financial leverage, D—the value of debt capital.

At n = 1, from BFO formula for WACC we get Myers [14] formula for 1–year company

$$WACC=k_0-\frac{\left(1+k_0\right)k_d}{1+k_d}{w}_{d}T$$

(10)

and at $n=\infty$ we get the Modigliani–Miller formula for WACC [2]:

$$WACC=k_0\cdot \left(1-w_{d}t\right)$$

(11)

Note that, before the BFO discovery in 2008, there were two results only: the Modigliani–Miller for perpetuity companies [1,2,3] and the Myers one for a year companies [14]. The accounting of the company’s finite age, as it was shown by BFO authors, leads to significant changes of all of the Modigliani–Miller results [1,2,3]. Besides, a number of qualitatively new effects in corporate finance, obtained in the Brusov–Filatova–Orekhova theory [13], are absent in the Modigliani–Miller theory.

(8)

Recently, we modified the Modigliani–Miller theory for the case of advanced payments of income tax [10] and have shown that obtained results are quite different from ones the in “classical” Modigliani–Miller theory.

Results and methodology of the Brusov–Filatova–Orekhova (BFO) theory are well–known in the world literature (for example, see references [15,16,17,18,19,20,21]). A few papers (see, for example, [21]) use the BFO theory in practical calculations.

2. Modification of the Brusov–Filatova–Orekhova (BFO) Theory for Companies with Advance Payments of Tax on Income

Below, modification of the Brusov–Filatova–Orekhova (BFO) theory for companies with advance payments of tax on income has been done. In Section 2.1, we derive formulas for the tax shield; in Section 2.2, we derive formulas for the company value; in Section 2.3, we consider the derivation of the weighted average cost of capital, WACC; and in Section 2.4, we derive formulas for the Equity cost.

2.1. Calculation of the Tax Shield

Let us calculate the tax shield within the Brusov–Filatova–Orekhova theory for the case of advance payments of tax on profit. The tax shield, TS, for period of n-years is equal to the sum of discounted values of benefits from the use of tax incentives

$${\left(TS\right)}_n=k_{d}Dt+\frac{k_{d}Dt}{1+k_d}+\frac{k_{d}Dt}{{\left(1+k_d\right)}^2}+\dots +\frac{k_{d}Dt}{{\left(1+k_d\right)}^{n-1}}$$

(12)

This expression represents a geometric progression with denominator

$$q=\frac{1}{{\left(1+k_d\right)}^{}}$$

(13)

After summing the progression, one obtains:

$${\left(TS\right)}_n=\frac{k_{d}Dt\left(1-{\left(1+k_d\right)}^{-n}\right)}{\left(1-{\left(1+k_d\right)}^{-1}\right)}=Dt\left(1-{\left(1+k_d\right)}^{-n}\right)\left(1+k_d\right)$$

(14)

In the classical Brusov–Filatova–Orekhova theory under payments at the end of periods, one has

$${\left(TS\right)}_n=Dt\left(1-{\left(1+k_d\right)}^{-n}\right)$$

(15)

2.2. Company Value

For the financially dependent company value V we have:

$$V=V_0+{\left(TS\right)}_n$$

(16)

$$V=V_0+Dt\left(1-{\left(1+k_d\right)}^{-n}\right)\cdot \left(1+k_d\right)$$

(17)

This formula differs from the equation for company value V in the case of payments of income tax at the end of the year

$$V=V_0+Dt\left(1-{\left(1+k_d\right)}^{-n}\right)$$

(18)

2.3. The Weighted Average Cost of Capital, WACC

Substituting

$$D=w_{d}V$$

(19)

into (17), we get

$$V\left(1-w_{d}t\left(1-{\left(1+k_d\right)}^{-n}\right)\cdot \left(1+k_d\right)\right)=V_0$$

(20)

Using the values of a financially dependent company, V, and financially independent company, V₀,

$$V=\frac{CF\left(1-{\left(1+WACC\right)}^{-n}\right)}{WACC}{;}^{}{}^{}{V}_0=\frac{CF}{k_0}\cdot \left(1-{\left(1+k_0\right)}^{-n}\right)$$

(21)

we come to the following intermediate equation

$$\begin{array}{l}\frac{CF\left(1-{\left(1+WACC\right)}^{-n}\right)}{WACC}\cdot \left(1-w_{d}t\cdot \left(1-{\left(1+k_d\right)}^{-n}\right)\cdot \left(1+k_d\right)\right)=\\ =\frac{CF}{k_0}\cdot \left(1-{\left(1+k_0\right)}^{-n}\right)\end{array}$$

(22)

and then to the final Brusov–Filatova–Orekhova equation for WACC for the case of advanced payments of income tax

$$\frac{\left(1-{\left(1+WACC\right)}^{-n}\right)}{WACC}=\frac{\left(1-{\left(1+k_0\right)}^{-n}\right)}{k_0\left(1-w_{d}t\cdot \left(1-{\left(1+k_d\right)}^{-n}\right)\cdot \left(1+k_d\right)\right)}$$

(23)

This formula differs from the classical Brusov–Filatova–Orekhova equation by the factor $\left(1+k_d\right)$ in the left denominator

$$\frac{\left(1-{\left(1+WACC\right)}^{-n}\right)}{WACC}=\frac{\left(1-{\left(1+k_0\right)}^{-n}\right)}{k_0\left(1-w_{d}t\cdot \left(1-{\left(1+k_d\right)}^{-n}\right)\right)}$$

(24)

2.4. Calculation of the Equity Cost

To calculate the equity cost k_e, one should use the equation of the WACC definition

$$WACC=k_e{w}_e+k_d{w}_d\left(1-t\right)$$

(25)

from where one gets the expression for k_e

$$k_e=\frac{WACC}{w_e}-\frac{k_d\left(1-t\right)w_d}{w_e}=WACC\left(1+L\right)-L{k}_d\left(1-t\right)$$

(26)

One should substitute WACC from Formula (12), calculating the equity cost k_e for the case of advanced payments of income tax and from Formula (13), calculating the equity cost k_e for the case of payments of income tax at the end of the year.

3. Results

Here, the dependence of the weighted average cost of capital, WACC, capital value, V, equity cost, k_e, on leverage level L for three-year and six-year companies, using Microsoft Excel, is being studied. We consider two types of payments of income tax: (1) at the end of the year and (2) in advance. As we mentioned above, for WACC we use Formulas (12) and (13), for capital value, V, we use Formulas (6) and (7) and for equity cost, k_e, we use Formula (15). BFO theory allows you to study companies of any age, and three- and six-year-old companies are given as examples to understand the impact of age on the main financial indicators of a company. A large database is held by the authors and can be made available to readers upon request. The paper uses data that gives an idea of the impact of advance payments on income tax on the main financial indicators of the company.

We use the following parameters: k₀ = 0.2; k_d = 0.18; t = 0.2; n = 3; 6; CF = 100. These parameters are typical for companies, and the results obtained at other parameters are similar and do not lead to a qualitative difference.

3.1. Dependence of the Weighted Average Cost of Capital, WACC, Capital Value, V, Equity Cost, k_e, on Leverage Level L for Three-Year Company

In

Table 1. Dependence of the weighted average cost of capital, WACC, equity cost, k_e and company value, V, on leverage level L in the cases of payments of tax on profit at the end of the year (1) and in the beginning of the year (2) for three-year company.

n = 3	WACC		ke		V
L	1	2	1	2	1	2
1	0.1749	0.1703	0.2057	0.1966	219.2281	220.8472
2	0.1664	0.1603	0.2113	0.1930	222.2455	224.4700
3	0.1622	0.1553	0.2168	0.1892	223.7856	226.3263
4	0.1596	0.1523	0.2222	0.1855	224.7199	227.4549
5	0.1579	0.1503	0.2277	0.1817	225.3471	228.2136
6	0.1567	0.1489	0.2331	0.1780	225.7973	228.7586
7	0.1558	0.1478	0.2386	0.1742	226.1361	229.1691
8	0.1551	0.1469	0.2440	0.1704	226.4003	229.4893
9	0.1545	0.1463	0.2495	0.1666	226.6122	229.7462
10	0.1541	0.1457	0.2549	0.1628	226.7858	229.9568

, the results of the study of the dependence of the weighted average cost of capital, WACC, capital value, V, and equity cost, k_e, on leverage level L for a three-year company are shown.

From Figure 1, it follows that WACC(L) decreases with L in both cases: advanced payments of income tax and payments at the ends of years. This means that debt financing is important and should be used by a company—it leads to a decrease of attracting capital cost with L. WACC turns out to be lower in the case of advanced payments of income tax; this tells about the importance of the use of advanced payments of income tax for companies.

From Figure 2, it follows that company value, V, increases with L in both cases; this follows from the decrease of attracting capital cost with L. Company value, V, turns out to be bigger in the case of advanced payments of income tax: this tells about the importance of the use of advanced payments of income tax for companies.

From Figure 3, it follows that equity cost k_e increases with leverage level L in the case of payments of income tax at the end of the year and decreases with leverage level L in the case of advanced payments of income tax. This means that the discovery of a qualitatively new effect that can greatly change the company’s dividend policy, because the economically justified amount of dividends is equal to the equity cost.

3.2. Dependence of the Weighted Average Cost of Capital, WACC, Capital Value, V, Equity Cost, k_e, on Leverage Level L for Six-Year Company

In

Table 2. Dependence of the weighted average cost of capital, WACC, equity cost, k_e and company value, V, on leverage level L in the cases of payments of tax on profit at the end of the year (1) and in the beginning of the year (2) for six-year company.

n = 6	WACC		ke		V
L	1	2	1	2	1	2
1	0.1743	0.1697	0.2047	0.1953	354.8940	359.2385
2	0.1657	0.1593	0.2090	0.1900	363.0242	369.1124
3	0.1613	0.1542	0.2131	0.1846	367.2305	374.2557
4	0.1586	0.1510	0.2172	0.1791	369.8015	377.4110
5	0.1569	0.1489	0.2213	0.1736	371.5355	379.5443
6	0.1556	0.1474	0.2254	0.1680	372.7841	381.0830
7	0.1547	0.1463	0.2294	0.1624	373.7261	382.2451
8	0.1539	0.1454	0.2335	0.1569	374.4620	383.1540
9	0.1534	0.1447	0.2376	0.1513	375.0529	383.8841
10	0.1529	0.1442	0.2416	0.1457	375.5377	384.4836

, the results of the study of the dependence of the weighted average cost of capital, WACC, capital value, V, and equity cost, k_e, on leverage level L for a six-year company are shown.

From Figure 4, it follows that, similar to the case of the three-year company, WACC(L) decreases with L in both cases: advanced payments of income tax and payments at the ends of years. This means that debt financing is important and should be used by a company—it leads to a decrease of attracting capital cost with L. WACC turns out to be lower in the case of advanced payments of income tax; this tells about the importance of the use of advanced payments of income tax for companies.

From Figure 5, it follows that, similar to the case of the three-year company, company value, V, for the six-year company increases with L in both cases; this follows from the decrease of attracting capital cost with L. Company value, V, turns out to be bigger in the case of advanced payments of income tax: this tells about the importance of the use of advanced payments of income tax for companies.

From Figure 6, it follows that, similar to the case of the three-year company, equity cost k_e for the six-year company increases with leverage level L in the case of payments of income tax at the end of the year and decreases with leverage level L in the case of advanced payments of income tax. This means the discovery of a qualitatively new effect that can greatly change the company’s dividend policy, because the economically justified amount of dividends is equal to the equity cost.

4. Comparison of Results for Three-Year and Six-Year Companies

In this paragraph, we compare the results for three-year and six-year companies.

From Figure 7, it follows that WACC decreases with company age: this is one of the important results of the classical BFO theory. In addition, for both ages of the company, WACC turns out to be lower in the case of advanced payments of income tax; this tells about the importance of the use of advanced payments of income tax for companies.

From Figure 8, it follows that the company value, V, increases with company age: this is one of the important results of the classical BFO theory. In addition, for both ages of the company, V turns out to be bigger in the case of advanced payments of income tax; this tells about the importance of the use of advanced payments of income tax for companies.

From Figure 9, it follows that the equity cost k_e increases with leverage level L in the case of payments of income tax at the end of the year and decreases with leverage level L in the case of advanced payments of income tax for both ages of the company. This means the appearance of a qualitatively new effect that can greatly change the company’s dividend policy, because the economically justified amount of dividends is equal to the equity cost. Equity cost k_e decreases with company age in both cases: this is one of the important results of the classical BFO theory.

5. Discussion and Conclusions

We derive for the first time the BFO formulas for WACC, V, k_e for the case of advanced payments of income tax. Making the calculations for the typical parameters for companies using these formulas within Microsoft Excel, we get the following results (see Table 1 and Table 2 and Figure 1, Figure 2, Figure 3, Figure 4, Figure 5, Figure 6, Figure 7, Figure 8 and Figure 9).

• WACC(L) decreases with L in both cases: advanced payments of income tax and payments at the ends of years. This means that debt financing is important and should be used by a company—it leads to a decrease of attracting capital cost with L.
• WACC turns out to be lower in the case of advanced payments of income tax; this tells about the importance of the use of advanced payments of income tax for companies.
• WACC decreases with company age: this is one of the important results of the classical BFO theory.
• Company value, V, increases with L in both cases; this follows from the decrease of attracting capital cost with L.
• Company value, V, turns out to be bigger in the case of advanced payments of income tax: this tells about the importance of the use of advanced payments of income tax for companies.
• Company value, V, increases with company age.
• Equity cost k_e decreases with company age in both cases: this is one of the important results of the classical BFO theory.
• Equity cost k_e increases with leverage level L in the case of payments of income tax at the end of the year.
• Equity cost k_e decreases with leverage level L in the case of advanced payments of income tax. This means the discovery of a qualitatively new effect that can greatly change the company’s dividend policy, because the economically justified amount of dividends is equal to the equity cost.

The obtained results allow coming to the following conclusions. Advance income tax payments are beneficial to both parties: to companies, because they lead to a decrease of cost of attracting capital and increase of company values; to the regulator, because earlier replenishment of the budget ensures an increase in the stability of budget revenues. Thus, the regulator should extend the practice of tax payments in advance by the companies.

An important conclusion drawn in this paper is that the tax shield is very important, and the way it is formed (payments at the end of the year or in advance) leads to very important consequences, changing all the financial indicators of the company, such as the cost of raising capital and company value and radically changing the company’s dividend policy. With payments at the end of the year, the equity cost increases with the leverage level; this means that the amount of dividends should increase with the increase in the use of debt financing, since the economically justified amount of dividends is the cost of equity. With advance payments of income tax, the equity cost increases with the leverage level; this means that the amount of dividends should decrease with the increase in the use of debt financing: this is a pioneering result that radically changes the company’s dividend policy. The novelty of the current consideration is as follows:

• we consider for the first time the generalization of the BFO theory for the case of advance payments on income tax.
• we show that the impact of the transition to advance payments is much more significant than in the case of a perpetuity limit (the “classical” Modigliani–Miller theory)
• we discovered a qualitatively new effect in the dependence of equity cost on leverage: this is a pioneering result that radically changes the company’s dividend policy.
• we developed the recommendations to the regulator to expand the practice of advance payments on income tax, giving to it a clear understanding that such a practice is beneficial to both parties: companies and the state.

One of the limitations of the current study is that we use the BFO theory with constant income: we are planning to generalize the BFO theory for the case of variable income in our next paper. As well, we are planning to consider the frequent advanced payments of tax on profit.