Influence of Method and Frequency of Profit Tax Payments on Company Financial Indicators

Abstract

In practice, profit tax payments are (1) made more frequently than annually and (2) can be made in advance. To study the influence of these two factors on the financial indicators of a company, we generalized the Brusov–Filatova–Orekhova (BFO) theory for the case of advance profit tax payments with an arbitrary frequency for the first time. Using modified BFO formulae, we showed that all financial indicators of a company, such as company value, the weighted average cost of capital (WACC) and equity cost (ke), depend on the frequency of the profit tax payments. We found that the WACC increased with the payments and the company value decreased with the payments. This meant that more infrequent payments could be beneficial for the company. The tilt angle of the equity cost (ke(L)) also increased with the payments. Depending on the age of the company, the equity cost either decreased with L for all payment frequencies or increased for some frequencies. We compared the obtained results to those that we described recently for profit tax payments at the end of the financial period and found them to be totally different. We found that in spite the fact that the WACC decreased with the payments and the company value increased with the payments, the WACC value in this case turned out to be bigger and the company value turned out to be smaller than in the case of advance profit tax payments of any frequency. This underlined the importance of advance profit tax payments. Regulator recommendations were also developed to encourage the practice of advance profit tax payments due to the understanding of the benefits of this for both parties: the companies and the state. A new effect was discovered: the decrease in equity cost with an increase in the level of leverage (L).

1. Introduction

In practice, profit tax payments are (1) made more frequently than annually and (2) can be made in advance. Recently, the Brusov–Filatova–Orekhova (BFO) theory [1] was generalized for the case of profit tax payments with an arbitrary frequency. Using modified BFO formulae, it was shown that all financial indicators of a company depend on the frequency of profit tax payments. The weighted average cost of capital (WACC) decreases with the payments and the company value increases with the payments. A new effect was thus discovered: the decrease in equity cost with an increase in the level of leverage (L). Due to the fact that the economically justified amount of dividends is equal to the equity cost, this can significantly change the dividend policy of a company.

More frequent profit tax payments are beneficial for both parties: the company and the tax regulator. For the company, this practice increases the company value and it helps the tax regulator due to the time value of money.

In current paper, for the first time, the Brusov–Filatova–Orekhova (BFO) theory was generalized for the case of advance profit tax payments with an arbitrary frequency. We compared the obtained results to those that we described recently for profit tax payments at the end of the financial period [1] and found them to be totally different.

We showed that in spite the fact that the WACC decreases with the payments and the company value increases with the payments in this case [1], the WACC values turned out to be bigger and the company value turned out to be smaller than in case of advance profit tax payments of any frequency. This underlined the importance of advance profit tax payments.

The novelty and originality of this study lie in the fact that the simultaneous influence of two effects was investigated for the first time: (1) advance profit tax payments and (2) frequent profit tax payments.

Before this study, we generalized the Brusov–Filatova–Orekhova (BFO) theory to (1) the case of frequent profit tax payments at the end of the financial period and (2) the case of advance annual profit tax payments.

In this article, we also compared the obtained results to the results of consideration (1) and found a large difference between the results. Thus, in this paper, an in-depth study of frequent profit tax payments was carried out for both possible cases of payments: advance and at the end of the financial period.

The robustness of the outcomes was provided by the use of the modern Brusov–Filatova–Orekhova (BFO) theory of capital cost and capital structure, which has been tested in real economic practice and its correct generalization for the case of frequent advance profit tax payments has been proven.

The structure of the paper is as follows.

In the introduction, we present a literature review of the development of the capital structure and capital cost theory (Section 1.1). The Brusov–Filatova–Orekhova (BFO) theory is generalized for frequent advance profit tax payments for the first time in Section 2, The modified formulae are derived for the tax shield in Section 2.1, company value in Section 2.2 and the equity cost and WACC in Section 2.3.

In Section 3, using the generalized BFO formulae that were obtained in Section 2 and Microsoft Excel, we numerically calculate the dependence of a company’s financial parameters, such as WACC, company value and equity cost, on the level of leverage for an arbitrary frequency of profit tax payment for three- and six-year-old companies (Section 3.1 and Section 3.2, respectively).

We considered frequent advance profit tax payments. In Section 3, we also compare the obtained results to those that were found previously for frequent profit tax payments tax at the end of the financial period [1]. This section also compares the results for companies of different ages (three- and six-year-old companies). In Section 4, the discussion and conclusions are presented.

1.1. A Literature Review on the Development of the Capital Cost and Capital Structure Theory

In this section, we present an overview of the development of the capital cost and capital structure theory. Following the traditional empirical approaches, the first quantitative theory of capital cost and capital structure was proposed the Nobel Prize winners Modigliani and Miller (the MM theory) in 1958 [2]. Among the many limitations of this theory, two main shortcomings can be distinguished: the non-accounting of taxes and the infinite lifetime of companies. The first constraint was removed by Modigliani and Miller themselves [3,4], who obtained the following formulae.

The tax shield (TS) had the following form:

TS = DT

(1)

Company value (V) and financially independent companies (V₀) were expressed as:

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

(2)

For WACC, Modigliani and Miller obtained the following formula:

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

(3)

For equity cost (k_e), they had:

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

(4)

In 1969, the capital asset pricing model (CAPM) was combined with the Modigliani–Miller theory by Hamada [5], which accounted for both the business and financial risk of companies and used the below formula for the equity cost (k_e) of financially dependent companies:

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

(5)

where b_U is the β–coefficient of a company with L = 0.

Corporate and individual taxes were then taken into account by Miller in 1977 [6]. The following formula was obtained for unleveraged company value:

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

(6)

where T_S is the profit tax rate for an individual investor for their ownership of corporation stock, T_C is the tax rate for corporate profit and T_D is the profit tax interest rate for the provision of credit to other investors or companies.

In [7,8,9,10], a more general expression for WACC than the Modigliani–Miller (MM) version was obtained [7]:

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

(7)

where k₀ is the equity cost of the unleveraged company, k_d is the debt cost, k_TS is the expected return on the tax shield, V is the leveraged company value, V_TS is the value of the tax shield and D is the debt value.

Derived in [9], Formula (7) is more general than the Modigliani–Miller (MM) expression, so some additional conditions are necessary for its use in practice. When the WACC value is constant over time, the leveraged company value can be found by discounting the WACC from the unleveraged company cash flows. For this specific case, the formulae can be found in textbooks [9,10].

In 1963, Modigliani and Miller [3] supposed that the level of debt was constant. The expected after-tax cash flow of a financially independent company was also fixed, thus V₀ was constant. By that assumption, kTS = kd and the tax shield value was TS = tD. Thus, for the financially dependent company value, we used the ordinary Modigliani–Miller (MM) formula for WACC instead of Formula (7):

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

(8)

From our point of view, the “classical” Modigliani–Miller (MM) theory supposed that the debt cost and expected return on the tax shield were equal (due to the fact that both of them are debt-like in nature), which is much more reasonable and so we modified the “classical” Modigliani–Miller (MM) in [11].

A study on the influence of tax pressure on the financial balance of energy companies was carried out in [12]. The results showed that tax pressure has a stronger influence on the financial equilibrium (both in the short term and long term) of oil and electricity companies than gas companies. These results are useful for the managers of energy companies who underestimate the evolution of the financial equilibrium of the company because they take into account various possible financial crises.

A study on the influence of financial liquidity and financial solvency on the performance of healthcare companies was conducted in [13] using econometric models. From the empirical evidence, it follows that certain financial parameters such as current liquidity ratio, quick liquidity ratio and financial leverage significantly influence company performance, as measured by the return on assets, gross margin ratio, operating margin ratio, taxes, earnings before interest, amortization and depreciation.

The limitation that was related to the infinite lifetime of companies was removed in 2008 by Brusov, Filatova and Orekhova [14], who developed the modern theory of capital cost and capital structure (the BFO theory), which is applicable to companies of all ages.

Modifications to the calculations for the tax shield and company value (unleveraged, V₀; leveraged, V) were required for the generalization of the MM theory (see the formulae below):

$$TS=k_{d}DT{\displaystyle \sum _{t=1}^n{\left(1+k_d\right)}^{-t}}=DT\left[1-{\left(1+k_d\right)}^{-n}\right].$$

(9)

$$V_0=CF\left[1-{\left(1+k_0\right)}^{-n}\right]/k_0;V=CF\left[1-{\left(1+WACC\right)}^{-n}\right]/WACC.$$

(10)

$$\frac{1-{\left(1+WACC\right)}^{-n}}{WACC}=\frac{1-{\left(1+k_0\right)}^{-n}}{k_0\left[1-{\omega }_{d}T\left(1-{\left(1+k_d\right)}^{-n}\right)\right]}.$$

(11)

where S is the equity capital value, $w_d=\frac{D}{D+S}$ is the debt capital, $k_e,w_e=\frac{S}{D+S}$ is the equity capital, $L=D/S$ is the value of financial leverage and D is the debt value.

The Myers formula for a one-year company [15] can be easily obtained from Formula (11) by substituting n = 1:

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

(12)

Then, by substituting $n=\infty$, we arrive at the Modigliani–Miller formula for WACC [2]:

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

(13)

Until 2008, when the BFO theory was created, there were only two options: the Modigliani–Miller theory for perpetual companies [2,3,4] and the Myers theory for one-year companies [15]. As the authors of the BFO showed, taking the finite age of a company into account leads to significant changes in all Modigliani–Miller results [2,3,4]. In addition, a number of the new effects that are observed within corporate finance using the Brusov–Filatov–Orekhova theory [14] are absent in the Modigliani–Miller theory.

In [11], the Modigliani-Miller theory was modified for the case of advance profit tax payments and significant differences were found between the modified theory and the “classical” Modigliani-Miller theory.

In the literature, the methodology and results of the Brusov–Filatova–Orekhova (BFO) theory are well known (for example, see references [16,17,18,19,20,21,22,23,24,25,26,27]). A number of papers (see, for example, [22,23,24]) have used the BFO theory in practical calculations.

The authors of [20] valuated the capital costs of energy companies by including an investor and market risk approach. The study also concerned a WACC intra-industry analysis the companies, which was related to the sector characteristics of revenue, total assets, company age and market capitalization.

In [23], the influence of the overconfidence of finance managers on the capital structure decisions of family-run businesses in India was studied. It was shown that the capital structure decisions of managers could be explained by measurable managerial characteristics. In [24], the correlation between company risk and capital structure was explored using datasets from sugar and cement companies in Pakistan. It was shown that the role of risk assessment and capital structure is vital for the sustainable growth of companies and the increase in the wealth of shareholders.

The authors of [25] considered the adjusted present value method, the free cash flow (FCF) method, the flow-to-equity method and the relationships between these methods. The authors departed from Modigliani and Miller method and used a stationary FCF method and the Miles and Ezzell method to consider FCF as a first-order autoregressive possession. The authors derived DCF valuation formulae for annuities. The authors found (1) the correct discount rate for the tax shield when the free cash flow is a first-order autoregressive annuity and (2) the tax shield valuation of a first-order autoregressive free cash flow annuity.

The author of [26] studied the impacts of internal and external corporate governance mechanisms on the financial performance of banks in the MENA region during the COVID-19 pandemic. The results showed that the corporate governance measures of the presence of independent members on the board of directors, strong legal protection, a high concentration of ownership and the lack of political pressure on board members had positive effects on the financial indicators of banks.

In [27], the influence of leverage level on the expected equity returns of listed companies was studied. The existence of an optimal capital structure to maximize the expected equity returns was discussed. The authors thought that this problem should be discussed from the perspective of maximizing shareholder wealth and not from the perspective of maximizing company value due to the existence of financial distress costs and agency costs. Using Gebhardt–Lee–Swaminathan (GLS) model to measure the implied capital costs and to measure the expected equity returns, the authors empirically found that the leverage level had a positive correlation with the equity returns of a listed company. The relationship between the leverage level and the expected equity returns appeared to an inverse “U”:

-

When the leverage level fell below the optimal level, increasing the leverage could increase the expected equity returns;

-

When the leverage level was higher than the optimal level, deleveraging was beneficial to increase the expected equity returns.

Within a standard capital structure model, the authors of [28] investigated the leverage decisions of over 1500 companies that were listed in the ASX for 2000–2012 and divided the sample into mining and non-mining industries. Applying a dummy variable approach, the authors showed that there were fundamental differences between two these types of companies when making leverage decisions. It turned out that mining companies were more sensitive to profitability and asset tangibility, whereas neither profitability nor asset tangibility were significant for non-mining companies. The obtained results suggested that industry type matters for companies when making leverage decisions.

In [18], the authors discussed the disagreement in the financial literature about the meaning of the “value of tax shields”. Although it is accepted that the tax deductibility of interest increases the value of a firm, the correct valuation of this added value is controversial. Using a risk-neutral approach, the authors derived a general formula for the valuation of tax shields, which shows that this value equals the summation of the discounted future tax savings. As soon as the authors specified a leverage level policy and cash flow dynamics, they obtained some well-known formulae for the calculation of tax shields.

2. The Modified Brusov–Filatova–Orekhova (BFO) Theory for the Case of Frequent Advance Profit Tax Payments

In this section, we generalize the Brusov–Filatova–Orekhova (BFO) theory for the case of frequent advance profit tax payments. The expressions for the tax shield, company value, WACC and equity cost are presented in Section 2.1, Section 2.2 and Section 2.3 respectively.

In this section, we use the following definitions.

D	Debt Capital Value
S	Equity Capital Value
$k_d,w_d=\frac{D}{D+S}$	Debt Capital Cost and Share
$k_e,w_e=\frac{S}{D+S}$	Equity Capital Cost and Share
$L=D/S$ WACC	Leverage Level Weighted Average Cost of Capital

k₀, the equity cost for a financially independent company; p, the number of payments per year; T, profit tax.

2.1. The Tax Shield Calculation

We started with the calculation of the tax shield for the case of frequent advance profit tax payments using the Brusov–Filatova–Orekhova theory (where p is the number of payments per year when payments are made at the beginning of the financial period). For a period of n years, the tax shield (TS) was equal to the sum of the discounted values of benefits from the use of tax incentives:

$${\left(TS\right)}_n=\frac{k_{d}Dt}{p}+\frac{k_{d}Dt}{p{\left(1+k_d\right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$p$}\right.}}+\frac{k_{d}Dt}{p{\left(1+k_d\right)}^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$p$}\right.}}+\dots +\frac{k_{d}Dt}{p{\left(1+k_d\right)}^{\raisebox{1ex}{$np$}\!\left/ \!\raisebox{-1ex}{$p$}\right.}}$$

(14)

We used a geometric progression with the denominator $q=\frac{1}{{\left(1+k_d\right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$p$}\right.}}$.

After summation, we obtained:

$${\left(TS\right)}_n=\frac{k_{d}Dt\left(1-{\left(1+k_d\right)}^{-n}\right)}{p\left(1-{\left(1+k_d\right)}^{-\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$p$}\right.}\right)}=\frac{k_{d}Dt\left(1-{\left(1+k_d\right)}^{-n}\right)\cdot {\left(1+k_d\right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$p$}\right.}}{p\left({\left(1+k_d\right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$p$}\right.}-1\right)}$$

(15)

Using the classical Brusov–Filatova–Orekhova theory at p = 1, we obtained:

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

(16)

It was easy to obtain this result from Formula (15) by inputting the value of p = 1 for the number of profit tax payments.

2.2. Derivation of the Modified BFO Formula for the Weighted Average Cost of Capital (WACC)

We now present the modified BFO formula for the weighted average cost of capital (WACC) for the case of frequent advance profit tax payments (where p is the number of payments per year when the payments are made at the beginning of the financial period).

For the value of a leveraged company (V), we obtained:

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

(17)

where V₀ is the value of an unleveraged company. By substituting Formula (19) for TS, we obtained:

$$V=V_0+\frac{k_{d}Dt\left(1-{\left(1+k_d\right)}^{-n}\right)\cdot {\left(1+k_d\right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$p$}\right.}}{p\left({\left(1+k_d\right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$p$}\right.}-1\right)}$$

(18)

After substituting $D=w_{d}V$, we obtained:

$$V\left(1-\frac{k_d{w}_{d}t\left(1-{\left(1+k_d\right)}^{-n}\right)\cdot {\left(1+k_d\right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$p$}\right.}}{p\left({\left(1+k_d\right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$p$}\right.}-1\right)}\right)=V_0$$

(19)

Assuming that the values of a leveraged company (V) and an unleveraged company (V₀) were equal to:

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

(20)

respectively, we obtained:

$$\frac{CF\left(1-{\left(1+WACC\right)}^{-n}\right)}{WACC}\cdot \left(1-\frac{k_d{w}_{d}t\left(1-{\left(1+k_d\right)}^{-n}\right)\cdot {\left(1+k_d\right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$p$}\right.}}{p\left({\left(1+k_d\right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$p$}\right.}-1\right)}\right)=\frac{CF}{k_0}\cdot \left(1-{\left(1+k_0\right)}^{-n}\right)$$

(21)

From there, we could derive the modified BFO formula for the WACC of a company of age n years for the case of p profit tax payments per year (payments at the beginning of the financial period):

$$\frac{1-{\left(1+WACC\right)}^{-n}}{WACC}=\frac{CF\left(1-{\left(1+k_0\right)}^{-n}\right)}{k_0\left(1-\frac{k_d{w}_{d}t\left(1-{\left(1+k_d\right)}^{-n}\right)\cdot {\left(1+k_d\right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$p$}\right.}}{p\left({\left(1+k_d\right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$p$}\right.}-1\right)}\right)}$$

(22)

For p = 1, we obtained the modified BFO formula for advance annual profit tax payments:

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

(23)

2.3. Formulae for the Capital Value and Equity Cost

In Section 3, we present our investigation into the impact of the frequency of profit tax payments on the dependence of the WACC, capital value and equity cost on the leverage level of companies of different ages (3 or 6 years) using Microsoft Excel. For the WACC, we used Formula (10) and for capital value and equity cost, we used Formulas (24) and (25), respectively (see below).

The value of a company of age n could be calculated using the following formula:

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

(24)

Then, the equity cost could be found using the following equation:

$$\begin{array}{c}WACC=k_e{w}_e+k_d{w}_d\left(1-t\right)\\ k_e=\frac{WACC}{w_e}-\frac{k_d\left(1-t\right)w_d}{w_e}=WACC\left(1+L\right)-L{k}_d\left(1-t\right)\end{array}$$

(25)

where the WACC value is found using Formula (22).

3. Results and Discussions

We studied the impact of the frequency of advance profit tax payments on the dependence of the WACC, capital value and equity cost on the leverage level of companies of different ages (3 or 6 years) using Microsoft Excel. We considered the advance profit tax payments using the formulae that were obtained above: Formula (22) was used for WACC, Formula (24) was used for capital value and Formula (25) was used for equity cost. By using the BFO theory, we could study companies of any age. Three- and six-year-old companies were considered as examples to estimate the impact of age on the financial parameters of a company. We used a large database, which can be made available to interested readers upon request. We used data that showed the influence of advance profit tax payments with an arbitrary frequency on the financial parameters of the selected companies. Then, we compared the results of the calculations of two types of profit tax payments: (1) payments at the end of the financial period [1] and (2) at the beginning of the financial period (i.e., in advance).

The following parameters were used: k₀ = 0.2; k_d = 0.18; t = 0.2; n = 3 or 6; CF = 100. The chosen parameters were typical for companies and the results that were obtained using other parameters were similar and did not show any qualitative differences.

3.1. The Impact of the Frequency of Profit Tax Payments on the Dependence of the Weighted Average Cost of Capital, Capital Value and Equity Cost on the Leverage Level of a Three-Year-Old Company

In

Table 1. The dependence of the WACC on the leverage level (L) of a three-year-old company for advance profit tax payments with frequencies of p = 1, 2, 4, 6 and 12.

		WACC, n = 3 (2)
L	Wd	p = 1	p = 2	p = 4	p = 6	p = 12
1	0.5	0.1703	0.1715	0.1721	0.1723	0.1725
2	0.666667	0.1603	0.1619	0.1627	0.1629	0.1632
3	0.75	0.1553	0.1571	0.1580	0.1583	0.1586
4	0.8	0.1523	0.1542	0.1552	0.1555	0.1558
5	0.833333	0.1503	0.1523	0.1533	0.1536	0.1539
6	0.857143	0.1489	0.1509	0.1519	0.1522	0.1526
7	0.875	0.1478	0.1499	0.1509	0.1512	0.1516
8	0.888889	0.1469	0.1491	0.1501	0.1505	0.1508
9	0.9	0.1463	0.1484	0.1495	0.1498	0.1502
10	0.909091	0.1457	0.1479	0.1490	0.1493	0.1497

,

Table 2. The dependence of the company value (V) on the leverage level (L) of a three-year-old company for advance profit tax payments with frequencies of p = 1, 2, 4, 6 and 12.

		V
L	Wd	p = 1	p = 2	p = 4	p = 6	p = 12
1	0.5	220.8472	220.4234	220.2163	220.1479	220.0800
2	0.666667	224.4700	223.8866	223.6018	223.5079	223.4144
3	0.75	226.3263	225.6593	225.3339	225.2266	225.1199
4	0.8	227.4549	226.7365	226.3861	226.2705	226.1557
5	0.833333	228.2136	227.4603	227.0930	226.9719	226.8515
6	0.857143	228.7586	227.9802	227.6007	227.4756	227.3512
7	0.875	229.1691	228.3717	227.9829	227.8548	227.7274
8	0.888889	229.4893	228.6771	228.2811	228.1506	228.0208
9	0.9	229.7462	228.9220	228.5202	228.3878	228.2561
10	0.909091	229.9568	229.1228	228.7162	228.5823	228.4490

and

Table 3. The dependence of the equity cost (ke) on the leverage level (L) of a three-year-old company for advance profit tax payments with frequencies of p = 1, 2, 4, 6 and 12.

		ke
L	Wd	p = 1	p = 2	p = 4	p = 6	p = 12
1	0.5	0.1966	0.1990	0.2002	0.2005	0.2009
2	0.666667	0.1930	0.1977	0.2001	0.2008	0.2016
3	0.75	0.1892	0.1964	0.1999	0.2011	0.2022
4	0.8	0.1855	0.1951	0.1998	0.2013	0.2028
5	0.833333	0.1817	0.1937	0.1996	0.2015	0.2034
6	0.857143	0.1780	0.1923	0.1994	0.2017	0.2040
7	0.875	0.1742	0.1910	0.1992	0.2019	0.2046
8	0.888889	0.1704	0.1896	0.1990	0.2021	0.2052
9	0.9	0.1666	0.1882	0.1988	0.2023	0.2058
10	0.909091	0.1628	0.1868	0.1986	0.2025	0.2063

, we present the results of our study on the impact of the frequency of profit tax payments on the dependence of the WACC, capital value and equity cost on the leverage level of a three-year-old company with payment frequencies of p = 1, 2, 4, 6 and 12.

As can be seen from Figure 1, the WACC decreased with L for all frequencies (annual, semi-annual, quarterly, monthly, etc.) of advance profit tax payments. So, the debt financing led to a decrease in the corresponding capital cost with L and thus, its use by the company was important. The WACC values increased with the frequency of payments, which meant that more infrequent payments were beneficial for the company. The influence of the payment frequency was stronger for annual, semi-annual and quarterly payments and decreased for monthly payments.

As can be seen from Figure 2, the company value (V) increased with L for all frequencies (annual, semi-annual, quarterly, monthly, etc.) of advance profit tax payments. So, the debt financing led to an increase in the company value with L and thus, its use by the company was important. This was consistent with the decrease in WACC with the leverage level, as shown in the previous section. The company value decreased with the frequency of payments, which meant that more infrequent payments were beneficial for the company. The influence of the payment frequency was stronger for annual, semi-annual and quarterly payments and decreased for monthly payments. This was consistent with the WACC behavior that was shown in the previous section.

As can be seen from Figure 3, the equity cost (ke) depended on the leverage level in a linear manner. It was not expected for ke(L) to be linear because the BFO equation for the WACC was an n + 1 power equation. However, as can be seen from the figures and tables for the equity cost results, this occurred with a high accuracy. We called the relationship quasi-linear (or practically linear). Our entire extensive database showed that this was the case. The equity cost decreased for annual (p = 1), semi-annual (p = 2) and quarterly (p = 4) payments and increased for monthly (p = 12) and bi-monthly payments (p = 6). The tilt angle of ke(L) increased with p and the transition from ke increasing with L to ke decreasing with L occurred at p = 4.

The economically justified amount of dividends was equal to the equity cost; therefore, the decrease in the equity cost with the leverage level signaled the discovery of a new effect that could significantly change the company’s dividend policy.

Below, we compare the dependence of the WACC, company value and equity cost on the leverage level of a three-year-old company for profit tax payments that were (1) made at the end of the financial period (data from Ref. [1]) and (2) made at the beginning of the financial period (i.e., advance payments) with frequencies of p = 2, 4, 6 and 12.

The comparison of the dependence of the WACC on the leverage level (L) of a three-year-old company for profit tax payments that were (1) made at the end of the financial period and (2) made at the beginning of the financial period (i.e., advance payments) with frequencies of p = 2, 4, 6 and 12 is shown in Figure 4.

The WACC(L) decreased with L in both cases: advance profit tax payments and payments at the end of the financial year. This meant that debt financing was important and should be used by the company as it led to a decrease in the corresponding capital cost with L.

In the case of profit tax payments that were made at the end of the financial year, the WACC(L) decreased with p, while in the case of advance profit tax payments, the WACC(L) increased with p. However, in spite of this, the WACC(L) always turned out to be lower in the case of advance profit tax payments. From Figure 4, it can be seen, for example, that WACC(L = 10) = 0.1504 at p = 12 for profit tax payments that were made at the end of the financial year while WACC(L = 10) = 0.1497 at p = 12 for advance profit tax payments. The WACC(L) curves for two these cases never crossed, i.e., the WACC values for advance profit tax payments always turned out to be lower than in the case of profit tax payments that were made at the end of the financial year. This demonstrated the importance of the use of advance profit tax payments for companies because the lower values of WACC corresponded to higher company values.

The comparison of the dependence of the company value (V) on the leverage level (L) of a three-year-old company for profit tax payments that were (1) made at the end of the financial period and (2) made at the beginning of the financial period (i.e., advance payments) with frequencies of p = 2, 4, 6 and 12 is shown in Figure 5.

Figure 5 shows that the company value increased with L for all payment frequencies (annual, semi-annual, quarterly, monthly, etc.) in both cases: advance profit tax payments and payments the end of the financial period. So, the debt financing led to an increase in the company value with L and thus, it was important and should be used by the company. This was consistent with the decrease in the WACC with L, as shown in the previous section. The company value decreased with the frequency of payments in the case of profit tax payments being made at the beginning of the financial period (i.e., advance payments), which meant that more infrequent payments were beneficial for the company. The company value increased with the frequency of payments in the case of profit tax payments being made at the end of the financial period. However, in spite of this, V(L) always turned out to be bigger in the case of advance profit tax payments. From Figure 5, it can be seen, for example, that V(L = 10) = 228.1849 at p = 12 for profit tax payments that were made at the end of the financial year, while V(L = 10) = 228.4490 at p = 12 for advance profit tax payments. Note that the V(L) curves that corresponded to these two cases never crossed. The influence of the payment frequency was stronger for annual, semi-annual and quarterly payments and decreased for monthly payments. This was consistent with the WACC behavior that was shown in the previous section.

The comparison of the dependence of the equity cost (ke) on the leverage level (L) of a three-year-old company for profit tax payments that were (1) made at the end of the financial period and (2) made at the beginning of the financial period (i.e., advance payments) with frequencies of p = 2, 4, 6 and 12 is shown in Figure 6.

From Figure 6, it can be seen that the equity cost (ke) depended on the leverage level (L) in a linear manner in both cases ((1) and (2)) for all values of p. In the case of profit tax payments being made at the end of the financial period, the tilt angle of ke(L) decreased with p but ke(L) continued to increase with L for all values of p. In the case of advance profit tax payments, the tilt angle of ke(L) increased with p and the transition from ke increasing with L to ke decreasing with L occurred at p = 4. Additionally, ke(L) decreased with L for annual (p = 1), semi-annual (p = 2) and quarterly (p = 4) payments and increased for monthly (p = 12) and bi-monthly payments (p = 6). The economically justified amount of dividends was equal to the equity cost; therefore, the decrease in the equity cost with the leverage level signaled the discovery of a new effect that could significantly change the dividend policy of a company. This effect only occurred in the case of advance profit tax payments. Note that with the increase in p, the ke(L) curves for the two cases ((1) and (2)) approached each other but never crossed.

3.2. The Impact of the Frequency of Profit Tax Payments on the Dependence of the Weighted Average Cost of Capital, Capital Value and Equity Cost on the Leverage Level of a Six-Year-Old Company

In

Table 4. The dependence of the WACC on the leverage level (L) of a six-year-old company for advance profit tax payments with frequencies of p = 1, 2, 4, 6 and 12.

		WACC, n = 6 (2)
L	Wd	p = 1	p = 2	p = 4	p = 6	p = 12
1	0.5	0.1697	0.1709	0.1715	0.1717	0.1719
2	0.666667	0.1593	0.1610	0.1618	0.1621	0.1623
3	0.75	0.1542	0.1560	0.1569	0.1572	0.1575
4	0.8	0.1510	0.1530	0.1540	0.1543	0.1546
5	0.833333	0.1489	0.1510	0.1520	0.1524	0.1527
6	0.857143	0.1474	0.1496	0.1506	0.1510	0.1513
7	0.875	0.1463	0.1485	0.1496	0.1499	0.1503
8	0.888889	0.1454	0.1477	0.1487	0.1491	0.1495
9	0.9	0.1447	0.1470	0.1481	0.1484	0.1488
10	0.909091	0.1442	0.1464	0.1475	0.1479	0.1483

,

Table 5. The dependence of the company value (V) on the leverage level (L) of a six-year-old company for advance profit tax payments with frequencies of p = 1, 2, 4, 6 and 12.

		V
L	Wd	p = 1	p = 2	p = 4	p = 6	p = 12
1	0.5	359.2385	358.0973	357.5406	357.3571	357.1746
2	0.666667	369.1124	367.5078	366.7265	366.4692	366.2133
3	0.75	374.2557	372.4010	371.4988	371.2017	370.9064
4	0.8	377.4110	375.4000	374.4222	374.1003	373.7805
5	0.833333	379.5443	377.4263	376.3969	376.0581	375.7214
6	0.857143	381.0830	378.8871	377.8201	377.4690	377.1201
7	0.875	382.2451	379.9901	378.8947	378.5342	378.1761
8	0.888889	383.1540	380.8525	379.7347	379.3669	379.0014
9	0.9	383.8841	381.5452	380.4093	380.0356	379.6643
10	0.909091	384.4836	382.1139	380.9631	380.5845	380.2084

and

Table 6. The dependence of the equity cost (ke) on the leverage level (L) of a six-year-old company for advance profit tax payments with frequencies of p = 1, 2, 4, 6 and 12.

		ke
L	Wd	p = 1	p = 2	p = 4	p = 6	p = 12
1	0.5	0.1953	0.1978	0.1990	0.1994	0.1997
2	0.666667	0.1900	0.1950	0.1974	0.1982	0.1990
3	0.75	0.1846	0.1920	0.1957	0.1969	0.1981
4	0.8	0.1791	0.1891	0.1939	0.1955	0.1971
5	0.833333	0.1736	0.1860	0.1921	0.1941	0.1961
6	0.857143	0.1680	0.1830	0.1903	0.1927	0.1951
7	0.875	0.1624	0.1799	0.1885	0.1913	0.1941
8	0.888889	0.1569	0.1769	0.1867	0.1899	0.1931
9	0.9	0.1513	0.1738	0.1848	0.1885	0.1921
10	0.909091	0.1457	0.1707	0.1830	0.1870	0.1911

, we present the results of our study on the impact of the frequency of profit tax payments on the dependence of the WACC, capital value and equity cost on the leverage level of a six-year-old company with payment frequencies of p = 1, 2, 4, 6 and 12.

As can be seen from Figure 7, the WACC decreased with L in the case of advance profit tax payments for all payment frequencies (annual, semi-annual, quarterly, monthly, etc.). So, debt financing led to a decrease in the corresponding capital cost with L and thus, should be used by the company. The WACC values increased with the frequency of payments, which meant that more infrequent payments were beneficial for the company. The influence of the payment frequency was stronger for annual, semi-annual and quarterly payments and decreased for monthly payments.

As can be seen from Figure 8, the company value (V) increased with L in the case of advance profit tax payments for all payment frequencies (annual, semi-annual, quarterly, monthly, etc.). This was consistent with the decrease in the WACC with the leverage level, as shown in the previous section. The company value decreased with the frequency of payments, which meant that more infrequent payments were beneficial for the company. The influence of the payment frequency was stronger for annual, semi-annual and quarterly payments and decreased for monthly payments. This was consistent with the WACC behavior that was shown in the previous section.

As can be seen from Figure 9, the equity cost (ke) depended on the leverage level (L) in a linear manner. It decreased for annual (p = 1), semi-annual (p = 2) and quarterly (p = 4) payments and increased for monthly (p = 12) and bi-monthly payments (p = 6). The economically justified amount of dividends was equal to the equity cost; therefore, the decrease in the equity cost with the leverage level signaled the discovery of a new effect that could significantly change the dividend policy of the company. Note that for the three-year-old company, ke increased with L for monthly (p = 12) and bi-monthly payments (p = 6) and the transition from decreasing to increasing behavior occurred at p = 4.

The comparison of the dependence of the WACC on the leverage level (L) of a six-year-old company for profit tax payments that were (1) made at the end of the financial period and (2) made at the beginning of the financial period (i.e., advance payments) with frequencies of p = 2, 4, 6 and 12 is shown in Figure 10.

The WACC(L) decreased with L in both cases: profit tax payments that were made at the beginning of the financial period and payments that were made at the end of the financial period. This meant that the debt financing led to a decrease in the corresponding capital cost with L and should be used by the company.

The WACC(L) decreased with p in the case of profit tax payments being made at the end of the financial period, while in the case of profit tax payments being made at the beginning of the financial period (i.e., advance payments), the WACC(L) increased with p. However, in spite of this, the WACC(L) always turned out to be lower in the latter case. From Figure 10, it can be seen, for example, that WACC(L = 10) = 0.1490 at p = 12 for profit tax payments that were made at the end of the financial year while WACC(L = 10) = 0.1483 at p = 12 for advance profit tax payments. The WACC(L) curves for two these cases never crossed, i.e., the WACC values for advance profit tax payments always turned out to be lower than in the case of profit tax payments that were made at the end of the financial year. Thus, the use of advance profit tax payments was quite important for the company because the lower values of WACC corresponded to higher company values. This conclusion is valid for companies of any age.

The comparison of the dependence of the company cost (V) on the leverage level (L) of a six-year-old company for profit tax payments that were (1) made at the end of the financial period and (2) made at the beginning of the financial period (i.e., advance payments) with frequencies of p = 2, 4, 6 and 12 is shown in Figure 11.

As can be seen from Figure 11, the company value (V) increased with L for all payment frequencies (annual, semi-annual, quarterly, monthly, etc.) in both cases: profit tax payments that were made at the beginning of the financial period (i.e., advance payments) and profit tax payments that were made at the end of the financial period. So, the debt financing led to an increase in the company value with the leverage level and thus, should be used by the company. This was consistent with the decrease in the WACC with the leverage level, as shown in the previous section. The company value decreased with the frequency of payments in the case of advance profit tax payments, which meant that more infrequent payments were beneficial for the company, and increased with the frequency of payments in the case of profit tax payments that were made at the end of the financial period. However, in spite of this, the V(L) always turned out to be bigger in the case of advance profit tax payments. From Figure 11, it can be seen, for example, that V(L = 10) = 379.4635 at p = 12 for profit tax payments that were made at the end of the financial year while V(L = 10) = 380.2084 at p = 12 for advance profit tax payments. Note that the V(L) curves that corresponded to these two cases never crossed. The influence of the payment frequency was stronger for annual, semi-annual and quarterly payments and decreased for monthly payments. This was consistent with the WACC behavior that was shown in the previous section.

The comparison of the dependence of the equity cost (ke) on the leverage level (L) of a six-year-old company for profit tax payments that were (1) made at the end of the financial period and (2) made at the beginning of the financial period (i.e., advance payments) with frequencies of p = 2, 4, 6 and 12 is shown in Figure 12.

From Figure 12, it can be seen that the equity cost (ke) depended on the leverage level (L) in a linear manner in both cases ((1) and (2)) for all values of p (similar to the case of the three-year-old company). In the case of profit tax payments that were made at the end of the financial period, the tilt angle of ke(L) decreased with p, but ke(L) continued to increase with L at p = 2, 4 and 6 and we only observed the transition to a slight decrease with leverage level at p = 12. Note that for the three-year-old company, this transition was absent and ke(L) increased with L for all values of p.

In the case of profit tax payments that were made at the beginning of the financial period (i.e., advance payments), the tilt angle of ke(L) increased with p, but ke(L) decreased with L for all payment frequencies. The economically justified amount of dividends was equal to the equity cost; thus, the discovery of the decrease in equity cost with the leverage level represented a new effect that could greatly change the company’s dividend policy. This effect only occurred in the case of advance profit tax payments. Note that with the increase in p, the ke(L) curves for the two cases ((1) and (2)) approached each other but never crossed.

4. Conclusions

In this paper, we studied the influence of frequent advance profit tax payments on the main financial indicators of a company. For this, we generalized the Brusov–Filatova–Orekhova (BFO) theory for the case of advance profit tax payments with an arbitrary frequency for the first time. We derived modified BFO formulae and showed that (1) all BFO formulae could change and (2) all of the financial parameters of a company, such as WACC, company value and equity cost, depended on the frequency of profit tax payments. The weighted average cost of capital (WACC) increased with the payments and the company value decreased with the payments. This meant that more infrequent payments were beneficial for the companies. The tilt angle of the equity cost (ke(L)) also increased with the payments. Depending on the company age, ke(L) either decreased with L for all payment frequencies or a transition from the decrease to an increase in ke with L occurred for some frequencies.

We compared the obtained results to those that we recently obtained for frequent profit tax payments that were made at the end of the financial period [1] and found them to be totally different. We showed that in spite the fact that the WACC decreased with the payments and the company value increased with the payments in this case [1], the WACC values turned out to be bigger and the company values turned out to be smaller than in the case of frequent advance profit tax payments for all payment frequencies. This underlined the importance of advance profit tax payments. Regulators should extend the practice of advance income tax payments to profit tax payments.

The economically justified amount of dividends was equal to the equity cost; thus, the discovered decrease in the equity cost with the leverage level represented a new effect that could greatly change a company’s dividend policy. In the case of profit tax payments that were made at the end of the financial period, the tilt angle of ke(L) decreased with the payments, but ke(L) continued to increase with L at p = 2, 4 and 6 and we only observed the transition to a slight decrease with leverage level at p = 12. Note that for the three-year-old company, this transition was absent and ke(L) increased with L for all values of p.

In the case of advance profit tax payments, the tilt angle of ke(L) increased with the payments, but ke(L) decreased with L for all payment frequencies for the six-year-old company. For the three-year-old company, ke(L) decreased at p = 1, 2 and 4 and increased at p = 6 and 12. Thus, for the three-year-old company, the transition from the decreasing ke(L) behavior to the ke(L) increasing behavior occurred at p = 6, while for the six-year-old company, this transition was absent.

The novelty of the paper is as follows:

• We generalized the BFO theory for the case of advance profit tax payments with an arbitrary frequency for the first time;
• By comparing the obtained results to those for frequent profit tax payments at the end of the financial period, we showed that in spite the fact that the WACC decreased with the payments and the company value increased with the payments, the WACC value in this case turned out to be bigger and the company value turned out to be smaller than in case of frequent advance profit tax payments for all payment frequencies, which underlined the importance of advance profit tax payments;
• A new effect of the dependence of equity cost on leverage level was discovered and this pioneering result could radically change the company dividend policies. In the case of advance profit tax payments, the tilt angle of ke(L) increased with the payments, but ke(L) decreased with L for all payment frequencies for the six-year-old company and at p = 1, 2 and 4 for the three-year-old company, although it increased at p = 6 and 12. Thus, for the three-year-old company, the transition from the decreasing ke(L) behavior to the increasing ke(L) behavior occurred at p = 6, while this transition was absent for the six-year-old company;
• Regulator recommendations were developed to expand the practice of advance profit tax payments, which would be beneficial to both parties, the companies and the state, (1) this practice would lead to a decrease in the cost of raising capital and an increase in the company value for companies and (2) ensure an increase in the stability of budget revenues for the regulators.

There was one limitation of the current consideration: the BFO theory was used with the assumption of a constant income. We are going to modify the BFO theory for the case of variable incomes in the future.