# Two Types of Payments of Tax on Profit: Advanced Payments and at the End of Periods: Consideration within BFO Theory with Variable Profit

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## Abstract

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## 1. Introduction

_{0}, for the tax shield value, TS, and for the weighted average cost of capital, WACC. The formulas are derived simultaneously for the following two cases so they made be compared: for income tax payments made at the end of the periods, and for payments made in advance. The latter formula is obtained here for the first time.

_{e}; the company value, V; the influence of the growth rate, g; the cost of debt, k

_{d}; and the influence of the age of the company, n, on the dependence of the company’s financial indicators on debt financing, were studied. The obtained results are compared with those for the case of payments of income tax at the end of reporting periods. Recommendations were made for both companies and regulators on the payment of income tax.

#### 1.1. A Literature Review

_{e}take place without taxes:

_{0}is the unlevered company capitalization, EBIT is earnings before interest and taxes, and k

_{0}is the equity cost at leverage level L = 0.

_{e},

_{d}and w

_{d}are the cost and share of the company’s debt capital; and k

_{e}and w

_{e}are the cost and share of the equity capital. The equity cost increases linearly with the leverage level L (see (4)).

_{e}, can be obtained from the Modigliani–Miller theory with taxes,

_{e}(L) curve decreases when accounting for taxes.

_{e},

_{U}is the β–coefficient of the unlevered company. β–coefficient is a measure of systematic risk. It evaluates the tendency of a security’s profitability to move in parallel with the return of the stock market as a whole.

_{S}is the tax on income of an individual investor from his ownership of corporation stock, T

_{C}is the tax rate on corporate income, and T

_{D}is the tax rate on interest income from the provision from investors of credits to other investors and companies.

_{0}stands for the equity cost at zero leverage level, k

_{d}stands for the debt cost, k

_{TS}stands for the tax shield returns, V stands for the levered company value, and VTS stands for the tax shield value.

_{0}is also constant. We can then assume that k

_{TS}= k

_{d}and the tax shield value is TS = tD. Thus, for the levered company value, V, one obtains the ordinary Modigliani–Miller (MM) formula for WACC instead of Formula (10):

_{d}, and the expected return of the tax shield, k

_{TS}, are equal, since both of them are debt-based, and, thus, the “classical” Modigliani–Miller (MM) theory is much more reasonable.

_{0}, and levered, V) was required to modify the MM theory:

#### 1.2. Methods and Materials

_{d}, age of the company, n, etc.

## 2. The BFO Theory for Companies with Variable Profit and Advance Tax on Profit Payments

#### 2.1. The Value of a Financially Dependent Company, V

#### 2.2. The Value of a Financially Independent Company, V_{0}

_{0},

_{0}− g, and not k

_{0}.

#### 2.3. The Tax Shield Value, TS

_{0}(18), and of a financially dependent company, V, (14) one obtains the following expressions:

## 3. Results and Discussions

_{0}, k

_{d}) (k

_{0}is the equity cost at zero leverage level, L, and k

_{d}is the debt cost) has been created and is available upon request. To illustrate the obtained results and the conclusions, the results for the following typical financial indicators of the five- and ten-year-old companies are presented: k

_{0}= 0.26; k

_{d}= 0.22; t = 0.2; g = 0.1; 0.05; 0.0; −0.05; CF = 100 (CF is the income per period).

_{0}= 0.26). These curves WACC(L) show the decrease of WACC with leverage level, L, at all g values. The curves WACC(L) increase with the growth rate, g. This is the first manifestation of the fact that under variable income, WACC is no longer a discount rate. As we will see below, the discount rate role has been taken over by WACC–g (here, g is the growth rate).

_{0}and increase at g > k

_{0}. k

_{0}is the threshold value, g, separating the increasing WACC(L) curves from the decreasing ones, and for g = k

_{0}WACC = const = k

_{0}. In the first case (the BFO theory), the WACC(L) curves decrease with increasing leverage, L. for all g values. Note that in both the BFO- theory and in the MM- theory the WACC(L) curves increase with the rate g.

_{0}–g). They are then split into two curves, and the income tax advances correspond to the upper curve. This means that advance payments of income tax result in a higher value for the company, V, at any growth rate, g.

_{e}, on leverage level, L, and on growth rate, g, is studied using the GBFO theory at k

_{0}= 0.26; k

_{d}= 0.22 and g = 0.1; 0.05; 0.0; −0.05, for a five-year company for two types of tax on profit payments: at the end of periods (1) and advance payments (2).

#### 3.1. Calculations of the Equity Cost, k_{e}

- Higher growth rate, g, justifies higher dividends.
- If a company pays income tax at the end of periods, it must pay large dividends.
- If the company pays income tax in advance, dividends should be lower.

#### 3.2. Impact of k_{d} on Financial Indicators

#### 3.2.1. WACC

_{d}start from one point (0; 0.26), as shown in Figure 5. At all values of k

_{d}, WACC(L) decrease with leverage level L and with k

_{d}. All curves WACC(L) in the case of advance income tax payments lie below the curves in the case of income tax payments at the end of periods.

#### 3.2.2. The Discount Rate, WACC–g

_{d}start from one point (L = 0; k

_{e}= 0.21), as shown in Figure 6. (WACC–g) decreases with L at all values of k

_{d}. (WACC–g)(L) decrease with k

_{d}. This means that the tax shield tends to lower the value of the discount rate (WACC–g) and, hence, (as we will see below in Section 3.2.3) increase the value of the company, V. All curves (WACC–g) (L) in the case of advance income tax payments lie below the curves in the case of income tax payments at the end of periods.

#### 3.2.3. The Company Value, V

_{d}for a five-year company start from one point (0; 285), as shown in Figure 7. V(L) increases with L at all values of k

_{d}and V(L) increases with k

_{d}. This means that tax shield advantages increase the company’s capitalization, V. All curves V(L) in the case of advance payments of income tax lie above the curves in the case of the payment of income tax at the end of periods. This means that advance income tax payments are beneficial for the company, as they increase its capitalization.

_{d}start from one point (L = 0; k

_{e}= k

_{0}= 0.26), as shown in Figure 8, and k

_{e}increases with L at all values of k

_{d}. The slope of ke(L) decreases with the debt cost, kd. Because the equity cost, ke, determines the economically justified amount of dividends, debt cost, kd, impacts the dividend policy of the company. At a fixed cost of debt, kd, the slope of the straight line, ke(L), in the case of income tax payment at the end of the periods is higher than in the case of advance payments.

#### 3.3. Influence of Company Age, n, on Main Financial Parameters of the Company

_{0}= 0.26; k

_{d}= 0.22; t = 0.2; g = 0.2; and g = −0.2, for five-year and ten-year companies, is studied. A large difference between the behavior of the company’s main financial parameters with a positive and negative growth rate, g, was found.

#### 3.3.1. WACC(L)

#### 3.3.2. Discount Rate WACC–g

#### 3.3.3. Company Capitalization, V

#### 3.3.4. Equity Cost, ke

#### 3.3.5. Summary of Results

_{d}on the main financial parameters has been studied and the following results were found:

- -
- All curves, WACC(L), start from one point (0; 0.26) at all values of k
_{d}. WACC(L) at all values of k_{d}decrease with leverage level L. WACC(L) decrease with k_{d}. This means that tax shield leads to the decrease of the cost of raising capital. - -
- All curves, (WACC–g)(L), start from one point (0; 0.21) at all values of k
_{d}. At all values of k_{d}, (WACC–g)(L) decrease with L. With the increase of debt cost, k_{d}, (WACC–g)(L) decrease. Thus, the tax shield tends to lower the value of the discount rate (WACC–g) and, hence, increase the value of the company, V. - -
- At all values of k
_{d}all curves of the company value V(L) start from one point (0; 285) and increases with leverage level L. V(L) increases with k_{d}. Thus, the tax shield leads to the increase of the company value, V. - -
- At all values of k
_{d}, all curves of equity cost, ke(L), start from one point (0; 0.26) and increase with L. The slope of ke(L) decreases with kd. Thus, kd impacts the dividend policy of the company, because ke determines the economically justified amount of dividends.

_{d}, despite the fact that the financial parameters for cases (1) and (2) move in the same direction, there are significant differences between cases (1) and (2) from the quantitative point of view, as well as with respect to the interposition of the financial parameters.

## 4. Conclusions

- The generalization of the BFO theory for the case of variable income with advance payments of income tax.
- Generalized BFO formulas for the main financial parameters of the company have been derived.
- Using the obtained formulas, an investigation of the influence of the growth rate, g; the cost of debt, kd; and the company’s age, n, on the dependence of the company’s financial performance on debt financing, has been conducted.
- A comparison of the obtained results with those for the case of paying income tax at the end of the periods has been performed.
- The development of the recommendations for both companies and regulators on how to pay income tax has been created.
- The developed methodology makes it possible to study companies with growing profits and companies with decreasing profits, which is quite important in practice. Regarding the direction of future research, the proposed theory will be used in the future for a more detailed study of companies with both rising and falling profits.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**The dependence of WACC on leverage level L GBFO theory with payments of tax on profit at the end of periods (1) and as advance payments (2) at k

_{0}= 0.26; k

_{d}= 0.22; t = 0.2; g = 0.1; 0.05; 0.0; −0.05, for a five-year company.

**Figure 2.**The dependence of discount rate, WACC–g, on leverage level, L, in GBFO theory with payments of tax on profit at the end of periods (1) and as advance payments (2) at k

_{0}= 0.26; k

_{d}= 0.22; t = 0.2; g = 0.1; 0.05; 0.0; −0.05, for a five-year company.

**Figure 3.**The dependence of discount rate, WACC–g, on leverage level L in GBFO theory with payments of tax on profit at the end of periods (1) and advance payments (2) at k

_{0}= 0.26; k

_{d}= 0.22; t = 0.2; g = 0.1; 0.05; 0.0; −0.05, for a five-year company.

**Figure 4.**The dependence of equity cost, ke, on leverage level, L, in GBFO theory with payments of tax on profit at the end of periods (1) and advance payments (2) at k

_{0}= 0.26; k

_{d}= 0.22; t = 0.2; g = 0.1; 0.05; 0.0; −0.05 for a five-year company.

**Figure 5.**The dependence of WACC on leverage level, L, in GBFO theory with payments of tax on profit at the end of periods (1) and advance payments (2) at k

_{0}= 0.26; k

_{d}= 0.22; 0.2; 0.18 t = 0.2; g = 0.05, for a five-year company.

**Figure 6.**The dependence of discount rate, WACC–g, on leverage level, L, in GBFO theory with payments of tax on profit at the end of periods (1) and advance payments (2) at k

_{0}= 0.26; k

_{d}= 0.22; 0.2; 0.18; t = 0.2; g = 0.05, for a five-year company.

**Figure 7.**The dependence of company value, V, on leverage level, L, in GBFO theory with payments of tax on profit at the end of periods (1) and advance payments (2) at k

_{0}= 0.26; k

_{d}= 0.22; 0.2; 0.18; t = 0.2; g = 0.05, for a five-year company.

**Figure 8.**The dependence of equity cost, ke, on leverage level L in GBFO theory with payments of tax on profit at the end of periods (1) and advance payments (2) at k

_{0}= 0.26; k

_{d}= 0.22; 0.2; 0.18 t = 0.2; g = 0.05, for a five year company.

**Figure 9.**The dependence of WACC on leverage level, L, in GBFO theory with payments of tax on profit at the end of periods (1) and advance payments (2) at k

_{0}= 0.26; k

_{d}= 0.22; t = 0.2; g = 0.2, for five-year and ten-year companies.

**Figure 10.**The dependence of WACC on leverage level, L, in GBFO theory with payments of tax on profit at the end of periods (1) and advance payments (2) at k

_{0}= 0.26; k

_{d}= 0.22; t = 0.2; g = −0.2, for five-year and ten-year companies.

**Figure 11.**The dependence of discount rate, WACC–g, on leverage level, L, in GBFO theory with payments of tax on profit at the end of periods (1) and advance payments (2) at k

_{0}= 0.26; k

_{d}= 0.22; t = 0.2; g = −0.2, for five-year and ten-year companies.

**Figure 12.**The dependence of discount rate, WACC–g, on leverage level, L, in GBFO theory with payments of tax on profit at the ends of periods (1) and advance payments (2) at k

_{0}= 0.26; k

_{d}= 0.22; t = 0.2; g = 0.2 for five-year and ten-year companies.

**Figure 13.**The dependence of company value, V, on leverage level, L, in GBFO theory with payments of tax on profit at the end of periods (1) and advance payments (2) at k

_{0}= 0.26; k

_{d}= 0.22; t = 0.2; g = −0.2, for five-year and ten-year companies.

**Figure 14.**The dependence of company value, V, on leverage level, L, in GBFO theory with payments of tax on profit at the end of periods (1) and advance payments (2) at k

_{0}= 0.26; k

_{d}= 0.22; t = 0.2; g = 0.2, for five-year and ten-year companies.

**Figure 15.**The dependence of equity cost, ke, on leverage level, L, in GBFO theory with payments of tax on profit at the end of periods (1) and advance payments (2) at k

_{0}= 0.26; k

_{d}= 0.22; t = 0.2; g = −0.2, for five-year and ten-year companies.

**Figure 16.**The dependence of equity cost, ke, on leverage level, L, in GBFO theory with payments of tax on profit at the end of periods (1) and advance payments (2) at k

_{0}= 0.26; k

_{d}= 0.22; t = 0.2; g = 0.2, for five-year and ten-year companies.

**Table 1.**Comparison of the results in GBFO theory with payments of tax on profit at the end of periods (1) and advance payments (2) for parameters g (growth rate), k

_{d}(debt cost), and n (company age (for five-year and ten-year companies)) (↑ means an increase in the indicator with the current parameter; ↓ means a decrease in the indicator with the current parameter).

g Growth Rate | k_{d}Debt Cost | n Company Age | Comparison of (1) and (2) | |||||
---|---|---|---|---|---|---|---|---|

Payments at the Ends of Periods (1) | Advance Payments (2) | Payments at the Ends of Periods (1) | Advance Payments (2) | Payments at the Ends of Periods (1) | Advance Payments (2) | |||

WACC | ↑ | ↑ | ↓ | ↓ | g ≥ 0 | ↑ | ↑ | 1 ≥ 2 |

g ≤ 0 | ↓ | ↓ | ||||||

WACC–g | ↓ | ↓ | ↓ | ↓ | g ≥ 0 | ↑ | ↑ | 1 ≥ 2 |

g ≤ 0 | ↓ | ↓ | ||||||

V | ↑ | ↑ | ↑ | ↑ | g ≥ 0 | ↑ | ↑ | 1 ≤ 2 |

g ≤ 0 | ↑ | ↑ | ||||||

ke | ↑ | ↑ | ↓ | ↓ | g ≥ 0 | ↑ | ↑ | 1 ≤ 2 |

g ≤ 0 | ↓ | ↓ |

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**MDPI and ACS Style**

Brusov, P.; Filatova, T.; Kulik, V.
Two Types of Payments of Tax on Profit: Advanced Payments and at the End of Periods: Consideration within BFO Theory with Variable Profit. *J. Risk Financial Manag.* **2023**, *16*, 208.
https://doi.org/10.3390/jrfm16030208

**AMA Style**

Brusov P, Filatova T, Kulik V.
Two Types of Payments of Tax on Profit: Advanced Payments and at the End of Periods: Consideration within BFO Theory with Variable Profit. *Journal of Risk and Financial Management*. 2023; 16(3):208.
https://doi.org/10.3390/jrfm16030208

**Chicago/Turabian Style**

Brusov, Peter, Tatiana Filatova, and Veniamin Kulik.
2023. "Two Types of Payments of Tax on Profit: Advanced Payments and at the End of Periods: Consideration within BFO Theory with Variable Profit" *Journal of Risk and Financial Management* 16, no. 3: 208.
https://doi.org/10.3390/jrfm16030208