# Chapter 3CAPITAL COST  DYNAMIC CONCEPT (josavere)

In strictly financial terms, if a company does not generate value for shareholders, that is, it does not obtain returns higher than the cost of capital, it is not fulfilling its reason for being. Verification of this very basic statement requires arithmetic calculations that serve to establish the difference between profitability indicators (operating profit, net, and others/equity) and the cost of capital.

The cost of capital is a management tool of great importance that is needed for the evaluation of new investment projects, in the valuation of companies in progress, and in the measurement of the business environment.

Briefly let us remember the possible components of the financial structure of a company, that is to say:
Suppliers (C1)
Loans of short term  (C2)
Loans of long term  (C3)
Labor liabilities (C4)
Bonds  (C5)
Common shares  (C6)
Preferred shares (C7)
Retained profits  (C8)

 ASSETS Current Assets Capital of Work Fixed assets
 LIABILITIES AND PATRIMONY Current liabilities Liabilities in the long term Patrimony

So that the financial structure is adopted, it must have a component of equity capital and long-term debt that sufficiently covers the fixed assets and the required minimum with current assets to operate. It must have to use to the maximum possible, of lines of credit of promotion that exist the particular case and to complete a combining debt, in a proportion with adapted indicating of cover that does not imply financial risk, and equity capital: common shares, preferred shares and retention of profits.
Go to analyze the cost of the different components of the capital structure:

1. SUPPLIERS (C1)

They offer credit, which implicitly has a financial cost equivalent to the interest rate and the time. The discount by payment on counted represents the cost of this source.

 FV: known (future value) PV: known (present value) n: known (time) i: ? (cost of the supplier)

If the discount pays attention technically, it must be superior to the rates of the market so that it is attractive and consequently turns out very expensive not to take advantage of them.

2. SHORT-TERM LOANS (C2)

The preparation of a graph is suggested that represents the cash flow and that indicates all the payments (specific commissions, expenses, interest, and others) and the net income. The calculation of the effective rate using the financial computer, or any other method represents the cost of this source (C2).

3. LONG-TERM LOAN (C3)

The analysis is similar to the previous one. In both cases, it is very important to consider the risk of the country for indebtedness in foreign currency. It is clear that the indebtedness as short and long term t imply the payment of interests, which are deductible of taxes, the reason why in principle, the cost of the debt is minor who the cost of the other sources of capital. The reduction calculates applying the factor to the cost previously obtained (1- t), being t, the rate of taxes.

C (1 - t) = Cost of short time debt= C2

C (1 - t) = Cost of long time debt = C3

It is recommended special care of any additional condition that is agreed to. For example: if for a loan of two million, an average of a million is due to maintaining during three months or those that really are, (by unnecessary extensions), is over- cost equivalent to the difference between the interests that are recognized, in case that and those exist and received to the effective interest rate.

4. LABOR LIABILITIES (C4)

It is important in some countries; base on the Actuarial Calculation, the actuaries properly authorized considers the cost, which is deductible from taxes.

C4 (1 - t) = cost of labor debts = C4

5. BONDS (C5)

There are special modalities of loan that directly take the companies from domestic or international investors; consist of a certificate that it indicates that a company took in loan money that is committed to reimburse in a future date plus a periodic amount of interests. For its emission, it is important to consider the risk of the country for foreign investors. Example:

Bonds of the nominal value of \$1’000.000

Sale price: \$900.000

Interest: 26% annual

Date of emission: In 21/2.000

Date of victory: 4 years later

The previous thing indicates that from the financial point of view, simply it is a debt with special characteristics and that a cost has that calculates elaborating a graph of the cash flow and applying a formula of financial mathematics.

6. COMMON SHARES (C6)

The common or ordinary shareholders are the proprietors of the company. To increase the value of the share in the market constitutes the clearest objective of the management.

The common shares have a residual right: they receive payment after the interests and obligations with the state. Through its right to choose, they control the company appointing a board of directors and public auditor; they must align preferences to conserve its proportional part in the property of the company, in case that new emissions take place.

In addition, they must write to inspect accounting books, within the legal regulations; they can freely transfer the shares in the market; its responsibility has limited the value of the individual contributors, and logically it has right to a dividend like compensation for its investment, which is extracted like part of the net profits, the previous decision of the general assembly of the company, as far as the amount, the dates of payment and their form, which should be in cash or stock.

As part of the base of an indefinite life will be necessary to cancel dividends to perpetuity, consequently (d1, d2, ... dn) and its cost (C4) is deduced thus:

 P: price of the share (Value to calculate) n: periods d: dividend PV: considered sale price r: rate of discount of the investor

In the numerator, we are supposing extreme a fixed one through time, in which case they would be perpetual monthly payments and the cost:

Let us analyze a little the previous formula. The denominator (p) does not have any problem, it represents the net value received by each share; it frees the expenses of emission and positioning in the market.

Actually, the dividends (d) are subject to variation. If we assumed annual increases every year (g) the cost would be:

This formula assumes a constant growth (g). In the practical one is unreal to suppose a constant dividend; we cannot either predict an equal increase every period no matter how efficient is the company is in favor of subject to the crisis. What do we do?

The scene of the real-life is the following one: the shareholder who wishes to invest guided by the financial indicators that the offer means to him:

a. Relation price /intrinsic value (Q of Tobin)

Q of Tobin = price of stock market / intrinsic value (a)
(a) intrinsic value = net patrimony / N° of shares in circulation
RPG = price in stock market / UPA (profit of share last year)

b. Relation price gain (RPG)

c. Relation Gain Price (RGP)

d. Index Beta: it determines the level of risk of the action compared with the market. In other words, it establishes what so sensible is the yield of the share before movements in the yield of the market.

BETA = 1 indicates that the yields of the share vary in proportion to the yields of the market.
BETA > 1 yield of the share varies more than proportionally to the market variation.
BETA < 1 yield than less proportional to the variation of the share in the market.

e. Yield of the dividends

f. Stock-exchange capitalization: supposedly indicates the value of the company in the stock market. it's also a theoretical concept because it implies that the pressure of the demand would not react in case their value is a low price.

g. Frequency of quotation: it indicates the number of rounds in which the shares in the run thing of the year have compromised.

h. Stock–exchange: it measures the dynamics of a share (facility to buy it or to sell it).

Base on this information, the investor will evaluate the stability of the dividend and the expectation of yield that the delay to calculate if he buys (invests or not).

 Po: market price IP: investor price d: dividends that will be maintained during the investment r: investor cut rate SPn: considered sale price at the moment in which hopes to redeem its investment

The comparison between the price calculated by the individual investor (P I ) and the price of the market (Po) will be the basis to make the decision whether to purchase or not. Yes P I > Po, buys and otherwise no.

The important is that the management of the company is oriented to increase the value of market of the share, objective that is obtained in the measurement that it obtains a rate of growth that widely surpasses the interest rates in the market that stable generates value; present good index of stock-exchange and other analyzed indicators previously. It is required financial projections, properly sustained because the shareholder makes a decision towards the future. It should prevail the created one culture because the joint-stock companies handle the money of the public in general.

By the arguments previously exposed more practice turns out to use as the cost of the common shares (C4) the rate of cut, which pays attention by enterprise policy like the minimum attractive return for the shareholders.

7. PREFERENTIAL SHARES (C7)

There is a hybrid among the debt and the own capital (common share). In practice behave like a debt. Besides the common characteristics of shares, the preferential have an independent, priority dividend of the result that be obtained for the common stockholders and its cost is equal to:

 pd: preferential dividend P: share net price

8. COST OF RETAINED PROFITS (C8)

The only reason that justifies profit retention on the part of a business is its capacity to obtain performances over the rate of cut of the individual stockholders, or to the cost of opportunity properly analyzed. Otherwise, it should deliver profits and leave that each stockholder arranges to his way of the I mount distributed. In practice, the decision turns out to be easy when it is a matter of companies dominated by a few associates (or by one), a very common case.

If it is a matter of open companies, the management should support with technical calculations a decision of this type, in whose case the cost is appraised with the rate of cut.

The rate of cut in itself is fixed by business policies, keeping in mind the characteristics of the companies and the conditions of the surroundings. The great advantage of the retention of profits consists of the agility of the process and elimination of the expenses inherent in the emission of shares, on behalf of the company, although its cost can be greater than the cost of the indebtedness because does not have a deduction of taxes.

THE COST OF CAPITAL

With the values considered for each one of the studied alternatives of financing previously, we come to prepare a matrix that serves to calculate the average of the different sources from financing which represents the capital cost a determined date, because this one changes periodically as they vary the financing sources. For that reason it is very advisable, use the spreadsheet the elaboration of a matrix that maintains updated the cost of capital of such form permanently that can be calculated as it is required for the decision making, following way:

 C1: cost of suppliers P1: participation of suppliers C2: cost of loans of the short time limit P2: participation of loans of the short time limit C3: long-range Cost of loans P3: long-range Participation loans C4: cost of the passive labor one P4: participation of the passive labor one C5: cost of the bonuses P5: participation of the bonuses C6: the common cost of stocks P6: common participation of stocks C7: preferential cost of stocks P7: participation of the preferential stocks C8: cost profits retained P8: participation profits retained

AI Opinion: The article "The Cost of Capital - Dynamic Concept" by José Saúl Velásquez Restrepo addresses a series of concepts related to the cost of capital in a company. Here is a summary and some thoughts on the key points of the article:
Importance of Cost of Capital: The article emphasizes the importance of cost of capital as a fundamental management tool. The cost of capital is essential for the evaluation of investment projects, the valuation of going concerns and the measurement of the business environment. This is true, since the cost of capital is crucial in determining whether a company is generating value for its shareholders.
Components of Financial Structure: The author mentions the possible components of a company's financial structure, which include suppliers, short- and long-term loans, labor liabilities, bonds, common stock, preferred stock, and retained earnings. The proper combination of these resources is essential to maintain a solid financial structure.
Calculation of the Cost of Capital Components: The article provides formulas and methods to calculate the cost of the various components of the capital structure, such as suppliers, short and long-term loans, labor liabilities, bonds, common shares, preferred shares and retained earnings. These calculations are essential in determining the total cost of capital.
Common Stock and Its Cost: The article discusses in detail the cost of common stock and how it relates to dividends and the discount rate. Additionally, key financial indicators that investors use to evaluate investing in common stocks are mentioned. The cost of common stock is crucial, as shareholders expect a return on their investment.
Preferred Stock: Preferred stock is mentioned as a hybrid between debt and equity, and a formula is offered to calculate its cost. Preferred stock is an important source of financing for many companies and has unique characteristics that must be considered when calculating its cost.
Cost of Retained Earnings: The article addresses the cost of retained earnings and highlights that companies should retain earnings only if they can generate returns above the cut-off rate of individual shareholders. This is an important reminder that profit retention must have a clear and beneficial purpose for shareholders.
Calculation of the Cost of Capital: The article concludes with the importance of calculating the cost of capital and how it can be done using a matrix that takes into account the costs and participation of each financing source. Keeping the cost of capital updated is essential for decision making.
Overall, the article provides a detailed and technical view on the cost of capital and its components. It is valuable reading for financial professionals and managers who wish to understand and calculate a company's cost of capital. It also highlights the importance of generating value for shareholders as the main objective of any company.

#### In order to calculate the cost of capital between the following matrix and introduce the corresponding information

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1. Usually they are not considered like capital sources, but actually if they are it.
2. Usually, they are not considered like capital sources, but actually if they are it.
3. They are part of the capital but they behave like debt.