In the global context of any economy there are economic units with temporary excesses and deficits of financial resources. Economic units with temporary excesses present a positive cash flow as a result of their income being higher than their expenses in the period; while in the deficit units, temporarily, current income does not cover the needs for disbursements in a certain period of time.
Both seek a way to balance their monetary balances, making their surpluses profitable or financing their deficit with external resources.
Companies need resources to carry out their operation, investment and financing strategies, these strategies allow opening more markets in other geographic locations, increasing production, expanding, building or acquiring new plants, making any other investment that the company sees as beneficial for itself or take advantage of an opportunity offered by the environment where you are working.
Searching for forms of financing can result in an important variety of different options. Thus, the promoter of an enterprise may be thinking of using his own capital, in financing an investment, or he may partner with other people, companies or resort to financial institutions, international financing organizations, or the state.
Every entrepreneur, every business administrator, more specifically, every economic entity, may at some point be forced to obtain the necessary funds for the operation of the business, that is, they must make financing decisions.
Sources of funding
Financing is the supply and efficient use of money, lines of credit, loans, funds of any kind that are used in the realization of a project or in the operation of a company.
Financing consists of obtaining the financial means necessary to meet the expenses of the company. Funding sources are the ways a company has at its disposal to raise funds.
Therefore: Financing is the act of providing money and credit to a company, organization or individual, that is, obtaining resources and means of payment to allocate them to the acquisition of goods and services, necessary for the development of the corresponding functions.
Funding sources classification
The sources of financing of the company can be classified according to the repayment period, origin or origin of the financing and enforceability or ownership of the funds obtained.
A.) According to the return period.
Financing sources can be classified according to the time it takes until the borrowed capital has to be repaid. From this perspective, a distinction can be made between short-term financing and long-term financing.
• Short-term financing: It is the one whose maturity or the repayment term is less than one year. Such are the cases of supplier credits (spontaneous liabilities) and bank lines of credit that the company can obtain to finance current assets (non-spontaneous liabilities).
• Long-term financing: It is one whose maturity (the repayment term) is greater than one year, or there is no obligation to repay it. These include non-current liabilities and capital contributions.
B.) According to the origin of the financing.
According to this classification, the sources of financing can be divided according to whether the resources have been generated within the company, or have arisen outside the company, although they have finally reached it. According to this criterion, a distinction can be made between internal and external financing.
• Internal financing: They are those funds that the company produces through its activity. By way of example, the following could be mentioned: reserves, depreciations, retained earnings, etc. (profits reinvested in the company itself).
• External financing: They are characterized because they come from investors (creditors or owners). Within this classification are very common: bank financing: credits and loans, issuance of obligations, capital increases, etc.
C.) According to the ownership of the fund obtained.
The sources of financing can be classified according to whether the means of financing belong to the owners of the company or whether they belong to persons or institutions outside the company.
• External financing means: They are part of the payable liability, because at some point they must be returned (they are due). They are very common: credits, loans, issuance of obligations, etc.
• Means of own financing: It is also called a non-payable liability because they do not have a maturity, they do not require repayment, except in the event of dissolution of the company. In this group we can mention: capital contributions, in this case we are talking about external own financing, depreciations, reserves and provisions, cases where we are talking about internal own financing.
A classification of the different sources of financing is summarized in the following figure:
Loans and credits
Long-term bank loans and credits are a foreign and external source of financing. Although both sources come from financial institutions, they differ in their use, therefore it is important to be able to distinguish between one or the other.
Bank credit is the authorization granted by the bank, through a contract to a client, to have, up to a predetermined limit, financial resources in a certain time, which may be used partially or totally, that is, the entity will make deliveries partial at the request of the client. It is used for circulating needs and has great operability. (Borrás, Riverón, Caraballo).
The bank loan is the financing granted by the bank, under contractual conditions, for a specified time, which is taken, in its entirety, by the applicant at the time of its concession. It is used to cover permanent financial needs and requires in each case the formalization of an independent contract. (Borrás, Riverón, Caraballo).
Differences between credits and loans.
1. In the credit, the bank makes available to the client up to a certain amount of money; the loan is the delivery of that amount.
2. The credits accrue interest for the bank only for the amount consumed or drawn at any time, and a commission, which acts as an interest, but at a much lower rate, on the part not drawn (difference between the credit limit and the part not arranged). However, the loan accrues interest on the entire outstanding debt (living capital), regardless of whether it is used or not by the borrower. In other words, the bank receives interest on the loan from the agreed time, even in the event that the borrower has not immediately applied the financing granted to cover anticipated needs.
3. In revolving credit (which is the most usual) the part arranged by the borrower can increase, maintain, or decrease over time over and over again, since it does not require predetermined periodic repayments and the credit can be used as many times as desired. In the loan, the outstanding debt never increases, generally decreases, since it requires the delivery of pre-established periodic amounts. Except for the case of the American loan, in which the entire debt is not amortized until maturity, that is, it remains constant.
4. The credit is implemented through a checking account. The loans, however, have nothing to do with checking accounts, only relating to them (or savings accounts) at the time of the entry of the periodic charge established in the loan contract. Generally, the financing granted through the loan is credited to a specific account for it, in the bank itself that grants it or in another that the client indicates.
Now, basically, we focus on the Loan Capital since its analysis constitutes the object of interest of this article.
The bank loan is a manifestation where the person agrees to repay the requested amount in the time or term defined according to the conditions established for said loan, plus accrued interest, insurance and associated costs, if any.
A loan is the financial operation in which an entity or person (the lender) gives another (the borrower) a fixed amount of money at the beginning of the operation, with the condition that the borrower returns that amount along with the agreed interest in a certain period. Amortization (repayment) of the loan is normally carried out through regular installments (monthly, quarterly, semi-annually, annually) throughout this period. Therefore, the operation has a previously determined life. Interest is charged on the total money borrowed.
When analyzing loans, basically four elements must be considered:
• Amount of the loan.
• Interest rate
• Amortization Term
• Amount of the amortization installment
Amount of the loan
Value, in monetary terms, of the amount requested, or principal, taken as a loan, which will be used by the borrower.
Interest
rate The interest rate (or interest rate) is the percentage at which a capital is invested in a unit of time, determining what is referred to as "the price of money in the financial market". Another definition not too far from the previous approach defines it as the price paid for having financial capital for a certain period of time (Porteiro, 2007), that is, the price that the financial entity will charge you for lending the money that is requested.
Amortization Term
Term agreed or negotiated for the return of the amount obtained, as a loan, plus the interest accrued in the elapsed period. The term can be given in years: 1, 2, 3… n, semesters, months.
The amortization fee
is the process by which the obligation is canceled, either by making a single payment or by a succession of payments made within a specified period.
The installments that make up the series of payments can be equal to each other, that is, constant or variable.
We call quotas to the periodic payments made by the borrower in consideration for the capital borrowed. (Borrás, Riverón, Caraballo). Each fee paid is integrated with two components; one part covers the payment of interest on the balance due and the other corresponds to the amortization of the principal owed. (Porteiro, 2007).
The amortization terms (depending on the method used) can include both the amortization fee (repayment of the borrowed capital, not including interest) as well as the interest fee (amount of interest to be paid at any given time), or contain only one of them.. (Borrás, Riverón, Caraballo).
Calculation Methods
In international practice, different methods are used for the amortization of bank loans, that is, for the return or refund of all, or part of the principal taken, and the payment of interest.
Basically, two procedures have been developed to determine the service of a debt, which are identified according to whether it is made up of variable or equal installments. In this material, four variants are developed, two that take into account the equality of quotas among themselves, and two others based on their variability.
Constant quota method
It is about making the amortization of the loan through constant installments, identical for each of the settlement periods. The capital granted at the beginning of the period is amortized through increasing amortization installments, based on a geometric progression. Interest rates, on the contrary, decrease as the life of the loan progresses. However, the sum of the amortizing parts and interest must be equal to the installment or amortization term.
Example: Suppose you are the financial director of a company that is studying the possibility of investing in one of its production facilities. A bank offers you 35% of the total to invest under the following conditions:
Loan amount: $ 5,000.00
Nominal interest with annual settlement: 10%
You are considering a term for the return of the principal plus interest of 5 years, the table for debt service, under the constant amortization method would be:
The first step is to determine the amount of the installments, which are the components of an income composed of five annuities whose present value, at the effective annual interest rate of 10%, is equivalent to the amount of the loan to be received.
In accordance with the above, the calculation of the current value of the five installments can be proposed as follows:
VA = C / (1 + 0.1) + C / (1 + 0.1) 2 + C / (1 +0.1) 3 + C / (1 + 0.1) 4 + C / (1 + 0.1) 5
Knowing that the current value amounts to 5,000, it is possible to determine the value of the quota as follows:
5,000 = C * at 5 ┐0.10
From where: C = 5,000 / a 5 ┐0.10
The amount of C can be obtained in Tables that record the value of a 5 ┐0.10, using financial calculators or electronic spreadsheets. The corresponding result in this case is:
C = 5,000 / 3,790787
C = 1,318.98
Once the uniform payment to be paid is determined annually, the part destined to the amortization of the loan or, amortizing part, and the interest that make up each installment are calculated. For the first past due period we have:
I (0,1) = D0 * i = 5,000 * 0.1 = 500
The amortizing part of the first installment would be:
C1 = A1 + I (0.1)
A 1 = C1 - I (0,1)
A 1 = 1,318.98 - 500 = 818.98
Therefore the balance due after the first payment would be:
D1 = D0 - A1
D1 = 5,000 - 818.98 = 4181.02
By repeating the same procedure, the amortizing part and the interest that make up the installments corresponding to the following years can be determined.
With the results obtained, the following table can be constructed.
Table 1.
Note: the year ¨0¨ corresponds to the period where the loan is received.
Looking at the table, it can be seen that interest is decreasing as the amortizing part is increasing.
It is an amount to clarify and the reader must be careful since the interest rate and its settlement period must be expressed in the same unit of time, so if the interest settlement had been semi-annual, the interest rate would have to be expressed. interest for a semester:
i = nominal i / m
Where m represents the settlement frequency.
Being the semi-annual settlement: i = 0.1 / 2 = 0.05
Constant installment method, American variant
Consists of a amortization operation in which, at the end of each settlement period, the accrued interest is paid exclusively, while that the principal is amortized at the maturity of the operation.
Following the example above:
Note that the amortization term, during the first four years of the loan, coincides with the interest installments of each of the periods, since these amounts constitute its only component for most of the term, being in the last year of the loan, where the installment includes, in addition to the interest corresponding to the balance owed, the amortizing part that is equivalent to the principal borrowed at the beginning of the operation.
Constant amortization method. (Variable amortization terms)
Here the installments or amortization terms are variable and what remains constant throughout the life of the loan is the amortizing part, which is obtained by dividing the principal of the loan by the number of settlement periods. Interest for each period is obtained by applying the interest rate to the living capital in each period. Thus, as the amount of living capital decreases, interest rates and amortization terms decrease.
Following the same example, the method is exemplified.
Note that the amortizing part of the principal is constant throughout the period and is determined by dividing the loan amount by the number of periods determined for the repayment of the loan.
Loan / Number of periods
5000/5 = 1000.
In addition to amortizing the principal, the interest generated by the passage of time must be paid. The item to be included in the first installment corresponds to the interest accrued during the first year, according to the following calculation:
Interest (0.1) = 5,000 * 0.1 = 500
Therefore, the installment to be paid in the first year would be:
C1 = A1 + I (0.1) = 1,000 + 500 = 1,500
Once the first installment has been paid, the principal due at time 1 will be equal to the principal minus the amortization in that period.
Balance due = 5,000 - 1,000 = 4,000
The interest generated during the second period it is determined from the balance due at the beginning of that period as
follows: Interest (0.1; 2) = 4,000 * 0.1 = 400
Successively applying the same analysis, you can determine the interest generated and the installments for years three, four and five.
As it appears from the reading of Table 3, the application of this method of constant amortization has as a consequence the existence of decreasing installments, because the interests included in each payment are decreasing because they are determined from the balance owed.
Variable amortization terms method in geometric progression.
In this method, the installments or amortization terms are variables in geometric progression. Each amortization term is calculated based on the previous one, increased by a ratio. The amortization terms are determined as the product of the predetermined rate of increase for the previous installment.
However, in order to extract the geometric sequence, we must previously calculate the amount of the first installment based on a formula that will later be made known to the reader.
Once the calculations have been made to obtain the different installments to be paid throughout the loan period, the rest of the amortization table is obtained in a similar way to the constant installment method.
Due to the progressiveness of the installments, the payment effort is progressive for the borrower, so its most frequent use is in long-term operations and investments for which an increasing recovery is expected.
The equivalences expressed by this method are the following:
A1 = x; A2 = x * R; A3 = x * R2… An = x * Rn-1
Alternatively, it can be stated in a similar way:
A1 = x; A2 = A1 * R; A3 = A2 * R… An = An-1 * R
Being:
x = Co * (1 + i - R) / 1- (1+ i) -n * Rn
On the other hand:
I1 = i * Co; I2 = i * (Co - A1); I3 = i * (Co - A1 - A2)… In = i * Con-1
A1 = TA1 - I1 = x - I1
A2 = TA2 - I2
An = TAn - In
Where:
x: first amortization rate
R: ratio of annual progressive variation
Co: loan amount
TA: amortization term
A: Amortization
I: interest
i: Interest rate
n: number of periods
Taking the example, we proceed to develop the method
In this example, the value of 1.06 was used as the annual progressive variation ratio (R).
The first amortization installment is determined as the result of the formula previously stated, in this case the solution proposes an amortization term for the first year of $ 1183. The installment corresponding to the second period can be determined by multiplying the installment of the previous period by the progressive variation ratio and so on for the rest of the years. Note that the value of the annual fee increases progressively at a rate of 1.06. The interest is decreasing since it is determined by applying the interest rate of the loan to the living capital, while the amortization balances are increasing since they must cover the difference between the amortization fee and the interest generated in the period, this procedure it is similar to that used for the constant quota method.
Grace Period
The granting of long-term loans to finance investments often includes the granting of grace periods.
The grace period is a condition by which the beginning of that part of the installment that contains the principal amortization is postponed. It is usually agreed on terms that take into account the liquidity capacity of the borrower.
The logic of the agreement rests on the criterion that the main source for the repayment of the debts is constituted by the funds derived from the operation of the company, in case the borrower is this. Therefore, it is very reasonable to be able to align the debt service with those periods where the company's financial projections allow it to identify, in the future, moments that do not contemplate limitations in obtaining those resources in order to be able to comply with previously agreed upon in the granting of the loan.
During the course of the grace period, interest is generated as a result of the loans received; This situation places borrowers in a position to meet such obligations. The practice has given treatment to this situation, reason why the grace period distinguishes between two different modalities, one, with payment of interest, and the other, with capitalization of these.
a-) With interest payment.
Under this approach, the borrower pays the bank the interest on the principal that originates during the grace period. Once concluded, the term granted as grace, will begin the computation of what is agreed for the repayment of the loan plus the interest that will be generated by the living capital until its final cancellation.
Returning to the example through which the exposed methods have been developed, we proceed to show the case. To facilitate calculations, the example is developed using the constant depreciation method.
It can be seen that during the first year of the loan, only the interest generated is paid, while the amortization of the capital only begins in the second period. In this case, only one year of grace has been conceived. Note that the interest of the first period is the same as that of the second, so if on the one hand a period is obtained for which there will be no disbursements intended to cover the amortizing part of the installment, on the other, the balance of total interest at Paying increases, and consequently, the total installments to be paid, by $ 250, with respect to the graceless alternative. The total amortization remains constant since it is intended for the total return of the principal.
b-) With capitalization of interests.
Sometimes it is established that the overdue interest is capitalized during the grace period, which indicates that the borrower did not make any disbursement related to the repayment of the debt in said period and that the interest generated is added to the principal, forming a new amount the which will accrue interest in favor of the bank, during those periods in which the loan is not paid in full.
It can be seen that at the end of the first period the capital owed is greater than the initial amount of the loan, the difference is constituted by the interest of the first year, which has been incorporated into the original debt. As of that moment, the amortizing parts are determined to pay off the loan increased by $ 500, at a rate of $ 1375 per year, adding the accrued interest on balances, thus composing the annual disbursable installment.
To see the application of the grace period and its variants to the rest of the methods discussed, see Annex 1.
The choice of a method.
After analyzing the operation of the main loan amortization methods, the question arises: What method to choose?
If we compare the methods previously developed, we will see that in all the total of the amortized amount corresponds to the principal received at the beginning, so the lender recovers the money borrowed. However, the amount of interest varies by method.
Note: In cases where grace exists, a period of one year was determined.
We see that in the methods of constant amortization and constant installment less interest is paid, being significantly higher in the American method and with variable terms in geometric progression.
If taking into consideration for the analysis, the incorporation of the grace period, we observe that in the variant with capitalization, the amortization methods and constant installments are again, where less interest is paid, even compared to the alternative where it is not acknowledges the existence of grace periods. Therefore, a solution could be to accept the grace period with capitalization of interest, calculated under these methods, taking as sole decision criterion the amount of interest to be paid.
Alternatively we could add that: the total to be amortized also varies in relation to whether or not the lender grants grace periods to the borrower.
Let us note that in situations in which grace periods are taken into account and the variant is accepted where the borrower is exempted from amortizing the principal and the payment of interest, the amount to be amortized at the end of the operation does not coincide with the loan. initially, it is increased by the effect of the capitalization of interest. In this situation, it would not be appropriate to take the option of accepting the grace period with capitalization of interest if we only took into account the criterion of the total to be amortized.
Therefore, the total of the installments to be paid at the end of the period will depend on the amortization method used and the granting, or not, by the borrower, of grace periods in any of its two variants described previously in this document.
An analysis of the previous table would allow us to identify that using as amortization method, those of constant amortization and quota, without the existence of grace periods, the total amortization terms to be paid are substantially lower than those obtained under the use of the American methods. and of variable quotas in geometric progression. Therefore, based on the criterion of the amount to be amortized and the total interest to be paid, these could be the best solutions.
But from this evidence we should not jump to conclusions. The fact that a method offers a greater or lesser amount to be paid should not be the criterion to consider for your choice, both for the lender and for the borrower, because the moment in which these payments occur is not taken into account. From a financial point of view, capitals do not have equal value depending on when they are located. Based on the principles of the value of money over time, to compare the different methods, we must update those flows that are obtained in each of them.
Net Present Value (NPV), a valuable technique.
NPV is an investment selection criterion based on the difference between the present value of the future flows that an investment will offer and the disbursements required for its execution. In other words, all the cash inflows and outflows that an investment will have to generate throughout its economically useful life are placed in the present and are compared.
For a better interpretation of the concept expressed by this indicator, it is convenient to reason about a simple but realistic case. It is about imagining a situation in which the initial investment of the project materializes in a single period, which is identified as "Year 0". Consequently, the cash flow of the first period (FC0) is reduced to the disbursement for the investment associated with its implementation. Thus, we have: FC0 = I0
The net cash flows corresponding to «Years 1 to n» are the income minus the annual cash outflows associated with the operation of the investment. The updated value of the total net income stream is defined as the sum of the current values of the expected annual flows, discounted at the minimum required rate of return. It is expressed:
J = n
CDF = ∑ FCJ / (1 + i) n
J = 1
Being:
CDF: Total sum of Discounted Cash Flows
I: Update rate or minimum profitability required
FCj: Net cash income for the year «J»
1 an: Series of years that make up the useful life of the investment
The Net Present Value (NPV) of a project is defined as:
NPV (i) = CDF - I0
Selection criteria
When examining the long term, it can be seen that all investment in a project is ultimately financed with its own funds. A part of these are contributed at the beginning, by integrating the initial capital (own funds plus external funds); the rest will be gradually incorporated, as the self-financing generated by the project replaces the creditors by repaying the loans received.
From the investor's point of view, obtaining the financing constitutes a deferral or deferral of his own financial effort, lowering the costs of the project for it and benefiting from the positive effect of leverage by perceiving the surplus that comes from the difference between the return generated by the assets and the cost of debt for initial financing of these.
The proposal that we will develop below, the application of which constitutes one more criterion to take into account for the selection of financing, is adapted based on that proposed by the Uruguayan specialist Julio César Porteiro in his book ¨ Evaluation of Investment Projects. Business Perspective ¨.
The proposed method is articulated in the following stages:
Project under the shareholders' approach, the money flows that each capitalization option will generate during its period of validity; Given this perspective, the contributions of the owner / s are recorded with a negative sign, the debt service payments carry a negative sign. It should not be omitted to record, with a positive sign, the tax benefit generated by the payment of interest, since it is a deductible expense for the payment of income tax.
Calculate the Net Present Value of the projected residual cash flow for shareholders, using the opportunity cost of own funds as the discount rate.
Select, discriminating, among the different options that are mutually exclusive, the one that promises the lowest NPV expressed in absolute terms, since these are financial flows that express costs.
Returning to the example for which each of the loan amortization methods has been developed.
Suppose you are the chief financial officer of a company that is considering investing in one of its production facilities. A bank offers you 35% of the total to invest under the following conditions:
Loan amount: $ 5000.00
Nominal interest with annual settlement: 10%
You are considering a term for the return of the principal plus interest of 5 years.
The opportunity cost rate for owners is 11% and the income tax is 35%.
As an example, the financial profile of the flows for the investor was used using the method: constant amortization. To see the financial profile determined by using the rest of the methods: See annex: 2.
Once the financial profile has been formulated and calculated in NPV for each of the alternatives, it is represented by means of a table for comparison.
The comparison between the alternatives leads to the election of bank financing using the American as the amortization method without granting grace periods. This criterion is based on its lower cost; in effect, from the investors' point of view, the method generates an updated cost that is $ 95 less than the variant of the same method, this time with grace granted and interest capitalization.
Note that when we compared the different alternatives taking into account the balance of interest to be paid and the total installments, this was apparently the least convenient.
The reasons that explain this advantage are based on the fact that the updating factors punish more rigorously those financial flows that are further from the present. The main disbursement associated with debt repayment, under this method, takes place precisely in the last year of the operation.
Conclusions
The search for financing can result in a wide range of alternatives, so the promoter of a venture must choose between one or several options. This can choose from, contribute their own capital, use third-party funds, appeal to the self-financing generated by the company, up to, use a mixture of all. Therefore, the act of endowing money, a company or organization can be basically classified by its maturity, its origin and ownership.
Financial institutions, in practice, constitute one of the most frequently used alternatives in the search for funds. Credits and loans occupy a relevant place through which resource claimants manage to establish contact with the desired financial assets. The difference between these two financing variants is manifested from the fact that bank credit has a predetermined limit of financial resources, in a determined time, which can be used totally or partially, generally to cover working capital needs. The loans are granted under contractual conditions, which are taken in their entirety and require in each case the formalization of an independent contract. Their employment is intended to cover long-term financial needs.
When analyzing loans, basically four elements must be considered: the amount of the loan, the interest rate, the repayment period of the obligation and the amount of each repayment installment. The modality of its calculation allows identifying between two procedures to determine the debt service; they are characterized according to whether they are made up of: constant or variable amortization terms. Within the first classify: constant and American quota method, the second: constant amortization and variable amortization terms in geometric progression.
The loan negotiations include, in addition to the aforementioned elements, the granting, or not, to the borrower, of grace periods, defined as: terms for which the borrower is exempted, in a first variant, and while the grace lasts, of just pay interest. A second situation recognizes that the borrower did not pay, in said period, the corresponding installment, accepting that the accrued interest will be capitalized by increasing the loan amount.
There is no single valid criterion for choosing the method. The ability to generate resources, interpreted from the projection of the company's flows, will sometimes have to condition solutions, which in some cases do not respond to the best choice according to the criteria of the most refined financing selection techniques.
However, you must be aware of a reality: depending on the business conditions, for the lender or the borrower, it is convenient or not to accelerate the recovery or amortization time of the loan.
The company could reflect on whether it borrows money and the return on its investment is not greater than the cost of the loan, it is convenient to pay off as soon as possible; If the return on investment is much higher than the cost of financing, it would be desirable to enjoy it as long as possible.
It is necessary to underline another extremely important idea, for the choice of the amortization method it is essential to adapt the amortization table to the projected cash budget of the company. This condition facilitates the operations of the same since the financing and its amortization are adapted to your needs and guarantees the recovery by the bank.
Bibliography
- Borrás F. y otros “Banca y seguros: una aproximación al mundo empresarial”. Alicante, 1998.Fabozzi F y Modiglianni F. “Mercados e Instituciones Financieras” Ed. Printice Hall, España, México.Fischer Stanley y otros Economía. Mc Graw Hill, EEUU, 1989.Sapag Chain Nassir y Reynaldo. Preparación y Evaluación de Proyectos. Mc Graw – Hill Interamericana de México, 1989.Porteiro Julio César. Evaluación de Proyectos de Inversión. Perspectiva Empresarial. Fundación de Cultura Universitaria, Uruguay, 2007.
Metodologías Consultadas
- Metodología del Ministerio de Economía y Planificación (Cuba), para la formulación y evaluación de Proyectos Industriales.Metodología del Banco Central de Cuba para la Evaluación de Inversiones.
Sitios Web visitados
- www.slideshare.net/spcortesg/fuentes-de-financiamiento-de-la-empresa.www.monografias.com/trabajos15/financiamiento/financiamiento.shtml#CREDBANCAR.www.monografias.com/trabajos32/curso-finanzas/curso- Finanzas.shtml.www.finanzasparatodos.es/es/productosyservicios/productosbancariosfinanciacion/prestamoshipotecarios.html.www.rincondelvago.com/amortizacion-de-prestamos.html
