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The french amortization method of a banking loan, cost of debt (Kd)

WHAT IS THE FRENCH AMORTIZATION METHOD OF A BANKING LOAN

In the following post it will be explained how to solve a banking loan following the French amortization method that is widely used in the financial industry.

The main characteristic of this methodology is that the installments or payments are always a fixed amount (“C”) comprised of interests (“I”) and amount amortized from the principal or amount borrowed (“K”).

A banking loan amortized by the French method will always have the following 5 columns:

  1. “K”: Outstanding debt or principal amount (money that the company owes).
  2. “C”: Fixed installment, comprised of interest and amount amortized.
  3. “I”: Interests paid in the period and defined by “Kd”.
  4. “A”: Amount amortized or paid back from the principal amount borrowed.
  5. Cash-flow generated by the loan.

The financial condition that must be met in any banking loan is that the present value of the banking debt cash-flows must be equal than the money borrowed in t=0, at the interest rate of the loan, defined as “Kd” or cost of debt. Under this financial equation, the fixed payment or installment formula is as follows, where the incognita “C” must be obtained:

Amount borrowed (K) = Fixed installment (C) * [(1-(1+interest)^(-time)] / interest

It is very important to note, that in the formula, the interest and time must be in the same time units. For example, if the payments are undertaken yearly, the installments “C” are yearly and the interest rate Kd must be a nominal yearly interest. The time period should be years. If the installments are monthly, the interest Kd must be a monthly nominal rate and the time must be in months. For example, if Kd=12% yearly and time t=5 years, but the payments are monthly, the interest rate to be used in the formula is 12%/12 months=1% and the time period=5*12=60 months.

Once the “C” fixed installment is calculated, we must calculate the interests paid in the period “t” (“I”). The outstanding amount or debt at the beginning of the period “t-1” (“D”)*interest yield “Kd” will produce an output of the interests paid in that period “t”. “C”-“I” will allow to calculate the amount amortized “A” in that period of time “t”. Then, the level of outstanding debt in “t” will be level of outstanding debt in “t-1” minus the amount amortized in “t”.

In order to validate that the banking loan has been correctly solved, the sum of all the amounts amortized must be the amount of money borrowed from the bank “K”. Additionally, the level of outstanding debt the last year must be zero. If these two conditions are not met, the banking loan table is wrong, and calculations must be revised.

Please find below an example of a banking loan table following the french amortization table and with the following conditions:

  1. “K”=Amount borrowed €7,729,890
  2. Frequency of payments: Semi-annual.
  3. Yearly nominal interest (“Kd”)=5%. Semi-annual nominal interest (5%/2=2,5%)
  4. Time: 3 years (3*2=6 semesters)

The we proceed to solve the problem:

  1. Applying the formula, the semi-annual fixed payments or installments, “C”=€1,403,361
  2. Semi-annual interests paid in the first semester: 2,5%*€7,729,890=€193,247
  3. Amortized amount in the first semester t=1: C-I=€1,403,361-€193,247=€1,210,114
  4. Outstanding debt level (“D”) at the end of the first semester (t=1)=€6,519,776
  5. Please note that the cash-flow calculation analyzes de cash inflows and outlays from the company perspective.
  6. If we repeat this calculation for each semester, we obtain the following table.
  7. Please note that the total amount of payments would be: 6*€1,403,361=€8,420,168 (€7,729,890 amount borrowed+€690,278 interests paid).

A BANKING LOAN TABLE (FRENCH AMORTIZATION METHOD)

French amortization method of solving a banking loan

WACC: Weighted average cost of capital, definition

WHAT IS THE FUNDING MIX OF A PROJECT AND THE WACC (WEIGHTED AVERAGE COST OF CAPITAL)

Once the total funding needs of a start-up project has been calculated, the following step would be to consider the potential funding sources where the funding can be obtained. The two major funding sources of any company/project are mainly:

  1. Equity funding (“E”) or amount of money borrowed from investors/shareholders/equity owners of a project/company.
  2. Banking debt (“D”) or amount of money borrowed from financial institutions or banks.

The funding mix ratio depends on the project risk, credit scoring/rating, country framework and start-up ecosystem for that specific country. For the case of Spain, according to Webcapital (2016), the funding mix ratio for start-up projects in Spain was 86% from shareholders (“E”) and 14% from banking debt (“D”).

It is very important to understand that this funding is not for free, and it has a yearly cost in percentage defined as “Ke” (cost of equity funding) and “Kd” (cost of banking debt funding). The “Ke” depends on the project characteristics and risk profile, and the “Kd” depends on the interest rates yield curve and risk profile of the project too (credit spread). As a general rule we could assume that Ke will be in the range of 15%-40% with an average value of 25%, and the Kd could range from 3%-8% with an average value of 5%. These metrics should be supported by any study/research depending of the project characteristics. The Ke metric usually is calculated using the “CAPM”, Capital Asset Pricing Model.

The Ke is defined as the minimum yearly profit expectations in percentage required by shareholders that invest in a project. If this Ke or minimum profit expectation is not achieved by the project, the shareholder or equity owner will not be satisfied with the project’s profitability according to the project’s risk profile. In the same way, the project should be able to pay back the amount of money borrowed from the bank (principal of the banking loan) and the yearly interest determined by Kd.

Once the funding mix ratio has been defined and the Ke and Kd have been calculated, the cost of the funding mix can be calculated, being defined as the“WACC” or Weighted Average Cost of Capital. This KPI or metric would be defined as the yearly weighted cost in percentage of the funding mix taking into account the Ke and Kd and the ratio %E and %D. The WACC formula is as follows:

WACC=%E*Ke+%D*Kd*(1-corporate taxes)

Let’s imagine a project with the following financing scheme:

  • Equity funding (E: 86%), Baking debt funding (D: 14%).
  • Ke (25%) and Kd (5%).
  • Corporate tax level: 25%.
  • The WACC=86%*25%+14%*5%*(1-25%)=22.03%. For every euro borrowed with the funding mix 86% (E) and 14% (D), and with a cost of funding Ke (25%) and Kd (5%), the weighted cost is €0.05, and the project should generate at least a profit/return of €0.05 to be able to pay back the funding sources and profit expectations, otherwise the project will be unprofitable.

EXAMPLE

In the following link it is explained how to determine the total funding needs of a start-up project. Using the methodology explained there, the entrepreneurs require for their start-up €55,213,500. If the funding mix is 86% equity (E) and 14% financial debt (D), the amount borrowed from the investors will be «E»=86%€55,213,500= €47,483,610 and from banks «D»=14%€55,213,500= €7,729,890.

The E=86%=€47,483,610 should be invested in the project through shares.

The cash-flow generated by the project should be able to payback to the investors (via dividends and share price increase) at least the minimum profit expectations defined by Ke=25%. In addition, the project cash-flow generation should be able to payback the principal of the banking loan («D»=€7,729,890) and the interests («Kd»=5%). In the following link there is an explanation of how a banking loan is solved following a French amortization method.

 

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