Borrowing (finance)
A loan is a longterm financial debt , while medium and shortterm debt is usually called ” credit “. A loan is a debt resulting from the granting of repayable term loans (funds paid under contractual provisions with the exception of current bank overdrafts) which participate, concurrently with equity, in the coverage of the sustainable financing needs of the bank. the company.
Typology and issues
Typology
It is possible to distinguish two types of loan:
 An undivided loan is a loan made to a single lender (usually a financial institution). He thus opposes the bond loan ^{1} .
 A bond is a loan that arises from the issuance of bonds that are spread among many lenders. It is therefore a loan reserved for large companies that can reassure investors.
The loan term is antonym ready for the one who provides the money. For the lender, it is a debt (a credit ), for the borrower, it is a debt .
Issues
The loan allows financing by preserving the property rights of the “buyerborrower” under the guise of any guarantee conditions. The loan makes it possible to provide a payment facility to households and finance the investment of private companies.
There is always a maximum debt capacity, which depends mainly on the income, the legal structure, the guarantees offered, but also for the company, the size, the profitability , the amount of equity . The borrower wishing to borrow a maximum must nevertheless endeavor to minimize the risks generated by this loan, as well for himself as for the community. Because a borrower is not necessarily rational, and that creditors can push to borrow more than it is sustainable, depending on the country, the law limits the maximum debt ratio. If a high debt ratio is likely to bring a high profitability from the point of view of the creditor (more interest paid back,), there is still a serious problem of trust related to the actual capacity of borrowers to repay their debts. Limiting the maximum debt ratio makes it possible to limit the situations of over indebtedness generating a loss of market confidence and an increase in the collective risk.
In terms of corporate strategy , borrowing represents a dependence on its external environment that it will strive to reduce ^{[ref. necessary]} . On the other hand, some activities, particularly real estate, may have an interest in using the highest possible debt in order to benefit from its leverage effect .
Characteristics of undivided loans
An undivided loan is a loan made to a single lender. The repayment follows the terms of depreciation and payment of interest stipulated in the contract (see repayment plan ). The repayment of the loan covers two different amounts:
 the amortization is the reimbursement of the borrowed capital, without taking into account the interests (the lender’s remuneration);
 the interest is the remuneration for the lender.
However, the term depreciation can also mean, depending on the context, the repayment of the loan as a whole (capital + interest).
The way these two sums are going to be repaid is conditioned by the repayment plan:
 Depreciation in fine consists of repaying principal and interest at one time, at maturity of the loan;
 depreciation by annuities, which may be at constant amortization or at constant annuities (see details below).
The annuity is the amount disbursed by conventional period for the repayment of the principal and the payment of the interest charge. The term annuity does not prejudge the duration of the period chosen. Classically, the term “monthly payment” is used when payments are made each month; quarterly or halfyearly are not used and annuity becomes the generic term, even for quarters.
 Annuity = amortization of capital at the end of the period + interest due for the period.
Calculation of interest
Usually, the interest due for a period is calculated as the product of the rate per period and the capital remaining due at the beginning of the period: it is called interest “in arrears”. However, some crops prefer an interest calculated on the basis of the remaining capital due at the end of the period considered: this is designated as “future interest”. The formulas described in the rest of this article, which use the “overdue” convention, must then be slightly modified.
Types of undivided repayments
There are three formulas: repayment in fine , constant depreciation (same portion of capital repaid each year) or constant annuity (same annuity each year).
The loan in fine
Interest has expired at the end of each period. It is proportional to the debt, and it depends on the duration (often it will be proportional). If on that date a payment (maturity) exceeds the interest, the capital (debt) is amortized by the difference; it increases by this difference if the payment is lower than the interest.
Algebraically: Amount due at maturity = Interest (+/ Amortization if necessary)


 New Capital = Old Capital (+/ Amortization if necessary)

Present value of capital = Old capital + Interest (+/ Amortization if necessary which represents the influence of the discount chosen by the capital contributors).
This equation can be considered as the modern foundation of all actuarial reasoning . Step by step, we arrive at the equality of the incoming and outgoing discounted flows when the loan is repaid. It allows rebuilding all financial formulas, bonds, etc.
Interest decreases over time and depreciates, and can be tax deductible, making the real weight of the first years of repayment much lighter. For example, this is a real estate investment under the law of Robien and generalized to any real estate loan contracted before May 2007 ^{2} .
The loan undivided constant depreciation
The depreciation each year is constant. This simple loan to calculate can have a tax or cash interest, but remains marginal compared to the constant annuity.
For a fee {\ displaystyle {{K} _ {0}}} borrowed during {\ displaystyle N} years at rates {\ displaystyle r} and reimbursed annually, amortization {\ displaystyle \ Delta K}, constant, is naturally: {\ displaystyle \ Delta K = {\ frac {{K} _ {0}} {N}}}
Interest for the year {\ displaystyle i} (we start with year 1) are worth as follows: {\ displaystyle {{I} _ {i}} = r {\ frac {{{K} _ {0}} (Ni + 1)} {N}}}
And the annuities {\ displaystyle a_ {i}} are determined by the formula: {\ displaystyle {{a} _ {i}} = {{a} _ {1}} – ({{K} _ {0}} {\ frac {r} {N}}) (i1)}
Each year, interest decreases as an arithmetic suite of reason {\ displaystyle r {\ frac {K_ {0}} {N}}} and first term {\ displaystyle {K_ {0}} {r}}.
Annuities also decrease as an arithmetic sequence of the same reason but of first term{\ displaystyle {K_ {0}} {r} + \ Delta {K}}.
NB. : It is implied here that the duration of the year, or of the period if it is the month, the quarter, the semester …, is conventionally constant, without taking into account fluctuations in the calendar. All these calculations are then approximate to the actual times.
Some software allows in particular to obtain credits directly attributable to IAS / IFRS.
The loan undivided constant annuity
This loan is very common for households and businesses. It is easier to value the level of risk experienced by the financial institution when the amount paid by the borrower is constant.
In this case, we calculate the amount of an annuity {\ displaystyle a} according to the capital lent {\ displaystyle K_ {0}}, interest rate {\ displaystyle r} and the number of annuities {\ displaystyle N}, thanks to the following formula:
{\ displaystyle a = {\ frac {r {{K} _ {0}}} {1 – {{\ left (1 + r \ right)} ^ { N}}}}}
This formula is obtained by calculating the present value of a temporary rent of constant flow. Indeed, we have the following relations for any period{\ displaystyle 1 \ leq i \ leq N} :
{\ displaystyle \ left \ {{\ begin {aligned} & {{I} _ {i}} = r {{K} _ {i1}} \\ & \ Delta {{K} _ {i}} = a – {{I} _ {i}} \\ {{K} _ {i}} = {{K} _ {i1}} – \ Delta {{K} _ {i}} \\ \ end {aligned}} \ right.}
or :
 {\ displaystyle K_ {i}} represents the remaining capital to be repaid after payment of the annuity {\ displaystyle i},
 {\ displaystyle \ Delta K_ {i}} is the depreciation part of the {\ displaystyle {{i} ^ {{\ serious {e}} me}}} annuity,
 {\ displaystyle I_ {i}} is the share of the interests of the {\ displaystyle {{i} ^ {{\ serious {e}} me}}} annuity.
So, we notice that the following {\ displaystyle (\ Delta K_ {n}}}is a geometric suite of reason {\ displaystyle (1 + r)} and first term {\ displaystyle arK_ {0}}. Indeed :
{\ displaystyle {\ begin {aligned} & \ Delta {{K} _ {i + 1}} = a – {{I} _ {i + 1}} \\ & = ar {{K} _ {i} } \\ & = ar \ left ({{K} _ {i1}} – \ Delta {{K} _ {i}} \ right) \\ & = \ left (ar {{K} _ {i 1}} \ right) + r \ Delta {{K} _ {i}} \\ & = \ Delta {{K} _ {i}} + r \ Delta {{K} _ {i}} \\ & = \ left (1 + r \ right) \ Delta {{K} _ {i}} \ end {aligned}}}
Moreover, thanks to the relationship {\ displaystyle K_ {0} = \ sum _ {i = 1} ^ {N} \ Delta K_ {i}} which binds the borrowed capital and the sum of {\ displaystyle N} terms of the geometric suite {\ displaystyle (\ Delta K_ {i})}, we have :
{\ displaystyle {{K} _ {0}} = \ left (ar {{K} _ {0}} \ right) {\ frac {{{\ left (1 + r \ right)} ^ {N}} 1} {r}}}
From where :
{\ displaystyle a = {\ frac {r {{K} _ {0}}} {{{\ left (1 + r \ right)} ^ {N}} – 1}} + r {{K} _ { 0}} = {\ frac {r {{K} _ {0}} {{\ left (1 + r \ right)} ^ {N}}} {{{\ left (1 + r \ right)} ^ {N}} – 1}} = {\ frac {r {{K} _ {0}}} {1 – {{\ left (1 + r \ right)} ^ { N}}}}}
Accounting for undivided loans
For businesses (excluding credit institutions), the loan is a liability to be credited against a contribution to the bank.
According to international standards, borrowings may be noncurrent liabilities (ie not related to the normal operating cycle or maturing in more than 12 months) or current depending on their duration.
Account Name  Debit  Credit 

Bank  …  
Banking Commission ( charge )  …  
Undivided loan  … 
At maturity, interest is to be noted.
Account Name  Debit  Credit 

Loan interest charge  …  
Bank  … 
In France (contrary to international standards), the banking commission can be included in an accrual and transfer account and then spread over a maximum period of the loan.
At the end of the year, an accrued interest is found to represent the latent interest payable at the next deadline impoverishment.
Loan guarantees undivided
The financier can ask the borrower for guarantees of various kinds. Thus, in case of non repayment of the loan by the borrower, the banks will have solutions making it easier to recover the funds they have advanced.
In the first place, the lender will ensure the creditworthiness of the borrower via a flow guarantee, which most often corresponds in quantity (amount) and quality (type of employment contract, seniority of the company, etc. .) of his income. Then comes the stock guarantee, which can take various forms such as bonding , pledge , pledge , mortgage , denier privilege, and so on. ^{3}
Guarantees are then “personal” as the bond or “real”, that is to say related to a value such as a mortgage on a building , bonds , warrants or debts ( discount ). (personal such as bail or actual such as pledge, pledge or mortgage depending on the nature of the good).
Characteristics of the bonds
Bond issues are loans that arise from the issuance of bonds that are spread among many lenders. These are therefore loans reserved for large companies because trust in the issuing company is fundamental.
 The amortization is the return of capital without considering the interest charges. It represents the number of bonds amortized in period ( N ) by the nominal value of the bond ( C ).
 The interest is the bond debt remaining to be paid at the beginning of the period by the interest rate.
 The annuity (or monthly , trimestrialité, etc.) is the sum disbursed periodically for repayment and interest expense.
 Annuity = amortization of bonds + interest
Terms of repayment
We find the three formulas: repayment in fine , constant amortization (same portion of capital repaid each year) or constant annuity (same annuity each year).
Credit in fine
The interest is regulated with the first constant annuities.
The capital is repaid either in one time after the payment of the interest, or with the following annuities.
The bond with constant amortization
The depreciation each year is constant. The formulas explained in the undivided constant damping section can be applied with certain peculiarities.
The periodic amortization Am of the loan is determined by the formula (same symbols):
{\ displaystyle Am_ {1} = N_ {1} \ times C = {\ frac {K_ {0}} {n}}}
Two particularities must be noted for this type of depreciation, often referred to as equal series :
 It is very common for depreciation in equal series to begin only after a delay of a few years, often onethird of the overall duration of the loan.
 In addition, to ensure the equality of bondholders, the choice of securities to be amortized for a given period is the subject of a draw. Thus, on the subscription date, the expected value of the current value of each security is identical.
The quasiconstant annuity bond
The formulas explained in the undivided constant annuity section can be applied with some special features. As the nominal value of each security to be amortized is fixed, for example € 1,000, the calculation of the amount to be amortized per period is only approximate; but, for a program comprising a large number of titles, this approximation is negligible.
Amortization of period 1:
{\ displaystyle Am_ {1} = {\ frac {N_ {0} \ times (1 + r)} {(1 + r ^ {i})}}}
With N number of bonds at a given moment.
Accounting for bond issues
The bond issue has the important feature of sometimes imposing a refund premium (difference between the redemption price and the issue price) in addition to the recognition of the loan.
It is normally necessary to record two different entries on the subscription date and on the release date, which separates the recognition of the redemption premium from the recognition of commissions. For simplicity we will record as follows:
Account Name  Debit  Credit 

Bank  …  
Banking Commission ( charge )  …  
Refund bonus  …  
Bond loan  … 
At maturity, interest is to be noted as for undivided loans.
In France (contrary to international standards), the banking commission can be included in an accrual and transfer account and then spread over a maximum duration of the loan.
At the end of the year, an accrued interest is found to represent the latent interest payable at the next deadline impoverishment.
At the end of the financial year, the redemption premium must be amortized and recorded as an expense .
Convertibility, redemption and bonds of bonds
Bond issues may include a clause allowing the conversion or redemption into other shares or bonds (OCO, OCA, ORA). The convertible bonds shall be provided to the original contract. They are fixed by the extraordinary general meeting. The possibility of nonconversion must be provided (except in the case of bonds redeemable in shares). In case of payment, they must be verified by the auditor . There are fixed rate window loans, the periods of which have exit options. The exit penalties are degressive.
Warrants may be attached to the bonds so that they allow this exercise prior to the exercise of the right to subscribe for the share or the obligation attached.
Financial Analysis: Corporate Debt Criteria
The loan creates a level of dependence on the external environment. The financial analysis the corporate finance enables a number of comparisons.
Examples of indicators related to loans:
 Debt capacity: Borrower’s earnings influence its debt capacity (for businesses, EBITDA may be the amount of the maximum annuity to pay).
 The financial structure ratio .
 In judging a company’s debt, banks often rely on the company’s Debt / Equity (D / CP) ratio . The acceptable level of D / CP of a company varies according to the profitability of its activity.
 To illustrate, a ratio of 1 will be considered important in an unprofitable but weak sector of activity in a very profitable sector of activity. Indeed, the profitability of the business sector directly affects the ability of the company to repay its debt. It should be kept in mind that the company’s level of debt directly influences the level of financial charges it bears.
 The financial autonomy ratio .
 The debt coverage rate , often better known by the Anglican DSCR, which expresses the ratio between the margin generated by a project and the annual debt payments.
Notes and references
 ↑ IstaOfppt , ” Chapter: Undivided loans ” [ archive ] , on Ista Ofppt (accessed January 5, 2017 )
 ↑ http://doc.impots.gouv.fr/aida2012/brochures_ir2012/lienBrochure.html?ud_050.html [ archive ] .
 ↑ ” The various guarantees of a mortgage – Real Estate Heritage Finance ” [ archive ] (accessed April 23, 2015 ) .