Annual percentage rate

The annual percentage rate of a whole of financial flows, like a bond loan banking or or of a Placement is its rate calculated according to the actuarial model , which is a simplification of the process of Actualisation.

This process consists in bringing back financial flows not directly comparable, because occurring on different dates, at the same base, in:

calculating the brought up to date value $VA (F_ {I})$ of each future $F_ {I}$ , positive or negative flow, of refunding, payment of interest or other

VA (F_ {I}) = F_ {I}. (1+Z_ {I}) ^ {- X_ {I}}

where

$F_ {I}$ is rising flow at the time where it will be available
$Z_ {I}$ is the up-dating rate applicable of the date of actualization to the date of flow $F_ {I}$
$Xi$ is time, expressed of many years, of the date of actualization at the date of flow $F_ {I}$ .

then adding all the $VA (F_ {I})$ obtained,

VA = \ sum_ {I} GOES (F_ {I})

what gives the brought up to date value . This one is then directly comparable with the accounting value or of market with this date, the loan, the loan, the obligation or the placement (after taking into account of the possible ancillary costs).

One immediately sees the difficulty inherent in this process: to determine rate $Z_ {I}$ , which is known under the name of Taux zero-coupon S. Until the years 1980, the lack of liquidity of the financial markets and the absence of arbitration between instruments which resulted from this, made the determination of the curves of rate zero-coupons hazardous and resulted in using in practice only one primitive version of the process, the actuarial model, which replace all the $Z_ {I}$ by only one rate $T$ , kind of average rate balanced of actualization , the annual percentage rate , generally obtained by gropings.

VA = \ sum_ {I} F_ {I}. (1+T) ^ {- X_ {I}}

Is one seeks to determine $VA$ and one must then estimate $T$ compared to exogenic sizes (rates noted on the money market or bond-holder, rate of inflation, required annual profitability, etc).

Is the value present $VA$ is known, for example contract the price of the obligation, and one must then solve the polynomial equation to above determine the annual percentage rate $T$ , thanks to iterative processes, like the Dichotomie or, more rapid and more effective, the Méthode of Newton.

The principal disadvantage of the actuarial model, which applies the same up-dating rate to all flows, with closest in time as with those most distant, is that it corresponds truly to reality only in the extremely rare case where one deals with Courbe of rate punt. In all the other cases, it brings distortions of valorization. Insufficient for the professionals of the financial markets, it largely covers nevertheless the needs for the private individuals and of SME , insofar as the inaccuracies which it generates are of the same order as their expenses of interventions on the aforementioned markets. In France, for the financial produced intended for the public , loans or loans, the legislator thus generally made obligatory the posting of the annual percentage rate .

Bond external (financial evaluation)

How to evaluate a credit or an investment thanks to the annual percentage rate

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