Annuity method

The annuity is within the investment theory a method of the classic dynamic investment calculation . The net present value of an investment is distributed over the useful life in such a way that the payment sequence from deposits and withdrawals is converted into the so-called annuity . In contrast to the net present value, it is not the overall target value that is determined, but the target value per period. The annuity factor is also the reciprocal of the pension present value factor .

The annuity method allows the assessment of expansion and replacement investments in terms of income maximization. In addition, investments with different acquisition values ​​and useful lives can be compared directly with one another without taking into account a differential investment.

Action

The annuity a is the product of the net present value and the annuity factor : ${\displaystyle C_{0}}$ ${\displaystyle ANF_{n,i}}$

${\displaystyle a=C_{0}\cdot ANF_{n,i}}$.

The annuity factor (also capital recovery factor ) is the reciprocal of the pension present value factor ( i : interest rate (e.g. 4.5% = 0.045); n : useful life, q = 1 + i : interest factor ):

${\displaystyle ANF_{n,i}={\frac {(1+i)^{n}\cdot i}{(1+i)^{n}-1}}={\frac {q^{n}\cdot (q-1)}{q^{n}-1}}}$

The unit of the annuity is monetary units (in the currency used for C) per period.

When using the annuity method, an investment is to be assessed positively if the annuity is greater than or equal to zero. In this case, at least the capital employed is returned, with interest at the discount rate . In terms of value, it is equivalent whether one receives the net present value today or the annuity distributed over the useful life.

See also

• Annuity loan

literature

• Klaus Olfert: Investment , 9th edition, Friedrich Kiehl Verlag, 2003, ISBN 3-470-70479-1 .
• Hans Blohm, Klaus Lüder, Christina Schaefer: Investment: Analysis of weak points in the investment area and investment calculation , 10th edition, Verlag Franz Vahlen, Munich 2012, ISBN 978-3-8006-3937-3 .
• Klaus-Dieter Däumler, Jürgen Grabe: Fundamentals of the investment and profitability calculation , 12th edition, Verlag Neue Wirtschafts-Briefe, 2007, ISBN 978-3-482-52302-1 .

Individual evidence

1. ↑ Klaus Olfert: Investment, 9th edition, Friedrich Kiehl Verlag, 2003, ISBN 3-470-70479-1 , p. 238.