Annuity method

The annuity method is a process that can be used to determine how much an investment costs and generates over a certain period of time. The annuity method is an instrument of investment calculation and allows several investments to be compared with one another.

Definition / explanation

Die Annuitätenmethode kann bei Investitionsentscheidungen helfen, indem sie die finanzwirtschaftlichen consequences von Investitionsentscheidungen periodenbezogen aufzeigt. Diese spezielle Form der Investitionsrechnung kann den Kapitalwert einer Investition auf die Nutzungsdauer verteilen, so dass Ein- und Auszahlungen in eine Annuität umgerechnet werden. Alle Zahlungen, die mit der Investition in Zusammenhang stehen, können so gleichmäßig auf die Nutzungsjahre aufgeteilt werden.

Der Unterschied zwischen der Net present value method und der Annuitätenmethode besteht darin, dass durch erstere Methode der Gesamtwert der Überschüsse ausgerechnet wird, während bei der Annuitätenmethode der jährliche durchschnittliche Einnahmenüberschuss – einschließlich der auf ihn fallenden Verzinsung – das Berechnungsergebnis bildet.

How is the annuity calculated?

An annuity is a periodically recurring payment that is constant in amount. The annuity consists of an interest component and a repayment component for a capital amount.

When calculating the annuity, the present value is first determined taking into account surpluses and discount factors. Then the cost of the acquisition is deducted from the present values to calculate the net present value of the investment. Finally, the value must be multiplied by the capital recovery factor (also called the annuity factor). In this way, the annual annuity can be determined.

If you use this instrument of investment calculation, an investment is considered advantageous if the annuity in the result is equal to zero or even greater. If this is the case, the investment will at least regain the capital plus interest in the amount of the discount rate.

The annuity method is rarely used in practice because it is very difficult to accurately estimate future payments.

Example calculation of the annuity method

The purchase of a new machine costs 80,000 euros, the discount rate is 10 %. The surpluses in the following five years are as follows:

Year 1: Surplus: 25,000 - discount factor: 0.909091 - present value: 22,727

Year 2: Surplus: 30,000 - discount factor: 0.826446 - present value: 24,793

Year 3: Surplus: 40,000 - discount factor: 0.751315 - present value: 30,053

Year 4: Surplus: 20,000 - discount factor: 0.683013 - present value: 13,660

Year 5: Excess: 10,000 - discount factor: 0.620921 - present value: 6,209

Total: 97.442
Acquisition value: 80.000
NPV: 17.442

Formula: d = C0 × [[qn (q - 1)] ÷ [qn - 1]]

Result: d = 17,442 × 0.263797 = EUR 4,601 / year

= The investment is therefore advantageous because it is greater than zero.

Summary

• the annuity method determines the annual average income surplus including interest
• An annuity is an annual return flow of capital that is above the discount rate
• an investment is to be assessed positively according to the annuity method if the annuity is greater than or equal to zero
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