Amortization calculation

The amortization calculation or capital return calculation or method (also: pay-off method , pay-back method or pay-out method or invoice ; from English : [to] pay off = "amortize" or [to] pay back = "pay back") is a method of static investment calculation and is used to determine the capital commitment period of an investment . The payback period of an investment, i.e. H. the period in which the acquisition costs are refinanced from the annual profits and depreciation of the investment.

invoice

Average method (static amortization calculation):

${\ displaystyle {\ text {Amortization time}} = {\ frac {\ text {Purchasing expenditure}} {\ text {average return flow per time unit}}}}$

The average return flow per year is not identical to the annual profit from the profit comparison statement . While the annual profit is the difference between average revenues and average costs , the annual return is the difference between current income and expenses .

In the event that the revenues become income and all costs, with the exception of imputed interest and depreciation, become expenses in the same period, the following relationship can be applied:

${\ displaystyle {\ text {annual return}} = {\ text {annual profit}} + {\ text {imputed interest}} + {\ text {imputed depreciation}}}$

Methods

Average
method (static amortization calculation): This method is used if the annual financial return (which is used to cover the purchase price) is the same. In this case, the amortization period corresponds to the above. Formula.
Cumulative method (dynamic amortization
calculation ): This method is used when the annual return flows from the investment are different. The annual returns are differentiated according to years and added step by step each year until their total amount corresponds to the investment amount (amortization time).

Input data

The capital employed (= net acquisition costs - purchase price reductions) and the annual returns of an investment property must be known.

example

Example calculation ignoring depreciation :

Automated evaluation of a database:

Project expenditure: € 2,000
Running costs per 1 month for maintenance: 150 € (calculated from processing time hourly rate of the employee)

Manual evaluation of a database:

Running costs per 1 month for the evaluation: 850 € (calculated from processing time hourly rate)
Profit = difference between manual and automated evaluation (running costs)

Amortization calculation:

Payback period = acquisition cost / profit

Payback period = € 2,000 / (€ 850 / month - € 150 / month)

Payback period = 2.86 months

Result: The automated evaluation is worthwhile after just 3 months.

criticism

The target time is only a subjective assessment of the entrepreneur.
The debit interest does not have to correspond to the credit interest (problem of perfect capital market).

The time value of money and thus also the risk assessment and all payment effects of the investment object after the amortization period have expired are completely disregarded . The amortization period may at most be a supplementary, but not a sole, criterion for an investment decision.

One can illustrate this connection with a simple example including the net present value method (also: net present value method or NPV method). Let us assume that the following three projects are available, all of which have the same risk and the opportunity costs of capital ( discount rate ) are a uniform 10%:

Project	${\ displaystyle C_ {0}}$	${\ displaystyle C_ {1}}$	${\ displaystyle C_ {2}}$	${\ displaystyle C_ {3}}$	Payback period	Net present value (NPV) at 10%
A.	−4,000	+1,000	+1,000	+10,000	3	+5,248
B.	−4,000	+1,000	+3,600	0	2	−116
C.	−4,000	+3,600	+1,000	0	2	+100

According to the decision rule described here, projects B and C should be preferred because they have the shortest payback period. However, project A makes the most economic sense because it has the highest net present value.

Further criticism is sparked by the fact that the use of the amortization calculation easily leads to investment recommendations that run counter to the actual intentions of the investor: Investments with a shorter amortization period are often preferred because they allegedly involve a lower risk . After all, the invested capital is reacquired more quickly, so that one escapes the uncertainties of the future more. In reality, however, investments with a short amortization period are much more risky than investments with a longer amortization period. Compare only low-interest federal securities with highly speculative stocks, which combine a high profit potential (= short amortization period) with a high risk.

literature

Manfred Weber: Commercial arithmetic from A to Z. Formulas, calculation examples, tips for practice . 8th edition. Haufe, 2005, ISBN 3-448-06778-4 , p. 226 ff
Hans Blohm: Investment . 8th edition. Vahlen, Munich 1995.
Klaus-Dieter Däumler: Basics of the investment and profitability calculation . 10th edition. New economic letters, Herne / Berlin 2000.
Gerd Schulte: Investments . Verlag Kohlhammer, Stuttgart 1999.

Individual evidence

↑ Manfred Weber: Commercial arithmetic from A to Z. Formulas, calculation examples, tips for practice . 8th edition. Haufe, 2005, ISBN 3-448-06778-4 , p. 226 ff. 419 p.

↑ Ralf Dillerup, Tobias Albrecht: Amortization calculation . In: Haufe Accounting Office. Vers. 3.2, Freiburg 2005, Haufeindex 1288473.

^ Lutz Kruschwitz: Investment calculation. 1993, 5th edition, de Gruyter, ISBN 3110139065 , p. 37ff

[1] Manfred Weber: Commercial arithmetic from A to Z. Formulas, calculation examples, tips for practice . 8th edition. Haufe, 2005, ISBN 3-448-06778-4 , p. 226 ff. 419 p.