APP, Accounting payback period

Assessing investments: Accounting approach

APP, Accounting payback period

Accounting payback period

The time required to recoup the costs of a project is called the accounting payback period and is abbreviated as APP.

The APP is calculated using the net return up to and including a specified period; that is the sum of the cash flows up to and including that period. The net return on the investment is the return up to and including the last period #n#.

The accounting payback period is therefore the first period in which the net return up to and including that period are not negative.

Objective With this method, the emphasis is on receiving back the invested amount as quickly as possible.

The accounting payback period in a project of the duration #n# is therefore a natural number less than or equal to #n#, unless the net return on the investment is negative. In the latter case, the APP is indefinite. Because we are talking about plans to make a profit (or at least not to make a loss), this is generally not an issue.

The concept of "Net return" is often referred to as EBIT in the accounting world. This stands for Earning Before Interest and Taxes .

We now convert the concept of APP into formulas.

Accounting payback period

Given an investment with the duration #n# and cash flows #C_0#, #C_1 ,\ldots, C_n#, the accounting payback period is the period #j# in which the net return up to and including period #j# is non-negative for the first time:

\[\sum_{i=0}^{k} C_i \lt 0\quad \text{voor alle }k\lt j\quad \text{ en }\quad \sum_{i=0}^{j} C_i \geq 0\]

So we calculate the net returns for the periods #1,2,\ldots# until we get a non-negative result. The first period for which this requirement is met is the accounting payback period.

When comparing two or more projects with the same accounting payback period, preference is given to the investment with the highest net return in the period in which the APP is achieved.

We now revisit the notion that APP is between 1 and #n#. Because #\sum_{i=0}^{0} C_i =C_0\lt 0#, the accounting payback period is at least #1#. It is reasonable to assume that the net return of the project, #\sum_{i=0}^{n} C_i #, is not negative; because otherwise the investment would not have aimed at profit. This assumption leads to the conclusion that the APP is indeed less than or equal to # n#.

The table below shows the cash flows of an investment.
\[\begin{array}{l|c} &\text{Cash flows}\\ \hline\ C_0 & -305\\\ C_1 & 150 \\ \ C_2 & 150 \\ \ C_3 & 150 \\ \ C_4 & 150 \\ \ C_5 & 150 \\ \end{array}\]
Determine the accounting payback period of the investment.

#APP=# #3#

To determine the accounting payback period, we first draw up the table with cumulative cash flows.
\[\begin{array}{c|c} j&\displaystyle \sum_{i=0}^{j} C_i\\ \hline\ 0 & -305\\\ 1 & -155 \\ \ 2 & -5 \\ \ 3 & 145 \\ \ 4 & 295 \\ \ 5 & 445 \\ \end{array}\]
The accounting payback period is the period in which the sum of cash flows is greater than or equal to #0# for the first time. Since

#\sum_{i=0}^{2}C_i =-5 \lt 0# and
#\sum_{i=0}^{3}C_i =145 \geq 0#,

it is the period #3#.

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