# Discounted payback period - Investments

## Discounted payback period

The above method is called the ordinary, simple payback period. When using it, future amounts of money are not discounted. However, it is often of interest for a firm to determine over what period of time the accumulated flow of discounted amounts of expected revenue streams will exceed the amount of initial investment. In this case, we can assume that the firm uses a discounted payback period that eliminates the shortage of the ordinary payback period due to the fact that all money flows received before the end of the project have equal weights when applying the latter.

To calculate the discounted payback period of a project with a duration of n steps with cash flows in the calculation steps C 1, C 2 , C 3, ..., C n and an acceptable discount rate r% , the following algorithm must be applied.

1. At the first stage, compare the values ​​of and C 0 :

• If , the discounted payback period of the project is one step in the calculation;

• If , then go to the second stage.

2. The second stage compares the value and C 0:

• If , the discounted period

the payback of the project will be equal to two steps of calculation;

• If , then go to the third stage of 2 ect.

The discounted payback period in this case is those t calculation steps for which the amount is discounted -

the cash flows generated by the project, for the first time exceed the value of C0, i.e. for the first time the condition will be fulfilled

In order to apply the discounted payback period, the firm also must independently set the payback rate of any similar project and compare the values ​​of the disk and the disk. Then you can formulate the discounted payback period: you should take the project for which the condition m is the disk ≤ k disk.

For example, the firm sets the desired discounted payback period of the project k disk = 2 years and considers the following projects (also assume that the acceptable discount rate r = 0.12):

 Project Co s, C2 C 3 C, 3 -60 +40 +30 +30 +40 4 -70 +30 +40 +50 +60 5 -80 +50 +60 +50 +60

If only simple payback lines were used to evaluate these projects and it was assumed that k = 2 years, then each of the three projects was acceptable, since for any of them m = k = 2 years.

To calculate the discounted payback period of projects, we define discounted cash flows:

 Project C 1/1.12 C 2/(1.12) 2 C 3/(1.12) 3 C 4 (/ (1.12) 4 3 -60 +35.7 +23.9 +21.4 +25.4 4 -70 +26.8 +31.9 +35.6 +38.1 5 -80 +44.6 +47.8 +35.6 +38.1

Calculations show that the discounted payback period of the first project is t disk = 3 years, for the second project the discounted payback period will also be three years, and for the third project - two years. Taking into account the established value k the disk = 2 years the company can accept only the third project under the rule of the discounted payback period.

However, this method also disregards all the amounts received after the deadline for the end of the project, as a result of which, from two projects with the same discounted payback period, the firm can choose one that has a lower net present value, i.e. which will give the company a smaller amount of profit.

To summarize, you can see that the evaluation of projects by the payback period has an indisputable advantage - the simplicity of the assessments. However, this method has serious drawbacks:

• The management of firms arbitrarily sets the desired terms k of the payback of projects, based sometimes on empirical provisions;

• There is no criterion for ranking projects by the payback period, and to select a project from several that meet the payback period rule, additional evaluation criteria must be used;

• The normal payback period does not take into account the time value of money and gives equal weight to all money flows that arrived before the end of the project;

• both the ordinary and discounted payback periods do not take into account the cash flows received from the project after the end of the payback period set by the firm k ;

• The method involves using calculation steps of the same length.

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