Payback period of investments with discounting (DPP)...

Payback period of investments with discounting (DPP)

The payback period of an investment with discounting

(Discounted Payback Period, DPP ) removes the shortage of the static method of the payback period of investments and takes into account the value of money in time, and the formula for calculating DPP, has the form

, where .

Obviously, in the case of discounting, the payback period increases, i.e. always DPP & gt; PP.

The simplest calculations show that such a reception in conditions of a low discount rate characteristic of a stable western economy improves the result by an imperceptible amount, but for a much higher discount rate characteristic of the United States economy, this gives a significant change in the estimated payback period. In other words, a project that is acceptable by the PP, criterion may be unacceptable by the DPP criterion

If you use the criteria PP and DPP in the evaluation of investment projects, decisions can be made on the basis of the following conditions: a) the project is accepted if the payback takes place; b) the project is accepted only if the payback period does not exceed the deadline set for the company.

Table 5.6. Data for determining PP and DPP for a project

Metric

The values ​​of the indicator for the steps of the calculation period (years)

0

1

2

3

4

5

6

7

8

9

10

Pure

Revenue

-120

10

20

30

50

50

60

60

70

85

95

Balance

clean

Revenue

-120

-110

-90

-60

-10

40

100

160

230

315

410

Discounting factor

1.00

0.91

0.83

0.75

0.68

0.62

0.56

0.51

0.47

0.42

0.39

The current value of PV net income (discounted net

REVENUE)

-120.00

9.09

16.53

22.54

34.15

31.05

33.87

30.79

32.66

36.05

36.63

Discounted balance of black hole

-120.00

-110.91

-94.38

-71.84

-37.69

-6.64

27.22

58.01

90.67

126.72

163.34

Example

Define the indicators PP and DPP and decide whether to accept the project (the project data is presented in Table 5.6) if the discount rate is 10%. The company does not accept projects with a payback period of more than 5 years.

From the example shown, it is clear that PP is equal to five years, and DPP is equal to six years. Thus, by the criterion of a simple pay-back period, the project should be accepted, and, based on the discounted pay-off period criterion, should be rejected.

In general, the definition of a payback period is ancillary to the net present value of the project or an internal rate of return. In addition, the lack of such an indicator as the payback period is that it does not take into account the subsequent inflows of money, and therefore may serve as an incorrect criterion for the attractiveness of the project.

Let's illustrate these positions with an example. It is required to evaluate the attractiveness of projects A and B (the data are presented in Tables 5.7 and 5.8, the discount rate is 5%).

Table 5.7. Data for the project A

Metric

The values ​​of the indicator for the steps of the calculation period (years)

0

1

2

3

4

5

Net Income

-1500

100

200

250

1300

1200

Net income balance

-1500

-1400

-1200

-950

350

1550

Discounting

multiplier

1.00

0.95

0.91

0.86

0.82

0.78

The current value of PV net income

-1500.0

95.2

181.4

216.0

1069.5

940.2

Discounted balance of black hole

-1500.0

-1404.8

-1223.4

-1007.4

62.1

1002.3

When calculating the following criteria values:

NPV

1002.35

PP

4

DPP

4

Table 5.8. Project Data B

Metric

The values ​​of the indicator for the steps of the calculation period (years)

0

1

2

3

4

5

Net Income (BH)

-1500

300

300

350

800

1300

Net income balance

-1500

-1200

-900

-550

250

1550

Discounting

multiplier

1.00

0.95

0.91

0.86

0.82

0.78

The current value of PV net income

-1500.0

285.7

272.1

302.3

658.2

1018.6

Discounted balance of black hole

-1500.0

-1214.3

-942.2

-639.8

18.3

1036.9

When calculating the following criteria values:

NPV

1036.91

PP

4

DPP

4

According to the payback period criterion and its variant, taking into account the discounting, these projects are equivalent, but in connection with the project B A, flow in the 5th year > becomes more attractive because its net present value is greater than the net present value of the project A (NPV B NPV A ). Thus, the criterion payback period assigns the same value to all cash flows during the restrictive period and does not take into account all subsequent payments, and hence can only serve as an auxiliary for the NPV test.

Another significant shortcoming of the criterion is the "payback period" in that, in contrast to the NPV criterion, the "payback period" does not have the additivity property. In this regard, when considering a combination of projects with this indicator, you must handle carefully, given this property.

Example

Compare projects A, B and C. Projects A and B are mutually exclusive, and project C - independent. Thus, when implementing projects for a commercial organization, it is possible to consider projects A or B, as well as a combination of L and C or B and C projects with sufficient financial resources (data on projects and their combinations are presented in Table 5.9). The results of the calculated indicators are presented in Table. 5.10.

Table 5.9. Data for projects A, B and C and their combinations

Metric

A

In

C

A + C

B + C

Payback period PP

2

1

3

2

3

Payback period DPP

2

1

3

3

3

If we consider project A or B, we should accept project B. If we consider projects A and C or B and C, then we must accept a combination of projects A and C, which contradicts the additivity rule, because projects A and C separately in projects the payback period is PP and DPP are the worst.

Table 5.10. The results of calculations for projects A, B and C

Metric

The value of the indicator by the steps of the calculation period

0

1

2

3

ProjectA

Net Income

-15

0

35

5

Net income balance

-15

-15

20

25

Discounting factor

1.00

0.89

0.80

0.71

The current value of PV net income

-15

0.0

27.9

3.6

Discounted balance of black hole

-15.0

-15.0

12.9

16.5

Payback period PP

2.0

Payback period DPP

2.0

Project B

Net Income

-15

20

5

25

Net income balance

-15

5

10

35

Discounting factor

1.00

0.89

0.80

0.71

The current value of PV net income

-15.0

17.9

4.0

17.8

Discounted balance of black hole

-15.0

2.9

6.8

24.6

Payback period PP

1.0

Payback period DPP

1.0

Project C

Net Income

-15

0

0

25

Net income balance

-15

-15

-15

10

Discounting

multiplier

1.00

0.89

0.80

0.71

The current value of PV net income

-15.0

0.0

0.0

17.8

Discounted balance of black hole

-15.0

-15.0

-15.0

2.8

Payback period PP

3.0

Payback period DPP

3.0

Projects A and C

Net Income

-30

0

35

30

Net income balance

-30

-30

5

35

Discounting

multiplier

1.00

0.89

0.80

0.71

The current value of PV net income

-30.0

0.0

27.9

21.4

Discounted balance of black hole

-30.0

-30.0

-2.1

19.3

Payback period PP

2.0

Payback period DPP

3.0

Projects B and C

Net Income

-30

20

5

50

Net income balance

-30

-10

-5

45

Discounting

multiplier

1.00

0.89

0.80

0.71

The current value of PV net income

-30.0

17.9

4.0

35.6

Discounted balance of black hole

-30.0

-12.1

-8.2

27.4

Payback period PP

3.0

Payback period DPP

3.0

However, the criterion payback period It is indifferent to the size of the initial investment and does not take into account the absolute volume of investments. Thus, this indicator can be used only for analysis of investments with a comparable volume of initial investments.

Sometimes the criterion "payback period can be decisive for the purpose of making investment decisions. In particular, this may be the case when the investments involve a high risk, and the shorter the payback period, the more such a project is preferable. In addition, the company's management may have a certain limit on the payback period, and this is due, first of all, to the problem of liquidity, i.e. the main task for the company is to make the investment pay off and as soon as possible. Thus, the PP and DPP criteria make it possible to judge the liquidity and riskiness of the project, as follows: the shorter the payback period, the less risky the project; The project is less liquid than the payback period. These criteria should be applied when the company is interested in increasing liquidity, as well as in industries where investments are associated with a high level of risk (for example, in industries with rapid technology change: computer systems, mobile communications, etc.).

In addition, the method has found its application and for calculating options for financing investment projects. Criteria PP and DPP are reasonable to count on projects financed by long-term obligations. In this case the payback period of the project should be less than the period of using borrowed funds.

In general, it can be concluded that the net present value method and the internal rate of return method combined with taking into account their advantages and disadvantages give correct results when justifying investment decisions. However, none of these indicators in itself is sufficient to decide whether to implement or reject the investment. The decision on investing should be made taking into account the values ​​of all the above criteria and the interests of all participants in the investment process. An important role in this decision should be played by the structure and the distribution of capital in time, attracted for the investment, as well as other factors, some of which lend themselves to substantive rather than mathematical accounting.

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