Net Present Value Method - International Financial Management

Net Present Value Method

One of the key and most used methods of assessing the quality of investment projects, especially in international practice, is the Net present value (NPV), based on the calculation of the magnitude of the possible increase in the value of the company as a result of the implementation of the relevant investment project. The formula for calculating the net present value is

where - cash inflows (cash flow) for the period V, r - the desired rate of profitability (profitability) i.e. that level of profitability of invested funds, which can be provided when they are placed in publicly available financial institutions and instruments. In other words, r - the opportunity cost (alternative cost) of the capital attracted to invest in the project in question; - initial investment of funds, or the amount of initial investment.

In reality, however, an investor may face a situation where the project does not involve one-time investment of capital, but multiple investments, when the investment is carried out for several temporary discrepancies. In this case, the formula for calculating the net present value takes a slightly different form:

where - investment costs for the period t.

Obviously, if the present value of the inflow of funds from the project exceeds the present value of the sum of all investments, the project in question will have a positive net present value. The positive value NPV for the project means that investment costs generate net cash flows with a return greater than alternative options in the market with the same level of risk; the profitability of the project exceeds the required profitability of the owners of capital. In this case, the project can be accepted for implementation, since the costs for it will be reimbursed and, in addition, its implementation will provide some revenue that increases the value of the company and the well-being of its shareholders.

Obviously, if several alternative projects are analyzed, a project with a large NPV should be accepted. Projects with NPV = 0 do not change the position of the owners of capital, as the company's valuation in this case does not change and the share price remains unchanged. But the adoption of such projects increases the company's assets by the amount of investment that may be of interest to management (increasing prestige, power, etc.).

Negative value NPV shows that the desired rate of profitability is not ensured and the project is unprofitable; he, as a rule, rejects. Of the several alternative projects, a project with a large NPV.

When calculating NPV different discount rates can be used. If the value of r is not constant, will vary from period to period, then it is necessary to apply individual discount factors to each cash flow, which will correspond to this calculation step. In this case, NPV is recommended to calculate by the formula

where .

At the same time, it is quite possible that a project acceptable at a constant discount rate may become unacceptable with a variable.

It is also important to note that the net present value is additive in the space-time aspect by the criterion, i.e. . Therefore, the net present value of a set of projects, for example the whole company, is equal to the sum of the reduced values ​​of the projects that make up it. This important property allows us to use this criterion when analyzing the optimality of the investment portfolio of projects. In addition, NPV takes into account both the lifetime of the project and all revenues (expenses) at all its stages.

Practically using the NPV method, the choice (justification) of the discount rate remains rather difficult.

Since a company can have a large number of shareholders, the discount rate of interest must meet the minimum requirements for the return on its capital of most of these individuals. Moreover, in companies with a certain share of borrowed capital, the discount rate should represent a return that satisfies all types of investors (shareholders and creditors) of the company. Therefore, for such a company, an acceptable discount rate will be the average weighted cost of capital

where - the price of - the source of the company's funds; - the specific weight of the first source in the total sum.

It should be noted that the validity of the use of this indicator in analytical calculations is associated with some reservations and conventions. In particular, its significance is influenced not only by the internal conditions of the company's activity, but also by the external situation on the financial market. Thus, when interest rates change, the rate of return on invested capital required by shareholders changes, which affects the value of WACC.

For the sake of completeness of the information required to calculate NPV, consider the typical cash flows in the enterprise.

Typical input cash flows:

• additional sales volume and an increase in the price of the goods;

• a decrease in average gross costs (a reduction in the cost of production);

• the residual value of the equipment at the end of the last year of the investment project (since the equipment can be sold or used for another project);

• Release of working capital at the end of the last year of the investment project (closing accounts of debtors, selling inventory balances, selling shares and bonds of other enterprises).

Typical Weekend Cash Flows:

• initial investment in the first year (s) of the investment project;

• increase in requirements for working capital in the first year (s) of the investment project (increase in accounts receivable to attract new customers, purchase of raw materials and components to start production);

• The cost of repair and maintenance of equipment;

• additional non-production costs (social, environmental, etc.).

Earlier, we noted that the resulting net cash flows are designed to ensure the return of the invested amount of funds and to obtain the maximum (if possible) income for investors. Consider how the cash flows split into input (output), using the NPV method to estimate a particular investment project.

Example. Companies Multicast it is necessary to make a choice between two models of new equipment, which it intends to use to increase the volume of its own production in order to enter the world market. Investments in equipment of the type A amount to $ 30 thousand, in equipment of the type B - 45 thousand dollars. with the same period of their operation for 5 years.

We calculate (Table 6.3) the net present value for both equipment models for the discount rate r = 20%.

Table 6.3

The net present value of the model A

Cash Flows, USD

Years

0

1

2

3

4

5

Core Assets

(30000)

-

-

-

-

-

Receipt from business activities

100000

120000

140,000

160000

180,000

Payments for business activities

(75000)

(90000)

(105000)

(120000)

(135000)

Cash flow before taxation

25000

30000

35000

40000

45000

Depreciation charges

6000

6000

6000

6000

6000

The taxable result

19000

24000

29000

34000

39000

Income tax

-

(9500)

(12000)

(14500)

(17000)

(19500)

Net result

-

9500

12000

14500

17000

19500

Depreciation charges

6000

6000

6000

6000

6000

Net cash flow

-

15500

18000

20500

23000

25500

Discount rate

1.0

1.2 1

1.2 2

1.2-3

1,2 - *

1.2-5

Discounted cash flow

(30000)

12917

12500

11863

11092

10248

The same cumulative result

-

12917

25417

37280

48372

58620

Based on the results of the calculations presented in Table. 6.3, for the A equipment, the net present value will be

Similar calculations for the B equipment are shown in Table. 6.4.

Table 6.4

The net present value of the model In

Cash Flows, USD

Years

0

1

2

3

4

5

Core Assets

(45000)

-

-

-

-

-

Receipt from business activities

-

100000

120000

140,000

160000

180,000

Payments

for business activities

-

(60000)

(72000)

(84000)

(96000)

(108,000)

Cash flow before taxation

-

40000

48000

56000

64000

72000

- Depreciation charges

-

9000

9000

9000

9000

9000

The taxable result

-

31000

39000

47000

55000

63000

Income tax

(15500)

(19500)

(23500)

(27500)

(31500)

Net result

-

15500

19500

23500

27500

31500

+ Depreciation charges

-

9000

9000

9000

9000

9000

Net cash flow

-

24500

28500

32500

36500

40500

Coefficient

discounting

1.0

1.2-1

1.2-2

1,2-Z

1.2

1.2-5

Discounted cash flow

(45000)

20417

19792

18808

17602

16276

The same cumulative result

-

20417

40209

59017

76619

92895

Net present value for equipment in the In

Comparison of net present values ​​for both models shows that the B model is preferred (47,895 & gt; 28,620).

In order to take into account inflation, when evaluating the effectiveness of investments, the discounting factor (profitability) should be adjusted by the inflation rate i according to the conclusions from the well-known Fisher effect:

whence

Example. Company Default plans to purchase new equipment at a price of $ 40,000, which, according to the company's administration, will provide $ 20,000 in cost savings (in the form of input cash flow for the next three years). During this period, the equipment will be completely worn out. The cost of the company's capital , and the expected rate of inflation per year.

We estimate first the project without taking into account inflation (Table 6.5).

Now let's take into account the effect of inflation in the calculation scheme (Table 6.6).

Table 6.5

Calculation NPV excluding inflation

Cash Flows, USD

Years

0

1

2

3

Core Assets

(40000)

-

-

-

Annual inflow of funds

-

20000

20000

20000

Net cash flow

(40000)

20000

20000

20000

Discount rate

1.0

1.16 1

1.16 2

1.16-3

Discounted cash flow

(40000)

17241

14,863

12813

The same cumulative result

-

17241

32 104

44917

Table 6.6

Calculation NPV with inflation

Cash Flows, USD

Years

0

1

2

3

Core Assets

(40000)

-

-

-

Annual real inflow of funds

-

20000

20000

20000

Inflation index

-

1.1

1.21

1.331

Indexed (nominal) inflow of funds

-

22000

24200

26620

Net cash flow

(40000)

22000

24,200

26620

1.0

1,276 1

1,276 2

1,276 s

Discounted cash flow

(40000)

17241

14863

12813

The same cumulative result

-

17241

32 104

44917

The answers for both options are exactly the same, which is quite natural in the case of the same inflation rate for all components of costs and revenues. For this reason, and taking into account the relatively low level of inflation in developed countries, the majority of Western companies tend not to take inflation into account when calculating the effectiveness of investment projects.

The criterion NPV has, as it follows from the above, both advantages and disadvantages. The obvious advantage of this approach is that this criterion is absolute, and therefore, taking into account the scale of investment. This allows you to calculate the increase in the value of the company, which is its main goal. However, disadvantages follow from advantage. The first is that the NPV is difficult, and in some cases impossible to normalize. For example, NPV a certain project is 200 thousand dollars. Is this a lot or not? It is very difficult to answer this question, especially if an alternative project is being considered.

The second drawback is related to the fact that NPV does not explicitly indicate what kind of investment efforts this or that result is achieved. Although in the calculation of NPV the size of the investment is taken into account, a relative comparison of investment costs with the results obtained is not carried out. And finally, the third drawback of the NPV criterion is that for an investor (and, of course, not only for him), it is important to have information about the payback period of the investment costs incurred.

Considering the above, in financial management, the criteria calculated as relative values, in particular such as the profitability index and the internal rate of return, were widely used.

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