The method of net present value of the investment project. NPV (net present value)

Economists of the company are modeling the circulation invested capital. In order to build models, cash flow and discounting methodologies are used cash flows. Base parameter financial model project business plan is the NPV, which we will consider in this article. This criterion has been economic analysis in the early nineties and up to the present day, it occupies the first position in the complex and comparative evaluation projects.

Fundamentals of evaluating the effectiveness of projects

Before we proceed directly to the understanding of NPV (net present value), I would like to briefly recall the main points of the valuation methodology. Its key aspects make it possible to most competently calculate a group of project performance indicators, including NPV. Among the project participants, the main figure interested in evaluation activities is the investor. His economic interest is based on the awareness of the acceptable rate of return, which he intends to extract from the activities of the allocation of funds. The investor acts purposefully, denying himself the consumption of available resources, and counts on:

• return on investment;
• compensation for your refusal in future periods;
• better conditions compared to possible investment alternatives.

Under the rate of return that is beneficial for the investor, we will understand the minimum allowable ratio of capital increment in the form of a company's net profit and the amount of investment in its development. This ratio over the project period should, firstly, compensate for the depreciation of funds due to inflation, possible losses in connection with the onset of risky events, and secondly, to provide a premium for abandoning current consumption. The amount of this premium corresponds to the entrepreneurial interests of the investor.

The measure of entrepreneurial interest is profit. The best prototype of a profit mechanism for valuation purposes investment project is a streaming reflection methodology Money(DS) from the standpoint of revenue and expenditure parts. This methodology is called cash flow (CF or cash flow) in Western management practice. In it, income is replaced by the concepts of "revenues", "inflows", and expenses - "disposal", "outflows". The fundamental concepts of cash flow in relation to an investment project are: cash flow, settlement period and calculation step (interval).

The cash flow for investment purposes shows us the receipts of DCs and their disposals arising in connection with project implementation during the entire duration of the billing period. The period of time during which there is a need to track the cash flows generated by the project and its results in order to evaluate the effectiveness of investments is called the calculation period. It represents the duration, which may extend beyond the time frame of the investment project, including the transitional and operational phases, until completion life cycle equipment. Intervals (steps) of planning are usually calculated in years, in some cases for small projects monthly interval breakdown can be applied.

Methods for calculating net income

Of great importance for the calculation of NPV and other indicators of the project is how income and expenses are formed in the form of inflows and outflows of DC. The cash flow methodology can be applied in a generalized form or in a form localized by groups of cash flows (in operational, investment and financial contexts). It is the second form of representation that makes it convenient to calculate net income as the simplest parameter for evaluating efficiency. Further, your attention is presented to the model of the relationship between the classical grouping of DS flows and grouping according to the subject-target attribute.

Scheme of two options for grouping flows of DS with interconnections

The nature of the content of the economic effect of investments is expressed in comparison of the total inflows and outflows of funds at each estimated step of the project task. Net income (CF or NPV) is calculated for the corresponding interval value i. Below are the formulas for calculating this indicator. The dynamics of black holes from project to project almost always repeats itself. In the first one or two steps, the value of the NP is negative, because the results of operating activities are not able to cover the size of the investments made. Then the sign changes, and in the following periods, net income increases.

Formula for calculating net income for period i

The cost of DS changes over time. This is due not only to inflation, but also to the fact that money itself can bring certain income. Therefore, the NPV should be brought to the start of the project through a discounting procedure that uses the net present value method. Thanks to him, the black hole receives the status of a new indicator called "net present value" or "net present value". We are no longer interested in incremental, but in the total discounted cash flow. Its formula is shown below.

The formula for the total discounted flow of DC

The parameters "", "discounted cash flow", "discount factor" will be covered in a separate material, revealing their financial and economic nature. I will only note that the benchmarks for the value of r in the project can be the levels of the WACC indicator, the refinancing rates of the Central Bank or the rate of return for an investor who is able to provide himself with more profitable alternative investments. The total discounted cash flow can be interpreted and calculated on its basis net present value (NPV).

NPV formula

The NPV shows us how much money the investor will be able to receive after the amount of investment and regular outflows reduced to the initial moment will be covered by the same inflows. The indicator "net present value" serves as a successful replica of the Western NPV indicator, which became widespread in Russia during the "boom" of business planning. In our country, this indicator is also called "net present value". Both the English and Russian interpretations of the NPV indicator have the same distribution. The formula for NPV is shown below.

NPV formula for the purpose of evaluating the effectiveness of a project activity

The net present value presented in the formula is the subject of much debate among practitioners. I do not pretend to own the truth, but I believe that domestic methodologists will have to bring some clarity to a number of issues and, perhaps, even correct the textbooks. I will make only a couple of remarks on the main nuances.

1. To calculate the “net present value” indicator, one should rely on the classical understanding of net cash flow (NCF) as a combination of operating, investment and financial flows. But investment investments should be separated from NCF, since common sense discount factors can be different for the two parts of this formula.
2. When calculating NPV (NPV), dividends associated with the project should be excluded from the NCF, since they serve as a form of withdrawal of the investor's final income and should not affect the value of the project's NPV.

The net present value, based on these comments, can have several interpretations of the formula, one of which is the option when the discount rate for the size of the investment is based on WACC or the inflation rate. At the same time, the base part of the NCF, adjusted to the initial period at the rate of return, reduces the net present value significantly more. Increased investor demand for the rate level r has its consequences, and the net present value decreases or even goes negative.

Net present value is not an exclusive measure of performance and should not be considered in isolation from a group of other criteria. However, NPV is the main evaluation parameter due to its ability to express the economic impact of the project. Even if the indicator turns out to be slightly above zero, the project can already be considered effective. The formula for calculating NPV in traditional form Western School of Management is presented below.

Project Net Present Value Formula

NPV calculation example

As we have established, the discount factor carries the investor's expectations for income from the project. And if during the billing period all project costs are covered by income, taking into account discounting, the event is able to meet these expectations. The sooner that moment comes, the better. The higher the net present value, the more efficient the project. NPV shows how much additional income an investor can expect. Consider specific example calculation of NPV. Its main prerequisites are:

• the value of the settlement period is 6 years;
• the chosen planning step is 1 year;
• the moment of initial investment corresponds to the beginning of step "0";
• need for getting borrowed money ignored, for simplicity we assume that the investments were made at the expense of equity firms, i.e. CF from financial activities not taken into account;
• two options for the discount rate are considered: option A, where r=0.1; option B, where r=0.2.

All initial data on investments and operating CF by years of the project are given in the table below.

Project NPV Calculation Example Data

As a result of filling in the bottom three rows of the table, we are able to calculate the indicators.

1. The net income of the project, it amounted to 3,000 thousand rubles (-300+200+600+1100+1900+2500-3000).
2. Net present value for r=0.1, amounting to 687 thousand rubles (-272+165+451+751+1180+1412-3000).
3. For the discount rate r=0.2 is -634 thousand rubles (-250+139+347+530+763+837-3000).

If we compare the three obtained values, then the conclusion suggests itself that at a rate of return of 10%, the project can be considered effective, while the investor's requirements for a rate of 20% exclude this event from the zone of his interests. This happens quite often. V last years in our economy, the value of the real rate of return is steadily declining, so there are relatively few strategic investors, mostly speculative ones.

In this article, we have considered the most popular indicator of evaluation, analysis of the economic efficiency of investments and project practice - NPV. When calculating the indicator, the net present value method is used, which allows you to adjust the cash flows generated in the project for changes in the time value of money. The advantage of this criterion is its ability to find the effect of investments adequate to economic realities, and the disadvantage is its closeness to the subjective view of the investor on the level of expected return.

Net present value ( net present effect, net present value ,) - the sum of the current values ​​of all predicted cash flows, taking into account the discount rate.

The net present value (NPV) method is as follows. 1. The current cost of costs is determined, i.e. the question is how much investment should be reserved for the project. 2. Calculate the present value of future cash receipts from the project, for which the revenues for each CF year are adjusted to the current date.

The calculation results show how much money would have to be invested now to obtain the planned income if the income rate were equal to the barrier rate (for an investor, the interest rate in a bank, etc., for an enterprise, the price of total capital or through risks). Summing up the present value of income for all years, we get the total present value of income from the project (PV):

3. The present value of investment costs is compared with the present value of income (PV). The difference between them is the net present value of income (NPV):

NPV shows net income or the investor's net loss from putting money into the project compared to keeping the money in the bank. If NPV > 0, then we can assume that the investment will increase the wealth of the enterprise and the investment should be made. At NPV< 0, то значит доходы от предложенной инвестиции недостаточно высоки, чтобы компенсировать риск, присущий данному проекту (или с точки зрения цены капитала не хватит денег на выплату дивидендов и процентов по кредитам) и инвестиционное предложение должно быть отклонено.

Net present value is one of the main indicators used in investment analysis, but it has several disadvantages and cannot be the only means of evaluating an investment. NPV determines the absolute value of the return on investment, and, most likely, the larger the investment, the greater the net present value. Hence, comparing multiple investments of different sizes using this metric is not possible. In addition, NPV does not determine the period after which the investment will pay off.

If capital investments related to the upcoming implementation of the project are carried out in several stages (intervals), then the calculation of the NPV indicator is carried out according to the following formula:

CFt - cash inflow in period t; It - the amount of investment (costs) in the t-th period; r - barrier rate (discount rate); n - the total number of periods (intervals, steps) t = 1, 2, ..., n (or the duration of the investment).

Typically for CFt, the value of t ranges from 1 to n; in the case when CFо > 0, they are classified as costly investments (example: funds allocated for an environmental program).

Example #1. The size of the investment is $115,000. Investment income in the first year: $32,000; in the second year: $41,000; in the third year: $43,750; in the fourth year: $38250. Barrier rate - 9.2%

Let's recalculate cash flows in the form of present values: PV 1 = 32000 / (1 + 0.092) = $29304.03 PV 2 = $41000 / (1 + 0.092) 2 = $34382.59 PV 3 = 43750 / (1 + 0.092) 3 = $33,597.75 PV 4 = $38,250 / (1 + 0.092) 4 = $26,899.29

NPV = (29304.03 + 34382.59 + 33597.75 + 26899.29) - 115000 = $9183.66

Answer: The net present value is $9183.66.

In general, the implementation of investment projects entails the emergence of three types of risks:

Own risk of the project - the risk that the actual cash flows during the implementation will be very different from the planned ones;

Corporate, or intercompany, risk is associated with the impact that the progress of the project may have on the financial condition of the enterprise;

Market risk characterizes the impact that the implementation of the project can have on the change in the value of the company's shares (ie, its market value).

When evaluating projects the most significant are the following types of uncertainties and investment risks:

risk associated with the instability of economic legislation and the current economic situation, investment conditions and the use of profits;

external economic risk (the possibility of introducing restrictions on trade and supplies, closing borders, etc.);

the uncertainty of the political situation, the risk of adverse socio-political changes in the country or region;

incompleteness or inaccuracy of information about the dynamics of technical and economic indicators, parameters new technology and technology;

fluctuations in market conditions, prices, exchange rates, etc.;

uncertainty of natural and climatic conditions, the possibility of natural disasters;

production and technological risk (accidents and equipment failures, manufacturing defects, etc.);

incompleteness or inaccuracy of information about the financial position and business reputation of enterprises - participants (possibility of non-payments, bankruptcies, failures of contractual obligations).

47 In the history of any science, there are not so many “revolutions”, i.e. situations where the dominant approach to the study of its subject (general vision and tools of analysis), and sometimes this subject itself, changes dramatically within a relatively short period of time.

The most significant revolution in the history of economic science, apparently, should be considered the marginalist revolution, which is usually dated to the 70s of the XIX century. The changes were so radical that science even changed its name (starting with W. S. Jevons and A. Marshall). After the marginalist revolution, the dominant economic (more precisely, microeconomic) theory becomes much more similar to the modern one than before it. In this sense, we can say that it is from this period that the history of modern microeconomic theory originates, whereas earlier it was possible to speak only about its prehistory.

By the beginning of the marginalist revolution, the classical and historical schools dominated economic thought. In different countries, the relationship between them evolved differently: for example, in England, classical political economy was in the lead, and the historical school was on the periphery, while in Germany the opposite situation existed. States that lagged behind the leader and failed to establish a division of labor with him, such as Spain, Portugal, the Ottoman Empire (Turkey) and Russia, more often applied protectionist policies, and in the field of economic thought the historical school set the tone.

Many researchers argue that, unlike representatives of the classical school, for whom the main theoretical problems were to determine the causes of the wealth of nations and economic growth and the distribution of income between social classes, marginalists put the problem of effective (optimal) allocation of data, existing resources at the forefront. However, it cannot be argued that the marginalists set themselves such a goal consciously. It would be more correct to say that the premise of efficient resource allocation was unconsciously laid in the foundation of marginalist theory. At the same time, her approach was distinguished by the following methodological features arising from each other.

1. Methodological individualism. In contrast to the holistic approach of the mercantilists and classics, who thought in terms of countries and classes, the marginalists adhered to methodological individualism, i.e. explained social (in this case, economic) phenomena by the behavior of individual individuals. Society as a whole was presented to marginalists as a collection of atomistic individuals.

2. Static approach. Marginalists were interested not in the dynamic, but in the static aspect of the economic system, not in the process, but in the architectonics, not in how the economy changes, but in how it works. Change and dynamics in this theoretical system were interpreted as a sequence of discrete static states (the so-called comparative statics). Marginalists were haunted by the question posed and broadly resolved by Smith in The Wealth of Nations: how can a system consisting of individuals pursuing their own interests exist and not collapse.

3. Balanced approach. Marginalists sought to explore not just a static state, but an equilibrium state that is resistant to short-term changes in economic variables.

4. Economic rationality. An individual's state is equilibrium if it is the most beneficial for him under given conditions in comparison with possible alternatives, i.e. optimal. Marginalists, as it were, sought to answer the question: “How does the world work if it is optimally arranged?” Therefore, it is no coincidence that the most important for the marginalist theory are the prerequisites for maximizing economic entities of their target functions: utility for consumers (households) and profits for producers (firms). In other words, the premise of the marginalist theory is the rational behavior of economic entities.

5. Limit analysis. The central place in the analytical arsenal of marginalism is occupied by marginal values ​​characterizing an additional single or infinitesimal increment of goods, incomes, labor efforts, etc., from which the “revolution” itself takes its name. In fact, with the help of marginal values, the principle of maximizing the objective function was concretized: if the addition of an additional unit of a consumed or produced good does not increase the overall level of utility or profit, then the initial state is already optimal and in equilibrium.

6. Mathematization. The principle of maximization made it possible to interpret economic problems as problems of finding a conditional extremum and to apply differential calculus and other mathematical tools of analysis.

Greetings! We continue the series of articles on methods for evaluating investments. Today I will talk about my "favorite" - the NPV of an investment project. I like this indicator for its transparency, visibility and the ability to "tie up" future cash flows to the current moment.

NPV is short for the English term Net Present Value. In Russian, this is translated as net present value (to the current time) or NPV. The same figure is often calculated as net present value or NPV.

In simple terms, the method of calculating NPV (or NPV) is the difference between all "outflows" and "inflows" of money, reduced to the current moment. It shows the amount of the total profit that the investor will receive from the project. But not in the form of a banal difference between income and expenses. And taking into account the time value and risks of all cash investments in an investment project.

NPV allows the investor to answer the following questions:

1. Is it really worth investing here?
2. Which of the several options to choose?
3. What is the IRR internal rate of return?

Sometimes the NPV is interpreted as the added value of the project. After all, investments are justified only if they fully return the initial investment, cover inflation and allow the investor to earn something on top.

NPV can be used to evaluate the effectiveness of investments in both real and financial projects.

How to calculate?

Formula

NPV = ∑t=1nCFt (1+r) t−IC

• NPV is net present value.
• CFt (Cash Flow) – cash flow in period t.
• IC (Invest Capital) - the initial costs of the investor.
• r is the discount rate.

Excel (two ways)

With built-in NPV function

The formula for calculating NPV "works" only if you set the discount rate correctly and highlight the "corridor" of net cash flow. We select in Excel "formula" - "financial" - "NPV".

• In the "Rate" field, specify the value of the discount rate (either manually or specify the address of the corresponding table cell).
• In the field "Value 1" we indicate the discounted cash flows. The easiest way to do this is to select a range of cells on the sheet with the “mouse” while holding down the left key.

Note! The selected range should not include the first cell with the initial investment! Otherwise, the NPV will be calculated incorrectly.

• Click OK.
• Select the cell with the calculated NPV value. Its calculation will appear in the formula bar (top).
• We add the formula manually. After the "=" sign, enter the amount of initial investment in the project and put the "+" sign. Or we indicate after "=" the address of the corresponding cell;

• Press the Enter button.

With the help of "manual" calculation

We fill in as many columns of the table as there are planned periods. If we do the calculation for five years, then there will be five columns. For each period, the following values ​​will be required:

• Net cash flow (expected receipts minus expected costs).
• Discount rate.
• NPV for each column according to the formula: cash flow for the period / (1 + discount rate). The sum at the bottom of the fraction is raised to the power of each period (1,2,3, and so on).

The total amount of NPV for each year will be the desired value.

Using a calculator

"Manual" evaluation is carried out in several stages.

Step 1. Determine the amount of initial investment (Invest Capital or IC). This includes all the money that we plan to invest at the initial stage, including indirect costs(for example, bank commission).

Step 2. Choose a time period t for analysis. It could be 2, 5 or 10 years old.

Step 3. Determine the flow of payments for each time period. If we calculate NPV for 5 years, then we should have five cash flows. They may differ from each other in amount or be identical.

Step 4. Determine the discount rate ® . Any money today has more value than in a year. In other words, 10,000 rubles in 2013 is a completely different 10,000 rubles than in 2018.

Step 5. Discounting our cash flows. Simply put, we reduce the cash receipts for each year by the discount rate. This will be the present value of the project.

Step 6. We add up all the received discounted flows. And from this amount we subtract the amount of the initial investment.

Important nuances

How to determine the discount rate R?

As a rule, the discount rate is the percentage at which an investor can attract financial resources. And there are many such ways:

• Bank loan.
• Loan from friends at a minimum interest.
• Sale of assets, withdrawal of money from other projects or personal savings.

In all these options, the cost of capital will be different! Even the loan rate will vary depending on financial stability company, terms, amount and availability of collateral.

How to find the discount rate? Most often, investors calculate the weighted average interest rates all potential sources.

This method of calculating the discount on capital is called WACC (short for Weighted Average Cost of Capital).

How to determine the amount of cash flows (CF)?

Perhaps this is the most difficult stage. We need to know in advance the sums of all receipts for the project and the costs of it. If this concerns a business or an investor company, then you will have to calculate the volumes and amounts of future sales, as well as make an accurate calculation of the entire cost part (rent, raw materials, taxes, wages, logistics, etc.).

How to interpret the result?

If NPV > 0, then the project will be profitable

If NPV< 0, то вариант убыточен. Нужно либо отказаться от него, либо пересмотреть исходные данные.

If NPV = 0, then the project will fully pay off the funds invested in it, but will not bring profit to the investor.

Simple calculation examples and practical application

We evaluate the NPV of the Coffee House project. We accept the discount rate at the level of 10%.

We calculate NPV according to the formula in Excel, not forgetting to separately enter the initial investment into it with the “-” sign.

NPV turned out to be negative (-22391 rubles). With such initial data, the Coffee House project will not even reach zero in five years. But it is possible that after a certain point in time, the business can become profitable.

There was an opportunity to profitably buy property in Bulgaria for rent for a symbolic $ 40,000. An acquaintance agreed to lend this amount for 5 years at 9% per annum (the discount rate is 0.09).

Estimated rental income for the year: from $13,000 to $19,000 (calculations were made by the management company).

Project analysis using NPV looks like this.

Substituting the values ​​in the formula in Excel, we get the discounted income NPV = $11139.

Pros and cons of the method

In my opinion, the advantages of the method include:

1. The specificity of the result. If NPV is greater than zero, then the project can be considered; if it is less than or equal to zero, then it can be abandoned or postponed for a while.
2. The ability to take into account the change in the value of money over time.
3. The discount rate allows you to take into account the risks associated with the project.

Cons of the indicator:

1. UNIDO criticizes the use of NPV to compare alternative projects. In the opinion of the organization, the unit value growth rate index is more suitable for this purpose.
2. In many cases it is not possible to correctly calculate the discount rate.
3. The amount of cash flows, being a forecast value, does not take into account the probability of an event outcome.

Other performance indicators of the investment project

Any investment project is evaluated by several indicators at once. In addition to NPV, investors often calculate the ROI index, internal norm IRR returns and, of course, the discounted DPP payback period.

I will talk about some of these indicators in future posts.

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The most important indicator of the effectiveness of an investment project is net present value(other names - NPV, integral economic effect, net present value, net present value, net present value, NPV) - accumulated discounted effect for the billing period. NPV is calculated using the following formula:

where P m - cash inflow on m-th step;

O m - cash outflow at the m-th step;

- discount factor at the m-th step.

In practice, a modified formula is often used

where is the amount of cash outflow at the m-th step without capital investments (investments) K m at the same step.

To assess the effectiveness of the investment project for the first K steps of the billing period, it is recommended to use the current NPV indicator (cumulative discounted balance):

(36)

Net present value is used for matching investment costs and future cash inflows, given in equivalent terms.

To determine the net present value, first of all, it is necessary to select a discount rate and, based on its value, find the appropriate discount factors for the analyzed billing period.

Once the present value of the cash inflows and outflows has been determined, the net present value is determined as the difference between the two. The result obtained can be either positive or negative.

Thus, the net present value indicates whether the investment will achieve the desired level of return over its economic life:

A positive net present value indicates that discounted cash receipts will exceed the discounted amount over the billing period capital investments and thereby provide an increase in the value of the company;

On the contrary, a negative net present value shows that the project will not provide a standard (standard) rate of return and, therefore, will lead to potential losses.

Example. Investments in the amount of 100,000 rubles. with annual cash receipts (annuity) for 6 years in the amount of 25,000 rubles. allow you to get a net present value of almost 16,000 rubles. assuming that the firm will apply a discount rate (i.e. standard rate of return) of 8% after tax. All initial investment will be recovered over a ~5 year period. The net present value of the project is RUB 15,575. increased the firm's capital by that amount in modern terms, which can protect the investor from possible risk, in the event that cash receipts are not accurately estimated and the project does not complete its economic life ahead of schedule.

Table - Net present value at a discount rate of E \u003d 8%, rub.

Example. We will calculate the net present value with an increase in the discount rate equal to 12%.

The net present value remains positive, but its value has decreased to 2,800 rubles. As the discount rate increases, ceteris paribus, the net present value decreases. With a discount rate of E = 14%, the net present value will decrease even more and become a negative value (-2,775 rubles).

Looking ahead a little, we note that the discounted payback period of investments (i.e., the period of time required for the cumulative net present value to become positive value) increases.

With a discount rate of 8%, the payback period will be about 5 years, while at E \u003d 12% - almost 6 years.

Table - Net present value at a discount rate of E \u003d 12%, rub.

The most effective is the use of the net present value indicator as a criterion mechanism showing the minimum standard return (discount rate) of investments over their economic life. If NTS is a positive value, then this means the possibility of obtaining additional income in excess of the standard return, with a negative net present value, the projected cash receipts do not provide a minimum standard return and return on investment. With a net present value close to 0, the standard return is barely secured (but only if estimates of cash flows and projected economic term life of the investment will prove to be accurate).

Despite all these advantages of investment valuation, the net present value method does not answer all questions related to economic efficiency investment. This method only answers the question of whether the analyzed investment option contributes to the growth of the firm's value or the investor's wealth in general, but does not say anything about the relative extent of such growth.

And this measure is always of great importance for any investor. To fill this gap, another indicator is used - the method of calculating the return on investment.

Net present value method ( English Net Present Value, NPV) has been widely used in budgeting capital investments and making investment decisions. Also, NPV is considered the best selection criterion for making or rejecting a decision on the implementation of an investment project, since it is based on the concept of the time value of money. In other words, the net present value reflects the expected change in the investor's wealth as a result of the project.

NPV formula

The net present value of a project is the sum of the present value of all cash flows (both incoming and outgoing). The calculation formula is as follows:

Where CF t is the expected net cash flow (the difference between the incoming and outgoing cash flow) for the period t, r is the discount rate, N is the project implementation period.

Discount rate

It is important to understand that when choosing a discount rate, not only the concept of the time value of money must be taken into account, but also the risk of uncertainty in the expected cash flows! For this reason, it is recommended to use the weighted average cost of capital as the discount rate ( English Weighted Average Cost of Capital, WACC) involved in the implementation of the project. In other words, WACC is the required rate of return on capital invested in a project. Therefore, the higher the risk of cash flow uncertainty, the higher the discount rate, and vice versa.

Project Selection Criteria

The decision rule for selecting projects using the NPV method is quite straightforward. A threshold value of zero indicates that the project's cash flows can cover the cost of capital raised. Thus, the selection criteria can be formulated as follows:

1. A single independent project must be accepted if the net present value is positive or rejected if it is negative. Zero value is the point of indifference for the investor.
2. If an investor is considering several independent projects, those with a positive NPV should be accepted.
3. If a number of mutually exclusive projects are being considered, the one with the highest net present value should be selected.

Calculation example

The company is considering two projects requiring the same initial investment of $5 million. At the same time, both have the same risk of cash flow uncertainty, and the cost of capital in the amount of 11.5%. The difference is that Project A expects major cash flows earlier than Project B. Details of expected cash flows are provided in the table.

We substitute the available data in the above formula to calculate the value of the net present value.

The discounted cash flows for the two projects are presented in the figure below.

If the projects are independent, the company must accept each of them. If the implementation of one project excludes the possibility of implementing another, Project A should be accepted, since it has a higher NPV.

Calculating NPV in Excel

1. Select output cell H6.
2. Click the button fx, Select a category " Financial", and then the function " NPV" from the list.
3. In field " Bid» select cell C1.
4. In field " Value1”, select the data range C6:G6, leave the " Value2» and press the button OK.

Since we have not accounted for the initial investment, select output cell H6 and add cell B6 in the formula bar.

Advantages and Disadvantages of the Net Present Value Method

The advantage of the NPV method for evaluating projects is the use of the discounted cash flow methodology, which makes it possible to estimate the amount of additionally created value. However, this method has a number of disadvantages and limitations that must be taken into account when making decisions.

1. Discount rate sensitivity. One of the main assumptions is that all project cash flows are reinvested at a discount rate. In fact, the level of interest rates is constantly changing due to changes in economic conditions and inflation expectations. However, these changes can be significant, especially in the long term. Therefore, the actual net present value may differ materially from its initial estimate.
2. Cash flows after the planned implementation period. Some projects may generate beyond the project's scheduled timeframe. These cash flows may provide additional value to the original estimate, but they are ignored by this method.
3. Management options. During the life cycle of the project, the company's management can take any actions that affect the timing of its implementation and scope in response to changes. market conditions. These actions may change both the timing and magnitude of expected cash flows, resulting in a change in the net present value estimate. Traditional discounted cash flow analysis does not take into account such changes.