The concept of the present present value of the project, the procedure for calculating. Net Present Value NPV (NPV) and Internal Rate of Return (IRR) in MS EXCEL. How to analyze the results

Net present value method ( English Net Present Value, NPV) has been widely used in capital budgeting and investment decision making. NPV is also 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 value of money in time. In other words, the NPV reflects the expected change in the investor's wealth as a result of the project.

NPV formula

The net present value of the 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 flows) 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 value of money in time should be considered, 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 ( 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. Consequently, the higher the risk of cash flow uncertainty, the higher the discount rate, and vice versa.

Project selection criterion

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

1. A separate independent project must be accepted if the net present value is positive or rejected if it is negative. Zero is the point of indifference for the investor.
2. If the investor is considering several independent projects, those that have a positive NPV should be accepted.
3. If you are considering a number of mutually exclusive projects, you should choose the one that will have the maximum net present value.

Calculation example

The company is considering the possibility of implementing two projects requiring the same initial investment of $ 5 million. At the same time, both have the same risk of uncertainty in cash flows, and the cost of raising capital in the amount of 11.5%. The difference is that for Project A the main cash flows are expected earlier than for Project B. Detailed information on the expected cash flows is presented in the table.

Substituting the available data into the above formula and calculating the net present value.

Discounted cash flows for the two projects are shown in the figure below.

If the projects are independent, the company must accept each one. If the implementation of one project excludes the possibility of the implementation of another, Project A should be accepted, since it is characterized by 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 a cell C1.
4. In field " Value1", Select the data range C6: G6, leave blank the field “ Value2»And press the button OK.

Since we did not factor in the initial investment, select output cell H6 and add cell B6 in the formula bar.

Advantages and Disadvantages of the NPV Method

The advantage of the NPV method for project appraisal is the use of the discounted cash flow methodology, which makes it possible to estimate the amount of additional value created. 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 the discount rate. In fact, the level of interest rates is constantly changing due to changes in economic conditions and expectations about the level of inflation. However, these changes can be significant, especially in the long term. Therefore, the actual value of the net present value may differ materially from its original estimate.
2. Cash flows after the planned implementation period... Some projects may generate after the planned project life. 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 a project, the company's management can take any actions that affect the timing of its implementation and scale in response to changes in market conditions. These actions can change both the time of occurrence and the amount of expected cash flows, which will lead to a change in the estimate of the net present value. Traditional discounted cash flow analysis does not take such changes into account.

Publications

Textbook "Evaluation of the effectiveness of investment projects"
Calculation and analysis of investment projects, preparation of business plans

Excel Financial Computing Technique Tutorial
Basic concepts of financial mathematics and recommendations for performing calculations

Discussions

Note! Discussions use the reverse sequence of messages (i.e. the last post from the top), and the beginning of a discussion is often located in the archives, links to which are located at the beginning of the page

Forum section: Investments, business plan, business valuation
In this section you can ask your questions or express your opinion on this term.

Determining the lifetime of the project
Determining the forecasting horizon used in calculating project performance

Finance for Dummies. NPV, IRR, Break-even-point, taxes etc.
A variety of issues related to the assessment of investment performance are discussed, many links

Assessment of investment projects in Russia: NPV vs. ROV
Alternative to using NPV when evaluating investment projects

Related Sections and Other Sites

Analysis of investment projects ""
Efficiency, risk, discounting, selection of projects for investment

See also:

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The discounted present value of the future cash flows of the investment project, less investments.

The net present value is calculated using the projected cash flows associated with the proposed investment using the following formula:

where NCFi is the net cash flow for the i-th period,
Inv - initial investment
r - discount rate (cost of capital raised for an investment project).

With a positive value of NPV, it is considered that this capital investment is effective.

The concept of net present value (NPV) is widely used in investment analysis to assess various types of investments. The above formula is only valid for the simple case of a cash flow structure where all investments are made at the beginning of the project. In more complex cases, the analysis may need to complicate the formula to account for the distribution of investment over time. More often than not, for this investment leads to the start of a project similar to income.

In MS Excel, the function = refinery () is used to calculate NPV.

Terms used in the calculator

Investments- placement of capital for the purpose of making a profit. Investment is an integral part of the modern economy. Investments differ from loans in the degree of risk for the investor (lender) - the loan and interest must be repaid within the agreed time frame, regardless of the profitability of the project, investments (invested capital) are returned and generate income only in profitable projects. If the project is unprofitable, investments may be lost in whole or in part.

Cash flow free- the cash flow that the company has after financing all investments that it finds appropriate to make; is defined as profit from operating activities after taxes plus depreciation minus investments.

Discount rate- This parameter reflects the rate of change in the value of money in the current economy. It is taken to be equal to either the refinancing rate, or the interest on long-term government bonds considered to be risk-free, or the interest on bank deposits.

To calculate investment projects, this parameter can be taken equal to the planned profitability of the investment project.

Net Present Value (NPV) Is the balance of all operating and investment cash flows, additionally taking into account the cost of capital used. The NPV of the project will be positive, and the project itself will be effective if the calculations show that the project covers its internal costs, and also brings the owners of capital income not lower than they demanded (not lower than the discount rate).

Investment profitability index (PI)- The indicator illustrates the ratio of return on capital to the amount of invested capital, the indicator of return on investment shows the relative profitability of the project or the discounted value of cash receipts from the project per unit of investment. The profitability index is calculated using the formula: PI = NPV / I, where I is investments.

Internal Rate of Return (IRR)- the interest rate at which the project is neither profitable nor unprofitable. For projects longer than two years, there is no formula for calculating this indicator; it can only be determined by iteration (or using a computer program that uses this method, for example, Excel). Determination in a graphical way is possible.

IMPORTANT: None of the listed investment efficiency indicators is sufficient for the acceptance of the project for implementation. At the same time, the ratio and distribution of own and borrowed funds, as well as other factors (the presence of preliminary agreements for the sale of project products; cash flow and the possibility of repayment of obligations according to your business plan; payback period and loan repayment period; debt coverage ratio, etc.) .).

Net Present Value (NPV).

Advantages and disadvantages of using

Net present value (NPV,Net present value) is one of the most important criteria for investment evaluation of projects.

The formula for calculating the net present value


where: CF t - cash flows; r is the discount rate; CF 0 - initial investment (negative).
Cash flows, which in the formula, as a rule, are formed for the periods under consideration: year, quarter, month. As a result, the cash flow, for example, monthly, will be equal to all cash receipts for the month.
CF = CF 1 + CF 2 +… + CF n

Net Present Value (NPV) allows you to compare different investment projects with each other. A positive NPV indicates that this investment is effective and attractive. If NPV<0, то доходы от инвестиций не могут покрыть риск по данному проекту. Чем выше значения чистой текущей стоимости, тем инвестиционно привлекательнее проект.

For calculating the discount rate, as a rule, they take a risk-free investment rate, for example, in government securities (GKO, OFZ), supplement it with compensation for risk (the risk of not implementing the project). Also, the discount rate can be determined by the market by the rate of return on the stock market for a project with the same level of risk.

Advantages and disadvantages of the net present value (NPV)
The advantages of net present value include:

• clarity of the indicator for management decisions when choosing an investment object;
• the use of the discount rate reflects the depreciation property of the value of money;
• the discount rate may include additional project risks.

The disadvantages of net present value include:

• the complexity of calculating the discount rate can distort the results of the NPV estimate.

  This is typical for complex projects that involve many risks;

• the complexity of forecasting cash flows. Although the cash flows of the enterprise are determined, these are only forecast values ​​that can change in the process;
• not taking into account the intangible benefits and values ​​of the enterprise.

Since cash flows can change over time and are of a probabilistic nature, they use simulation modeling with setting the possible probabilities of obtaining a particular cash flow. The probabilities for each cash flow are determined by experts. To solve the disadvantages of the net present value (NPV), a mixed approach is used, where intangible capital and future cash flows are estimated by experts or an expert group.

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Future and present value

Future value is a development of the concept of compound interest - this is the amount to which the current deposit will increase over the period from the moment it is placed on the account, subject to the accrual of compound interest.

The future value is the amount to which the current deposit will increase over the period from the moment it is placed on an account on which compound interest is accrued (the future value is sometimes called accrued value). For example, a deposit of 10,000 rubles, yielding 6% annually, calculated using the compound interest method, at the end of the first year will increase to 10,600 rubles (10,000 * 1.06 = 10,600). If the money had been left for another year, 6% would have been credited to the account balance of 10,600 rubles. Thus, by the end of the second year, the account would have had 11,236 rubles (10,600 * 1.06 = 11,236). To determine the future value by the end of year n, the above procedure must be repeated n times or 10,000 * (1+ 0.06) n. To simplify the calculation of the future values ​​of any initial investment, there are build-up factor tables. A set of such tables is presented in Appendix B.

The future value of the annuity.

Annuity is a flow of equal amounts of cash that occurs at regular intervals.

The amount of 10,000 rubles received at the end of each year annually for 10 years is an example of an annuity. Cash flows can be income inflows from investments or outflows of funds invested with the aim of generating future income. Investors are sometimes interested in determining the future value of an annuity. As a rule, this applies to the so-called regular annuity - one in which a regular flow of funds occurs at the end of each year. Future value can be determined mathematically using a calculator, computer, or appropriate financial tables. Here we use tables of accretion factors, or future value factors, for the annuity. The full set of accrual factor tables for an annuity is included in Appendix D. Accumulation factors represent the amount to which regular contributions of 1 currency made at the end of the year would increase under various combinations of periods and interest rates.

For example, a ruble deposited in a bank deposit, which accrues 8% at the end of each year, for a period of 6 years, would rise to 7.3359 rubles. In case of investing 10,000 rubles at the end of each year for 6 years at 8%, the total future cost will be 73,359 rubles (7.3359 * 10,000).

Present value- the flip side of future value. Present value, instead of measuring the value of the present amount at some point in the future, allows us to determine how much the future amount of money is worth today. Using the present value technique, you can calculate the present value of the amount that will be received in the future.

In determining the present value of the future amount of money, the main question is: how much money should be deposited today in an account that pays n percent in order to equate it with a certain amount that will be received in the future? The interest rate applied to find the present value is usually called the discount rate (or opportunity cost). It represents the annual rate of return that could now be obtained from a similar investment. The basic present value calculations are best illustrated with a simple example. Imagine that you have the opportunity to receive 10,000 rubles in exactly one year, starting today. If you could get 7% on similar types of investments, what is the largest possible amount of money you would pay for this opportunity? In other words, what is the present value of 10,000 rubles to be received in a year, discounted at a rate of 7%? Let X be the present value. To describe this case, the following equality is used:

X * (1 + 0.07) = 10,000 rubles. Solving the equation for X, we get:

X = 10,000 / (1 + 0.07) = 9345.79 rubles.

It should be clear from these calculations that the present value of 10,000 rubles, which will be received in a year and discounted at a rate of 7%, is 9345.79 rubles. In other words, 9,345.79 rubles placed on an account that pays 7% will increase to 10,000 rubles within a year. To check this conclusion, we multiply the factor of the future value increase for 7% and one year, or 1.07 by 9345.79 rubles. This amount will bring the future value of 10,000 rubles (1.07 * 9345.79).

Since the calculations of the present value of the amounts that will be received in the distant future are more complex than for investments for a year, in this case it is recommended to use the tables of the present value. A set of these tables is included in Appendix A. The discount factors in such tables represent the present value of 1 currency, calculated for various combinations of periods and discount rates. For example, the present value of 1 ruble, which is expected to be received in a year and discounted at a rate of 7%, is 0.9346 rubles. Based on this factor (0.9346), the present value of 10,000 rubles, which is expected to be received in a year at a rate of 7% discount, can be found by multiplying this factor by 10,000 rubles. The resulting present value of 9346 rubles (0.9346 * 10000) corresponds (with the exception of a small difference as a result of rounding) the value calculated earlier.

Another example will help you understand how present value tables are used.

The present value of 500 rubles, which is expected to be received in 12 years, discounted at a rate of 5%, can be calculated as follows:

Present value = 0.5568 * 500 = 278.4 rubles.

The number 0.5568 is the discount or value conversion factor for 12 periods and a discount rate of 5%.

Present value of annuity can be found in the same way using financial tables. A full set of such present value discounting factors for annuities is included in Appendix B. Factors in such tables represent the present value of a 1 currency annuity associated with various combinations of years and discount rates. For example, the present value of 1 ruble that will flow in every year over the next five years, discounted at a rate of 9%, will be 3.8897 rubles. If we use this discount factor, then the present value of a 500-ruble annuity for 5 years at a discount rate of 9% can be found by multiplying the annual income by this factor. In this case, the total present value will be 1,944.85 rubles (3.8897 * 500).

The present value concept can be used to select an appropriate investment instrument. Ignoring the risk at the moment, it is possible to determine that the investor would be satisfied with an investment instrument in which the present value of all future income (discounted at the appropriate rate) would be equal to or greater than the present value of the cost of acquiring it. Since the investment costs (or the purchase price) arise at the initial stage (at the zero point in time), then the costs and their present value are considered one and the same. If the present value of income was equal to the cost, the investor would receive a rate of return equal to the discount rate. If the present value of the earnings exceeded the costs incurred, the investor would receive a rate of return on the investment greater than the discount rate. Finally, if the present value of income were less than the cost, the investor would have received a return on investment that is less than the discount rate. Therefore, the investor would prefer only those investments for which the present value of income equals or exceeds costs; in these cases, the yield would be the same or higher than the discount rate.

Measuring income

In the process of investing, the problem arises of comparing income from various instruments, for which it is necessary to apply appropriate measures. One such meter is holding income. Period of ownership of the asset- this is the period during which a person wants to measure income from any investment instrument. When comparing income from different instruments, the use of holding periods of the same length lends greater objectivity to the analysis.

Income in the form of capital gains may not be realized, become “ paper "income. Capital gains are realized only when the investment instrument is actually sold at the end of the holding's period. Realized income - it is the income received by the investor during a certain period of ownership of the asset. Although capital gains may not be realized during the period over which total income is measured, they should be factored in when calculating the return.

When calculating, it should also be borne in mind that both current income and capital gains can be negative numbers. In addition, you need to keep in mind that capital losses can be caused by any investment instrument.

Net present value (NPV) method- one of the most commonly used methods for assessing cash flows.

Among the others - cash flow methods for equity and cash flow for all invested capital.

When calculating the weighted average cost of capital, each type of capital, be it ordinary or preferred shares, bonds or long-term debt, is accounted for with the appropriate weights. An increase in the weighted average cost of capital usually reflects an increase in risk.

To avoid double counting these tax shields, interest payments should not be deducted from cash flows. Equation 4.1 shows how to calculate cash flows (subscripts represent time periods):

CF t = EBIT t * (1 - τ) + DEPR t - CAPEX t - ΔNWC t + others t, (4.1)

• CF- cash flows;
• EBIT- profit before interest and taxes;
• τ - income tax rate;
• DEPR- depreciation;
• CAPEX- capital expenditures;
• ΔNWC- increase in net working capital;
• others- an increase in tax arrears, wage arrears, etc.

Then you need to calculate the terminal cost. This estimate is very important because most of the value of a company, especially a start-up, can be contained in terminal value. The generally accepted method for calculating a company's terminal value is the perpetual growth method.

Equation 4.2 presents the formula for terminal value calculation (TV) at the moment τ using the method of indefinite growth at indefinite growth rates g and a discount rate r.

Cash flows and discount rates used in the NPV method are usually represented by nominal values ​​( that is, they are not adjusted for inflation).

If cash flow is projected to be constant in inflation-adjusted dollar terms, a terminal growth rate should be used equal to the inflation rate:

TV T = / (r - g). (4.2)

Other commonly used terminal value calculation methods use price-earnings ratios and market to book value ratios, but such simplifications are discouraged. The company's net present value is then calculated using the formula in Equation 4.3:

NPV = + + +
+ ... + [(CF T + TV T) / (l + r) T]. (4.3)

The discount rate is calculated using Equation 4.4:

r = (D / V) * r d * (1 - τ) + (E / V) * r e, (4.4)

• r d- the discount rate for debt;
• r e
• τ - income tax rate;
• D- the market value of the debt;
• E
• V- D + E.

Even if the company's capital structure does not match the target's capital structure, the target values ​​for D / V and E / V should be used.

The cost of equity (g) is calculated using the Financial Assets Pricing Model (CAPM), see Equation 4.5:

r e = r f + β * (r m - r f), (4.5)

• r e- the discount rate for the share capital;
• r f- risk-free rate;
• β - beta or the degree of correlation with the market;
• r m- the market rate of return on ordinary shares;
• (r m - r f)- risk premium.

When determining a reasonable risk-free rate (r f), it is necessary to try to correlate the maturity of the investment project with the risk-free rate. The ten year rate is usually used. Estimates of the risk premium can vary greatly: for simplicity, you can take the value of 7.5%.

For non-public companies or companies spun off from public companies, the beta can be roughly calculated using publicly traded companies as an example. The beta for public companies can be found in the Beta Book or Bloomberg.

If the company has not reached its target capital structure, it is necessary to release the beta coefficient from financial leverage, and then calculate the beta coefficient, taking into account the target debt to equity ratio of the company. How to do this is shown in Equation 4.6:

β u = β l * (E / V) = β l *, (4.6)

• β u- beta coefficient without financial leverage;
• β l- beta coefficient taking into account financial leverage;
• E- the market value of the share capital;
• D- the market value of the debt.

The problem arises if there are no analogous companies, which often happens in situations with non-public companies. In this case, it is best to rely on common sense. Think about the cyclical nature of a particular company and whether the risk is systematic or diversified.

If financial statements are available, a “beta for earnings” can be calculated, which has some correlation with the beta of equity. The beta for earnings is calculated by comparing the net profit of a non-public company with a stock index such as the S&P 500.

Using a least squares regression technique, the slope of the best fit (beta) line can be calculated.

A sample calculation of NPV is shown below.

Example of valuation using the NPV method

Lo-Tech shareholders voted to stop diversification and decided to re-focus on core business areas. As part of this process, the company would like to sell Hi-Tech, its startup, a high-tech subsidiary.

Hi-Tech executives, looking to acquire the company, turned to George, a venture capitalist, for advice. He decided to evaluate Hi-Tech using the NPV method. George and Hi-Tech executives agreed on the predictions in the table (all in millions of dollars).

Initial data for analysis by the method of net present value (mln / USD)

The company has a net operating loss of $ 100 million that can be carried forward and offset by future earnings. In addition, Hi-Tech is forecast to generate further losses in its early years.

She can also carry forward these losses to future periods. The tax rate is 40%.

The average beta without leverage for the five high-tech peers is 1.2. Hi-Tech has no long-term debt. The yield on 10-year US Treasuries is 6%.

It is assumed that the required capital costs will be equal to the depreciation amount. The risk premium assumption is 7.5%. Net working capital is projected to be 10% of sales. EBIT is projected to grow by 3% per annum, indefinitely beyond 9 year.

As shown in the table below, George first calculated the weighted average cost of capital:

WACC = (D / V) * r d * (1 - t) + (E / V) * r e =
= 0 + 100% * = 15%.

Net Present Value Analysis
(USD million)
Calculation of the weighted average cost of capital

Net present value and sensitivity analysis.
Weighted average cost of capital (WACC)

He then estimated the cash flows and found the company to have a net present value of $ 525 million. As expected, the entire value of the company was contained in the terminal value ( the present value of cash flows was -44 million dollars, and with the net present value of the terminal value of 569 million dollars, the net present value was 525 million dollars).

Terminal cost was calculated as follows:

TV T = / (r - g) =
= / (15% - 3%) - $2,000.

George also performed scenario analysis to determine the sensitivity of the Hi-Tech valuation to changes in the discount rate and post-forecast growth rates. He compiled a table of scenarios, which is also presented in the table.

George's scenario analysis yielded a series of values ​​ranging from $ 323 to $ 876 million. Of course, such a wide range could not be an accurate guide to the real cost of Hi-Tech.

He noted that negative values ​​of cash flow at the initial stage and positive values ​​of cash flow in the future made the assessment very sensitive both to changes in the discount rate and to changes in growth rates in the post-forecast period.

George saw NPV as the first step in the valuation process and planned to use other methods to narrow the range of possible Hi-Tech values.

Advantages and Disadvantages of the NPV Method

Estimating the value of the company by discounting the related cash flows is considered a technically sound method. Compared to the method of using peers, the estimates obtained should be less susceptible to distortions that occur in the market of public and, even more often, non-public companies.

Given the many assumptions and calculations that are made during the assessment process, it is nevertheless unrealistic to arrive at a single or “point” value. Various cash flows should be valued according to the optimistic, most probable and pessimistic scenarios.

They must then be discounted using a range of values ​​for weighted average cost of capital and terminal growth rates (g) to obtain a likely range of estimates.

If you can set the likelihood of realization for each scenario, the weighted average will correspond to the expected value of the company.

Even with these adjustments, the NPV method has some drawbacks. First of all, we need beta ratios to calculate the discount rate.

A suitable equivalent company must demonstrate similar financial performance, growth prospects, and operating characteristics as the company we are evaluating. A public company with such characteristics may not exist.

Target capital composition is often also estimated using peers, and using peer companies to estimate target capital composition has many of the same disadvantages as looking for similar beta. In addition, the typical startup cash flow profile - high start-up costs and long-term revenues - means that most of the cost (if not all of the cost) is in terminal value.

Terminal values ​​are very sensitive to discount rate assumptions and terminal growth rates. Finally, recent financial research has raised questions about the acceptability of beta as the correct measure of a company's risk.

Numerous studies suggest that company size or the ratio of market value to book value might be more appropriate values, but in practice, few have tried to apply this approach to company valuation.

Another disadvantage of the NPV approach becomes apparent when valuing companies with changing capital structures or effective tax rates.

Changing capital structures are often associated with highly leveraged transactions such as buyouts.

The effective tax rates may change due to the use of tax deductions, for example, on net operating losses, or the discontinuation of tax subsidies that are sometimes received by young and high-growth companies.

When using the net present value method, the capital structure and the effective tax rate are taken into account in the discount rate (WACC), on the assumption that they are constant values. For the reasons listed above, in these cases it is recommended to use the adjusted present value method.

The indicator Net present value, or NPV of an investment project, allows you to determine what income the investor will receive in monetary terms as a result of his investments. In other words, the NPV of the project shows the size of financial receipts as a result of investments in an investment project, taking into account the associated costs, that is, the net present value. What is NPV in practice and how to calculate net present value will become clear from the below NPV-formula and explanations to it.

Concept and content of NPV value

Before moving on to the topic of NPV to say what it is and how to calculate it, you need to understand the meaning of the phrase from which the abbreviation is formed. For the phrase "Net present value" in the domestic economic and mathematical literature, you can find several traditional translation options:

1. In the first variant, typical for mathematical textbooks, NPV is defined as net present value (NPV).
2. The second option - net present value (NPV) - along with the first is considered the most used.
3. The third option - net present value - combines elements of the first and second transfers.
4. The fourth version of the translation of the term NPV, where PV is "present value", is the least widespread and is not widely used.

Regardless of the translation, the NPV value remains unchanged, and this term means that

NPV is such a net present value of value. That is, discounting a cash flow is just considered as the process of establishing its (flow) value by bringing the value of total payments to a certain (current) moment in time. Therefore, determining the value of net present value (NPV) becomes, along with IRR, another way to assess the effectiveness of investment projects in advance.

At the level of the general algorithm, in order to determine the prospects of a business project for this indicator, you need to take the following steps:

• estimate cash flow - initial investments and expected receipts,
• set the cost of capital - calculate the rate,
• discount incoming and outgoing cash flows at a specified rate indicator,
• sum up all discounted flows, which will give the value of NPV.

If the NPV calculation shows values ​​greater than zero, then the investment is profitable.... Moreover, the greater the number of NPV, the greater, other things being equal, the expected value of profit. Given that creditors' income is usually fixed, everything that the project will bring in excess of it belongs to the shareholders - with a positive NPV, the shareholders will earn. The reverse situation with NPV less than zero promises losses for investors.

It is possible that the net present value will be zero. This means that there is enough cash flow to replace the invested capital without profit. If the project is approved with NPV equal to zero, the size of the company will increase, but the share price will remain unchanged. But investing in such projects may be related to the social or environmental objectives of the initiators of the process, which makes it possible to invest in such projects.

NPV formula

The net present value is calculated using the calculation formula, which in a simplified form looks like PV - ICo, where PV is the current indicators of cash flow, and ICo is the size of the initial investment. In a more complex form, which shows the discounting mechanism, the formula looks like this:

NPV = - ICo + ∑ n t = 1 CF t / (1 + R) t

Here:

• NPV- net present value.
• CF – Cash Flow- cash flow (investment payments), and t next to the indicator is the time during which the cash flow is carried out (for example, a one-year interval).
• R – Rate- discount (rate: coefficient that discounts flows).
• n- the number of stages of the project, which determines the duration of its life cycle (for example, the number of years).
• ICo – Invested Capital- the initial invested capital.

Thus, NPV is calculated as the difference between the total cash flows updated at a certain point in time by risk factors and the initial investment, that is, the investor profit is considered as the added value of the project.

Since it is important for the investor not only a profitable investment, but also competent capital management over a long period of time, this formula can be further expanded so as to provide not one-time, but additional periodic investments and the inflation rate (i)

NPV = ∑ n t = 1 CF t / (1 + R) t - ∑ m j = 1 IC j / (1 + i) j

NPV calculation example

An example of a calculation for three conditional projects allows you to both calculate NPV and determine which of the projects will be more attractive for investment.

According to the conditions of the example:

• initial investment - ICo - in each of the three projects is equal to $ 400,
• rate of return - discount rate - is 13%,
• the profit that projects can bring (by years) is listed in the table for a 5-year period.

We will calculate the net present value in order to choose the most profitable project for investment. The discount factor 1 / (1 + R) t for an interval of one year will be t = 1: 1 / (1 + 0.13) 1 = 0.885. If we recalculate the NPV of each scenario by years with the substitution of defining values ​​in the formula, it turns out that for the first project NPV = 0.39, for the second - 10.41, for the third - 7.18.

According to this formula, the net present value is the highest for the second project, therefore, if we rely only on the NPV parameter, then it will be the most attractive for investment in terms of profit.

However, compared projects may have different durations (life cycle). Therefore, it is not uncommon for situations when, for example, when comparing three-year and five-year projects, the NPV will be higher for the five-year one, and the average value over the years for the three-year one. To avoid contradictions, the average annual rate of return (IRR) should also be calculated in such situations.

In addition, the volume of the initial investment and the expected profit are not always known, which creates difficulties in the application of calculations.

Difficulties in using calculations

As a rule, in reality, read (substituted in the formula) variables are rarely accurate. The main difficulty is the definition of two parameters: the assessment of all associated cash flows and the discount rate.

Cash flows are:

• initial investment - initial outflow of funds,
• annual inflows and outflows of funds expected in subsequent periods.

Taken together, the value of the flow indicates the amount of cash that is at the disposal of the enterprise or company at the current time. It is also an indicator of the financial stability of the company. To calculate its values, it is necessary to subtract Cash Outflows (CO) from the value of Cash Inflows (CI) - cash inflow, outflow:

When predicting potential receipts, it is necessary to determine the nature and degree of dependence between the influence of factors that form cash receipts and the very filling of the cash flow. The procedural complexity of a large complex project is also in the amount of information that must be taken into account. So in a project related to the release of a new product, it will be necessary to predict the volume of expected sales in pieces, while determining the price of each unit sold. And in the long term, in order to take this into account, it may be necessary to base forecasts on the general state of the economy, the mobility of demand depending on the development potential of competitors, on the effectiveness of advertising campaigns and a host of other factors.

In terms of operational processes, it is necessary to predict costs (payments), which, in turn, will require an estimate of prices for raw materials, rental rates, utilities, wages, exchange rate changes in the foreign exchange market and other factors. Moreover, if a multi-year project is planned, then estimates should be made for the corresponding number of years in advance.

If we are talking about a venture project that does not yet have statistical data on indicators of production, sales and costs, then the forecasting of monetary income is carried out on the basis of an expert approach. It is assumed that experts should correlate the growing project with its industry counterparts and, together with the development potential, assess the possibilities of cash receipts.

R - discount rate

The discount rate is a kind of alternative return that an investor could potentially receive. Due to the determination of the discount rate, the value of the company is estimated, which is one of the most frequent purposes of establishing this parameter.

The assessment is carried out on the basis of a number of methods, each of which has its own advantages and the initial data used in the calculation:

• CAPM model... The methodology allows to take into account the influence of market risks on the value of the discount rate. The appraisal is made on the basis of trading on the MICEX stock exchange, which determines the quotations of ordinary shares. In its advantages and choice of input data, the method is similar to the Fama and French model.
• WACC model... The advantage of the model is the ability to take into account the degree of efficiency of both equity and borrowed capital. In addition to the quotes of ordinary shares, the interest rates on the borrowed capital are taken into account.
• Ross model... It makes it possible to take into account macro- and micro-factors of the market, industry-specific features that determine the discount rate. Rosstat statistics on macroindicators is used as the initial data.
• Methods based on the return on equity, which are based on data from the balance sheet.
• Gordon's model... According to it, the investor can calculate the dividend yield, also relying on the quotes of ordinary shares, and also other models.

Changes in the discount rate and the value of net present value are interconnected by a non-linear relationship, which can simply be reflected in the graph. Hence follows the rule for the investor: when choosing a project - an investment object - it is necessary to compare not only the NPV values, but also the nature of their change depending on the rate values. The variability of the scenarios allows the investor to choose a less risky project for investments.

Since 2012, with the filing of UNIDO, the NPV calculation has been included as an element in the calculation of the rate of specific growth rate index, which is considered the optimal approach when choosing the best investment solution. The assessment method was proposed by a group of economists led by A.B. Kogan, in 2009. It allows you to effectively compare alternatives in situations where it is not possible to compare according to a single criterion, and therefore different parameters are used as the basis for comparison. Such situations arise when the analysis of investment attractiveness using traditional NPV and IRR methods does not lead to unambiguous results or when the results of the methods contradict each other.

Evaluation and analysis of investments use a number of special indicators, among which the net present value of an investment project occupies the most important position.

This indicator shows the economic efficiency of investments by comparing the discounted cash flows of capital costs and discounted cash flows of results in the form of net profit from the project. In other words, this indicator reflects the classic principle of evaluating efficiency: determining the ratio of "costs - benefits".

This indicator is called the NPV of an investment project (Net present value) and shows the investor what income in monetary terms he will receive as a result of investments in a particular project.

The formula for calculating this indicator is as follows:

• NPV is the net present value of the investment;
• ICo - initial invested capital (Invested Capital);
• CFt - (Cash Flow) from investments in the t-th year;
• r is the discount rate;
• n is the duration of the project life cycle.

Discounting cash flows is necessary so that the investor can estimate cash flows for the entire life cycle of the project at a particular moment of their investment. And of course, if NPV< 0, то, ни о каких вложениях речи быть не может. Проект рассматривается инвестором только при NPV ≥ 0. При равенстве NPV нулю, проект может быть интересен инвестору, если он имеет цель иную, нежели получение максимального дохода от инвестиций, например повышение социального статуса инвестора в обществе или экологический эффект.

NPV calculation example

The size of the net present depends on the size of the discount rate the higher the discount rate, the lower the NPV. The choice of the discount rate is based on comparing the hypothetical return on investment in other projects or comparing it with the cost of working capital. Such a comparison gives an idea to the investor about the barrier to the minimum return on investment in this particular investment option.

For example:

• the cost of the operating capital in the invested object provides a yield of 16%;
• banks' lending rates are 12-14%;
• bank deposits provide a yield of 11 -13%;
• the level of profitability of the financial market with the minimum degree of risk is at the level of 15%.

Obviously, the discount rate should be slightly higher than the maximum profitability of all possible investment options, that is, higher or at least equal to 16%. With an equal base rate of effective capital and the discount rate, we can talk about investing in the expansion of production on the existing technological and technical base of production.

The above formula for calculating NPV was based on the assumption that investments are made at the same time, at the beginning of the project. In life, such investments are often made over several years. In this case, the calculation formula takes the following form:

• ICt - investment in year t;
• T is the investment period.

In this formula, investment flows are also reported at the accepted discount rate.

In investment practice, there are quite often cases when the received profit is reinvested for a certain period. Most often, this situation occurs when there is a lack of funding for the project.

Then the calculation formula changes as follows:

d - interest rate of capital reinvestment.

For a comparative analysis of investment projects, their NPV indicators are measured. Investments with a large NPV are considered preferable.

The advantage of this indicator is the ability to determine the net accumulated value for the entire life cycle, which allows you to compare investment options for different life cycles. However, on the basis of this indicator, it is not always possible to answer the question of which of the options is more efficient in terms of profitability.

For example:

• 1 project in 3 years (life cycle) will receive NPV in the amount of 200 million rubles.
• 2 project within 5 years (life cycle) - 300 million rubles.

In this case, they can be compared by the average annual NPV:

• Option 1 - 66.67 million rubles;
• Option 2 - 60 million rubles.

Option 1 is preferable, despite the larger NPV in option 2. Therefore, for a more accurate assessment, they resort to using the average annual rate of return on investments IRR, or the compared options must have the same life cycle, then the option with a large NPV will be preferable.

Calculations of this indicator, especially for large investments, are complex not only technically, but also methodically. The first drawback is easily overcome by modern computing devices, and the second can affect the accuracy of the calculations and lead to incorrect project estimates. Therefore, with the calculation of this indicator, indicators of the discounted payback period DPP and the internal rate of return IRR are always calculated. Together, they provide high accuracy in calculating the economic efficiency of any investment project.