Question 57 Assessing the effectiveness of investments The effectiveness of investments is assessed using statistical and dynamic methods. Statistical methods for assessing the effectiveness of investments include calculating the payback period of investments SOI (PP), the rate of return and the coefficient

Investment projects can be assessed according to many criteria - in terms of their social significance, the scale of their impact on the environment, the degree of involvement of labor resources, etc. However, efficiency is central to these assessments.

In general, efficiency is understood as the correspondence of the results obtained from a project - both economic (in particular profit) and non-economic (relief of social tension in the region) - and the costs of the project.

The effectiveness of an investment project is a category that reflects the compliance of the project that generates this IP with the goals and interests of the project participants, which are understood as subjects of investment activity (discussed above) and society as a whole. Therefore, the term “effectiveness of an investment project” is understood as the effectiveness of the project. The same applies to performance indicators.

Among the basic principles and approaches that have developed in world practice to assessing the effectiveness of investment projects, adapted for the conditions of transition to a market economy, the following can be distinguished:

• modeling of flows of products, resources and funds;
• taking into account the results of market analysis, the financial condition of the enterprise applying for the implementation of the project, the degree of trust in the project managers, the impact of the project on the environment, etc.;
• determining the effect by comparing upcoming results and costs with a focus on achieving the required rate of return on capital and other criteria;
• bringing forthcoming expenses and income at different times to the conditions of their commensurability in terms of economic value in the initial period;
• taking into account the impact of inflation, delays in payments and other factors on the value of the funds used;
• taking into account the uncertainty and risks associated with the implementation of the project.

It is proposed to evaluate the following types of effectiveness:

1) the effectiveness of the project as a whole;

2) effectiveness of participation in the project.

The effectiveness of the project as a whole. It is assessed in order to determine the potential attractiveness of the project and the feasibility of its adoption for possible participants. It shows the objective acceptability of an individual entrepreneur, regardless of the financial capabilities of its participants. This efficiency, in turn, includes:

Public (socio-economic) effectiveness of the project;

Commercial effectiveness of the project.

Social efficiency takes into account the socio-economic consequences of the implementation of an investment project for society as a whole, including both the direct costs of the project and the results of the project, as well as “external effects” - social, environmental and other effects.

The commercial effectiveness of an investment project shows the financial consequences of its implementation for the individual entrepreneur, assuming that he independently makes all the necessary costs for the project and benefits from all its results. In other words, when assessing commercial efficiency, one should abstract from the capabilities of project participants to finance IP costs, conditionally assuming that the necessary funds are available.

Effectiveness of participation in the project. It is determined in order to verify the financial feasibility of the project and the interest of all its participants in it. This efficiency includes:

The effectiveness of enterprises’ participation in the project (its effectiveness for enterprises participating in the investment project);

Efficiency of investing in enterprise shares (efficiency for JSC shareholders - participants in the investment project);

The effectiveness of participation in the project of higher-level structures in relation to enterprises participating in the IP (national economic, regional, sectoral and other efficiency);

Budgetary efficiency of individual entrepreneurs (the effectiveness of state participation in the project in terms of expenses and revenues of budgets of all levels).

General scheme for assessing the effectiveness of an investment project. First of all, the social significance of the project is determined, and then the effectiveness of the IP is assessed in two stages. At the first stage, performance indicators of the project as a whole are calculated. Wherein:

• if the project is not socially significant (local project), then only its commercial effectiveness is assessed;
• for socially significant projects, their social effectiveness is first assessed (methods for such assessment are outlined in general terms in the “Methodological Recommendations”).

If such effectiveness is unsatisfactory, then the project is not recommended for implementation and cannot qualify for government support. If social efficiency is acceptable, then commercial efficiency is assessed. If the commercial efficiency of a socially significant individual entrepreneur is insufficient, it is necessary to consider various options for supporting it, which would increase the commercial efficiency of the individual entrepreneur to an acceptable level. If the conditions and sources of financing for socially significant projects are already known, then their commercial effectiveness need not be assessed.

The second stage of assessment is carried out after the development of a financing scheme. At this stage, the composition of participants is clarified and the financial feasibility and effectiveness of participation in the project of each of them is determined. We can formulate the main tasks that have to be solved when assessing the effectiveness of investment projects:

1. Assessing the feasibility of the project - checking whether it satisfies all actually existing restrictions of a technical, environmental, financial and other nature. Typically, all restrictions, except financial feasibility, are checked in the early stages of project formation. The financial feasibility of an investment project is ensuring such a structure of cash flows in which at each step of the calculation there is a sufficient amount of money to implement the project that generates this IP. Accordingly, the cash flows of an investment project are understood as the cash flows of the project associated with this individual entrepreneur.

2. Assessing the potential feasibility of implementing the project, its absolute effectiveness, that is, checking the condition according to which the total results of the project are no less valuable than the required costs of all types.

3. Assessment of the comparative effectiveness of the project, which is understood as an assessment of the advantages of the project under consideration compared to the alternative.

4. Evaluation of the most effective set of projects from their entire set. Essentially, this is an investment project optimization problem, and it generalizes the previous three problems. As part of solving this problem, it is possible to rank projects, that is, select the optimal project.

Basic methods for assessing the effectiveness of investment projects

There are two groups of methods for evaluating investment projects:

1. simple or static methods;

2. discounting methods.

Simple or static methods are based on the assumption of equal importance of income and expenses in investment activities and do not take into account the time value of money.

Simple ones include: a) calculation of the payback period; b) calculation of the rate of return.

The rate of return shows how much of the investment costs are recovered as profits. It is calculated as the ratio of net profit to investment costs:

Rate of return = Net profit / Investment costs.

Discounted methods for assessing the effectiveness of an investment project are characterized by the fact that they take into account the time value of money.

When economically assessing the effectiveness of an investment project, indicators widely known in world practice are used:

Present value (PV);

Net Present Value (NPV);

Payback period (PBP);

Internal rate of return (IRR);

Profitability Index (PI).

Present value (PV). The task of any investor is to find a real asset that would ultimately bring income that exceeds the cost of its acquisition. In this case, a complex problem arises: money must be spent today (at the moment t = 0) to purchase a real asset, but the investment usually does not give a return immediately, but after a certain period of time (at the moment t = 1). Consequently, to solve the problem, it is necessary to determine the cost of a real asset, taking into account the remoteness in time of future receipts (income) from its use.

In general, to find the present value PV of any asset (real or financial) used during a certain holding (investment) period, it is necessary to multiply the expected income stream from this asset (C) by the value 1/(1 + r):

PV = C * (1/(1+r)) ,

where r determines the return on the best alternative financial instrument with the same holding period and similar level of risk.

The value 1/(1+r) is called the discount factor (discount factor). The return on an alternative financial instrument r is called the discount rate. The discount rate determines the opportunity cost of capital because it characterizes how much benefit the firm missed out on by investing money in real assets rather than in the best financial alternative.

To determine the feasibility of purchasing a real asset worth C0 rubles, you must:

a) estimate what cash flow C1 expects from the real asset for the entire holding period;

b) find out which security with the same holding period has the same level of risk as the planned project;

c) determine the yield r of this security at the present time;

d) calculate the present value PV of the planned cash flow C1 by discounting the future income stream:

PV = C1 / (1+r) ;

e) compare investment costs C0 with the present value PV:

if PV > C0, then the real product can be purchased;

if PV = C0, then a real asset can be bought or not bought (that is, from an economic point of view, investing in a real asset has no advantage compared to investing money in securities or other objects).

If an investment project is designed for several steps (in particular, n years), then to find the present value of future income from the project it is necessary to discount all amounts Ct that the project must provide:

PV = Σ Ct / (1+r)^t .

For example, for an investment project designed for three years, the present value is estimated as follows:

PV = Ct / (1+r) + Ct / (1+r)^2 + Ct / (1+r)^3 .

Some funds can provide a continuous stream of income indefinitely. The present value of such a facility at a given and constant discount rate r is:

PV = Ct / (1+r) + Ct / (1+r)^2 + Ct / (1+r)^3 + ... = C / r .

The present value of an annuity that provides an income stream C for n periods (years) at a constant discount rate r is calculated using the formula:

PVannuity = C * Fannuity,

where F annuity is the annuity factor, which is determined as follows:

Annuity F = 1/r - 1/(1+r)^n .

Net Present Value (NPV)

The feasibility of acquiring a real asset can be assessed using net present value (NPV), which is understood as the net increase in the potential assets of the company due to the implementation of the project. In other words, NPV is defined as the difference between the present value of the PV of the asset and the amount of initial investment C0:

NPV = Σ Ct / (1+r)^n - C0 .

Payback period (PVR)

The payback period of a project is the period over which the initial investment costs are recovered, or the number of periods (calculation steps, for example, years) during which the accumulated amount of estimated future income streams will be equal to the amount of the initial investment. As a rule, the company itself sets an acceptable completion date for the investment project, for example, k steps. This period is determined by the company on the basis of its own strategic and tactical guidelines: for example, the company’s management rejects any projects lasting more than 5 years, since after 5 years the company is planned to be repurposed to produce other products.

When the completion date k of alternative projects is determined, then the payback period of the project under evaluation can be found by calculating how many calculation steps m the sum of cash flows C1+C2+...+Cm will be equal to or begin to exceed the value of the initial investment C0. In other words, to determine the payback period of a project, it is necessary to consistently compare the accumulated amounts of income with the initial investment. According to the payback period rule, a project can be accepted if the following condition is met: m

Internal rate of return (IRR)

The internal rate of return is the estimated discount rate at which the net present value of the project is zero.

It is found by solving the following equation:

NPV = C0 + C1/(1+IRR) + C2/(1+IRR)^2 + C3/(1+IRR)^3 + ... + Cn/(1+IRR)^n = 0 .

This equation is solved by iteration. To calculate IRR, you can use specially programmed calculators or computer programs. Rule of internal rate of return: it is necessary to accept those projects whose discount rate (that is, the opportunity cost of capital) is less than the internal rate of return of the project (r

The profitability index (PI) is understood as a value equal to the ratio of the present value of the expected cash flows from the project to the initial cost of investment:

The profitability index shows how much an investor receives per invested ruble. The rule of the profitability index is as follows: it is necessary to accept only those projects whose profitability index value exceeds one. When evaluating two or more projects that have a positive profitability index, you should choose the one that has a higher profitability index.

The effectiveness of the IP is assessed during the calculation period - the investment horizon from the start of the project to its liquidation. The start of a project is usually associated with the start date of investment in design and survey work. The calculation period is divided into calculation steps, which are time periods within which data is aggregated to estimate cash flows and cash flows are discounted.

Calculation steps are usually numbered (step 0, step 1, step 2, etc.). The duration of calculation steps is measured in years or fractions of a year, their sequence is counted from a fixed moment t0 = 0, taken as the base one. For reasons of convenience, the moment of the beginning or end of the zero step is usually taken as the base one. If several projects are being compared, it is recommended to choose the same base point for them. When the base moment coincides with the beginning of the zero step, the moment of the beginning of step number m is denoted by tm, but if the base moment coincides with the end of step 0, then tm denotes the end of the calculation step m. The duration of different steps may vary.

Source - Maksimova V.F. Investment management: Educational and practical manual. – M.: Publishing house. EAOI center. 2007. – M., 2007. – 214 p.

The following are recommended as the main indicators used to calculate the commercial efficiency of individual entrepreneurs:

net present value of the project (NPV);

return on investment index (PI);

internal rate of return (IRR);

payback period (PBP).

Conditions for financial feasibility and performance indicators are calculated on the basis of cash flows, the specific components of which depend on the type of performance being assessed.

The most important indicator of project effectiveness is the net present value of the project (other names: NPV - net present value, integral economic effect).

The net current (discounted) value of a project is the difference between the amount of cash receipts from the implementation of the project reduced to the initial point in time and the amount of discounted costs necessary to implement the project:

where b t is the discount factor;

CFtek (t) - cash flow from operating (current) activities;

CFin (t) - cash flow from investment activities.

Discount rate calculation

The discount rate (r) is the rate of return that investors would typically receive from investments of similar content and degree of risk. This is the minimum level of return on investment equal to the effective interest rate on long-term loans in the capital market or the interest rate paid by the recipient of the loan. In other words, the discount rate should be the minimum rate of return below which the entrepreneur would consider the investment unprofitable for himself.

The discount factor is calculated using the formula:

For financial investments, the interest rate is taken as the rate of income from alternative investments in the most reliable securities or the interest on a bank deposit. The discount rate for risky projects should be higher than for absolutely reliable ones. The real discount rate can be calculated using the formula:

where r r bank is the real deposit interest rate; K project risk - risk adjustment - a coefficient showing how many percent the investment project under consideration is riskier compared to keeping money in a bank. The relationship between nominal and real interest rates is given by I. Fisher’s formula:

where r n bank is the nominal interest rate on deposits in the bank;

k inf - rate (index) of inflation.

Let's calculate the real deposit interest rate:

0,0092 = 0,9 %

Calculation of discount rates

Let's calculate the discount factor for the first year:

The discount factor values ​​are presented in Table 6.5.

Table 6.5 - Discount factor for each year of the project

Calculation of the net present value of the project

Let's determine the net present value of the project:

The initial data necessary for calculating NPV are presented in Table 6.6.

Table 6.6 - Initial data for calculating NPV

Discounted cash flows are presented in Table 6.7.

Table 6.7 - Discounted cash flows

NPV = (-6,670.00 - 2,922.94 - 2,588.96 + 0.00 + 2,031.13+ 0.00) + (0.00 +

2 126,56+ 3 530,13+ 5 364,02+ 5 050,91+ 2 796,12) = 8 716,96

NPV = 8,716.96 thousand rubles.

NPV rule: investment projects with NPV>0 are applied for implementation, or from the proposed project options, the one with the maximum NPV value is recommended for implementation. In our case, NPV>0, i.e. return on capital exceeds invested capital. Therefore, this project is subject to implementation.

Return on Investment:

PI (Profitability index) is an indicator of return on investment that allows you to determine the extent to which an investor’s wealth increases per 1 ruble of investment.

Return on investment - calculated as the ratio of return on capital to invested capital:

PI = 18867.74/ 10150.77 = 1.86

In this project, the return on capital is 1.86 times the amount of investment.

In our case, PI > 1. Therefore, we can conclude that investing in this project is profitable.

Payback period

PBP (payback period) is the number of years during which sales income, minus costs and taxes, reimburses the initial investment.

PBP is determined by the formula:

where b is investment taking into account discounting, b = 12181.9 thousand rubles;

a - the number of the year in which the return on investment occurs;

с - value of discounted flows CF current *b t on an accrual basis

from the initial moment of time to the year designated “a”, thousand rubles;

d - value of CF current *b t per year “a+1”, thousand rubles.

To calculate the payback period of the project, we will draw up table 6.8.

Table 6.8 - Calculation of the payback period

Let's calculate the payback period of the project:

PBP = 3.2 years.

This gives us a period of time during which the investments required to implement this project will pay off.

Maximum cash outflow

MDO (Max cash outflow) is the maximum cash outflow.

The maximum cash outflow is the negative greatest value of the net present value, which is calculated on an accrual basis. This indicator reflects the required amount of project financing. MDO = 7466.38 thousand rubles. A graphical display of the dynamics of the NPV indicator represents the financial profile of the project.

Let's calculate the NPV value on an accrual basis:

NPV 0 = - 6,670.00+ 0 = - 6,670.00 thousand rub.

NPV 1 = - 6,670.00+ (-2,922.94) + 2,126.56= - 7,466.38 thousand rubles.

NPV 2 = - 7,466.38 + (-2,588.96) + 3,530.13 = - 6,525.22 thousand rubles.

NPV 3 = - 6,525.22+ 0.00 + 5,364.02= - 1,161.20 thousand rubles.

NPV 4 = - 1,161.20+ 2,031.13+ 5,050.91= 5,920.84 thousand rubles.

NPV 5 = 5,920.84 + 0.00 + 2,796.12 = 8,716.96 thousand rubles.

The project financial profile chart reflects the dynamics of the NPV indicator during the billing period. The graph is constructed based on NPV values ​​with a cumulative total by year of the calculation period (see Figure 6.1). The data is shown in table 6.9.

Table 6.9 - Net present value by project year

Figure 6.1 - Project financial profile chart

The last thing in this section is to determine the internal rate of return - IRR.

IRR (Internal rate of return) is the internal rate of return. By definition, the internal rate of return (sometimes called profitability) is the value of the discount rate at which the net present value of the project is zero.

IRR is determined from the following equation:

The solution is made by selection using the EXCEL program. To do this, it is convenient to draw up table 6.10. Using the data from Table 6.10, we build a graph “Internal rate of return” (see Figure 6.2).

Table 6.10 - Internal rate of return

Figure 6.2 - Internal rate of return

We get, with IRR = 0.403, NPV = 0

Purpose of the lecture: to learn calculate cash flows and indicators of commercial efficiency of an investment project.

If the project is recognized as socially effective, then they move on to assessing its commercial value. efficiency. In Methodological recommendations for assessment efficiency investment project provides a list of commercial indicators efficiency [ 6 ] :

Conditions of commercial efficiency investment project is a positive value of the integral NPV, as well as the values ​​of IDI and IDI exceeding one.

In order to correctly evaluate commercial efficiency investment project, it is necessary to correctly determine cash flows, the values ​​of which are used in the calculations. Any cash flow F represents the difference between the inflow P and outflow O of funds:

The procedure for calculating cash inflows and outflows varies depending on the nature of the cash flow. Outflow of funds from investment activities– these are all investments related to the implementation of the project (investments in fixed assets, in the initial working capital, in intangible assets). Inflow of funds from investment activities is formed in the event of the sale of assets and is determined by the income from this sale. Operational activities are activities related to the production and sale of products. The outflow of funds from operating activities includes the cost of production less depreciation and the cost of paying taxes and other mandatory payments. The influx of funds from operating activities is revenue from sales of products [7].

Example. Calculate cash flows from investment and operating activities to assess commercial efficiency project, if investments amount to 18,000 thousand rubles. are carried out in the first year of implementation of the investment project, and production begins in the second year. The project life cycle is 8 years. In the last year of the life cycle, assets are sold. Income from the sale of assets is 50 thousand rubles. The cost of production is 5 thousand rubles/piece. , unit price – 7 thousand rubles. PC. Production and sales volume – 12,000 pcs./year. The annual amount of taxes and other obligatory payments is 30 thousand rubles. Annual amount depreciation charges– 80 thousand rubles.

Solution.

Let's consider cash flow from investment activities. In our task, the outflow of funds from investment activities will amount to 18,000 thousand rubles. (investment), and the influx of funds from investment activities– 50 thousand rubles. (income from the sale of assets). We know that investments are made in the first year project life cycle, and the sale of assets - in the last (eighth) year. This means that the cash flow from investment activities in the first year it will be -18,000 thousand rubles. , and in the last year - 50 thousand rubles. From the second to the seventh year inclusive cash flow from investment activities will be equal to zero, because during these years no operations related to investment activities are carried out.

Cash flow from operating activities should be calculated from the second to eighth years of the life cycle. In the first year this cash flow is not calculated because there is no production yet this year. First of all, you should calculate the cost of annual production volume and annual revenue.

The cost of annual production volume is calculated as the product of the cost per unit of production and the annual production volume:

Annual revenue is calculated as the product of unit price and annual sales volume:

To calculate the annual amount cash flow from operating activities, the cost price should be deducted from the revenue (while excluding depreciation from its composition) and the annual amount of taxes and other mandatory payments:

Let's arrange the calculations in the form of a table (table 5.1):

The problem we solved is a fairly simple case: the production volume is exactly equal to the sales volume and does not change during project life cycle, other parameters do not change (cost and unit price, amount of tax payments). In more complex cases cash flow from operating activities will be calculated separately for each year of the life cycle of the investment project.

Having calculated cash flows, proceed to the calculation of commercial efficiency indicators.

Example. Using the data from the previous example, estimate the commercial efficiency investment project at a discount rate of 15%.

Solution.

To assess the commercial effectiveness of the project, we use cash flows, which were already calculated in the previous example. Net income and net present value must be calculated at each calculation step. Let's make the calculation in tabular form (Table 5.2):

The integral NPV amounted to 70,792 thousand rubles.

Purpose of the lecture: to learn calculate cash flows and indicators of commercial efficiency of an investment project.

If the project is recognized as socially effective, then they move on to assessing its commercial value. efficiency. In Methodological recommendations for assessment efficiency investment project provides a list of commercial indicators efficiency [ 6 ] :

Conditions of commercial efficiency investment project is a positive value of the integral NPV, as well as the values ​​of IDI and IDI exceeding one.

In order to correctly evaluate commercial efficiency investment project, it is necessary to correctly determine cash flows, the values ​​of which are used in the calculations. Any cash flow F represents the difference between the inflow P and outflow O of funds:

The procedure for calculating cash inflows and outflows varies depending on the nature of the cash flow. Outflow of funds from investment activities– these are all investments related to the implementation of the project (investments in fixed assets, in the initial working capital, in intangible assets). Inflow of funds from investment activities is formed in the event of the sale of assets and is determined by the income from this sale. Operational activities are activities related to the production and sale of products. The outflow of funds from operating activities includes the cost of production less depreciation and the cost of paying taxes and other mandatory payments. The influx of funds from operating activities is revenue from sales of products [7].

Example. Calculate cash flows from investment and operating activities to assess commercial efficiency project, if investments amount to 18,000 thousand rubles. are carried out in the first year of implementation of the investment project, and production begins in the second year. The project life cycle is 8 years. In the last year of the life cycle, assets are sold. Income from the sale of assets is 50 thousand rubles. The cost of production is 5 thousand rubles/piece. , unit price – 7 thousand rubles. PC. Production and sales volume – 12,000 pcs./year. The annual amount of taxes and other obligatory payments is 30 thousand rubles. Annual amount depreciation charges– 80 thousand rubles.

Solution.

Let's consider cash flow from investment activities. In our task, the outflow of funds from investment activities will amount to 18,000 thousand rubles. (investment), and the influx of funds from investment activities– 50 thousand rubles. (income from the sale of assets). We know that investments are made in the first year project life cycle, and the sale of assets - in the last (eighth) year. This means that the cash flow from investment activities in the first year it will be -18,000 thousand rubles. , and in the last year - 50 thousand rubles. From the second to the seventh year inclusive cash flow from investment activities will be equal to zero, because during these years no operations related to investment activities are carried out.

Cash flow from operating activities should be calculated from the second to eighth years of the life cycle. In the first year this cash flow is not calculated because there is no production yet this year. First of all, you should calculate the cost of annual production volume and annual revenue.

The cost of annual production volume is calculated as the product of the cost per unit of production and the annual production volume:

Annual revenue is calculated as the product of unit price and annual sales volume:

To calculate the annual amount cash flow from operating activities, the cost price should be deducted from the revenue (while excluding depreciation from its composition) and the annual amount of taxes and other mandatory payments:

Let's arrange the calculations in the form of a table (table 5.1):

The problem we solved is a fairly simple case: the production volume is exactly equal to the sales volume and does not change during project life cycle, other parameters do not change (cost and unit price, amount of tax payments). In more complex cases cash flow from operating activities will be calculated separately for each year of the life cycle of the investment project.

Having calculated cash flows, proceed to the calculation of commercial efficiency indicators.

Example. Using the data from the previous example, estimate the commercial efficiency investment project at a discount rate of 15%.

Solution.

To assess the commercial effectiveness of the project, we use cash flows, which were already calculated in the previous example. Net income and net present value must be calculated at each calculation step. Let's make the calculation in tabular form (Table 5.2):

The integral NPV amounted to 70,792 thousand rubles.