DYNAMIC METHODS OF EVALUATION OF INVESTMENT PROJECTS.
Net present value
(Net Present Value - NPV)
In modern published works, the following terms are used to name the criteria of this method:
- net present value;
- net present value;
- net present value;
- net present value;
- general financial result from the implementation of the project;
- current value.
The Methodological Recommendations for Evaluating the Efficiency of Investment Projects (second edition) - Moscow, "Economics", 2000 - proposed the official name of this criterion - net present value (NPV).
The value of the net present value (NPV) is calculated as the difference between the discounted cash flows of income and expenses incurred in the course of the investment for the forecast period.
The essence of the criterion is to compare the present value of future cash receipts from the implementation of the project with the investment costs necessary for its implementation.
Application of the method involves the sequential passage of the following stages:
- Calculation of cash flow of the investment project.
- The choice of a discount rate that takes into account the Return on alternative investments and the risk of the project.
- Determination of net present value.
NPV or NPV for a constant discount rate and one-time initial investment is determined by the following formula:
Where
I 0 - the value of the initial investment;
С t - money note from the sale of investments at time t;
t - calculation step (year, quarter, month, etc.);
i is the discount rate.
Cash flows must be settled at current or deflated prices. When forecasting income by year, it is necessary, whenever possible, to take into account all types of Revenues of both a production and non-production nature that may be associated with this project. So, if at the end of the project implementation period it is planned to receive funds in the form of the liquidation value of the equipment or the release of part of the working capital, they should be accounted for as income of the corresponding periods.
The basis of calculations by this method is the premise of a different value of money over time. The process of translating the future value of cash flow into the current is called discounting (from the English discont - to reduce).
The discount rate is called the discount rate (discount), and the factor F = 1 / (1 + i) t is called the discount factor.
If the project involves not a one-time investment, but a consistent investment of financial resources over a number of years, then the formula for calculating NPV is modified as follows:
Where
I 0 - the value of the initial investment;
С t - money note from the sale of investments at time t;
t - calculation step (year, quarter, month, etc.);
i is the discount rate.
The conditions for making an investment decision based on this criterion are as follows:
if NPV> 0, then the project should be accepted;
if NPV <0, then the project should not be accepted;
if NPV = 0, then the adoption of the project will bring neither profit nor loss.
The basis of this method is the following of the main target setting determined by the investor - maximizing its final state or increasing the value of the company. Following this target setting is one of the conditions for a comparative assessment of investments based on this criterion.
A negative value of the net present value indicates the inappropriateness of decisions on financing and implementation of the project, since if NPV <0, then if the project is adopted, the value of the company will decrease, that is, the owners of the company will incur a loss and the main target setting is not performed.
A positive value of the net present value indicates the feasibility of making decisions on the financing and implementation of the project, and when comparing investment options, the option with the highest NPV is considered preferable, since if NPV> 0, then if the project is accepted, the value of the company, and therefore the welfare of its owners will increase. If NPV = 0, then the project should be accepted provided that its implementation will enhance the flow of income from previously implemented capital investment projects. For example, expanding the land for parking at a hotel will increase the flow of real estate income.
The implementation of this method involves a number of assumptions that need to be checked for the degree to which they correspond to reality and on what results lead to possible deviations.
These assumptions include:
- the existence of only one objective function - the cost of capital;
- specified period of project implementation;
- data reliability;
- belonging of payments to certain points in time;
- the existence of a perfect capital market.
When making decisions in the investment sphere, one often has to deal not with one goal, but with several target settings. If you use the method of determining the cost of capital, these goals should be taken into account when finding a solution outside the process of calculating the cost of capital. In this case, methods for making multi-purpose decisions can also be analyzed.
The term of operation must be established in the analysis of efficiency before the application of the method of determining the cost of capital. For this purpose, methods for determining the optimal operating life can be analyzed, unless it is set in advance for technical or legal reasons.
In fact, when making investment decisions there is no reliable data. Therefore, along with the proposed method for calculating the value of capital on the basis of predicted data, it is necessary to analyze the degree of uncertainty, at least for the most important investment objects. Investing methods in the face of uncertainty serve this purpose.
In the formation and analysis of the method, it is assumed that all payments can be attributed to certain points in time. The time interval between payments is usually equal to one year. In fact, payments can be made at shorter intervals. In this case, attention should be paid to the compliance of the step of the billing period (calculation step) with the condition for granting a loan. For the correct application of this method, it is necessary that the calculation step be equal to or a multiple of the term for calculating interest on a loan.
The assumption of a perfect capital market is also problematic, in which financial resources can be attracted or invested at any time and in unlimited amounts at a single calculated interest rate. In reality, such a market does not exist, and interest rates for investing and borrowing funds, as a rule, differ from each other. As a result, the problem arises of determining a suitable interest rate. This is especially important, since it has a significant impact on the value of capital.
When calculating NPV, discount rates that differ by year can be used. In this case, it is necessary to apply individual discount factors to each cash flow that will correspond to this calculation step. In addition, it is possible that a project acceptable at a constant discount rate may become unacceptable with a variable.
The net present value indicator takes into account the value of money over time, has clear decision criteria and allows you to choose projects for the purpose of maximizing the value of the company. In addition, this indicator is an absolute indicator and has the additivity property, which allows you to add the indicator values for various projects and use the total indicator for projects in order to optimize the investment portfolio.
With all its advantages, the method has significant drawbacks. Due to the difficulty and ambiguity of forecasting and generating cash flow from investments, as well as the problem of choosing a discount rate, there may be a risk of underestimating the risk of the project.
Profitability Index (PI)
Profitability index (profitability, profitability) is calculated as the ratio of the net present value of cash inflow to the net present value of cash outflow (including initial investment):
where I 0 is the investment of the enterprise at time 0;
With t is the cash flow of the enterprise at time t;
i is the discount rate.
P k - the balance of the accumulated flow.
or
The conditions for the adoption of the project for this investment criterion are as follows:
- if PI> 1, then the project should be accepted;
- if PI <1, then the project should be rejected;
- if PI = 1, the project is neither profitable nor unprofitable.
It is easy to notice that when evaluating projects with the same initial investment, the PI criterion is fully consistent with the NPV criterion.
Thus, the PI criterion has an advantage when choosing one project from a series having approximately the same MPV values, but different volumes of the required investments. In this case, the one that provides greater investment efficiency is more profitable. In this regard, this indicator allows you to rank projects with limited investment resources.
The disadvantages of the method include its ambiguity when discounting separately cash inflows and outflows.
Internal Rate of Return (IRR)
Under the internal rate of return, or internal rate of return, investment (JRR) understand the value of the discount rate at which the NPV of the project is zero:
IRR = i, where NPV = f (i) = 0
The meaning of calculating this coefficient when analyzing the effectiveness of planned investments is as follows: IRR shows the maximum allowable relative level of expenses that can be associated with this project. For example, if the project is fully funded by a commercial bank loan, the IRR value indicates the upper limit of the acceptable level of the bank interest rate, the excess of which makes the project unprofitable.
In practice, any enterprise finances its activities from various sources. As a fee for the use of financial resources advanced in the activities of the enterprise, it pays interest, dividends, remuneration, etc., that is, it incurs some reasonable expenses for maintaining its economic potential. The indicator characterizing the relative level of these incomes can be called the price of advanced capital (capital cost - SS). This indicator reflects the minimum return on the capital invested in its activities that has developed at the enterprise, its profitability and is calculated by the arithmetic average formula.
The economic meaning of this indicator is as follows: the company can make any investment decisions, the level of profitability of which is not lower than the current value of the SS indicator (price of the source of funds for this project). It is with him that the IRR calculated for a specific project is compared, while the relationship between them is as follows:
- if IRR> SS, then the project should be accepted;
- if IRR <CC, then the project should be rejected;
- if IRR = CC, then the project is neither profitable nor unprofitable.
Another interpretation option is to interpret the internal rate of return as a possible discount rate at which the project is still profitable by the NPV criterion. The decision is made on the basis of comparing IRR with normative profitability; at the same time, the higher the value of the internal rate of return and the greater the difference between its value and the selected discount rate, the greater the margin of safety of the project. This criterion is the main guideline when making an investment decision by an investor, which does not detract from the role of other criteria.
To calculate the IRR using discount tables, two values of the discount coefficient i 1 <i 2 are selected so that in the interval (i 1, i 2 ) the function NPV = f (i) changes its value from "+" to "-" or from "-" to "+".
Then apply the formula:
where i 1 is the value of the discount coefficient at which f (i 1 )> 0 (f (i 1 ) <0),
r 2 is the value of the discount coefficient at which f (i 2 ) <0 <f (i 2 )> 0).
Modified internal rate of return
(Modified Internal Rate of Return, IRR)
The modified rate of return (MIRR) eliminates a significant shortcoming of the internal rate of return for a project that arises in the event of repeated outflows of funds. An example of such a repeated outflow is the purchase in installments or the construction of a property, carried out over several years. The main difference of this method is that reinvestment is carried out at a risk-free rate, the value of which is determined based on the analysis of the financial market.
In Russian practice, this may be the yield on a fixed-term foreign currency deposit offered by the Savings Bank of Russia. In each case, the analyst determines the value of the risk-free rate individually, but, as a rule, its level is relatively low.
Thus, discounting costs at a risk-free rate makes it possible to calculate their total current value, the value of which allows you to more objectively assess the level of return on investment, and is a more correct method in the case of investment decisions with extraordinary cash flows.
Discounted payback period
(Discounted Payback Period, DPP)
The Discounted Payback Period (DPP) eliminates the drawback of the static method of the payback period of investments and takes into account the value of money over time, and the corresponding formula for calculating the discounted payback period, DPP, looks like:
DPP = min n at which
Obviously, in the case of discounting, the payback period increases, that is, always DPP> PP.
The simplest calculations show that such a technique, given the low discount rate characteristic of a stable Western economy, improves the result by an imperceptible amount, while for a significantly higher discount rate typical of the Russian economy, this gives a significant change in the estimated payback period. In other words, a project acceptable by the PP criterion may not be acceptable by the DPP criterion.
When using the criteria of PP and DPP in evaluating investment projects, decisions can be made based on the following conditions:
a) the project is accepted if the payback takes place;
b) the project is accepted only if the payback period does not exceed the deadline set for a particular company.
In the general case, the determination of the payback period is auxiliary in relation to the net present value of the project or the internal rate of return. In addition, the disadvantage of such an indicator as the payback period is that it does not take into account subsequent cash inflows, and therefore can serve as an incorrect criterion for the attractiveness of the project.
STATIC METHODS OF EVALUATION OF INVESTMENT PROJECTS.
Payback Period (Payback Period, PP)
The most common static indicator for evaluating investment projects is the payback period (Payback Period - PP).
The payback period is understood as the period of time from the moment the project is launched until the moment the facility is operated in which the operating income becomes equal to the initial investment (capital costs and operating costs).
This indicator answers the question: when will the full return on invested capital occur? The economic meaning of the indicator is to determine the period for which the investor can return the invested capital.
To calculate the payback period, the elements of the payment series are summed up on an accrual basis, forming the balance of the accumulated flow, until the amount assumes a positive value. The sequence number of the planning interval, in which the balance of the accumulated flow takes a positive value, indicates the payback period expressed in planning intervals.
The general formula for calculating the PP indicator is:
PP = min n at which
where P t is the value of the balance of the accumulated flow;
1 B is the value of the initial investment.
Upon receipt of a fractional number, it is rounded up to the nearest integer. Often, the PP indicator is calculated more accurately, that is, the fractional part of the interval (settlement period) is also considered; at the same time, an assumption is made that within one step (billing period), the balance of accumulated cash flow varies linearly. Then the "distance" of the beginning of the step to the moment of payback (expressed in the duration of the calculation step) is determined by the formula:
where P to - is the negative value of the accumulated flow balance at the step to the moment of recoupment;
P to + is the positive value of the accumulated flow balance at the step after the payback moment.
For projects with constant income at regular intervals (for example, annual constant income - annuity), you can use the following payback period formula:
PP = I 0 / A
where PP - payback period in the planning intervals;
I 0 - the amount of initial investment;
A is the size of the annuity.
It should be borne in mind that the elements of the payment series in this case must be ordered by sign, that is, first an outflow of funds (investment) is implied, and then an inflow. Otherwise, the payback period may not be calculated correctly, since when the sign of the payment series is reversed, the sign of the sum of its elements can also change.
Investment Rate of Return (ARR)
Another indicator of a static financial evaluation of a project is the Investment Rate of Return (ARR). This ratio is also called the accounting rate of return or the coefficient of profitability of the project.
There are several algorithms for calculating ARR.
The first calculation option is based on the ratio of the average annual profit (minus deductions to the budget) from the project for the period to the average investment:
ARR = P r / (1/2) I cf. 0
where P r is the average annual amount of profit (minus deductions to the budget) from the implementation of the project,
I cf. 0 - the average amount of initial investments, if it is assumed that after the project implementation period all capital costs will be written off.
Sometimes the project profitability indicator is calculated on the basis of the initial investment:
ARR = P r / I 0
Calculated on the basis of the initial investment, it can be used for projects that create a stream of even income (for example, annuity) for an indefinite or sufficiently long period.
The second calculation option is based on the ratio of the average annual amount of profit (minus deductions to the budget) from the project for the period to the average investment taking into account the residual or liquidation value of the initial investment (for example, taking into account the liquidation value of the equipment at the end of the project):
ARR = P r / (1/2) * (I 0 -I f ),
where P r - the average annual amount of profit (minus deductions to the budget) from the project;
I 0 - the average value of the initial investment;
I f - residual or residual value of the initial investment.
The advantage of an investment performance indicator is ease of calculation. At the same time, it has significant disadvantages. This indicator does not take into account the value of money over time and does not involve discounting, respectively, does not take into account the distribution of profits by years, and, therefore, is applicable only for evaluating short-term projects with a uniform income stream. In addition, it is impossible to assess the possible differences in projects related to different implementation periods.
Since the method is based on the use of accounting characteristics of the investment project - the average annual profit, the coefficient of investment efficiency does not quantify the growth of the economic potential of the company. However, this ratio provides information on the impact of investments. On the financial statements of the company. The financial statements are sometimes the most important when analyzing the attractiveness of a company by investors and shareholders.
Данный материал подготовлен по книге "Коммерческая оценка инвестиций"
Авторы: И.А. Бузова, Г.А. Маховикова, В.В. Терехова. Издательство "ПИТЕР", 2003 год.
08/18/2019