We conduct classical fundamental analysis ourselves. We determine the fair price according to the formula. We make an investment decision. Features of the fundamental analysis of debt assets, bonds, bills. (10+)
Classical (fundamental) analysis
Universal formula for a fair price
Classical (fundamental) analysis based on the premise that the investee has a fair price. This price can be calculated using the formula:
Si - the amount of income that will be received from investment in the i-th year, counting from the current to the future, ui - the alternative return on investment for this period (from the current moment to i-th payments amounts).
For example, you purchase a bond with maturity in 3 years with a lump sum payment of the entire amount of principal and interest on it. The amount of payment on the bond, together with interest, will be 1,500 rubles. Let us determine the alternative return on investments, for example, by the return on a deposit in Sberbank. Let it be 6% per annum. The opportunity return is 106% * 106% * 106% = 119%. The fair price is equal to 1260.5 rubles.
The above formula is not very convenient, since the alternative return is usually assumed by years (even in the example, we took the annual return and raised it to the third power). Let's convert it to an annual alternative returns
here vj is the alternative return on investment for the jth year.
Why are all assets not worth their fair price?
Despite its simplicity, the above formula does not allow you to accurately determine the value of the investment object, as it contains indicators that need to be predicted for future periods. The alternative return on investment in the future is unknown to us. We can only guess what rates will be in the market at that moment. This introduces especially large errors for instruments with long maturities or without them (stocks, consoles). With the amount of payments, too, not everything is clear. Even for debt securities (fixed-income bonds, bills of exchange, etc.), for which, it seems, the payment amounts are determined by the terms of issue, the actual payments may differ from the planned ones (and the formula contains the amounts of actual, not planned payments ). This occurs when a debt is defaulted or restructured, when the issuer is unable to pay the full amount promised. For equity securities (shares, shares, shares, etc.), the amounts of these payments generally depend on the performance of the company in the future, and, accordingly, on the general economic situation in those periods.
Thus, it is impossible to accurately calculate the fair price using the formula. The formula gives only a qualitative idea of the factors affecting the fair price. Based on this formula, it is possible to develop formulas for a rough estimate of the asset price.
Estimation of the fair price of a debt asset (with fixed payments), bonds, promissory notes
AT new formula Pi - the amount promised to be paid in the relevant period, ri - the discount based on our assessment of the reliability of investments. In our previous example, let us estimate the reliability of investments in Sberbank as 100%, and the reliability of our borrower as 90%. Then the estimate of the fair price will be 1134.45 rubles.
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Financial and economic calculations are most often associated with the assessment of time-distributed cash flows. Actually for these purposes, and need a discount rate. From the point of view of financial mathematics and investment theory, this indicator is one of the key. Methods are built on it. investment appraisal business based on the concept of cash flows, with its help, a dynamic assessment of the effectiveness of investments, both real and stock, is carried out. To date, there are already more than a dozen ways to select or calculate this value. Mastering these methods allows a professional investor to make more informed and timely decisions.
But, before moving on to the methods of justifying this rate, let's look at its economic and mathematical essence. Actually, two approaches are applied to the definition of the term "discount rate": conditionally mathematical (or process), as well as economic.
The classic definition of the discount rate stems from the well-known monetary axiom: “Money today is worth more than money tomorrow.” Hence, the discount rate is a certain percentage that allows you to bring the cost of future cash flows to their current cost equivalent. The fact is that many factors influence the depreciation of future income: inflation; risks of not receiving or not receiving income; lost profits arising from the emergence of a more profitable alternative investment opportunity Money in the process of implementing a decision already made by the investor; systemic factors and others.
By applying a discount rate in their calculations, an investor discounts, or discounts, expected future cash income to the current point in time, thereby taking into account the above factors. Discounting also allows the investor to analyze cash flows over time.
In this case, the discount rate and the discount factor should not be confused. The discount factor is usually used in the calculation process as a kind of intermediate value calculated on the basis of the discount rate according to the formula:
where t is the number of the forecast period in which cash flows are expected.
The product of the future value of the cash flow and the discount factor shows the current equivalent of the expected income. However, the mathematical approach does not explain how the discount rate itself is calculated.
For these purposes, it is used economic principle, according to which the discount rate is some alternative return on comparable investments with the same level of risk. A rational investor, making a decision to invest money, will agree to the implementation of his "project" only if its profitability turns out to be higher than the alternative and available on the market. This is not an easy task, since it is very difficult to compare investment options by level of risk, especially in the absence of information. In the theory of investment decision making, this problem is solved by decomposing the discount rate into two components - the risk-free rate and risks:
The risk-free rate of return is the same for all investors and is subject only to the risks of the economic system. The remaining risks are assessed by the investor independently, as a rule, on the basis of an expert assessment.
There are many models to justify the discount rate, but all of them in one way or another correspond to this basic fundamental principle.
Thus, the discount rate is always the sum of the risk-free rate and the total investment risk concrete investment asset. The starting point for this calculation is the risk-free rate.
risk free rate
The risk-free rate (or risk-free rate of return) is the expected rate of return on assets for which financial risk equals zero. In other words, this is the return on absolutely reliable options for investing money, for example, on financial instruments, the profitability of which is guaranteed by the state. We emphasize that even for absolutely reliable financial investments absolute risk cannot be absent (in this case, the rate of return would also tend to zero). The risk-free rate includes the risk factors of the economic system itself, risks that no investor can influence: macroeconomic factors, political events, changes in legislation, extraordinary anthropogenic and natural events, etc.
Therefore, the risk-free rate reflects the lowest possible return acceptable to the investor. The investor must choose the risk-free rate for himself. You can calculate the average rate from several options for potentially risk-free investments.
When choosing a risk-free rate, an investor should take into account the comparability of his investments with a risk-free option according to such criteria as:
Scale or total cost of investment.
Investment period or investment horizon.
The physical possibility of investing in a risk-free asset.
Equivalence of denomination of rates in currency, and others.
Rates of return on fixed-term ruble deposits in banks of the highest reliability category. In Russia, such banks include Sberbank, VTB, Gazprombank, Alfa-Bank, Russian Agricultural Bank and a number of others, a list of which can be viewed on the website Central Bank RF. When choosing a risk-free rate in this way, it is necessary to take into account the comparability of the investment period and the period of fixing the rate on deposits.
Let's take an example. We use the data of the website of the Central Bank of the Russian Federation. As of August 2017, weighted averages interest rates on deposits in rubles for up to 1 year amounted to 6.77%. This rate is risk-free for most investors who invest for up to 1 year;
Yield on Russian government debt financial instruments. In this case, the risk-free rate is fixed in the form of yield on (OFZ). These debt securities are issued and guaranteed by the Ministry of Finance of the Russian Federation, therefore they are considered the most reliable financial asset in RF. With a maturity of 1 year, OFZ rates currently range from 7.5% to 8.5%.
Level of yield on foreign government securities. In this case, the risk-free rate equals the return government bonds USA with maturities from 1 to 30 years. Traditionally, the US economy is international rating agencies estimated at highest level reliability, and, consequently, the yield of their government bonds and is recognized as risk-free. However, it should be taken into account that the risk-free rate in this case is denominated in dollars and not in rubles. Therefore, for the analysis of investments in rubles, an additional adjustment for the so-called country risk is necessary;
Yield on Russian government Eurobonds. This risk-free rate is also denominated in dollar terms.
The key rate of the Central Bank of the Russian Federation. At the time of this writing, the key rate is 9.0%. It is believed that this rate reflects the price of money in the economy. An increase in this rate entails an increase in the cost of a loan and is a consequence of an increase in risks. This tool should be used with great care, as it is still a directive, not a market indicator.
Interbank lending market rates. These rates are indicative and more acceptable than key rate. Monitoring and a list of these rates are again presented on the website of the Central Bank of the Russian Federation. For example, as of August 2017: MIACR 8.34%; RUONIA 8.22%, MosPrime Rate 8.99% (1 day); ROISfix 8.98% (1 week). All these rates are short-term and represent the yield on lending operations of the most reliable banks.
Discount rate calculation
To calculate the discount rate, the risk-free rate should be increased by the risk premium that the investor assumes when making certain investments. It is impossible to assess all risks, so the investor must independently decide which risks and how should be taken into account.
On the value of the risk premium and, ultimately, the discount rate greatest influence provides the following options:
The size of the issuing company and the stage of its life cycle.
The nature of the liquidity of the company's shares in the market and their volatility. The most liquid stocks generate the least risk;
Financial condition share issuer. stable financial position increases the adequacy and accuracy of forecasting the company's cash flow;
Business reputation and perception of the company by the market, investors' expectations regarding the company;
Industry affiliation and risks inherent in this industry;
The degree of exposure of the activity of the issuing company to macroeconomic conditions: inflation, fluctuations in interest rates and exchange rates etc.
A separate group of risks includes the so-called country risks, that is, the risks of investing in the economy of a particular state, for example, Russia. Country risks are usually already included in the risk-free rate if the rate itself and the risk-free yield are denominated in the same currencies. If the risk-free return is in dollar terms, and the discount rate is needed in rubles, then it will be necessary to add country risk as well.
This is just a short list of risk factors that can be taken into account in the discount rate. Actually, depending on the method of assessing investment risks, the methods for calculating the discount rate differ.
Let us briefly consider the main methods for justifying the discount rate. To date, more than a dozen methods for determining this indicator have been classified, but they are all grouped in the following way(from simple to complex):
Conditionally "intuitive" - based rather on the psychological motives of the investor, his personal beliefs and expectations.
Expert, or qualitative - based on the opinion of one or a group of specialists.
Analytical - based on statistics and market data.
Mathematical, or quantitative - require mathematical modeling and the possession of relevant knowledge.
An "intuitive" way to determine the discount rate
Compared to other methods this way is the simplest. The choice of the discount rate in this case is not mathematically justified in any way and represents only the desire of the investor, or his preference for the level of profitability of his investments. An investor can rely on his previous experience, or on the profitability of similar investments (not necessarily his own), if he knows the information about the profitability of alternative investments.
Most often, the discount rate is “intuitively” calculated approximately by multiplying the risk-free rate (as a rule, this is just the deposit rate or OFZ) by some adjustment factor of 1.5, or 2, etc. Thus, the investor, as it were, “estimates” the level of risks for himself.
For example, when calculating discounted cash flows and fair value companies in which we plan to invest, as a rule, we use the following rate: average rate on deposits, multiplied by 2, if we are talking about blue chips and apply higher odds when it comes to 2nd and 3rd tier companies.
This method is the simplest practice for a private investor and is used even in large investment funds experienced analysts, but he is not held in high esteem among academic economists, because he allows for “subjectivity”. In this regard, in this article we will give an overview of other methods for determining the discount rate.
Calculation of the discount rate based on expert judgment
The expert method is used when investments involve investing in shares of companies in new industries or activities, start-ups or venture funds, and also when there are no adequate market statistics or financial information about the issuing company.
The expert method for determining the discount rate consists in polling and averaging the subjective opinions of various specialists about the level, for example, the expected return on specific investments. The disadvantage of this approach is the relatively high proportion of subjectivity.
It is possible to increase the accuracy of calculations and somewhat level subjective assessments by decomposing the rate into a risk-free level and risks. The investor chooses the risk-free rate on his own, and the assessment of the level of investment risks, the approximate content of which we described earlier, is already carried out by experts.
The method is well applicable for investment teams that employ investment experts of various profiles (currency, industry, raw materials, etc.).
Calculation of the discount rate by analytical methods
There are many analytical ways to justify the discount rate. All of them are based on the theory of economics of the firm and financial analysis, financial mathematics and business valuation principles. Let's give some examples.
Calculation of the discount rate based on profitability indicators
In this case, the discount rate is justified on the basis of various indicators profitability, which in turn are calculated from the data and . As a base indicator, return on equity (ROE, Return On Equity) is used, but there may be others, for example, return on assets (ROA, Return On Assets).
It is most often used to evaluate new investment projects within an existing business, where the nearest alternative rate of return is precisely the profitability of the current business.
Calculation of the discount rate based on the Gordon model (model of constant growth of dividends)
This method of calculating the discount rate is acceptable for companies that pay dividends on their shares. This method assumes the fulfillment of several conditions: the payment and positive dynamics of dividends, the absence of restrictions on the life of the business, stable growth company income.
The discount rate in this case is equal to the expected return on equity of the company and is calculated by the formula:
Given methods applicable to evaluate investments in new projects of the company, by the shareholders of this business, who do not control profits, but receive only dividends.
Calculation of the discount rate by quantitative analysis methods
From the point of view of investment theory, these methods and their variations are the main and most accurate. Despite the many varieties, all these methods can be reduced to three groups:
Models of cumulative construction.
Valuation Models capital assets CAPM (Capital Asset Pricing Model).
Models of the weighted average cost of capital WACC (Weighted Average Cost of Capital).
Most of these models are quite complex, requiring a certain mathematical or economic skill. We'll consider general principles and basic calculation models.
Cumulative building model
Within the framework of this method, the discount rate is the sum of the risk-free rate of expected return and the total investment risk for all types of risk. The method of substantiating the discount rate based on risk premiums to the risk-free level of return is used when it is difficult or impossible to evaluate the relationship between risk and return on investment in the analyzed business using mathematical statistics. AT general view the calculation formula looks like this:
Capital asset pricing model CAPM
The author of this model is Nobel laureate in Economics W. Sharp. The logic of this model does not differ from the previous one (the rate of return is the sum of the risk-free rate and risks), the method of assessing investment risk is different.
This model is considered fundamental, since it establishes the dependence of profitability on the degree of its exposure external factors market risk. This relationship is estimated through the so-called "beta" coefficient, which is essentially a measure of the elasticity of the asset's return to a change in the average market returns similar assets in the market. In general, the CAPM model is described by the formula:
Where β is the “beta” coefficient, a measure of systematic risk, the degree of dependence of the assessed asset on the risks of the economic system itself, and the average market return is average return in the market for similar investment assets.
If the "beta" coefficient is higher than 1, then the asset is "aggressive" (more profitable, changing faster than the market, but also more risky in relation to analogues in the market). If the "beta" coefficient is below 1, then the asset is "passive" or "protective" (less profitable, but also less risky). If the "beta" coefficient is equal to 1, then the asset is "indifferent" (its profitability changes in parallel with the market).
Calculation of the discount rate based on the WACC model
Estimating the discount rate based on the company's weighted average cost of capital allows you to estimate the cost of all sources of financing for its activities. This indicator reflects the actual costs of the company to pay for borrowed capital, equity capital, and other sources, weighted by their share in the total liability structure. If the company's actual return is above WACC, then it generates some added value for its shareholders, and vice versa. That is why the WACC indicator is also considered as a barrier value of the required return for the company's investors, that is, the discount rate.
The calculation of the WACC indicator is carried out according to the formula:
Of course, the range of methods for justifying the discount rate is quite wide. We have described only the main methods most often used by investors in a given situation. As we said earlier in our practice, we use the simplest, but quite effective "intuitive" way to determine the rate. The choice of a specific method always remains with the investor. You can learn the whole process of making investment decisions in practice in our courses at. We teach deep analytics techniques already at the second level of training, at advanced training courses for practicing investors. You can evaluate the quality of our training and take the first steps in investing by signing up for ours.
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Consider two main solution concepts actual problem discount rate definitions — and .
The concept of alternative returns
Within the framework, the risk-free discount rate is determined either at the level of deposit rates of banks of the highest reliability category, or equated to the refinancing rate of the Central Bank of Russia (this approach is proposed in the methodological recommendations developed by Sberbank of the Russian Federation). The discount rate can also be determined by the I. Fisher formula.
AT methodological recommendations various discount rate types. commercial norm are usually determined taking into account concepts of alternative returns. My own discount rate assessed by project participants. True, in principle, a coordinated approach is also possible, when all project participants are guided by commercial norm discount.
For projects of high social importance, determine the social rate of discount. She characterizes minimum requirements to the so-called public efficiency implementation investment project. It is usually installed centrally.
Calculate also budget discount rate reflecting opportunity cost use budget funds and established by the executive authorities of the federal, subfederal or municipal level.
In each specific case, the level of decision-making depends on the budget from which the given investment project is financed.
The concept of the weighted average cost of capital
It is an indicator that characterizes the cost of capital in the same way as the rate bank interest characterizes the cost of borrowing.
The difference between the weighted average cost of capital and bank rate is that this indicator does not imply equal payments, instead it requires that the total present return of the investor be the same as that would provide a uniform payment of interest at a rate equal to the weighted average cost of capital.
Weighted average cost of capital widely used in investment analysis, its value is used for discounting expected investment returns, project payback calculations, business valuation, and other applications.
Discounting future cash flows at a rate equal to the weighted average cost of capital, characterizes the depreciation of future income in terms of specific investor and subject to its requirements for return on invested capital.
Thus, alternative yield concept and concept of weighted average cost of capital suggest different approaches to determining the discount rate.
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Live in modern world constantly exposes a person to all sorts of tests, including financial ones. Not every person can say with certainty that he is financially secure, because most people, as a rule, have only one source of income - the money they receive for the work they do. And it doesn’t matter if it’s for hire or own business, the important thing is that there is only one source of income. But what if, for some reason, this source ceases to bring money? It is for this reason that some people think about additional sources of income. And for those who do not think, we strongly recommend doing this, because. in the future, and in the present, it can do an excellent service. We'll look at a few options below. alternative sources inflow of finance and some of their nuances.
In general, sources of income can be divided into active and passive. Active ones are those in which we are directly involved in making a profit and make efforts to receive money. Passive are those in which a person practically does not make any efforts to make a profit and his investments (time, effort, money) work for him. Let's figure out which active or passive source income can become additional?
Active additional sources of income
In fact, a situation where there may be a need for additional finance, or simply not enough money earned at the main place of work, can arise for everyone. You can, of course, try to achieve a promotion in your career, an increase in wages, or look for a higher paying place, but it is not a fact that this will succeed. You can try to find a second job, but where to get the time and energy for it, if you are already fully busy? But there is a way out: you need to pay attention to your hidden resources, which in everyday bustle we can simply not notice, which means we don’t use them. They can become the basis of an active additional source of income.
Knowledge
Think about what this moment you have knowledge, but which you do not use to create additional profit. What are you good at? What can you teach? What can you talk about or on what topic can you advise? What ideas did/do you have that you didn't pay enough attention to? Surely you will be able to find something interesting. In addition, if you wish, you can learn something new: take some courses, get a new specialty or a second or even third education, and then use the knowledge gained to make money in a new field.
Technical Resources
One of the most powerful technical resources Today, almost everyone has a home - it's a computer. Usually it is purchased for studying, watching movies, listening to music and other entertainment, but it can also be used as a means of earning money. If you have Internet access and some free time, you can look online for ways to generate additional income. The situation is similar with the presence of a car - it can be used for various kinds of part-time work: as a taxi, for delivering sushi or pizza, etc. Make a list of what you have and see if there is any way you can use it to your advantage.
Hobbies, hobbies, interests, talents
Every person has some distinctive feature: someone writes beautifully, someone understands technology, someone gets along wonderfully with animals. What are you good at doing? Even the simplest ability to embroider or knit beautifully can become an additional source of income. And if you like it, that's even better! What are your hobbies? What are your interests? Can your area of interest serve as a starting point for creating another source of income? Show your imagination, activate your creativity and try to come up with some interesting ideas that you can implement and improve your financial condition.
Time
Time is the most valuable resource that a person has, but which is often completely mediocrely wasted. Analyze what you spend your time on: how many hours a day do you have useless activities? And how much do you spend on finding a new way to earn money? You must learn your time resource: engage in self-development and personal growth, spiritual practices, analyze your knowledge, technical resources, skills, hobbies, hobbies and interests in order to learn how to turn them into money. This, of course, does not mean that you can not relax and have fun. But if you have a need for additional funds, then "business - time, fun - an hour."
So, with active additional sources of income, we figured it out. The main direction of work is now clear and if you wish, you can find some other interesting active way to earn money. Let's move on to passive sources.
Passive additional sources of income
Oddly enough, the very concept passive income quite unusual for Russians, although in the West they have known him for a long time, and in some schools they even teach financial literacy. In our country, this topic has been studied very little. And this is mainly due to the stereotypes imposed and brought up in the last decades of the last century. On post-Soviet space It was the person who achieved everything that he has, making tremendous efforts, that was considered successful. However, at all times the most successful, wealthy and wealthy have always been people with such qualities as sharpness of mind, prudence, and able to profit from their investments. But let's leave these arguments for another time, and consider those sources of income that can be considered passive, as well as available to people with low and middle incomes.
Pension
A pension is a regular cash benefit that is paid to people who have reached retirement age who have a disability or who have lost their breadwinner. But, to our great regret, the size of the pension in our country, to put it mildly, leaves much to be desired. Yes, and many people never live to retirement age, and thousands of pensions go into the "bottomless abyss" of our state. That is why only not the families of those people who did not live to see their retirement? Interest Ask. In general, no matter how ridiculous it may sound, a pension is a source of additional passive income.
Bank account
Anyone can open a bank account and deposit money into it at interest. And this can already be considered a source of passive income. But there are a few things to consider here. If the invested amount is small, then the interest of the bank, taking into account inflation, often only contributes to saving money and saving them from depreciation, i.e. it cannot be called a source of passive income. But if the amount is large and the percentage of accruals exceeds the inflation index, then the capital will constantly grow - this is passive income. In short, in order to make a profit at interest, it is worth putting only large amounts.
Securities
Own securities very profitable, because this allows you to receive a minimum of 10 to 30 percent of profit per year. But it is recommended to engage in securities only with the help of an experienced specialist in this field. He will be able to offer several investment options that will be the most optimal for you. The richest people in the world resort to working with securities, therefore, if there is an opportunity to start acting in this direction, then in no case should it be missed.
big business
Speaking of a big business, it should be borne in mind that its creation requires a considerable investment of time, effort and finance. But the result is worth it. If the company is “strongly on its feet” and it is run by competent people, then it may well become an excellent source of passive income and even allow the person (or group of people) who organized it to go to. The owner should only control the work of the organization and have a plan of action in case of force majeure.
Website on the Internet
If you approach the issue of creating a site seriously and come to grips with its promotion, then after a while it will be able to bring solid profits to its owner. Contextual advertising, affiliate programs and other ways of monetizing the site play a huge role here. It is interesting that a person is able to create a website both with the help of competent specialists (for a substantial fee, of course), and quite independently, having learned this and having studied all the subtleties of the issue.
Royalties
If you can write good book, which will be relevant and in demand by readers, then until the end of your life you will be able to receive royalties from the sales of your work. And this applies not only to books, but also to inventions, ideas, projects, websites and other creations, regardless of the direction of the activity. Just think how much money a man named Seth Wheeler made when he patented toilet paper in 1871?!
In conclusion, I just want to say that if you really want to create an additional source of income (and even more so if there are several), then you will have to seriously think and reconsider many components of your life: habits, beliefs, personal and, of course, apply for this a lot of effort. And although it is not easy, but it is worth it. You just need to want it - everything is in your hands!
Estimating cash flows and bringing them to one point in time can be done on a nominal or real basis.
Nominal cash flows and memorial rates. Nominal cash flows - it sums of money, expressed in prices that change due to inflation, i.e. payments that will actually be paid or received at various future points (intervals) of time. When calculating them, a constant increase in the price level in the economy is taken into account, and this affects the monetary assessment of the costs and results of making an investment decision (Fig. 3.3).
For example, having decided to implement a project of opening a mini-bakery for baking and selling bakery products, we must take into account the projected increase in prices for bread, flour, etc. in the calculations of expected cash flows. over the life of the project and index the cash flows accordingly raising coefficient.
Rice. 3.3.
Nominal rate of alternative (required) return is the rate that actually exists in the market for investment decisions of a given level of risk. During a period of high inflation, such rates increase in order to compensate investors for losses from inflationary price increases due to increased income. Conversely, nominal rates are relatively low during periods of price stabilization. Based on this, these rates are said to include inflation premium.
Real cash flows and real discount rates. Real cash flows - these are flows expressed at a constant price scale in effect at the time the investment decision is justified. Thus, they are estimated without taking into account inflationary price increases (Fig. 3.4). However, cash flows should still be indexed by a decreasing or increasing coefficient if they (or their individual elements) grow faster or slower than inflation.
Rice. 3.4.
The real rate of the alternative (required) return is this is the rate "cleared" of the inflation premium. It reflects the part of the investor's income that is formed in excess of compensation for inflationary price increases.
Real rate (g) calculated by the formula
where gr - real rate; G - nominal rate; to - inflation rate. All rates are expressed in fractions of a unit.
Example. The bank interest rate on deposits is 6%, and inflation during this period is expected to be at the level of 10%. What is the real rate of return offered by the bank?
Real cash flows are discounted at real rates, nominal - at nominal.
The basic calculation rule is that:
- o real cash flows should be discounted at real alternative rates of return;
- o Nominal cash flows should be discounted using nominal discount rates.
Thus, there are two approaches to estimating cash flows, each of which has its pros and cons.
Advantages and disadvantages of the valuation method at constant (fixed) prices. The advantage of valuation on a real basis is that with an aggregated calculation of cash flows there is no need to predict future inflationary price growth - it is enough to know the current inflation rate and current current period prices. At the same time, to carry out such a calculation, more or less strict fulfillment of the following hypothesis is necessary: all prices for products, raw materials, materials, etc., taken in determining cash flows, change in the same proportion in accordance with the level of inflation in the economy. Another "minus" - with this approach, there are difficulties in analyzing project financing systems (interest rates on loans provided for the implementation of an investment decision must also be brought to real rates, which gives rise to distrust of the results of the calculation on the part of creditors). For example, they give money at 14% per annum, and the real rate appears in the calculations - 4%. In addition, the budget of the project, drawn up on a nominal basis, looks more realistic.
Let's consider a principled approach to valuation on a real and nominal basis using an example.
Example. The manager of the company assumes that the project will require investments in the amount of 350 million rubles. and in the first year of implementation will give a cash flow of 100 million rubles. In each subsequent year for five years, cash flow will increase by 10% due to inflationary growth in product prices and costs. For the sixth and final year, a total cash flow of 123 million rubles will be received from the sale of equipment. It needs to be determined whether it is beneficial this project if the nominal rate of opportunity return is 20% per annum.
Cash flow for the project, taking into account inflationary growth is shown in Table. 3.6.
TABLE 3.6.
Net present value is calculated as follows:
ypy> Oh, so the project is profitable.
We will evaluate the same project on a real basis. The real alternative rate of return is calculated by the formula
According to the condition, only inflationary growth in prices is expected. Therefore, the subsequent cash flow up to the sixth year will be stable and equal to 100: 1.1 = 90.91 million rubles. Cash flow last year, calculated on a constant price scale, is equal to
As can be seen, both methods gave almost the same result, which is explained by the same assumptions laid down in the conditions of the example for both approaches (the discrepancies are related to the approximation error allowed in the calculations).
