Let's consider two main solution concepts actual problem determining the discount rate — And .
Alternative Return Concept
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 is equal to the refinancing rate Central Bank Russia (this approach was proposed in the methodological recommendations developed by Sberbank of the Russian Federation). The discount rate can also be determined using I. Fisher’s formula.
IN Methodical recommendations various types of discount rates. Commercial norm, as a rule, is determined taking into account alternative income concepts. My own discount rate project participants evaluate independently. True, in principle, a coordinated approach is also possible, when all project participants are guided by the commercial discount rate.
For projects with high social significance, determine social norm discount. It characterizes the minimum requirements for the so-called social efficiency of the implementation of an investment project. It is usually installed centrally.
They also calculate budget discount rate, reflecting opportunity cost use budget funds and installed executive bodies authorities at the federal, subfederal or municipal level.
In each specific case, the level of decision-making depends on which budget finances the investment project.
Weighted average cost of capital concept
It is an indicator that characterizes the cost of capital in the same way that the bank interest rate characterizes the cost of borrowing a loan.
The difference between the weighted average cost of capital and the bank rate is that this indicator does not imply straight-line payments, but instead requires that the investor's total present return be the same as what would be provided by a straight-line 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 to discount expected returns from investments, calculate the return on projects, in business valuation and other applications.
Discounting futures cash flows with a rate equal to the weighted average cost of capital, characterizes the depreciation of future income from the point of view of a particular investor and taking into account his requirements for the return on invested capital.
Thus, alternative income concept And weighted average cost of capital concept suggest different approaches to determining the discount rate.
We carry out classical fundamental analysis ourselves. We determine the fair price using the formula. We make an investment decision. Features of fundamental analysis of debt assets, bonds, bills. (10+)
Classical (fundamental) analysis
Universal fair price formula
Classical (fundamental) analysis is based on the premise that the investee has a fair price. This price can be calculated using the formula:
Si is the amount of income that will be received from investing in the i-th year, counting from the current moment to the future, ui is the alternative return on investment for this period (from the current moment to i-th payments amounts).
For example, you purchase a bond that matures in 3 years with a lump sum payment of the entire principal amount and interest on it. The amount of payment on the bond together with interest will be 1,500 rubles. We will determine the alternative return on investment, for example, by the return on a deposit in Sberbank. Let it be 6% per annum. The alternative return will be 106% * 106% * 106% = 119%. The fair price is equal to 1260.5 rubles.
The given formula is not very convenient, since alternative returns are usually assumed by year (even in the example we took the annual return and raised it to the third power). Let's convert it to annual alternative return
here vj is the alternative return on investment for the jth year.
Why aren't all assets worth their fair price?
Despite its simplicity, the above formula does not allow one to accurately determine the value of the investment object, since it contains indicators that need to be predicted for future periods. We do not know the alternative return on investments in the future. We can only guess what rates will be on the market at that moment. This introduces especially large errors for instruments with long or no maturities (shares, consoles). With the amount of payments, too, not everything is clear. Even for debt securities (fixed income bonds, bills, etc.), for which, it seems, the payment amounts are determined by the terms of issue, actual payments may differ from the planned ones (and the formula contains the amounts of real, not planned payments ). This occurs during a default or debt restructuring where the issuer is unable to pay the entire amount promised. For equity securities (shares, interests, shares, etc.), the amounts of these payments generally depend on the company's future performance, and accordingly, on the general economic conditions 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 influencing the fair price. Based on this formula, formulas can be developed for approximate assessment of the asset price.
Estimation of the fair price of a debt asset (with fixed payments), bonds, bills
In the new formula, Pi is the amount promised to be paid in the corresponding period, ri is a discount based on our assessment of the reliability of the investment. 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 fair price estimate will be 1134.45 rubles.
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Financial and economic calculations most often involve the assessment of cash flows distributed over time. Actually, for these purposes a discount rate is needed. From the point of view of financial mathematics and investment theory, this indicator is one of the key ones. Methods are built on it investment assessment 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. Today, 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 methods for justifying this rate, let’s understand its economic and mathematical essence. Actually, two approaches are used to define the term “discount rate”: conventionally mathematical (or process), and economic.
The classic definition of the discount rate comes 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 reduce the value of future cash flows to their current cost equivalent. The fact is that many factors influence the depreciation of future income: inflation; risks of non-receipt or shortfall of income; loss of profit arising when a more profitable alternative investment opportunity appears cash in the process of implementing a decision already made by the investor; systemic factors and others.
By applying the discount rate in his calculations, the investor brings 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 distributed over time.
However, one should not confuse the discount rate and the discount factor. The discount factor is usually operated in the calculation process as a certain intermediate value, calculated on the basis of the discount rate using the formula:
where t is the number of the forecast period in which cash flows are expected.
The product of the future 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, the economic principle is applied, 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 implement his “project” only if its profitability turns out to be higher than the alternative one available on the market. This is not an easy task, since it is very difficult to compare investment options by risk level, especially in conditions of lack 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 itself. The investor assesses the remaining risks independently, usually based on expert assessment.
There are many models for justifying the discount rate, but they all correspond in one way or another to this basic fundamental principle.
Thus, the discount rate always consists of the risk-free rate and the total investment risk of a particular investment asset. The starting point in this calculation is the risk-free rate.
Risk-free rate
The risk-free rate (or the risk-free rate of return) is the expected rate of return on assets for which its own financial risk equal to zero. In other words, this is the yield on absolutely reliable investment options, for example, on financial instruments whose profitability 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 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, emergency man-made and natural events, etc.
Therefore, the risk-free rate reflects the minimum possible return acceptable to the investor. The investor must choose the risk-free rate for himself. You can calculate the average bet from several potentially risk-free investment options.
When choosing a risk-free rate, an investor must take into account the comparability of his investments with the risk-free option according to such criteria as:
The scale or total cost of the investment.
Investment period or investment horizon.
The physical possibility of investing in a risk-free asset.
Equivalence of denominated rates in foreign currency, and others.
Return rates on time ruble deposits in banks of the highest reliability category. In Russia, such banks include Sberbank, VTB, Gazprombank, Alfa-Bank, Rosselkhozbank and a number of others, a list of which can be viewed on the website of the Central Bank of the Russian Federation. When choosing a risk-free rate using this method, it is necessary to take into account the comparability of the investment period and the period for fixing the deposit rate.
Let's give an example. Let's use the data from the website of the Central Bank of the Russian Federation. As of August 2017, the weighted average interest rates on deposits in rubles for up to 1 year were 6.77%. This rate is risk-free for most investors investing for up to 1 year;
Yield level on Russian government debt financial instruments. In this case, the risk-free rate is fixed in the form of the yield on (OFZ). These debt securities are issued and guaranteed by the Ministry of Finance of the Russian Federation, and therefore are considered the most reliable financial asset in the Russian Federation. With a maturity of 1 year, OFZ rates are at current moment from 7.5% to 8.5%.
Yield level on foreign government securities. IN in this case The risk-free rate is equal to the yield on US government bonds with maturities from 1 to 30 years. Traditionally, the US economy is assessed by international rating agencies at highest level reliability, and, consequently, the yield of their government bonds is considered risk-free. However, it should be taken into account that the risk-free rate in this case is denominated in dollar rather than ruble equivalent. Therefore, to analyze investments in rubles, an additional adjustment is necessary for the so-called country risk;
Yield level on Russian government Eurobonds. This risk-free rate is also denominated in dollar terms.
Key rate of the Central Bank of the Russian Federation. At the time of writing this article, the key rate is 9.0%. This rate is considered to reflect the price of money in the economy. An increase in this rate entails an increase in the cost of the loan and is a consequence of an increase in risks. This tool should be used with great caution, since it is still a guideline and not a market indicator.
Interbank lending market rates. These rates are indicative and more acceptable compared to 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 in nature and represent the profitability of 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 should be taken into account and how.
The following parameters have the greatest impact on the risk premium and, ultimately, the discount rate:
The size of the issuing company and the stage of its life cycle.
The nature of the liquidity of the company's shares on the market and their volatility. The most liquid stocks generate the least risk;
Financial condition issuer of shares. A stable financial position increases the adequacy and accuracy of forecasting the company's cash flow;
Business reputation and market perception of the company, investor expectations regarding the company;
Industry affiliation and risks inherent in this industry;
The degree of exposure of the issuing company’s activities to macroeconomic conditions: inflation, fluctuations 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.
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's briefly look at 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 as follows (from simple to complex):
Conventionally “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 method is the simplest. The choice of discount rate in this case is not mathematically justified in any way and represents only the investor’s desire, or his preference about 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 information about the profitability of alternative investments is known to him.
Most often, the discount rate is “intuitively” calculated approximately by multiplying the risk-free rate (as a rule, this is simply the rate on deposits 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 values of companies in which we plan to invest, we typically use the following rate: the average deposit rate multiplied by 2 if we are talking about blue chips and apply more high odds, if we are talking about 2nd and 3rd tier companies.
This method is the easiest for a private investor to practice and is used even in large investment funds by experienced analysts, but it is not held in high esteem among academic economists because it allows for “subjectivity.” In this regard, in this article we will give an overview of other methods for determining the discount rate.
Calculation of discount rate based on expert assessment
The expert method is used when investments involve investing in shares of companies in new industries or activities, startups or venture funds, and also when there is no adequate market statistics or financial information about the issuing company.
The expert method for determining the discount rate consists of surveying and averaging the subjective opinions of various specialists about the level, for example, of the expected return on a specific investment. The disadvantage of this approach is the relatively high degree of subjectivity.
You can increase the accuracy of calculations and somewhat level out subjective assessments by decomposing the bet into a risk-free level and risks. The investor chooses the risk-free rate independently, and the assessment of the level of investment risks, the approximate content of which we described earlier, is 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 using analytical methods
There are quite a lot of analytical ways to justify the discount rate. All of them are based on theories of firm economics and financial analysis, financial mathematics and business valuation principles. Let's give a few examples.
Calculation of the discount rate based on profitability indicators
In this case, the justification for the discount rate is carried out on the basis of various profitability indicators, which in turn are calculated based on data and. The profitability indicator is used as a base equity(ROE, Return On Equity), but there may be others, for example, return on assets (ROA, Return On Assets).
Most often it is 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 (constant dividend growth model)
This method of calculating the discount rate is acceptable for companies paying dividends on their shares. This method requires the fulfillment of several conditions: payment and positive dynamics dividends, no restrictions on the life of the business, stable growth of the company's income.
The discount rate in this case is equal to the expected return on the company's equity capital and is calculated using the formula:
This method is applicable for assessing investments in new company projects by shareholders of this business who do not control profits, but only receive dividends.
Calculation of the discount rate using quantitative analysis methods
From the perspective 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:
Cumulative construction models.
Capital asset pricing models CAPM (Capital Asset Pricing Model).
WACC (Weighted Average Cost of Capital) models.
Most of these models are quite complex and require certain mathematical or economic skills. We will consider general principles and basic calculation models.
Cumulative construction model
Within 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 justifying the discount rate based on risk premiums to the risk-free level of return is used when it is difficult or impossible to assess the relationship between risk and return on investment in the business being analyzed using mathematical statistics. IN general view The calculation formula looks like this:
CAPM Capital Asset Pricing Model
The author of this model is Nobel laureate in Economics W. Sharp. The logic of this model is no different from the previous one (the rate of return is the sum of the risk-free rate and risks), but the method for assessing investment risk is different.
This model is considered fundamental because it establishes the dependence of profitability on the degree of its exposure external factors market risk. This relationship is assessed through the so-called “beta” coefficient, which is essentially a measure of the elasticity of an asset’s return to changes in the average market return of similar assets on 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 the average return on the market of similar investment assets.
If the “beta” coefficient is above 1, then the asset is “aggressive” (more profitable, changes faster than the market, but also more risky in relation to its analogues on the market). If the beta coefficient is below 1, then the asset is “passive” or “defensive” (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 discount rate based on WACC model
Estimating the discount rate based on the company's weighted average cost of capital allows us to estimate the cost of all sources of financing its activities. This indicator reflects the company’s actual costs for paying for borrowed capital, equity capital, and other sources weighted by their share in general structure passive. If a company's actual profitability is higher than the 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 WACC indicator is calculated using 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” method of determining the rate. The choice of a specific method always remains with the investor. You can learn the entire process of making investment decisions in practice in our courses at. We teach in-depth analytical techniques already at the second level of training, in advanced training courses for practicing investors. You can evaluate the quality of our training and take your first steps in investing by signing up for our courses.
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Profitable investments for you!
When assessing effectiveness investment projects theory, in some cases 1, recommends using WACC as a discount rate. In this case, it is proposed to use the profitability of alternative investments (projects) as the price of equity capital. Alternative return (profitability) is a measure of lost profits, which, according to the concept of alternative costs based on the ideas of Friedrich von Wieser on the marginal utility of costs, are considered as expenses when evaluating options for investment projects proposed for implementation. At the same time wide circle The authors understand alternative income as the profitability of projects that have low risk and guaranteed minimum profitability. Examples are given - lease of land and buildings, foreign currency bonds, time deposits of banks, government and corporate securities with low risk, etc.
Therefore, when evaluating two projects - analyzed A and alternative B, we must subtract the profitability of project B from the profitability of project A and compare the result obtained with the profitability of project B, but taking into account the risks.
This method allows us to make more intelligent decisions about the advisability of investing in new projects.
For example:
The profitability of project A is 50%, the risk is 50%.
The profitability of project B is 20%, the risk is 10%.
Let us subtract the profitability of project B from the profitability of project A (50% - 20% = 30%).
Now let’s compare the same indicators, but taking into account the project risks.
Profitability of project A = 30% * (1-0.5) = 15%.
The profitability of project B is 20% * (1-0.1) = 18%.
Thus, wanting to get an additional 15% return, we risk half of our capital invested in the project. At the same time, by implementing familiar and therefore low-risk projects, we guarantee ourselves an 18% return and, as a result, the preservation and increase of capital.
The approach to investment evaluation described above, justified by the theory of opportunity costs, is quite reasonable and is not rejected by practitioners.
But, can alternative income be considered as capital raising costs when calculating WACC?
In our opinion no? Despite the fact that we subtracted the income of the alternative project B from the income of the evaluated project A, conditionally considering them as expenses of project A, they did not cease to be income.
The calculation discussed in table No. 1 only says that in order to fulfill your desire to receive a return of 15%, you need to ensure a return on assets of 11.5% or higher. We emphasize once again that a profitability of 15% is only your desire.
But is this your cost of equity? Maybe they are only 5% of your invested capital and why wouldn't you be happy with a 10% return like Molly?
In this case, the weighted cost of capital will not be 11.5%, but 9%, but there is income! There is profit! (9% minus 5%).
Reduce your expenses on capital, get more of it from circulation and get rich!
So how can you reduce the cost of raising equity capital to zero? Can. And this is not sedition, if you look closely at what we mean by the term “expenses”.
Expenses are not the amounts transferred by you for the goods, not the money paid to employees and not the cost of raw materials included in the costs of manufactured and sold products. All this does not take away your property, your benefits.
Expenses are a decrease in assets or an increase in liabilities.
The owner, when using his own capital, will incur expenses in two cases:
1. Payments from profits, for example: dividends, bonuses and other payments, such as taxes, etc.
2. If part or all of the equity capital is not involved in business turnover.
Let's look at this in more detail.
Let us turn to the mentioned concept of opportunity costs and the theory of the relationship between the cost of money and time.
The concept of opportunity costs suggests using as their income the income from investments in a business that has least risk and guaranteed profitability. If we continue this logic, it becomes clear that the least risk will occur if we refuse to invest in this business. At the same time, the income will be the least. They will both be zero.
Of course, financial analysts, and simply sensible people, will immediately say that both real and relative loss of assets due to inactivity will be inevitable.
Real costs are caused by the need to maintain the quantitative and qualitative safety of capital.
Relative costs are associated with changes in the market price of assets and changes in the welfare of the company under study, relative to the welfare of other entrepreneurs.
If your capital does not work, but your neighbor’s capital functions properly and brings him income, then the greater this income, the richer the neighbor becomes relative to you. Together with your neighbor, you will receive a certain average profitability for your business, which is precisely a measure of the growth of your neighbor’s wealth and your relative losses. In other words, if you do not provide returns above the market average, then your share in the total volume operating on the capital market has decreased. This means you have incurred expenses.
What will be their size?
The calculation can be done like this.
The cost of capital is equal to the difference between the return on assets in the industry under study and the return on assets of the company.
For example. Return on assets of the manufacturing industry is 8%. Your company's return on assets is 5%. This means you have lost 3%. These are your relative costs. This is the relative price of your capital.
Since industry profitability indicators do not fluctuate significantly, it is quite possible to predict their values using the usual trend.
What does this give us? In our opinion, the following:
1. Greater opportunities for standardizing the calculation of the price of equity capital than using alternative returns, since there are quite a lot of alternative options for investing capital in a business that has low risk and guaranteed profitability.
2. The proposed approach limits liberties, and therefore, in our opinion, increases objectivity when comparing effectiveness various options investment projects.
3. Perhaps this will reduce the mistrust of practitioners in the calculations of financial analysts. The simpler the better.
Let's move on. What happens if the company's return on assets is equal to the industry average? Will the price of equity become zero? Theoretically, yes, if there are no payments from profits. Our well-being relative to the state of the business community will not change. In practice this is unattainable. Since, there are necessarily payments and obligations arise that reduce the amount of our own capital and, accordingly, reduce the assets belonging to us. Even if the enterprise does not operate, it must pay property taxes, etc.
Therefore, the price of a company’s equity capital should consist not only of the price calculated based on the average industry return on assets, but also the price determined on the basis of dividend payments and other payments from profits, possibly including payments to the budget and off-budget funds. It may be appropriate to take into account the costs associated with the stakeholder business model when calculating WACC.
When calculating WACC, factors that reduce the price of capital sources should also be taken into account. For example, the price of such a source of financing as accounts payable is the amount of fines paid by the company for late payments to suppliers. But doesn’t the company receive the same penalty payments from customers for late payments on accounts receivable?
What does the WACC indicator ultimately reflect? In our opinion, it is a measure of the economic efficiency of an existing business or investment project.
A negative WACC indicates efficient work management of the organization, since organizations receive economic profit. The same applies to investment projects.
The WACC value within the range of changes in return on assets from zero to industry average values indicates that the business is profitable, but not competitive.
The WACC indicator, the value of which exceeds the industry average return on assets, indicates an unprofitable business.
So, end of the WACC speculation? No. Corporate mysteries lie ahead.
“If you don’t deceive, you won’t sell, so why frown?
Day and night - a day away. Next, how will it turn out"