Discount rate 10 discount factor. Discount rate: formula and calculation example
Let's touch on such a complex economic term as the discount rate, consider the existing modern methods its calculation and direction of use.
The discount rate and its economic meaning
Discount rate (analogue: comparison rate, rate of return) is the interest rate that is used to revalue future capital at the current moment. This is done because one of the fundamental laws of economics is the constant depreciation of value ( purchasing power, cost) of money. The discount rate is used in investment analysis when an investor decides on the prospect of investing in a particular object. To do this, he leads the future value of the investment object to the present (current). By conducting a comparative analysis, he can decide on the attractiveness of the object. Any value of an object is always relative, so the discount rate is the very basic criterion with which the investment efficiency is compared. Depending on different economic tasks The discount rate is calculated in different ways. Consider the existing methods for estimating the discount rate.
Methods for estimating the discount rate
Let's consider 10 methods for estimating the discount rate for evaluating investments and investment projects of an enterprise/company.
- CAPM Capital Asset Valuation Models;
- Modified CAPM Capital Asset Valuation Model;
- Model by E. Fama and K. French;
- Model M. Carhart;
- Dividend Model constant growth(Gordon);
- Calculation of the discount rate based on the weighted average cost of capital (WACC);
- Calculation of the discount rate based on return on equity;
- Market multiplier method
- Calculation of the discount rate based on risk premiums;
- Calculation of the discount rate based on expert assessment;
Calculation of the discount rate based on the CAPM model
Capital asset valuation model - CAPM ( CapitalassetPricingModel) was proposed in the 1970s by W. Sharp (1964) to estimate the future return on shares/capital of companies. The CAPM reflects future returns as a risk-free return and a risk premium. As a result, if the expected return on a stock is lower than the required return, investors will refuse to invest in this asset. The factor that determines the future rate in the model was taken as market risk. The formula for calculating the discount rate for the CAPM model is as follows:
where: r i – expected return on shares (discount rate);
r f is the yield on a risk-free asset (for example: government bonds);
r m - market return, which can be taken as the average return on the index (MICEX, RTS - for Russia, S & P500 - for the USA);
β is the beta coefficient. It reflects the riskiness of an investment in relation to the market, and shows the sensitivity of changes in stock returns to changes in market returns;
σ im is the standard deviation of the change in stock return depending on the change in market return;
σ 2 m is the dispersion of the market return.
Advantages and Disadvantages of the CAPM Capital Asset Pricing Model
- The model is based on the fundamental principle of the relationship of stock returns market risk, which is its advantage;
- The model includes only one factor (market risk) to estimate the future performance of a stock. Researchers such as Y. Fama, K. French and others introduced additional parameters into the CAPM model to increase its forecasting accuracy.
- The model does not take into account taxes, transaction costs, stock market opacity, etc.
Calculation of the discount rate according to the modified CAPM model
The main disadvantage of the CAPM model is its single-factor approach. Therefore, adjustments for unsystematic risk are also included in the modified capital asset pricing model. Unsystematic risk is also called specific risk, which occurs only under certain conditions. Formula for calculating the modified CAPM model (modifiedCapitalassetPricingModel ,MCAPM) is as follows:
where: r i – expected return on shares (discount rate); r f is the yield on a risk-free asset (for example, government bonds); r m – market profitability; β is the beta coefficient; σ im is the standard deviation of the change in stock return from the change in market return; σ 2 m is the dispersion of market returns;
r u is the risk premium, which includes the non-systematic risk of the company.
As a rule, experts are used to assess specific risks, because they are difficult to formalize by means of statistics. The table below shows the various risk adjustments ⇓.
Specific risks | Risk adjustment, % |
State influence on tariffs | 0,4% |
Changes in prices for raw materials, materials, energy, components, rent | 0,2% |
Management risk of the owner/shareholders | 0,2% |
Influence of key suppliers | 0,3% |
Influence of seasonality of demand for products | 0,4% |
Conditions for raising capital | 0,3% |
In total, the adjustment for specific risk is: | 1,8% |
For example, let's calculate the adjusted discount rate, so if the CAPM model returns 10%, then the risk-adjusted discount rate will be 11.8%. Using the modified model allows you to more accurately determine the future rate of return.
Calculation of the discount rate according to the model of E. Fama and K. French
One of the modifications of the CAPM model was the three-factor model of E. Fama and K. French (1992), which began to take into account two more parameters that affect the future rate of return: company size and industry specifics. Below is the formula for the three-factor model by E. Fama and K. French:
where: r – discount rate; r f is the risk-free rate; r m – profitability of the market portfolio;
SMB t is the difference between the returns of the weighted average portfolios of shares of small and large capitalization;
HML t is the difference between the returns of weighted average stock portfolios with large and small ratios book value to market value;
β, si, h i - coefficients that indicate the influence of parameters r i , r m , r f on the profitability of the i-th asset;
γ is the expected profitability of the asset in the absence of the influence of 3 risk factors on it.
Calculation of the discount rate based on the model of M. Karhat
The three-factor model of E. Fama and K. French was modified by M. Carhart (1997) by introducing the fourth parameter for assessing the possible future profitability of a stock - the moment. The moment reflects the rate of price change for a certain historical period of time, when the fourth parameter is used in the model for assessing the profitability of a stock in the future, it is taken into account that the rate of price change also affects the future rate of return. Below is the formula for calculating the discount rate according to the M. Carhart model:
where: r – discount rate; WMLt - the moment, the rate of change in the value of the stock for the previous period.
Calculation of the discount rate based on the Gordon model
Another method for calculating the discount rate is to use the Gordon model (Constant Growth Dividend Model). This method has some restrictions on its use, because in order to estimate the discount rate, it is necessary that the company issues ordinary shares with dividend payments. Below is the formula for calculating the cost equity enterprises (discount rates):
where:
DIV is the amount of expected dividend payments per share per year;
P is the placement price of shares;
fc is the cost of issuing shares;
g is the growth rate of dividends.
Calculation of the discount rate based on the weighted average cost of capital WACC
Method for estimating the discount rate based on the weighted average cost of capital (eng. WACC, Weighted Average Cost of Capital) one of the most popular and shows the rate of return that should be paid for the use investment capital. Investment capital can consist of two sources of financing: equity and debt. Often, WACC is used both in financial and investment analysis to assess the future return on investment, taking into account the initial conditions for the return (profitability) of investment capital. economic sense calculation of the weighted average cost of capital consists in calculating the minimum allowable level of profitability (profitability, profitability) of the project. This indicator is used to evaluate the investment in an existing project. The formula for calculating the weighted average cost of capital is as follows:
where: r e ,r d – expected (required) return on equity and debt, respectively;
E/V, D/V - share of own and borrowed capital. The sum of own and borrowed capital forms the capital of the company (V=E+D);
t is the income tax rate.
Calculation of discount rate based on return on equity
The advantages of this method lie in the possibility of calculating the discount rate for enterprises that are not listed on the stock market. Therefore, to assess the discount, indicators of return on equity and borrowed capital are used. These indicators are easily calculated by balance sheet items. If the company has both own and borrowed capital, then the indicator is used - return on assets (Return On Assets, ROA). The formula for calculating the return on assets is presented below:
The next of the methods for estimating the discount rate through the return on equity (Return On Equity, ROE), which shows the efficiency/profitability of enterprise (company) capital management. The profitability ratio shows what rate of return the company creates at the expense of its capital. The formula for calculating the coefficient is as follows:
Developing this approach in assessing the discount rate through assessing the return on capital of an enterprise, a more accurate indicator can be used as a criterion for evaluating the rate - the return on capital employed (ROCE,returnOnCapitalEmployed). This indicator, unlike ROE, uses long-term liabilities (through shares). This indicator can be used for companies that have preferred shares in the stock market. If the company does not have them, then the ROE equals ROCE. The indicator is calculated by the formula:
Another variation of the return on equity ratio is the return on average capital employed ROACE (Return on Average Capital Employed).
In fact, this indicator corresponds to ROCE, its main difference lies in the averaging of the cost of capital employed (Equity + long-term liabilities) at the beginning and end of the estimated period. The formula for calculating this indicator:
ROACE can often replace ROCE, for example in the EVA formula. Let us analyze the feasibility of using profitability ratios to assess the discount rate ⇓.
Calculation of the discount rate based on expert judgment
If you want to estimate the discount rate for venture project, then the use of the CAPM, Gordon model and WACC methods is impossible, therefore experts are used to calculate the rate. The essence of expert analysis lies in the subjective assessment of various macro, meso and micro factors that affect the future rate of return. Factors that have a strong influence on the discount rate: country risk, industry risk, production risk, seasonal risk, managerial risk, etc. For each individual project, experts identify their most significant risks and evaluate them using scores. The advantage of this method is the ability to take into account all the possible requirements of the investor.
Discount rate calculation based on market multiples
This method is widely used to calculate the discount rate for enterprises that have issues ordinary shares in the stock market. As a result, the market multiple E/P is calculated, which translates as EBIDA/Price. Advantages this approach lies in the fact that the formula reflects industry risks when assessing a company.
Calculation of the discount rate based on risk premiums
The discount rate is calculated as the sum of the risk-free interest rate, inflation and risk premium. As a rule, this method of estimating the discount rate is carried out for various investment projects, where it is difficult to statistically assess the amount of possible risk / return. The formula for calculating the discount rate, taking into account the risk premium:
where:
r is the discount rate;
r f is the risk-free interest rate;
r p is the risk premium;
I is the percentage of inflation.
The discount rate formula consists of the sum of the risk-free interest rate, inflation, and risk premium. Inflation was singled out as a separate parameter, because the depreciation of money goes on constantly, this is one of the most important laws of the functioning of the economy. Let's consider separately how each of these components can be evaluated.
Methods for estimating the risk-free interest rate
To assess the risk-free one, such financial instruments are used that give profitability at zero risk, that is, absolutely reliable. In reality, no instrument can be considered absolutely reliable, just the probability of losing money when investing in it is extremely small. Consider two methods for estimating the risk-free rate:
- The yield on risk-free government bonds (GKO - government short-term zero-coupon bonds, OFZ - bonds federal loan) issued by the Ministry of Finance of the Russian Federation. Government bonds have the highest reliability rating, so they can be used to calculate the risk-free interest rate. The yield on these types of bonds can be viewed on the website of the Central Bank of the Russian Federation (cbr.ru) and on average it can be taken as 6% per annum.
- Yield on 30-year US bonds. The average yield on these financial instruments is 5%.
Methods for estimating the risk premium
The next component of the formula is the risk premium. Since risks always exist, their impact on the discount rate should be assessed. There are many assessment methods additional risks investments, consider some of them.
Methodology for assessing risk adjustments from Alt-Invest
Alt-Invest's methodology includes in the risk adjustment the following types of risks, presented in the table ⇓.
Methodology of the Government of the Russian Federation No. 1470 (dated 11/22/97) for estimating the discount rate for investment projects
The purpose of this methodology is to evaluate investment projects for implementation public investment. Specific risk and adjustment for them will be calculated through expert assessment To calculate the basic (risk-free) discount rate, the refinancing rate of the Central Bank of the Russian Federation was used, this rate can be viewed on the official website of the Central Bank of the Russian Federation (cbr.ru). The specific risks of the project are assessed by experts in the presented ranges. The maximum discount rate for this method will be 61%.
Risk free interest rate | |
FROM refinancing rate of the Central Bank of the Russian Federation | 11% |
risk premium | |
Specific risks | Risk adjustment, % |
Investments for the intensification of production | 3-5% |
Increasing product sales | 8-10% |
The risk of introducing a new type of product to the market | 13-15% |
R&D costs | 18-20% |
Methodology for calculating the discount rate Vilensky P.L., Livshits V.N., Smolyaka S.A.
Specific risks | Risk adjustment, % |
1. The need to conduct R&D (with previously unknown results) by specialized research and (or) design organizations: | |
duration of R&D less than 1 year | 3-6% |
duration of R&D over 1 year: | |
a) R&D is carried out by one specialized organization | 7-15% |
b) R&D is complex and is carried out by several specialized organizations | 11-20% |
2. Characteristics of the applied technology: | |
Traditional | 0% |
New | 2-5% |
3. Uncertainty in the volume of demand and prices for manufactured products: | |
existing | 0-5% |
new | 5-10% |
4. Instability (cyclicality, seasonality) of production and demand | 0-3% |
5. Uncertainty external environment during the implementation of the project (mining and geological, climatic and other natural conditions, aggressiveness of the external environment, etc.) | 0-5% |
6. Uncertainty in the process of mastering the applied equipment or technology. The possibility for participants to ensure compliance with technological discipline | 0-4% |
Methodology for calculating the discount rate by Ya. Khonko for various classes of investments
The scientist Ya. Honko presented a methodology for calculating risk premiums for various classes of investments/investment projects. These risk premiums are presented in aggregate form, and the investor needs to choose the investment objective and, in accordance with it, the risk adjustment. Below are the aggregate risk adjustments depending on the purpose of the investment. As you can see, with an increase in the size of the risk, the ability of the enterprise / company to enter new markets, expand production and increase competitiveness also increases.
Summary
In this article, we looked at 10 methods for estimating the discount rate that use different approaches and assumptions in the calculation. The discount rate is one of the central concepts in investment analysis, it is used to calculate indicators such as: NPV, DPP, DPI, EVA, MVA, etc. It is used in estimating the value of investment objects, shares, investment projects, management decisions. When choosing an assessment method, it is necessary to take into account for what purposes the assessment is made and what initial conditions. This will allow for the most accurate assessment. Thank you for your attention, Ivan Zhdanov was with you.
The discount rate is the rate of return. The indicator affects both the decision to invest funds and the valuation of the company or separate species business. We calculate the discount rate by several methods and give recommendations to avoid errors in the calculations.
What is a discount rate in simple words
Discounting is value determination cash flows relating to future periods (future income at the moment). For a correct assessment of future income, you need to know the forecast values of revenue, expenses, investments, , the residual value of the property, as well as the discount rate, which is used to evaluate the effectiveness of investments.
From an economic point of view is the rate of return on invested capital required by the investor. In other words, it can be used to determine the amount that an investor will have to pay today for the right to receive the expected income in the future. Therefore, the key decisions depend on the value of the indicator, including when choosing investment project.
Example
When implementing project “A”, the investor receives an income of 500 rubles at the end of the year for three years. When implementing project "B", the investor receives an income at the end of the first and at the end of the second year for 300 rubles, and at the end of the third year - 1100 rubles. The investor needs to choose one of these projects.Assume that the investor has set the rate at 25% per annum. The present value (NPV) of projects "A" and "B" is calculated as follows:
where Pk - cash flows for the period from the 1st to the nth years;
r - discount rate - 25%;
I - initial investment - 500.
NPV A \u003d - 500 \u003d 476 rubles;
NPV B \u003d - 500 \u003d 495.2 rubles.
Thus, the investor will choose project "B". However, if he sets a discounted rate, for example, equal to 35% per annum, then the current costs of projects "A" and "B" will be equal to 347.9 and 333.9 rubles. respectively (the calculation is similar to the previous one). In this case, project "A" is more preferable for the investor.
Therefore, the investor's decision depends entirely on the value of the indicator; if it is more than 30.28% (with this value of NPV A = NPV B), then project “A” is preferable, if less, then project “B” will be more profitable.
VIDEO: How to Calculate Net Present Value in Excel
There are various methods for calculating the discount rate. Consider the main ones in descending order of objectivity.
Calculation of the discount rate using the CAPM method
To calculate the discount rate, the Capital Assets Pricing Model (CAPM) method, which is based on the assessment of the company's capital, works most effectively and accurately in practice. Read more about how to use the CAPM method for calculation in the material of the Financial Director magazine.
Determination of the weighted average cost of capital
Most often, in investment calculations, the discount rate is defined as weighted average cost of capital (weighted average cost of capital - WACC), which takes into account the cost and cost borrowed money. This is the most objective calculation method. Its only drawback is that in practice not all enterprises can use it (this will be discussed below).
Calculation of the cost of equity
For determining cost of equity the long-term asset valuation model is applied ( capital assets pricing model - CAPM).
The discount rate (yield) of equity (Re) is calculated by the formula:
R e \u003d R f + B (R m - R f),
where R f is the risk-free rate of return;
B is a coefficient that determines the change in the price of the company's shares compared to the change in share prices for all companies in this market segment;
(R m – R f) - market risk premium;
R m - average market rates of return on the stock market.
Let us consider in detail each of the elements of the long-term asset valuation model.
Rate of return on investment in risk-free assets (Rf). As risk-free assets, government securities are usually considered. In Russia, these are Russian Eurobonds Russia-30 with a maturity of 30 years.
B factor. This ratio reflects the sensitivity of the returns on securities of a particular company to changes in market (systematic) risk. If B = 1, then the fluctuations in the prices of the shares of this company completely coincide with the fluctuations of the market as a whole. If B = 1.2, then we can expect that in the event of a general rise in the market, the value of the shares of this company will rise 20% faster than the market as a whole. Conversely, in the event of a general decline, the value of its shares will decline 20% faster than the market as a whole.
In Russia, information on the values of the B-coefficients of companies whose shares are the most liquid can be found in information releases rating agency AK & M, as well as on its website in the "Ratings" section. In addition, B-factors are calculated by analytical services investment companies and large consulting firms such as Deloitte & Touche CIS.
Market risk premium (R m - R f). This is the amount by which the average market rate of return in the stock market exceeded the rate of return on risk-free securities for a long time. It is calculated on the basis of statistical data on market premiums over an extended period. According to Ibbotson Associates, the long-term expected market premium, based on data on the difference between the arithmetic average returns in the stock market and the return on risk-free investments in the US from 1926 to 2000, is 7.76%. This value can be used for calculations and Russian companies(in a number of textbooks, the market risk premium is assumed to be 5%).
WACC Calculation
If a project is financed not only by its own capital, but also by borrowed capital, then the profitability of such a project should compensate not only for the risks associated with investment own funds but also the cost of borrowing capital. The cost of both own and borrowed funds can be taken into account using the weighted average cost of capital (WACC), which is calculated by the formula:
WACC \u003d R e (E / V) + R d (D / V) (1 - t c),
where R e - the rate of return on own (share) capital, calculated, as a rule, using the CAPM model;
E - market value of own own (share) capital. Calculated as product total ordinary shares of the company and the price of one share;
D - market value of borrowed capital. In practice, it is often determined by financial statements as the company's loans. If this data cannot be obtained, then available information on the ratio of equity and debt capital of similar companies is used;
V = E + D - the total market value of the company's loans and its share capital;
R d - the rate of return on the borrowed capital of the company (the cost of raising borrowed capital). These costs include interest on bank loans And corporate bonds companies. At the same time, the cost of borrowed capital is adjusted taking into account the income tax rate. The meaning of the adjustment is that interest on servicing loans and borrowings is charged to the cost of production, thereby reducing tax base on income tax;
t c - income tax rate.
Example
Let's calculate the rate using the weighted average cost of capital (WACC) model for the Norilsk Nickel company, taking into account the current conditions in the Russian economy.
For calculations, we will use the following data as of mid-February:
Rf = 8.5% (rate on Russian European bonds);
B = 0.92 (for Norilsk Nickel, according to AK&M rating agency);
(Rm - Rf) = 7.76% (according to Ibbotson Associates).
Thus, the return on equity is equal to:
Re = 8.5% + 0.92 × 7.76% = 15.64%.
E/V = 81% - the share of the market value of equity capital (E) in the total cost of capital (V) of Norilsk Nickel (according to the author).
Rd = 11% is the weighted average cost of borrowing for Norilsk Nickel (according to the author).
D/V = 19% - the share of the company's borrowed capital (D) in the total cost of capital (V).
tc = 24% - income tax rate.
So WACC = 81% x 15.64% + 19% x 11% x (1 - 0.24) = 14.26%.
As we have already noted, not all enterprises can use the approach described above. First, it does not apply to companies that are not public joint-stock companies, therefore, their shares are not traded on stock markets. Secondly, firms that do not have sufficient statistics to calculate their B-factor, as well as those that cannot find an analogue company whose B-factor they could use in their own calculations, will not be able to apply this method. Such companies should use other calculation methods to determine the discount rate.
Risk premium method
One of the most common methods for determining the discount rate in practice is the cumulative method for assessing the risk premium. This method is based on the assumptions that:
- if investments were risk-free, then investors would demand a risk-free return on their capital (i.e., a rate of return corresponding to the rate of return on investments in risk-free assets);
- the higher the investor estimates the risk of the project, the higher the requirements he makes to its profitability.
Based on these assumptions, the so-called “risk premium” must be taken into account in the calculation. Accordingly, the formula will look like this:
R = Rf + R1 + ... + Rn
where R is the discount rate;
Rf is the risk-free rate of return;
R1 + ... + Rn - risk premiums for various risk factors.
The presence of one or another risk factor and the value of each risk premium in practice are determined by an expert.
Determining the discount rate by expert means
The easiest way to determine the discount rate, which is used in practice, is to determine it by expert means or based on the requirements of the investor. The approximate value of the adjustments for the risk of not receiving the income provided for by the project is presented in Table 1.
Table 1. Adjustments for the risk of non-receipt of project revenues
However, it should be taken into account that the expert method will give the least accurate results and may lead to distortion of the project evaluation results. Therefore, when determining the indicator by expert means or by the cumulative method, it is imperative to analyze the sensitivity of the project to a change in the discount rate. Then the investor will be able to more accurately assess the risks and its effectiveness.
Example
Consider conditional projects "A" and "B" from the first example. The results of the analysis of their sensitivity to changes in the discount rate are presented in Table. 2.
table 2. Project Sensitivity Analysis
There are other alternative approaches to the calculation, for example, using the theory of arbitrage pricing or the dividend growth model. However, these theories are quite complex and rarely applied in practice, so they are not considered within the framework of this article.
Practical application issues
When calculating, one must not forget to take into account a number of important points. Otherwise, there is a danger of making mistakes.
The volatility of the capital structure. During the calculation period of the project, the structure may change (for example, as the loan is paid off, the debt decreases and at some point becomes zero). Hence the question: how to calculate the discount rate in such a situation?
To determine a single discount rate for the entire period of the project, I propose to use the optimal capital structure. That is, the optimal ratio of equity and borrowed funds, at which the cost of capital (WACC) is minimal. But it is important to keep in mind that in practice the cost of equity is higher than that of debt, so as leverage increases, WACC decreases. However, as debt obligations grow, the risk of bankruptcy increases and, accordingly, debt service costs increase, and the cost of borrowed capital increases. Accordingly, when a certain level of the ratio of borrowed and own funds is reached, WACC also begins to grow.
Income tax volatility. When determining the cost of capital, taking into account the tax shield, you sometimes encounter the problem of choosing an estimated income tax rate. If during the calculation period the company operates within one of the standard tax regimes, then no questions arise - the statutory tax rate. However, there are cases when the income tax rate is not constant. For example, when a project is taxed at a reduced rate for a certain period of time (most often during the period of repayment of borrowed funds or during the first years of implementation). In this situation, two options can be distinguished.
1. If one rate (for example, preferential) is valid at the beginning of the project and then for a significant part of the time of its implementation (more than half), then you can take it for calculation.
2. If the rate changes periodically and does not remain at the same level for a long time within the billing period, then it is necessary to calculate its weighted average value using the formula:
t is the project implementation period;
T1, T2, …, TN - effective income tax rates for time periods.
If the company has several separate subdivisions falling under tax laws different countries, the rate should be calculated as a weighted average based on several rates and volumes of the taxable base.
where T is the weighted average income tax rate;
p - the total profit of the enterprise (it is recommended to take profit values for the entire period of implementation);
T1, T2, …, TN - effective income tax rates in the territories of various countries;
p1, p2, …, pN - profit in different countries (for calculation it is recommended to take data for the entire period of implementation).
Accounting for inflation. If the project is calculated at inflation-adjusted prices, then nominal rate discounting adds inflation. It can be taken into account in two ways. First: when the rate is calculated for each discounting step separately, then the forecast value of inflation in this time period is added. Second: in the case of calculating a single rate for the entire project calculation period, the average value of the forecast inflation indicator for the project calculation period is added.
Summing up, we note that most enterprises in the process of work are faced with the need to determine the discount rate. Therefore, it should be remembered that the most accurate value of this indicator can be obtained using the WACC method, while other methods give a significant error.
Discounting from the English "discounting" - casting economic values for different periods of time to a given period of time.
If you do not have an economic or financial education behind you, then this term is most likely not familiar to you and is unlikely this definition explains the essence of "discounting", rather - it will confuse even more.
However, it makes sense for a prudent owner of his budget to understand this issue, since each person finds himself in a situation of “discounting” much more often than it seems at first glance.
Discounting - information from Wikipedia
Description of discounting in simple words
What Russian is not familiar with the phrase "know the value of money"? This phrase comes to mind as soon as the line at the checkout approaches, and the buyer once again looks at his grocery basket to remove "unnecessary" goods from it. Still, in our time we have to be prudent and economical.
Discounting is often understood as economic indicator, which determines the purchasing power of money, their value after a certain period of time. Discounting allows you to calculate the amount that you need to invest today in order to receive the expected return some time later.
Discounting as a tool for predicting future profits is in demand among business representatives at the stage of planning the results (profit) from investment projects. Future results may be announced at the beginning of the project or during the implementation of its subsequent stages. To do this, the given indicators are multiplied by the discount factor.
Discounting also "works" in the interests of ordinary person not associated with the world of big investments.
For example, all parents strive to give their child a good education, and, as you know, it can cost a lot of money. Not everyone has it at the time of admission financial opportunities(cash reserve), so many parents think about the "stash" (a certain amount of money spent past the cash register family budget), which can help out in X-hour.
Let's say that in five years your child will graduate from school and decide to enter a prestigious European university. Preparatory courses at this university cost $2,500. You are not sure that you can carve out this money from the family budget without prejudice to the interests of all family members. There is a way out - you need to open a deposit in a bank, for this it would be good to first calculate the amount of the deposit that you must open in the bank now, so that at X hour (that is, five years later) you will receive 2500, provided that the maximum favorable interest, which the bank can offer, say -10%. To determine how much future spending (cash flow) is worth today, we make a simple calculation: Divide $2,500 by (1.10) 2 to get $2,066. This is what discounting is.
Simply put, if you want to know what the value of the amount of money you will receive or intend to spend in the future, then you should "discount" this future amount (income) at the rate of interest offered by the bank. This rate is also called the "discount rate".
In our example, the discount rate is 10%, $2,500 is the amount of the payment (or cash outflow) after 5 years, and $2,066 is the discounted value of the future cash flow.
Discount formulas
All over the world it is customary to use special English terms to denote the current (discounted) and future value: future value (FV) And present value (PV). It turns out that $ 2,500 is FV, that is, the value of money in the future, and $ 2,066 is PV, that is, the value at this point in time.
Formula for calculation discounted value for our example it looks like this: 2500 * 1/(1+R) n = 2066.
General discount formula: PV = FV * 1/(1+R)n
- Factor by which the future value is multiplied 1/(1+R)n, is called the "discount factor",
- R- interest rate
- N is the number of years from a date in the future to the present.
As you can see, these mathematical calculations are not so difficult and not only bankers can do it. In principle, you can give up on all these figures and calculations, the main thing is to capture the essence of the process.
Discounting is the path of cash flow from the future to today - that is, we go from the amount we want to receive after a certain amount of time to the amount that we must spend (invest) today.
Life formula: time + money
Let's imagine another situation familiar to everyone: you have "free" money, and you went to the bank to make a deposit of, say, $2,000. $2,000 deposited in the bank today bank rate 10% tomorrow will cost $2,200, that is, $2,000 + deposit interest 200 (=2000*10%) . It turns out that in a year you will be able to receive 2200 dollars.
If we represent this result in the form of a mathematical formula, then we have: $2000*(1+10%) or $2000*(1,10) = $2200 .
If you deposit $2,000 for a period of two years, that amount will convert to $2,420. We consider: $2000 + interest for the first year $200 + interest for the second year $220 = 2200*10% .
The general formula for increasing the contribution (without additional contributions) for two years looks like this: (2000*1,10)*1,10 = 2420
If you want to extend the term of the deposit, your income on the deposit will increase even more. To find out the amount that the bank will pay you in a year, two or, say, five years, you need to multiply the deposit amount with a multiplier: (1+R) N.
Wherein:
- R is the interest rate expressed as fractions of a unit (10% = 0.1),
- N indicates the number of years.
Discounting and accrual operations
Thus, it is possible to determine the value of the contribution at any time point in the future.
Calculating the future value of money is called "accrual".
The essence of this process can be explained by the example of the well-known expression “time is money”, that is, over time, the monetary contribution grows due to the increment of annual interest. All modern banking system where time is money.
When we discount, we move from the future to today, and when we “increase”, the trajectory of money movement is directed from today to the future.
Both "calculation chains" (both discounting and building up) make it possible to analyze possible changes in the value of money over time.
Discounted Cash Flow Method (DCF)
We have already mentioned that discounting - as a tool for predicting future profits - is necessary to calculate the project's efficiency assessment.
So, when assessing the market value of a business, it is customary to take into account only that part of the capital that is capable of generating income in the future. At the same time, many points are important for the business owner, for example, the time of receipt of income (monthly, quarterly, at the end of the year, etc.); what risks may arise in connection with profitability, etc. These and other features that affect the valuation of a business are taken into account by the DCF method.
Discount coefficient
The method of discounting cash flows is based on the law of the "falling" value of money. This means that over time, money "cheapens", that is, it loses its value compared to its current value.
It follows from this that it is necessary to build on the assessment at the current moment, and correlate all subsequent cash flows or outflows with today. This will require a discount factor (Kd), which is needed to convert future earnings to present value by multiplying Kd by the cash flows. The calculation formula looks like this:
where: r- discount rate, i– time period number.
DCF calculation formula
The discount rate is the main component of the DCF formula. It shows what size (rate) of profit a business partner can expect when investing in a project. The discount rate takes into account various factors, depending on the object of assessment, and may include: inflation component, assessment of capital shares, return on risk-free assets, refinancing rate, interest on bank deposits and not only.
It is generally accepted that a potential investor will not invest in a project whose value will be higher than the present value of the future income from the project. Likewise, an owner would not sell his business for a price that is less than the estimated value of future earnings. As a result of the negotiations, the parties will agree on a market price, which is equivalent to the current value of the projected income.
The ideal situation for an investor is when internal norm the profits (discount rate) of the project are higher than the costs associated with finding funding for the business idea. In this case, the investor will be able to “earn” the way banks do, that is, accumulate money at a reduced interest rate, and invest it in a project at a higher rate.
Discounting and investment projects
The discounted cash flow method is in line with the investment motives of the business.
This means that an investor who invests in a project does not acquire technical or human resources in the form of a team of highly qualified specialists, modern offices, warehouses, high-tech equipment, etc., but the future flow of money. If we continue this thought, it turns out that any business “releases” the only product on the market - this is money.
The main advantage of the discounted cash flow method is that this valuation method, the only one of all existing ones, is focused on the future development of the market, which contributes to the development of the investment process.
One of the most important criteria for evaluating an investment project is the discount factor. High-quality business planning involves the mandatory accounting of changes in the value of money over time, so all future cash flows should be brought to the current state. Let us dwell in more detail on what the discount factor is and how to determine its value.
The concept of the discount factor and its meaning
The cash flow discount factor is a numerical indicator, using which you can understand how much money you can get after a certain time, taking into account the time factor and possible risk. Thus, the cash flows in the future are adjusted to the state on the day of analysis.
In business design, "money now" is always preferable to "money later" because it can be invested in another business and receive income or placed on bank deposit and receive a fixed percentage. Therefore, before investing, the investor must be sure that during the life cycle of the project he will not only not lose money from cheaper money, but will also be able to make a profit.
The time interval during which the undertaking is implemented and brings profit to the participants is set in advance. It, as a rule, is determined by the normative terms of using the installed equipment, after which the technical capabilities of production are exhausted. The objectivity of calculations largely depends on the correct definition of the time frame of the undertaking.
The value of the discount factor is used in different situations:
- efficiency mark economic activity any company;
- calculation of the effectiveness of the investment project;
- consideration of alternative options for investing funds both between different initiatives and within one enterprise (choosing the most promising development path);
- multilateral settlements and lending.
This indicator actually establishes a certain standard of costs or capital receipts when investing it in another endeavor. In other words, the coefficient (or factor) makes it possible to determine the percentage by which the expected income should be multiplied in order to reach a specific amount in relation to the current state.
Method for determining the value of the indicator
Let's take a closer look at how to calculate the discount factor. Usually we are talking about multi-step calculation of prospects and economic efficiency investment undertaking, therefore, brings the volume of the flow to nth step by the time of bringing.
The total cash flow looks like this:
PV = FV * 1/(1+R)n
- PV is the present value;
- FV is the future value.
This formula highlights the component that determines the value of the reduction factor. Actually, the formula for calculating the discount factor looks like this:
CD = 1/(1+R) n
wherein:
- R - set value;
- n is the number of periods (steps), which is the number of years (months) from the future to the current moment.
The resulting index is always less than one. It shows the value of one invested monetary unit(ruble, euro, dollar) after a certain time, subject to the conditions that are accepted for calculation.
the most important integral part to calculate the coefficient is the discount rate, which is also called the discount rate. For its definitions, there are a number of methods based on various principles:
- dividend method (Gordon model);
- the cost of capital assets of the enterprise (the CAPM model and its numerous modifications);
- availability of borrowed and own funds (WACC model);
- return on equity method (ROE, ROA, ROACE, ROCE);
- method of calculating risk premiums (cumulative);
- expert method based on subjective forecasts of specialists.
The rate of inflation, the cost of long-term deposits or loans, the size of the Central Bank, etc. can be taken as the discount rate. In any case, what this criterion will be, the investor decides at his own peril and risk. If the discount rate is set incorrectly or it does not take into account all the main risks, then the reduction factor will also be incorrect. This will give the investor an incorrect forecast, which can lead to losses.
Another component of the formula is the life cycle of an undertaking, that is, the number of considered periods during which the project will generate . The more precisely these two inputs are set, the more accurate the final result will be.
Examples of Calculating Cash Flows Using the Discount Factor
Let's consider an example of calculation. The businessman invests 800 thousand rubles in a new six-year project. According to the business plan presented by the initiator, in 6 years he will be able to receive 1.5 million rubles in a one-time payment. A discount rate of 12% was determined in a cumulative way, while the percentage of the discount rate is recorded when calculating as a part of unity (0.12). Now, using the standard formula, we can calculate the value of the factor:
kd = 1 / (1 + 0,12) 6
kd = 1 / 1,9738
kd = 0,5066
We got a reduction factor of 0.5066. After that, according to the discounting formula, the indicators of the cost of the reduced cash flow are calculated:
PV = FV * 1/(1+R)n.
PV = 1500000 * 0.5066
PV=759900
From the result obtained, one can draw a disappointing conclusion for the investor that under such starting conditions, he should not expect not only profit, but even a simple return on invested money. Therefore, such a proposal should be rejected or proposed to change the main conditions of the project, if it is acceptable (to reduce the implementation period or reduce the discount rate).
Assume that the discount rate in our example is reduced to 10%. In this case, the value of the coefficient will be 0.5645, and the reduced cash flow will increase to 846,750 rubles, which will make the project profitable. A similar situation arises if the implementation period is reduced to 5 years at a rate of 12%: the factor will be 0.5674, and the flow will be 851,100 rubles.
It should be noted that in order to determine the discount factor, there is no need to dive into mathematical formulas every time. To simplify this task, a table of discount coefficients has been developed and is widely used in practice. It is built according to the standard scheme, like the tables of Pythagoras or Bradis, that is, the dimensions are indicated on one axis interest rates, on the other - time intervals. To find the desired indicator, it is enough to find the cell where they intersect, it contains the value of the coefficient with an accuracy of up to ten thousandths (up to the fourth decimal place).
All the above values of the coefficients are taken from this table. This greatly speeds up the calculations and makes it possible to calculate without any extra effort. alternative options development of events.
We considered a problem that provided for the payment of money in one payment after the end of the project. In practice, situations are much more common when payments are made annually. Then, for the correctness of calculations, it is necessary to find the reduction coefficient for each year separately. For example, our investor will receive his one and a half million over 6 years of the life cycle of the initiative at a discount rate of 10% in equal installments of 250 thousand rubles a year (i.e. as an annuity):
Using the formula for annual calculations, you can find the coefficients separately for each period, and then sum them up:
CF 1 | CF2 | CF-N | |||
NPV= | ----- | + | ------ | +...+ | ------ |
(1+ R) | (1+ R) 2 | (1+ R)6 |
PV = 227272 + 206611 + 187828 + 170765 + 155279 + 141083 = 1088838 rubles.
If you use the table of annuity payment coefficients, then it will be enough to multiply the average annual payment by the factor indicated in the desired cell of the table (in this case, it is 4.3553).
PV = 250000 * 4.3553 = 1088825 rubles
Thus, we see that the indicator found by the formula is practically the same as the value determined using the tables (1088838 versus 1088825).
Some features of practical calculations of the reduction factor
In conclusion, I would like to dwell on a few more points related to bringing cash flows that Internet users ask about. In particular, the question arises how to calculate the factor when the step is given in different units, such as years and months, and whether the formulas differ in such calculations.
With a discount period of one month, the coefficient is calculated using the following formula:
1/(1+R) to the extent (Month - 1) / 12,
- R is the discount rate;
- Month – number of the ordinal month of the project.
For an annual reduction period, the following calculation mechanism is used:
1 / (1 + R) to the extent Year - 1,
- Year - the serial number of the year of the life cycle of the undertaking.
If the period is considered quarterly, then for each month of the quarter, an indicator equal to last month in a quarter, that is, for 1, 2 and 3 months, an indicator of 3 months is taken, etc.
Also on the forums they discuss the situation when regulatory authorities sometimes require to calculate the reduction coefficient according to the formula CD = 1/(1+R)^(n-0.5) instead of standard CD = 1/(1+R)^n.
This approach is called the average annual discounting model. Here, discounting is carried out as of the middle of the calendar year (or reduction period), and not at its beginning or end.
Average period discounting is used in cases where there is a constant uniform inflow of money (for example, from work industrial enterprise). Although among experts, opinions on the appropriateness of this method of calculation differ.
The discount factor, due to its flexibility, is widely used by economists and financiers. It shows perspective and potential return individual project in a time period. At the same time, this financial instrument there is a serious drawback: it works well in states with stable markets and well-established market mechanisms. Its application in countries that are characterized by a transition economic model, threatens with significant inaccuracies, since it is very difficult to adequately calculate many risks for finding the discount rate in such conditions.