Everyone knows about deposits and calculation rules. Bank interest is added to the due amount and we get the amount of funds at the end of the period. For example, $1000 was deposited in the bank. at 20% per annum. Calculation of the total amount at the end of the year: 1000 divided by 100% and multiplied by 120% (100% + 20%). Everything is simple and clear.
However, how can you determine how much you need to invest to get 1000 rubles? in a year. For this, a discount rate is used. The concept is used to assess the profitability of a business and long-term investment.
Concept
“Discount” can be translated as a concession for advance payment. Literally, it means bringing an economic indicator for a certain time period to a given period. In the absence of economic education, it is easy to get confused in such terminology. But a prudent owner should look into the issue, since most people are unaware of their participation in “discounting.” For example, a merchant promises to sell goods at a specified price in a year, when a ship with goods arrives.
However, he needs financial resources to purchase goods that will participate in the exchange transaction. There are two ways to get money: go to a banker for a loan or borrow funds from future buyers. The merchant should explain to the latter about the discount rate in simple language. If clients understand, the success of the event will be ensured.
The discount rate is used for the following purposes:
- Calculation of business profitability. An investor must know the size of the profit in the future in order to invest funds with the desired return.
- Evaluation of the organization's activities. Existing profits do not guarantee good profitability.
- Profitability planning. The investment option chosen should have the maximum return compared to alternative options. For example, one business will have a certain profit after 1 year, while another will bring in more money, but only after two years. Both proposals should be compared on the same denominator. For clarity, let's look at a practical example. Two businessmen approached a potential investor. They ask to invest 2 million in their business. The first one promises to return 3 million in two years, the second - 5 million in 6 years. How to calculate the discount rate when attracting borrowed capital?
Discounting in everyday life
Every Russian has thought at least once about the “value of money.” It is especially noticeable when shopping in supermarkets, when you have to remove “unnecessary” goods from the grocery basket. Nowadays it is necessary to be economical and prudent. Discounting is often understood as an economic indicator that shows the purchasing power of money and its value over a certain period of time. Discounting is used to predict profits for investment projects. Future results can be estimated at the beginning of the project or during its implementation when multiplied by the discount factor. But this concept applies not only to investments, but also in everyday life. For example, parents want to pay for their child’s education at a prestigious institution. But not everyone has the opportunity to pay the fee at the time of admission. Then they begin to think about the “stash”, which is intended for hour X. In 5 years, the child is planned to enter a European university. The cost of preparatory courses is 2500 USD. For many, it is unrealistic to allocate such an amount from the family budget without harming the interests of other members. The solution is to open a deposit in a financial institution in advance. But how to determine the deposit amount in order to receive 2500 USD in five years? The deposit rate is 10%. Calculation of the initial amount: 2500/(1+0.1)^5 = 1552 USD This is called discounting.
In simple words, if you want to know the future value of a certain amount, you should “discount” it at a bank rate, which is called the discount rate. In the example given, it is equal to 10%, 2500 USD. - cash flow (payment amount) in 5 years, 1552 USD - discounted value of cash flow.
Discounting will be the opposite of the investment. For example, when investing 100 thousand rubles at 10% per annum, the result is 110 thousand rubles: 100,000* (100% + 10%)/100%.
A simplified calculation of the final amount will help determine the profitability of the investment. However, it is subject to adjustments.
When determining income for a couple of years, they resort to exponentiation. A common mistake is to multiply by the total interest amount to account for "interest on interest." Such calculations are acceptable in the absence of interest capitalization.
To determine the discount rate, you need to find the initial investment amount: multiply the final profit by 100%, and then divide by the amount of 100% increased by the rate. If investments go through several cycles, then the resulting figure is multiplied by their number.
In the international format, the English-language terms Future value and present value are used. In the described example, FV is 2500 USD, PV is 1552 USD. General form of discounting:
PV = FV*1/(1+R)^n
1/(1+R)^n- discount factor;
R- interest rate;
n- number of cycles.
The calculations are quite simple; not only bankers can perform them. But the calculations can be ignored if you understand the essence of the process.
Discounting- change in cash flow from the future to the present, i.e. The path of finance goes from the amount that is required to be received at a certain moment to the amount that will be invested.
Money + time
Let's consider another common situation: there are free funds that you decide to deposit in the bank at interest. Amount - 2000 USD, interest rate - 10%. In a year, the depositor will already have 2200 USD at his disposal, since the interest on the deposit will be 200 USD.
If we bring all this to a general formula, we get:
2000*(100%+10%)/100% = 2000*1.1 = 2200 USD
If you put 2000 USD for 2 years, then the total amount will be 2420 USD:
1 year 2000*1.1 = 2200 USD
Year 2 2200*1.1 = 2420 USD
There is an increase without additional contributions. If the investment period is extended, the income will increase even more. For each move of keeping funds on deposit, the total amount of the deposit for the previous year is multiplied by (1+R) or the initial amount of investment is multiplied by (1+R)^n.
Cumulative method
To simplify the calculations, use a table of coefficients. When using it, you no longer need to calculate the investment amount and profitability using the formula several times. It is enough to multiply the final profit by the coefficient from the table to get the desired investment.
Formula for determining the discount factor:
K = 1/(1+Pr)^B,
Where IN- number of cycles;
Pr- interest rate per cycle.
For example, for a two-year investment at 20%, the coefficient is:
1*/(1+0,2)^2 = 0,694
Discounting tables are similar to Bradis tables, which help students identify roots, cosines, and sines.
Discount factor tables make calculations easier. However, this calculation method is not suitable for large investments. The given values are rounded to thousandths (3 decimal places), which leads to a large error when investing in millions.
Using the table is simple: if the rate and the number of periods are known, the required coefficient is found at the intersection of the required columns and rows.
Practical use
When the discount rate increases, the payback period for investments increases. The decision to invest funds should be made when calculations show the desired payback period and correspond to the capital investment plan.
A simplified calculation is made using the return on investment period formula. It is based on the quotient between funds received and invested. The main disadvantage of this method is that the assumption of uniform income is applied.
The given formulas do not take into account market risks. They can only be used for theoretical calculations. To bring the calculation closer to reality, they resort to graphical analysis. The graphs present data on the movement of finances in a certain time interval.
Discounting and escalation
Using a simple formula, the size of the contribution is determined at the desired time point. Calculating the future value of money is called “accretion.” The essence of this process is easy to understand from the expression “time is money” - over time, the size of the deposit increases by the size of the increment with annual interest. The entire banking system is based on this principle.
When discounting, the movement of calculations goes from the future to the present, and when “building up” - from the present to the future.
Discounting and building up help analyze the possibility of changes in the value of funds.
Investment projects
Discounting of funds corresponds to the investment motives of the business. That is, the investor invests money and receives not human (qualified specialists, team) or technical resources (equipment, warehouses), but a flow of money in the future. A continuation of this thought would be “the product of any business is money.” The discounting method is the only one that exists, the orientation of which is aimed at development in the future, which allows the investment project to develop.
An example of choosing an investment project. The owner of funds (600 rubles) was asked to invest them in the implementation of projects “A” and “B”. The first option gives an income of 400 rubles for three years. Project “B” after the first two years of implementation will allow you to receive 200 rubles, and after the third - 10,000 rubles. The investor determined the rate to be 25%. Let's determine the current cost of both projects:
project “A” (400/(1+0.25)^1+400/(1+0.25)^2+400/(1+0.25)^3)-600 = (320+256+204 )-600 = 180 rubles
project “B” (200/(1+0.25)^1+200/(1+0.25)^2+1000/(1+0.25)^3)-600 = (160+128+512 )-600 = 200 rubles
Thus, the investor must choose the second project. However, if the rate increases to 31%, both options will be equivalent.
Present value
Present value is the present value of a future cash flow or future payment without the prepayment “discount.” It is often called present value - future cash flow relative to today. However, these are not exactly the same concepts. It is possible to bring not only one future value to the current time, but also the present value to the desired time in the future. Present value is more extensive than discounted value. In English there is no concept of present value.
Discounting method
It was previously mentioned that discounting is a tool for predicting future profits - assessing the effectiveness of a current project.
When evaluating a business, they take into account that part of the assets that are capable of generating income in the future. Business owners take into account the time it takes to generate income and the likely risks to making a profit. The listed factors are taken into account when assessing using the DCF method. It is based on the principle of “falling” value - the money supply constantly “gets cheaper” and loses value. The starting point will be the present value against which future cash flows are related. For this purpose, the concept of discount factor (K) was introduced, which helps to bring future flows to current ones. The main component of the DCF method is the discount rate. It determines the rate of return when investing in a business project. The discount rate can take into account various factors: inflation, refinancing rate, valuation of capital shares, interest on deposits, return on risk-free assets.
It is believed that an investor should not finance a project if its cost becomes higher than the present value of future earnings. Likewise, a business owner will not sell his assets for less than the price of future earnings. During negotiations, the two parties will come to a compromise in the form of the equivalent value on the day of the transaction of the projected assets.
An ideal investment option if the discount rate (internal rate of return) is greater than the cost of finding financing for the business idea. This will allow you to earn like banks - money will be accumulated at a reduced rate, and the deposit will be made at a higher rate.
Additional calculations
Determining the discount rate is inaccurate without analyzing some terms and concepts:
- The rate of return is the amount of investment at which the amount of net present income will be 0.
- Net cash flow - costs are subtracted from total gross receipts. Direct and indirect expenses (tax deductions, legal support) should be included here.
Only an expert can determine the exact value of a company’s profitability, based on the company’s internal analysis.
Advanced calculations
In economics, a somewhat complicated calculation is used, which takes into account a number of risks. The formulas use the following concepts:
- Risk-free, expected and market returns. Used in the Sharpe formula to determine economic risks.
- Adjusted Sharpe model. Determines the influence of market factors: changes in the cost of resources, government policy, price fluctuations.
- Amount of capital investment, features of the industry. The data is used in a more accurate version of French and Fama.
- Changes in the value of an asset are used in the Carhart formula.
- Dividend payments and issue of shares. Similar calculations are due to Gordon. His method allows you to accurately study the stock market and analyze the value of joint stock companies.
- Weighted average price. Apply before determining the discount rate in the cumulative method and accounting for borrowed funds.
- Profitability of property. They are used to analyze the financial activities of a company whose assets are not listed on the stock market.
- Subjective factor. Used in multifactor analysis of an organization’s activities by third-party experts.
- Market risks. Taken into account when determining the discount rate based on the ratio of risky to risk-free investment.
In 1997, the Russian government published its own methodology for calculating the risk discount rate. Experts at the time estimated the risks at 47%. This indicator is not used in conventional formulas, but it is mandatory when calculating investments in foreign projects.
Various calculation methods allow you to evaluate potential investments and build a plan for the allocation of financial resources. When analyzing the economic activities of companies on the market, theoretical calculations will give the expected effect if local realities are taken into account. Simple calculations will help predict profitability, but it will be highly subject to fluctuations. For forecasting, you need to use complex formulas that take into account most risks in the financial and stock markets. More accurate data will be obtained only through internal analysis of the company.
Let's touch on such a complex economic term as the discount rate, consider existing modern methods for calculating it and areas of use.
Discount rate and its economic meaning
Discount rate (analog: comparison rate, rate of return)- This is the interest rate that is used to reestimate the value of future capital at the current moment. This is done due to the fact that one of the fundamental laws of economics is the constant depreciation of the value (purchasing power, cost) of money. The discount rate is used in investment analysis when an investor decides about the prospect of investing in a particular object. To do this, he reduces 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 acts as the basic criterion with which the effectiveness of an investment is compared. Depending on different economic objectives, the discount rate is calculated differently. Let's consider existing methods for estimating the discount rate.
Methods for estimating discount rates
Let's consider 10 methods for estimating the discount rate for evaluating investments and investment projects of an enterprise/company.
- Capital Asset Valuation Models CAPM;
- Modified capital asset valuation model CAPM;
- Model by E. Fama and K. French;
- Model M. Carhart;
- Constant Growth Dividend Model (Gordon);
- Calculation of discount rate based on weighted average cost of capital (WACC);
- Calculation of discount rate based on return on equity;
- Market multiplier method
- Calculation of discount rate based on risk premiums;
- Calculation of the discount rate based on expert assessment;
Calculation of discount rate based on the CAPM model
Capital Asset Pricing Model – CAPM ( CapitalAssetPricingModel) was proposed in the 70s by W. Sharp (1964) to estimate the future return on shares/capital of companies. The CAPM model reflects future returns as the return on a risk-free asset 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. Market risk was taken as a factor determining the future rate in the model. The formula for calculating the discount rate using the CAPM model is as follows:
where: r i – expected return on the stock (discount rate);
r f – return 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 – beta coefficient. Reflects the riskiness of the 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 changes in stock returns depending on changes in market returns;
σ 2 m – dispersion of market returns.
Advantages and disadvantages of the CAPM capital asset pricing model
- The model is based on the fundamental principle of linking stock returns with market risk, which is its advantage;
- The model includes only one factor (market risk) to estimate the future return of a stock. Researchers such as Y. Fama, K. French, and others have introduced additional parameters into the CAPM model to increase its forecasting accuracy.
- The model does not take into account taxes, transaction costs, opacity of the stock market, etc.
Calculation of the discount rate using the modified CAPM model
The main disadvantage of the CAPM model is its one-factor nature. Therefore, the modified capital asset pricing model also includes adjustments for unsystematic risk. Unsystematic risk is also called specific risk, which appears only under certain conditions. Calculation formula for modified CAPM model (ModifiedCapitalAssetPricingModel,MCAPM) is as follows:
where: r i – expected return on the stock (discount rate); r f – return on a risk-free asset (for example, government bonds); r m – market return; β – beta coefficient; σ im is the standard deviation of the change in stock return from the change in market return; σ 2 m – dispersion of market returns;
r u – risk premium, including the company’s unsystematic risk.
As a rule, experts are used to assess specific risks because they are difficult to formalize using statistics. The table below shows various risk adjustments ⇓.
| Specific risks | Risk adjustment, % |
| Government 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% |
| The influence of seasonality in demand for products | 0,4% |
| Conditions for raising capital | 0,3% |
| Total adjustment for specific risk: | 1,8% |
For example, let’s calculate the discount rate taking into account adjustments, so if according to the CAPM model the yield is 10%, then taking into account risk adjustments the discount rate will be 11.8%. Using a modified model allows you to more accurately determine the future rate of return.
Calculation of the discount rate using 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 influence the future rate of profit: company size and industry specifics. Below is the formula of the three-factor model of E. Fama and K. French:
where: r – discount rate; r f – risk-free rate; r m – profitability of the market portfolio;
SMB t is the difference between the returns of weighted average portfolios of small and large capitalization stocks;
HML t is the difference between the returns of weighted average portfolios of shares with large and small ratios of 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 return of the asset in the absence of the influence of 3 risk factors on it.
Calculation of the discount rate based on the M. Karhat model
The three-factor model of E. Fama and K. French was modified by M. Carhart (1997) by introducing a fourth parameter to assess the possible future return of a stock - moment. The moment reflects the rate of price change over a certain historical period of time; when the fourth parameter is used in the model for estimating the profitability of a stock in the future, it is taken into account that the future rate of return is also affected by the rate of price change. Below is the formula for calculating the discount rate using the M. Carhart model:
where: r – discount rate; WMLt – moment, rate of change in the value of a stock over 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 limitations 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 of equity capital of an enterprise (discount rate):
Where:
DIV – the amount of expected dividend payments per share for the year;
P – share placement price;
fc – costs of issuing shares;
g – dividend growth rate.
Calculation of discount rate based on 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 of investment capital. Investment capital can consist of two sources of financing: equity and debt. WACC is often used both in financial and investment analysis to estimate future investment returns, taking into account the initial conditions for the return (profitability) of investment capital. The economic meaning of calculating the weighted average cost of capital is to calculate the minimum acceptable level of profitability (profitability, profitability) of the project. This indicator is used to evaluate investments 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 capital, respectively;
E/V, D/V – share of equity and debt capital. The sum of equity and borrowed capital forms the company's capital (V=E+D);
t – profit tax rate.
Calculation of discount rate based on return on equity
The advantages of this method include the ability to calculate the discount rate for enterprises that are not listed on the stock market. Therefore, to evaluate the discount, return on equity and debt capital indicators are used. These indicators are easily calculated from balance sheet items. If an enterprise has both equity and borrowed capital, then the indicator used is return on assets. (Return On Assets, ROA). The formula for calculating the return on assets ratio is presented below:
The next method for estimating the discount rate through return on equity is (Return On Equity, ROE), which shows the efficiency/profitability of capital management of an enterprise (company). The profitability ratio shows what rate of profit the company creates using 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 the enterprise, a more accurate indicator can be used as a criterion for assessing the rate - return on capital employed (ROCEReturnOnCapitalEmployed). This indicator, unlike ROE, uses long-term liabilities (through shares). This indicator can be used for companies that have preferred shares on the stock market. If the company does not have them, then the ROE ratio is equal to ROCE. The indicator is calculated using the formula:
Another type of return on equity ratio is return on average capital employed ROACE. (Return on Average Capital Employed).
In fact, this indicator corresponds to ROCE, its main difference is the averaging of the cost of capital employed (Equity capital + long-term liabilities) at the beginning and end of the period being assessed. The formula for calculating this indicator:
The ROACE indicator can often replace ROCE, for example, in the EVA economic value added formula. Let us present an analysis of the feasibility of using profitability ratios to estimate the discount rate ⇓.
Calculation of discount rate based on expert assessment
If you need to estimate the discount rate for a venture project, then using the CAPM, Gordon model and WACC methods is impossible, so experts are used to calculate the rate. The essence of expert analysis is a subjective assessment of various macro, meso and micro factors affecting the future rate of profit. Factors that have a strong influence on the discount rate: country risk, industry risk, production risk, seasonal risk, management risk, etc. For each individual project, experts identify their most significant risks and evaluate them using scoring. The advantage of this method is the ability to take into account all possible investor requirements.
Calculation of discount rate based on market multipliers
This method is widely used to calculate the discount rate for enterprises that issue ordinary shares on the stock market. As a result, the market E/P multiplier is calculated, which is translated as EBIDA/Price. The advantages of this approach are that the formula reflects industry risks when valuing a company.
Calculation of 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 estimate the amount of possible risk/return. Formula for calculating the discount rate taking into account the risk premium:
Where:
r – discount rate;
r f – risk-free interest rate;
r p – risk premium;
I – inflation percentage.
The discount rate formula consists of the sum of the risk-free interest rate, inflation and the risk premium. Inflation was singled out as a separate parameter because money depreciates constantly; this is one of the most important laws of the functioning of the economy. Let us consider separately how each of these components can be assessed.
Methods for estimating the risk-free interest rate
To assess the risk-free value, financial instruments are used that provide profitability with zero risk, that is, absolutely reliable. In reality, no instrument can be considered absolutely reliable; it’s just that the probability of losing money when investing in it is extremely small. Let's consider two methods for estimating the risk-free rate:
- Yield on risk-free government bonds (GKOs - government short-term zero-coupon bonds, OFZs - federal loan bonds) issued by the Ministry of Finance of the Russian Federation. Government bonds have the highest safety 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.
- US 30-year bond yield. The average yield on these financial instruments is 5%.
Methods for estimating 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 methods for assessing additional investment risks; let’s look at some of them.
Methodology for assessing risk adjustments from the Alt-Invest company
The Alt-Invest methodology includes the following types of risks in the risk adjustment, presented in table ⇓.
Methodology of the Government of the Russian Federation No. 1470 (dated November 22, 1997) for assessing the discount rate for investment projects
The purpose of this methodology is to evaluate investment projects for public investment. Specific risks and adjustments for them will be calculated through expert assessment. To calculate the base (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). Specific project risks are assessed by experts in the presented ranges. The maximum discount rate using this method will be 61%.
| Risk-free interest rate | |
| WITH refinancing rate of the Central Bank of the Russian Federation | 11% |
| Risk premium | |
| Specific risks | Risk adjustment, % |
| Investments to intensify production | 3-5% |
| Increasing product sales volume | 8-10% |
| The risk of introducing a new type of product to the market | 13-15% |
| Research costs | 18-20% |
Methodology for calculating the discount rate Vilensky P.L., Livshits V.N., Smolyak 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% |
| R&D duration 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 technology used: | |
| Traditional | 0% |
| New | 2-5% |
| 3. Uncertainty in demand volumes and prices for manufactured products: | |
| existing | 0-5% |
| New | 5-10% |
| 4. Instability (cyclicality, seasonality) of production and demand | 0-3% |
| 5. Uncertainty of the external environment during the implementation of the project (mining, geological, climatic and other natural conditions, aggressiveness of the external environment, etc.) | 0-5% |
| 6. The uncertainty of the process of mastering the technique or technology used. Participants have the opportunity to ensure compliance with technological discipline | 0-4% |
Methodology for calculating the discount rate by Y. Honko for various classes of investments
Scientist J. Honko presented a methodology for calculating risk premiums for various classes of investments/investment projects. These risk premiums are presented in aggregate form and require the investor to select an investment objective and a risk adjustment accordingly. Below are aggregated risk adjustments based on investment objective. As you can see, as the amount of risk increases, the enterprise/company’s ability to enter new markets, expand production and increase competitiveness also increases.
Resume
In the article, we looked at 10 methods for estimating the discount rate, which 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 assessing the value of investment objects, shares, investment projects, and management decisions. When choosing an assessment method, it is necessary to take into account the purposes for which the assessment is being made and what the initial conditions are. This will allow for the most accurate assessment. Thank you for your attention, Ivan Zhdanov was with you.
The most important component of the success of any enterprise is a thorough comprehensive analysis of the initial data and expected prospects of the project. In particular, in order to understand what kind of profit an investor can expect, it is necessary to calculate not just the amount of income, but the discounted income. Therefore, let’s take a closer look at what discounting is and where it is used.
Discounting future income is part of a comprehensive system for assessing the current economic condition of the company and selecting proposed investment projects, i.e. analysis of their economic efficiency. The concept of discounting, as a way of determining the purchasing power of money in foreign practice, is mandatory when assessing the effectiveness of a project and is part of the accounting reporting system. In Russia, this mechanism is also becoming increasingly popular.
First, let's look at determining the discount rate. From the point of view of economic science, discounting is the calculation of the value of a future cash flow by bringing it to the current point in time.
Despite the fact that the definition given above conveys the main essence of discounting quite clearly, it can be stated in other words, namely, as an adjustment of the future value of money to its present value. Any company that attracts funds from outside is obliged to return them to the lender or investor after a certain time, as well as pay a reward for them.
The discounting principle is based on an economic law that states that over time the same amount of money has different values (purchasing power). There may be several reasons for this:
- inflation processes and expectations;
- there is a risk of not receiving the expected income;
- the opportunity to receive additional income by investing money in an alternative project or on a bank deposit at a favorable interest rate.
The following systems or types of discounting are distinguished depending on the time of receipt of funds:
- the present value of a one-time payment shows how much money needs to be invested in order to receive a one-time payment in the expected amount at a set percentage;
- The present value of annuity payments shows how much money needs to be invested at a specific interest rate in order to receive the expected income in equal parts over a certain time.
Having money “here and now” is always more profitable than “sometime later”, since the above factors affecting capital over time do not apply to them. Bringing cash flows helps to calculate the level of profitability of an undertaking, taking into account the discount. This is the essence of discounting.
How cash flows are reduced
Discounted income is determined by multiplying the amount of the payment received by a certain coefficient. The calculation formula, in general, looks like this:
PV = FV * 1 / (1 + r)n
- PV – value at the current time;
- FV – expected (future) value;
- n – time (number of steps, or periods).
The first factor in this formula characterizes the amount of money expected from the implementation of the initiative. The second factor is called the discount factor (or factor). It characterizes the value of a dollar, ruble or other monetary unit invested in a project after a certain period of time (in months or years), provided that the discount rate is set correctly. Each multiplier must be calculated as accurately as possible, since the less correctly its value is set, the less objective the final result will be.
The discount factor can be calculated independently, but it is easier and more expedient to find its value in special tables, where the indicators of the calculation period and the discount rate are indicated in the rows and columns. The value you are looking for is located in the intersection cell of the corresponding column and row.
The discounting operation begins with establishing a barrier rate (discount rate), based on which calculations will be made. The barrier rate is a certain standard of profitability that is suitable for the investor, and which can be obtained by investing money in any alternative project or by opening a bank deposit. Thus, the discount rate is a determination of the direction of investment, the choice of a specific option relative to other possible ones.
The discount rate is an indicator that is set directly by the investor who plans to implement an initiative and wants to determine his discounted income. The value of this indicator is influenced by a number of factors:
- inflation percentage;
- economic indicators of the company and the size of its capital;
- the cost of money in the financial market;
- average bank interest rate on long-term loans or deposits;
- price level for components, raw materials and finished products;
- changes in the economic situation (excise taxes, taxes, minimum wage level).
Given the volatility of these variables, the correct calculation of the discount rate is a critical element of the entire process of bringing financial flows to the current moment. There are different calculation systems, the most famous of them are:
- WACC model (based on weighted average capital);
- CAPM method (based on the valuation of capital assets);
- Gordon model (based on the amount of dividends from the company's securities);
- ROE, ROA and their modifications (based on return on equity);
- risk premium method (for each type of risk a certain amount is added to the discount rate).
In addition, capital discounting requires a clear definition of the time period for the implementation of the undertaking, that is, the life cycle of the investment project. If the initiative is short-term and the time factor does not have time to significantly affect the value of money, then the reduction procedure can be neglected. If we are talking about longer time periods, then the discounting procedure is mandatory. The longer the life cycle of a project, the less it is necessary to rely on actual economic indicators; forecasting the situation, taking into account general trends in economic development, comes to the fore.
Net present value
When we are talking about a certain stream of payments that occurs at regular intervals (CF = CF1 + CF2 + … + CFN), then if we apply the reduction operation to each such payment, we can arrive at the discounted cash flow formula:
| CF 1 | CF 2 | CF N | |||
| PV = | ----- | + | ------ | +...+ | ------ |
| (1+r) | (1+r) 2 | (1+r)N |
As an example of such a flow, we can consider the net present value indicator (NPV or NPV). This is the difference between the investments made and the sum of all inflows and outflows of funds for the investment project, taking into account the reduction. In fact, NPV indicates the amount by which the value of the company will increase as a result of the implementation of an investment project. Income discounting allows a businessman to compare several offers designed for different implementation periods and choose the most profitable one.
The calculation formula used generally looks like this:
NPV (NPV) = - IC +ƩCFt/ (1 + i)t,
in which:
- IC – initial investments in the initiative, they have a negative value, since these are costs that should pay off in the future;
- CFt – reduced injections of money (the difference between income and costs) in each t period, with the value t = 1…n;
- i is the value of the discount rate.
If the net present value exceeds zero, then the offer is perceived as profitable for the investor, otherwise it is rejected. With a zero NPV value, the undertaking will not bring profit, but it will pay off; it can be implemented if the project has an important social component.
Examples of discounting
Let's look at a couple of discounting problems. A man lent a friend a certain amount of money, say 10 thousand dollars. The debtor offers him a choice of two options: return the entire amount immediately now or give 12 thousand dollars, but after 3 years.
To calculate the profitability of this proposal, you need to know the cash flow reduction system. If we take the interest rate on a bank deposit in the amount of 9% as the discount rate, then using the reduction formula, we can find out how much the entire borrowed amount will cost after 3 years:
PV = 12000 * 1 / (1 + 0.09) 3 = 12000 * 1 / 1.295 = 12000 * 0.7722 = $9266.4.
Consequently, it is more profitable to take out the debt today, since an additional 2 thousand dollars over 3 years does not cover the dynamics of the depreciation of money. If the received funds are deposited into a deposit account at the same 9% per annum, then after 3 years we will receive: 10,000 * 1.09 * 1.09 * 1.09 = $12,950, which is much more profitable than the option proposed by the partner.
If we assume that after the same period the debtor will return not 12, but 15 thousand dollars, then the situation may change dramatically:
PV = 17000 * 1 / (1 + 0.09) 3 = 17000 * 1 / 1.295 = 17000 * 0.7722 = $13127.4.
Now the situation is turning in such a way that it is more profitable to agree with the proposal to defer settlement, since the profit received will be higher than the lump sum at the moment and the alternative investment on the deposit.
Let's look at how to calculate net present value based on the use of a cash flow reduction system. An investment company invests 100 thousand dollars in a venture for 4 years, the discount rate is calculated by assessing risks and is set at 12%, one year is taken as the calculation step.
Net cash flows (NCF) are distributed by year as follows:
- 1 year – $35,000;
- 2 year – $38,000;
- 3 year – $40,000;
- Year 4 – $45,000.
Using the formula, we find the value of the reduced flows at each of the calculation steps:
- 1 year – 35000 / (1 + 0.12) = 31250;
- 2 year – 38000 / (1 + 0.12)2 = 30293;
- 3 year – 40000 / (1 + 0.12)3 = 28472;
- Year 4 – 45000 / (1 + 0.12)4 = 28598.
Total for 4 years: $118,613.
NPV = 118613 – 100000 = $18613.
As a result, we come to the conclusion that NPV has a value above zero, therefore, such a proposal will be of interest to investors, since if the predicted conditions are maintained throughout the life cycle of the initiative, the project will bring profit.
Another interesting example of the application of the money reduction rule is the discounting of invoices. Sometimes there are cases when suppliers or contractors need to receive money earlier than the one specified in the contract. For example, a new profitable offer has appeared that requires an urgent investment of funds, and there are still 2 weeks before payment for the goods supplied by the company.
There are companies that provide such a service (factoring): they confidentially buy an unpaid invoice from the supplier at a discount. Sometimes customers agree to pay for delivery at an earlier date, but at the same time apply the discounting rule. That is, if goods are delivered in the amount of 1 million rubles, and the supplier asks to pay for the goods 14 days ahead of schedule, then the customer can agree to this by setting his own discount rate (let's say 30%). You can calculate the amount by which the total payment will be reduced:
1,000,000 * 30% / 365 days * 14 days = 58,708 rubles.
Consequently, the amount to be paid is 941,292 rubles. The company selling the invoice will be able to compensate for the lost discount by making a more profitable investment or increasing the turnover of funds.
Which is used when reducing future financial flows to their current value. Its calculation is perhaps one of the most pressing and complex issues that arises in the financial assessment of any investment project. Its correctness determines what final value the current monetary value will have.
If a low rate is applied, the discounted value of expected future cash flows may be too high. This will entail the investor choosing an ineffective project, as a result of which he will suffer serious losses. An excessively high rate, in turn, can lead to losses, which are actually a lost opportunity to generate income.
The discount rate, therefore, represents the rate of return in percentage that the investor should receive on the invested capital. That is, a project is considered attractive for an investor when the rate of return for it is higher than the discount rate of any other possible investment of capital that has a similar risk.
The discount rate, on the other hand, is a risk- and time-sensitive reflection, since the actual money that a person has at the moment is much preferable (it has a greater value) to an equal amount of money that he expects to receive in the future.
This is due to several reasons, say, the fact that:
- there is always a risk of simply not receiving the expected amount;
- the available amount could generate a profit, say, if it were deposited in a bank.
- the available amount will lose its purchasing power as a result of inflation.
The discount rate includes the following parameters:
- investment risk coefficient (for each specific case);
- the minimum level of profitability that can be guaranteed.
The discount rate, which is calculated using various methods, is often determined experimentally in practice. This takes into account both the requirements of the investor and the investment bank that attracts the funds required.
In Russian conditions, it is always associated with a variable level of risk, and therefore with constantly changing levels of income and expenses. For this reason, in practice, the profitability of a project is rarely calculated without taking into account the discount rate.
The method of discounting financial flows, which takes into account discounting, of course, reflects the existing value of income much more accurately.
The most common methods for determining the discount rate for financial capital flows include the following models:
1. For your own:
- valuation of capital assets;
- cumulative construction.
2. For investment:
- weighted average cost of capital.
The fundamental point in the discounting process is the establishment of a certain discount rate. From an economic point of view, the discount rate is the rate of return that could be obtained if the given funds were available to the organization. With help, they determine the amount that the investor will have to pay today in order to have the right to receive the expected amount in the future.
The discount rate is required to:
- make a more accurate calculation of the project’s profitability;
- compare the obtained indicators of an existing project with the lowest rate of return when investing in a similar business.
Discounting from the English “discounting” is the reduction of 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 unfamiliar to you and this definition is unlikely to explain the essence of “discounting”; rather, it will confuse it even more.
However, it makes sense for a prudent owner of his budget to understand this issue, since every 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 takes another look at his grocery cart to remove “unnecessary” items from it. Of course, because in our time we have to be prudent and economical.
Discounting is often understood as an economic indicator that determines the purchasing power of money and its value after a certain period of time. Discounting allows you to calculate the amount that will need to be invested today in order to receive an expected return over time.
Discounting, as a tool for predicting future profits, is in demand among business representatives at the stage of planning results (profits) from investment projects. Future results may be announced at the start of the project or during its subsequent stages. To do this, the specified indicators are multiplied by the discount factor.
Discounting also “works” for the benefit of the average person who is not involved in 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 the financial capabilities (cash reserve) at the time of admission, so many parents think about a “nest egg” (a certain amount of money spent past the family budget cash register), which can help out in an hour.
Let's say that in five years your child graduates from school and decides to enroll in a prestigious European university. Preparatory courses at this university cost $2,500. You are not sure that you will be able to carve out this money from the family budget without infringing on the interests of all family members. There is a way out - you need to open a deposit in a bank, for a start it would be good to calculate the amount of the deposit that you should open in the bank now, so that at hour X (that is, five years later) you receive 2500, provided that the maximum favorable interest rate that can offer the bank, say -10%. To determine how much a future expenditure (cash flow) is worth today, we do a simple calculation: Divide $2500 by (1.10)2 and get $2066. This is discounting.
Simply put, if you want to know what the value of a sum of money you will receive or plan to spend in the future is, then you should “discount” that future sum (income) at the interest rate offered by the bank. This rate is also called the “discount rate”.
In our example, the discount rate is 10%, $2,500 is the payment amount (or cash outflow) in 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 current (discounted) and future values: 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.
The formula for calculating the discounted value for our example is: 2500 * 1/(1+R) n = 2066.
General discounting formula: PV = FV * 1/(1+R)n
- Coefficient by which future value is multiplied 1/(1+R)n, is called the “discount factor”,
- R– interest rate,
- N– the number of years from a date in the future to the present.
As you can see, these mathematical calculations are not that complicated and not only bankers can do it. In principle, you can give up on all these numbers and calculations, the main thing is to grasp 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 in a certain amount of time to the amount we must spend (invest) today.
Formula of life: time + money
Let's imagine another situation familiar to everyone: you have “free” money, and you come to the bank to make a deposit of, say, $2,000. Today, $2,000 deposited in the bank at a bank rate of 10% will cost $2,200 tomorrow, that is, $2,000 + interest on the deposit 200 (=2000*10%) . It turns out that in a year you can get $2,200.
If we present 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 two years, that amount converts to $2,420. We calculate: $2000 + interest accrued in the first year $200 + interest in the second year $220 = 2200*10% .
The general formula for increasing the deposit (without additional contributions) over two years looks like this: (2000*1,10)*1,10 = 2420
If you want to extend the deposit term, your deposit income 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.
In this case:
- R is the interest rate expressed in fractions of a unit (10% = 0.1),
- N— denotes the number of years.
Discounting and accretion operations
In this way, it is possible to determine the amount of the contribution at any time point in the future.
Calculating the future value of money is called "accretion."
The essence of this process can be explained using the example of the well-known expression “time is money”, that is, over time, the monetary deposit grows due to an increase in annual interest. The entire modern banking system operates on this principle, 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” (discounting and escalation) 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 an assessment of the effectiveness of the project.
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 a 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 business valuation are taken into account by the DCF method.
Discount factor
The discounted cash flow method is based on the law of the “falling” value of money. This means that over time money “gets cheaper”, that is, it loses value compared to its current value.
It follows from this that it is necessary to build on the current assessment, and correlate all subsequent cash flows or outflows with today. This will require a discount factor (Df), which is necessary to reduce future income to the present value by multiplying Kd by the payment streams. The calculation formula looks like this:
Where: r– discount rate, i– number of the time period.
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 evaluation, and may include: the inflation component, valuation of capital shares, return on risk-free assets, refinancing rate, interest on bank deposits and more.
It is generally accepted that a potential investor will not invest in a project whose cost will be higher than the present value of the future income from the project. Likewise, an owner will not sell his business for less than the estimated value of future earnings. Following the negotiations, the parties will agree on a market price that is equivalent to the today's value of the projected income.
The ideal situation for an investor is when the internal rate of return (discount rate) of the project is higher than the costs associated with finding financing 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 meets the investment motives of a business.
This means that an investor who invests money 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 a future flow of money. If we continue this idea, it turns out that any business “releases” a single product to the market - 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.
