What is cash flow discounting. Discounted cash flow method in real estate valuation How to discount cash flow
Do you know what discounting means? If you are reading this article, then you have already heard this word. And if you have not yet fully understood what it is, then this article is for you. Even if you are not going to take the Dipifre exam, but just want to understand this issue, after reading this article, you can clarify for yourself the concept of discounting.
This article explains in plain language what is discounting. Using simple examples, it shows the technique for calculating the present value. You will learn what a discount factor is and how to use it
The concept and formula of discounting in plain language
To make it easier to explain the concept of discounting, let's start from the other end. To be more precise, let's take an example from life, familiar to everyone.
Example 1 Imagine you walk into a bank and decide to deposit $1,000. Your $1,000 deposited in the bank today, at a bank rate of 10%, will be worth $1,100 tomorrow: $1,000 today + deposit interest 100 (=1000*10%). In total, in a year you will be able to withdraw $1,100. If we express this result through a simple mathematical formula, we get: $1000*(1+10%) or $1000*(1.10) = $1100.
In two years, the current $1,000 will be $1,210 ($1,000 plus first year interest $100 plus second year interest $110=1100*10%). The general formula for the increment of the contribution for two years: (1000 * 1.10) * 1.10 \u003d 1210
Over time, the value of the contribution will continue to grow. To find out how much you are due from the bank in a year, two, etc., you need to multiply the amount of the deposit by the multiplier: (1 + R) n
- where R is the interest rate expressed as fractions of a unit (10% = 0.1)
- N - number of years
In this example, 1000*(1.10) 2 = 1210. From the formula it is obvious (and from life too) that the deposit amount after two years depends on the bank interest rate. The larger it is, the faster the contribution grows. If the bank interest rate were different, for example, 12%, then in two years you would be able to withdraw approximately $ 1250 from the deposit, and if you calculate more precisely 1000 * (1.12) 2 = 1254.4
In this way, you can calculate the amount of your contribution at any time in the future. The calculation of the future value of money in English is called "compounding". This term is translated into Russian as "building" or tracing paper from English as "compounding". Personally, I prefer the translation of this word as “increment” or “growth”.
The meaning is clear - over time, the monetary contribution increases due to the increment (increase) in annual interest. On this, in fact, the entire banking system of the modern (capitalist) model of the world order is built, in which time is money.
Now let's look at this example from the other end. Let's say you need to repay a debt to your friend, namely: in two years to pay him $1210. Instead, you can give him $1,000 today, and your friend will put that amount in the bank at a 10% annual rate, and in two years, withdraw exactly the required amount of $1,210 from the bank deposit. That is, these two cash flows: $1000 today and $1210 in two years - are equivalent each other. It doesn't matter what your friend chooses - these are two equal possibilities.
EXAMPLE 2. Let's say in two years you need to make a payment in the amount of $1,500. What will this amount be equivalent to today?
To calculate today's value, you need to work backwards: $1,500 divided by (1.10) 2 equals about $1,240. This process is called discounting.
In simple terms, then discounting is determining the present value of a future amount of money (or more correctly, future cash flow).
If you want to find out how much an amount of money you either receive or plan to spend in the future is worth today, then you need to discount that future amount at a given interest rate. This rate is called "discount rate". In the last example, the discount rate is 10%, $1,500 is the amount of the payment (cash outflow) after 2 years, and $1,240 is the so-called discounted value future cash flow. In English, there are special terms for today's (discounted) and future value: future value (FV) and present value (PV). In the example above, $1500 is the future value of FV and $1240 is the present value of PV.
When we discount, we move from the future to today.
Discounting
When we build up, we go from today into the future.
Accretion
The formula for calculating the present value or the discounting formula for this example is: 1500 * 1/(1+R) n = 1240.
Mathematical in the general case will be as follows: FV * 1/(1+R) n = PV. It is usually written in this form:
PV = FV * 1/(1+R)n
Factor by which the future value is multiplied 1/(1+R)n is called the discount factor from the English word factor in the meaning of "coefficient, multiplier".
In this discounting formula: R is the interest rate, N is the number of years from a date in the future to the current moment.
In this way:
- Compounding or Increment is when you go from today's date to the future.
- Discounting or Discounting is when you go from the future to today.
Both "procedures" take into account the effect of changes in the value of money over time.
Of course, all these mathematical formulas immediately make an ordinary person sad, but the main thing is to remember the essence. Discounting is when you want to know the present value of a future amount of money (which you will have to spend or receive).
I hope that now, having heard the phrase "the concept of discounting", you will be able to explain to anyone what is meant by this term.
Is present value a discounted value?
In the previous section, we found out that
Discounting is the determination of the present value of future cash flows.
Isn't it true that in the word "discounting" one hears the word "discount" or in Russian a discount? Indeed, if you look at the etymology of the word discount, then already in the 17th century it was used in the meaning of “deduction for early payment”, which means “discount for early payment”. Even then, many years ago, people took into account the time value of money. Thus, one more definition can be given: discounting is the calculation of a discount for paying bills quickly. This "discount" is a measure of the time value of money or time value of money.
The discounted value is the present value of the future cash flow (i.e. the future payment minus the "discount" for fast payment). It is also called the present value, from the verb "to bring". In simple words, present value is future amount of money reduced to the current moment.
To be precise, discounted value and present value are not absolute synonyms. Because you can bring not only the future value to the current moment, but also the current value to some point in the future. For example, in the very first example, we can say that $1,000 adjusted to the future (two years from now) at a rate of 10% equals $1,210. That is, I want to say that the present value is a broader concept than the present value.
By the way, there is no such term (present value) in English. This is our purely Russian invention. In English, there is the term present value (current value) and discounted cash flows (discounted cash flows). And we have the term present value, and it is most often used in the meaning of "discounted" value.
Discount table
A little higher I already cited discount formula PV = FV * 1/(1+R) n, which can be described as:
The present value is equal to the future value multiplied by a factor called the discount factor.
The discount factor 1/(1+R) n , as can be seen from the formula itself, depends on the interest rate and the number of time periods. In order not to calculate it every time according to the discounting formula, they use a table showing the coefficient values depending on the% rate and the number of time periods. Sometimes it is called a "discount table", although this is not quite the correct term. it discount factor table, which are calculated, as a rule, with an accuracy of four decimal places.
Using this table of discount factors is very simple: if you know the discount rate and the number of periods, for example, 10% and 5 years, then at the intersection of the corresponding columns is the coefficient you need.
Example 3 Let's take a simple example. Let's say you have to choose between two options:
- A) get $100,000 today
- B) or $150,000 in one lump sum in exactly 5 years
What to choose?
If you know that the bank rate on 5-year deposits is 10%, then you can easily calculate what the amount of $150,000 receivable in 5 years equals to the current moment.
The corresponding discount factor in the table is 0.6209 (cell at the intersection of row 5 years and column 10%). 0.6209 means that 62.09 cents received today equals $1 due in 5 years (at a rate of 10%). Simple proportion:
So $150,000*0.6209 = 93.135.
93,135 is the discounted (present) value of $150,000 receivable in 5 years.
It's less than $100,000 today. In this case, a tit in the hands is really better than a pie in the sky. If we take 100,000 dollars today, put them on a bank deposit at 10% per annum, then after 5 years we will get: 100,000*1.10*1.10*1.10*1.10*1.10 = 100,000*( 1.10) 5 = $161,050. This is a more profitable option.
To simplify this calculation (calculating the future value given today's value), you can also use the ratio table. By analogy with the discount table, this table can be called a table of increment (increment) coefficients. You can build such a table yourself in Excel if you use the formula to calculate the increment factor: (1+R)n.
This table shows that $1 today at 10% will be worth $1.6105 in 5 years.
Using such a table, it will be easy to calculate how much money you need to put in the bank today if you want to receive a certain amount in the future (without replenishing the deposit). A slightly more complicated situation arises when you not only want to deposit money today, but also intend to add a certain amount to your contribution every year. How to calculate this, read the following article. It is called annuity formula.
A philosophical digression for those who have read this far
Discounting is based on the famous postulate "time is money". If you think about it, this illustration has a very deep meaning. Plant an apple tree today and in a few years your apple tree will grow and you will be picking apples for years. And if today you do not plant an apple tree, then in the future you will not try apples.
All we need is to decide: plant a tree, start our own business, take the path that leads to the fulfillment of a dream. The sooner we begin to act, the greater the harvest we will receive at the end of the journey. We need to turn the time allotted to us in our lives into results.
"The seeds of flowers that bloom tomorrow are planted today." That's what the Chinese say.
If you dream of something, do not listen to those who discourage you or question your future success. Don't wait for luck, start as early as possible. Turn the time of your life into results.
Large table of discount factors (opens in a new window):
Investing means investing free financial resources today in order to obtain stable cash flows in the future. How not to make a mistake and not only return the invested funds, but also make a profit from investments?
This article provides not only the formula and definition of IRR, but there are examples of calculating this indicator (in Excel, graphical) and interpreting the results. Two examples from life that every person faces
At its core, the discount rate in the analysis of investment projects is the interest rate at which the investor attracts financing. How to calculate it?
- What is discounted cash flow.
- What are the benefits of discounted cash flow.
- What are the steps in the discounting process?
- What methods of discounting cash flow are.
- How to calculate discounted cash flow.
The concept of discounting cash flows is defined by the Ministry of Finance. The document, approved on June 21, 1999, spells out all the methodological recommendations that will help evaluate the effectiveness of investment actions. Discounting is defined as the reduction of financial indicators that relate to different time periods of the future, to how much they carry value at the moment.
This Methodological Regulation is based on the idea that the same amount of money has a different value in different time periods. That is, a thousand rubles today will be more valuable than a thousand rubles in a month. With proper management of money in a month, this thousand rubles will bring good income.
Cash flow discounting makes sense to apply when:
- There are strong arguments that the cash flows in the future will be very different from the current ones.
- There is a lot of data that helps to calculate and justify the return on investment, for example, in the field of real estate.
- Something large and multifunctional, for example, a shopping and entertainment center, acts as an object of assessment. Or it is at the stage of commissioning.
- Cash flows of profits or costs vary greatly and depend on the season.
Benefits of Discounted Cash Flows
When compared with other methods, cash flow discounting allows for a deep and detailed study. Can evaluate a business, which does not have stability in the movement of financial flows. This is due to the fact that special coefficients are used to apply the method and special channels for receiving funds are taken into account.
The instability of many commercial facilities and assets leads to the fact that their purchase or lease is approached very carefully. Financial flows can both decrease and increase greatly. Therefore, discounting cash flows allows you to carry out the calculation of cash flow as close as possible to the real one.
An investor or stakeholder necessarily considers an asset for how much profit it will receive in the future. The determining factor is the ratio between how much he will pay for the asset now and how much it will bring him profit over a certain time period or how much it can be realized in the future.
Cash flow discounting has a number of advantages:
- Takes into account market dynamics.
- Operates in an uneven structure of cash flows.
- Used in almost all cases.
There are also weaknesses, such as the emotional factor, due to which the personal interest of the appraiser and sympathy for a particular asset can lead to errors in forecasting.
Stages of cash flow discounting
In order for the results of the calculations to be close to the most real development of events, it is necessary to act according to a certain plan. You can supplement your actions or reduce them depending on the scale of the calculation and the specifics of the cash flow. In general, we advise you to navigate the steps described below.
Period selection
Choosing the right time period is an important step. If you choose too short a period, then your calculation will not be effective, will not be of strategic importance to the business. When choosing a very long period, there is a risk of not taking into account hidden factors, and the calculation will be unrealistic. In the world, a period of 5-10 years is used, in Russia - usually less.
Flow Definition
We determine the type of cash flow that we will investigate. It is possible to use the value of finance, which increase or decrease in the process. The main data at this stage will be financial and economic reports for the current and previous periods, as well as market analysis, made taking into account the errors. Here you need to take into account different types of income and losses:
- total income (minus asset tax and business expenses);
- total income according to analysts' forecasts;
- net operating income without investment cash and loan repayments;
- financial flows before and after fixed fees.
Reversion calculation
This is the residual value. That is, the value of the object being appraised is calculated after it ceases to be profitable. The reversion can be calculated on the example of identical objects in Russia or using authoritative forecasts of the market situation. You also need to calculate the capitalization rate or income for the year following the forecast time period.
Rate calculation
At the stage of calculating the discount rate, it is necessary to correctly predict future earnings. To do this, you can use any economic methods: compare investments, add up potential risks, calculate the percentage of similar transactions, monitor the market. The calculation of the rate should take place strictly based on clear economic calculations.
Practical use
Then you can go directly to the discounting method, using the calculated and initial indicators. To calculate the discounted cash flow, the following indicators are used:
- cash flow in a certain time period;
- rate of future income;
- time forecast period;
- the number of projected segments of cash flows and others.
Methods for Calculating Discounted Cash Flows
- Addition of risks.
- Percent allocation.
- Market monitoring.
Risk stacking
This method is based on the fact that calculating the discounted cash flow at a rate is quite risky. In this case, the calculation is made on the basis of the totality of all risks that exist. The rate in this case is equal to the sum of the risk-free rate and the risk premium. These values are calculated by summing the indicators of known and potential risk factors.
The cumulative construction method is also widely used, since in some areas (for example, in real estate) this method is the simplest and most effective. Using cumulation, you can evaluate any type of assets (vehicles, special equipment, equipment), as well as calculate capitalization ratios.
How to manage risks: case
Why is systematic risk management so important? How and why to classify risks? How to structure risk management work? Which of your managers should be responsible for which risks? You will find the answers in the risk management case from the CEO magazine.
Percent allocation
This method is used when the rate of return is calculated as a percentage rate. The value is calculated by relying on data from similar enterprises or projects. The calculation algorithm is based on hypotheses about the amount of future cash flows.
When calculating, you need to take into account the volumes and values \u200b\u200bof the initial information - this way you can choose the right formulas. An accurate calculation of the cash flow discount rate can be made by taking all the information from the investor (when investing) and finding out what percentage corresponds to the average cash flow of the enterprise.
Once the data is available, the economist will use it to calculate a discount rate for similar cash flows. It is necessary to take into account the specifics of the financial dynamics of each calculated flow. If errors are used, then the result will be a minimal deviation of the actual development of events from the expected one.
The selection method consists of several steps. First, we model and study real cash flows, then we make economic calculations of indicators that will be useful for further analysis. Only after that, using statistics and other methods, we calculate the cash flow under study.
Market assessment
Evaluation or monitoring of the market implies a long-term constant analysis of the situation on the market and tracking financial indicators that are identical to the cash flow under study. The information collected is summarized according to territorial and temporal criteria. It is easier to work with these data, as they more clearly reflect the real situation.
Also, market assessment involves a comparative analysis, verification of the relevance and authenticity of the deviations used by the coefficients. This data is constantly updated. Each type of income or loss must be calculated using its own indicators and calculations; average values and calculations at the stage of information accumulation will not be effective.
Market monitoring allows you to get more practical and theoretical information about identical cash flows and more accurately calculate the cash flow under study.
How to Calculate Discounted Cash Flow
Before calculating the discounted flow, a large amount of data must be prepared. It is necessary to make the most detailed analysis of past financial statements, to identify the average profits and costs. Then the market condition, the dynamics of changes in asset prices and other indicators necessary for calculations are examined. After that, forecasts of future cash flows are made based on the reports provided.
Features of calculations
The object under study is evaluated according to such indicators of profit as gross (actual and potential), net (operating) and profit before tax. The discounted cash flow calculation has the following features:
- Tax and economic depreciation are not real cash flow movements, as they depend on conditions and may change over time. Therefore, the calculation of potential profit is made without depreciation.
- Investments in an object or asset are subtracted from net operating income. Thus, the value of the financial flow is calculated most accurately.
- When the investment value of an object is assessed, all interest payments on loans are deducted from net income. But if you are calculating the market value of an object, then there is no need to take into account the costs of covering loans and credits.
- When calculating the cost of maintaining an object, its operational characteristics, it is necessary to take into account the costs of the owner of the object and subtract them from the real gross profit.
Calculation example
Let's create a table of indicators for the company "Horns and Hooves". In it, we use those indicators that will be needed in the forecast period.
Net profit |
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Depreciation |
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Working capital |
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Investments |
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Debt |
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Cash flow |
The “investments” column contains data related to the costs of supporting and developing the business. Since these are costs, they can be negative.
Working capital can be both positive and negative.
Next, take some percentage of the discount rate. Let's say it's 10%. Let's calculate the increase in cash flow. As an example, we take the growth rate indicator for the period after the forecast. We will write this indicator as “G” and call it the G-rate. After that, we calculate the amount of cash flow for the first post-forecast year. The formula looks like this: Cp = 133 * 1.01 / (0.10 - 0.01) = 1493
After that, you need to divide all the cash flow values by the appropriate discount rate. This must be done for each year of the forecast period and must be done separately for the post-forecast period.
Cash flow |
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Discount rate |
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Discount cash flow |
In our sample calculation, the sum of all discounted flow values was 1350. So we calculated the value of the Horns and Hooves company using the discounted cash flow method.
Of course, you should use your numbers when calculating discounted cash flow. The example should serve as a guideline only.
Conclusion
You can estimate the value of a company or any asset using discounted cash flow. Since for investors the ratio of profit and costs for the acquisition is principal, this is reflected in the discounted cash flow.
To get correct results, you need to know the stages of discounting and choose the appropriate method. This will depend on the specifics of the object or company under study.
An in-depth calculation is best done with the help of qualified economists, as this will reduce the factor of personal sympathy for the object or company that is being investigated, and also help to avoid errors in the calculations.
The discounting method is based on an economic law that reflects the essence of the method and describes the decreasing value of money. According to this law, over time, money gradually depreciates (loses its value) compared to its current value. Other changes may occur with the value of money. In order to take into account the process of such a change in calculations (for example, when calculating the potential economic efficiency of investment), it is necessary to take the current moment of assessment as a starting point, and then bring the amount of future cash flows (inflow and outflow of funds) to the present moment, determining the amount of change in the value of money.
Discounted Cash Flow is exactly the calculation that allows this to be done using a discount factor. How to calculate discounted cash flow will be shown in the article.
DCF value
The English phrase Discounted Cash Flow, meaning discounting, is usually presented in formulas as the abbreviation DCF or, in the Russian version, DDP. An investor who makes a decision on the most profitable investment uses this result in a number of other income approach methods to more accurately predict the future situation and choose economic and financial strategies. Among them:
- NPV– method of net present value (NPV). The formula for its calculation, similar to the DCF formula, differs in that NPV also includes initial investment costs.
- IRR is the internal rate of return.
- NUS is the equivalent of an annual annuity.
- PI- index of profitability.
- NFV is the net future value.
- NRR is the net rate of return.
- DPP is the discounted payback period.
So, for example, the introduction of the DCF parameter into the formulas for calculating the payback period (DPP) makes the calculation results practically more reliable, since it is the change in the value of money over time that makes it possible to assess the general prospects of the project in motion. Due to the consideration of the movement factor in assessing the effectiveness of investment projects, such methods are also commonly called dynamic.
Discounting methods are included as components of the income approach, and as such help to calculate the overall value of the business and its potential. Even with the instability of financial flows, the discounted cash flow method is justifiably applicable, since it demonstrates high accuracy. To improve the accuracy, the calculation is carried out taking into account the specific characteristics and methods of receipt of funds.
However, the Discounted Cash Flow Method also has disadvantages. Among the main ones, most often, two are called:
- Changes in the economic, political, social environment affect the discount rate, but it is always quite difficult to predict changes in this rate for any long period.
- It is also difficult to predict the change in the size of future cash flows, taking into account all external and internal circumstances.
However, the method is actively used if it is likely that the profitability of future financial flows will begin to differ from the profitability at the moment, if the flows depend on seasonality, if the construction project is underway, and in a number of other cases. In order to bring to the current moment the net cash flow (NPF) is used.
Discounted Cash Flow Formula
The coefficient is needed to bring the potential return to the current value. To do this, the value of the coefficient is multiplied by the value of the flows. The coefficient itself is calculated according to the following formula, where the letter “r” denotes the discount rate (it is also called the “rate of return”), and the letter “i” in the value of the degree indicates the time period.
where, in addition to the previous designations, “CF” means cash flows in time periods “i”, and “n” is the number of periods in which financial flows are received.
Under cash flows - Cash Flow (CF) in valuation practice is understood as:
- taxable income,
- net operating income,
- net “cash” flow (excluding costs for the reconstruction of the facility, for operation and land tax).
The calculation algorithm involves the passage of several stages, including the analysis of the discounted cash flow.
- Determination of the period for forecasting. As a rule, a predictable period of time is predicted with stable economic growth rates. In states with a well-developed market economy, it is 5-10 years. In domestic practice, a period of 3-5 years is traditionally considered.
- Forecasting incoming and outgoing cash payments. This is done through hindsight based on financial statements (if any), industry research, market characteristics, etc.
- Discount rate calculation.
- Calculation of cash flow for each period of time.
- Bringing the received flows to the original period by multiplying them by the discount factor.
- Determination of the total value - the stage at which the total accumulated discounted cash flow is calculated.
The key parameter in the formula is the size of the bet. It determines the rate of return that an investor who invests in a project should expect. The rate depends on a number of factors:
- weighted average cost of capital,
- inflation component,
- additional rate of return for risk,
- return on risk-free assets,
- interest on bank deposits,
- and etc.
To evaluate it in investment analysis, there are several methods. The most popular methods for calculating the discount rate are listed below.
The methods differ in different approaches, each of which is characterized by specific advantages and disadvantages.
- CAPM model valuation of capital assets, introduced in the 70s by W. Sharp to determine the profitability of shares. The strength of the model is considered to take into account the relationship between market risk and stock return. In the original model, this factor was the only accounting one. Transaction costs, stock market opacity, taxes and other factors were not taken into account. Later, to increase the accuracy, Yu. Fama and K. French applied additional parameters.
- Gordon Model. Another name for it is the constant growth dividend model. The “minus” of the method is that it is applicable only if the company has ordinary shares with constant dividend payments, and the “plus” is the relative ease of calculation.
- Model WACC– weighted average cost of capital. One of the most popular methods for demonstrating the rate of return that must be paid for the investment part of the capital. The economic meaning of the method is in calculating the minimum allowable profitability value (profitability level). This result can be applied to the evaluation of investments in an already existing project.
- Method for estimating risk premiums. The method uses additional risk criteria not provided by other models. However, this assessment is subjective, which refers to the shortcomings of the method.
- Peer review method. Among the advantages - the ability to take into account non-standard risk factors and fine-tuning the individual analysis. Among the shortcomings is the subjective perception of the situation. The expert evaluates meso-macro and micro factors, which, in his opinion, will affect the rates of return. Each project will have its own specific set of significant risks.
There are a number of other simple and complex methods, but in the following example, the discount rate will be calculated for clarity and transparency of the main formula as the sum of the “risk-free rate” and the “risk premium”. The first component of the equation - the risk-free rate - in the calculation example is equal to 15% - the key rate of the Central Bank of the Russian Federation. This is a fraction of the return on a risk-free asset. The second component - the risk premium - is set by an expert in the amount of 8% based on a conditional assessment of production, innovation, social, technological and other risks. This is the rate of return on existing risks. In total, the discount rate will be considered equal to 23%.
Calculation example
Our calculation example will correspond to the domestic tradition of choosing a forecasting period in the range of 3-5 years. Let's take an average of 4 years for a conditional project with a discount rate of 23%.
- Let's write out for each year the projected amount of income in rubles (CI) and the amount of cash expenditure (CO). Here we choose an annual interval for analysis and we will calculate the discounted cash flows, first for each individual year, and then the discounted cash flow for all 4 years. The projected expense will be stable, while the income will vary from year to year.
- First year: +95K and -30K
- Second year: +47k and -30k
- Third year: +54K and -30K
- Fourth year: +41k and -30k
- We calculate the difference between income and expenses for each year. It turns out that the amounts of such differences for 1-4 periods will be 65, 17, 24 and 11 thousand rubles, respectively.
- We bring financial flows to the initial period. We use the coefficients 1/(1+0.23) to calculate i, which discount each flow. Here, in place of the dividend, there will be a difference between income and expenses for each year, which we calculated at the previous stage. In place of the divisor is a coefficient, in which the value of 0.23 is a discount rate of 23%, and "i" in the degree corresponds to the number of the year for which we are calculating.
- 65000/(1+0,23) = 52845
- 17000/(1+0,23) 2 = 11237
- 24000/(1+0,23) 3 = 12897
- 11000/(1+0,23) 4 = 4806
(*The results are written in rubles rounded to whole numbers).
- We add the received amounts together, which gives DCF = 81785 rubles.
Since the indicator ultimately has a positive value, we can talk about further analysis of the project's prospects. Investment analysis requires using the discounted cash flow method and comparing the totals of several alternative projects so that they can be ranked by attractiveness.
Discounting is based on the fact that any amount received in the future is currently of lesser value. With the help of discounting in financial calculations, the time factor is taken into account. The idea of discounting is that it is preferable for a company to receive money today, rather than tomorrow, since being invested in innovations, they will already bring some additional income tomorrow. In addition, postponing the receipt of money for the future is risky: under adverse circumstances, they will bring less income than expected.
The difference between the future and present value is called discount.
Discount coefficients are calculated using the compound interest formula:
where / - interest rate, expressed as a decimal fraction (discount rate);
tp- year of bringing costs and results (calculated year);
t- year, the costs and results of which are reduced to the estimated one.
Under the condition of reduction to the year of the beginning of the implementation of innovations, we have tp= 0 and, therefore,
If the rate of interest on capital i is positive, the discount factor is always less than one (otherwise, money today would be worth less than money tomorrow).
The method of calculating compound interest is that in the first period the accrual is made on the initial amount of the loan, then it is added to the accrued interest, and in each subsequent period interest is accrued on the already accrued amount. Thus, the basis for calculating interest is constantly changing. This method is sometimes referred to as "percentage by percentage".
The lower the interest rate and the shorter the period of time, the higher the present value of future income.
By means of discounting it is determined net present value of the project. Also known as net present value "net present income".
The general rule of thumb for decision making is that innovation should be undertaken if the expected return on capital is at least (or equal to) the market rate of interest on loans. Interest plays an important role in solving the problem of efficient distribution of resources in a market economy: choosing the most profitable of the possible innovative solutions. Comparing the level of return on capital with the interest rate is one way to justify the effectiveness of innovation.
Using formulas relating the present and future value of cash, one can obtain a formula for determining the discounted (reduced to the present, or updated) future value of cash flows generated in different years by the investment in question. Discounting
The concept of "discounting" (from English, discounting - cost reduction, markdown) is one of the key in the theory of investment analysis.
Discounting is the operation of calculating the present value (English, present value - present value, present value, etc.) of monetary amounts relating to future periods of time.
The opposite of discounting, the calculation of the future value of an initial amount of money, is called accumulation or compounding and is easily illustrated by an example of an increase in the amount of debt over time at a given interest rate:
where F- future;
R - modern value (initial value) of the amount of money; G - interest rate (in decimal terms);
N- number of interest periods.
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The transformation of the above formula in the case of solving the inverse problem looks like this:
Discounting methods are used if it is necessary to compare the amounts of cash receipts and payments spaced over time. In particular, the key measure of investment performance is the net present value ( NPV)- represents the sum of all cash flows (receipts and payments) arising during the period under review, given (recalculated) at one point in time, which, as a rule, is chosen as the moment the investment was started.
As follows from all that has been said, the interest rate used in the formula for calculating the present value is no different from the usual rate, which in turn reflects the cost of capital. In the case of using discount methods, this rate, however, is usually called the discount rate (comparison rate, barrier rate, discount rate, reduction factor, etc.).
A qualitative assessment of the effectiveness of an investment project largely depends on the choice of the discount rate. There are a large number of different methods to justify the use of one or another value of this rate. In the most general case, you can specify the following options for choosing a discount rate:
- the minimum return on an alternative way of using capital (for example, the rate of return on reliable marketable securities or the rate of deposit in a reliable bank);
- the existing level of return on capital (for example, the company's weighted average cost of capital);
- the cost of capital that can be used to implement this investment project (for example, the rate on investment loans);
- the expected level of return on invested capital, taking into account all the risks of the project.
The rates listed above differ mainly in the degree of risk, which is one of the components of the cost of capital. Depending on the type of discount rate chosen, the results of calculations related to the assessment of the effectiveness of investments should also be interpreted.
The accumulated amount of discounted returns should be compared with the amount of investment.
The total accumulated amount of discounted income for P years will be equal to the sum of the corresponding discounted payments.
In the article we will talk in detail about discounting cash flows, the calculation and analysis formula in Excel.
Discounting cash flows. Definition
Cash flow discounting (English Discounted cash flow, DCF, discounted value) is the reduction of the value of future (expected) cash payments to the current moment in time. Discounting cash flows is based on the important economic law of diminishing value of money. In other words, over time, money loses its value compared to the current one, so it is necessary to take the current moment of assessment as a starting point and bring all future cash receipts (profits / losses) to the present. For this purpose, a discount factor is used.
How to calculate the discount factor?
Discount coefficient is used to convert future earnings to present value by multiplying the discount factor and the cash flows. The formula for calculating the discount factor is shown below:
where: r is the discount rate, i is the number of the time period.
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Discounting cash flows. Calculation formula
DCF( discounted cash flow– discounted cash flow;
CF ( Cashflow) - cash flow in time period I;
r is the discount rate (rate of return);
n is the number of time periods for which cash flows appear.
The key element in the discounted cash flow formula is the discount rate. The discount rate shows what rate of return an investor should expect when investing in a particular investment project. The discount rate uses many factors that depend on the object of assessment, and may include: inflation component, return on risk-free assets, additional rate of return for risk, refinancing rate, weighted average cost of capital, interest on bank deposits, etc.
Calculating the rate of return (r) for discounting cash flows
There are many different ways and methods for estimating the discount rate (rate of return) in investment analysis. Let us consider in more detail the advantages and disadvantages of some methods for calculating the rate of return. This analysis is presented in the table below.
Methods for estimating the discount rate |
Advantages |
Flaws |
CAPM Models | Ability to account for market risk | One-factor, the need for the presence of ordinary shares in the stock market |
Gordon Model | Ease of calculation | The need for ordinary shares and constant dividend payments |
Weighted average cost of capital (WACC) model | Accounting for the rate of return of both equity and debt capital | Difficulty in assessing return on equity |
Model ROA, ROE, ROCE, ROACE | Ability to take into account the return on capital of the project | Not taking into account additional macro, micro risk factors |
E/P method | Accounting for the market risk of the project | Availability of quotes on the stock market |
Method for estimating risk premiums | Using Additional Risk Criteria in Estimating the Discount Rate | Subjectivity of risk premium estimation |
Judgment-Based Appraisal Method | Possibility to take into account weakly formalized project risk factors | Subjectivity of expert assessment |
You can learn more about the approaches to calculating the discount rate in the article "".
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★ (calculation of Sharpe, Sortino, Trainor, Kalmar, Modiglanchi beta, VaR ratios) + rate movement forecasting |
Example of calculating discounted cash flow in Excel
In order to calculate discounted cash flows, it is necessary for the selected time period (in our case, annual intervals) to describe in detail all the expected positive and negative cash payments (CI - Cashinflow, CO CashOutflow). The following payments are taken for cash flows in valuation practice:
- Net operating income;
- Net cash flow excluding operating costs, land tax and facility refurbishment;
- Taxable income.
In domestic practice, as a rule, a period of 3-5 years is used; in foreign practice, the assessment period is 5-10 years. The entered data is the basis for further calculation. The figure below shows an example of entering initial data in Excel.
The next step is to calculate the cash flow for each of the time periods (column D). One of the key tasks in assessing cash flows is to calculate the discount rate, in our case it is 25%. And was obtained by the following formula:
Discount rate= Risk free rate + Risk premium
The key rate of the Central Bank of the Russian Federation was taken as the risk-free rate. The key rate of the Central Bank of the Russian Federation is currently 15% and the premium for risks (production, technological, innovative, etc.) was calculated by an expert at the level of 10%. The key rate reflects the return on a risk-free asset, and the risk premium shows an additional rate of return on the existing risks of the project.
You can learn more about calculating the risk-free rate in the following article: ""
After that, it is necessary to bring the received cash flows to the initial period, that is, multiply them by the discount factor. As a result, the sum of all discounted cash flows will give the present value of the investment object. The calculation formulas will be as follows:
Cash flow (CF)=B6-C6
Discounted cash flow (DCF)= D6/(1+$C$3)^A6
Total discounted cash flow (DCF)= SUM(E6:E14)
As a result of the calculation, we received the discounted value of all cash flows (DCF) equal to 150,981 rubles. This cash flow has a positive value, which indicates the possibility of further analysis. When conducting an investment analysis, it is necessary to compare the final values of the discounted cash flow for various alternative projects, this will allow them to be ranked according to the degree of attractiveness and efficiency in creating value.
Investment analysis methods using discounted cash flows
It should be noted that discounted cash flow (DCF) in its calculation formula is very similar to net present value (NPV). The main difference lies in the inclusion of initial investment costs in the NPV formula.
Discounted cash flow (DCF) is used in many methods for evaluating the effectiveness of investment projects. Due to the fact that these methods use discounted cash flows, they are called dynamic.
- Dynamic methods for evaluating investment projects
- Net present value (NPV,Netpresentvalue)
- Internal rate of return ( IRR, Internal Rate of Return)
- profitability index (PI, Profitability Index)
- Annuity equivalent (NUS, Net Uniform Series)
- net rate of return ( NRR, Net Rate of Return)
- Net future value ( nfv,NetFuturevalue)
- Discounted payback period (DPP,Discountedpayback period)
You can learn more about the methods for calculating the effectiveness of investment projects in the article "".
Besides only discounting cash flows, there are more sophisticated methods that additionally take into account the reinvestment of cash payments.
- Modified net rate of return ( MNPV, Modified Net Rate of Return)
- Modified rate of return ( MIRR, Modified Internal Rate of Return)
- Modified net present value ( MNPV,modifiedpresentvalue)
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★ (calculation of Sharpe, Sortino, Trainor, Kalmar, Modiglanchi beta, VaR ratios) + rate movement forecasting |
Advantages and Disadvantages of the DCF Measure of Discounted Cash Flows
+) The use of the discount rate is an undoubted advantage of this method, as it allows you to bring future payments to the current value and take into account possible risk factors when assessing the investment attractiveness of the project.
-) The disadvantages include the difficulty of predicting future cash flows for an investment project. In addition, it is difficult to reflect changes in the external environment in the discount rate.
Summary
Cash flow discounting is the basis for calculating many coefficients for evaluating the investment attractiveness of a project. We analyzed the example of the algorithm for calculating discounted cash flows in Excel, their existing advantages and disadvantages. Ivan Zhdanov was with you, thank you for your attention.