Notes:
1. The discount factor (discount factor) is set by the formula:
Where r is the discount rate, %; t- billing period, years.
2. 
In a similar manner, the discount factor for project No. 2 is determined.
Based on the data in Table. 10.6, determine the net present effect (NPE) for investment projects:
NPI1 \u003d 17368 - 14000 - 3368 thousand rubles;
NPI2 \u003d 16442 - 13400 \u003d 3042 thousand rubles.
So, a comparison of NPI indicators for projects confirms that the first of them is more effective than the second. NPI on it for 326 thousand rubles. (3368 -- 3042), or 9.7% more than in the second project. However, under project No. 1, the amount of capital investments for 600 thousand rubles. (14,000 - 13,400), or 4.3%, higher than in the second project, and their return in the form of future cash flow is lower than in project No. 2 by 2,000 thousand rubles. (20,000 - 22,000). In the case of the implementation of project No. 1, the investor needs to find additional funding(internal or external) in the amount of 600 thousand rubles. Therefore, he must choose for himself the most appropriate option, taking into account the available financial possibilities.
It should be noted that the NPI indicator is absolute, so it can be summed up and compared with other similar projects. In addition, it can be used not only for a comparative assessment of the effectiveness of projects at the preliminary stage of their consideration, but also as a criterion for the expediency of their implementation. Projects for which the NPI is negative or equal to zero are unacceptable for the investor, since they will not bring him additional income on invested capital. Projects with a positive NPI increase the investor's initial capital advance.
The CPE method is not an absolutely correct criterion for:
Fluctuations in the discount rate during the project implementation period due to changes in economic conditions in the investment goods market;
Choosing between a project with a large initial capital cost and a project with a significantly lower investment (3 million and 500 thousand rubles); it is obvious that if the influx Money will not be, then under the first project the enterprise will lose 6 times more than under the second one;
Choosing between a project with a large NPI and a long payback period and a project with a lower NPI and a short payback period (up to one year). Consequently, the NPE method does not allow to judge the profitability threshold and the margin of financial strength;
The choice of discount rate, especially in the conditions of the unstable Russian economy (bank interest rates, weighted average cost of capital, etc.).
Despite the noted shortcomings, this method (NPV) is recognized in international practice as the most reliable in the system of criteria for evaluating the effectiveness of investment projects.
The indicator - discounted yield index (FIR) is calculated by the formula:
(144)
where HC is the present value of cash flows; I - the amount of investments aimed at the implementation of the project (if the investments are at different times, it is also reduced to the present value).
Using the data for two projects, we determine the discounted profitability index for them:
DID1=1.241 (17,368/14,000);
DID2=1.241 (17,368/14,000);
Therefore, according to this parameter, the efficiency of the projects is approximately the same. If the value of the yield index is less than or equal to one, then the project is rejected, since it will not bring the investor additional income. Projects with a value of this indicator greater than one are accepted for implementation. It should be noted that with the growth of the absolute value of NPE (in the numerator of formula 144), the value of the discounted profitability index also increases, and vice versa. At zero NPI, the yield index is always equal to one. This means that only one of them can be taken as a criterion for the implementation of the project - NPI or profitability index. In practice, when comparative evaluation recommend considering both indicators and making the right investment decision.
Among the key points for the successful implementation of a business plan is the calculation of the discount factor. Very often, business plan customers have a vague idea of the significance of this parameter, and sometimes they don’t even understand why it needs to be calculated.
Discounting is a calculation of the amount of cash flows that relate to the future. In other words, it is the definition of future income at the current moment.
The discount factor makes it possible to evaluate the amount of investment, taking into account the risk and the time factor. Time for any project is an important critical factor, since the money that is received at the moment is more preferable than the money that is expected in the future period. After all, "today's" funds can be invested or saved, and receive income or interest.
In order to determine the time interval for the implementation of the project, it is necessary to first set a deadline date for its completion, equal to the expected number of years (days or months), after which the project will be considered technically unacceptable. Until this date, limited, for example, by the period of use of the equipment, the project will be able to make a profit. Getting the timing right is important, as becomes apparent when calculating future costs and benefits in a business plan. The lengthening or shortening of the project duration determines the range of time over which costs are expected to accrue and revenues to be generated. Therefore, the estimate of the duration of the project must be realistic, regardless of how much it will increase or decrease its attractiveness.
Discount rate calculation:
Let us introduce the notation:
PV - present value, modern value, initial amount.
FV - future value, future value, accumulated amount. I = (FV - PV) - interest money, interest money, interest. Represents the amount of income.
Profitability assessment financial transactions in terms of interest money, I is rarely used, because depends on the initial amount of PV and the accrual period. A more convenient indicator is interest rate characterizing the growth rate.
r = I / PV = (FV - PV) / PV - interest, interest rate.
Usually, the interest rate is known from the terms of a financial transaction (for example, from the terms of a deposit or loan agreement), then for the accumulated amount you can write:
FV = PV * (1 + r).
Thus, knowing the interest rate and the initial amount, we determine the accumulated amount.
For example:
Initial amount (PV) = 300,000 rubles.
Interest rate (r) = 17% (0.17)
FV \u003d 300,000 * (1 + 0.17) \u003d 351,000 rubles. - accumulated amount.
When solving discounting problems, it is necessary to solve the inverse problem: knowing the accumulated amount, determine the initial amount, or the amount at another previous moment. To do this, by analogy with the interest rate, we determine the discount rate (discount rate):
d = I / FV = (FV-PV) / FV - discount rate, discount rate, discount rate.
Example: d = (351,000 - 300,000) / 351,000 = 0.145 (14.5%)
Discount factor P, which determines the present value of the payment that will be made in n years at a discount rate d, is determined by the formula:
P = 1 / (1 +d) n
P - always less than one and determines the quantitative value of the present value of one dollar, ruble or any other monetary unit in the future, subject to the conditions adopted for its calculation. The total future payment is determined by multiplying the discount factor by the value of the asset or liability being discounted.
net present value method - NPV.
NPV(Net Present Value, NPV), net present value - the amount of the estimated stream of payments, reduced to the current (at the moment) value. Bringing to the current value is given at a given discount rate.
This method takes into account the dependence of cash flows over time.
If the calculated net worth payment flow is greater than zero (NPV>0), then during its life the project will reimburse the initial costs and provide a profit.
It is also worth noting that the greater the NPV (positive), the more likely our business plan is to receive investments and the more preferable it will look against the background of other business projects.
A negative NPV means that the target rate of return is not met and the project is unprofitable.
At NPV=0 the project only pays for the costs, but does not generate income. However, such a project has arguments in its favor - if it is implemented, production volumes will increase, i.e. the company will grow in size.
Formula for calculating NPV:
For a cash flow consisting of N periods (steps), we can write:
F.C. = F.C. 1 +FC 2 + … + FC N ,
FC - total cash flow
FC 1 etc. - cash flows all periods
NPV=FC 1 /(1+D)+FC 2 /(1+D) 2 +FC 3 /(1+D) 3 …etc.
Where D is the discount rate. It reflects the rate of change in the value of money over time, the higher the discount rate, the greater the rate.
Discounting from the English "discounting" - casting economic values for different periods of time to a given period of time.
If you have no economic or financial education, then this term is most likely not familiar to you and this definition is unlikely to explain the essence of "discounting", rather, it will confuse even more.
However, it makes sense for a prudent owner of his budget to understand this issue, since each person finds himself in a situation of “discounting” much more often than it seems at first glance.
Discounting - information from Wikipedia
Description of discounting in simple words
What Russian is not familiar with the phrase "know the value of money"? This phrase comes to mind as soon as the line at the checkout approaches, and the buyer takes another look at his grocery cart to remove the “unnecessary” product from it. Still, in our time we have to be prudent and economical.
Discounting is often understood as economic indicator, which defines purchasing power money, their value over a certain period of time. Discounting allows you to calculate the amount that you need to invest today in order to receive the expected return some time later.
Discounting as a tool for predicting future profits is in demand among business representatives at the stage of planning the results (profit) from investment projects. Future results may be announced at the beginning of the project or during the implementation of its subsequent stages. To do this, the given indicators are multiplied by the discount factor.
Discounting also "works" in the interests of ordinary person not associated with the world of big investments.
For example, all parents strive to give their child a good education, and, as you know, it can cost a lot of money. Not everyone has it at the time of admission financial opportunities (cash reserve), so many parents think about the "stash" (a certain amount of money spent past the cash register family budget), which can help out in X-hour.
Let's say that in five years your child will graduate from school and decide to enter a prestigious European university. Preparatory courses at this university cost $2,500. You are not sure that you can carve out this money from the family budget without prejudice to the interests of all family members. There is a way out - you need to open a deposit in a bank, for this it would be good to first calculate the amount of the deposit that you must open in the bank now, so that at X-hour (that is, five years later) you will receive 2500, provided that the maximum favorable interest, which the bank can offer, say -10%. To determine how much future spending (cash flow) is worth today, we make a simple calculation: Divide $2,500 by (1.10) 2 to get $2,066. This is what discounting is.
Simply put, if you want to know what the value of the amount of money you will receive or intend to spend in the future, then you should "discount" this future amount (income) at the rate of interest offered by the bank. This rate is also called the "discount rate".
In our example, the discount rate is 10%, $ 2,500 is the payment amount (or cash outflow) in 5 years, and $2,066 is the present value of the future cash flow.
Discount formulas
All over the world it is customary to use special English terms to denote the current (discounted) and future value: future value (FV) and present value (PV). It turns out that $ 2,500 is FV, that is, the value of money in the future, and $ 2,066 is PV, that is, the cost of this moment time.
The formula for calculating the present value for our example looks like this: 2500 * 1/(1+R) n = 2066.
General discount formula: PV = FV * 1/(1+R)n
- Factor by which the future value is multiplied 1/(1+R)n, is called the "discount factor",
- R- interest rate
- N is the number of years from a date in the future to the present.
As you can see, these mathematical calculations are not so difficult and not only bankers can do it. In principle, you can give up on all these figures and calculations, the main thing is to capture the essence of the process.
Discounting is the path of cash flow from the future to today - that is, we go from the amount we want to receive after a certain amount of time to the amount that we must spend (invest) today.
Life formula: time + money
Let's imagine another situation familiar to everyone: you have "free" money, and you went to the bank to make a deposit of, say, $2,000. $2,000 deposited in the bank today bank rate 10% tomorrow will cost $2,200, that is, $2,000 + deposit interest 200 (=2000*10%) . It turns out that in a year you will be able to receive 2200 dollars.
If we represent this result in the form of a mathematical formula, then we have: $2000*(1+10%) or $2000*(1,10) = $2200 .
If you deposit $2,000 for a period of two years, that amount will convert to $2,420. We consider: $2000 + interest for the first year $200 + interest for the second year $220 = 2200*10% .
The general formula for increasing the contribution (without additional contributions) for two years looks like this: (2000*1,10)*1,10 = 2420
If you want to extend the term of the deposit, your income from the deposit will increase even more. To find out the amount that the bank will pay you in a year, two or, say, five years, you need to multiply the deposit amount with a multiplier: (1+R) N.
Wherein:
- R is the interest rate expressed as fractions of a unit (10% = 0.1),
- N indicates the number of years.
Discounting and accrual operations
Thus, it is possible to determine the value of the contribution at any time point in the future.
Calculating the future value of money is called "accrual".
The essence of this process can be explained by the example of the well-known expression “time is money”, that is, over time cash deposit grows at the expense of an increment by annual percentages. All modern banking system where time is money.
When we discount, we move from the future to today, and when we “increase”, the trajectory of money movement is directed from today to the future.
Both "calculation chains" (both discounting and building up) make it possible to analyze possible changes in the value of money over time.
Discounted Cash Flow Method (DCF)
We have already mentioned that discounting - as a tool for predicting future profits - is necessary to calculate the project's efficiency assessment.
So when evaluating market value business, it is customary to take into account only that part of the capital that is capable of generating income in the future. At the same time, many points are important for the business owner, for example, the time of receipt of income (monthly, quarterly, at the end of the year, etc.); what risks may arise in connection with profitability, etc. These and other features that affect the valuation of a business are taken into account by the DCF method.
Discount coefficient
The method of discounting cash flows is based on the law of the "falling" value of money. This means that over time, money "cheapens", that is, it loses its value compared to its current value.
It follows from this that it is necessary to build on the assessment at the current moment, and correlate all subsequent cash flows or outflows with today. This will require a discount factor (Kd), which is needed to convert future earnings to present value by multiplying Kd by the cash flows. The calculation formula looks like this:
where: r- discount rate, i– time period number.
DCF calculation formula
The discount rate is the main component of the DCF formula. It shows what size (rate) of profit a business partner can expect when investing in a project. The discount rate takes into account various factors, depending on the object of assessment, and may include: inflation component, assessment of capital shares, return on risk-free assets, refinancing rate, interest on bank deposits and not only.
It is generally accepted that a potential investor will not invest in a project whose value will be higher than the present value of the future income from the project. Likewise, an owner would not sell his business for a price that is less than the estimated value of future earnings. As a result of negotiations, the parties will agree on market price, which is equivalent to today's value of projected earnings.
The ideal situation for an investor is when internal norm the profits (discount rate) of the project are higher than the costs associated with finding funding for the business idea. In this case, the investor will be able to “earn” the way banks do, that is, accumulate money at a reduced interest rate, and invest it in a project at a higher rate.
Discounting and investment projects
The discounted cash flow method is in line with the investment motives of the business.
This means that an investor who invests in a project acquires non-technical or human resources in the form of a team of highly qualified specialists, modern offices, warehouses, high-tech equipment, etc., and the future flow of money. If we continue this thought, it turns out that any business “releases” the only product on the market - this is money.
The main advantage of the discounted cash flow method is that this valuation method, the only one of all existing ones, is focused on the future development of the market, which contributes to the development of the investment process.
Highly specialized material for professional investors
and students of the Fin-plan course "".
Financial and economic calculations are most often associated with the assessment of time-distributed cash flows. Actually for these purposes, and need a discount rate. From the point of view of financial mathematics and investment theory, this indicator is one of the key. Methods are built on it. investment appraisal business based on the concept of cash flows, with its help, a dynamic assessment of the effectiveness of investments, both real and stock, is carried out. To date, there are already more than a dozen ways to select or calculate this value. Mastering these methods allows a professional investor to make more informed and timely decisions.
But, before moving on to the methods of justifying this rate, let's look at its economic and mathematical essence. Actually, two approaches are applied to the definition of the term "discount rate": conditionally mathematical (or process), as well as economic.
The classic definition of the discount rate stems from the well-known monetary axiom: “Money today is worth more than money tomorrow.” Hence, the discount rate is a certain percentage that allows you to bring the cost of future cash flows to their current cost equivalent. The fact is that many factors influence the depreciation of future income: inflation; risks of not receiving or not receiving income; lost profit arising from the appearance of a more profitable alternative investment opportunity in the process of implementing a decision already made by the investor; systemic factors and others.
By applying a discount rate in their calculations, an investor discounts, or discounts, expected future cash income to the current point in time, thereby taking into account the above factors. Discounting also allows the investor to analyze cash flows over time.
In this case, the discount rate and the discount factor should not be confused. The discount factor is usually used in the calculation process as a kind of intermediate value calculated on the basis of the discount rate according to the formula:
where t is the number of the forecast period in which cash flows are expected.
The product of the future value of the cash flow and the discount factor shows the current equivalent of the expected income. However, the mathematical approach does not explain how the discount rate itself is calculated.
For these purposes, it is used economic principle, according to which the discount rate is some alternative return on comparable investments with the same level of risk. A rational investor, making a decision to invest money, will agree to the implementation of his "project" only if its profitability turns out to be higher than the alternative and available on the market. This is not an easy task, since it is very difficult to compare investment options by level of risk, especially in the absence of information. In acceptance theory investment decisions this problem is solved by decomposing the discount rate into two components - the risk-free rate and risks:
The risk-free rate of return is the same for all investors and is subject only to the risks of the economic system. The remaining risks are assessed by the investor independently, as a rule, on the basis of an expert assessment.
There are many models to justify the discount rate, but all of them in one way or another correspond to this basic fundamental principle.
Thus, the discount rate is always the sum of the risk-free rate and the total investment risk of a particular investment asset. The starting point for this calculation is the risk-free rate.
risk free rate
The risk-free rate (or risk-free rate of return) is the expected rate of return on assets for which financial risk equals zero. In other words, this is the return on absolutely reliable options for investing money, for example, on financial instruments, the profitability of which is guaranteed by the state. We emphasize that even for absolutely reliable financial investments absolute risk cannot be absent (in this case, the rate of return would also tend to zero). The risk-free rate includes the risk factors of the economic system itself, risks that no investor can influence: macroeconomic factors, political events, changes in legislation, extraordinary anthropogenic and natural events, etc.
Therefore, the risk-free rate reflects the lowest possible return acceptable to the investor. The investor must choose the risk-free rate for himself. You can calculate the average rate from several options for potentially risk-free investments.
When choosing a risk-free rate, an investor should take into account the comparability of his investments with a risk-free option according to such criteria as:
Scale or total cost of investment.
Investment period or investment horizon.
The physical possibility of investing in a risk-free asset.
Equivalence of denomination of rates in currency, and others.
Rates of return on fixed-term ruble deposits in banks of the highest reliability category. In Russia, such banks include Sberbank, VTB, Gazprombank, Alfa-Bank, Russian Agricultural Bank and a number of others, a list of which can be viewed on the website Central Bank RF. When choosing a risk-free rate in this way, it is necessary to take into account the comparability of the investment period and the period of fixing the rate on deposits.
Let's take an example. We use the data of the website of the Central Bank of the Russian Federation. As of August 2017, the weighted average interest rates on deposits in rubles for up to 1 year amounted to 6.77%. This rate is risk-free for most investors who invest for up to 1 year;
Yield on Russian government debt financial instruments. In this case, the risk-free rate is fixed in the form of yield on (OFZ). These debt securities are issued and guaranteed by the Ministry of Finance of the Russian Federation, therefore they are considered the most reliable financial asset in RF. With a maturity of 1 year, OFZ rates currently range from 7.5% to 8.5%.
Level of return on foreign government securities. In this case, the risk-free rate equals the return government bonds USA with maturities from 1 to 30 years. Traditionally, the US economy is international rating agencies estimated at highest level reliability, and, consequently, the yield of their government bonds and is recognized as risk-free. However, it should be taken into account that the risk-free rate in this case is denominated in dollars and not in rubles. Therefore, for the analysis of investments in rubles, an additional adjustment for the so-called country risk is necessary;
Yield on Russian government Eurobonds. This risk-free rate is also denominated in dollar terms.
The key rate of the Central Bank of the Russian Federation. At the time of this writing, the key rate is 9.0%. It is believed that this rate reflects the price of money in the economy. An increase in this rate entails an increase in the cost of a loan and is a consequence of an increase in risks. This tool should be used with great care, as it is still a directive, not a market indicator.
Interbank lending market rates. These rates are indicative and more acceptable than key rate. Monitoring and a list of these rates are again presented on the website of the Central Bank of the Russian Federation. For example, as of August 2017: MIACR 8.34%; RUONIA 8.22%, MosPrime Rate 8.99% (1 day); ROISfix 8.98% (1 week). All these rates are short-term and represent the yield on lending operations of the most reliable banks.
Discount rate calculation
To calculate the discount rate, the risk-free rate should be increased by the risk premium that the investor assumes when making certain investments. It is impossible to assess all risks, so the investor must independently decide which risks and how should be taken into account.
On the value of the risk premium and, ultimately, the discount rate greatest influence provides the following options:
The size of the issuing company and the stage of its life cycle.
The nature of the liquidity of the company's shares in the market and their volatility. The most liquid stocks generate the least risk;
Financial condition share issuer. stable financial position increases the adequacy and accuracy of forecasting the company's cash flow;
Business reputation and perception of the company by the market, investors' expectations regarding the company;
Industry affiliation and risks inherent in this industry;
The degree of exposure of the activity of the issuing company to macroeconomic conditions: inflation, fluctuations in interest rates and exchange rates etc.
A separate group of risks includes the so-called country risks, that is, the risks of investing in the economy of a particular state, for example, Russia. Country risks are usually already included in the risk-free rate if the rate itself and the risk-free yield are denominated in the same currencies. If the risk-free return is in dollar terms, and the discount rate is needed in rubles, then it will be necessary to add country risk as well.
This is just a short list of risk factors that can be taken into account in the discount rate. Actually, depending on the method of assessing investment risks, the methods for calculating the discount rate differ.
Let us briefly consider the main methods for justifying the discount rate. To date, more than a dozen methods for determining this indicator have been classified, but they are all grouped in the following way(from simple to complex):
Conditionally "intuitive" - based rather on the psychological motives of the investor, his personal beliefs and expectations.
Expert, or qualitative - based on the opinion of one or a group of specialists.
Analytical - based on statistics and market data.
Mathematical, or quantitative - require mathematical modeling and the possession of relevant knowledge.
An "intuitive" way to determine the discount rate
Compared to other methods, this method is the simplest. The choice of the discount rate in this case is not mathematically justified in any way and represents only the desire of the investor, or his preference for the level of profitability of his investments. An investor can rely on his previous experience, or on the profitability of similar investments (not necessarily his own), if he knows the information about the profitability of alternative investments.
Most often, the discount rate is “intuitively” calculated approximately by multiplying the risk-free rate (as a rule, this is just the deposit rate or OFZ) by some adjustment factor of 1.5, or 2, etc. Thus, the investor, as it were, “estimates” the level of risks for himself.
For example, when calculating discounted cash flows and fair value companies in which we plan to invest, as a rule, we use the following rate: the average rate on deposits, multiplied by 2, if we are talking about blue chips and apply higher odds when it comes to 2nd and 3rd tier companies.
This method is the simplest practice for a private investor and is used even in large investment funds experienced analysts, but he is not held in high esteem among academic economists, because he allows for “subjectivity”. In this regard, in this article we will give an overview of other methods for determining the discount rate.
Calculation of the discount rate based on expert judgment
The expert method is used when investments involve investing in shares of companies in new industries or activities, start-ups or venture funds, and also when there are no adequate market statistics or financial information about the issuing company.
The expert method for determining the discount rate consists in polling and averaging the subjective opinions of various specialists about the level, for example, the expected return on specific investments. The disadvantage of this approach is the relatively high proportion of subjectivity.
It is possible to increase the accuracy of calculations and somewhat level subjective assessments by decomposing the rate into a risk-free level and risks. The investor chooses the risk-free rate on his own, and the assessment of the level of investment risks, the approximate content of which we described earlier, is already carried out by experts.
The method is well applicable for investment teams that employ investment experts of various profiles (currency, industry, raw materials, etc.).
Calculation of the discount rate by analytical methods
There are many analytical ways to justify the discount rate. All of them are based on the theory of economics of the firm and financial analysis, financial mathematics and business valuation principles. Let's give some examples.
Calculation of the discount rate based on profitability indicators
In this case, the discount rate is justified on the basis of various indicators profitability, which in turn are calculated from the data and . The profitability indicator is used as the base equity(ROE, Return On Equity), but there may be others, for example, return on assets (ROA, Return On Assets).
Most often used to evaluate new investment projects within an existing business, where the nearest alternative rate profitability is precisely the profitability of the current business.
Calculation of the discount rate based on the Gordon model (model of constant growth of dividends)
This method of calculating the discount rate is acceptable for companies that pay dividends on their shares. This method assumes the fulfillment of several conditions: the payment and positive dynamics of dividends, the absence of restrictions on the life of the business, stable growth company income.
The discount rate in this case is equal to the expected return on equity of the company and is calculated by the formula:
Given methods applicable to evaluate investments in new projects of the company, by the shareholders of this business, who do not control profits, but receive only dividends.
Calculation of the discount rate by quantitative analysis methods
From the point of view of investment theory, these methods and their variations are the main and most accurate. Despite the many varieties, all these methods can be reduced to three groups:
Models of cumulative construction.
Capital Asset Pricing Model (CAPM).
Models of the weighted average cost of capital WACC (Weighted Average Cost of Capital).
Most of these models are quite complex, requiring a certain mathematical or economic skill. We'll consider general principles and basic calculation models.
Cumulative building model
Within the framework of this method, the discount rate is the sum of the risk-free rate of expected return and the total investment risk for all types of risk. The method of substantiating the discount rate based on risk premiums to the risk-free level of return is used when it is difficult or impossible to evaluate the relationship between risk and return on investment in the analyzed business using mathematical statistics. AT general view the calculation formula looks like this:
Capital asset pricing model CAPM
The author of this model is Nobel laureate in Economics W. Sharp. The logic of this model does not differ from the previous one (the rate of return is the sum of the risk-free rate and risks), the method of assessing investment risk is different.
This model is considered fundamental, since it establishes the dependence of profitability on the degree of its exposure external factors market risk. This relationship is assessed through the so-called "beta" coefficient, which is essentially a measure of the elasticity of an asset's return to a change in the average market return of similar assets in the market. In general, the CAPM model is described by the formula:
Where β is the “beta” coefficient, a measure of systematic risk, the degree of dependence of the assessed asset on the risks of the economic system itself, and the average market return is average return in the market for similar investment assets.
If the "beta" coefficient is higher than 1, then the asset is "aggressive" (more profitable, changing faster than the market, but also more risky in relation to analogues in the market). If the "beta" coefficient is below 1, then the asset is "passive" or "protective" (less profitable, but also less risky). If the "beta" coefficient is equal to 1, then the asset is "indifferent" (its profitability changes in parallel with the market).
Calculation of the discount rate based on the WACC model
Estimating the discount rate based on the company's weighted average cost of capital allows you to estimate the cost of all sources of financing for its activities. This indicator reflects the actual costs of the company to pay for borrowed capital, equity capital, and other sources, weighted by their share in the total liability structure. If the company's actual return is above WACC, then it generates some added value for its shareholders, and vice versa. That is why the WACC indicator is also considered as a barrier value of the required return for the company's investors, that is, the discount rate.
The calculation of the WACC indicator is carried out according to the formula:
Of course, the range of methods for justifying the discount rate is quite wide. We have described only the main methods most often used by investors in a given situation. As we said earlier in our practice, we use the simplest, but quite effective "intuitive" way to determine the rate. The choice of a specific method always remains with the investor. You can learn the whole process of making investment decisions in practice in our courses at. We teach deep analytics techniques already at the second level of training, at advanced training courses for practicing investors. You can evaluate the quality of our training and take the first steps in investing by signing up for ours.
If the article was useful to you, like and share it with your friends!
Profitable investment to you!
Everyone knows about deposits and calculation rules. Add to the amount due bank interest and get the amount of funds at the end of the period. For example, 1000 USD was put into the bank. under 20% per annum. Calculation of the total at the end of the year: 1000 divided by 100% and multiplied by 120% (100% + 20%). Everything is simple and clear.
However, how to determine how much you need to invest in order 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 paying in advance. Literally, it means bringing the economic indicator for a certain time period to a given interval. In the absence of an economic education, it is easy to get confused in such terminology. But a prudent owner should look into the matter, since most people do not suspect their participation in "discounting". For example, a merchant promises to sell goods for specified value in a year, when the ship arrives with the goods.
However, he needs financial resources ah for the purchase of goods that will participate in the exchange operation. There are two ways to get money: apply to a banker for a loan or take funds from future buyers. The merchant must plain language explain to the latter about the discount rate. If customers understand, then the success of the event will be ensured.
The discount rate is used for the following purposes:
- Calculation of business profitability. The investor must know the amount of profit in the future in order to invest funds with the desired return.
- Evaluation of the organization's activities. Available profit does not guarantee good profitability.
- Yield planning. The chosen investment option should have the maximum return compared to alternative options. For example, one business will have a certain profit in 1 year, while another will bring in more funds, but only after two years. Both proposals should be compared with the same denominator. For clarity, consider an example from practice. Two businessmen approached a potential investor. They ask to invest 2 million in their business. The first 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 real life
Every Russian at least once thought about the "value of money." It is especially noticeable during shopping in supermarkets, when you have to remove “unnecessary” goods from the grocery basket. At present, it is necessary to be economical and prudent. Discounting is often understood as an economic indicator that shows the purchasing power of money, the value over a certain period of time. Discounting is used to predict profits for investment projects. Future results can be spoken at the beginning of the project or during its implementation when multiplied by the discount factor. But this concept is applicable not only to investments, but also in ordinary life. For example, parents want to pay for their child's education in a prestigious institution. But not everyone has the opportunity to pay a fee at the time of receipt. Then they start thinking about the “stash”, which is intended for the X hour. After 5 years, the child is scheduled to enter a European university. The cost of preparatory courses is 2500 USD. It is unrealistic for many to allocate such an amount from the family budget without prejudice to the interests of other members. Exit - open a deposit in advance financial institution. But how to determine the amount of the contribution in order to receive 2500 USD in five years? Deposit rate 10%. Calculation of the initial amount: 2500/(1+0.1)^5 = 1552 c.u. This is called discounting.
In simple terms, if you want to know the future value a certain amount, then you should "discount" it at the bank rate, which is called the discount rate. In the given example, it is equal to 10%, 2500 c.u. - cash flow (payment amount) after 5 years, 1552 c.u. is the discounted value of the cash flow.
Discounting will be the reciprocal of investing. 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 return on 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 amount of interest to account for "interest on interest". Such calculations are permissible 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 terms Future value and present value are used. In the example described, FV is 2500 USD, PV is 1552 USD. General form discounting:
PV = FV*1/(1+R)^n
1/(1+R)^n- discount factor;
R- interest rate;
n- the 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
Consider another common situation: there are available funds which it was decided 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 amount to 200 USD.
If you bring it all to general formula, then it will come out:
2000*(100%+10%)/100% = 2000*1.1 = 2200 c.u.
If we put 2000 c.u. for 2 years, then the total amount will be 2420 USD:
1 year 2000 * 1.1 \u003d 2200 c.u.
2 year 2200 * 1.1 \u003d 2420 c.u.
Extensions are available at no additional cost. If the investment period is extended, then the income will increase even more. For each course of keeping funds on deposit, the total amount of the deposit for the previous year is multiplied by (1+R) or the initial investment amount is multiplied by (1+R)^n.
Cumulative Method
To simplify the calculations, a table of coefficients is used. When it is applied, it is no longer necessary to calculate the amount of investment and profitability several times using the formula. It is enough to multiply the final profit by the coefficient from the table to get the desired investment.
The formula for determining the discount factor:
K \u003d 1 / (1 + Pr) \u003d B,
where AT- the number of cycles;
Etc- interest rate per cycle.
For example, for a two-year investment at 20%, the ratio is:
1*/(1+0,2)^2 = 0,694
Discount tables are similar to Brady's tables, which help students determine roots, cosines, and sines.
Discount factor tables simplify calculations. However, this method of calculation is not suitable for large investments. The given values are rounded to thousandths (3 digits after the decimal point), which leads to a large error when investing a million dollars.
Using the table is simple: if the rate and the number of periods are known, the desired coefficient is found at the intersection of the required columns and rows.
Practical use
Increasing the discount rate increases the payback period of the investment. The decision to invest funds should be made when the calculations show the desired payback period and are consistent with the capital investment plan.
A simplified calculation is made according to the formula for the return on investment period. It is based on the quotient between received and invested funds. The main disadvantage of the method is the assumption of a uniform income.
The above formulas do not take into account market risks. They can only be used for theoretical calculation. To bring the calculation closer to reality, they resort to graphical analysis. The graphs represent data on the movement of finance in a certain time interval.
Discounting and building up
Using a simple formula, determine the size of the contribution at the desired time point. Calculating the value of money in the future is called "build-up". The essence of this process is easy to understand by the expression "time is money" - over time, the size of the contribution increases by the increment of 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 to analyze the possibility of changes in the cost of funds.
Investment projects
Discounting of funds is consistent with the investment motives of the business. That is, the investor invests and receives non-human (qualified specialists, team) or technical resources(equipment, warehouses), and the flow of money in the future. The continuation of this thought will be "the product of any business is money." The discounting method is the only one of the existing ones, the orientation of which is aimed at development in the future, which allows the investment project to develop.
Selection example investment project. The owner of the funds (600 rubles) was offered 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 get 200 rubles, and after the third - 10,000 rubles. The investor has set a rate of 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 is raised to 31%, both options will be equivalent.
Present value
Present value is the present value of a future cash flow or a future payment without a "discount" for an upfront payment. It is often referred to as the present value - the future cash flow, correlated to today. However, these are not exactly the same concepts. It is possible to bring to the current time not only one future value, but also the present value to the desired time in the future. Present value is more extensive than present value. There is no concept of present value in English.
Discount method
It was previously mentioned that discounting is a tool for predicting future profits - evaluating the effectiveness of the current project.
When evaluating a business, they take into account that part of the assets that can generate income in the future. Business owners take into account the time to generate income and the likely risks for profit. These factors are taken into account when assessing by the DCF method. It is based on the principle of "falling" value - money supply constantly "cheaper" and loses in value. The starting point will be present value to which future cash flows are related. For this, the concept of the 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. Various factors can be taken into account in the discount rate: inflation, the refinancing rate, the assessment of capital shares, the interest on the deposit, the return on risk-free assets.
It is believed that the investor should not finance the project if its cost becomes higher than the present value of the income in the future. 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 an 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 funding for business ideas. This will allow you to earn like banks - the money will be accumulated according to reduced rate, and the contribution will happen - at the highest.
Additional calculations
The definition of 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 value is 0.
- Net cash flow - costs are subtracted from total gross receipts. Direct and indirect costs (tax deductions, legal support) should be included here.
Only an expert can determine the exact value of the company's profitability, based on the internal analysis of the company.
Complicated 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.
- Sharpe's corrected model. Determines the influence of market factors: changes in the cost of resources, government policy, price fluctuations.
- The volume of investments, 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 Carhart's 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 the property. Used for analysis financial activities a company whose assets are not listed on the stock market.
- subjective factor. It is used in multifactorial analysis of the organization's activities by third-party experts.
- Market risks. It is taken into account when determining the discount rate based on the ratio of risky to riskless investment.
In 1997, the Russian government published its own methodology for calculating the risk discount rate. Experts of the time estimated the risks at 47%. This indicator is not used in the usual 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 funds. When analyzing the economic activity of companies in the market, theoretical calculations will give the expected effect if local realities are taken into account. simple calculations help predict returns, but they will be highly volatile. For forecasting, you need to use complex formulas that take into account most of the risks in the financial and stock market. More accurate data will be obtained only through internal analysis of the company.
