Discount rate. Discount rate Alternative income
Cash flows can be assessed and reduced to one point in time on a nominal or real basis.
Nominal cash flows and premium rates. Nominal cash flows - These are monetary amounts expressed in prices that change due to inflation, i.e. payments that will actually be paid or received at various future points (intervals) of time. When calculating them, the constant increase in the price level in the economy is taken into account, and this affects the monetary assessment of the costs and results of making an investment decision (Fig. 3.3).
For example, having decided to implement a project to open a mini-bakery for baking and selling bakery products, we must take into account the projected increase in prices for bread, flour, etc. when calculating expected cash flows. over the life of the project and index cash flows accordingly increasing coefficient.
Rice. 3.3.
Nominal rate of alternative (required) return is the rate that actually exists in the market for investment decisions of a given level of risk. During periods of high inflation, such rates increase in order to compensate investors for losses from inflationary price increases through increased income. On the contrary, nominal rates are relatively low during periods of price stabilization. Based on this, these rates are said to include inflation premium.
Real cash flows and real discount rates. Real cash flows - These are flows expressed at a constant price scale in effect at the time the investment decision is justified. Thus, they are assessed without taking into account inflationary price increases (Figure 3.4). However, cash flows must still be indexed by a decreasing or increasing factor if they (or their individual elements) grow faster or slower than inflation.
Rice. 3.4.
The real rate of alternative (required) return - This is the rate “cleared” of the inflation premium. It reflects the part of the investor's income generated in excess of compensation for inflationary price increases.
Real rate (g) calculated by the formula
Where gr - real rate; G - nominal rate; To - inflation rate. All rates are expressed in fractions of a unit.
Example. The bank interest rate on deposits is 6%, and inflation during this period is expected to be 10%. What is the real rate of return offered by the bank?
Real cash flows are discounted at real rates, nominal - at nominal rates.
The basic calculation rule is that:
- o real cash flows should be discounted at real alternative rates of return;
- o Nominal cash flows should be discounted using nominal discount rates.
Thus, there are two approaches to estimating cash flows, each of which has its own pros and cons.
Advantages and disadvantages of the valuation method in constant (fixed) prices. The advantage of an assessment on a real basis is that with an aggregated calculation of cash flows there is no need to predict future inflationary price increases - it is enough to know the current level of inflation and prices in force in the current period. At the same time, to carry out such a calculation, it is necessary to more or less strictly fulfill the following hypothesis: all prices for products, raw materials, materials, etc., accepted when determining cash flows, change in the same proportion in accordance with the level of inflation in the economy. Another “minus” is that with this approach, difficulties arise in analyzing project financing systems (interest rates on loans provided to implement an investment decision must also be adjusted to real rates, which creates distrust in the calculation results on the part of creditors). For example, they give money at 14% per annum, but the real rate appears in the calculations - 4%. In addition, the project budget drawn up on a nominal basis looks more realistic.
Let's look at the principle approach to valuation on a real and nominal basis using an example.
Example. The company manager assumes that the project will require investments of 350 million rubles. and in the first year of implementation will give a cash flow of 100 million rubles. In each subsequent year for five years, cash flow will increase by 10% due to inflationary increases in product prices and costs. In the sixth and final year, a total cash flow of 123 million rubles will be received from the sale of equipment. It is necessary to determine whether a given project is profitable if the nominal alternative rate of return is 20% per annum.
The cash flow for the project, taking into account inflationary growth, is shown in table. 3.6.
TABLE 3.6.
Net present value is calculated as follows:
YRU> Oh, that means the project is profitable.
We will evaluate the same project on a real basis. The real alternative rate of return is calculated using the formula
According to the condition, only inflationary price increases are expected. Therefore, the subsequent cash flow until the sixth year will be stable and equal to 100: 1.1 = 90.91 million rubles. The cash flow of the last year, calculated on a constant price scale, is equal to
As you can see, both methods gave almost the same result, which is explained by the same assumptions laid down in the example conditions for both approaches (the discrepancies are associated with the approximation error allowed in the calculations).
Index funds allow you to earn income from investing in the stock market completely passively. For example, if you invest in a fund based on the S&P 500 index, your money will be invested in the overall market, and you won't have to worry about how to manage your money or whether to sell or buy shares of certain companies. All these points will be managed by the fund, which forms its investment portfolio depending on the state of a particular index.
You can also choose a fund that covers any index. There are funds involved in various business sectors - energy, precious metals, banking, emerging markets and others. All you have to do is decide for yourself that this is what you want to do, then invest the money and relax. From now on, your stock portfolio will run on autopilot.
Make videos for YouTube
This area is developing very quickly. You can make videos of absolutely any category - music, educational, comedy, movie reviews - anything... and then post it on YouTube. Then you can connect Google AdSense to these videos, and automatic advertising will appear in them. When viewers click on these ads, you will earn money from Google AdSense.
Your main task is to create decent videos, promote them on social networks and maintain a sufficient number of them to provide yourself with income from several clips. Shooting and editing a video is not that easy, but once done, you will have a source of completely passive income that can last for a very long time.
Not sure you'll succeed on YouTube? Michelle Phan combined her love of cosmetics and drawing with making videos, gained more than 8 million subscribers, and now launched her own company with a capitalization of $800 million.
Try Affiliate Marketing and Start Selling
This is a passive income technique that is more suitable for owners of blogs and active Internet sites. You can start promoting any products on your website and receive a fixed fee or a percentage of sales.
Making money this way is not as difficult as you might think because many companies are interested in selling their products in as many places as possible.
You can find partnership offers either by contacting manufacturers directly or on specialized websites. It is best if the advertised product or service is interesting to you or matches the theme of the site.
Make your photos profitable online
Do you like photography? If so, you may be able to turn this into a source of passive income. Photo banks such as and can provide you with a platform for selling photos. You will receive a percentage or flat rate for each photo sold to a website client.
In this case, each photo represents a separate source of income that can work again and again. All you need to do is create a portfolio, upload it to one or more platforms, and that's where your active work will end. All technical issues related to photo sales are resolved using the web platform.
Buy high-yield stocks
By creating a portfolio of high-yield stocks, you will receive a source of regular passive income with an annual interest rate that is much higher than the interest on bank deposits.
Don't forget that high-yielding stocks are still stocks, so there's always the possibility of capital overvaluation. In this case, you will receive profit from two sources - from dividends and return on invested capital. To purchase these shares and complete the appropriate forms, you will need to create a brokerage account.
Write an e-book
Of course, this can be quite a time-consuming process, but once you write a book and publish it on marketplaces, it can provide you with income for years. You can sell the book on your own website or enter into a partnership agreement with other sites that are similar in theme to the book.
Write a real book and get royalties
Just like writing an e-book, there's a lot of work involved at first. But when the work is completed and the book goes on sale, it will become a completely passive source of income.
This is especially true if you manage to sell your book to a publisher who will pay you a royalty on the sales. For each copy sold, you will receive a percentage, and if the book is popular, these percentages can add up to significant amounts. Moreover, these payments can last for years.
Mike Piper of ObviousInvestor.com recently did just that. He wrote a book, Investing Plain, which was sold only on Amazon. The first book became so profitable that he created a whole series. These books total .
Get cashback on credit card transactions
Many credit cards offer cash back ranging from 1% to 5% of the purchase price. You still go shopping and spend money, right?
Such bonuses allow you to provide yourself with a kind of passive “income” (in the form of reduced spending) from actions that you perform anyway.
Sell your own products online
The possibilities in this area are endless: you can sell almost any product or service. It could be something you created and made yourself, or it could be a digital product (software, DVDs, or instructional videos)
For trading, you can use a specialized resource, if suddenly you do not have your own website or blog. In addition, you can enter into a partnership agreement by offering goods to sites on relevant topics or using platforms like (American marketplace for selling digital information products - editor's note).
You can learn how to sell products online and earn quite a lot from it. This may not be completely passive income, but it is certainly more passive than a regular job that you have to go to every morning.
Invest in real estate
This method falls more into the category of semi-passive income, since investing in real estate involves at least a small level of activity. However, if you have a property that you're already renting out, it's mostly just a matter of maintaining it.
Additionally, there are professional property managers who can manage your property for a commission of approximately 10% of the rent. Such professional managers help make the process of receiving profits from such investments more passive, but they will take part of it.
Another way to invest in real estate is to pay off a loan. If you take out a loan to buy a property that you will rent out, your tenants will pay off that debt a little each month. When the full amount is paid, your profits will increase dramatically, and your relatively small investment will turn into a full-fledged program for quitting your day job.
Buy a blog
Thousands of blogs are created every year, and many of them end up abandoned after some time. If you can acquire a blog with enough visitors—and therefore enough cash flow—it can be a great source of passive income.
Most blogs use Google AdSense, which pays once a month for advertising placed on the site. To provide additional income, you can also enter into partnership agreements. Both of these income streams will be yours if you own a blog.
From a financial perspective, blogs typically sell for 24 times the monthly income the blog can generate. That is, if a site can earn $250 per month, most likely you can buy it for $3,000. This means that by investing $3,000, you can receive $1,500 annually.
You may be able to buy the site for less money if the owner really wants to get rid of this asset. Some sites contain “eternal” materials that will not lose relevance and will generate income years after publication.
Bonus tip: If you buy such a site and then fill it with fresh content, you will be able to increase your monthly income, and you will be able to sell the site again after some time for a significantly higher price than you paid when buying it.
Finally, instead of purchasing a blog, you can create your own. This is also a good way to earn money.
Create a website that sells
If there is a product that you know a lot about, you can start selling it on a specialized website. The technique is the same as when selling a product of your own making, except that you do not have to deal with the production itself.
After some time, you may find that you can add similar products. If this happens, the site will begin to generate significant profits.
If you can find a way to ship products directly from the manufacturer to the buyer, you won't even have to get your hands dirty. This may not be 100% passive income, but it’s very close to it.
Invest in real estate investment trusts (REITs)
Let's say you decide to invest in real estate, but you don't want to devote any attention or time to it. Investment trusts can help you with this. They are something like a fund that owns various real estate projects. The funds are managed by professionals, so you don't have to interfere with their work at all.
One of the main advantages of investing in REITs is that they typically pay higher dividends than stocks, bonds and bank deposits. You can also sell your interest in the trust at any time, making such assets more liquid than owning real estate on your own.
Become a passive business partner
Do you know a successful company that needs capital to expand its business? If so, you can become something of a short-term angel and provide that capital. But instead of giving a loan to the owner of the company, ask for a share of the shares. In this case, the owner of the company will manage the work of the company, while you will be a passive partner, also taking part in the business.
Every small business needs a source of referrals to support sales. Make a list of entrepreneurs whose services you use regularly and whom you can recommend for cooperation. Contact them and find out if they have a system for paying for referrals.
The list could include acquaintances: accountants, landscape designers, electricians, plumbers, carpet cleaners—anyone. Be prepared to recommend the services of these people to your friends, relatives and colleagues. You can earn a commission on every referral just by talking to people.
Don’t underestimate referral programs in the professional sphere either. If the company you work for offers bonuses for referring new employees or new clients, take advantage of it. This is very easy money.
Rent out your unused property on Airbnb
The concept appeared only a few years ago, but very quickly spread throughout the world. Airbnb allows people to travel the world and pay much less to stay than in regular hotels. By participating in Airbnb, you can use your home to host guests and earn extra money just from renting.
The amount of income will depend on the size and condition of your home and its location. Naturally, if your home is located in an expensive city or near a popular resort, the income will be much higher. This is a way to make money from free spaces in your home that would otherwise be empty.
Write an application
Apps can be an incredibly lucrative source of income. Think about how many people have smartphones today. Yes, almost everything! People are downloading apps like crazy—and for good reason.
Apps make people's lives easier. Whether it's helping you post pretty pictures or keeping track of tasks, there's always an app that's useful to someone.
You might ask: If there are so many apps out there, why would you try to create another one? Is there too much competition? This is all true, but fresh, creative ideas can benefit. If you can come up with something unique, you can make money from it.
Don't know how to program? No problem, you can learn. There are a lot of different courses on the Internet, including free ones. Alternatively, you can hire a developer to create an app based on your idea.
The end result is an application that will potentially generate relatively passive income.
Create online courses
Every person is an expert in something. Why not create an online course about your passion?
There are several ways to create and deliver your own online courses. One of the easiest ways is to use sites like
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Life in the modern world constantly exposes a person to all sorts of tests, including financial ones. Not every person can say with confidence that he is financially secure, because most people, as a rule, have only one source of income - money received for the work they do. And it doesn’t matter whether it’s hired work or your own business, the important thing is that there is only one source of income. But what to do if suddenly for some reason this source stops bringing in money? It is for this reason that some people think about additional sources of income. And for those who don’t think twice, we strongly recommend doing this, because... in the future, and even in the present, this can serve as an excellent service. Below we will look at several options for alternative sources of financial inflow and some of their nuances.
In general, sources of income can be divided into active and passive. Active ones are those in which, in order to make a profit, we are directly involved and make efforts to generate money. Passive are those in which a person makes practically no effort to make a profit and his investments (time, effort, money) work for him. Let's figure out what active or passive source of income can become an additional source?
Active additional sources of income
In fact, a situation where there may be a need for additional finance, or simply not enough money earned at the main place of work, can arise for anyone. You can, of course, try to get a promotion in your career, increase your pay, or look for a higher-paying job, but it’s not a fact that you will succeed. You can try to find a second job, but where can you find the time and energy for it if you’re already full-time? But there is a way out: you need to pay attention to your hidden resources, which in the everyday bustle we may simply not notice, which means we don’t use them. They can become the basis of an active additional source of income.
Knowledge
Think about what knowledge you currently have, but which you are not using to create additional profit. What can you do? What can you teach? What can you tell us about or what can you advise on? What ideas did/do you have that you didn't pay enough attention to? Surely you will be able to find something interesting. In addition, if you wish, you can learn something new: take some courses, get a new specialty or a second or even third education, and then use the acquired knowledge to earn money in a new field.
Technical Resources
One of the most powerful technical resources today is in almost everyone’s home – a computer. It is usually purchased for studying, watching movies, listening to music and other entertainment, but it can also be used as a means of earning money. If you have access to the Internet and some free time, you can search the Internet for ways to generate additional income. The situation is similar with having a car - it can be used for various kinds of part-time work: as a taxi, for delivering sushi or pizza, etc. Make a list of what you have and think about how you can use it for profit.
Hobbies, hobbies, interests, talents
Each person has some distinctive feature: someone writes beautifully, someone understands technology, someone gets along great with animals. What are you good at doing? Even the simplest skill in beautiful embroidery or knitting can become an additional source of income. And if you like it, that's even better! What are your hobbies? What are your interests? Could your area of interest be the starting point for creating another source of income? Show your imagination, activate your creativity and try to come up with some interesting ideas that you can bring to life and improve your financial condition.
Time
Time is the most valuable resource that a person has, but which is often completely wasted. Analyze what you spend your time on: how many hours a day do you spend on pointless activities? How much do you devote to finding a new way to earn money? You must learn with your time resource: engage in self-development and personal growth, spiritual practices, analysis of your knowledge, technical resources, skills, hobbies, hobbies and interests in order to learn how to turn them into money. This, of course, does not mean that you cannot relax and have fun. But if you have a need for additional funds, then “time for business, time for fun.”
So, we have dealt with active additional sources of income. The main direction of work is now clear and, if desired, you can find any other interesting active way of earning money. Let's move on to passive sources.
Passive additional sources of income
Oddly enough, the very concept of passive income is quite unusual for Russians, although in the West they have been familiar with it for a long time, and in some schools they even teach financial literacy. In our country, this topic has been studied very little. And this is mainly due to the stereotypes imposed and brought up in the last decades of the last century. In the post-Soviet space, the person who achieved everything he had through enormous efforts was considered successful. However, at all times, the most successful, wealthy and wealthy people have always been those with such qualities as mental acuity, prudence, and the ability to make a profit from their investments. But let’s leave these considerations for another time, and consider those sources of income that can be considered passive, as well as accessible to people with low and middle income levels.
Pension
A pension is a regular cash benefit that is paid to people who have reached retirement age, are disabled, or have lost their breadwinner. But, unfortunately, the size of the pension in our country, to put it mildly, leaves much to be desired. And many people never reach retirement age, and thousands of pensions go into the “bottomless abyss” of our state. Why not the families of those people who did not live to see retirement? Interest Ask. In general, no matter how funny it may sound, a pension is a source of additional passive income.
Bank account
Anyone can open a bank account and deposit money into it at interest. And this can already be considered a source of passive income. But there are several points to consider here. If the invested amount is small, then the bank’s interest rate, taking into account inflation, often only contributes to saving money and preserving it from depreciation, i.e. This cannot be called a source of passive income. But if the amount is large and the percentage of accruals exceeds the inflation index, then the capital will constantly grow - this is passive income. In short, in order to make a profit, only large sums should be deposited at interest.
Securities
Owning securities is very profitable, because... this allows you to receive a minimum of 10 to 30 percent profit per year. But it is recommended to deal with securities only with the help of an experienced specialist in this field. He will be able to offer several investment options that will be most optimal for you. The richest people in the world resort to working with securities, therefore, if there is an opportunity to start acting in this direction, then under no circumstances should you miss it.
Big business
When talking about a big business, it should be borne in mind that its creation requires a considerable investment of time, effort and finance. But the result is worth it. If the company “stands firmly on its feet” and is managed by competent people, then it may well become an excellent source of passive income and will even allow the person (or group of people) who organized it to move into. The owner must only monitor the organization’s work and have an action plan in case of force majeure.
Internet site
If you approach the issue of creating a website seriously and work closely on its promotion, then after a while it will be able to bring substantial profits to its owner. Contextual advertising, affiliate programs and other methods of site monetization play a huge role here. The interesting thing is that a person can create a website both with the help of competent specialists (for a substantial fee, of course), and completely independently, having learned how to do this and studied all the intricacies of the issue.
Royalties
If you can write a good book that is relevant and in demand by readers, then for the rest of your life you will be able to receive royalties from the sales of your work. And this applies not only to books, but also to inventions, ideas, projects, websites and other creations, regardless of the focus of the activity. Just think how much money a man named Seth Wheeler made when he patented toilet paper in 1871?!
In conclusion, I just want to say that if you really want to create an additional source of income (and even more so, if there are several), then you will have to seriously think and reconsider many components of your life: habits, beliefs, personal and, of course, put in effort for this a lot of effort. And even if it is not easy, it is worth it. You just need to want it - everything is in your hands!
Let's consider two main concepts for solving the current problem of determining the discount rate — And .
Alternative Return Concept
Within the framework, the risk-free discount rate is determined either at the level of deposit rates of banks of the highest category of reliability, or is equated to the refinancing rate of the Central Bank of Russia (this approach is proposed in the methodological recommendations developed by Sberbank of the Russian Federation). The discount rate can also be determined using I. Fisher’s formula.
The Methodological Recommendations indicate various types of discount rate. Commercial norm, as a rule, is determined taking into account alternative income concepts. My own discount rate project participants evaluate independently. True, in principle, a coordinated approach is also possible, when all project participants are guided by the commercial discount rate.
For projects of high social significance, determine the social discount rate. It characterizes the minimum requirements for the so-called social efficiency of the implementation of an investment project. It is usually installed centrally.
They also calculate budget discount rate, reflecting opportunity cost use of budget funds and established by executive authorities at the federal, subfederal or municipal level.
In each specific case, the level of decision-making depends on which budget finances the investment project.
Weighted average cost of capital concept
It is an indicator that characterizes the cost of capital in the same way that the bank interest rate characterizes the cost of borrowing a loan.
The difference between the weighted average cost of capital and the bank rate is that this indicator does not imply straight-line payments, but instead requires that the total present value of the investor be the same as what would be provided by a straight-line payment of interest at a rate equal to the weighted average cost of capital.
Weighted average cost of capital Widely used in investment analysis, its value is used to discount expected returns on investments, calculate return on projects, in business valuation and other applications.
Discounting future cash flows at a rate equal to the weighted average cost of capital, characterizes the depreciation of future income from the point of view of a particular investor and taking into account his requirements for the return on invested capital.
Thus, alternative income concept And weighted average cost of capital concept suggest different approaches to determining the discount rate.
Highly specialized material for professional investors
and students of the Fin-plan course "".
Financial and economic calculations most often involve the assessment of cash flows distributed over time. Actually, for these purposes a discount rate is needed. From the point of view of financial mathematics and investment theory, this indicator is one of the key ones. It is used to build methods of investment valuation of a business based on the concept of cash flows, and with its help, a dynamic assessment of the effectiveness of investments, both real and stock, is carried out. Today, there are already more than a dozen ways to select or calculate this value. Mastering these methods allows a professional investor to make more informed and timely decisions.
But, before moving on to methods for justifying this rate, let’s understand its economic and mathematical essence. Actually, two approaches are used to define the term “discount rate”: conventionally mathematical (or process), and economic.
The classic definition of the discount rate comes from the well-known monetary axiom: “money today is worth more than money tomorrow.” Hence, the discount rate is a certain percentage that allows you to reduce the value of future cash flows to their current cost equivalent. The fact is that many factors influence the depreciation of future income: inflation; risks of non-receipt or shortfall of income; lost profits that arise when a more profitable alternative opportunity to invest funds appears in the process of implementing a decision already made by the investor; systemic factors and others.
By applying the discount rate in his calculations, the investor brings or discounts expected future cash income to the current point in time, thereby taking into account the above factors. Discounting also allows the investor to analyze cash flows distributed over time.
However, one should not confuse the discount rate and the discount factor. The discount factor is usually operated in the calculation process as a certain intermediate value, calculated on the basis of the discount rate using the formula:
where t is the number of the forecast period in which cash flows are expected.
The product of the future cash flow and the discount factor shows the current equivalent of the expected income. However, the mathematical approach does not explain how the discount rate itself is calculated.
For these purposes, the economic principle is applied, according to which the discount rate is some alternative return on comparable investments with the same level of risk. A rational investor, making a decision to invest money, will agree to implement his “project” only if its profitability turns out to be higher than the alternative one available on the market. This is not an easy task, since it is very difficult to compare investment options by risk level, especially in conditions of lack of information. In the theory of investment decision making, this problem is solved by decomposing the discount rate into two components - the risk-free rate and risks:
The risk-free rate of return is the same for all investors and is subject only to the risks of the economic system itself. The investor assesses the remaining risks independently, usually based on expert assessment.
There are many models for justifying the discount rate, but they all correspond in one way or another to this basic fundamental principle.
Thus, the discount rate always consists of the risk-free rate and the total investment risk of a particular investment asset. The starting point in this calculation is the risk-free rate.
Risk-free rate
The risk-free rate (or risk-free rate of return) is the expected rate of return on assets for which their own financial risk is zero. In other words, this is the yield on absolutely reliable investment options, for example, on financial instruments whose profitability is guaranteed by the state. We emphasize that even for absolutely reliable financial investments, absolute risk cannot be absent (in this case, the rate of return would tend to zero). The risk-free rate includes the risk factors of the economic system itself, risks that no investor can influence: macroeconomic factors, political events, changes in legislation, emergency man-made and natural events, etc.
Therefore, the risk-free rate reflects the minimum possible return acceptable to the investor. The investor must choose the risk-free rate for himself. You can calculate the average bet from several potentially risk-free investment options.
When choosing a risk-free rate, an investor must take into account the comparability of his investments with the risk-free option according to such criteria as:
The scale or total cost of the investment.
Investment period or investment horizon.
The physical possibility of investing in a risk-free asset.
Equivalence of denominated rates in foreign currency, and others.
Return rates on time ruble deposits in banks of the highest reliability category. In Russia, such banks include Sberbank, VTB, Gazprombank, Alfa-Bank, Rosselkhozbank and a number of others, a list of which can be viewed on the website of the Central Bank of the Russian Federation. When choosing a risk-free rate using this method, it is necessary to take into account the comparability of the investment period and the period for fixing the deposit rate.
Let's give an example. Let's use the data from the website of the Central Bank of the Russian Federation. As of August 2017, the weighted average interest rates on deposits in rubles for up to 1 year were 6.77%. This rate is risk-free for most investors investing for up to 1 year;
Yield level on Russian government debt financial instruments. In this case, the risk-free rate is fixed in the form of the yield on (OFZ). These debt securities are issued and guaranteed by the Ministry of Finance of the Russian Federation, and therefore are considered the most reliable financial asset in the Russian Federation. With a maturity of 1 year, OFZ rates currently range from 7.5% to 8.5%.
Yield level on foreign government securities. In this case, the risk-free rate is equal to the yield on US government bonds with maturities from 1 year to 30 years. Traditionally, the US economy is assessed by international rating agencies at the highest level of reliability, and, consequently, the yield of their government bonds is considered risk-free. However, it should be taken into account that the risk-free rate in this case is denominated in dollar rather than ruble equivalent. Therefore, to analyze investments in rubles, an additional adjustment is necessary for the so-called country risk;
Yield level on Russian government Eurobonds. This risk-free rate is also denominated in US dollars.
Key rate of the Central Bank of the Russian Federation. At the time of writing this article, the key rate is 9.0%. This rate is considered to reflect the price of money in the economy. An increase in this rate entails an increase in the cost of the loan and is a consequence of an increase in risks. This tool should be used with great caution, since it is still a guideline and not a market indicator.
Interbank lending market rates. These rates are indicative and more acceptable compared to the key rate. Monitoring and a list of these rates are again presented on the website of the Central Bank of the Russian Federation. For example, as of August 2017: MIACR 8.34%; RUONIA 8.22%, MosPrime Rate 8.99% (1 day); ROISfix 8.98% (1 week). All these rates are short-term in nature and represent the profitability of lending operations of the most reliable banks.
Discount rate calculation
To calculate the discount rate, the risk-free rate should be increased by the risk premium that the investor assumes when making certain investments. It is impossible to assess all risks, so the investor must independently decide which risks should be taken into account and how.
The following parameters have the greatest influence on the risk premium and, ultimately, the discount rate:
The size of the issuing company and the stage of its life cycle.
The nature of the liquidity of the company's shares on the market and their volatility. The most liquid stocks generate the least risk;
Financial condition of the issuer of shares. A stable financial position increases the adequacy and accuracy of forecasting the company's cash flow;
Business reputation and market perception of the company, investor expectations regarding the company;
Industry affiliation and risks inherent in this industry;
The degree of exposure of the issuing company’s activities to macroeconomic conditions: inflation, fluctuations 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.
This is just a short list of risk factors that can be taken into account in the discount rate. Actually, depending on the method of assessing investment risks, the methods for calculating the discount rate differ.
Let's briefly look at the main methods for justifying the discount rate. To date, more than a dozen methods for determining this indicator have been classified, but they are all grouped as follows (from simple to complex):
Conventionally “intuitive” - based rather on the psychological motives of the investor, his personal beliefs and expectations.
Expert, or qualitative - based on the opinion of one or a group of specialists.
Analytical – based on statistics and market data.
Mathematical, or quantitative, require mathematical modeling and the possession of relevant knowledge.
An “intuitive” way to determine the discount rate
Compared to other methods, this method is the simplest. The choice of discount rate in this case is not mathematically justified in any way and represents only the investor’s desire, or his preference about the level of return on his investments. An investor can rely on his previous experience, or on the profitability of similar investments (not necessarily his own) if information about the profitability of alternative investments is known to him.
Most often, the discount rate is “intuitively” calculated approximately by multiplying the risk-free rate (as a rule, this is simply the rate on deposits or OFZ) by some adjustment factor of 1.5, or 2, etc. Thus, the investor, as it were, “estimates” the level of risks for himself.
For example, when calculating discounted cash flows and fair values of companies in which we plan to invest, we typically use the following rate: the average deposit rate multiplied by 2 if we are talking about blue chips and use higher coefficients if we are talking about companies 2nd and 3rd echelons.
This method is the easiest for a private investor to practice and is used even in large investment funds by experienced analysts, but it is not held in high esteem among academic economists because it allows for “subjectivity.” In this regard, in this article we will give an overview of other methods for determining the discount rate.
Calculation of discount rate based on expert assessment
The expert method is used when investments involve investing in shares of companies in new industries or activities, startups or venture funds, and also when there is no adequate market statistics or financial information about the issuing company.
The expert method for determining the discount rate consists of surveying and averaging the subjective opinions of various specialists about the level, for example, of the expected return on a specific investment. The disadvantage of this approach is the relatively high degree of subjectivity.
You can increase the accuracy of calculations and somewhat level out subjective assessments by decomposing the bet into a risk-free level and risks. The investor chooses the risk-free rate independently, and the assessment of the level of investment risks, the approximate content of which we described earlier, is carried out by experts.
The method is well applicable for investment teams that employ investment experts of various profiles (currency, industry, raw materials, etc.).
Calculation of the discount rate using analytical methods
There are quite a lot of analytical ways to justify the discount rate. All of them are based on theories of firm economics and financial analysis, financial mathematics and business valuation principles. Let's give a few examples.
Calculation of the discount rate based on profitability indicators
In this case, the justification for the discount rate is carried out on the basis of various profitability indicators, which in turn are calculated based on data and. The basic indicator is return on equity (ROE, Return On Equity), but there may be others, for example, return on assets (ROA, Return On Assets).
Most often it is used to evaluate new investment projects within an existing business, where the nearest alternative rate of return is precisely the profitability of the current business.
Calculation of the discount rate based on the Gordon model (constant dividend growth model)
This method of calculating the discount rate is acceptable for companies paying dividends on their shares. This method presupposes the fulfillment of several conditions: payment and positive dynamics of dividends, no restrictions on the life of the business, stable growth of the company’s income.
The discount rate in this case is equal to the expected return on the company's equity capital and is calculated using the formula:
This method is applicable to evaluate investments in new projects of a company by shareholders of this business, who do not control profits, but only receive dividends.
Calculation of the discount rate using quantitative analysis methods
From the perspective of investment theory, these methods and their variations are the main and most accurate. Despite the many varieties, all these methods can be reduced to three groups:
Cumulative construction models.
Capital asset pricing models CAPM (Capital Asset Pricing Model).
WACC (Weighted Average Cost of Capital) models.
Most of these models are quite complex and require certain mathematical or economic skills. We will look at general principles and basic calculation models.
Cumulative construction model
Within this method, the discount rate is the sum of the risk-free rate of expected return and the total investment risk for all types of risk. The method of justifying the discount rate based on risk premiums to the risk-free level of return is used when it is difficult or impossible to assess the relationship between risk and return on investment in the business being analyzed using mathematical statistics. In general, the calculation formula looks like this:
CAPM Capital Asset Pricing Model
The author of this model is Nobel laureate in economics W. Sharp. The logic of this model is no different from the previous one (the rate of return consists of the risk-free rate and risks), but the method for assessing investment risk is different.
This model is considered fundamental because it establishes the dependence of profitability on the degree of its exposure to external market risk factors. This relationship is assessed through the so-called “beta” coefficient, which is essentially a measure of the elasticity of an asset’s return to changes in the average market return of similar assets on the market. In general, the CAPM model is described by the formula:
Where β is the “beta” coefficient, a measure of systematic risk, the degree of dependence of the assessed asset on the risks of the economic system itself, and the average market return is the average return on the market of similar investment assets.
If the “beta” coefficient is above 1, then the asset is “aggressive” (more profitable, changes faster than the market, but also more risky in relation to its analogues on the market). If the beta coefficient is below 1, then the asset is “passive” or “defensive” (less profitable, but also less risky). If the “beta” coefficient is equal to 1, then the asset is “indifferent” (its profitability changes in parallel with the market).
Calculation of discount rate based on WACC model
Estimating the discount rate based on the company's weighted average cost of capital allows us to estimate the cost of all sources of financing its activities. This indicator reflects the company's actual costs for paying for borrowed capital, equity capital, and other sources, weighted by their share in the overall liability structure. If a company's actual profitability is higher than the WACC, then it generates some added value for its shareholders, and vice versa. That is why the WACC indicator is also considered as a barrier value of the required return for the company’s investors, that is, the discount rate.
The WACC indicator is calculated using the formula:
Of course, the range of methods for justifying the discount rate is quite wide. We have described only the main methods most often used by investors in a given situation. As we said earlier in our practice, we use the simplest, but quite effective “intuitive” method of determining the rate. The choice of a specific method always remains with the investor. You can learn the entire process of making investment decisions in practice on our courses at. We teach in-depth analytical techniques already at the second level of training, in advanced training courses for practicing investors. You can evaluate the quality of our training and take your first steps in investing by signing up for our courses.
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