There are three methods of calculating the discount rate used to assess the value of a business:
- Capital Asset Pricing Model (CAPM).
- The method of cumulative construction.
- Weighted average cost of capital (WACC) method.
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The discount rate is used to bring the value of future cash flows to the present value (at the current point in time). This operation is called , it is the inverse of the calculation operation compound interest. Such an operation is necessary due to the fact that the amount of money available on this moment, is of greater value than the same amount that will be received in the future.
Cash flow discounting is used for business valuation purposes in the following cases:
- Within the forecast period.
- As part of the present value of individual assets and liabilities. For example, to calculate the cost of a loan debt, if it is assumed that repayment will occur over a long period of time.
The discount rate is calculated from capital asset pricing models (CAPM) or cumulative construction method if the full cash flow. Both of these methods of calculation include as initial stage calculation of the risk-free interest rate.
Risk free interest rate
The risk-free rate (also called the risk-free rate of return) is the percentage of return that can be earned by investing in zero-risk assets.
A zero-risk asset must meet the following conditions:
- The rate of return is known before the investment is made.
- The risk of capital loss is minimal even if force majeure occurs.
- The lifetime of the asset (circulation period) is commensurate with the residual life of the business being valued.
Usually such conditions are met by government bonds or deposits for an appropriate period in reliable banks. In this case, the value of the risk-free rate is about 4-5%. This so-called nominal risk-free rate, the value of which does not take into account the rate of inflation.
Real risk-free rate taking into account the inflation rate is calculated by the formula:
Rf = Rn + I + Rn*I, where
Rn - nominal risk-free rate
I - inflation rate
An example of calculating the real risk-free rate
Nominal risk-free rate Rn = 4%
Inflation rate I = 7%
Real risk-free rate:
Rf = 0.04 + 0.07 + 0.07*0.04 = 0.1128 = 11.28%
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Capital Asset Pricing Model (CAPM)
The discount rate calculated by this model takes into account the systematic risk, i.e. risk inherent in the entire market or market segment.
Calculation formula for the CAMP model:
R = Rf + β*(Rm-Rf), where
Rm- Average rate market returns
Rf - Real risk-free rate
β is a measure of the risk of the valued business in relation to the market (beta coefficient).
Sometimes the basic formula for calculating the CAPM model is supplemented with three additional terms (three standard risk premiums):
R \u003d Rf + β * (Rm-Rf) + Rmb + Rzk + Rst
Rmb - risk premium for investing in small business
Rзк - premium for the risk of investing in a closed company
Rst - country risk premium
Cumulative construction method
Takes into account the non-systematic risks inherent in the specific business being assessed.
The formula for calculating the discount rate using the cumulative construction method:
Rk = Rf + (R1 + R2 + ... + Rn) + (Rmb + Rbk + Rst), where
Rf - Real risk-free rate
R1, ..., Rn - one or more of the following risk factors:
- Key figure factor
- Leadership Quality Factor
- Funding source factor
- Factor of production diversification
- Customer diversification factor
- The resource constraint factor
- Other risk factors specific to the business or industry being assessed.
Rmb, Rzk, Rst - three standard bonuses.
Weighted average cost of capital (WACC) method
The discount rate is calculated using the WACC method - the weighted average cost of capital, if debt-free cash flow is discounted during business valuation. That is, the cash flow in which the receipt of a loan, the payment of a loan and the payment of interest on a loan are not taken into account.
1st cycle - textile factories, industrial use of coal. 2nd cycle - coal mining and ferrous metallurgy, railway construction, steam engine. 3rd cycle - heavy engineering, electric power industry, inorganic chemistry, steel production and electric motors. 4th cycle - production of automobiles and other machines, chemical industry, oil refining and internal combustion engines, mass production. 5th cycle - development of electronics, robotics, computing, laser and telecommunications technology. 6th cycle - perhaps NBIC convergence (convergence of nano-, bio-, information and cognitive technologies). After the 2030s (2050s according to other sources), a technological singularity is possible, which at the moment cannot be analyzed and predicted. Thus, the Kondratiev cycles are likely to end closer to 2030.
18. Equation of exchange by Irving Fisher. Nominal and real interest rates (formula).
Fisher's equation - the equation describing the relationship between the tempo inflation, nominal and real interest rates:
where is the nominal interest rate;
Real interest rate;
The rate of inflation.
The equation shows that the nominal interest rate can change for two reasons:
due to changes in the real interest rate;
due to the rate of inflation.
Distinguish between nominal and real interest rates.
Real interest rate is the interest rate minus inflation.
The relationship of the real nominal rate and inflation in the general case is described by the following (approximate) formula:
Nominal interest rate
Real interest rate
Expected or projected rate of inflation.
Irving Fisher proposed a more precise formula for the relationship between real, nominal rates and inflation, expressed by the Fisher formula named after him:
For and both formulas give the same value. It is easy to see that for small values of the inflation rate, the results differ little, but if inflation is high, then Fisher's formula should be applied.
According to Fisher, the real interest rate should be numerically equal to marginal productivity of capital.
11. The level of cyclical unemployment: the law a. Okun. Economic losses from the operation of the law a. Okun (on the graph of the as curve).
Studies of the relationship between the rate of increase in real GDP and the unemployment rate are expressed in the so-called Okun's law. Okun's Law(the law of the natural rate of unemployment) - if the actual unemployment rate exceeds the natural rate by 1%, then the gap between the actual GDP and the potential one is 2.5% unemployment.
Economic costs - a consequence of the operation of Okun's law - the lag of the actual volume of GDP from its potential volume.
12. Cycle and trend. Characteristics of the phases of the economic cycle.
Business cycles - cyclical changes in the economic environment, regular fluctuations in the level of business activity from economic recovery (boom) to recession (economic depression). Four relatively clearly distinguishable phases are distinguished in business cycles: peak, decline, bottom(or "lowest point") and climb.
Climb occurs after reaching the lowest point of the cycle (bottom). It is characterized by a gradual increase in employment and production. Many economists believe that low inflation rates are inherent in this stage. There is an introduction of innovations in the economy with a short payback period. Demand deferred during the previous recession is realized. 
Peak, or the top of the business cycle, is " highest point» economic recovery. In this phase, unemployment usually reaches its highest low level or disappears completely, production capacities operate at maximum or close to it load, that is, almost all material and labor available in the country are involved in production. resources. Usually, though not always, inflation rises during peaks. The gradual saturation of markets increases competition, which reduces the rate of return and increases the average payback period. The need for long-term lending is growing with a gradual decrease in the ability to repay loans. Recession (recession) is characterized by a reduction in production volumes and a decrease in business and investment activity. As a result, unemployment increases. Officially, the phase of the economic downturn, or recession, is considered to be a fall in business activity that lasts more than three months in a row. Bottom(depression) of the economic cycle is the "trough" of production and employment. It is believed that this phase of the cycle is usually not long.
1The subject of macroeconomics and its place in the structure of the socio-economic formation.
Macroeconomics- studies the functioning of the national economy as a whole. The patterns of development of productive forces and production relations on the scale of the whole society. The objects of research are: gross national product; the national income of society; general price level; employment and unemployment across society; inflation, etc.
Economic theory-science, predstavl. a system of knowledge, a cat. describes, explains and predicts the functioning of certain economies. phenomena. John Keynes differentiated the economy into positive (characterized as a positive economy, describes what is in the national economy at the moment) and normative (characteristic of those economic processes and phenomena that should occur in the future)
ME began to develop in the 20-30s of the last century. The author of the term is Ragnar Frisch.
Subject of ME study:
Functioning of the national economy; -analysis of ext. links that unite the entire economy into a single whole; - the inclusion of the national economy in the world.
Subject of study-circulation of resources and funds in the economy-models---:
F. Quesnay's table, 2) K. Marx's reproduction schemes, 3) balance method, 4) system of national accounts.
Methodology for calculating the ME indicators: by total expenses, by total income, by the value added method
Economic growth, 2) price stability, 3) full employment, 4) equilibrium of foreign trade operations, in which exports are equal to imports (“magic quadrangle”)
Inflation is defined as the process of an increase in the general (average) price level in the economy, which is equivalent to a decrease in the purchasing power of money. Inflation is called uniform if the rate of general inflation does not depend on time (on the step number of the calculation period). Inflation is called homogeneous if the rate of change in the prices of all goods and services depends only on the step number of the calculation period, but not on the nature of the goods or services. Inflation is said to be constant if its rate does not change over time.
There are two main indicators (parameters) that characterize inflation: the inflation rate and the inflation index. Below we give a definition and give formulas for calculating both indicators (parameters) of inflation.
Inflation is estimated over a certain period of time.
So, to assess inflation at the end of the period in relation to the period, two main indicators are used:
1) the rate (level) of inflation - the relative increase in the average price level in the period under review
2) inflation index (price change index) - an increase in the average price level in the period under review
Relationship between rate and inflation index
The question arises - at what interest rate increase will only compensate for inflation? If a we are talking about simple interest, then the minimum allowable (barrier) rate:
For compound interest:
A rate greater than is called a positive interest rate.
The owners of money make various attempts to compensate for the depreciation of money. The most common is the adjustment of the interest rate at which the accumulation is carried out, i.e. an increase in the rate by the amount of the so-called inflationary premium, in other words, the rate is indexed. The final value can be called the gross rate.
Let's discuss methods for determining the gross rate. If we are talking about full compensation for inflation in the amount of the gross rate at , then we find the required value from the equality:
where is the gross rate
From here gross rate for simple interest:
The value of the gross rate for is found from the equality:
From here gross rate for compound interest:
The last formula is called Fisher formula. Sometimes it is also written as:
where i - real rate percent
In practice, the inflation-adjusted rate is often calculated differently, namely:
The last formula, compared to the previous one, contains one additional term, which, if the values are small, can be neglected. If they are significant, then the error (not in favor of the owner of the money) will become very noticeable.
The interest rate characterizes the cost of using borrowed funds in the financial market. Rising interest rates mean that loans in the financial market will become more expensive and less accessible to potential borrowers. One of the reasons for the increase in interest rates is the increase in inflation. To describe the relationship between the interest rate and inflation, it is necessary to introduce the concepts of real and nominal interest rates.
The nominal interest rate (R) is the interest rate not adjusted for inflation.
The real interest rate (r) is the interest rate adjusted for the inflation rate.
With data on the inflation rate (π) and the nominal interest rate (R), the real interest rate (r) can be calculated using the Fisher formula:
If 0% ≤ π ≤ 10%, then the approximate formula can be used to calculate the real interest rate: r ≈ R – π
If we express the nominal rate from the approximate formula, that is, R ≈ r + π, then we get an effect called the Fisher effect. In accordance with this effect, two main components and, accordingly, two main causes of changes in the nominal interest rate can be distinguished: real interest and the inflation rate. However, when a financial institution (bank) sets the nominal interest rate, it usually comes with some expectations about the future rate of inflation. Therefore, the formula can be formalized to the following form: R ≈ r+, where is the expected inflation rate.
Then, in accordance with the Fisher effect, the dynamics of the nominal interest rate is largely determined by the dynamics of the expected inflation rate.
nominal and real exchange rates.
Exchange rate national currency is the most important macroeconomic indicator.
The nominal exchange rate is the ratio of the values of two currencies (in the exchange office we see exactly the nominal figures).
The real exchange rate is the ratio of the values of goods produced in different countries, or the ratio in which the goods of one country can be exchanged for similar goods of another country.
= × , where is the real exchange rate, P* is the price of foreign goods (in dollars), P is the price of domestic goods (in rubles), is the nominal exchange rate of the dollar against the ruble.
The change in the real exchange rate, based on the formula, is influenced by two factors: the nominal exchange rate and the ratio of prices abroad and in our country. In other words, an increase in the nominal exchange rate of the dollar (and, accordingly, a fall in the nominal exchange rate of the ruble) has a positive effect on the competitiveness of the domestic economy, while growth has a negative effect.
Approximate formula (for small changes): ∆% ≈ ∆% + - π
Purchasing power parity.
Purchasing power parity is the amount of one currency, expressed in units of another currency, required to purchase the same product or service in the markets of both countries.
= , - absolute PPP (prices for goods suitable for international exchange, when converted into one currency, should be the same)
∆% ≈ π - , ∆% = 0 - relative PPP (the nominal exchange rate is adjusted to compensate for the difference in inflation rates)
Question #10
Economic growth and cycle. Long- and short-term processes in the economy. What is a "recession" according to the NBER definition? Signs of an economic recession / recovery. Pro- and countercyclical indicators. Leading and lagging indicators. Recession and "overheating" - what is their danger? Economic growth and its possible sources. Decomposition of economic growth.
The economic growth is the long-term trend of increasing real GDP. To measure growth use:
1. Absolute growth or growth rate of real GDP;
2. Similar indicators per capita for a certain period of time.
IMPORTANT:
1) trend, this means that real GDP should not necessarily increase every year, it only means the direction of the economy, the so-called "trend";
2) long-term, because the economic growth is an indicator characterizing the long-term period, and, therefore, we are talking about an increase in potential GDP (i.e., GDP at full employment of resources), an increase in the production capabilities of the economy;
3) real GDP (rather than nominal, the growth of which can occur due to an increase in the price level, even with a reduction in real output). That's why important indicator economic growth is an indicator of the value of real GDP.
the main objective economic growth- the growth of well-being and the increase in national wealth.
The generally accepted quantitative measure of economic growth are indicators of absolute growth or growth rates of real output in general or per capita:
Business cycle- these are several periods of different activity to the economy (according to the US National Bureau of Economic Analysis).
Recession according to NBER (National Bureau of Economic Analysis)- a significant decline in economic activity that has spread throughout the economy, lasting more than several months and noticeable in the dynamics of production, employment, real incomes and other indicators.
Let's start right away with the formulation of the Fisher hypothesis (Fisher effect), which states that the nominal interest rate depends on two quantities: the real interest rate and the inflation rate. This dependency has the following form:
i=r+π, where
i - nominal interest rate;
r is the real interest rate;
π is the inflation rate in the country.
This formula got its name from the American economist Irving Fisher, who made a significant contribution to the theory of money.
Thus, according to the Fisher formula, the nominal interest rate (which is essentially nothing more than the price of a loan), as well as the price of any consumer product or service, is subject to adjustment through the inflation rate.
Fisher's formula allows you to evaluate the real profitability of investments. So, for example, an investor who invests money in a bank at 12% per annum has a different real income at different values of inflation rates. If inflation during the year is 6%, then the real interest received by the investor will be:
r=i-π=0.12-0.06=6%
If we assume that the inflation rate for the year reaches a value of 12%, then the efficiency of investments at a given nominal interest rate will be reduced to zero:
r=i-π=0.12-0.12=0
Complete Fisher formula
The above is a simplified formula. The full version looks like this:
As you can see, the full formula differs from the approximate one by the presence of the product rπ. Simple math shows us that as the values of r and π decrease, their sum does not decrease as rapidly as their product. Therefore, as π and r tend to zero, the product rπ can be neglected.
See for yourself, with values of π and r equal to 10%, their sum will be 0.1 + 0.1 = 0.2 = 20%, and their product: 0.1x0.1 = 0.01 = 10%. And with the values of π and r equal to 1%, their sum will be equal to 0.01 + 0.01 = 0.02 = 2%, and the product of everything: 0.01x0.01 = 0.0001 = 0.01%. That is, than less valueπ and r, the more accurate results are given by the approximate Fisher formula.