Otherwise, it is sometimes also called the equation of exchange or cash flow. In its general form, this equation establishes the relationship between such quantities as:

• The amount of money in circulation (money supply);
• The rate at which the circulation of this money supply occurs. In the general case, it represents the average frequency with which, in a given period of time, the same monetary unit is used to exchange for services and goods of domestic production. In the short term, this value changes very slowly, so it can be taken as a constant;
• Current price level;
• Current output (expressed in the total number of goods produced). Usually, for this formula, it is assumed that all production facilities are fully loaded.

The formula for this relationship looks like this:

As can be seen from the above equation, the money supply is directly proportional to such parameters as the current price level and the current volume of production. And at the same time, the value of the money supply is inversely proportional to the speed of its turnover.

Thus, this equation is one of the pillars on which the monetarist doctrine in the economy is based.

Monetarism is a theory in modern macroeconomics, the main thesis of which is the assertion that the main factor in the development of the economy is the amount of money in circulation.

The formula was derived back in 1911 by the outstanding representative of the neoclassical school of economics, the American economist Irving Fisher.

In essence, this equation is a formal expression of the quantity theory of money.

Strictly speaking, the very formulation of the quantity theory of money in economics boils down to the fact that the purchasing power of money, coupled with the price level, is completely determined by the amount of money that is in circulation.

It should be noted here that this formulation is valid for conditions of stable (normal) economic development. In this case, indeed, the change in the money supply is primary, and only after it, as a consequence, does the change in purchasing power and the price level occur.

In the case of the so-called disproportion in economic development, a completely opposite picture can be observed. In this case, first there is a change in the price level, and only after it does the value of the money supply change.

By the way, the Cambridge School of Political Economy gives a slightly different interpretation of the quantity theory of money. In this case, more importance is attached to the choice of consumers, in contrast to the above interpretation of Irving Fisher, in which the technological factors of production are decisive.

As formulated by the Cambridge School, the quantity theory of money is based on the following equation:

Within the framework of the quantity theory of money, another interpretation of the Fisher formula was proposed:

One of the conclusions arising from this interpretation is that price stability (in a particular country) directly depends on how much the money supply in circulation corresponds to the total volume of commodity transactions (including the volume of production, services, trade and etc.).

Violation of this balance leads to the fact that the price level begins to destabilize:

It should be borne in mind that the Fisher formula, by and large, is more of a theoretical expression of the quantity theory of money and is not intended for direct calculations on it.

At present, the Fisher equation is recognized as true by far from all representatives of the modern economic school. In its justification, a number of inaccuracies are found, due to which the final formula cannot reflect the true state of affairs in the economy.

In particular, an article by Yury Vladimirovich Liferenko, published in one of the issues of the Finance and Credit magazine in 2015, can be cited as an example of this kind of criticism.

This article, in particular, points out the mistakes of the Bank of Russia related to the fact that, in the process of carrying out its regulatory activities, it largely relies on the quantity theory of money (illustrated by the very Fisher formula). It is said that its regulatory function is, to put it mildly, insufficiently effective due to the fact of the fallacy of this theory.

The following is a proof of the failure of the Fisher formula and, as a result, it is said that its use (either in theoretical or practical form) is unacceptable as a tool for regulating the real economy.

As the main argument for the fallacy of the Fisher equation, the fact that the right side of the Fisher formula, which is the PQ expression, is incorrect is given. A comparison is made with the formula derived by Karl Marx (illustrating the law of money circulation) and having the following form:

As you can see, outwardly this formula is very similar to the one that Irving Fisher later deduced. Naturally, he could not be unaware of its existence (for most of his life, he taught political economy) and, presumably, took it as the basis for his research. However, the conclusions from the formula of K. Marx are completely opposite. The left side of the formula, represented by the amount of money in the economy (money supply) M, in this case is a function of its right side, represented by the price level and the volume of goods.

This, in turn, means that the price level and the volume of goods determine the amount of money that is necessary for their circulation, and not vice versa, as the quantity theory of money, expressed by the Irving Fisher equation, claims.

According to the author of the article, Fisher, most likely, deliberately distorted some facts in order to present the indivisible component of Marx's formula ΣP i Q i in a simpler and, most importantly, mathematically separable form of a simple product of P and Q.

This representation allowed him to divide the right side and write the formula as:

And this fundamentally changes the conclusion that Marx made. Now it turns out that the amount of money, in essence, determines the level of prices in the economy. That is, we see nothing but the formulation of the quantity theory of money.

In reality, such an expression as PQ cannot exist in principle. This is explained by the fact that there is no concept of price without reference to a specific product (i). As well as there can be no such thing as the volume of production in principle, it must also be tied to any particular product (i).

And finally, it is impossible to separate the price from the quantity of goods (P from Q) in this formula, since the price of any good is always inextricably linked with its quantity. For example, they say that the price of bread is 20 rubles per loaf (twenty rubles per loaf) and cannot be broken into two independent elements, such as 20 rubles and 1 loaf.

That is, initially correct is still an expression in the form of ΣP i Q i , which, by the way, underlies the formula for calculating GDP. And Fisher's formula was originally built on erroneous premises, which indicates not only that it is incorrect in principle, but also about the failure of the entire quantity theory of money in general.

Irving Fisher is an American neoclassical economist. Born February 27, 1867 in Saugerties, pc. New York. He made a great contribution to the creation of the theory of money, and also derived the “Fischer equation” and the “exchange equation”.

His works were taken as the basis for modern methods for calculating the level of inflation. In addition, they helped in many ways to understand the patterns of inflation and pricing.

Full and simplified Fisher's formula

In a simplified form, the formula will look like this:

i = r + p

• i - nominal interest rate;
• r is the real interest rate;
• π is the rate of inflation.

This entry is approximate. The smaller the values ​​of r and π, the more accurate this equation is.

The following would be more accurate:

r = (1 + i)/(1 + π) - 1 = (i - π)/(1 + π)

Quantity Theory of Money

The quantity theory of money is an economic theory that studies the impact of money on the economic system.

In accordance with the model put forward by Irving Fisher, the state must regulate the amount of money in the economy in order to avoid their lack or excess.

According to this theory, the phenomenon of inflation arises due to non-observance of these principles.

Insufficient or excessive amount of money supply in circulation entails an increase in the rate of inflation.

In turn, the growth of inflation implies an increase in the nominal interest rate.

• Rated the interest rate reflects only the current income from deposits, excluding inflation.
• Real The interest rate is the nominal rate of interest minus the expected rate of inflation.

Fisher's equation describes the relationship between these two indicators and the rate of inflation.

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How to use to calculate the return on investment

Suppose you make a deposit of 10,000, the nominal interest rate is 10%, and the inflation rate is 5% per year. In this case, the real interest rate will be 10% - 5% = 5%. Thus, the real interest rate is the lower, the higher the inflation rate.

It is this rate that should be taken into account in order to calculate the amount of money that this deposit will bring you in the future.

Interest calculation types

As a rule, the accrual of interest on profits occurs in accordance with the compound interest formula.

Compound interest is a method of accruing interest on profits, in which they are added to the principal amount and subsequently participate in the creation of new profits.

A short summary of the compound interest formula looks like this:

K = X * (1 + %)n

• K is the total amount;
• X is the initial amount;
• % - percentage value of payments;
• n is the number of periods.

At the same time, the real interest that you receive by making a deposit at compound interest will be the lower, the higher the inflation rate.

At the same time, for any type of investment, it makes sense to calculate the effective (real) interest rate: in essence, this is the percentage of the initial deposit that the investor will receive at the end of the investment period. Simply put, it is the ratio of the amount received to the amount originally invested.

r(ef) = (P n - P)/P

• r ef is the effective percentage;
• Pn is the total amount;
• P is the initial contribution.

Using the compound interest formula, we get:

r ef = (1 + r/m) m - 1

Where m is the number of accruals for the period.

International Fisher effect

The international Fisher effect is an exchange rate theory put forward by Irving Fisher. The essence of this model is the calculation of present and future nominal interest rates in order to determine the dynamics of changes in the exchange rate. This theory works in its purest form if capital moves freely between states whose currencies can be correlated with each other in value.

Analyzing the precedents of rising inflation in different countries, Fisher noticed a pattern in the fact that real interest rates, despite the growth in the amount of money, do not increase. This phenomenon is explained by the fact that both parameters are balanced over time through market arbitrage. This balance is maintained for the reason that the interest rate is set taking into account the risk of inflation and market forecasts for the currency pair. This phenomenon has been named Fisher effect .

Extrapolating this theory to international economic relations, Irving Fisher concluded that a change in nominal interest rates has a direct impact on the appreciation or depreciation of the currency.

This model has not been tested in real conditions. Its main disadvantage It is generally accepted that it is necessary to fulfill purchasing power parity (the same cost of similar goods in different countries) for accurate forecasting. And, besides, it is not known whether the international Fisher effect can be used in modern conditions, taking into account fluctuating exchange rates.

Inflation forecasting

The phenomenon of inflation is an excessive amount of money circulating in the country, which leads to their depreciation.

The classification of inflation occurs on the basis of:

uniformity - the dependence of the inflation rate on time.

Uniformity — distribution of influence on all goods and resources.

Inflation forecasting is calculated using inflation index and hidden inflation.

The main factors in forecasting inflation are:

• change in the exchange rate;
• increase in the amount of money;
• change in interest rates;

Another common method is to calculate the inflation rate based on the GDP deflator. For forecasting in this technique, the following changes in the economy are recorded:

• profit change;
• change in payments to consumers;
• changes in import and export prices;
• change in rates.

Calculation of return on investment, taking into account the level of inflation and without it

The formula for return without taking into account inflation will look like this:

X \u003d ((P n - P) / P) * 100%

• X - profitability;
• P n - total amount;
• P - initial payment;

In this form, the final profitability is calculated without taking into account the time spent.

X t \u003d ((P n - P) / P) * (365 / T) * 100%

Where T is the number of days the asset is held.

Both methods do not take into account the impact of inflation on profitability.

Yield adjusted for inflation(real yield) should be calculated using the formula:

R = (1 + X) / (1 + i) - 1

• R - real profitability;
• X is the nominal rate of return;
• i is inflation.

Based on the Fisher model, one main conclusion can be drawn: inflation does not generate income.

The increase in the nominal rate due to inflation will never be greater than the amount of money invested that has depreciated. In addition, a high inflation rate implies significant risks for banks, and the compensation of these risks lies on the shoulders of depositors.

Application of the Fisher Formula in International Investments

As you can see, in the above formulas and examples, high inflation always reduces the return on investment, at a constant nominal rate.

Thus, the main criterion for the reliability of an investment is not the amount of payments in percentage terms, but inflation target.

Description of the Russian investment market using the Fisher formula

The above model is clearly seen on the example of the investment market of the Russian Federation.

The fall in inflation in 2011-2013 from 8.78% to 6.5% led to an increase in foreign investment: in 2008-2009 they did not exceed 43 billion rubles. dollars a year, and by 2013 reached the mark of 70 billion. dollars.

The sharp increase in inflation in 2014-2015 led to a decrease in foreign investment to a historic low. Over these two years, the amount of investments in the Russian economy amounted to only 29 billion rubles. dollars.

At the moment, inflation in Russia has fallen to 2.09%, which has already led to an influx of new investments from investors.

In this example, you can see that in matters of international investment, the main parameter is the real interest rate, which is calculated according to the Fisher formula.

How is the inflation index for goods and services calculated?

The inflation index or consumer price index is an indicator that reflects changes in the prices of goods and services purchased by the population.

Numerically, the inflation index is the ratio of prices for goods in the reporting period to prices for similar goods in the base period.

i p = p 1 / p

• i p - inflation index;
• p 1 - prices for goods in the reporting period;
• p 2 - prices for goods in the base period.

Simply put, the inflation index indicates how many times prices have changed over a certain period of time.

Knowing the inflation index, we can draw a conclusion about the dynamics of inflation. If the inflation index takes on values ​​greater than one, then prices are rising, which means that inflation is also growing. The inflation index is less than one — inflation takes negative values.

To predict changes in the inflation index, the following methods are used:

Laspeyres formula:

I L = (∑p 1 * q) / (∑p 0 * q 0)

• I L is the Laspeyres index;
• The numerator is the total cost of goods sold in the previous period at the prices of the reporting period;
• The denominator is the real value of goods in the previous period.

Inflation, when prices rise, is given a high estimate, and when prices fall, it is underestimated.

Paasche index:

Ip = (∑p 1 * q) / (∑p 0 * q 1)

The numerator is the actual cost of products of the reporting period;

The denominator is the actual cost of the products of the reporting period.

Ideal Fisher Price Index:

I p = √ (∑p 1 * q) / (∑p 0 * q 1) * (∑p 1 * q) / (∑p 0 * q 0)

Accounting for inflation when calculating an investment project

Accounting for inflation in such investments plays a key role. Inflation can affect project implementation in two ways:

• in kind- that is, entail a change in the project implementation plan.
• In terms of money- that is, affect the final profitability of the project.

Ways to influence the investment project in the event of an increase in inflation:

1. Change in currency flows depending on inflation;
2. Accounting for the inflation premium in the discount rate.

An analysis of the level of inflation and its possible impact on an investment project requires the following measures:

• consumer index accounting;
• forecasting changes in the inflation index;
• forecasting changes in the income of the population;
• forecasting the amount of cash collections.

Fisher's formula for calculating the dependence of the cost of goods on the amount of money

In general, Fisher's formula for calculating the dependence of the cost of goods on the amount of money has the following entry:

• M - the volume of money supply in circulation;
• V is the frequency with which money is used;
• P - the level of cost of goods;
• Q - quantities of goods in circulation.

By transforming this record, we can express the price level: P=MV/Q.

The main conclusion from this formula is the inverse proportionality between the value of money and its quantity. Thus, for the normal circulation of goods within the state, it is required to control the amount of money in circulation. An increase in the quantity of goods and prices for them requires an increase in the amount of money, and, in the case of a decrease in these indicators, the money supply should be reduced. This kind of regulation of the amount of money in circulation is assigned to the state apparatus.

Fisher's formula as applied to monopoly and competitive pricing

Pure monopoly presupposes, first of all, that one producer completely controls the market and is perfectly aware of its state. The main goal of a monopoly is to maximize profit at minimum cost. The monopoly always sets the price above the marginal cost and the output is lower than under perfect competition.

The presence of a monopoly producer in the market usually has serious economic consequences: the consumer spends more money than in a highly competitive environment, while prices rise along with an increase in the inflation index.

If the change in these parameters is taken into account in the Fisher formula, then we will get an increase in the money supply and a constant decrease in the number of circulating goods. This situation leads the economy into a vicious cycle in which an increase in the rate of inflation leads to an increase only to an increase in prices, which in the end stimulates the rate of inflation even more.

The competitive market, in turn, reacts to an increase in the inflation index in a completely different way. Market arbitrage leads to the conformity of prices to the conjuncture. Thus, competition prevents an excessive increase in the money supply in circulation.

An example of the relationship between changes in interest rates and inflation for Russia

On the example of Russia, you can see the direct dependence of interest rates on deposits on inflation

Thus, it can be seen that the instability of external conditions and the increase in volatility in the financial markets makes the Central Bank lower rates when inflation rises.

“Inflation is when with your money you can no longer buy as much as in those days when you had no money,” ironically American writer Leonard Louis Levinson.

Admit that no matter how sad, but it's true. Constant inflation eats away at our income.

We make investments, counting on certain percentages, but what do we have in reality?

To answer these and similar questions, the Fisher formula has been developed. Inflation, money supply, price level, interest rates and real profitability - we read about this in the article.

Relationship between money supply and prices - Fisher's equation

Regulation of the amount of money in circulation and the price level is one of the main methods of influencing the market-type economy. The relationship between the quantity of money and the price level was formulated by representatives of the quantity theory of money. In a free market (market economy) it is necessary to regulate economic processes to a certain extent (Keynesian model).

Fisher formula: inflation

The regulation of economic processes is carried out, as a rule, either by the state or by specialized bodies. As the practice of the 20th century showed, many other important economic parameters depend on the amount of money used in the economy, primarily the level of prices and the interest rate (the price of a loan). The relationship between the price level and the amount of money in circulation was clearly formulated within the framework of the quantity theory of money.

Prices and the amount of money are directly related. Depending on various conditions, prices may change due to changes in the money supply, but the money supply can also change depending on changes in prices.

Undoubtedly, this formula is purely theoretical and unsuitable for practical calculations. Fisher's equation does not contain any single solution; within the framework of this model, multivariance is possible. At the same time, under certain tolerances, one thing is certain: the price level depends on the amount of money in circulation. Usually two assumptions are made:

1. the speed of money turnover is a constant value;
2. All production capacities on the farm are fully utilized.

The meaning of these assumptions is to eliminate the influence of these quantities on the equality of the right and left sides of the Fisher equation. But even if these two assumptions are met, it cannot be unconditionally asserted that the growth of the money supply is primary, and the rise in prices is secondary. The dependence here is mutual.

Under conditions of stable economic development, the money supply acts as a regulator of the price level. But with structural imbalances in the economy, a primary change in prices is also possible, and only then a change in the money supply.

Fisher's formula (the equation of exchange) determines the amount of money used only as a medium of circulation, and since money performs other functions, the determination of the total need for money involves a significant improvement in the original equation.

The amount of money in circulation

The amount of money in circulation and the total amount of commodity prices are related as follows:

The above formula was proposed by representatives of the quantity theory of money. The main conclusion of this theory is that in each country or group of countries (Europe, for example) there must be a certain amount of money corresponding to the volume of its production, trade and income. Only in this case price stability will be ensured. In the case of an inequality in the quantity of money and the volume of prices, changes in the price level occur:

• MV = PT - prices are stable;
• MV > PT - prices are rising (inflationary situation).

Thus, price stability is the main condition for determining the optimal amount of money in circulation.

Source: "grandars.ru"

Fisher Formula: Inflation and Interest Rates

Economists call bank interest the nominal rate of interest, and the increase in your purchasing power the real rate of interest. If we designate the nominal interest rate as i, and the real interest rate as r, inflation as π, then the relationship between these three variables can be written as follows: r = i - π, i.e. The real interest rate is the difference between the nominal interest rate and the inflation rate.

Regrouping the terms of this equation, we see that the nominal interest rate is the sum of the real interest rate and the inflation rate: i = r + π. An equation written in this form is called the Fisher equation. It shows that the nominal interest rate can change for two reasons: due to changes in the real interest rate or due to changes in the inflation rate.

The quantity theory of money and Fisher's equation show how an increase in the money supply affects the nominal rate of interest. According to the quantity theory of money, a 1% increase in the money supply causes an increase in the inflation rate by 1%.

According to the Fisher equation, a 1% increase in the inflation rate, in turn, causes a 1% increase in the nominal interest rate. This relationship between the rate of inflation and the nominal rate of interest is called the Fisher effect.

It is necessary to distinguish between two different concepts of the real interest rate:

1. the real interest rate expected by the borrower and lender when issuing a loan (exante real interest rate) – i.e. expected, supposed;
2. the actual real interest rate is expost.

Lenders and borrowers are not in a position to predict the future rate of inflation with complete certainty, but they have certain expectations about this. Denote by π the actual rate of inflation in the future, and by e the expected future rate of inflation. Then the real interest rate exante will be equal to i - πе, and the real interest rate expost will be equal to i - π x v.

How is the Fisher effect modified to account for the difference between expected and actual future inflation rates? The Fisher effect can be more accurately represented as follows: i = r + πе.

The demand for money in real terms depends on both the level of income and the nominal interest rate. The higher the level of income Y, the greater the demand for cash reserves in real terms. The higher the nominal interest rate i, the lower the demand for them.

Source: "infomanagement.ru"

Nominal and real interest rate - Fisher effect

The nominal interest rate is the market interest rate without inflation, reflecting the current valuation of monetary assets.

The real interest rate is the nominal interest rate minus the expected rate of inflation.

For example, the nominal interest rate is 10% per annum and the projected inflation rate is 8% per annum. Then the real interest rate will be: 10 - 8 = 2%.

The difference between the nominal rate and the real one makes sense only in conditions of inflation or deflation.

The American economist Irving Fisher put forward an assumption about the relationship between the nominal, real interest rate and inflation, called the Fisher effect, which states that the nominal interest rate changes by the amount at which the real interest rate remains unchanged.

In formula form, the Fisher effect looks like this:

For example, if the expected inflation rate is 1% per year, then the nominal rate will increase by 1% in the same year, therefore, the real interest rate will remain unchanged. Therefore, it is impossible to understand the process of making investment decisions by economic agents without taking into account the difference between the nominal and real interest rates.

Let's take a simple example: let's say you intend to give someone a loan for one year in an inflationary environment, what is the exact interest rate you set? If the growth rate of the general price level is 10% per year, then setting the nominal rate at 10% per annum with a loan of 1,000 CU, you will receive CU 1,100 in a year.

But their real purchasing power will no longer be the same as a year ago. Nominal income increment of CU100 will be "eaten" by 10% inflation. Thus, the distinction between nominal and real interest rates is important for understanding exactly how contracts are made in an economy with an unstable general price level (inflation and deflation).

Source: "economicportal.ru"

Fisher effect

The effect, as a phenomenon, as a pattern, was described by the great American economist Irving Fisher in 1896. The general idea is that there is a long-term relationship between expected inflation and the interest rate (yield on long-term bonds). Content - an increase in expected inflation causes approximately the same increase in the interest rate and vice versa.

The Fisher Equation is a formula for quantifying the relationship between expected inflation and the interest rate.

Simplified equation: if the nominal interest rate N is 10, the expected inflation I is 6, R is the real interest rate, then the real interest rate is 4 because R = N – I or N = R + I.

The exact equation. The real interest rate will differ from the nominal one as many times as the prices change. 1 + R = (1 + N)/(1 + I). If we open the brackets, then in the resulting equation, the value of NI for N and I less than 10% can be considered tending to zero. As a result, we get a simplified formula.

Calculating the exact equation with N equal to 10 and I equal to 6 will give the following value of R.
1 + R = (1 + N)/(1 + I), 1 + R = (1 + 0.1)/(1 + 0.06), R = 3.77%.

In the simplified equation, we got 4 percent. It is obvious that the boundary of the application of the simplified equation is the value of inflation and the nominal rate of less than 10%.

Source: "dictionary-economics.ru"

Essence of inflation

Imagine that in a secluded northern village, all workers had their wages doubled. What will change in a local store with the same offer, for example, chocolate? How would its equilibrium price change? Why does the same chocolate become more expensive? The money supply available to the population of this village increased, and demand increased accordingly, while the amount of chocolate did not increase.

As a result, the price of chocolate has risen. But the rise in the price of chocolate is not yet inflation. Even if all foodstuffs in the village rise in price, this will still not be inflation. And even if all goods and all services in this village rise in price, this will not be inflation either.

Inflation is a long-term sustained increase in the general price level. Inflation is the process of depreciation of money, which occurs as a result of the overflow of circulation channels with the money supply. How much money must circulate in the country in order for the price level to be stable?

The equation of exchange - Fisher's formula - allows you to calculate the money supply needed for circulation:

where M is the amount of money in circulation;
V is the velocity of money, which shows how many times 1 ruble changes hands in a certain period of time;
P is the average price per unit of output;
Y - real gross domestic product;
RU - nominal GDP.

The equation of exchange shows that every year the economy needs the amount of money that is required to pay for the value of the GDP produced. If more money is put into circulation or the velocity of circulation is increased, then the price level rises.

When the growth rate of the money supply exceeds the growth rate of the mass of commodities: MU > RU,
equilibrium is restored as a result of rising prices: MU = R|U.

An overflow of money circulation channels can occur if the velocity of money circulation increases. The same consequences can be caused by a reduction in the supply of goods on the market (a drop in production).

The degree of depreciation of money is determined in practice by measuring the rate of price growth.

In order for the price level in the economy to be stable, the government must maintain the growth rate of the money supply at the level of the average growth rate of real GDP. The amount of money supply is regulated by the Central Bank. Emission is the issuance of an additional amount of money into circulation.

Depending on the rate of inflation, inflation is conditionally distinguished:

• moderate
• galloping
• high
• hyperinflation.

If prices rise slowly, up to about 10% per year, then one usually speaks of moderate, “creeping” inflation.

If there is a rapid and abrupt increase in prices, measured in double digits, then inflation becomes galloping. With such inflation, prices rise no more than twice.

Inflation is considered high when prices rise by more than 100%, that is, prices rise several times.

Hyperinflation occurs when the depreciation of money becomes self-sustaining and uncontrollable, and the growth rates of prices and the money supply become exceptionally high. Hyperinflation is usually associated with war, economic disruption, political instability, and erroneous government policies. The rate of price growth during hyperinflation exceeds 1000%, i.e., during the year, prices rise by more than 10 times.

The intensive development of inflation causes distrust of money, and therefore there is a massive desire to turn it into real values, the "flight from money" begins. There is an increase in the velocity of circulation of money, which leads to an acceleration of their depreciation.

Money ceases to fulfill its functions, and the monetary system comes into complete disorder and decline. This is manifested, in particular, in the introduction into circulation of various monetary surrogates (coupons, cards, other local monetary units), as well as hard foreign currency.

The collapse of the monetary system as a result of hyperinflation, in turn, causes the degradation of the entire national economy. Production is falling, normal economic ties are being disrupted, and the share of barter transactions is growing. There is a desire for economic isolation of various regions of the country. Growing social tension. Political instability is manifested in the lack of trust in the government.

This also reinforces distrust of money and its depreciation.

A classic example of hyperinflation is the state of German money circulation after the First World War in 1922-1923, when the rate of price growth reached 30,000% per month, or 20% per day.

Inflation manifests itself differently in different economic systems. In a market system, prices are formed under the influence of supply and demand; depreciation of money is open. In a centralized system, prices are formed by directives, inflation is suppressed, hidden. Its manifestations are the shortage of goods and services, the growth of monetary savings, the development of the shadow economy.

Factors causing inflation can be both monetary and non-monetary. Let's consider the main ones. Demand-pull inflation is the result of excessive growth in government spending, consumers and private investment. Another cause of inflation in demand may be the issue of money to finance government spending.

In cost inflation, prices rise as firms increase their costs of production. For example, wage growth, if it outpaces labor productivity growth, can cause cost inflation.

• Inflation is a general rise in prices. It is caused by the excess of the growth rate of the money supply over the mass of commodities.
• According to the rate of price growth, four types of inflation are distinguished, of which the strongest is hyperinflation, which destroys the economy.
• Inflation is unpredictable. People with fixed incomes suffer the most from its consequences.

Source: "knigi.news"

How to correctly calculate the real yield adjusted for inflation

Probably everyone knows that the real yield is the yield minus inflation. Everything rises in price - products, goods, services. According to Rosstat, over the past 15 years, prices have increased 5 times. This means that the purchasing power of money that has just been lying in the nightstand all this time has decreased by 5 times, before they could buy 5 apples, now 1.

In order to somehow preserve the purchasing power of their money, people invest it in various financial instruments: most often these are deposits, currency, real estate. More advanced ones use stocks, mutual funds, bonds, precious metals. On the one hand, the amount of investments is growing, on the other hand, they are depreciating due to inflation.

If you subtract the inflation rate from the nominal rate of return, you get the real rate of return. It can be positive or negative. If the return is positive, your investment has multiplied in real terms, that is, you can buy more apples, if it is negative, it has depreciated.

Most investors calculate real returns using a simple formula:

Real Return = Nominal Return - Inflation

But this method is inaccurate. Let me give you an example: let's take 200 rubles and put them on a deposit for 15 years at a rate of 12% per annum. Inflation over this period is 7% per year. If we consider the real yield using a simple formula, we get 12-7=5%. Let's check this result by counting on the fingers.

For 15 years, at a rate of 12% per annum, 200 rubles will turn into 200 * (1 + 0.12) ^ 15 = 1094.71. Prices during this time will increase by (1+0.07)^15=2.76 times. To calculate the real profitability in rubles, we divide the amount on the deposit by the inflation coefficient 1094.71/2.76=396.63. Now, to translate the real yield into percentages, we consider (396.63/200)^1/15 -1 * 100% = 4.67%. This is different from 5%, that is, the test shows that the calculation of real yield in the "simple" way is not accurate.

where Real Rate of Return - real yield;
nominal rate - nominal rate of return;
inflation rate - inflation.

We check:
(1 + 0.12) / (1 + 0.07) -1 * 100% \u003d 4.67% - Converges, so the formula is correct.

Another formula that gives the same result looks like this:

RR=(nominal rate-inflation)/(1+inflation)

The greater the difference between nominal yield and inflation, the greater the difference between the results calculated by the "simple" and "correct" formulas. This happens a lot in the stock market. Sometimes the error reaches several percent.

Source: "activeinvestor.pro"

Calculation of inflation. Inflation indices

The inflation index is an economic indicator that reflects the dynamics of prices for services and goods that the population of the country pays for, that is, for those products that are purchased for further use, and not for overproduction.

The inflation index is also called the consumer price index, which is an indicator of measuring the average level of prices for consumer goods over a certain period of time. Different methods and formulas are used to calculate the inflation index.

Calculation of the inflation index using the Laspeyres formula

The Laspeyres index is calculated by weighing the prices of 2 time periods according to the same consumption volumes of the base period. Thus, the Laspeyres index reflects the change in the cost of services and goods of the base period that has occurred over the current period.

The index is defined as the ratio of consumer spending on the purchase of the same set of consumer goods, but at current prices (∑Qo×Pt), to spending on the purchase of goods and services in the base period (∑Qo×Po):

where Pt - prices in the current period, Qo - prices for services and goods in the base period, Po - the number of services and goods produced in the base period (as a rule, 1 year is taken for the base period).

It should be noted that the Laspeyres method has significant drawbacks due to the fact that it does not take into account changes in the structure of consumption.

The index only reflects changes in income levels, not taking into account the substitution effect, when the prices of some goods fall and this leads to an increase in demand. Consequently, the method of calculating the inflation index according to the Laspeyres method in some cases gives a slightly overestimated value.

Calculation of the inflation index using the Paasche formula

Another way to calculate the inflation index is based on the Paasche formula, which also compares the prices of two periods, but in terms of consumption volumes of the current period:

where Qt are prices for services and goods in the current period.

However, the Paasche method also has its own significant drawback: it does not take into account price changes and does not reflect the level of profitability. Therefore, when prices for some services or products decrease, the index overestimates, and when prices increase, it underestimates.

Calculation of the inflation index using the Fisher formula

In order to eliminate the shortcomings that are inherent in the Laspeyres and Paasche indices, the Fisher formula is used to calculate the inflation index, the essence of which is to calculate the geometric mean of the 2 above indices:

Many economists consider this formula to be ideal, as it compensates for the shortcomings of the Laspeyres and Paasche formulas. But, despite this, experts in many countries prefer the choice of one of the first two methods.

For example, for international reporting, the Laspeyres formula is used, since it takes into account that some goods and services may, in principle, fall out of consumption in the current period for one reason or another, in particular during the economic crisis in the country.

Gross domestic product deflator

An important place among inflation indices is occupied by the GDP deflator - a price index that includes all services and goods in the consumer basket. The GDP deflator allows you to compare the growth in the general level of prices for services and goods over a certain economic period.

This indicator is calculated in the same way as the Paasche index, but measured as a percentage, that is, the resulting number is multiplied by 100%. As a rule, the GDP deflator is used by the state statistical offices for reporting.

Big Mac Index

In addition to the above official methods for calculating the inflation index, there are also such non-traditional methods for determining it, such as the Big Mac or hamburger index. This method of calculation makes it possible to study how the same products are valued in different countries today.

The well-known hamburger is taken as the basis, and all because it is sold in many countries of the world, it has a similar composition almost everywhere (meat, cheese, bread and vegetables), and the products for its manufacture, as a rule, are of domestic origin.

Thus, the most expensive hamburgers today are sold in Switzerland ($6.81), Norway ($6.79), Sweden ($5.91), the cheapest ones are in India ($1.62), Ukraine ($2.11), Hong Kong ($2.12). As for Russia, the cost of a hamburger here is $2.55, while in the US a hamburger costs $4.2.

What does the hamburger index say? The fact that if the cost of a Russian Big Mac in terms of dollars is lower than the cost of a hamburger from the United States, then the official exchange rate of the Russian ruble is underestimated against the dollar.

Thus, it is possible to compare the currencies of different countries, which is a very simple and easy way to convert national currencies.

Moreover, the cost of a hamburger in each country directly depends on the volume of production, prices for raw materials, rent, labor and other factors, so the Big Mac index is one of the best ways to see the mismatch in the value of currencies, which is especially important in a crisis when a “weak” currency gives some advantages in terms of prices and costs for products, and an expensive currency becomes simply unprofitable.

Borscht index

In Ukraine, after carrying out, to put it mildly, unpopular reforms, an analogue of the Western Big Mag index was created, which has the patriotic name "borscht index". In this case, the study of price dynamics is carried out exclusively on the cost of the ingredients that make up the national Ukrainian dish - borscht.

However, if in 2010-2011 the borscht index could “save the situation” by showing the people that a plate of borscht now costs a little less, then in 2012 the situation changed dramatically. So, the borscht index showed that in September 2012 the average borscht set, consisting of vegetables, costs as much as 92% more than in the same period last year.

This rise in prices has led to the fact that the volume of purchases of vegetables by the population in Ukraine has decreased by an average of 10-20%.

As for meat, on average it has risen in price by 15-20%, but by this winter a rapid rise in price up to 30-40% is expected due to the increase in prices for fodder grain. On average, borscht made from potatoes, meat, beets, carrots, onions, cabbage, tomatoes and a bunch of greens is taken as the basis for assessing changes in the price level according to the borscht index.

Source: "provincialynews.ru"

Exchange rate and inflation

Inflation is the most important indicator of the development of economic processes, and for the currency markets - one of the most significant benchmarks. Currency dealers are watching inflation data very carefully. From the perspective of the foreign exchange market, the impact of inflation is naturally perceived through its relationship with interest rates.

Since inflation changes the ratio of prices, it also changes the benefits actually received from the income generated by financial assets. This impact is usually measured using real interest rates (Real Interest Rates), which, unlike conventional (nominal, Nominal Interest Rates) take into account the depreciation of money that occurs due to the general rise in prices.

An increase in inflation reduces the real interest rate, since some part must be deducted from the income received, which will simply go to cover the price increase and does not give any real increase in the benefits (goods or services) received.

The simplest way to formally account for inflation is to consider the nominal rate i minus the inflation coefficient p (also given as a percentage) as the real interest rate,

A more accurate relationship between interest rates and inflation is provided by Fisher's formula. For obvious reasons, government securities markets (interest rates on such securities are fixed at the time of their issue) are very sensitive to inflation, which can simply destroy the benefits of investing in such instruments.

The effect of inflation on government securities markets is easily transferred to closely related currency markets: the dumping of bonds denominated in a certain currency crs, which occurred due to rising inflation, will lead to an excess in the cash market in this currency crs, and consequently, to a fall in it. exchange rate.

In addition, the inflation rate is the most important indicator of the "health" of the economy, and therefore it is carefully monitored by central banks.

The means of combating inflation is to raise interest rates. Rising rates divert part of the cash from business turnover, as financial assets become more attractive (their profitability grows along with interest rates), loans become more expensive; as a result, the amount of money that can be paid for goods and services produced falls, and consequently the rate of price growth also decreases.

Because of this close relationship with central bank rate decisions, foreign exchange markets closely monitor inflation indicators. Of course, individual deviations in inflation levels (for a month, a quarter) do not cause the reaction of central banks in the form of changes in rates; central banks follow trends, not individual values.

For example, low inflation in the early 1990s allowed the FED to keep the discount rate at 3%, which was good for economic recovery. But in the end, inflation indicators ceased to be essential benchmarks for the currency markets.

Since the nominal discount rate was small, and its real version generally reached 0.6%, this meant for the markets that only upward movement of inflation indices made sense. The downtrend in the US discount rate was broken only in May 1994 when the FED raised it, along with the federal funds rate, as part of a pre-emptive inflation control measure. True, raising rates then could not support the dollar.

The main published indicators of inflation are the consumer price index (consumer price index), the producer price index (producer price index), and the GDP deflator (GDP implicit deflator). Each of them reveals its own part of the overall picture of price growth in the economy. Figure 1 illustrates the growth of consumer prices in the UK over the past 12 years.

Figure 1 UK consumer prices

This figure directly represents the cost of some consumer basket; the growth rate of this basket value is the commonly published consumer price index. On the chart, the growth rate is depicted by the slope of the trend line, along which the main upward trend in prices goes.

It is clearly seen that after overcoming the problems of 1992, which led to the exit of England from the European monetary union, the reforms carried out brought the economy to a different growth line, along which the price increase (the slope of the right trend line) is much less than it was at the end of the previous decade and in features - in 91-92 years.

An example of the actions of the central bank, based on its position on inflationary processes, and the reaction of the foreign exchange market caused by them, is shown in Figure 2, which shows a chart of the British pound against the dollar.

Figure 2. Chart of the British pound; Bank of England rate hike on September 8, 1999 and reaction to rumors of another hike

On September 8, 1999, a meeting of the Bank of England Monetary Policy Committee was held. None of the experts predicted then an increase in interest rates, since economic indicators did not show clear signs of inflation, and the pound was already estimated too high. True, on the eve of the meeting there were many comments that the increase in rates of the Bank of England in 1999 or early 2000 is inevitable.

But no one predicted it for this meeting. Therefore, the decision of the Bank to raise its main interest rate by a quarter of a percent came as a surprise to everyone, which shows the first sharp rise in the pound.

The Bank explained its decision by the desire to prevent further price increases, signs of which he saw in the overheated housing market, strong consumer demand and the possibility of inflationary pressure from wages, since unemployment in England was at a fairly low level. Although it is possible that the Bank's decision was influenced by the recently implemented FED rate hike.

The second rise in the chart the next day was caused by active discussion in the market about the inevitability of a new rate hike soon (rate hike is a common term for raising central bank rates in market slang); there were, apparently, many willing not to be late to buy a pound before it rose even more. The fall of the pound at the end of the week was due to the reaction to the US inflation data, which will be discussed later.

Inflation and interest rates

The connection between inflation and the conditions of money circulation can be demonstrated on the basis of the basic equation of the theory of money, if we write it for the relative changes in its constituent values, which shows that under these conditions, price growth (inflation) is completely determined by the regulatory actions of the central bank through a change in the money supply.

In reality, of course, the causes of inflation are quite complex and numerous, the growth of the money supply is only one of them.

Suppose some amount S was invested for the same period at an interest rate i (which is called the nominal interest rate, nominal interest rate), that is, the amount S will turn over the same period into S -> S(l + i). At the beginning of the period under review (at the old prices), it was possible to purchase the amount of goods Q=S/P for the amount S.

The real interest rate is called the interest rate in real terms, that is, determined through the increase in the volume of goods and services. In accordance with this definition, the real interest rate r will give for the same period under consideration the change in the volume Q,

Collecting all the above relations, we get,

Q(l + r) = S(l + i)/ P(l + p) = Q * (1 + i)/ (1 + p),

whence we obtain the expression for the real interest rate in terms of the nominal interest rate and the inflation rate,

r=(l+i)/(l+p)-l.

The same equation, written in a slightly different form,

characterizes the well-known Fisher effect in macroeconomics.

Fisher formula and monopoly price increase

Apparently, there are two types of prices: competitive and monopoly. The mechanism of competitive pricing is well researched. With a stable money supply, it never leads to an irrevocable rise in prices. When there is a market shortage of a commodity, the enterprises that produce it may temporarily raise prices.

However, after a certain period of time, capital will flow into this sector of the economy, that is, where a high rate of profit has temporarily formed. The influx of capital will make it possible to create new capacities for the production of scarce goods, and after a certain time an excess of this goods will form on the market. In this case, prices may even fall below the general level, as well as below the cost level.

Ideally, with the complete absence of monopolies in the market and with some constant technological progress, in the absence of an excess money supply in circulation, the market economy does not produce inflation. On the contrary, such an economy is characterized by deflation.

Monopoly is another matter. They discourage competition and can inflate prices at will. The growth of monopolies is often a natural consequence of competition. When weak competitors die and only one winner remains in the market, it becomes a monopolist. Monopolies are general and local. Some of them are natural (unremovable).

Other monopolies are established temporarily, but this does not make it easier for consumers and the entire economy of the country. They fight monopolies. All countries with developed market economies have antitrust laws. However, this is a recognition of the fact that monopolies cannot be dealt with by market methods alone. The state forcibly divides large monopolies. But in their place, oligopolies can form.

Price collusion is also pursued by the state, but it is not easy to prove. Sometimes certain monopolies, especially those engaged in energy, transport and military production, are placed under strict state control, just as was done in the socialist countries.

The arbitrary increase in prices by monopolies is an important point in the theory of cost-push inflation.

So, suppose there is a certain monopoly that intends to use its position in the market to raise prices, that is, in order to increase its share of income in the country's total NI. It could be an energy, transport or information monopoly.8 It could be a trade union, which could actually be considered a labor sales monopoly. (John Keynes himself considered trade unions to be the most aggressive monopolies in this respect).

Monopolies include the state, which collects taxes as a payment for the services it provides to maintain security, order, social security, and so on. Let's start with one of the possible cases. Let's say a private monopoly raised its tariffs (either the government increased taxes, or the unions won higher wages). In this case, we accept the condition that the money supply M remains constant.

Then, for one turnover of the money supply, the following condition is satisfied:

Thus, all changes in the equation, if they occur at all, will have to occur on the right side of the equation (p * q). There is a change - it is an increase in the weighted average price p. Therefore, an increase in price will necessarily lead to a decrease in the volume of q sold.

• Under conditions of invariability of the money supply for one circulation period, a monopoly increase in prices leads to a reduction in the sale (and production) of goods.
• However, one more, more optimistic conclusion can be drawn: Inflation caused by monopolies, given a constant money supply, cannot last as long as inflation caused by the printing of money. A complete halt in production cannot be beneficial to the monopolies. There is a limit to which it is advantageous for a private monopoly to raise tariffs.

In support of the conclusions of the Fisher formula, we can find any number of examples in the history of economics. Strong inflation is usually accompanied by a reduction in production. However, in this case, almost always, money emission was also added to the monopoly increase in prices. At the same time, with strong inflation, there is often a relative contraction in the money supply.

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 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, the smaller the values ​​of π and r, the more accurate results are given by the approximate Fisher formula.

Using the I. Fisher formula, you can get the formula for finding the real rate of return

Example

What real rate of return will an investor provide himself if the projected rate of inflation is 12% per year, and the declared rate of return is 16%?

Thus, when determining the integral indicators of the effectiveness of an investment project, both the nominal and the real discount rate can be used as the discount rate. The choice depends on the nature of the cash flow. If the cash flow is presented in basic and deflated prices, then the real discount rate should be used. If the cash flow is presented at the forecast price level, then a nominal discount rate should be used.

4.5. Analysis of the financial condition of the enterprise -
project participant

The need to analyze the financial condition in investment design arises when making a loan application to the bank. The borrowing company must confirm its solvency. In addition, the assessment of the effectiveness of the investment project should be supplemented by calculations on the impact of the project implementation on the main financial indicators of the enterprise participating in the project.

In accordance with the Methodology for evaluating investment projects, four groups of indicators are used to solve the task:

1. Liquidity ratios, which characterize the ability of the enterprise to repay its short-term obligations:

current liquidity ratio;

Quick liquidity ratio;

Absolute liquidity ratio.

The methodology for calculating liquidity ratios is detailed in section 3.5 of the textbook.

2. Indicators of solvency and financial stability, used to assess the ability of an enterprise to meet its long-term obligations:

- the ratio of borrowed and own funds;

– coefficient of long-term attraction of borrowed funds;

– coverage ratio of long-term liabilities.

The methodology for calculating the ratio of borrowed and own funds is given in section 3.6 of the textbook.

Long-term borrowing ratio () is calculated by the formula

where - long-term liabilities; - equity.

Long-term liabilities coverage ratio () is calculated by the formula

where P H- net profit; BUT- depreciation; D SC– increase in own capital during the year; D AP– increase in borrowed funds during the year; TO- the amount of investments made in the reporting year; PDO- payments on long-term obligations (repayment of loans and payment of interest on them).

3. Turnover ratios, are used to evaluate the effectiveness of operating activities:

– capital turnover ratio;

– equity turnover ratio;

– inventory turnover ratio;

- the turnover ratio of receivables;

- the average period of turnover of accounts payable.

The methodology for calculating turnover ratios is detailed in section 3.9 of the textbook.

4. Profitability indicators, are used to assess the current profitability of an enterprise participating in the project:

- profitability of sales in terms of profit before tax and net profit;

– return on assets (capital) in terms of profit before taxation and net profit;

– return on equity.

The methodology for calculating profitability indicators is detailed in section 3.8 of the textbook.

The specified list of indicators can be supplemented at the request of individual project participants and financial structures.

The indicators are analyzed in dynamics and compared with the indicators of similar enterprises.

The methodology for a more complete analysis of the financial condition of the enterprise is given in section 3 of this textbook.