Nominal and real interest rates. Fischer's formula and the Fischer effect
Inflation is the process of raising the prices of goods and services over time. The inflation index is used to determine its level.
Inflation concept. History of appearance
Inflation as a phenomenon in the financial system was known to the ancient world. However, in those days it was different from what we see today. For example, inflation was caused by over-minting or the use of copper instead of precious metals in their manufacture. Such a process had the common name "spoilage of the coin". By the way, historians even managed to find data on the depreciation of the currency of Ancient Rome sestertia.
Until the middle of the last century, inflation was perceived by the population as a natural disaster. And only after the introduction of widespread statistical accounting of the activities of business entities in the United States, Japan and many Western European countries, it was possible to curb inflation. At the same time, the producers' property rights were not infringed upon. In addition, the measures taken did not have a negative impact on the level of competition for goods and services in the domestic markets. It should be noted that, in addition to statistical control, the creation of a system of distributed price regulators played an important role in curbing inflation.
Inflation in the USSR
There was no inflation in the Soviet Union. Except for the so-called "deficit". The fact is that in the USSR there was such an organization as the State Price Committee under the Council of Ministers of the USSR. Its functions included regulation of the relationship between producers and consumers. This happened by controlling production costs and profits.
This standardization was carried out by the Scientific Research Institute of Planning and Standards under the USSR State Planning Committee (NIIPiN). His tasks included the development of profit margins that would be scientifically substantiated. In addition, the institute has worked to determine the rates of intermediate consumption, as well as other costs of various institutions and organizations, taking into account their regional, sectoral and technological characteristics.
Inflation forecast
In order to accurately predict the future activities of an enterprise, it is necessary to evaluate not only its own internal resources, but also additional factors that do not depend on the organization. These factors are a consequence of the characteristics of the external environment, but at the same time have a great influence on the performance of each manufacturer. These parameters include inflation, which can be predicted using the formula for calculating inflation.
The source of macroeconomic information is government bodies that analyze and make forecasts regarding the economic and financial situation. In addition, they monitor trends in changes in the exchange rate of the national currency, price increases, as well as assess the structure of the cost of goods and services not only in the country, but throughout the world. In the process of forecasting the financial and economic development of an enterprise, it is necessary to take into account inflationary changes. They have a significant impact on many aspects of an organization's activities.
Inflation index
One of the main and visual indicators of the depreciation of money is the inflation index. The formula by which it is calculated helps to determine the overall increase in the value of goods and services in a certain period of time. It is determined by adding the base price level at the beginning of the reporting period (taken to be equal to one) and the inflation rate for the considered interval. The inflation formula in this case is as follows: II m = 1 + TI m, where
ТИ т - annual inflation rate. This indicator characterizes the general increase in the price level during a given time period and is expressed as a percentage. In turn, this indicator is calculated using the inflation rate formula: TI t = (1 + TI m) 12 -1, where
TI m is the average monthly inflation rate, provided that it is uniform throughout the year.
When planning the company's annual budget, the following indicators should be considered:
1) inflation that changes over time. Here it is necessary to take into account the fact that the dynamics of inflation often does not coincide with fluctuations in exchange rates;
2) the possibility of including several monetary units in the budget;
3) heterogeneity of inflation. In other words, prices for various types of goods, services, resources change in different ways and their growth rates may differ;
4) government regulation of the cost of certain groups of goods and services.
Accounting for inflation when calculating the profitability of financial transactions
When calculating the required level of income from financial transactions, it is necessary to take into account the inflation factor. At the same time, the tools that are used in the calculations are designed to ensure the determination of the amount of the so-called "inflationary premium", as well as the general level of nominal yield. The presence in this formula for calculating the level of inflation allows the company to compensate for inflationary losses, as well as to obtain the required level of net profit.
Calculating the "inflationary premium"
To calculate the required inflation premium, the following formula is used:
Pi = P x TI,
where Pi is the volume of the inflationary premium for a specific period of time,
P is the initial value of the money supply,
ТИ - inflation rates for the considered time interval in the form of a decimal fraction.
The formula for accounting for inflation when determining the total required level of income from a financial transaction is as follows: Dn = Dr + Pi,
where Дн is the total nominal volume of the required income of the financial transaction. This takes into account the factor of inflation for the considered time period.
Dr - the real amount of the required income from the financial transaction in the considered period of time. This indicator is calculated using simple or compound interest. The real interest rate is used in the calculation process.
Pi is the inflationary premium for the period under review.
Calculating the required yield
To calculate the required rate of return on financial transactions, taking into account the inflation rate, the formula is as follows:
УДн = (Дн / Др) - 1.
Here UDN is the required degree of profitability from financial transactions taking into account inflation in the form of a decimal fraction, Dn is the total nominal volume of the required income of a financial transaction in the considered period of time, Dp is the real amount of the required income from the financial transaction in a given time interval.
Accounting for the inflation factor using foreign currencies
It should be emphasized that it is rather difficult to make an accurate forecast of inflation rates using the formula. In addition, this process is time consuming, and the result largely depends on the impact of subjective factors. Therefore, you can use another effective financial management tool.
It consists in converting funds that will be received in the form of income from financial transactions into one of the main and stable world currencies. This will completely eliminate the inflation factor. In this case, the current rate at the time of the calculations is used.
Fischer's formula
Fischer's formula for inflation was first published in his 1911 edition of The Purchasing Power of Money. Until today, it is a reference point for those specialists in the field of macroeconomics who are convinced of the dependence of its growth on the amount of money in circulation. The author of the formula is the American economist and mathematician Irving Fisher. The essence of the formula is the definition and attitude to credit funds, interest and crisis phenomena. It looks like this: MV = PQ,
where M is the volume of money supply in circulation, V is the velocity of circulation of the mass of cash, P is the price, and Q is the amount of products and services sold. Fisher's formula for inflation is a macroeconomic ratio and still serves as one of the most important and used tools. In simple terms, this equation shows a directly proportional relationship between the level of prices for goods and services and the volume of their production, on the one hand, and the amount of money supply in circulation, on the other. At the same time, the mass of money is inversely proportional to the speed of circulation of the total mass of cash.
Money supply in Russia
At the moment, the rate of turnover of the money supply in the Russian economy shows a tendency to slow down. At the same time, sharp jumps in this indicator, as a rule, correspond to sudden changes in the ruble exchange rate against major world currencies. The slowdown in the circulation of the money supply has two main reasons. The first is to reduce the growth rate of the gross domestic product. The second reason is the increase in inflation rates. In the future, this state of affairs may lead to a situation where the money supply will simply become immense.
Here it is necessary to return to Fischer's formula and emphasize one curious detail. The rate of turnover of the money supply is a consequence of the parameters of the equation. At the moment, there is no established methodology for monitoring this indicator. Nevertheless, the very formula of inflation, due to its simplicity and ease of understanding, has taken root in modern macroeconomic theory.
One of the main problems of the monetary policy of the RF leadership is the frivolous attitude to the high refinancing rate. This, in turn, is the reason for the fall in the level of industrial production and the stagnation of the agricultural sector of the economy. The country's leading economists understand the pernicious nature of this approach.
But today we have to state with regret that the government officials of the Central Bank and the Ministry of Finance, who are responsible for monetary policy, follow the interests of the monopolists. It is beneficial for these groups of entrepreneurs to preserve the existing alignments in the dynamics of price changes and their structure.
Let's start right away with the formulation of the Fisher hypothesis (the Fisher effect), which states that the nominal interest rate depends on two quantities: the real interest rate and the inflation rate. This dependence has the following form:
i = r + π, where
i is the nominal interest rate;
r is the real interest rate;
π - 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 Fisher's formula, the nominal interest rate (which is essentially nothing more than the price of credit), like the price of any consumer good or service, is subject to correction through the inflation rate.
Fisher's formula allows you to estimate the real return on investment. So, for example, an investor who invests 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 percentage 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 12%, then the investment efficiency at a given nominal interest rate will be reduced to zero:
r = i-π = 0.12-0.12 = 0
Fisher's complete formula
Above is the formula in its simplified form. Its full version is as follows:
As you can see, the complete formula differs from the approximate one by the presence of the product rπ. Simple mathematics 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 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 all: 0.01x0.01 = 0.0001 = 0.01%. That is, the smaller the values of π and r, the more accurate the results are given by Fisher's approximate formula.
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 affordable for potential borrowers. One of the reasons for the rise in the interest rate is the intensification of inflation. To describe the relationship between the interest rate and inflation, it is necessary to introduce the concepts of real and nominal interest rates.
Nominal interest rate (R) - the interest rate not adjusted for the inflation rate.
Real interest rate (r) - 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 Fisher's formula:
If 0% ≤ π ≤ 10%, then an approximate formula can be used to calculate the real interest rate: r ≈ R - π
If we express the nominal rate from an approximate formula, that is, R ≈ r + π then we get an effect called the Fisher effect. In accordance with this effect, two main components can be distinguished and, accordingly, two main reasons for the change in the nominal interest rate: real interest and inflation rate. However, when a financial institution (bank) determines the nominal interest rate, it usually proceeds from 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.
The exchange rate of the national currency is the most important macroeconomic indicator.
The nominal exchange rate is the ratio of the values of the two currencies (at the exchange office we see exactly the nominal values).
The real exchange rate is the ratio of the values of goods produced in different countries, or the ratio in which goods from one country can be exchanged for similar goods from another country.
= ×, where is the real exchange rate, P * is the price of a foreign product (in dollars), P is the price of a domestic product (in rubles), is the nominal exchange rate of the dollar against the ruble.
Based on the formula, the change in the real exchange rate 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 - negatively.
Approximate formula (for small changes): ∆% ≈ ∆% + - π
Purchasing power parity.
Purchasing power parity is the amount of one currency, expressed in terms 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, must be the same)
∆% ≈ π -, ∆% = 0 - relative PPP (the nominal exchange rate is adjusted to compensate for the difference in inflation rates)
Question number 10
Economic growth and cycle. Long- and short-term processes in the economy. What is a “recession” as defined by the NBER? Signs of 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- long-term trend of real GDP growth. 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 means only the direction of movement of the economy, the so-called "trend";
2) long-term, since the economic growth is an indicator characterizing a long-term period, and, therefore, we are talking about an increase in potential GDP (i.e., GDP at full employment of resources), about an increase in the production capabilities of the economy;
3) real GDP (and not nominal, the growth of which can occur due to an increase in the price level, and even with a reduction in real production). Therefore, an important indicator of economic growth is the indicator of the size of real GDP.
The main goal of economic growth- an increase in prosperity and an increase in national wealth.
The generally accepted quantitative measure of economic growth is the indicators of absolute growth or growth rates of the real volume of output as a whole or per capita:
Economic cycle- these are several periods of different activity towards 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, spreading throughout the economy, lasting more than several months and noticeable in the dynamics of production, employment, real incomes and other indicators.
Topic 7. Special issues of financial management
Methodical instructions
Getting started looking at examples and solving problems on your own, you need to carefully read the content on the relevant issue of the topic. The basic concept in this topic is the concept of the time value of money, the concept of a trade-off between risk and reward. The most important concepts: inflation, level, rate and inflation index, financial condition, financial insolvency, bankruptcy, financial restructuring, enterprise value, business value. These concepts should be learned and understood in their relationships.
This topic is final. Therefore, here are tasks that raise questions of the preceding topics.
In solving problems, formulas are used, the explanation of which is presented in the content. To make it easier to find the necessary clarifications in the content, the numbering of formulas and designations in the workshop are the same as in the content.
7.1. Financial management in an inflationary environment
This section uses the following conventions:
d - rate of return,%;
- the minimum allowable profitability,%;
- risk-free profitability,%;
F (FV) - future (accrued) value, den. units;
Inflation index,%;
P (PV) - present (discounted) value, den. units;
r - real rate of return,%;
- rate adjusted for inflation (nominal),%;
- the minimum allowable profitability,%;
- inflation rate,%;
V is the increase in value (the amount of interest received), den. units
In some problems, additional designations are introduced.
Task 7.1.1.
The minimum required yield is 12% per annum. The inflation rate is 11%. What should be the nominal rate?
Methodical instructions:
Answer: The nominal rate must be at least 24.32%.
Task 7.1.2.
Determine the nominal interest rate for a financial transaction if the efficiency level is to be 7% per annum, and the annual inflation rate is 22%.
Methodical instructions: use formula (7.1.10).
Answer: The nominal rate is 30.54%, while the real rate is 7%.
Task 7.1.3.
Deposits are accepted at 14%. What is their real rate of return at 11% inflation?
Methodical instructions: use formula (7.1.10).
Note that the real return is less than the simple difference between the interest rate and the inflation rate:
Answer: The real return is 2.7%.
Task 7.1.4.
The expected inflation rate is 2% per month. Determine the quarterly and annual inflation rate.
Methodical instructions:
1) using the inflation rate per month:
2) using the inflation rate per quarter:
Answer: The quarterly inflation rate is 6.12%, the annual inflation rate is 26.82%.
Task 7.1.5.
Determine the real profitability when placing funds for a year at 14% per annum, if the inflation rate for the year is 10%.
Methodical instructions:
Answer: The real yield is 3.63% per annum.
Task 7.1.6.
The client invests 20 thousand rubles in the bank for a year, inflation is 18%. The client wants his contribution to bring 6% of annual income. What percentage should the client make a deposit?
Methodical instructions: use formula (7.1.10).
Answer: To receive an annual income of 6% per annum, the rate on a loan, adjusted for inflation, must be at least 25.08%.
Task 7.1.7.
The client invests 20 thousand rubles in the bank for a year. at 6% per annum, inflation is 18%. What result will the depositor get from this operation?
Methodical instructions: use formulas (2.1.1), (2.1.3) and (7.1.10).
3. Real interest:
Answer: Nominally (countably), the client receives 1200 rubles. in addition to its 20 thousand rubles. However, the depreciation of money as a result of inflation leads to the fact that the real value of the amount received is less than the invested amount by 2033.9 rubles.
Task 7.1.8.
The inflation rates in the next 5 years are projected annually as follows: 14%, 12%, 8%, 7%, 5%. How will prices change over the next five years?
Methodical instructions:
2) introduce the notation: - the inflation rate in the t -th year, - the price index in the t -th year, - the price index for n n years; - average one-day rate of price change.
Given: |
Solution: The price index for 5 years is calculated as the product of annual indices: And the annual index, in turn, is equal to:, hence Thus, over the five-year period, prices will increase by 1.55 times, or by 55% (for comparison, we calculate the simple sum of the inflation rates, which turns out to be significantly lower than the calculated one: 14 + 12 + 8 + 7 + 5 = 46 < 55). |
Let's find the average annual inflation rate for the five years:
, i.e., the average annual inflation rate is:
1 — 1,0916 = 0,0916 = 9,16 %.
Let's find the average daily inflation rate over 5 years:
That is, the average daily inflation rate is 0.024%.
Let's find the average daily inflation rate in the 2nd year of the analyzed five-year period:
, that is, the average daily inflation rate in the 2nd year is 0.031%.
Answer: Over the five-year period, prices will increase 1.55 times or 55%, while the average annual rate of growth in prices will be 9.16%, the average daily rate - 0.024%.
Task 7.1.9.
There is a project that requires an investment of 20 million rubles. The minimum allowable yield is 5% per year. Income from the project will be received in 2 years in the amount of 26 million rubles. Risk-free rate of return - 8% per year. The beta is 0.9. The expected inflation rate is 10%. The average market rate of return on similar projects is 18% per annum.
Methodical instructions
d
Given: P = 20 million rubles. F = 26 million rubles.
Accept the project? |
Solution: The nominal profitability of the project is:
The assessment of the feasibility of implementing a project can be done in three ways:
Let's consider these methods. |
First way. To find the real profitability of the project, we will use the formula for determining the future value (2.1.7), taking into account inflation (7.1.8) and risk (2.5.13):
Transforming this formula, we get:
To calculate d, you must first calculate the risk premium (formula 2.5.13):
The real profitability is not only less than the minimum allowable, but in general this project is relatively unprofitable, so its implementation is not advisable.
Second way. Based on the formula (*), we determine the maximum acceptable investment:
The result obtained means that the project is not acceptable if investments are available on the market.
If we do not take into account the conditions of investments in the market (average profitability, risk), but take into account only inflation, then the profitability of the project will be:
And in this case, the expected profitability is less than the minimum allowable, that is, the project is unacceptable.
The third way... Based on the average market conditions and the amount of investments, we will calculate the minimum acceptable income and compare it with the expected one.
Acceptable income (f. (*)) With an investment of 20 million rubles. will be:
This result once again confirms the conclusion made about the unacceptability of the project in question.
Answer: The project is unacceptable.
Task 7.1.10.
You can buy a package of zero-coupon bonds for 9 thousand rubles. The bonds mature in 2 years. The nominal price of the package is 12 thousand rubles. The expected inflation rate is 10%. Is it worth buying a package of bonds if you need a real income of at least 4% per annum?
Methodical instructions:
Answer: The package of bonds should be purchased, since its real yield is higher than the minimum allowable.
Task 7.1.11.
The investor invests 1 million rubles in the investment object for 3 years. Required real interest rate of return 5% per annum. The projected average annual inflation rate is 10%. Determine the minimum amount of money that this investment object should bring to the investor so that it makes sense for the investor to invest money in it, and evaluate the feasibility of investing money in the investment object, which, in accordance with the business plan, should bring the investor 1,500 thousand rubles in 3 years. R.
Methodical instructions: use formulas (2.1.7), (7.1.10);
Answer: In order for the investment to be expedient, the project must bring at least 1.54 million rubles in three years, so the investment is impractical.
Task 7.1.12.
The rise in prices for 3 years was 7%. Estimate the average annual rate and inflation index.
Methodical instructions: 1) use formulas (2.1.7) and (2.1.9);
2) introduce the notation: - average annual inflation rate, - inflation rate for n years.
We get: 
Answer: The average annual inflation rate is 2.28%, the annual inflation rate is 1.0228, or 102.28%.
Task 7.1.13.
The citizen has entered into a deposit agreement at 15% per annum. The forecasted inflation rate is 1% per month. Estimate the real interest rate.
Methodical instructions: 1) use formulas (2.1.7) and (2.1.9);
2) introduce the notation: - inflation rate per month, - annual inflation rate.
We find the real return (interest rate) using Fisher's formula:
Answer: Real interest rate (yield) 2.04% per year.
Task 7.1.14.
The need for the company's working capital in the reporting year was $ 1.2 million, the profit was $ 0.5 million. The inflation rate was 15%. Can a company withdraw all profits from circulation and use them for social needs?
Methodical instructions: 1) use the formula (2.1.7);
2) introduce the designations: - annual inflation rate, OBSo - the need for working capital in the reporting year, OBSP - the planned need for working capital, Po - profit in the reporting year, Ps - profit for social needs.
ObS = ObSp - ObSo = 1.32 - 1.2 = 0.12 million dollars.
Consequently, the following can be directed to social needs:
Ps = Po - obS = 0.5 - 0.12 = 0.38 million dollars.
Answer: An enterprise can spend no more than 380 thousand dollars for social needs.
Task 7.1.15.
Assess the impact of inflation on the balance sheet of an enterprise for a certain period. Build models that describe the financial condition of the enterprise at the end of the period, as well as calculate the profit or loss it received as a result of price changes. During the period under review, no business transactions were made. The inflation rate was 12%. The rate of change in the current valuation of non-monetary assets was 18%. The balance of the enterprise at the initial moment t 0 is presented in table. 7.1.1.
Table 7.1.1 - The balance of the enterprise at the moment t 0, mln.
Methodical instructions: 1) study clause 7.1.2 of the content; 2) take into account that inflationary profit is an increase in capital due to price increases, as well as due to inflationary growth in the excess of monetary liabilities over monetary assets; 3) introduce the designations: NA - non-monetary assets; MA - monetary assets; SK - equity capital; MO - monetary liabilities; B0 - balance sheet currency (advanced capital) at the beginning of the period; B 1 - balance sheet currency at the end of the period; P and - inflationary profit.
MA + HA = SK + MO |
12 + 85 = 30 + 67 |
Inflationary profit is zero (P and = 0), since the impact of inflation is not reflected in the accounting and reporting.
Situation 2. Accounting is carried out in monetary units of the same purchasing power (methodology GPL) , taking into account the general price index.
There are two possible options for consideration. V first this option assumes the recalculation of non-monetary assets taking into account the price index. The balance equation will take the form:
MA + HA (1 + Ti) = SK + HATi + MO |
12 + 85 (1 + 0,12) = 30 + 850,12+67 |
Received change ONTi= 85 0.12 = 10.2 million rubles. can be interpreted as a change in the owners' capital (SK - revaluation of non-current assets) and, accordingly, as inflationary profit (P and).
Second The (more rigorous and methodologically correct) option involves taking into account the impact of inflation by comparing monetary assets and monetary liabilities. This approach is due to the fact that monetary liabilities in an inflationary environment bring indirect income, and monetary assets - an indirect loss. In this version, the balance equation will be as follows:
MA+ HA (l + Ti) = MO+ SC (1+ Ti) + Ti(MO - MA) |
12 + 85 1,12 = 67 + 30 1,12 + 0,12 (67 — 12) |
12 + 95,2 = 67 + 33,6 + 6,6 |
Due to inflation, the amount of advanced capital increased by:
B = B 1 - B 0 = 107.2 - 97.0 = 10.2 million rubles.
However, not all of the growth was due to the self-increase in the value of equity capital due to the depreciation of the ruble, namely:
SK = 33.6 - 30 = 3.6 million rubles.
Due to the excess of monetary liabilities over monetary assets, an inflationary profit was obtained:
P u = Ti (MO - MA) = 0.12 (67 - 12) = 6.6 million rubles.
Situation 3. Accounting is carried out at current prices (methodology SSA) using individual price indices The balance equation is as follows:
In our case, since the individual price indices of all non-monetary assets are the same, this equation will take the form:
12 + 85 1,18 = 30 + 67 + 85 0,18
The notional income obtained as a result of price changes can be interpreted either as inflationary profit or as inflationary capital gains:
P u = 112.3 - 97.0 = 15.3 million rubles.
Situation 4. Accounting is carried out in current prices and monetary units of the same purchasing power (combined method), the balance equation is as follows:
This model reflects both the impact of inflation and changes in prices for specific types of assets, products and goods.
Due to inflation and the rise in asset prices of this enterprise, the value of the advanced capital increased by:
B = B 1 - B 0 = 112.3 - 97.0 = 15.3 million rubles.
including due to the self-growth of the value of equity capital, ensuring the preservation of its purchasing power for:
SK = 30 1.12 - 30 = 3.6 million rubles;
due to the relative change in the prices of the assets of the enterprise in comparison with the inflation rate - by:
HA = HA (r - Ti) = 85 (0.18 - 0.12) = 5.1 million rubles,
due to the excess of monetary liabilities over monetary assets - by:
(MO - MA) = Ti (MO - MA) = 0.12 (67-12) = 6.6 million rubles.
Thus, the total increase in the advanced capital was:
B = SK + HA + (MO - MA) = 3.6 + 5.1 + 6.6 = 15.3 million rubles.
The last two increments can be interpreted as inflationary profit and calculated using the formula
P u = HA + (MO - MA) = 5.1 + 6.6 = 11.7 million rubles.
Answer: 1) in the case of keeping records at constant prices, the inflationary profit is zero; 2) in the case of accounting in monetary units of the same purchasing power, taking into account the general price index, the inflationary profit is equal to 6.6 million rubles. (the entire capital gain of 10.2 million rubles can be considered as inflationary profit); 3) in the case of keeping records at current prices using individual price indices, the inflationary profit is 15.3 million rubles; 4) in the case of accounting in current prices and monetary units of the same purchasing power, inflationary profit is 11.7 million rubles.
Task 7.1.16.
The predicted value of the average monthly rate of price growth is 3%. Over what period of time will the money depreciate: a) 2 times, b) 3 times?
Methodical instructions: 1) use formulas (7.1.5) and (7.1.6);
2) introduce the notation: - one-day rate of price change; n - number of days; k is the number of times by which money is depreciated; 3) so that a certain amount is depreciated in k k.
Given: |
Solution: |
Find the one-day inflation rate (30 days in a month).
Thus, the one-day inflation rate is 0.0986%, that is, daily prices increase by 0.0986%, which leads to an increase in prices for the year by 42.6%. From formula (24.8) it follows that a certain sum S depreciated in k times, the value of the coefficient of the decline in the purchasing power of the monetary unit should be equal to 1 / k or, which is the same, the price index should be equal to k.
The original amount is depreciated 2 times (k = 2):
Hence the required number of days. n= 703 days
The original amount is depreciated 3 times (k = 3):
Hence the required number of days. n= 1115 days.
Answer: With an average monthly inflation rate of 3%, any initial amount that is not moving, for example, dead in the form of money as a reserve of funds, will be devalued by half in 703 days, that is, in about 1.9 years, and 3 times in 1115 days ., i.e. after 3 years.
Task 7.1.17.
The minimum required yield is 15% per annum. The inflation rate is 10%. What should be the nominal rate?
Methodical instructions: use formula (7.1.10).
Task 7.1.18.
The expected inflation rate is 3% per month. Determine the quarterly and annual inflation rate.
Methodical instructions: 1) use formulas (2.1.7) and (2.1.9);
2) introduce the following notation: - inflation rate per month, - inflation rate per quarter, - annual inflation rate.
Task 7.1.19.
You can buy a package of zero-coupon bonds for 6 thousand rubles. The bonds mature in 2 years. The nominal price of the package is 12 thousand rubles. The expected inflation rate is 11%. Should you buy a package of bonds if you need a real income of at least 5%?
Methodical instructions: 1) use formulas (2.1.7) and (7.1.10);
2) introduce the notation: P - the real value of the bond package, n - the maturity date of the bonds, N - the par value of the bond package.
Task 7.1.20.
Determine the nominal interest rate for a financial transaction if the efficiency level is to be 8% per annum, and the annual inflation rate is 13%.
Methodical instructions: use formula (7.1.10).
Task 7.1.21.
The client invests 20 thousand rubles in the bank for a year. inflation is 14%, the client wants his contribution to bring 7% of annual income. What percentage should the client make a deposit?
Methodical instructions: 1) use formula (7.1.10).
Task 7.1.22.
The inflation rates in the next 4 years are projected annually as follows: 14%, 12%, 10%, 9%. How will prices change in 4 years?
Methodical instructions: 1) use formulas (7.1.5) and (7.1.6);
2) introduce the notation: - the inflation rate in the t -th year, - the price index in the t -th year, - the price index for n years; - the average annual value of the index for n years; - one-day rate of price change.
Task 7.1.23.
Deposits are accepted at 11%. What is their real rate of return at 13% inflation?
Methodical instructions: use formula (7.1.10).
Task 7.1.24.
Determine the real profitability when placing funds for a year at 13% per annum, if the inflation rate for the year is 12%.
Methodical instructions: use formula (7.1.10).
Task 7.1.25.
The client invests 20 thousand rubles in the bank for a year. at 10% per annum, inflation is 12%. What result will the depositor get from this operation?
Methodical instructions: 1) use formulas (2.1.1), (2.1.3), (7.1.10).
Task 7.1.26.
There is a project that requires an investment of 22 million rubles. The minimum allowable yield is 6% per year. Income from the project will be received in 2 years in the amount of 28 million rubles. Risk-free rate of return 6% per year. The beta is 0.8. The expected inflation rate is 11%. The average market rate of return on similar projects is 16% per annum.
Should this project be accepted?
Methodical instructions : 1) use formulas (2.1.7), (2.5.13) and (7.1.8);
2) introduce the notation: n - project implementation period, - beta coefficient, - average market profitability, - nominal profitability of the project, d- real profitability of the project, - risk premium, - maximum acceptable investments, - profitability adjusted for inflation, - minimum acceptable income.
Task 7.1.27.
Estimate the projected annual inflation rate if it is known that the projected monthly inflation rate is 3%.
Methodical instructions : use formulas.
Task 7.1.28.
1 million rubles are invested in the investment object for 2 years. In 2 years, the investor will receive 2 million rubles from this object. The projected average annual inflation rate is 13%. Estimate the real income received by the investor and the financial losses caused by inflation.
Methodical instructions : use formulas.
Task 7.1.29.
The investor is invited to invest 8 million rubles in the investment object. In 2 years, in accordance with the business plan, he can receive 12 million rubles. The projected average annual inflation rate is 13%. Assess the feasibility of investing in this object if the investor is satisfied with a real income of at least 2.5 million rubles.
Methodical instructions : use formulas.
Task 7.1.30.
The predicted value of the average monthly rate of price growth is 4%. Over what period of time will the money depreciate: a) 2 times, b) 3 times?
Methodical instructions : use formulas.
7.3. Bankruptcy and financial restructuring
Methodical instructions : Consider various methods of diagnosing bankruptcy on the example of one enterprise, the balance sheet and profit and loss account of which is presented in table. 7.3.1 and 7.3.2.
Write down the calculation formulas using the line numbers of the balance sheet or the profit and loss statement (for example, “p. 250 (1)” means the amount of short-term financial investments, and “p. 010 (2)” - revenue). The value of the coefficients at the beginning and end of the year shall be designated by the letters "n" and "k", enclosed in brackets.
Table 7.3.1 - Data of the balance sheet of the FM enterprise, thousand rubles.
Assets |
Code p. |
For the beginning of the year |
At the end of the year |
Passive |
Code p. |
For the beginning of the year |
At the end of the year |
I. Non-current assets |
III. Capital and reserves |
||||||
Fixed assets |
Authorized capital |
||||||
Construction in progress |
Extra capital |
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Long-term fin. attachments |
Reserve capital |
||||||
Total for Section I |
Undestributed profits |
||||||
Total for Section III. |
|||||||
II. Current assets |
IV. long term duties |
||||||
Loans and credits |
|||||||
including: |
Total for Section IV |
||||||
raw materials |
V. Short-term liabilities |
||||||
work in progress costs |
Loans and credits |
||||||
finished products |
Accounts payable |
||||||
Future expenses |
including: |
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VAT on purchased assets |
suppliers and contractors |
||||||
Accounts receivable (over a year) |
organization personnel |
||||||
Accounts receivable (up to a year) |
state extrabudgetary funds |
||||||
Short-term financial investments |
budget (taxes and fees) |
||||||
Cash |
Debts to participants |
||||||
Total for Section II |
revenue of the future periods |
||||||
Provisions for future expenses |
|||||||
Total for Section V |
|||||||
Table 7.3.2 - Data of the profit and loss statement of the FM enterprise, thousand rubles.
Index |
For the reporting year |
|
Revenue (net) |
||
Cost of goods sold |
||
Gross profit |
||
Business expenses |
||
Administrative expenses |
||
Sales profit |
||
Percentage to be paid |
||
Non-operating income |
||
Profit before tax |
||
Current income tax |
||
Net profit of the reporting period |
Task 7.3.1.
Determine the solvency class of the enterprise "FM" based on a simple scoring model.
Methodical instructions: 1) use the table (7.3.1) of the content; 2) initial data - in tables.
2) current liquidity ratio:
K tl = s.290 (1) / s. 690 (1).
K tl (n) = 754/981 = 0.769;
K tl (k) = 875/832 = 1.052.
K tl (average) = (0.769 + 1.052) / 2 = 0.910;
3) the coefficient of financial independence:
K fn = s. 490 (1) / s. 700 (1).
K fn (n) = 2195/3396 = 0.646;
K fn (k) = 2430/3542 = 0.686.
K fn (average) = (0.646 + 0.686) / 2 = 0.666.
Points for the return on total capital ratio:
B 1 = (19.9 - 5) / (9.9 - 1) x (8.8 - 1) + 5 = 18.06.
Points for the current ratio: B 2 = 0.
Points for the financial independence ratio:
B 3 = (19.9 - 10) / (0.69 - 0.45) x (0.666 - 0.45) + 10 = 18.91.
The total score: B = 18.06 + 0 + 18.91 = 36.97, which corresponds to the class of enterprises with an average level of solvency.
Answer: The company has an average level of solvency.
Task 7.3.2.
Estimate the likelihood of bankruptcy of an enterprise using the Tafler and Tishou model. The initial data are presented in table. 7.3.1 and 7.3.2.
Methodical instructions: use formula (7.3.10).
K 3 = s.690 (1) / s.300 (1) = (981 + 832) / (3396 + 3542) = 0.261;
K 4 = s.010 (2) / s.300 (1) = 4217 / (3396 + 3542) = 0.608.
Z = 0.53 (-0.32) + 0.13 0.704 + 0.18 0.261 + 0.16 0.608 = 0.065< 0,2.
According to this model, bankruptcy is highly probable.
Answer: In accordance with this model, bankruptcy is very likely, however, it should be remembered that this model was developed in conditions that are not similar to the modern Russian economy, therefore, the obtained conclusion cannot be considered as completely reliable.
Task 7.3.3.
To assess the financial stability of an enterprise according to the method of V.V. Kovalev and O. N. Volkova. The initial data are presented in table. 7.3.1 and 7.3.2.
Methodical instructions: use formula (7.3.12).
K 2 = s. 290 (1) / s. 690 (1) = (754 + 875) / (981 + 832) = 0.9;
K 3 = s. 490 (1) / (s. 590 (1) + s. 690 (1)) = (2195 + 2430) / (220 + 280 + 981 + 832) = 2.0;
K 4 = s. 190 (2) / s. 300 (1) = (4214 - 3912 - 140 - 458 - 18 + 12) / ((3396 + 3542) / 2) = -0.9;
K 5 = s. 190 (2) / s. 010 (2) = (4214 - 3912 - 140 - 458 - 18 + 12) / 4217 = -0.7.
The total weighted sum of the odds will be:
N = 25 6.2 + 25 0.9 + 20 2 + 20 (-0.9) + 10 (-0.7) = 214.5> 100.
Answer: In accordance with this methodology, the situation at the enterprise is normal.
Tasks for independent solution
Task 7.3.4.
Methodical instructions: 1) the initial data are presented in table. 7.3.1 and 7.3.2; 2) use formula (7.3.1).
Task 7.3.5.
Determine the class of financial stability of the enterprise "FM" according to the methodology of Dontsova and Nikiforova.
Methodical instructions: 1) the initial data are presented in table. 7.3.1 and 7.3.2; 2) use table. 7.3.2 content.
Task 7.3.6.
Determine the probability of bankruptcy of the FM enterprise according to the Altman model.
Methodical instructions: 1) the initial data are presented in table. 7.3.1 and 7.3.2; 2) use the formula 7.3.8.
Task 7.3.7.
Determine the Z-score according to the Fox model of the FM enterprise.
Methodical instructions: 1) the initial data are presented in table. 7.3.1 and 7.3.2; 2) use the formula 7.3.9.
Task 7.3.8.
Determine the probability of delay in payments of the FM enterprise according to the Connan and Golder model.
Methodical instructions: 1) the initial data are presented in table. 7.3.1 and 7.3.2; 2) use the formula 7.3.11.
print version
Irving Fisher is an American economist, a representative of the neoclassical direction in economics. Born February 27, 1867 in Sogertis, pcs. New York. He made a great contribution to the creation of the theory of money, as well as derived the "Fisher's equation" and "the equation of exchange".
His works were taken as the basis of modern methods for calculating the inflation rate. In addition, they greatly helped to understand the laws governing the phenomenon of inflation and pricing.
Fisher's complete and simplified formula
In simplified form, the formula will look like this:
i = r + π
- i is the nominal interest rate;
- r is the real interest rate;
- π - inflation rate.
This entry is approximate. The smaller the values of r and π, the more precisely this equation is fulfilled.
The following record will be more accurate:
r = (1 + i) / (1 + π) - 1 = (i - π) / (1 + π)
Quantitative theory of money
The quantitative theory of money is an economic theory that studies the impact of money on an economic system.
In accordance with the model put forward by Irving Fisher, the state should regulate the volume of money supply in the economy in order to avoid their lack or excessive amount.
According to this theory, the phenomenon of inflation occurs due to non-observance of these principles.
Insufficient or excessive amount of money supply in circulation leads to an increase in the rate of inflation.
In turn, the rise in inflation implies an increase in the nominal interest rate.
- Nominal the interest rate reflects only the current income from deposits, excluding inflation.
- Real the interest rate is the nominal interest rate minus the expected inflation rate.
Fisher's equation describes the relationship between these two indicators and the rate of inflation.
Video
How to apply 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 annum. In this case, the real interest rate will be 10% - 5% = 5%. Thus, the higher the inflation rate, the lower the real interest rate.
It is this rate that should be taken into account in order to calculate the amount of money that this contribution will bring you in the future.
Interest calculation types
As a rule, the accrual of interest on profit occurs in accordance with the compound interest formula.
Compound interest is a method of calculating profit interest, in which they are added to the principal amount and then they themselves participate in the creation of new profit.
A short notation of the compound interest formula looks like this:
K = X * (1 +%) n
- K is the total amount;
- X is the initial amount;
- % - percentage of payments;
- n is the number of periods.
At the same time, the real interest that you will receive by making a contribution at compound interest will be the less, 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, it is the percentage of the initial investment 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 - effective interest;
- 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 charges for the period.
International Fischer effect
The International Fisher Effect is a theory of the exchange rate put forward by Irving Fisher. The essence of this model is to calculate present and future nominal interest rates in order to determine the dynamics of changes in the exchange rate. This theory works in its pure form if capital moves freely between states, whose currencies can be correlated with each other in value.
Analyzing the precedents of inflation growth in different countries, Fischer noticed a regularity 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 because the interest rate is set taking into account the inflation risk and market forecasts for the currency pair. This phenomenon is called Fisher effect .
Extrapolating this theory to international economic relations, Irving Fisher concluded that changes in nominal interest rates have a direct impact on the rise in price or depreciation of the currency.
This model has never been tested in real conditions. Its main disadvantage it is generally accepted that it is necessary to meet 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 the excessive amount of money circulating in the country, which leads to their depreciation.
Inflation is classified according to the following features:
Uniformity - the dependence of the rate of inflation on time.
Uniformity - spreading influence to all goods and resources.
Inflation forecasting is calculated using the inflation index and latent inflation.
The main factors in forecasting inflation are:
- change in the exchange rate;
- an 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, this methodology fixes the following changes in the economy:
- change in profit;
- changes in payments to consumers;
- changes in import and export prices;
- change in rates.
Calculation of investment returns with and without inflation
The formula for the rate of return without inflation will look like this:
X = ((P n - P) / P) * 100%
- X - profitability;
- P n - the total amount;
- P - initial payment;
In this form, the final profitability is calculated without taking into account the time spent.
X t = ((P n - P) / P) * (365 / T) * 100%
Where T is the number of days the asset was held.
Both methods ignore the impact of inflation on profitability.
Inflation rate(real profitability) should be calculated using the formula:
R = (1 + X) / (1 + i) - 1
- R - real profitability;
- X is the nominal rate of return;
- i - inflation.
Based on the Fisher model, one main conclusion can be drawn: inflation does not generate income.
The rise in the nominal rate due to inflation will never be greater than the amount of money invested that has depreciated. In addition, the high rate of inflation growth implies significant risks for banks, and depositors are responsible for compensating for these risks.
Application of Fisher's formula in international investment
As you can see in the above formulas and examples, the level of high inflation always lowers 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 by means of the Fisher formula
The above model can be clearly seen on the example of the investment market of the Russian Federation.
The drop in inflation in 2011-2013 from 8.78% to 6.5% led to an increase in foreign investments: in 2008-2009 they did not exceed 43 billion rubles. dollars a year, and by 2013 reached 70 billion rubles. dollars.
The sharp increase in inflation in 2014-2015 led to a decrease in foreign investment to historical lows. 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 dropped to 2.09%, which has already led to an inflow of new investments from investors.
In this example, it can be noted that in matters of international investment, the main parameter is precisely the real interest rate, which is calculated according to Fisher's formula.
How the inflation index of goods and services is calculated
The inflation index or consumer price index is an indicator that reflects the change 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 reference 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 reference period.
Simply put, the inflation index indicates how many times prices have changed over a certain period of time.
Knowing the inflation index, one can draw a conclusion about the dynamics of inflation. If the inflation index takes on values greater than one, then prices rise, which means that inflation also grows. The inflation index is less than one - inflation takes negative values.
The following methods are used to predict changes in the inflation index:
Laspeyres formula:
I L = (∑p 1 * q) / (∑p 0 * q 0)
- I L - 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)
Numerator - the actual cost of the products of the reporting period;
The denominator is the actual value of the products for the reporting period.
Fisher's ideal price index:
I p = √ (∑p 1 * q) / (∑p 0 * q 1) * (∑p 1 * q) / (∑p 0 * q 0)
Taking inflation into account 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 monetary terms- that is, to affect the final profitability of the project.
Ways to influence an investment project in the event of an increase in inflation:
- Change in currency flows depending on inflation;
- Accounting for the inflation premium in the discount rate.
Analysis of the inflation rate and its possible impact on the investment project requires the following measures:
- consumer index accounting;
- forecasting changes in the inflation index;
- forecasting changes in the population's income;
- forecasting the volume of cash collections.
Fisher's formula for calculating the dependence of the value of goods on the amount of money
In general, Fisher's formula for calculating the dependence of the value of goods on the amount of money has the following record:
- M is the volume of money supply in circulation;
- V is the frequency with which money is used;
- P - the level of the cost of goods;
- Q - the number of goods in circulation.
By transforming this record, you can express the price level: P = MV / Q.
The main conclusion from this formula is the inverse proportion between the value of money and its quantity. Thus, for normal circulation within the state, control of the amount of money in circulation is required. An increase in the number of goods and prices for them requires an increase in the amount of money, and, in the event of a decrease in these indicators, the money supply should be reduced. This kind of regulation of the amount of money in circulation is entrusted to the state apparatus.
Fisher's formula as applied to monopoly and competitive pricing
Pure monopoly presupposes, first of all, that one manufacturer has complete control over the market and is perfectly informed about its state. The main goal of a monopoly is to maximize profits with minimal costs. The monopoly always sets the price higher than the value of the marginal cost, and the volume of output is lower than in perfect competition.
The presence of a monopoly manufacturer in the market usually has serious economic consequences: the consumer spends more money than in the conditions of fierce competition, while the rise in prices occurs along with the rise in the inflation index.
If the change in these parameters is taken into account in Fisher's formula, then we get an increase in the money supply and a constant decrease in the number of goods in circulation. This situation leads the economy to a vicious cycle in which an increase in inflation leads to an increase only to an increase in prices, which ultimately further stimulates the rate of inflation.
A competitive market, in turn, reacts to an increase in the inflation index in a completely different way. Market arbitrage brings prices to market conditions. 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, one can notice 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 forces the Central Bank to reduce rates when inflation rises.
