Regulation of the amount of money in circulation and the price level is one of the main methods of influencing the 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 () it is necessary to regulate economic processes to a certain extent (Keynesian model). 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 has shown, many other important economic parameters depend on the one used in the economy, primarily the price level and interest rate (credit prices). 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.
Fisher's equation
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.
The exchange equation looks like this:
Fisher formula
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. However, under certain tolerances, one thing is certain: The price level depends on the amount of money in circulation. Usually two allowances are made:
- the rate of money turnover is a constant value;
- 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 disproportions in the economy, a primary change in prices is also possible, and only then a change in the money supply (Fig. 17).
Normal economic development:
Disproportion of economic development:
Fisher formula (exchange equation) determines the amount of money used only as a medium of exchange, and since money also 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 quantitative 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 will the price stability. In the case of an inequality in the quantity of money and the volume of prices, changes in the price level occur:
In this way, price stability- the main condition for determining the optimal amount of money in circulation.
In the evaluation process, it must be taken into account that nominal and real (that is, including and not including the inflation component) risk-free rates.
Nominal interest rate- is the market interest rate, pre-inflation, reflecting the current valuation of monetary assets.
Real interest rate is the market interest rate adjusted for inflation
When converting the nominal rate into the real one and vice versa, it is advisable to use the formula of the American economist Fisher, derived by him back in the 30s:
Rн = Rр + Jinf + Rр * Jinf
Rр = (Rн – Jinf) / (1+ Jinf)
where: Rн - nominal rate;
Rp - real rate;
Jinf - annual growth rate of inflation.
It is important to note that when using nominal income streams, the capitalization ratio (and its components) must be calculated in nominal terms, and when using real income streams, in real terms. To convert nominal income flows into real ones, the nominal value must be divided by the corresponding price index, that is, the ratio of the price level for the year in which the cash flows arise to the price level of the base period, expressed as a percentage.
For example:
A property leased under a net lease will bring in $1,000 annually for 2 years. The price index in the current period is 140% and is expected to be 156.7% next year and 178.5% next year. To convert nominal values into real ones, they must be expressed in base year prices. We construct a basic price index for each of the three years. The price indices of the current year are equal to 140/140 = 1, for the forecast period: the first year - 156.7/140 = 1.119; the second year - 178.5/140 = 1.275.
Thus, the real value of the nominal $1,000 that will be received in the first forecast year is $1,000/1.119 = $893.65, in the 2nd year ($1,000/1.275) = $784.31) .
Thus, as a result of inflationary adjustment, retrospective information used in the assessment is brought to a comparable form, as well as inflationary price increases are taken into account when making forecasts. cash flows.
General idea– there is a long-term relationship between the expected inflation and the interest rate (yield on long-term bonds).
Fisher's 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.
Calculation according to the exact equation with N equal to 10 and I equal to 6 will give next value 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's obvious that border application simplified equation - the value of inflation and the nominal rate of less than 10%.
Ticket 4
1. Relationship between the level of profitability and advanced capital. Discounted payback period of the project (for example).
Yield and profitability- performance indicators of the organization.
Profitability characterizes the ratio (level) of profit to advanced capital or its elements; sources of funds or their elements; the total amount of current expenses or their elements. Profitability indicators reflect the amount of profit received by the organization for each ruble capital, assets, income, expenses, etc.
Advance Capital- finances invested in production for profit, and not one-time, but regular. These funds are used to purchase materials, equipment, buildings and much more that is necessary for the production process. Therefore, this indicator is important for increasing the profitability of the enterprise.. After all, an entrepreneur, investing finances, plans to get more profit and in a much shorter time..
Profitability is an indicator that determines the amount of profit received from each unit of invested funds. If the enterprise is competitive and operates efficiently, then the indicator will grow.
The company's growth process is greatly influenced by the turnover of advanced capital. The increase in speed leads to a reduction in the production cycle and faster profit.
Increasing the rate of turnover of advanced capital leads to a reduction in the production cycle and faster profit.
To speed up the turnover, the following processes must be followed:
· Purchasing only high quality raw materials.
· Optimize the work of the logistics department.
Regularly stimulate the sale of goods in various ways.
· Introduce innovations in production aimed at reducing the production process.
Now let's move from theory to practice and see how to calculate the return on advanced capital.
For calculations, apply following formula return on advanced capital:
Rav. k. \u003d (Pr / av. k.) x 100%, where:
Rav. k. - profitability of the advanced capital;
Pr - net profit of the company;
av. k. - advanced capital.
This indicator is calculated both to determine the general financial condition of the enterprise, and for the investor to create a package of information, on the basis of which he makes a decision on cooperation.
Discounted payback period(Discounted payback period, DPP) is one of the most common and understandable indicators for evaluating the effectiveness of an investment project.
Discounting, in fact, characterizes the change in the purchasing power of money, that is, their value, over time. Based on it, a comparison of current prices and prices of future years is made.
The discounted payback period of an investment (Discounted Payback Period, DPP or DPВP) is the point in time when the present value of the income received from the project will equal the amount of investment costs.
To calculate this indicator, the formula is used:
CFT-annual income
- the sum of all investments
− investment completion date
When using the DPP (and PP) criterion when evaluating investment projects, decisions can be made based on the following conditions:
- the project is accepted if the payback takes place;
The project is accepted only if the payback period does not exceed the deadline set for a particular company.
DPP Benefits:
- Accounting for the value of money over time;
- taking into account the fact of unequal cash flows arising at different points in time.
Disadvantages of DPP::
- unlike the NPV indicator, it does not have the property of additivity.
Does not take into account subsequent cash inflows, and therefore may serve as an incorrect criterion for the attractiveness of the project.
In general the determination of the payback period is of an auxiliary nature relative to the project's net present value or internal rate of return.
Discount coefficientor the barrier rate is an indicator used to bring the amount of cash flow in the n-period of evaluating the effectiveness of an investment project, in other words, the discount rate is The interest rate used to convert future income streams into a single present value.
Considering the mechanism for forming the payback period indicator, one should pay attention to a number of its features that reduce the potential for its use in the system for evaluating the effectiveness of investment projects.
The first feature of the payback period indicator is that it does not take into account those amounts of net cash flow that are formed after the payback period of investment costs:
Graph of net cash flow formation for a real investment project during its full life cycle
So, for investment projects with long term operation after their payback period, a much larger amount of net cash flow can be obtained than from investment projects with short term operation (with a similar and even faster payback period of the latter).
The second feature of the payback period indicator, which reduces its estimated potential, is that its formation is significantly affected (ceteris paribus) by the time period between the start of the project cycle and the start of the project operation phase. The longer this period is, the correspondingly higher is the indicator of the payback period of the project.
The third feature of the payback period, which determines the mechanism of its formation, is a significant range of its fluctuations under the influence of changes in the level of the accepted discount rate. The higher the level of the discount rate adopted in the calculation of the present value of the initial indicators of the payback period. the more its value increases and vice versa. It can be used as one of the auxiliary indicators at the stage of selection of investment projects in the investment program of the enterprise (in this case, investment projects with a higher payback period, if other evaluation indicators are equal, will be rejected by the enterprise).
It is reasonable to understand the discounted payback period as the period for which the investment in the project under consideration will give the same amount of cash flows, given by the time factor (discounted) to the present moment, which could be received over the same period from an alternative available for purchase investment asset.
For investment planning and the selection of anti-crisis investment projects, the indicator of the discounted payback period of the project is practically important, first of all, because it indicates that time horizon in the business plan of the investment project, within which the cash flow forecast for the project should be especially reliable.
Mathematically, Fisher's Equation The equation looks like this:
real interest rate + inflation = nominal interest rate;
Here R is the real interest rate;
N is the nominal interest rate;
Pi - ;
The Greek letter Pi is commonly used to represent . It should not be confused with the pi constant used in geometry.
For example, if you put a certain amount of money in a bank at 10% per annum, with an inflation rate of 7%, then the nominal interest rate under such conditions will be 10%. The real rate will be only 3%.
Application of the Fisher Equation in Economics
If inflation is taken into account, then this is not a real interest rate, but a nominal rate that is adjusted or changes with inflation. The inflation rate used in evaluating the equation is the expected rate of inflation over the life of the loan. In Fisher's theory, the hypothesis was put forward that the count should be constant. The rate of inflation is taken into account differently when determining the interest rate of a loan within areas affected by current activities, technology and other world events that affect the real economy.
This equation can be applied both before the conclusion of the contract, and after the fact, that is, as a loan analysis. If the equation is used to evaluate credit ex post. For example, it can help determine purchasing power and calculate the cost of a loan. It is also used to help lenders determine what the interest rate should be. By using this formula, lenders can take into account the planned loss of purchasing power and therefore charge favorable interest rates.
The Fisher equation is commonly used in estimating investment amounts, bond yields, and ex post investment calculations.
Fisher also owns, which determines the dependence of the price and the amount of money in circulation. Many economic indicators depend on the amount of money. First of all, these are prices and rates on loans. Moreover, in conditions of stable economic development, the volume of money supply regulates prices. In the case of structural imbalances, the primary change in prices is possible, and only then there is a change in the cash supply. It turns out that depending on changes in various conditions in the economy, political life countries, ecology prices can change, but vice versa can change due to an increase or decrease in prices. The formula looks like this:
Here M is the amount of money in circulation;
V is the rate of their turnover;
P - the price of the goods;
Q - volume, or quantity of goods
This formula is purely theoretical, since it does not contain a unique solution. However, we can conclude that the dependence of prices and money supply is mutual. In developed economies (a single country or a group of countries) with one currency, the amount of money in circulation must correspond to the level of the economy (production volume), the level of trade and income. Otherwise, it will be impossible to ensure price stability, which is the main condition for determining the amount of cash in circulation.
Inflation is defined as the process of an increase in the general (average) price level in the economy, which is equivalent to a decrease in the purchasing power of money. Inflation is called uniform if the rate of general inflation does not depend on time (on the step number of the calculation period). Inflation is called homogeneous if the rate of change in the prices of all goods and services depends only on the step number of the calculation period, but not on the nature of the goods or services. Inflation is said to be constant if its rate does not change over time.
There are two main indicators (parameters) that characterize inflation: the inflation rate and the inflation index. Below we give a definition and give formulas for calculating both indicators (parameters) of inflation.
Inflation is estimated over a certain period of time.
So, to assess inflation at the end of the period in relation to the period, two main indicators are used:
1) the rate (level) of inflation - the relative increase in the average price level in the period under review
2) inflation index (price change index) - an increase in the average price level in the period under review
Relationship between rate and inflation index
The question arises - at what interest rate increase will only compensate for inflation? If a we are talking about simple interest, then the minimum allowable (barrier) rate:
For compound interest:
A rate greater than is called a positive interest rate.
The owners of money make various attempts to compensate for the depreciation of money. The most common is the adjustment of the interest rate at which the accumulation is carried out, i.e. an increase in the rate by the amount of the so-called inflationary premium, in other words, the rate is indexed. The final value can be called the gross rate.
Let's discuss methods for determining the gross rate. If we are talking about full compensation for inflation in the amount of the gross rate at , then we find the required value from the equality:
where is the gross rate
From here gross rate for simple interest:
The value of the gross rate for is found from the equality:
From here gross rate for compound interest:
The last formula is called Fisher formula. Sometimes it is also written as:
where i - real interest rate
In practice, the inflation-adjusted rate is often calculated differently, namely:
The last formula, compared to the previous one, contains one additional term, which, if the values are small, can be neglected. If they are significant, then the error (not in favor of the owner of the money) will become very noticeable.
Let's start right away with the formulation of the Fisher hypothesis (Fisher effect), which states that the nominal interest rate depends on two quantities: the real interest rate and the inflation rate. This dependency has the following form:
i=r+π, where
i - nominal interest rate;
r is the real interest rate;
π is the inflation rate in the country.
This formula got its name from the American economist Irving Fisher, who made a significant contribution to the theory of money.
Thus, according to the Fisher formula, the nominal interest rate (which is essentially nothing more than the price of a loan), as well as the price of any consumer product or service, is subject to adjustment through the inflation rate.
Fisher's formula allows you to evaluate the real profitability of investments. So, for example, an investor who invests money in a bank at 12% per annum has a different real income at different values of inflation rates. If inflation during the year is 6%, then real interest received by the investor will be:
r=i-π=0.12-0.06=6%
If we assume that the inflation rate for the year reaches a value of 12%, then the efficiency of investments at a given nominal interest rate will be reduced to zero:
r=i-π=0.12-0.12=0
Complete Fisher formula
The above is a simplified formula. The full version looks like this:
As you can see, the full formula differs from the approximate one by the presence of the product rπ. Simple math shows us that as the values of r and π decrease, their sum does not decrease as rapidly as their product. Therefore, as π and r tend to zero, the product rπ can be neglected.
See for yourself, with values of π and r equal to 10%, their sum will be 0.1 + 0.1 = 0.2 = 20%, and their product: 0.1x0.1 = 0.01 = 10%. And with the values of π and r equal to 1%, their sum will be equal to 0.01 + 0.01 = 0.02 = 2%, and the product of everything: 0.01x0.01 = 0.0001 = 0.01%. That is, than less valueπ and r, the more accurate results are given by the approximate Fisher formula.