Multipliers in macroeconomics, types and formulas. Investment multiplier

Instructions

According to Keynes's theory, any increase in investment leads to a multiplicative process, which is expressed in an increase in the level of investment by more than the initial increase in investment. Keynes called this effect the multiplier effect. k (multiplier) = income increase / investment increase. The strength of the multiplier effect depends on the marginal propensity to save and consume. If the values ​​of these indicators are relatively constant, then determining the multiplier will not be difficult.

Since Y = C + I, the increase in income (Y) will be equal, respectively, to the sum of the increase in consumption (C) and the increase in investment (I).

According to the formula for the marginal propensity to consume: MPC = C / Y, we obtain: C = Y * MPC.
Substitute this expression into the equation above (Y = C + I).
We get: Y = Y * MPC + I.
Therefore: Y * (1 - MPC) = I.

Next: income increase Y = (1 / 1 – MPS) * investment increase I, but since k = Y increase / I increase, therefore Y increase = k * I increase. This means that k = 1 / 1 – MPS = 1 / MPS, where k is the investment multiplier.

Thus, the investment multiplier is the inverse of the marginal propensity to save. The multiplier operates in both forward and reverse directions.

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Helpful advice

The investment multiplier reflects the positive impact of investment on other industries. J.M. With his theory, Keynes proposed, in addition to investment, to also regulate national income by raising taxes to withdraw savings in order to increase state investment.

The multiplier effect can be caused not only by an increase in investment, but also by other components of autonomous costs (total costs). Then we talk about the total expenditure multiplier; it also works in the opposite direction.

Sources:

• Gross rent multiplier method

The tax multiplier is a negative coefficient that shows the change in national income depending on changes in taxes. An increase in taxes leads to a decrease in household income.

The essence of the tax multiplier

There are so-called multiplier effects in economics. They arise in cases where a change in spending leads to a larger change in equilibrium GDP.

The most famous is Keynes. It reflects how much income levels increase as a result of increases in government and other spending.

The tax multiplier has less impact on reducing demand than the government spending multiplier on increasing it. It has the following effect: when taxes increase, the gross national product decreases; when taxes decrease, it grows. It is worth noting that there is always a time interval of several months to a year between changes in the tax rate and national income.

The stronger impact of government spending on domestic consumption is due to its direct entry into aggregate demand.

How does the tax multiplier work? Thus, when taxes for the population are reduced, consumers have the opportunity to spend more, and accordingly, they increase their spending on consumer goods. Reducing the tax burden for entrepreneurs stimulates the growth of investment.

The impact of government spending and taxes on income and consumption is the main thing when the state chooses fiscal (budgetary and tax) policy instruments. With priority expansion of the public sector of the economy, expenses also increase. This leads to an increase in personal income, production of goods, and a decrease in unemployment. However, such positive effects are achieved only if the increase in government spending is caused not only by an increase in the tax burden.

The stronger impact of government spending on domestic consumption is due to the fact that they are directly included in aggregate demand and their changes are reflected in its value.

If it is necessary to contain inflation, taxes are increased. Today, fiscal policy is one of the main means of achieving sustainable progressive economic development.

If government spending and taxes simultaneously increase by the same amount, then equilibrium production will also increase by the same amount. With a balanced budget, the multiplier is always equal to one.

Tax multiplier calculation

A change in tax policy usually has the potential to have a multidirectional impact on the economy. It is the tax multiplier that allows you to translate impact measures into quantitative values. It is equal to the ratio of the ultimate capacity

In economic theory cartoonist– a category used to identify and collate relationships where a multiplying result occurs. Globally renowned academic economist J.M. Keynes, the author of macroeconomic theory, called cartoonist om indicator, the one that characterizes the connection between the metamorphosis of income and the metamorphosis of investments.

Instructions

1. According to Keynes's theory, any increase in investment sets in motion a multiplicative process, one that is expressed in an increase in the level of national income by a larger amount than the primary increase in investment. Keynes called this result the result cartoonist A. k ( cartoonist) = income of profits / income of investments. The strength of the result depends on the marginal inclination to save and consume cartoonist A. If the values ​​of these indicators are tangentially continuous, then determine cartoonist won't be difficult.

3. From the fact that Y = C + I, the income income (Y) will be equal, respectively, to the sum of the consumption income (C) and the investment income (I).

4. According to the formula for the marginal propensity to consume: MPC = C / Y, we get: C = Y * MPC. Substitute this expression into the equation above (Y = C + I). We get: Y = Y * MPC + I. Consequently: Y * (1 – MRS) = I.

5. Further: income income Y = (1 / 1 – MPS) * investment income I, but since k = income Y / income I, therefore income Y = k * income I. This means that k = 1 / 1 – MPS = 1 / MPS, where k – cartoonist investments.

6. Thus, cartoonist investment is the reciprocal of the marginal propensity to save. The multiplier operates in both forward and reverse directions.

Tip 2: How to determine marginal propensity to consume

In the current economy, an indicator such as the marginal inclination To consumption. Its calculation is necessary to determine the country’s need for a particular product. Moreover, the magnitude of the metamorphosis of costs for goods, the amount of imports and exports, as well as the total volume of production must be known.

You will need

• - calculator;
• – the magnitude of the metamorphosis of total costs;
• – the magnitude of import metamorphosis;
• – the amount of government spending;
• - amount of investment;
• – the amount spent on production;
• – the value of the net national product.

Instructions

1. To calculate the marginal inclination to consumption total costs need to be determined. Add up the sum of the costs of consumption of a particular product, investment, government spending, and net exports. The latter value is found by subtracting the amount of imports from the amount of exports.

2. Determine the amount of net national product, the value of which must be in equilibrium, that is, total production equals total expenditures. As usual, this indicator can be calculated by summing up all costs.

3. Determine the value of the multiplier, which is calculated by dividing the deviation from the amount of the net national product (it is found by subtracting the total amount of metamorphosis from the NNP, which is calculated by subtracting the smaller indicator from the larger value) by the amount of the initial metamorphosis of total costs.

4. Limit inclination To consumption is determined further. From the value of the metamorphosis of total production costs, subtract the amount of deviation from the net national product indicator. Multiply the resulting total by the amount of increase (decrease) in NNP.

5. Limit inclination To consumption should be calculated in order to determine the tier of production. If total expenses are equal or approximately equal to the amount of money needed to purchase a certain volume of products, then the production tier is equilibrium.

6. Calculation of the maximum inclination to consumption production is needed to determine the consumed share of metamorphosis in total income. As usual, the value of the marginal inclination is less than one. If you know the indicator of the marginal inclination to save, then draw up a proportion from which it will be clear that the values ​​are inversely proportional to each other.

The tax multiplier is a negative indicator, one that shows the metamorphosis of national income depending on the metamorphosis of taxes. An increase in taxes leads to a decrease in household income.

The essence of the tax multiplier

In economics there are so-called multiplier results. It appears in cases where the metamorphosis of costs leads to a greater change in equilibrium GDP. The Keynes multiplier is especially important. It reflects how much the level of profits increases as a result of the growth of government and other costs. The tax multiplier has less impact on reducing demand than the multiplier of government costs on its increase. It has a further result - when taxes increase, the gross national product decreases, and when taxes decrease, it grows. It is worth noting that between changes in the tax rate and national income there is always a time interval of several months to a year. The more powerful impact of government spending on domestic consumption is due to their direct entry into complex needs. How does the tax multiplier work? Thus, when taxes for the population are reduced, buyers are likely to spend more, and accordingly, they increase their spending on consumer goods. Reducing the tax burden for entrepreneurs stimulates the growth of investment. The influence of government spending and taxes on the amount of income and consumption is the main one when the state chooses fiscal (budgetary and tax) policy instruments. With priority expansion of the public sector of the economy, costs also increase. This leads to an increase in the income of the population, the production of goods, as well as a decrease in unemployment. However, such positive results are achieved only if the increase in government spending is caused not only by an increase in the tax burden. The greater power of government spending on moral consumption is due to the fact that they easily enter into a complex need and their metamorphoses are reflected in its value. If it is necessary to contain the inflationary rise, taxes increase. Today, fiscal policy is one of the main means of achieving sustainable progressive economic development. If government spending and taxes simultaneously increase by the same amount, then equilibrium production will also increase by the same amount. With a balanced budget, the multiplier is invariably equal to one.

Tax multiplier calculation

Changes in tax policy are traditionally likely to have a multidirectional impact on the economy. It is the tax multiplier that makes it possible to translate measures of influence into quantitative values. It is equal to the ratio of the marginal ability to consume to the marginal ability to save with a minus value. Let's say the value of the marginal ability to consume is 0.9, and to save - 0.3. Then the tax multiplier will be equal to -3. Accordingly, a $1 increase in taxes reduces national income by $3. Like the government spending multiplier, the tax multiplier can go both ways.

As paradoxical as it may seem, Russian animation is rightfully considered one of the best in the world; there are only a few animators in the country. At the same time, there are always a lot of people who want to get this interesting creative profession.

The initial stage of preparing an animator

Young people who dream of becoming an animator most likely imagine themselves in the future as production designers of animated films. However, this field of activity also involves another, fascinating, but caring job of creating countless images that make up a cartoon in the technical workshops of a film studio. Experts are trained to work in the workshops in only one educational institution in the Russian Federation. This is the Moscow highly professional artistic lyceum of animation cinematography No. 333. Admission to it is carried out on the basis of complete secondary education. However, it is not easy to get here from a distance. To begin with, the applicant must submit at least 10 creative works to the competition, and after that pass exams in drawing, storyboarding and the Russian language. Over the course of 2 years of study, students learn both typical artistic disciplines (academic drawing, painting, etc.) and subjects directly related to the process of creating animation: for example, phasing and drawing. Upon graduation from the lyceum, graduates are awarded the qualification “cartoonist.” In addition to this unique educational institution, there are many professional lyceums where they are trained in the specialty “designer with computer graphics and animation skills.” It is also possible to enter there after finishing 11th grade, having successfully passed exams in drawing, painting and the Russian language. Of course, they don’t teach classical animation here, but many modern studios haven’t worked with shabby special technology for a long time. It is much more expensive than computer technology, and there are few real experts on it. So knowledge of modern computer technologies used to create animation is even more relevant.

The path to the top of the profession

Those who want to get closer to the top of the profession by creating personal animated films can continue their education at higher educational institutions. The basic university where animators are trained is the All-Union State University of Cinematography. True, it is very difficult to get there. The competition for it is enormous, and the selection is very severe. Applicants entering the specialty “animated film artist” or “computer graphics and animation artist” are first required to submit work to participate in an advance creative competition. After successfully passing it, they will have to pass exams in painting, drawing, composition, history, Russian language and literature. The subsequent fate of the animator depends greatly on his gift and hard work. If he manages to make truly brilliant, exciting, original animated films for children and adults, film studios will be happy to see him.

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Helpful advice
The investment multiplier reflects the correct impact of investment on other branches. J.M. With his theory, Keynes proposed, in addition to investment, to also regulate national income by increasing taxes in order to withdraw savings in order to increase state investment. The result of the multiplier can be caused not only by the inflow of investments, but also by other components of independent expenses (total costs). Then we talk about the total cost multiplier; it also works in the opposite direction.

Evgeniy Malyar

Bsadsensedinamick

# Investments

Definition of the term and its essence

Even a slight increase in costs will lead to an increase in production of the equivalent product several times. Conversely, a reduction of appropriations by a few percentage points causes a significant, several-fold, drop in some macroeconomic indicators.

Article navigation

• Manifestation of multiplier economic effects
• What is the marginal propensity to save and consume?
• Investment multiplier - the essence of the concept
• How to calculate the Keynes investment multiplier coefficient
• Application of the formula for calculating the Keynes multiplier
• Keynes investment multiplier chart
• An example of the Keynes investment multiplier effect
• What is an investment accelerator
• Conclusion

Every modern graduate of an economics university knows about the works of John Maynard Keynes (1883–1946). This outstanding financial researcher created a coherent theory that in many ways conflicts with classical ideas about the market. This article will talk in simple terms about the Keynes investment multiplier and other macroeconomic phenomena that explain its action.

Manifestation of multiplier economic effects

This phenomenon may have been noticed before, but it was first scientifically described in the early 30s by the British economist Baron Kahn. The essence of his observations is that in some cases the market reacts disproportionately to subtle changes in conditions.

Even a slight increase in costs will lead to an increase in production of the equivalent product several times. Conversely, a reduction of appropriations by a few percentage points causes a significant, several-fold, drop in some macroeconomic indicators. Kahn was the first to formulate the correct definition.

The phenomenon of a disproportionate market reaction to relatively low disturbances is called the “multiplier effect” (translated from Latin as “multiplier”).

This fact contradicted the prevailing economic theories of that time, according to which the consequences should approximately correspond to the costs (plus or minus, taking into account the characteristics of the business and the talents of management).

The multiplier effect called into question the validity of Smith's concept of the self-equalizing market and its ability to easily reach an equilibrium state without external government intervention. However, the emergence of the World Economic Crisis of 1929–1933 became a more powerful argument for opponents of classical concepts.

Even earlier, the so-called paradox of frugality was formulated, the principle of which is familiar at the everyday level to every poor person who is forced to save on everything. Its essence is that the population’s desire to create a reserve “for a rainy day” negatively affects the gross domestic product (GDP).

The observation can also be considered obvious: money, being passively “in the stash”, does not participate in the general financial turnover. They do not benefit not only their owner, but also the entire national economy.

What is the marginal propensity to save and consume?

The Keynesian approach to the study of previously studied phenomena was manifested in the fact that he examined the dependence of consumer activity on changing income levels.

To begin with, again about all the understandable everyday circumstances. It is known that all funds available to business entities (including ordinary citizens) can be divided into two parts:

• The first will be “consumed”, that is, spent on its own needs.
• The second represents savings (if there is anything left).

The structure of the budget (family, business, economic, state or personal - it doesn’t matter) is described by the following formulas:

Where:
APC – coefficient of average consumer propensity (colloquially called the degree of wastefulness);
PR – amount spent on consumer purposes;
D – total amount of income.

The second formula illustrates, on the contrary, the average level of stinginess, that is, the desire to hoard:

Where:
SNA – coefficient of average accumulative propensity;
NK – amount invested in savings;
D – total amount of income.

It is easy to notice that both dimensionless coefficients add up to one: their denominator is the same (D), and PR + NK = D. They are called average because they do not take into account the dynamics of changes in expenses and income during the billing period.

For example, in six months a company earned 1000 monetary units, of which it spent 680 on employee benefits and other costs. Then the average accumulation coefficient over 6 months will be equal to 0.32, and consumption, respectively, 0.68. The total is 1.

These studies can be useful for economic analysis, but from a Keynesian point of view, it is the dynamics that are of much greater interest. In other words, it is necessary to understand how changes in consumer and savings activity will manifest themselves as the level of income increases or decreases.

In this case, there was a need to introduce other concepts: “marginal” propensities to consume and save.

The mathematical method is similar to the differential approach: the formula takes into account not absolute values, but the ratio of their increments:

Where:

PRk – the amount of the consumed (spent) part of the budget at the end of the billing period;
PR n– the amount of the consumed part of the budget at the beginning of the billing period;
Dk – amount of income at the end of the billing period;

The coefficient of marginal propensity to save is calculated similarly:

Where:
MRN – coefficient of marginal propensity to accumulate;
NKk – the amount of the accumulated part of the budget at the end of the billing period;
NKn – the amount of the accumulated part of the budget at the beginning of the billing period;
Dk – amount of income at the end of the billing period;
Day – amount of income at the beginning of the billing period;

∆D – change in the amount of income for the billing period.

The result of adding both marginal propensity coefficients will also always be one, since their changes in sum form a general increase or decrease in the financial capabilities of the business entity:

Where:
∆NK – change in the amount of savings for the billing period;
∆PR – change in the amount of consumption for the billing period;
∆D – change in the amount of income for the billing period.

Based on these coefficients of marginal propensities to save and consume, one can draw conclusions about how much influence changes in income have on the activity of spending and saving processes. True, these conclusions will be reliable only in narrow time periods of the graphs, for which linearity can be conditionally accepted.

For the national economy, it is always preferable for the citizens of the country to want to buy as many goods and services as possible.

Research by R.F. Kahn was largely concerned with studying the influence of employment and well-being of the population on their consumer and savings activity.

Keynes's merit is that he revealed the dependence of the rapid growth of investment expenditures on an increase in income.

Investment multiplier - the essence of the concept

According to the concept, the investment multiplier is a coefficient whose value is inversely proportional to the indicator of the marginal propensity to save:

Where:

MPC – marginal propensity to consume coefficient.

The same formula, taking into account the relationship between the marginal propensities to consume and accumulate, can be presented differently:

Where:
MIC – Keynes investment multiplier;
MRN – coefficient of marginal propensity to accumulate.

The multiplier theory shows why relatively small increases in investment compared to national income cause a much more significant increase in a number of indicators that characterize the macroeconomy (employment level, per capita income, etc.).

In order to understand the idea embedded by the author in his model, one should delve a little deeper into the psychology of the mass consumer. In this case, what matters is that growing income entails an increase in expenses at a lagging pace, which means a percentage expansion of the savings sector of the budget.

For example, an employee’s salary was increased by 50%, but he began to spend only 20% more on various benefits, putting the rest aside “for a rainy day.”

At the same time, Keynes identifies three main motives that encourage hoarding:

1. The need to collect money for regular expenses to maintain the household (for individuals) or to ensure a cash balance (for companies).
2. Fear of worsening economic situation. This is a “just in case” insurance fund created to cover unexpected costs.
3. Possibility of speculative use of available funds. In this case, one of the functions of money is manifested, namely accumulative. At the same time, it is desirable that they “work”, that is, bring additional income.

The interest of the state and big business is to use all measures to reduce the amount of money savings of the population and stimulate their launch into circulation or spending. Investment activity demonstrates the greatest profitability and attractiveness.

How to calculate the Keynes investment multiplier coefficient

The main problem in calculating the investment multiplier coefficient is collecting objective initial data. Or rather, only two numbers are actually needed. The entire GDP is divided into two parts, therefore, the total amount is required to begin with. A share of the national product is also required, expressing the consumer or investment activity of the population and enterprises in the country.

Despite the complexity of accounting for components and cash flows, and even in dynamics, this task is solvable. Statistics come to the rescue; its role in budget planning is paramount.

Application of the formula for calculating the Keynes multiplier

The Keynesian concept is based on the assumption of equality of budget revenue and expenditure items. In the current modern situation, one should take into account such a widespread phenomenon as a deficit, but the great economist died back in 1946, before he lived to see our turbulent days. Therefore, the situation considered in this article will be the simplest: the state budget is simplistically accepted as a closed system:

Where:
PH – total expenses of the population for all goods and services consumed by them;
I – total investments of all forms;
GR – the amount of the expenditure part of the state budget;
CHE is the amount of so-called net exports, but in fact it is a foreign trade surplus (with a + sign) or deficit (with a minus sign).
DN – total income of the population;
MFN – savings of citizens and enterprises that make up business receivables;
BUT – the amount of paid tax liabilities;
TPI – payments from foreign counterparties (transfers).

It is clear that the left side of the equation contains expenses, and the right side contains income. At the same time, they reflect a conditional balance in which demand is equal to supply.

First of all, the population directs its income to cover basic needs, that is, consumption. What remains can be accumulated. It follows from this that the amounts of consumption and savings are directly dependent on the amount of income.

Now you can proceed to calculating the limiting value of the propensity coefficient to consume or accumulate. It doesn’t matter from which side you approach solving the problem. It is important that the change in income during the calculation period and the corresponding increase (or decrease) in consumption and savings activity are shown.

Where:
MPC – coefficient of marginal propensity to consume;
∆PR – change in the amount of consumption for the billing period;
∆D – change in the amount of income for the billing period.

The investment multiplication coefficient is the inverse value of the marginal propensity to consume coefficient:

In turn, it is associated with the coefficient of marginal propensity to accumulate MRN (MRN = 1- MRN).

Keynes investment multiplier chart

The graphical representation of the dependence of investment activity is a curve.

If the propensity to consume is plotted on the x-axis, it is upward.

If the variable is the propensity to accumulate, it is downward sloping.

An example of the Keynes investment multiplier effect

A natural question arises about what this animation is for and what can be proven with its help. The concept of a multiplier illustrates the extremely acute reaction of the investment market to any change in the macroeconomic environment. The reasons for this phenomenon are the chain reaction caused by contributions to industry enterprises. Let's look at an example to demonstrate the consequences of an investment.

100 million was invested in the enterprise. This amount was spent on materials, components, wages and other expense items.

The income received by suppliers was allocated to consumption and savings in the ratio of 30% and 70%, respectively. In other words, the administration of the enterprise and its employees will receive 30 million, which can be accumulated.

In addition, producers of goods and services purchased with the funds consumed will also receive additional income. Based on the same ratio of 30 to 70, they will be able to accumulate:

Primary investment is a kind of detonator of the reaction of multiplication of the gross product.

What is an investment accelerator

The interaction of the previous effect with the subsequent reaction of the market is a common phenomenon in economics. If investment entails, as Keynes' multiplier theory states, an increase in gross domestic product, then the reverse mechanism also operates, although with some time delay.

In practice, this means that the funds earned and multiplied as a result of the initial investment play the role of an accelerator of investment activity in the next business period (fiscal year).

The obviousness of this effect served as the basis for introducing the concept of an investment accelerator.

The accelerator as an indicator of the dependence of the growth of investment activity on annual GDP growth is calculated using the formula:

Where:
AI – investment acceleration coefficient;
GDPpg – the amount of gross domestic product for the previous year;
GDPppg – the amount of gross domestic product for the year before last;
Ipg – the amount of investment for the last year;
Ippg – the amount of investment for the year before last;
∆GDP – the amount of annual growth of gross domestic product;
∆I – the amount of annual investment growth.

It is obvious that the described effects are interrelated, therefore the multiplier-accelerator model represents a single system in which causes become consequences and vice versa.

Similar phenomena are observed in other areas of human knowledge. For example, in electrical engineering the effect of self-induction is known.

Conclusion

None of the currently existing scientific theories is comprehensive. The realities of the modern world show that investment activity is influenced by many factors that John Maynard Keynes, when putting forward his multiplier principle, did not take into account. It is stimulated not only by the victory of wastefulness over hoarding.

In addition, the principle of functioning of the world economy today is somewhat different than at the time when the Bretton Woods monetary system was in effect. Nowadays, according to one witty economist, “people buy unnecessary things with money they haven’t earned.”

However, this does not mean that the multiplier and accelerator are outdated. The need to encourage people to spend is recognized by the governments of most countries. To achieve this, effective measures are being taken, including reducing taxes on confirmed purchases, inexpensive consumer loans, etc. However, this is a topic for a separate article.

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When making investments, this is one of the main issues of economic analysis of an enterprise. Consumer income is divided into savings and means for consumption. The multiplier effect takes into account investment and consumer income and predicts a numerical increase in national profits.

Despite the fact that this coefficient was invented about 100 years ago, it is still popular when analyzing the activities of an enterprise. With its help, they predict not only the development of a single organization, but the economic development of entire states.

Meaning of the term

Multiplier is a term (from the Latin multiplicator - multiplying) that has many meanings. In the field of analysis of financial and economic activity, it denotes a coefficient reflecting the dependence of income growth on investments. It was introduced into economic theory in 1931 by the English economist R. Kahn.

A positive effect was shown in a public works enterprise. The experiment showed that with an increase in demand for certain services, the volume of work grew in all related industries and the number of employees increased significantly. What is the meaning of the multiplier in economics?

The cartoon effect has a chain reaction. The creation by the state of favorable conditions for the development and emergence of business by making certain investments will lead to new monetary investments in the country's economy.

The multiplier is an indicator that reflects how much the gross product will increase as the volume of invested funds increases. For example, investments increased by 10 million rubles, while the gross product increased by 30 million rubles. In this case, the multiplier is 3.

The multiplier grows when consumers use their financial resources to increase consumption, thereby generating increased demand. If the consumer shows a desire to accumulate earned funds, the multiplier decreases.

The multiplier effect works if it is possible to increase production capacity without the global costs of labor and production modernization.

Kinds

To analyze the financial activities of an enterprise, a set of parameters is used: various types of income and expenses, different classes of investments, as well as other cash flows. There was a need to divide the concept of “multiplier” into types, depending on these indicators.

This is how financial multipliers appeared. There are many types of multipliers adapted for different fields of activity; they can be divided into groups:

• money supply multipliers;
• investment spending multipliers;
• government spending multipliers;
• consumer spending multipliers;
• tax multipliers.

The significance of the multiplier effect implies the presence of various conditions, which is why such a variety of species arose. Let's look at the most common ones.

Expense multiplier

It exists in conjunction with the acceleration principle, which is calculated as the ratio of investments this year and national profits in the past. It helps to evaluate the results of what has been done and plan future development.

The spending multiplier is defined as the dependence of the national gross product on changes in spending. It is a numerical coefficient that reflects how the final result of an enterprise’s activities (income) depends on an increase or decrease in spent funds.

When calculating the expense multiplier, it is important to understand that all invested funds, on the one hand, are expenses, but on the other hand, they bring profit. The slightest reduction in investment, due to increased thriftiness of the population, will lead to a reverse multiplying effect and a decrease in income.

Net tax multiplier

This type and essence of the multiplier, like all previous ones, is related to the volume of product consumption. The numerical coefficient means how many times the total total expenditures exceeded the amount of net taxes.

Net taxes are funds paid by residents to the treasury, excluding transfer payments such as pensions. Accordingly, the value of the net tax multiplier is directly affected by transfer payments, because when they increase, the total amount of net taxes decreases.

To maintain the balance and stability of the economy while increasing taxation, it is also necessary to increase government transfer expenses. Do not forget that this can lead to economic stagnation.

Autonomous tax multiplier

In economic theory, there is a model that considers the option when the amount of income is not taken into account, in which case a multiplier of autonomous taxes arises.

Changes in household income depend on the amount of taxation and significantly affect the value of the multiplier. In addition, as income increases, its amount begins to be divided into consumption and savings, which also affects the multiplier effect.

It is worth noting that the net tax multiplier is less than the autonomous tax multiplier. This is due to the fact that a change in household income due to an increase or decrease in taxation leads to a change in consumption and demand.

Gross rent multiplier

This is a term used to evaluate real estate properties. Shows how the price at which an object is sold depends on the gross income from the sale. To evaluate real estate, the gross rental multiplier method is used. It includes the following steps:

1. An analysis of the possible or actual gross income from the sale is carried out.
2. You need to search for 3 or more similar properties and compare prices and potential (actual) gross income from the sale.
3. Changes are made to the assessed value of your property.
4. The gross multiplier for each object is calculated.
5. The average multiplier among those received is calculated.
6. The market value of your property is determined by multiplying the average multiplier by the calculated gross income from the sale.

How is it calculated?

The gross rental multiplier is an indicator that is calculated as the price for which the property is sold and the potential or actual gross income from the sale.

The coefficient, which determines the ratio of all funds invested in an enterprise and the organization’s assets, is most often used in the banking industry and depends on the bank’s ability to attract new funds in the form of deposits and issued loans.

The calculation is as follows: the amount of profit and interest expenses is divided by the assets of the enterprise, the resulting value is multiplied by 100. From the resulting amount, it is necessary to subtract the quotient of the funds raised and assets to capital.

Capital multiplier

He shows:

• how effective is the difference between the interest rates of loans issued and the rate on deposits placed with the bank?
• quality of deposited and issued cash flows;
• quality of work of own and borrowed capital.

The capital multiplier is a kind of indicator of the bank’s performance. Its meaning helps to make appropriate decisions to change the work of the organization.

Application in business valuation

For valuation work, a number of multipliers are used, taking into account different capital structures. The main species involved in the assessment are:

1. The multipliers have arrived. Determined by dividing the price of a business by its revenue, profit before or after taxes, or dividends. The denominator depends on what multiplier effect you want to know.
2. Balance sheet multiplier. It is calculated by dividing the real price of the business by the value of assets, according to the balance sheet.
3. Natural animator.

All these multipliers can be called estimated. They show the relationship between the real market price of an organization and its financial base.

Economics is a science present in all spheres of society. The ability to use its laws will improve the quality of life and predict possible difficulties. The development of the country's economy directly depends on investment. Creating favorable market conditions will lead to increased investment and, as a result, increased GNP.

Price multiples are the basis for determining the value of a company within the comparative approach. The multiplier is calculated as the ratio of the market price of the stock and the financial indicator of the company's performance (Ronova, 2008).

where: M is the value of the multiplier; P is the actual market value of one share of a similar company or the value of the business of a similar company; Base - multiplier base (the value of the performance indicator of a similar company per share, or the gross value of this indicator).

Since the number of shares in circulation can change through the issue or redemption of part of the shares, when calculating the multiplier, it is better to use indicators per share price. To calculate the price/earnings multiplier (P/E), the stock price on the stock exchange on the analyzed date is used in the numerator, and net profit according to financial accounting standards is used in the denominator (Teplova, 2011). In this case, the share price is determined by the market every minute, and the profit value is fixed for the last reporting year, for the last 4 quarters, or the expected profit value for the analyzed year is used. If analysts use earnings for the last fiscal year or the last 12 months as the denominator, they will therefore get the current P/E multiple (often denoted P0/E0). When calculating forward P/E, the value of the forecast profit for the year is used, which is more preferable, according to analysts (the common designation P 0 / E 1) (Teplova, 2011).

Also an important point when determining the value of the multiplier is the concept of “business value”: in foreign literature, this concept means the cost of invested capital:

where: EV - market value of invested capital

MC - market capitalization of the company;

D is the market value of long-term debt;

Cash is the most liquid asset.

In this case, the multiplier will be calculated as the ratio of the market value of capital to the multiplier base.

Unlike foreign literature and practice, in Russia “business value” is understood as the valuation of 100% of the company’s shares. It is important to note that there are differences in accounting principles in the United States (GAAP) and in Russia, which may lead to incorrect assessment results. For example, “according to American standards, depreciation is not taken into account in the cost of goods sold, but in Russian reporting, depreciation is displayed in the amount of cost of sales.”

Also, some multipliers have their own calculation features. Thus, using the EV/EBITDA indicator requires adjustments for non-operating items such as excess cash, the presence of an option program or operating leases (Chaddae et al., 2004). Excess cash not included in EBITDA is subtracted from EV. At the same time, EBITDA must be reduced by employee options. Since operating leasing unevenly reduces EV and EBITDA, therefore, the company's assets and debt increase by its amount. These adjustments allow us to obtain a fairly high estimate.

The price/dividend multiplier can be calculated both on the basis of actual dividends paid and on the basis of potential dividend payments. “In this case, potential dividend payments mean dividends calculated for a group of similar companies based on a comparison of their actual dividend payments and net profit.” When using this multiplier, you need to make sure that dividends are paid stably, both in the company being evaluated and in peer companies. Moreover, it is important that "the amount of dividends is calculated at the annual percentage rate, even if dividends are paid quarterly."

Using multiples is one of the simplest methods for assessing the value of a company. However, there are rules for their use, since any multiplier can be defined by analysts in different ways.

The first problem that analysts may encounter is the different ways in which multiples are calculated. For example, most appraisers define the P/E multiple as the ratio of market price to earnings per share. However, there are various methods for calculating it. Traditionally, the numerator is the current price, but it is possible to use the average price over the past six months or year. The denominator may also vary: some analysts use earnings per share for the last financial year (resulting in the current multiple), others use earnings for the last 4 quarters (tracking multiple) or expected earnings per share (forward P/E). (Damodaran, 2004). As a result, appraisers will receive different multiplier values.

Moreover, analysts use the results depending on their personal inclinations: during a period of earnings growth, the forward P/E multiple will be lower than the tracking multiple, and the current multiple will be the maximum compared to the previous two. Thus, a pessimistic analyst will argue that the P/E multiple is overvalued using its current value, while an optimistic analyst will argue that the multiple is low (using the forward P/E).

The second problem in determining the multiplier is the consistency of the numerator and denominator. The numerator of the multiplier can be represented by the value of the company's share price, which characterizes the value of equity, or the value of equity debt minus cash (enterprise value). The denominator can be a measure of equity (earnings per share, net income, cost of equity capital) or a measure of the firm (operating income, operating income minus depreciation, book value of the company's equity) (Damodaran, 2004). When calculating the multiplier, it is important that the numerator and denominator reflect the same indicator - the value of equity or the value of the company.

However, in practice, inconsistent multipliers are sometimes used. These multiples include the ratio of price to operating profit before depreciation and amortization. In this case, the indicator reflecting the value of equity capital is divided by the indicator reflecting the value of the company. Thus, when comparing the values ​​of this multiple for different firms in the industry, companies burdened with debt will be characterized as undervalued, while they may be overvalued or correctly valued.

When evaluating a company using the comparative method, a multiplier is calculated for each analogous company, after which these values ​​are compared with each other. At this stage, the third problem of applying the method under consideration arises - uniformity. It is important that the selected multipliers are calculated in the same way, which is difficult due to the fact that the tax year for different companies begins and ends in different months. As a result of these inconsistencies, stock prices when calculating forward P/E will in one case be related to earnings for some companies from July to June, and for others - for the period from January to December (Damodaran, 2004). This discrepancy will have little impact in the case of mature sectors, as earnings in these companies do not change dramatically over six months. However, for high-growth sectors, this has a significant impact on the size of the multiple.

After calculating the required multiples, the analyst selects the multiple value that will be used to calculate the value of the company being evaluated. In practice, the following methods are used to calculate the required multiplier (Ronova, 2008):

• 1. The arithmetic mean of all calculated multipliers for peer companies;
• 2. Weighted average value (evaluators assign weights in accordance with the value of the denominator of the multiplier);
• 3. Median value of all calculated multipliers for peer companies.

The method of using the median value is the most common in practice, as it is considered the most accurate (Chirkova, 2009). However, research by Teplova and Dyachenko showed that this method for calculating the threshold multiplier value is best only for emerging capital markets. In the case of countries that are characterized by a distribution of multipliers close to normal (for example, the USA), the preferred method for calculating the threshold value is the arithmetic mean (Teplova, 2011).