Showing posts with label profit. Show all posts
Showing posts with label profit. Show all posts

Reasons behind aiming at reasonable profit rather than maximum profit by most of firms

In economic theories, it is assumed that maximizing profits is the basic objective of every firm. The volume of profit is regarded as the primary measure of the success of a business. But in recent days, it has been realized that many firms, particularly big one do not operate on the principle of profit maximization in terms of marginal costs and revenues. Instead, the firms set standards or targets of reasonable profits.

This is because of so many reasons. The firms may limit profit or aim at only reasonable profits due to following reasons:
  1. Discourage potential competitors: When a firm earns large profit under profit maximizing objective. It is likely to attract potential competitors to enter the field and capture the market share enjoyed by it. They adopt the practices such as infringement of patent rights, copying of product designs, encroachment upon the firm’s sources of raw materials, etc. To discourage such tendency, a firm may adopt the policy of limiting profits rather than maximization. The danger of potential competition is more serious when the firm enjoys a weak monopoly situation. However, there is no guarantee that limiting profits may prevent potential competition.
  2. Project a favorable image to the public and government: The earning of high profits shows the enjoying of monopoly power. It may create an impression that the firm is exploiting the consumers. Hence, the public may appeal the government for nationalization of the firm or to exercise some sort of regulation of prices, profits and dividends. Therefore, the firms may aim at only reasonable profit. Restraining demand for wage hike. When there is high profit the labors may demand higher wages. This is particularly true in the industries having strong trade unions. Hence, such industries may not like to maximize profits. Because, this may lead to wage price spiral.
  3. Maintaining consumer goodwill: The consumer goodwill is of great importance to the industries. The consumers show their resentment and think that they are being exploited when prices are set too high. The consumers expect a fair price in terms of cost of production. Similarly, if a firm exploits a short-term situation, it may seriously damage its image, reputation and long-run interests. Hence, the profit restraint is adopted to maintain consumer goodwill.
  4. Keeping internal control: Another reason for restraining profits is management’s desire to maintain control of the firm. The management gives strong preference to liquidity, abhors debt and may not like expansion. Because maximizing profits may require entering new areas of production involving heavy investments and thus, reducing liquidity and losing control.
  5. Maintaining congenial working conditions: Profit restraint is also adopted to maintain congenial working conditions within a firm. There is growing awareness about the social responsibilities of management. There is increasing concern with the direct effects of management’s decision upon workers, consumers and the business cycle.
  6. Attainment of industry leadership: If a firm aims at achieving industry leadership, the firm may try for maximum sales or manufacturer of maximum product lines. Hence, profit maximization will not get the priority. The entrepreneur may merely seek to earn a satisfactory profit level so as to maintain certain share of market or a certain level of sales.
  7. Avoiding risk: Profit maximization may require setting up new ventures, which may have number of uncertainties. The project appeared profitable at the outset may turn out to be unprofitable.

It is now clear that all firms may not aim at profit maximization. But they try to achieve satisfactory level of profit to cover the risks of economic activity and to avoid loss. A business cannot survive if there is continuous loss. Profits are indispensable to remain alive. Profits are essentially means to an end, and the end of continuity and growth of the firm.

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Criteria of Setting the Standard of Reasonable Profit | Capital Return | Plowback Rate | Popular conceptions of reasonable profit

The appropriate criteria should be prepared to set up the level of standard. According to Joel Dean, the criteria of setting the standard are as follows:

1. Capital Return

This criterion is related to how much return should be earned to attract outside capital. Likewise, this criterion is related to acquiring adequate income required for adequate capital formation. The machines can be replaced and building, machine and working capital can be added from capital formation.


The firms should set the rate sufficient to attract outside capital or equity capital. Due to this, if new equity capital has to be issued it does not adversely affect the interest of the existing shareholders. Similarly, people are ready to buy immediately as soon as the equity capital is issued. This is possible that adequate dividend is provided in past. For this, profit standard should be designed on the basis of the cost of new capital in the capital market. Although this standard seems to be theoretically popular, many imaginary and guess-based decisions will have to be made to set up the capital-attracting rate of return, for example:
  1. First, the capital-attracting rate depends on the ratio of the capital structure of the company like bond, preferred stock, and common stock.
  2. Second, problems are whether to base the standard of earning on the cost of present capital or long run average cost.
  3. Third, problem is to acquire the relevant indicator of the cost of capital of the company in the market. It is not a simple problem. Because, the cost of capital widely differ in different industries and private companies. Such differences arise due to the difference in growth prospect, cyclical stagnation, capital structure and ability of the management.

2. Plowback Rate

This criterion is related to how much earning is necessary to spend on the development of the firm completely from retained profits. According to this criterion, adequate amount of total profit should be retained for the required growth rate without resorting to capital market. But since large retained earnings may encourage the competitors for entry, it should be determined carefully. Beside, the retained earnings is in complete control of the management and can waste in project inside the company. If that amount is distributed to the shareholders that may be to the high-earning project due to the competition in the capital market. Since plowback rate depends on the need of the company, competition, politics of the shareholders and public relations, it is more individualistic.

3. Normal Earning

This criterion is related to how much the companies or comparable firms have, normally earned. According to this criterion, profit should be equal to the earning made by the companies or industry in normal period. It is appropriate for the firm to compare with its past earning. For this, the past earning level of the company should be have been adequate to attract capital, shareholders should have been invited. Beside this, the profit of other industries with comparable output and risks may also be good standard. For this, care should be taken in the selection of comparable companies. Likewise, broad average of all industry or broad sample of the companies may also be used. Beside the problem of selecting comparable companies, there is also the problem of determining normal period. Profit should not have occurred due to the reason such as war. Since there is fluctuation in the income of the companies, the selection of the period is very important in setting standard.

4. Popular conceptions of reasonable profit

This standard is related to what the normal persons regard as reasonable profit. The standard of reasonable profit may be based on the survey made to know the opinion of general public relating to fair profit. Such survey provides good profit standard. It has been found in the survey that some regard 10 percent on sale and some 25 percent profit margin as reasonable.

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Role and Functions of Profits in the Market Economy

Profits play an important role in a free market economy or in a mixed economic system also. First, profits serve as a single to change the rate of output or for the firms to enter or leave the industry. Second, profits play a critical role in providing incentive to introduce innovations and increase productive efficiency and take risks.

Thus, high economic profits being earned in an industry serve as a signal for the consumers who want more of the commodity being produced by that industry. These profits indicate to the firm to expand output of the commodity and for the new firms to enter the industry to gain a share of economic profits that exist in the industry. As a result, more resources will be allocated to the output of that industry. On the other hand, below normal profits in an industry serve as a signal that either less output of the industry is demanded by the consumers or inefficient production methods are being used by the firms. In response to the lower demand for the product, the firms will reduce their output and also some firms will leave the industry. As a result, some productive resources will be released from that industry and made available for the production of other goods. If the lower profits are due to the inefficient production and organization, this will induce firm to improve efficiency by changing the production methods or make organizational changes to reduce costs.

In a free market economy, in the first standpoint profit motive drives a free-market economy. Although it has been observed that sometimes managers and entrepreneurs in a free market system are influenced by greed and desire for wealth, and break laws to make money or profits by exploiting the consumers or workers. Profits, in general, perform useful function of sending signals for changing levels of output of various products and for reallocation of resources among them.

Secondly, above normal rate of profits in a free enterprise system is an essential reward for introducing innovations and taking risks. No entrepreneur will introduce new products or more efficient production methods or undertake investment in risky projects unless there is chance of making profits. Some firms continue to earn above-normal rate of profit year after year as they continually introducing new products, new production methods and providing good customer services.

And finally, in market economy changes in demand for the product often occur due to cyclical and structural changes. Besides, new strategies of rival firms also affect the demand for the product of a firm. All these uncertain and unanticipated changes involve a good deal of risk. An important function of economic profits is to reward entrepreneurs for taking these risks involved in making investment and organizing factors for the production of products.

However, in some cases firms are also able to make super normal profits by virtue of their having monopoly power may be due to some legal patent and license obtained from the government, the economies of large scale production, exclusive control over essential raw materials which prevent the other firms from producing the same product or service. These enable the monopoly firms to charge higher prices and thereby make large economic profits. Therefore, even in free market economies, steps are taken to prevent the emergence of monopolies through anti-trust laws.

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Difference between Accounting Profit and Economic Profit | Business Profit Versus Economic Profit

The term ‘profit’ is originated from the Latin word and its meaning is ‘to make progresses’. The word ‘profit’ has different meaning to different people like businessmen, accountants, tax collectors, workers and economists. The term is often used in a loose polemical (emotional) sense that hides its real significance.


In a general sense, profit is regarded as income accruing to the equity holders, in the same sense as wages accrue to the labor; rent accrues to the owners of rentable assets; and interest accrues to the money lenders. To a layman, profit means all income that flow to the investors. To an accountant, profit means the excess of revenue over all paid-out costs including both manufacturing and overhead expenses. It is more or less the same as net profit. For all practical purposes, profit or business income means profit in accounting sense plus non-allowable expenses. Economist’s concept of profit is of ‘Pure Profit’ called ‘economic profit’ or ‘just profit’. Pure profit is a return over and above the opportunity cost, i.e. the income which a businessman might expect from the second best alternative use of his resources. These two concepts of profit are discussed below in detail.

Business Versus Economic Profit


It is necessary to know the nature of profits because profit influences business activities. How do profits arise, what determines the volume of profits or stream expected future profits are important issues that need explanation. Profits or expected profit stream from a productive activity or an investment project play a crucial role in decision making by managers. But, as mentioned earlier, the term profits, as used in economics, differs from that generally used by business community. Therefore, it is necessary to explain first the difference between business profits and economic profits.

A business profit is an accounting concept of profit and represents the residual sales revenue to the owners of the firm after making payments to all other factors or resources the firm uses. These payments to hired factors include the wages to hired labor, interest on borrowed capital, rent on land and factory buildings and expenditure on raw materials used by the firm. The expenditures on these factors or resources hired on purchased by the firms are call explicit costs. Business profit refers to the sales revenue of the firm minus its explicit costs. In accounting sense, profit is defined as the residue of sales revenue minus the explicit accounting costs (or out-of-pocket expenditures of doing business). It is the amount available to provide rewards to the shareholders who have supplied the firm’s equity capital after payment for all other resources the firm uses. The explicit costs are the costs like wages, rent fuel, raw materials, interest on loans and depreciation. Thus,

Business Profits = Total sales revenue – Explicit costs

It is the concept of business profits that is generally used by the business community and accountants.

Economists also define profit as the excess of revenue over the cost of doing business. However, economists include the implicit costs of the inputs provided by the owners including entrepreneurial effort and capital in calculating profit. Economic profit is the difference between total revenues and total economic cost (including the economic or opportunity cost of owner-supplied resources such as capital and time). Economic cost or opportunity cost is the highest valued alternative opportunity that must be sacrificed or foregone as a result of choosing an alternative. The owner-entrepreneur uses his own capital for which he/she should be paid. The normal rate of return on capital is to be given to the owner as the minimum return necessary to attract and continue investment. Similarly, the opportunity cost of owner effort is determined by the value that could be received in an alternative activity. Hence, economic profit is business profit minus the implicit costs of capital and any other owner-provided inputs used by the firm.

In their calculation of economic profit, economists deduce not only explicit costs but also implicit costs from the sales revenue of the firm. The implicit costs refer to the opportunity costs of the resources provided by the firm’s owners themselves including capital and entrepreneurial ability. These self-owned factors must be paid if they are to be employed by the firm in its own production process otherwise they will be employed elsewhere on hired basis. Thus, economists take into account the normal rate of return on capital used by the owner of the firm in its own business and the transfer earnings of the owner-entrepreneur as costs of doing business.

The economic profit represents the sales revenue of the firm in excess of both explicit and implicit costs. Therefore,

Economic Profits = Sales revenue – Explicit costs – implicit costs

While explaining maximization of short-run profits or present value of the steam of expected future profits, economists assume that it is economic profits that owner-entrepreneur or managers of corporations seek to maximize. The concept of economic profits brings into sharp center the questions: why the profit which is over and above the normal rate of return on equity capital and reward for entrepreneurial ability in case of owner-entrepreneur exists and what is its role in a free enterprise system. In long-run, equilibrium economic profits will be zero if all firms work in perfectly competitive market. Then, how do economic profits, positive or negative, come into existence. The various theories of profit provide explanation for the existence of economic profits.

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Williamson’s Model of Managerial Discretion | Behavioral Relations Involved in Williamson's Model

The managerial theory of firm developed by Oliver E. Williamson states that managers apply discretion in making and implementing policies to maximize their own utility rather than trying for the maximization of profit which ultimately maximize own utility subject to minimum profit. Profit works as a limit to the top managers’ behavior in the sense that the financial market and the shareholders require a minimum profit to
be paid out in the form of dividends, otherwise the job security of managers is put in danger. Hence, managers look at their self-interest while making decision on price and selling quantity of output. Manager’s decision on price and output differs from the decisions of profit maximizing firm.

Utility maximization of managers guided by their own self-interest is possible, like in Baumol’s sales maximization model, only in a corporate type of business organization with the separation of ownership and management functions. Such organizational structure permits the managers of a firm to pursue their own self-interest, subject only to their ability to keep effective control over the firm. In particular managers are fairly certain of keeping hold of their power (i) if profits at any time are at an acceptable level, (ii) if the firm shows a reasonable rate of growth over time, and (iii) if sufficient dividends are paid to keep the stockholders happy.

Williamson’s model suggests that manager’s self-interest focuses on the achievement of goals in four particular areas, namely:
  1. High salaries
  2. Staff under their control
  3. Discretionary investment expenditures
  4. Fringe benefits (i.e., additional employee benefit: an additional benefit provided to an employee, for example, a company car or health insurance)

This model depends on some assumptions which are:
  1. Weakly competitive environment.
  2. A divorce of ownership from control of firm (manager is free to perform any action)
  3. A capital market imposes minimum profit constraint (manager’s work for minimum profit imposed by a capital market).

According to Williamson, managers want ‘utility’ which is the same things as happiness or satisfaction. Top managers and chief executive officers reveal expenditure preference that is they derive utility expenditure on staff (S), managerial emoluments (M), and discretionary profits. The discretionary profit is defined as the profit level higher than the level necessary for long-term survival.

The managerial utility function includes such variables as salaries, security, power, status, prestige and professional excellence. Of these variables, only the first variable ‘salaries’ is measurable. The others are non pecuniary. Therefore, in order to make them operational, they must be expressed in terms of other variables with which they are related and which are measurable. This is captured by the concept of expense preference, which is defined as the satisfaction which managers again form certain types of expenditures. In particular, staff expenditures on well being (slack payments) and funds available for discretionary investment gives a positive satisfaction to the managers because these expenditures are a source of security and reflect the power, status, prestige and professional achievement of managers.

Staff expenditures, emoluments and discretionary investment expenses are measurable in money terms and will be used as proxy-variables to replace the non-operational concepts (e.g. power, status, prestige, professional excellence) appearing in the managerial utility function. With this background, the utility function of the managers may be written in the form,

U = f  (  S,   M,   ID)

Where S = staff expenditure, including managerial salaries; M = managerial emoluments; and ID = discretionary investment; f(S, M, ID) is the utility function.

Managers have “expense preferences”, maximization of utility derived from;
(i) amount spent on staff (S)
(ii) additions to manager’s salaries and benefits in the form of “perks” (M)
(iii) discretionary profit (D) which exceed the minimum required to satisfy the shareholder’ available as a source of finance for “pet project”.

Different definitional and behavioral relations are involved in Williamson’s model. They are introduced below:
 
i) Demand of the firm

It is assumed that the firm has a known downward sloping demand curve defined by the function.
Q  = f1(P, S, Ɛ)

P = f2(Q, S, Ɛ)

Where, Q = output,
P = price,
S = staff expenditure,
Ɛ = (Greek letter epsilon) = the condition of the environment or a demand-shift parameter reflecting autonomous changes in demand;
f1(P, S, Ɛ) and f2(Q, S, Ɛ) are the market demand equation for the firm’s product.

An increase in staff expenditure (S) is supposed to cause an upward shift to the demand curve and thus allow the charging of a higher price. The same holds for any other change in the environment, which shifts upwards the demand curve of the firm.

ii) Production cost

The total cost of production (C) is assumed to be an increasing function of output (Q).

So,
C = f3 (Q)

Where,
δC / δQ > 0 (i.e., total cost increases with the increase in the level of output, and vice versa)

iii) Actual Profit (π)

The actual profit is defined as revenue from sales (R), minus the production costs (C), and minus the staff expenditure (S) or actual profits are the difference between total revenue earned less the production costs (C) and expenditure on staff (S). This is symbolically expressed as:

π = R – C – S

iv) Reported Profit πR
This is the profit reported to the tax authorities. Reported profit (πR) is the difference between actual profits and supplementary or nonessential managerial expenditure as represented by management slack. It is the actual minus the managerial emoluments (M) which are tax deductible. So,

πR = π – M = R – C - S – M

v) Minimum Profit (π0)
Minimum profit (π0) is the amount of profits (after tax) which is required to be paid as acceptable dividend to satisfy the owner-shareholders of the firm. If the shareholders do not get reasonable dividends they may sell their shares and thereby expose the firm to the risk of being taken over by others, or alternatively they will vote for the dismissal of the top management. Both of these actions by the shareholders will reduce the job security of the top managerial team. Hence, managers must earn some minimum profits for the shareholders in the form of dividends to keep the shareholders satisfied so as to ensure manager’s job security. To meet this objective, the reported profits must be large enough to be equal to minimum profit (π0) plus the tax (T) that must be paid to the government. This is mathematically expressed as:

πR  ≥  π0 + T

The tax function is of the form T = Ť + t. πR

Where, t = marginal tax rate or unit profit tax; Ť = a lump sum tax

vi) Discretionary investment (ID)
Discretionary investment is the amount left from the reported, after subtracting the minimum profit (π0) and the tax (T). The mathematical expression for this definitional relationship is:

ID = πR - π0 – T

vii) Discretionary profit (πD)
This is the amount of profit left after subtracting from the actual profit (π), the minimum profit requirement (π0) and the tax (T). The mathematical expression for this definitional relationship is:

πD = ππ0 – T

Thus, there are three types of profit concepts discussed in Williamson’s managerial utility maximization model of the firm;
- actual profits (π)
- reported profit (πR)
- minimum profits (π0).

Discretionary profits should be carefully distinguished from discretionary investment. As explained earlier, discretionary profits are the amount left after minimum profit (π0) and tax (T) and are deducted from actual profits (πD = ππ0T) but discretionary investment equals reported profits minus minimum profits and tax. Thus, we have discretionary investment

ID = πRπ0 – T

Since difference between reported profits (πR) and actual profits (π) arise / occur due to management slack, discretionary profits can be stated as under;

πD = ID + expenditure due to management slack. Thus, if management slack is zero

πR = π and πD = ID

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H. A. Simon opines that firms aim at satisfying rather than maximizing profit | Simon's Satisficing Theory

H. A. Simon opines that firms aim at satisfying rather than maximizing profit.

H.A. Simon has propounded this model in 1955, he argued that the real business world is full of uncertainty. Accurate and adequate data are not readily available where data are available, managers have little time and ability to process data and managers work under a number of constraints. Under such conditions, it is not possible for the firms to act in terms of rationality postulated under profit maximization hypothesis.

Nor do the firms seek to maximize sales, growth or anything else. Instead they seek to achieve a ‘satisfactory profit’, a ‘satisfactory growth’, and so on.

This behavior of firms is termed as satisfactory behavior of firms in which a firm is a coalition of different groups connected with the various activities of the firm e.g. shareholders, managers, workers, input supplier, customers, bankers, tax authorities and so on. All, if these groups have some kinds of expectations often conflicting from the firm, and the firm seeks to satisfy all in one way or another.

Simon said that a firm has normally an aspiration level. An aspiration level is the level of achievement, which the firm hopes for in a particular field. For example, if a firm hopes to increase sales in the present year by 10%, it is his aspiration level about sales. The aspiration level of profit will depend on past experience and in fixing in future uncertainties will be taken into account. If it is easily attained, the aspiration level will be raised. If it proves difficult to attain, it will be revised downwards. When the actual performance of a firm falls short of an aspiration level, ‘search activity’ will be started so that remedial action can be taken to achieve the aspiration level by better performance. Search activity is the search for new alternatives of action.

But there is limit to search activities because of the cost to be incurred in obtaining information. Hence, all alternatives will not be explored. A satisfactory alternative course of action will be selected. Since the firm limits search activity due to involvement of costs, it does not maximize profit. Hence, the firms aim at ‘satisfying’, rather than ‘maximizing’. If the aspiration level is nearer to profit, the result that can be obtained under the assumption of satisfying is similar to the result under the assumption of profit maximization.

The aspiration level of the firm means the demarcation between the satisfactory and unsatisfactory results.
 
Criticisms of Simon’s Satisficing Theory

This theory has the following weaknesses which are as follows:
  1. The main weakness of the satisficing theory of Simon is that he has not specified the ‘target’ level of profits which a firm aspires to reach. Unless that is known, it is not possible to point output the precise areas of conflict between the objectives of profit maximizing and satisficing.
  2. As commended by Boumol and Quant, it is constrained maximization with only constraints and no maximization.
  3. Simon does not clarify a satisfactory level of performance based on a certain level of rate of profits. According to Simon, there may be many satisfactory levels depending upon the groups that cooperate in the firm. It is difficult for the firm to choose such a profit rate that satisfies all groups function within the firm. Thus, the operational value of Simon’s model is limited.

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Value of Maximization Theory of Firm | Superiority of Maximization Theory

In managerial economics, the primary objective of management is assumed to be maximization of the firm’s value. The value can be defined as the present value of the firm’s expected future cash flows. Cash flows may be for now, be equated to profits, therefore the value of the firm today, its present value, is the value of its expected future profits, discounted back to the present at an appropriate interest rate.

The essence of the model with which are concerned expressed as follows:
 
Value of the firm = PV of expected future profits


Where,
PV is the abbreviation for the present value, and so forth represent the expected profits in each year ‘t’, ‘i’ is the appropriate interest rate.
 
Since profits are equal to total revenue (TR) minus total cost (TC), equation (i) may be written as


Maximizing equation (ii) involves the determinants of revenues, costs and the discount rates in each future year of some unspecified time. Revenues, costs and the discount rates are interrelated, complicating the problem even more.

A firm’s total revenues are directly determined by the quantity of its products sold and the process received, for managerial decision making, the important considerations relate to factors that affect prices and quantities, and to the interrelationships between them. These factors include the choice of products of the firm designs, manufactures and sells the advertising-strategies, it employs, the pricing it established, the general state of the economy it encounters and the nature of the competition it faces in the market place. In short, revenue relationship encompasses both demand and supply considerations.

The cost relationships involved in producing a firm’s products are similarly complex. Costs require examination of alternative production systems, technological options, input possibilities, and so on. The prices of the factors of production play an important role in cost determination, and thus factors supply considerations are important.

Finally, there is the relationship between the discount rate and the company’s production mix, physical assets and financial structure. These factors affect the cost of availability of financial resources for the firm and ultimately determine the discount rate used by investors to establish a value of the firm.

To determine the optional course of action requires that marketing, production and financial decisions as well as decisions related to personnel, product distribution and so on be combined into a single integrated system, one which shows how any action affects all parts of the firm. The economic model of the firm provides a basis for this integration and the principles of economic analysis enable to analyze the important interrelations.

Superiority of Maximization Theory


Shareholder wealth maximization is the basic goal of any business firm because of the following reasons:
  1. Efficient allocation of resources: It provides guideline for making decision of firm and also promotes an efficient allocation of resources. Resources are generally allocated by taking into consideration the expected return and risk associated to course of action. The market value of stock itself reflects the risk return trade off associated to any investor in the capital market. 
  2. Separation between ownership and management: The goal of shareholder wealth maximization is also justifiable from the view point of separation of ownership and management in a business firm. Stockholders provides funds to operate a business firm and they appoint a team of management to run the firm. 
  3. Residual owners: Shareholders are the last to share in earnings and assists of the company. Therefore, shareholders wealth is maximized, and then all other with prior claim that shareholder could be satisfied. 
  4. Emphasis on cash flow: Wealth maximization goal uses cash flows rather than accounting profit as the basic input for decision making. The use of cash flow is clearer because it uniformly means profit after tax plus non-cash outlays to all. 
  5. Recognizes time value of money: It also recognizes the time value of money. All the cash flow generated over the life of the business firms are discounted back to present value using required rate of return and decision is based on the present value of future returns.
  6. Consideration risk: Wealth maximization objective also considers the risks associated to the streams of future cash flows. Depending on the degree of risk, a proper required rate of return is determined to discount back the future streams of cash flows. Greater the risk larger will be the required rate of return and vice-versa.

The complexities involved in the fully integrated decision making analysis limit its use to major planning decisions. The decision process involved in both fully integrated and partial optimization problems takes place in two steps, one must apply various techniques to determine the optimal decision.

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