LECTUREPEDIA - Ajarn Paul Tanongpol, J.D.; M.B.A.;B.A.; CBEST
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I.

INDIVIDUAL FINANCIAL DECISIONS

The calculation of the present value of future income is categorized into two types according to its occurrence: single or multiple periods. Both cases assume that the investor is banking on the certainty of market performance and perfect information in the market. Certainty of market performance means that the market will yield the returns on investment as expected. Perfect information means that every participant in the market has the same information and can access that information free of charge. These assumptions are best illustrated by the Stock Exchange Commission (SEC) regulation governing insider trading. In order to assume perfect information, insider law discourages corporate insiders to use internal information to trade in the stock market in assuring fairness to all market participants. Both assumptions: market certainty and perfect information, are no longer valid in calculating the present value of future income because events in the capital market showed that the market is uncertain and information in the market is imperfect.

The market is uncertain because the scope and scale of market participants are not uniform. Some participants are large, others are small. Some participants enter the market for a longer period, while others remain in the market only for a short time. The size of participants is determined by the amount of capital they infuse into the market. Small participants are negligible because their continuing presence in and exit from the market does not effect or shock the market. Large participants, on the other hand, such as Enron in the early 2000s and Lehman Brothers in 2008 shake the market and send out a lasting shock wave throughout the market when they fall.

Market information is imperfect because market chattering leads to misinterpretation of information and investors act ideosyncratically. The trading of commodities through the use of future contract, for instance, is a good illustration of imperfect information. Future trading can occur only when buyers and sellers set themselves on polar opposite in their interpretation of the same information. One is convinced that the future price of the commodity will decrease while another believes that it will increase. This ideosyncracy culminates into future contracts speculation.

This study begins with the basic assumption of the present value of future income and modifies these assumptions in order to reflect market uncertainty and the imperfection of information.

Present value of an income in a single period:

                                                                                                            [1]

       =          present value of income;

        =          current income; and

        =          next year’s income

i           =          riskless interest rate

Present value of income in multiple periods:

                                                                                                                                  [2]

The function can be simplified as:

                                                                                             [3]

        =          income time t

        =          interest rate in period j from j-1 to time j.

            In the financial industry, equation [3] has been accepted as a conventional representation of present value for future income calculated in multiple periods. Experience in the market showed that exogenous events affect future income. These are systematic shock resulted from the failure of large corporations. For example, in 2004, the market witnessed the fall of Enron, followed by Arthur Andersen, and Lehman Brothers in 2008. Other large corporations, such as Morgan Stanley, Meryl Lynch, and J.P. Morgan also face the threat of potential collapse. The fumbling of these corporate giants sends negative reverberation throughout the market. The simplicity of equation [3] can no longer support the algebraic assumption of perfect information in the market. From the experience of Lehman Brothers debacle in 2008, we now know that, all income streams or future earnings are subject to the law of uncertainty, imperfect information, and imperfect competition. For these reasons, equation [3] must be modified to reflect market reality.

            The modification of the present value of future income must begin with the definition of the term expectation. If there is an expectation to receive an income in the future, in a form of a lump sum or as a stream of cash flow, the individual must anticipate exogenous event that will interfere with the materialization of that income. These exogenous events are commonly known as “shocks.”

            Let  represent the total income in the future. The expectation of the income is written as:

                                                                                                                  [4]

 is the expectation of the outcome  at time t However, this expectation is a bare expectation or blind hope based on the assumption that it is certain the event will occur without any intervention. This expectation is not rational because in the market, the outcome of an event is influenced by the exogenous factors that no one can control; however, we can anticipate these uncertainties. Therefore, in order to be rational, the expected outcome must be modified to account for the effect of exogenous variable:

                                                                                                      [5]

 and         =          parameters;

                 =          conditional expectation;

                  =          period in year;

                 =          exogenous variables or shock:

                                     is serially uncorrelated random variable with zero mean.

Equation [5] changes expectation into conditional expectation. By taking external shock into consideration, the original expectation becomes a rational expectation.

            Recall that equation [3] defines the present value of income as ; similar to equation [4],  in equation [3] lacks internal consistency for failing to anticipate exogenous variables that may shock the system, and results in . Therefore, equation [4] must also be rationalized to take exogenous shock into account:

                                               [6]

                =          expected income adjusted for exogenous shock

                    =           as explained in equation [5].

The total effect of the shock is the product of the exogenous variables multiplied by the expected outcome :

;

As the result, the revised present value of future income () is the difference between the expected present value of income () and the actual impact of the exogenous shock.

            As equation [5] demonstrates, the value of the expected income under rational expectation model is not equal to the original expectation: . From this relationship, we can generally state that in case of negative shock, it is likely that > , under a condition of positive shock < , and if there is no shock =  which is not a likely outcome.

            In case of a single period calculation of the present value of an income, the modification under rational expectation model, equation [1] is rewritten as:

                                                                           [7]

            The theoretical rationale for the modification is supported in the reasoning for the rejection of conventional assumptions of perfect market. These assumptions include: costless capital market; neutral personal taxes; competitive market; equal access; homogenous expectation; costless information; costless financial distress; and salable tax loss. All these assumptions are impractical.

Costless capital market. This assumption is false because there are transaction costs in the market. The buy and sell orders in the stock market incur costs. No one can buy or sell stock in the stock market freely. There is no such a thing as an arms-length transaction. All trade orders must go through intermediary called stock brokers. Costless capital market also assumes that the government does not interfere with the market; however, the government actively interferes with the capital market. The stock market is regulated by the SEC. Trade in goods and services, outside of the stock market, is also regulated under anti-trust law. Regulation at any level to which ever extent increases transaction costs. State regulation is interference. Interference of any kind is costly. Therefore, the assumption of costless capital market is unreasonable.

Neutral personal tax. To the extent that capital gain tax is a fixed rate income tax, this assumption is true. However, in practice tax law is not neutral in application. Income is taxed on progressive rate; capital gain is taxed on a fixed rate. All income tax law favors the rich over the poor and the middle class. Market participants in higher income bracket have more flexibility in gaining favorable treatment under income tax law. Depreciation, contribution, tax saving insurance and investment vehicles credits benefit persons in the higher income bracket.

Competitive market. In order for this assumption to hold true, there must be substitutes of securities in the market and the firm cannot affect interest rate in the market by its action. This assumption fails in cases where large firms, such as Lehman Brothers’ bankruptcy in 2008can affect the discount rate in the bond market.

Equal access. In order for this assumption to be true, investors and firms must be able to borrow and lend money under the same terms and conditions. It is evident that this assumption is false. Bank lending policy and lending rates of any lenders depends on the cash, credit, and character of the borrower. Borrowers would not have the same profile; therefore, their access to the loans in the capital market is not equal.

Homogenous expectation. In order for this assumption to be true, all market participations must have the same expectation. This assumption is false. If everyone has the same expectation, the market will stand still. The transactions in the stock market are evidence to show that expectations among investors vary. Some investors expects the prices of certain securities to rise, other investors expects such prices to fall. The differences in these expectations result in the buying and selling of securities in the market.

Costless information. In order for this assumption to be true, information must be free. However, in practice, information is not free. Firms and individual investors do not have access to the same information. In a large market where information flow is rapid, the selection and analysis of information is a value added activity; therefore, it is not costless. Information is made available at a price willing to bear by the market. Whatever that cost may be, it is greater than zero.

Costless financial distress. In order for this assumption to be true, the financial distress of one firm must not incur costs for other market participants. However, the experience of the Lehman Brothers in 2008showed that the bankruptcy of one firm affects all market participants. In fact, the failure of the Lehman Brothers affects even participants in the market far from where Lehman Brothers used as its theater of operation.s

Salable tax loss. In order for this assumption is true, both firms and individual may sell their tax losses. This assumption is half-truth. Firms may sell their tax losses to the extent that corporate income tax law allows merger and acquisition of non-profitable firms to consolidate their income tax filing. However, individual investors are not as fortunate. It is not possible for the individual to buy and sell tax losses without raising the ire of the Revenue Department.

            Equations [1] through [7] have practical implications on the firm’s operations. In marketing, optimal revenue is raised through the modeling of the constant-mix line as demonstrated in Figure 1.0. There is a relationship between next year’s income and the revenue from sale. In order for the firm to produce income, it must generate revenue. Revenue depends on sale. It is myopic to assume that the only source of income for the firm comes from raising new money in the capital market. Money raised through floating bonds or selling securities in the market are capital inflow. Capital is a financial resource used as a capital input. The expected income is an output. This output comes from the employment of money raised in the capital market; therefore, there is a direct connection between expected income and sales. A brief review f basic marketing concepts to explain sales and its effect on revenue is in order.

            Conventional marketing theory assumes that sale is a result of the right mix between advertising and sales promotion. This theory is known as the constant-mix model. Although the four factors of marketing mix: product, price, place, and promotion, are drivers of revenue, in the final analysis it is undeniable that advertising and sales promotion are to of the most influential factors. Nevertheless, the constant-mix model is limited by its quadratic form in allocating the factors to x-, y- and z-axes.

Figure: 1.0: Revenue Level as a Product of Advertisement and Sales Promotion.

Source: Philip Kotler, Marketing Management: Analysis, Planning, Implementation, and Control, 6^th ed. (Prentice-Hall International Edition, 1998), p. 94.

            However, the quantity of sale in Figure 1.0 does not consider potential shock in the market that would affect the company’s revenue. These shocks may be in a form of an introduction of new technologies or procedures in the industry, entry of new comers in the industry, or the exit of large corporations from the market, i.e. the Lehman Brothers, Enron, Kmart, and Arthur Andersen. In order for the constant-mix line to reflect the reality of the market, the graph must be modified to include the exogenous variables as summarized by equation [7]. The exogenous variable is added to the lower quadrant of the y-axis as. It is placed at the y-axis because all exogenous variables are assumed to be negative shock that effects external and internal operating environments of the firm. When  = 0, an ideal state but not practicable, the sales revenue depends entirely on the constant-mix between advertisement and sales promotion. However, if <0, the negative shock will adversely affect the revenue line as shown in Figure 2.0.

Figure: 2.0: Adjustment of sale quantity (Q₁<Q₂) after the introduction of exogenous variable.

            The negative shock may come from numerous events, i.e. changes in interest rate, changes in exchange rate, or even the exit of large market players, such as Lehman Brothers in 2008, from the market. The negative shock will pull the sales revenue line downward: . The change also affects the break even point (BEP). It is worth repeating that future income depends on revenue, and revenue depends on sale. The pattern of sales revenue can be explained by the constant-mix model using promotion and advertising as the independent variable. However, the exogenous variable may lead to revenue short-fall. The firm’s performance is influenced by the internal and external operating factors. For that reason a third independent variable  is introduced into the constant-mix model.

Figure 3.0: Adjusted revenue after the introduction of exogenous variable (E).

SOURCE: Philip Kotler, Marketing Management: Analysis, Planning, Implementation, and Control, 6^th ed. (Prentice-Hall International Edition, 1998), p. 506.

            The negative shock () depresses the company’s total revenue line downward. As the result, the break even point (BEP) also increases from . The firm is required to sell at  in order to meet the new BEP. The negative shock affects the firm’s revenue through price adjustment. Revenue is a product of net price () multiplied by quantity (). The quantity is a multiplier; it is not affected by E. As the result of the shock, the quantity (Q) will also be reduced. The firm would have to respond to a reduction in sale. Most likely, the firm will adjust its net price. Net price is defined as price (P) minus allowance per unit. With the introduction of shock into the equation, net price must be modified. Originally, net price is defined as:

The modified equation for net price is expressed as:

            Revenue depends on sales; sales depend on price. If market shock affects demand in the market; in order to remain competitive, the firm must make price adjustment in order to stimulate sales. There are no means to stimulate sales other than price reduction or adjustment of allowance. Firms often make price adjustment through price reduction. For example, department stores or hypermarkets, such as Tesco Lotus, Carrefour, and Big C, announce price reduction in order to stimulate sales. At the retail level, the reduction of price in response to exogenous shock in slow time may be effective. However, in the long run, there will be an adjustment to the shock. Many firms will also reduce their prices in order to stimulate sales. If many firms respond uniformly, then the effect will be blunted because the negative shock in the market will produce long-term price adjustment by all producers. This tendency towards central price theorem will lead to two possible outcomes: permanent and impermanent price adjustment.

            If the effect of the exogenous shock is long lasting, price adjustment will be impermanent. Under such circumstances, firms engages in price adjustment in time of shock will gain more market share when the market return to normalcy. Firms that adjust their prices downward will attract more customers during the market downtime. Firms that resist negative market shock will face new level of competition when the market returns to equilibrium. This competition comes from the newly expanded market adjusters. Matured firms that can withstand market shock will not adjust their price. This inflexibility is self-defeating. The ability to withstand market signifies strength. This strength may come from the firm’s scale and scope of business. Scale refers to the size of the firm. Scope refers to the product lines offered by the firm. Unless they are used efficiently, the firm’s scale and scope may work against its own interests. By failing to adjust to the market change or shock, the firm will dilute its market share during market downtime. In order to remain competitive in the long run,  must be adjusted to .

            The second option that the firm may exercise is to maintain price level, but adjust its allowance: . Usually, allowance is given to wholesalers. This option will not have a direct effect on quantity demanded because only distributors will benefit. Since the increase of k value will give distributors more incentives to buy more, it does not necessarily translate into lower price to consumers. The indirect effect on consumers, assuming that distributors will reduce their prices, is speculative. Therefore, this is not an effective option for the firm to engage in allowance adjustment.

Last modified: 11/11/08