Present value and opportunity cost

Not all investments carry the same risk. An office building project is riskier than investing in government securities, but probably less risky than investing in a biotechnology start-up. Suppose, according to your estimates, the project is associated with the same risk as investments in the stock market (investments in stocks), and the profitability of the latter is projected at 12%. Then exactly 12% is a suitable value for the opportunity cost of raising capital. This is exactly the return that you refuse by not investing in securities comparable in risk to your project. Now you can recalculate the net present value:

NPV = PV − $350,000 = $357,143 − $350,000 = $7,143

If other investors agree with your income forecast of $400,000. and with your assessment of its inherent risk, your property under construction should be worth $357,143. If you tried to sell it for more, you would not find a buyer, because then the expected return on investment in real estate would be lower than the 12% that can be obtained in the stock market. The office building still generates a net value addition, but much less than our previous calculations show.

The value of an office building depends on the timing of cash flows and their inherent uncertainty. Income in the amount of 400 thousand dollars. would cost exactly $400,000 if it could be obtained immediately. If building an office building is as secure as investing in government securities, a 1-year delay reduces the cost to $373,832. If it carries the same risk as investing in the stock market, the uncertainty reduces the value by another $16,689, to $357,143.

Unfortunately, valuing assets over time and uncertainty is often more difficult than our example suggests.

So, we have come to the conclusion that the construction of an office building is a good thing, since its cost exceeds the costs associated with it, that is, it has a positive net present value. To calculate the value, we figured out how much to pay in order to get the same return on investment directly in securities. The present value of the project is equal to the future proceeds from it, discounted by the yield of these securities.

The same can be expressed in another way: our real estate project makes sense because its return exceeds the cost of capital. The return on investment is simply the ratio of profit to initial costs:

The cost of capital (the cost of raising capital), we recall, is equal to the return lost due to the refusal to invest in securities. If building the office building in our example carries the same risk as investing in the stock market, then a 12% return is forgone. Since the 14% return on an office building is greater than the 12% opportunity cost, you should proceed with the project.

Here are two equivalent rules that should guide investment decisions.

1. Rule of net present value: make investments that have a positive net present value.

2. Rule of return: make investments whose return exceeds their opportunity cost.

The opportunity cost of raising capital is such an important concept that it deserves additional attention and another example. Let's say the following opportunity opens up before you: invest $100,000 today, so that at the end of the year, depending on the general state of the economy, you will receive a return of:

You reject optimistic (rise) and pessimistic (recession) forecasts. This leaves you with an expected return of Q = $110,000. , that is, a 10% return on your investment ($100,000). But what is the correct discount rate?

You start looking for common stocks with the same risk as your investment opportunity. Shares X turned out to be the most suitable. Their price for the next year, in the normal state of the economy, is projected at $110. The price will be higher in an upturn, lower in a downturn, but the proportion of change is the same as your investment ($140 up, $80 down). In general, you conclude that stock X and your investment carry the same risk.

The current price of shares of X is $95.65. per share, their expected return is 15%:

This is the same expected return that you give up by investing in your project, instead of investing in the stock market. In other words, this is the opportunity cost of your project.

In order to estimate the cost of the project, you need to discount the expected cash flow at these opportunity costs:

This is the amount that would cost investors in the stock market to buy the expected cash flow of $110,000. (They could get it by buying 1,000 shares of X.) This is exactly how much investors will be willing to pay you for your project.

The net present value of the project is obtained by subtracting the initial investment:

NPV = $95,650 - $100,000 = -$4,350

The project costs $4,350. less than what was spent on it. There is no point in taking him on.

Note that you would come to the same conclusion by comparing a project's expected return with its inherent cost of capital:

The expected return of the project, equal to 10%, is less than the 15% that investors expect to earn by investing in the stock market, so, whatever one may say, the project is useless.

Of course, in real life, one cannot reduce the true state of the economy to just a "recession", "normal" or "upswing". In addition, we adopted another simplistic assumption, establishing an absolute correspondence between the return on 1000 shares of X and the proceeds from the investment project. However, the main idea of ​​this example is quite consistent with real life. Remember: the opportunity cost of raising capital (the cost of capital) for an investment project is equal to the expected return that investors demand from common stocks or other securities that are subject to the same risk as the project. By calculating the present value of the project, that is, discounting its cash flow at opportunity cost, you get the amount that investors (including the shareholders of your own company) are willing to pay for the project. Whenever you find and launch a project with a positive net present value (i.e., a project whose present value exceeds the required investment in it), you make your company's shareholders richer.

For example, this circumstance can be misleading. Imagine that a banker comes to you and says: “Your company is a well-established reliable enterprise, and you have little debt. My bank is willing to lend you the $100,000 you need for the project at 8% per annum.” Does this mean that the capital cost for the project is 8%? If so, your project is afloat: its present value at 8% is $110,000/1.08 = $101,852, or a net present value of $101,852. - 100 000 dollars. = +1852 dollars.

But this is not true. First, the interest rate on the loan has nothing to do with the risk of the project: it only reflects the well-being of your current business. Second, whether you take out a loan or not, you still have to choose between a project with an expected return of only 10%, or stocks that carry equivalent risk but have an expected return of 15%. A financial manager who borrows money at 8% and invests it at 10% is not only stupid, but desperately stupid if the company or its shareholders have the opportunity to borrow at 8% and invest with the same risk, but with a return 15%. So it is the expected return on stocks of 15% that represents the opportunity cost of raising capital for the project.

Rationale for the net present value rule

Until now, our familiarity with net present value has remained very superficial. The phrase "accumulating value" as a company's goal sounds quite reasonable. But the net present value rule is more than just a requirement of basic common sense. We need to understand what this rule is about and why managers look to the bond and equity markets to determine the opportunity cost of raising capital.

In our previous example, only one person (you) invested 100% of the money in a new office building and got a 100% return on it. But in a corporation, investments are made on behalf of and at the expense of thousands of shareholders with different risk appetites and different preferences for choosing between current or future income (and therefore consumption). What if a project that for Mrs. Smith clearly has a positive net present value, for Mr. Jones will be in deep red? Could it happen that the goal of maximizing the value of the firm will be unacceptable for some of them?

The answer to both questions is the same: no. Both Smith and Jones can always reach an agreement if they have unhindered access to the capital market. We will show this with another simple example.

Suppose you are able to foresee your future earnings. Unable to save from your current income or take out a loan against future income, you will be forced to postpone consumption until you receive it. And this case is very inconvenient, to say the least. If the bulk of the income that is due to you in your life falls on some more or less distant future, then the result may be that today you are in danger of hunger, and tomorrow (or sometime later) - overconsumption. This is where the capital market comes in handy. Simply put, the capital market is a market in which people exchange today's and future money among themselves. Thanks to him, you can eat normally now and in the future.

We will now show how a well-functioning capital market helps investors with different income “schedules” and consumption patterns to agree on whether to take on an investment project. Imagine two investors with different tastes and aspirations. One of them is Ant, who prefers to save money for the future; the other is the Dragonfly, which squanders all its income with extraordinary ease, not at all caring about tomorrow. Now suppose that they both have the same opportunity: to acquire a stake in a $350,000 office building project that yields a guaranteed return of $400,000 at the end of the year. (i.e. the yield is about 14%). The interest rate is 7%. At this rate, both Ant and Dragonfly can borrow or lend money in the capital market.

Undoubtedly, Ant would gladly invest in an office building. Every hundred dollars invested today in this project will allow him to spend $114 at the end of the year, while the same hundred dollars invested in the capital market will bring him only $107.

And what would the Dragonfly do if she wants to spend money right now, and not in a year? Perhaps she will neglect the investment opportunity and immediately squander all her cash? Hardly, since the capital market allows you to both lend money and borrow it. Every hundred dollars that Dragonfly invests in an office building will bring her $114 at the end of the year. Any bank that knows that Dragonfly will have a guaranteed income at the end of the year will not hesitate to lend her $114/1.07 = $106.54 today. So, if the Dragonfly invests in an office building and then takes out a loan against future income, it will be able to spend today not 100, but 106.54 dollars.

The figure clearly illustrates this example (our heroes are denoted here by M and C, respectively). The horizontal axis represents the amount of money that can be spent today; the vertical axis represents the next year's expenditures. Suppose, initially, both the Ant and the Dragonfly have the same amount - $ 100 each. If each of them fully invests his 100 dollars. on the capital market, then at the end of the year both will receive $ 100 for expenses. x 1.07 = $107 The straight line connecting these two points (in the figure, this is the line closest to the origin of the coordinates) displays combinations of current and future consumption for the following possible options: when nothing is invested, when one or another part of the cash is invested, and when all available funds are invested on the capital market at 7% per annum. (The interest rate determines the slope of this straight line.) Any intermediate point of the straight line (between the points of intersection with the coordinate axes) is reached when one or another part of the $100 cash. today is spent and the rest is invested in the capital market. Let's say someone might prefer to spend $50. today and 53.50 dollars. next year. But our Ant and Dragonfly unanimously rejected such intermediate (“residual”) patterns of consumption.

The straight line with the arrow (highlighted) in the figure indicates the proceeds from investing $100. in an office building project. The return on these investments is 14%, so today's $100. will turn in a year into 114 dollars.

The Dragonfly (C) wants to consume right now, while the Ant (M) wants to wait. But each of them is happy to invest. M prefers to invest not at 7%, but at 14%, which increases the point of intersection of the straight line with the arrow (which is highlighted in blue) with the vertical axis. C also invests (at the same 14%) and then borrows money at 7%, thereby turning $100 intended for current consumption into $106.54. With his investment, C will have $114 to pay off his debt in a year. The net present value of this investment is $106.54. - 100 dollars. =+6.54 USD

The sloping straight line on the right in the figure (the one that is farthest from the origin) reflects the increase in the planned expenses of the Ant and Dragonfly in the event that they decide to invest their 100 dollars. to an office building. The Fisted Ant, who has no intention of spending anything today, can invest $100. in the construction of an office building and at the end of the year to receive 114 dollars. for expenses. Motivated Dragonfly also invests $100. in an office building, but at the same time it takes $114 / 1.07 = $106.54. for future income. It is quite obvious that nothing stands in the way of these spending plans. Indeed, the right line represents all possible combinations of current and future spending available to an investor who invests $100. into the construction of an office building and in doing so takes out a loan against some future income.

It is easy to see from the figure that the present value of Dragonfly and Ant's participation in the office building project is $106.54 and the net present value is $6.54. (this is the difference between the $106.54 present value and the $100 initial investment). Despite their differences in taste, Dragonfly and Ant both benefit from investing in an office building and then using capital market opportunities to achieve a desirable balance between today's consumption and consumption at the end of the year. In fact, in making their investment decisions, both of them seem to willingly follow the two equivalent rules that we formulated rather superficially at the end of the section. We can now rephrase them as follows.

1. Rule of net present value: invest in any project with a positive net present value. The latter is the difference between the discounted or present value of the future cash flow and the value of the initial investment.

2. Rule of return: invest in any project whose return exceeds the return on equivalent investments in the capital market.

What would happen if the interest rate were not 7, but 14.3%? In this case, the net present value of the office building would be zero:

In addition, the profitability of the project, which is 400,000 dollars / 350,000 dollars. - 1 = 0.143, or 14.3%, would be exactly equal to the interest rate on the capital market. In this case, both of our rules show that the project is teetering on the verge of “between light and darkness,” which means that investors should not care whether the firm will take it on or not.

As you can see, if the interest rate were 14.3%, neither the Dragonfly nor the Ant would gain anything from investing in an office building. The ant at the end of the year would have the same amount of money to spend, regardless of how he initially disposed of his money - invested in an office building or invested in the capital market. In the same way, Dragonfly would not have received any benefit by investing in an office building with a 14.3% return and at the same time taking out a loan at the same 14.3%. She might as well have spent all of her initial cash at once.

In our example, Dragonfly and Ant placed the same funds in an office building project and willingly took part in it. This unanimity is explained by their equal opportunities to borrow and lend money. Whenever a firm discounts cash flow at a financial market rate, it is making the implicit assumption that its shareholders have free and equal access to competitive capital markets.

It is easy to see that the absence of a well-established and well-functioning capital market undermines the logic of our net present value rule. As an example, let's assume that the Dragonfly does not have the opportunity to take out a loan against future income, or in principle there is such an opportunity, but the price of the loan is too high to take advantage of it. In such a situation, the Dragonfly would most likely prefer to use its cash right away, rather than invest it in an office building and wait until the end of the year to start spending money. If Dragonfly and Ant were shareholders of the same company, it would be difficult for a manager to reconcile their conflicting interests and goals.

No one will unequivocally assert that capital markets are perfectly competitive. Financial decisions should take into account taxes, transaction costs and other factors that limit perfect competition. But by and large, capital markets work quite well. And this is at least one good reason why NPV should be relied upon when setting corporate goals. Another reason is that the net present value rule is simply common sense; as we shall see later on, it leads to apparently ridiculous results much less frequently than its main "competitors" - other common criteria for making investment decisions. In the meantime, just briefly touching on the problems of market imperfection, we, like a shipwrecked economist, will simply assume that we have a life jacket, and, mentally dressed in it, calmly swim to the shore.

So far, our rationale for the net present value rule has been limited to two assumptions: that cash flow extends over only two time periods, and that cash flow is inherently certain. However, the rule is also true for uncertain cash flows that continue into the distant future. In support of this, the following arguments can be cited.

1. The financial manager must act in the interests of the owners of the firm, that is, its shareholders. Every shareholder strives for three goals:

a) to be as rich as possible, that is, to maximize your real wealth;

b) turn this wealth into some temporary pattern of consumption desirable for him (or for her);

c) have the freedom to choose the risk characteristics of this consumption pattern.

2. But shareholders do not need the help of a financial manager to achieve the best temporary consumption pattern. They are able to manage this themselves, as long as they have unhindered access to competitive capital markets. In addition, they are free to choose the risk characteristics of their consumption pattern by investing in more or less risky securities.

3. How then can the financial manager help the shareholders of the firm? Only one way: by increasing the market value of each shareholder's stake in the firm. To do this, he must take advantage of any investment opportunity that has a positive net present value.

Shareholders, while having different preferences, show remarkable unanimity about the amounts they are willing to invest in real assets. On this basis, they can unite in one company and, without risk to themselves, entrust the conduct of business to professional managers. Managers do not need to know anything about the tastes and preferences of shareholders and should not inspire them with their own tastes and preferences. Their goal is to maximize the net present value. Once they have succeeded, managers can sit back and relax with the confidence that they have done their best work for the benefit of their shareholders.

From this follows the fundamental condition for the successful functioning of the modern capitalist economy. The separation of ownership from management is of great importance for most corporations, so delegation of management authority is indispensable. It's nice to know that all managers can be given one simple instruction: to maximize net present value.

Sometimes you hear managers say that their corporations have different goals. Thus, a manager may say that his job is to maximize profits. Well, that sounds very reasonable. After all, don't shareholders prefer a profitable company to a loss-making one? However, profit maximization in its purest form is unreasonable to proclaim as a corporate goal. There are several reasons for this.

1. The task of “maximizing profits” immediately gives rise to the question: “Profit of what year?”. Shareholders may not want a manager to build next year's earnings at the expense of later years' earnings.

2. The company can increase future profits by reducing the payment of dividends and investing these funds in investment projects. But with a low return on such investments, this runs counter to the interests of shareholders.

3. Different accountants use different methods of profit calculation. You may find that a solution that improves earnings from one accountant's point of view worsens it from another.

Principal corollary

We have shown that managers serve the best interests of shareholders by investing in projects with a positive net present value. But this brings us back to the principal-agent problem. How can shareholders (principals) make sure that managers (agents) do not pursue their own interests exclusively? Shareholders cannot constantly monitor managers to see if they are shirking their responsibilities or maximizing the value of their own wealth. However, there are several organizational arrangements that more or less ensure that the manager's heart is in the pocket of the shareholders.

Members of the company's board of directors are elected by shareholders and, in theory, represent their interests. True, sometimes the board of directors is portrayed as a weak-willed extras, always taking the side of management. However, when problems arise in the operation of the company, and managers do not offer a viable plan for revival, the board of directors does its job. In recent years, at companies such as Eastman Kodak, General Motors, Xerox, Lucent, Ford Motors, Sunbeam, Lands End, top executives have been forced to leave their posts when profitability began to fall and the need for an updated business strategy became clear. .

Considering that the work of the corporation leaves much to be desired, and the members of the board of directors are not energetic enough to call managers to order, the shareholders may try to change the board of directors at the next election. If this succeeds, the new board of directors will recruit a new management team. However, such attempts to re-elect the board of directors are a rather expensive and thankless task (rare of them succeed). Therefore, “dissident” shareholders usually do not engage in an unequal battle, but instead simply sell their shares.

However, the sale of shares in itself carries a very powerful message. If a stock is dumped by quite a few holders, the price of the stock goes down. This hurts the reputation of managers and their earnings. CEOs receive part of their remuneration for their work in the form of bonuses tied to the level of profit, or in the form of stock options, which provide good returns when the stock price rises, but lose all value when the price falls below a certain threshold level. In theory, this should encourage managers to increase profits and increase the share price.

Do managers defend the interests of shareholders?

If company leaders fail to maximize value, they are always at risk of a hostile takeover. The lower the price of a company's stock falls (whether as a result of poor management or bad policies), the easier it is for another firm or group of investors to buy a controlling stake in its shares. In such a situation, the old management team is likely to be left out and replaced by new managers ready to make the changes needed to realize the true value of the company.

The mechanisms described largely ensure that there are few lazy or shareholder-disregarding managers in the top management of large American corporations. Moreover, these mechanisms contain strong incentives for managers to work hard.

We have presented managers as agents working for the shareholders of their firms. But perhaps it is worth asking the question: "Is it desirable for managers to act in the selfish interests of shareholders?" Doesn't the focus on the enrichment of shareholders mean that managers should behave like greedy traders, brutally trampling on the weak and helpless? Don't they have a broader responsibility—to their employees, customers, suppliers, and to the community in which the firm is located?

The main part of this book is devoted to financial policies that increase the value of the firm. None of the varieties of such a policy requires the infringement of the weak and helpless. In most cases, expedient deeds (value maximization) do not in the least contradict good deeds. If a firm is profitable, then it is one whose customers are satisfied and whose employees are devoted; the same firms whose customers and employees are dissatisfied with them are more likely to experience a decline in profits and a decline in stock prices.

Of course, in business, as in any area of ​​life, ethical problems arise; and when we call the goal of the firm the maximization of shareholder wealth, we do not mean that everything else should be left to chance. Laws are part of the deterrent against apparently dishonest behavior by managers, but for most managers, more than the letter of the law or the provisions of official employment contracts is important. In business and finance, as in other daily activities, there are unwritten and unspoken rules of conduct. In order to work productively together, we must trust each other. The largest financial transactions are often “formalized” with a simple handshake, and each of the parties knows that in the future, even with a bad turn of events, the other side will not break his word. Any incident that weakens this mutual trust is detrimental to us all.

Should managers protect the interests of shareholders?

In many financial transactions, one party is better informed than the other. It is very difficult to get complete and reliable information about the quality of the assets or services that you are buying. This situation opens up wide scope for dubious financial manipulations and illegal scams, and since unscrupulous businessmen are much more likely than respectable entrepreneurs to jump from place to place, airport registration lists are full of traces of financial fraudsters.

Honest firms counter this with a demonstrative commitment to long-term customer relationships, a good business name, and financial integrity. Large banks and investment companies are well aware that their most valuable asset is their business reputation. They do not miss the opportunity to emphasize the long history of their existence and their unfailingly responsible behavior. Any event that undermines this reputation can cause them enormous material damage.

Consider, for example, the Salomon Brothers stock market scandal that erupted in 1991. A company trader tried to circumvent the rules restricting its participation in a Treasury bond auction; to do this, he made bids on behalf of several clients of Salomon Brothers, without notifying them of this and without obtaining their consent. When the forgery was discovered, Salomon Brothers had to fork out a lot to settle the case: almost $ 200 million. It took to pay a fine and another 100 million dollars. - to establish a special fund to satisfy civil claims. In addition, the value of Salomon Brothers shares immediately fell by more than $300 million. In fact, the shares fell in price by almost a third, reducing the company's market value by $1.5 billion.

What explains such a dramatic decline in the value of Salomon Brothers? Mainly the fears of investors who felt that the company's business would suffer from the loss of customers who had lost confidence in her. The damage done to Salomon Brothers by the tarnished reputation far outweighed the sheer costs of the scandal, and outweighed by hundreds or even thousands of times the benefits the company could have derived from illegal bidding.

In this chapter, we introduced the concept of present value as an asset valuation tool. Calculating present value (PV) is simple. All you have to do is discount the future cash flow at the appropriate rate r, commonly referred to as the opportunity cost of raising capital, or the marginal return:

Net present value (NPV) is equal to the sum of present value and initial cash flow:

Recall that C 0 is negative if the initial cash flow is an investment, that is, a cash outflow.

The discount rate is determined by the yield prevailing in the capital markets. If the future cash flow is absolutely reliable, the discount rate is equal to the interest rate on risk-free securities such as US government debt. If the amount of future cash flow is subject to uncertainty, then the expected cash flow should be discounted by the expected return on securities with a similar risk.

Cash flows need to be discounted for two simple reasons: first, because a dollar today is worth more than a dollar tomorrow, and second, because a safe dollar is worth more than a risky dollar. The present value and net present value formulas express these ideas in terms of numbers. The capital market is a market where reliable and risky future cash flows are bought and sold. That's why we look at the rates of return prevailing in the capital markets to determine what discount rate to use given time and cash flow risk. By calculating the present value of assets, we are actually estimating how much people would pay for them, given that there are alternative investment opportunities in the capital markets.

The concept of net present value confirms the feasibility of separating ownership from management within a corporation. A manager who invests only in assets with a positive net present value serves the best interests of each of the owners of the firm - despite their differences in wealth and tastes. This is possible thanks to the capital market, which allows each shareholder to form their own investment portfolio according to their needs. In particular, the firm does not need to adjust its investment policy so that future cash flows are in line with shareholders' preferred temporary patterns of consumption. Shareholders themselves can perfectly move funds forward or backward in time as long as they have free access to competitive capital markets. In fact, their choice of this or that temporary pattern of consumption is limited only by two circumstances: their personal wealth (or lack thereof) and the interest rate at which they can borrow or lend money. The financial manager is not able to influence the interest rate, but it is in his power to increase the wealth of shareholders. This can be done by investing in assets with a positive net present value.

There are several organizational mechanisms that give some assurance that managers pay close enough attention to the value of the firm:

• the board of directors strictly monitors the work of managers;
• it is difficult for lazy people and hacks to hold on to their posts under the onslaught of more energetic managers. Such competition often arises within an individual company, but it also operates outside: poorly performing firms are very often the targets of hostile takeovers; as a result, as a rule, the management team is completely renewed;
• Managers are motivated by incentive schemes such as stock options, which pay well when the price of the stock (and hence the wealth of the shareholders) rises and depreciate otherwise.

If managers seek to add value to shareholders, this does not mean that they are neglecting other, broader responsibilities to society. Managers act honestly and fairly towards employees, customers, and suppliers, partly because they see it as a common good, but partly for quite pragmatic reasons: they are well aware that the most valuable asset of the company is its reputation. Of course, there are ethical issues in financial activities, and whenever some unscrupulous manager abuses his position, we all begin to trust each other a little less.

Early works on net present value:

I. Fisher. The Theory of Interest. 1965 (reprint of 1930 edition). J. Hirschleifer. On the Theory of Optimal Investment Decision // Journal of Political Economy. 66:329-352. 1958. August.

For a more detailed discussion of the subject, see:

E. F. Fama and M. H. Miller. The Theory of Finance. New York: Holt, Rinehart and Winston, 1972.

If you want to delve deeper into how managers can be more motivated to maximize shareholder wealth, consider the following papers:

M. C. Jensen and W. H. Meckling. Theory of the Firm: Managerial Behavior, Agency Costs, and Ownership Structure // Journal of Financial Economics. 3:305-360. October 1976.

E. F. Fama. Agency Problems and the Theory of the Firm // Journal of Political Economy. 88:288-307. April 1980

However, needless to say, there are some types of real estate, the appraiser is practically unable to determine the value of; for example, no one knows the potential price at which the Taj Mahal or the Parthenon or Windsor Castle could be sold.

Here and below, abbreviations derived from English names are used as symbols of terms in the text and formulas: PV - from present value (present value), NPV - from net present value (net present value), DF - from discount factor (coefficient discounting), D - from debt (debt, debt), E - from equity (own, or equity, capital), etc. (A complete list of terms in Russian and English, as well as the corresponding abbreviations (symbols) is contained in the Index at the end of the book.) - Note. editor.

Let's check ourselves. If you invest $373,832 at 7% per annum, then at the end of the year your original investment plus interest income in the amount of 0.07 x 373,832 dollars will be returned to you. = $26,168 The total amount you will receive is $373,832. + 26 168 USD = $400,000 Pay attention to this: 373,832 x 1.07 = 400,000.

We will define “expected” more precisely in Chapter 9. For now, it suffices to understand that expected revenue reflects a realistic forecast, not an optimistic or pessimistic one.

You can verify the equivalence of these rules yourself. Let's put them another way: if the yield of 50,000/350,000 is greater than r, then the net present value of -350,000 + 400,000/(1+r) must be greater than zero.

These rules may conflict with each other when cash flows continue for more than two periods. We will deal with this problem in Chapter 5.

We assume that recession and recovery are equally likely, that is, that the expected (average) outcome is $110,000. Let, for example, the probabilities of recession, normality, and recovery—that is, each of these probabilities—be equal to Y3. Then the expected return: Q = ($80,000 + $110,000 + $140,000)/3 = $110,000

The exact ratio between current and future consumption that each person chooses depends on his individual preferences. Readers familiar with economic theory know that such a choice can be shown by superimposing indifference curves specific to each individual. The preferred combination will be at the intersection of the interest rate line and the individual's indifference curve. In other words, each individual will borrow or lend up to the point where 1 plus the interest rate equals the marginal rate of time preference (ie the slope of the indifference curve). For a more rigorous presentation of graphical analysis of investment decisions and the choice between current and future consumption, see the Braley-Myers website at www://mhhe.com/bm/7e.

Some managers, for fear of displeasing any of their interest groups, generally deny that they are engaged in profit or value maximization. We recall one survey of businessmen in which they were asked whether they were trying to maximize profits. Respondents indignantly dismissed this suggestion, arguing that their responsibility extended far beyond the narrow and selfish goal of making a profit. But when the question was slightly modified and businessmen were asked whether they could increase profits by raising or lowering the selling price of their products, they replied that none of these changes would lead to a further increase in profits. (See: G. J. Stigler. The Theory of Price. 3rd. ed. New York: Macmillan Company, 1966.)

Under US law, a contract may be valid even if it is not in writing. Of course, it is wiser to keep the necessary documentation, but an oral contract is recognized as valid if it can be proved that the parties have reached full and unconditional mutual understanding and agreement. For example, in 1984 Getty Oil management verbally agreed to a proposal to merge Pennzoil. Then Texaco came out with a better offer and outbid the auction. But Pennzoil sued, claiming Texaco had violated a valid contract, and won.

For more on this issue, see: A. Schleifer and L. H. Summers. Breach of Trust in Corporate Takeovers// Corporate Takeovers: Causes and Consequences. Chicago: University of Chicago Press, 1988.

See: Clifford W. Smith, Jr. Economics and Ethics: The Case of Salomon Brothers // Journal of Applied Corporate Finance. 5. 1992. Summer. P. 23-28.