Brealey−Meyers: Principles of Corporate Finance, Seventh Edition I Value Present Value and the Opportunity Cost of Capital © The McGraw−Hill Companies, 2003 CHAPTER TWO PRESENT VALUE A N D T H E OPPORTUNITY COST OF CAPITAL 12 Brealey−Meyers: Principles of Corporate Finance, Seventh Edition I Value Present Value and the Opportunity Cost of Capital © The McGraw−Hill Companies, 2003 COMPANIES INVEST IN a variety of real assets These include tangible assets such as plant and machinery and intangible assets such as management contracts and patents The object of the investment, or capital budgeting, decision is to find real assets that are worth more than they cost In this chapter we will take the first, most basic steps toward understanding how assets are valued There are a few cases in which it is not that difficult to estimate asset values In real estate, for example, you can hire a professional appraiser to it for you Suppose you own a warehouse The odds are that your appraiser’s estimate of its value will be within a few percent of what the building would actually sell for.1 After all, there is continuous activity in the real estate market, and the appraiser’s stock-in-trade is knowledge of the prices at which similar properties have recently changed hands Thus the problem of valuing real estate is simplified by the existence of an active market in which all kinds of properties are bought and sold For many purposes no formal theory of value is needed We can take the market’s word for it But we need to go deeper than that First, it is important to know how asset values are reached in an active market Even if you can take the appraiser’s word for it, it is important to understand why that warehouse is worth, say, $250,000 and not a higher or lower figure Second, the market for most corporate assets is pretty thin Look in the classified advertisements in The Wall Street Journal: It is not often that you see a blast furnace for sale Companies are always searching for assets that are worth more to them than to others That warehouse is worth more to you if you can manage it better than others But in that case, looking at the price of similar buildings will not tell you what the warehouse is worth under your management You need to know how asset values are determined In other words, you need a theory of value This chapter takes the first, most basic steps to develop that theory We lead off with a simple numerical example: Should you invest to build a new office building in the hope of selling it at a profit next year? Finance theory endorses investment if net present value is positive, that is, if the new building’s value today exceeds the required investment It turns out that net present value is positive in this example, because the rate of return on investment exceeds the opportunity cost of capital So this chapter’s first task is to define and explain net present value, rate of return, and opportunity cost of capital The second task is to explain why financial managers search so assiduously for investments with positive net present values Is increased value today the only possible financial objective? And what does “value” mean for a corporation? Here we will come to the fundamental objective of corporate finance: maximizing the current market value of the firm’s outstanding shares We will explain why all shareholders should endorse this objective, and why the objective overrides other plausible goals, such as “maximizing profits.” Finally, we turn to the managers’ objectives and discuss some of the mechanisms that help to align the managers’ and stockholders’ interests We ask whether attempts to increase shareholder value need be at the expense of workers, customers, or the community at large In this chapter, we will stick to the simplest problems to make basic ideas clear Readers with a taste for more complication will find plenty to satisfy them in later chapters Needless to say, there are some properties that appraisers find nearly impossible to value—for example, nobody knows the potential selling price of the Taj Mahal or the Parthenon or Windsor Castle 13 Brealey−Meyers: Principles of Corporate Finance, Seventh Edition 14 PART I I Value © The McGraw−Hill Companies, 2003 Present Value and the Opportunity Cost of Capital Value 2.1 INTRODUCTION TO PRESENT VALUE Your warehouse has burned down, fortunately without injury to you or your employees, leaving you with a vacant lot worth $50,000 and a check for $200,000 from the fire insurance company You consider rebuilding, but your real estate adviser suggests putting up an office building instead The construction cost would be $300,000, and there would also be the cost of the land, which might otherwise be sold for $50,000 On the other hand, your adviser foresees a shortage of office space and predicts that a year from now the new building would fetch $400,000 if you sold it Thus you would be investing $350,000 now in the expectation of realizing $400,000 a year hence You should go ahead if the present value (PV) of the expected $400,000 payoff is greater than the investment of $350,000 Therefore, you need to ask, What is the value today of $400,000 to be received one year from now, and is that present value greater than $350,000? Calculating Present Value The present value of $400,000 one year from now must be less than $400,000 After all, a dollar today is worth more than a dollar tomorrow, because the dollar today can be invested to start earning interest immediately This is the first basic principle of finance Thus, the present value of a delayed payoff may be found by multiplying the payoff by a discount factor which is less than (If the discount factor were more than 1, a dollar today would be worth less than a dollar tomorrow.) If C1 denotes the expected payoff at period (one year hence), then Present value (PV) ϭ discount factor ϫ C1 This discount factor is the value today of $1 received in the future It is usually expressed as the reciprocal of plus a rate of return: Discount factor ϭ 1ϩr The rate of return r is the reward that investors demand for accepting delayed payment Now we can value the real estate investment, assuming for the moment that the $400,000 payoff is a sure thing The office building is not the only way to obtain $400,000 a year from now You could invest in United States government securities maturing in a year Suppose these securities offer percent interest How much would you have to invest in them in order to receive $400,000 at the end of the year? That’s easy: You would have to invest $400,000/1.07, which is $373,832.2 Therefore, at an interest rate of percent, the present value of $400,000 one year from now is $373,832 Let’s assume that, as soon as you’ve committed the land and begun construction on the building, you decide to sell your project How much could you sell it for? That’s another easy question Since the property will be worth $400,000 in a year, investors would be willing to pay $373,832 for it today That’s what it would Let’s check this If you invest $373,832 at percent, at the end of the year you get back your initial investment plus interest of 07 ϫ 373,832 ϭ $26,168 The total sum you receive is 373,832 ϩ 26,168 ϭ $400,000 Note that 373,832 ϫ 1.07 ϭ $400,000 Brealey−Meyers: Principles of Corporate Finance, Seventh Edition I Value Present Value and the Opportunity Cost of Capital © The McGraw−Hill Companies, 2003 CHAPTER Present Value and the Opportunity Cost of Capital cost them to get a $400,000 payoff from investing in government securities Of course, you could always sell your property for less, but why sell for less than the market will bear? The $373,832 present value is the only feasible price that satisfies both buyer and seller Therefore, the present value of the property is also its market price To calculate present value, we discount expected payoffs by the rate of return offered by equivalent investment alternatives in the capital market This rate of return is often referred to as the discount rate, hurdle rate, or opportunity cost of capital It is called the opportunity cost because it is the return foregone by investing in the project rather than investing in securities In our example the opportunity cost was percent Present value was obtained by dividing $400,000 by 1.07: PV ϭ discount factor ϫ C1 ϭ 400,000 ϫ C1 ϭ ϭ $373,832 1ϩr 1.07 Net Present Value The building is worth $373,832, but this does not mean that you are $373,832 better off You committed $350,000, and therefore your net present value (NPV) is $23,832 Net present value is found by subtracting the required investment: NPV ϭ PV Ϫ required investment ϭ 373,832 Ϫ 350,000 ϭ $23,832 In other words, your office development is worth more than it costs—it makes a net contribution to value The formula for calculating NPV can be written as NPV ϭ C0 ϩ C1 1ϩr remembering that C0, the cash flow at time (that is, today), will usually be a negative number In other words, C0 is an investment and therefore a cash outflow In our example, C0 ϭ Ϫ$350,000 A Comment on Risk and Present Value We made one unrealistic assumption in our discussion of the office development: Your real estate adviser cannot be certain about future values of office buildings The $400,000 represents the best forecast, but it is not a sure thing If the future value of the building is risky, our calculation of NPV is wrong Investors could achieve $400,000 with certainty by buying $373,832 worth of United States government securities, so they would not buy your building for that amount You would have to cut your asking price to attract investors’ interest Here we can invoke a second basic financial principle: A safe dollar is worth more than a risky one Most investors avoid risk when they can so without sacrificing return However, the concepts of present value and the opportunity cost of capital still make sense for risky investments It is still proper to discount the payoff by the rate of return offered by an equivalent investment But we have to think of expected payoffs and the expected rates of return on other investments.3 We define “expected” more carefully in Chapter For now think of expected payoff as a realistic forecast, neither optimistic nor pessimistic Forecasts of expected payoffs are correct on average 15 Brealey−Meyers: Principles of Corporate Finance, Seventh Edition 16 PART I I Value Present Value and the Opportunity Cost of Capital © The McGraw−Hill Companies, 2003 Value Not all investments are equally risky The office development is more risky than a government security but less risky than a start-up biotech venture Suppose you believe the project is as risky as investment in the stock market and that stock market investments are forecasted to return 12 percent Then 12 percent becomes the appropriate opportunity cost of capital That is what you are giving up by not investing in equally risky securities Now recompute NPV: 400,000 ϭ $357,143 1.12 NPV ϭ PV Ϫ 350,000 ϭ $7,143 PV ϭ If other investors agree with your forecast of a $400,000 payoff and your assessment of its risk, then your property ought to be worth $357,143 once construction is underway If you tried to sell it for more, there would be no takers, because the property would then offer an expected rate of return lower than the 12 percent available in the stock market The office building still makes a net contribution to value, but it is much smaller than our earlier calculations indicated The value of the office building depends on the timing of the cash flows and their uncertainty The $400,000 payoff would be worth exactly that if it could be realized instantaneously If the office building is as risk-free as government securities, the one-year delay reduces value to $373,832 If the building is as risky as investment in the stock market, then uncertainty further reduces value by $16,689 to $357,143 Unfortunately, adjusting asset values for time and uncertainty is often more complicated than our example suggests Therefore, we will take the two effects separately For the most part, we will dodge the problem of risk in Chapters through 6, either by treating all cash flows as if they were known with certainty or by talking about expected cash flows and expected rates of return without worrying how risk is defined or measured Then in Chapter we will turn to the problem of understanding how financial markets cope with risk Present Values and Rates of Return We have decided that construction of the office building is a smart thing to do, since it is worth more than it costs—it has a positive net present value To calculate how much it is worth, we worked out how much one would need to pay to achieve the same payoff by investing directly in securities The project’s present value is equal to its future income discounted at the rate of return offered by these securities We can say this in another way: Our property venture is worth undertaking because its rate of return exceeds the cost of capital The rate of return on the investment in the office building is simply the profit as a proportion of the initial outlay: Return ϭ profit investment ϭ 400,000 Ϫ 350,000 ϭ 143, about 14% 350,000 The cost of capital is once again the return foregone by not investing in securities If the office building is as risky as investing in the stock market, the return foregone is 12 percent Since the 14 percent return on the office building exceeds the 12 percent opportunity cost, you should go ahead with the project Brealey−Meyers: Principles of Corporate Finance, Seventh Edition I Value Present Value and the Opportunity Cost of Capital © The McGraw−Hill Companies, 2003 CHAPTER Present Value and the Opportunity Cost of Capital Here then we have two equivalent decision rules for capital investment:4 • Net present value rule Accept investments that have positive net present values • Rate-of-return rule Accept investments that offer rates of return in excess of their opportunity costs of capital.5 The Opportunity Cost of Capital The opportunity cost of capital is such an important concept that we will give one more example You are offered the following opportunity: Invest $100,000 today, and, depending on the state of the economy at the end of the year, you will receive one of the following payoffs: Slump Normal Boom $80,000 $110,000 $140,000 You reject the optimistic (boom) and the pessimistic (slump) forecasts That gives an expected payoff of C1 ϭ 110,000,6 a 10 percent return on the $100,000 investment But what’s the right discount rate? You search for a common stock with the same risk as the investment Stock X turns out to be a perfect match X’s price next year, given a normal economy, is forecasted at $110 The stock price will be higher in a boom and lower in a slump, but to the same degrees as your investment ($140 in a boom and $80 in a slump) You conclude that the risks of stock X and your investment are identical Stock X’s current price is $95.65 It offers an expected rate of return of 15 percent: Expected return ϭ expected profit investment ϭ 110 Ϫ 95.65 ϭ 15, or 15% 95.65 This is the expected return that you are giving up by investing in the project rather than the stock market In other words, it is the project’s opportunity cost of capital To value the project, discount the expected cash flow by the opportunity cost of capital: PV ϭ 110,000 ϭ $95,650 1.15 This is the amount it would cost investors in the stock market to buy an expected cash flow of $110,000 (They could so by buying 1,000 shares of stock X.) It is, therefore, also the sum that investors would be prepared to pay you for your project To calculate net present value, deduct the initial investment: NPV ϭ 95,650 Ϫ 100,000 ϭ Ϫ$4,350 You might check for yourself that these are equivalent rules In other words, if the return 50,000/350,000 is greater than r, then the net present value Ϫ 350,000 ϩ [400,000/(1 ϩ r)] must be greater than The two rules can conflict when there are cash flows in more than two periods We address this problem in Chapter We are assuming that the probabilities of slump and boom are equal, so that the expected (average) outcome is $110,000 For example, suppose the slump, normal, and boom probabilities are all 1/3 Then the expected payoff C1 ϭ (80,000 ϩ 110,000 ϩ 140,000)/3 ϭ $110.000 17 Brealey−Meyers: Principles of Corporate Finance, Seventh Edition 18 I Value Present Value and the Opportunity Cost of Capital © The McGraw−Hill Companies, 2003 PART I Value The project is worth $4,350 less than it costs It is not worth undertaking Notice that you come to the same conclusion if you compare the expected project return with the cost of capital: Expected return on project ϭ expected profit investment 110,000 Ϫ 100,000 ϭ 10, or 10% ϭ 100,000 The 10 percent expected return on the project is less than the 15 percent return investors could expect to earn by investing in the stock market, so the project is not worthwhile Of course in real life it’s impossible to restrict the future states of the economy to just “slump,” “normal,” and “boom.” We have also simplified by assuming a perfect match between the payoffs of 1,000 shares of stock X and the payoffs to the investment project The main point of the example does carry through to real life, however Remember this: The opportunity cost of capital for an investment project is the expected rate of return demanded by investors in common stocks or other securities subject to the same risks as the project When you discount the project’s expected cash flow at its opportunity cost of capital, the resulting present value is the amount investors (including your own company’s shareholders) would be willing to pay for the project Any time you find and launch a positive-NPV project (a project with present value exceeding its required cash outlay) you have made your company’s stockholders better off A Source of Confusion Here is a possible source of confusion Suppose a banker approaches “Your company is a fine and safe business with few debts,” she says “My bank will lend you the $100,000 that you need for the project at percent.” Does that mean that the cost of capital for the project is percent? If so, the project would be above water, with PV at percent ϭ 110,000/1.08 ϭ $101,852 and NPV ϭ 101,852 Ϫ 100,000 ϭ ϩ$1,852 That can’t be right First, the interest rate on the loan has nothing to with the risk of the project: It reflects the good health of your existing business Second, whether you take the loan or not, you still face the choice between the project, which offers an expected return of only 10 percent, or the equally risky stock, which gives an expected return of 15 percent A financial manager who borrows at percent and invests at 10 percent is not smart, but stupid, if the company or its shareholders can borrow at percent and buy an equally risky investment offering 15 percent That is why the 15 percent expected return on the stock is the opportunity cost of capital for the project 2.2 FOUNDATIONS OF THE NET PRESENT VALUE RULE So far our discussion of net present value has been rather casual Increasing value sounds like a sensible objective for a company, but it is more than just a rule of thumb You need to understand why the NPV rule makes sense and why managers look to the bond and stock markets to find the opportunity cost of capital Brealey−Meyers: Principles of Corporate Finance, Seventh Edition I Value Present Value and the Opportunity Cost of Capital © The McGraw−Hill Companies, 2003 CHAPTER Present Value and the Opportunity Cost of Capital In the previous example there was just one person (you) making 100 percent of the investment and receiving 100 percent of the payoffs from the new office building In corporations, investments are made on behalf of thousands of shareholders with varying risk tolerances and preferences for present versus future income Could a positive-NPV project for Ms Smith be a negative-NPV proposition for Mr Jones? Could they find it impossible to agree on the objective of maximizing the market value of the firm? The answer to both questions is no; Smith and Jones will always agree if both have access to capital markets We will demonstrate this result with a simple example How Capital Markets Reconcile Preferences for Current vs Future Consumption Suppose that you can look forward to a stream of income from your job Unless you have some way of storing or anticipating this income, you will be compelled to consume it as it arrives This could be inconvenient or worse If the bulk of your income comes late in life, the result could be hunger now and gluttony later This is where the capital market comes in The capital market allows trade between dollars today and dollars in the future You can therefore eat moderately both now and in the future We will now illustrate how the existence of a well-functioning capital market allows investors with different time patterns of income and desired consumption to agree on whether investment projects should be undertaken Suppose that there are two investors with different preferences A is an ant, who wishes to save for the future; G is a grasshopper, who would prefer to spend all his wealth on some ephemeral frolic, taking no heed of tomorrow Now suppose that each is confronted with an identical opportunity—to buy a share in a $350,000 office building that will produce a sure-fire $400,000 at the end of the year, a return of about 14 percent The interest rate is percent A and G can borrow or lend in the capital market at this rate A would clearly be happy to invest in the office building Every hundred dollars that she invests in the office building allows her to spend $114 at the end of the year, while a hundred dollars invested in the capital market would enable her to spend only $107 But what about G, who wants money now, not in one year’s time? Would he prefer to forego the investment opportunity and spend today the cash that he has in hand? Not as long as the capital market allows individuals to borrow as well as to lend Every hundred dollars that G invests in the office building brings in $114 at the end of the year Any bank, knowing that G could look forward to this sure-fire income, would be prepared to lend him $114/1.07 ϭ $106.54 today Thus, instead of spending $100 today, G can spend $106.54 if he invests in the office building and then borrows against his future income This is illustrated in Figure 2.1 The horizontal axis shows the number of dollars that can be spent today; the vertical axis shows spending next year Suppose that the ant and the grasshopper both start with an initial sum of $100 If they invest the entire $100 in the capital market, they will be able to spend 100 ϫ 1.07 ϭ $107 at the end of the year The straight line joining these two points (the innermost line in the figure) shows the combinations of current and future consumption that can be achieved by investing none, part, or all of the cash at the percent rate offered in the capital market (The interest rate determines the slope of this line.) Any other point along the line could be achieved by spending 19 Brealey−Meyers: Principles of Corporate Finance, Seventh Edition 20 I Value © The McGraw−Hill Companies, 2003 Present Value and the Opportunity Cost of Capital PART I Value FIGURE 2.1 Dollars next year The grasshopper (G) wants consumption now The ant (A) wants to wait But each is happy to invest A prefers to invest at 14 percent, moving up the burgundy arrow, rather than at the percent interest rate G invests and then borrows at percent, thereby transforming $100 into $106.54 of immediate consumption Because of the investment, G has $114 next year to pay off the loan The investment’s NPV is 106.54 Ϫ 100 ϭ ϩ6.54 114 107 A invests $100 in office building and consumes $114 next year 100 106.54 Dollars now G invests $100 in office building, borrows $106.54, and consumes that amount now part of the $100 today and investing the balance.7 For example, one could choose to spend $50 today and $53.50 next year However, A and G would each reject such a balanced consumption schedule The burgundy arrow in Figure 2.1 shows the payoff to investing $100 in a share of your office project The rate of return is 14 percent, so $100 today transmutes to $114 next year The sloping line on the right in Figure 2.1 (the outermost line in the figure) shows how A’s and G’s spending plans are enhanced if they can choose to invest their $100 in the office building A, who is content to spend nothing today, can invest $100 in the building and spend $114 at the end of the year G, the spendthrift, also invests $100 in the office building but borrows 114/1.07 ϭ $106.54 against the future income Of course, neither is limited to these spending plans In fact, the right-hand sloping line shows all the combinations of current and future expenditure that an investor could achieve from investing $100 in the office building and borrowing against some fraction of the future income You can see from Figure 2.1 that the present value of A’s and G’s share in the office building is $106.54 The net present value is $6.54 This is the distance be7 The exact balance between present and future consumption that each individual will choose depends on personal preferences Readers who are familiar with economic theory will recognize that the choice can be represented by superimposing an indifference map for each individual The preferred combination is the point of tangency between the interest-rate line and the individual’s indifference curve In other words, each individual will borrow or lend until plus the interest rate equals the marginal rate of time preference (i.e., the slope of the indifference curve) A more formal graphical analysis of investment and the choice between present and future consumption is on the Brealey–Myers website at www://mhhe.com/bm/7e Brealey−Meyers: Principles of Corporate Finance, Seventh Edition I Value Present Value and the Opportunity Cost of Capital CHAPTER © The McGraw−Hill Companies, 2003 Present Value and the Opportunity Cost of Capital tween the $106.54 present value and the $100 initial investment Despite their different tastes, both A and G are better off by investing in the office block and then using the capital markets to achieve the desired balance between consumption today and consumption at the end of the year In fact, in coming to their investment decision, both would be happy to follow the two equivalent rules that we proposed so casually at the end of Section 2.1 The two rules can be restated as follows: • Net present value rule Invest in any project with a positive net present value This is the difference between the discounted, or present, value of the future cash flow and the amount of the initial investment • Rate-of-return rule Invest as long as the return on the investment exceeds the rate of return on equivalent investments in the capital market What happens if the interest rate is not percent but 14.3 percent? In this case the office building would have zero NPV: NPV ϭ 400,000/1.143 Ϫ 350,000 ϭ $0 Also, the return on the project would be 400,000/350,000 Ϫ ϭ 143, or 14.3 percent, exactly equal to the rate of interest in the capital market In this case our two rules would say that the project is on a knife edge Investors should not care whether the firm undertakes it or not It is easy to see that with a 14.3 percent interest rate neither A nor G would gain anything by investing in the office building A could spend exactly the same amount at the end of the year, regardless of whether she invests her money in the office building or in the capital market Equally, there is no advantage in G investing in an office block to earn 14.3 percent and at the same time borrowing at 14.3 percent He might just as well spend whatever cash he has on hand In our example the ant and the grasshopper placed an identical value on the office building and were happy to share in its construction They agreed because they faced identical borrowing and lending opportunities Whenever firms discount cash flows at capital market rates, they are implicitly assuming that their shareholders have free and equal access to competitive capital markets It is easy to see how our net present value rule would be damaged if we did not have such a well-functioning capital market For example, suppose that G could not borrow against future income or that it was prohibitively costly for him to so In that case he might well prefer to spend his cash today rather than invest it in an office building and have to wait until the end of the year before he could start spending If A and G were shareholders in the same enterprise, there would be no simple way for the manager to reconcile their different objectives No one believes unreservedly that capital markets are perfectly competitive Later in this book we will discuss several cases in which differences in taxation, transaction costs, and other imperfections must be taken into account in financial decision making However, we will also discuss research which indicates that, in general, capital markets function fairly well That is one good reason for relying on net present value as a corporate objective Another good reason is that net present value makes common sense; we will see that it gives obviously silly answers less frequently than its major competitors But for now, having glimpsed the problems of imperfect markets, we shall, like an economist in a shipwreck, simply assume our life jacket and swim safely to shore 21 Brealey−Meyers: Principles of Corporate Finance, Seventh Edition 22 PART I I Value Present Value and the Opportunity Cost of Capital © The McGraw−Hill Companies, 2003 Value 2.3 A FUNDAMENTAL RESULT Our justification of the present value rule was restricted to two periods and to a certain cash flow However, the rule also makes sense for uncertain cash flows that extend far into the future The argument goes like this: A financial manager should act in the interests of the firm’s owners, its stockholders Each stockholder wants three things: a To be as rich as possible, that is, to maximize current wealth b To transform that wealth into whatever time pattern of consumption he or she desires c To choose the risk characteristics of that consumption plan But stockholders not need the financial manager’s help to achieve the best time pattern of consumption They can that on their own, providing they have free access to competitive capital markets They can also choose the risk characteristics of their consumption plan by investing in more or less risky securities How then can the financial manager help the firm’s stockholders? There is only one way: by increasing the market value of each stockholder’s stake in the firm The way to that is to seize all investment opportunities that have a positive net present value Despite the fact that shareholders have different preferences, they are unanimous in the amount that they want to invest in real assets This means that they can cooperate in the same enterprise and can safely delegate operation of that enterprise to professional managers These managers not need to know anything about the tastes of their shareholders and should not consult their own tastes Their task is to maximize net present value If they succeed, they can rest assured that they have acted in the best interest of their shareholders This gives us the fundamental condition for successful operation of a modern capitalist economy Separation of ownership and control is essential for most corporations, so authority to manage has to be delegated It is good to know that managers can all be given one simple instruction: Maximize net present value Other Corporate Goals Sometimes you hear managers speak as if the corporation has other goals For example, they may say that their job is to maximize profits That sounds reasonable After all, don’t shareholders prefer to own a profitable company rather than an unprofitable one? But taken literally, profit maximization doesn’t make sense as a corporate objective Here are three reasons: “Maximizing profits” leaves open the question, Which year’s profits? Shareholders might not want a manager to increase next year’s profits at the expense of profits in later years A company may be able to increase future profits by cutting its dividend and investing the cash That is not in the shareholders’ interest if the company earns only a low return on the investment Different accountants may calculate profits in different ways So you may find that a decision which improves profits in one accountant’s eyes will reduce them in the eyes of another Brealey−Meyers: Principles of Corporate Finance, Seventh Edition I Value Present Value and the Opportunity Cost of Capital © The McGraw−Hill Companies, 2003 CHAPTER Present Value and the Opportunity Cost of Capital 23 2.4 DO MANAGERS REALLY LOOK AFTER THE INTERESTS OF SHAREHOLDERS? We have explained that managers can best serve the interests of shareholders by investing in projects with a positive net present value But this takes us back to the principal–agent problem highlighted in the first chapter How can shareholders (the principals) ensure that management (their agents) don’t simply look after their own interests? Shareholders can’t spend their lives watching managers to check that they are not shirking or maximizing the value of their own wealth However, there are several institutional arrangements that help to ensure that the shareholders’ pockets are close to the managers’ heart A company’s board of directors is elected by the shareholders and is supposed to represent them Boards of directors are sometimes portrayed as passive stooges who always champion the incumbent management But when company performance starts to slide and managers not offer a credible recovery plan, boards act In recent years the chief executives of Eastman Kodak, General Motors, Xerox, Lucent, Ford Motor, Sunbeam, and Lands End were all forced to step aside when each company’s profitability deteriorated and the need for new strategies became clear If shareholders believe that the corporation is underperforming and that the board of directors is not sufficiently aggressive in holding the managers to task, they can try to replace the board in the next election If they succeed, the new board will appoint a new management team But these attempts to vote in a new board are expensive and rarely successful Thus dissidents not usually stand and fight but sell their shares instead Selling, however, can send a powerful message If enough shareholders bail out, the stock price tumbles This damages top management’s reputation and compensation Part of the top managers’ paychecks comes from bonuses tied to the company’s earnings or from stock options, which pay off if the stock price rises but are worthless if the price falls below a stated threshold This should motivate managers to increase earnings and the stock price If managers and directors not maximize value, there is always the threat of a hostile takeover The further a company’s stock price falls, due to lax management or wrong-headed policies, the easier it is for another company or group of investors to buy up a majority of the shares The old management team is then likely to find themselves out on the street and their place is taken by a fresh team prepared to make the changes needed to realize the company’s value These arrangements ensure that few managers at the top of major United States corporations are lazy or inattentive to stockholders’ interests On the contrary, the pressure to perform can be intense 2.5 SHOULD MANAGERS LOOK AFTER THE INTERESTS OF SHAREHOLDERS? We have described managers as the agents of the shareholders But perhaps this begs the question, Is it desirable for managers to act in the selfish interests of their shareholders? Does a focus on enriching the shareholders mean that managers must act as greedy mercenaries riding roughshod over the weak and helpless? Do Brealey−Meyers: Principles of Corporate Finance, Seventh Edition 24 I Value Present Value and the Opportunity Cost of Capital © The McGraw−Hill Companies, 2003 PART I Value they not have wider obligations to their employees, customers, suppliers, and the communities in which the firm is located?8 Most of this book is devoted to financial policies that increase a firm’s value None of these policies requires gallops over the weak and helpless In most instances there is little conflict between doing well (maximizing value) and doing good Profitable firms are those with satisfied customers and loyal employees; firms with dissatisfied customers and a disgruntled workforce are more likely to have declining profits and a low share price Of course, ethical issues arise in business as in other walks of life, and therefore when we say that the objective of the firm is to maximize shareholder wealth, we not mean that anything goes In part, the law deters managers from making blatantly dishonest decisions, but most managers are not simply concerned with observing the letter of the law or with keeping to written contracts In business and finance, as in other day-to-day affairs, there are unwritten, implicit rules of behavior To work efficiently together, we need to trust each other Thus huge financial deals are regularly completed on a handshake, and each side knows that the other will not renege later if things turn sour.9 Whenever anything happens to weaken this trust, we are all a little worse off.10 In many financial transactions, one party has more information than the other It can be difficult to be sure of the quality of the asset or service that you are buying This opens up plenty of opportunities for financial sharp practice and outright fraud, and, because the activities of scoundrels are more entertaining than those of honest people, airport bookstores are packed with accounts of financial fraudsters The response of honest firms is to distinguish themselves by building long-term relationships with their customers and establishing a name for fair dealing and financial integrity Major banks and securities firms know that their most valuable asset is their reputation They emphasize their long history and responsible behavior When something happens to undermine that reputation, the costs can be enormous Consider the Salomon Brothers bidding scandal in 1991.11 A Salomon trader tried to evade rules limiting the firm’s participation in auctions of U.S Treasury bonds by submitting bids in the names of the company’s customers without the customers’ knowledge When this was discovered, Salomon settled the case by paying almost $200 million in fines and establishing a $100 million fund for payments of claims from civil lawsuits Yet the value of Salomon Brothers stock fell by Some managers, anxious not to offend any group of stakeholders, have denied that they are maximizing profits or value We are reminded of a survey of businesspeople that inquired whether they attempted to maximize profits They indignantly rejected the notion, objecting that their responsibilities went far beyond the narrow, selfish profit motive But when the question was reformulated and they were asked whether they could increase profits by raising or lowering their selling price, they replied that neither change would so The survey is cited in G J Stigler, The Theory of Price, 3rd ed (New York: Macmillan Company, 1966) In U.S law, a contract can be valid even if it is not written down Of course documentation is prudent, but contracts are enforced if it can be shown that the parties reached a clear understanding and agreement For example, in 1984, the top management of Getty Oil gave verbal agreement to a merger offer with Pennzoil Then Texaco arrived with a higher bid and won the prize Pennzoil sued—and won— arguing that Texaco had broken up a valid contract 10 For a discussion of 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) 11 This discussion is based on Clifford W Smith, Jr., “Economics and Ethics: The Case of Salomon Brothers,” Journal of Applied Corporate Finance (Summer 1992), pp 23–28 Brealey−Meyers: Principles of Corporate Finance, Seventh Edition I Value Present Value and the Opportunity Cost of Capital © The McGraw−Hill Companies, 2003 CHAPTER Present Value and the Opportunity Cost of Capital 25 far more than $300 million In fact the price dropped by about a third, representing a $1.5 billion decline in the company’s market value Why did the value of Salomon Brothers drop so dramatically? Largely because investors were worried that Salomon would lose business from customers that now distrusted the company The damage to Salomon’s reputation was far greater than the explicit costs of the scandal and was hundreds or thousands of times more costly than the potential gains Salomon could have reaped from the illegal trades In this chapter we have introduced the concept of present value as a way of valuing assets Calculating present value is easy Just discount future cash flow by an appropriate rate r, usually called the opportunity cost of capital, or hurdle rate: Present value 1PV2 ϭ SUMMARY C1 1ϩr Net present value 1NPV2 ϭ C0 ϩ C1 1ϩr Remember that C0 is negative if the immediate cash flow is an investment, that is, if it is a cash outflow The discount rate is determined by rates of return prevailing in capital markets If the future cash flow is absolutely safe, then the discount rate is the interest rate on safe securities such as United States government debt If the size of the future cash flow is uncertain, then the expected cash flow should be discounted at the expected rate of return offered by equivalent-risk securities We will talk more about risk and the cost of capital in Chapters through Cash flows are 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 one Formulas for PV and NPV are numerical expressions of these ideas The capital market is the market where safe and risky future cash flows are traded That is why we look to rates of return prevailing in the capital markets to determine how much to discount for time and risk By calculating the present value of an asset, we are in effect estimating how much people will pay for it if they have the alternative of investing in the capital markets The concept of net present value allows efficient separation of ownership and management of the corporation A manager who invests only in assets with positive net present values serves the best interests of each one of the firm’s owners, regardless of differences in their wealth and tastes This is made possible by the existence of the capital market which allows each shareholder to construct a personal investment plan that is custom tailored to his or her own requirements For example, there is no need for the firm to arrange its investment policy to obtain a sequence of cash flows that matches its shareholders’ preferred time patterns of consumption The shareholders can shift funds forward or back over time perfectly well on their own, provided they have free access to competitive capital markets In fact, their plan for consumption over time is limited by only two things: their personal wealth (or lack of it) and the interest rate at which they can borrow or lend The financial manager cannot affect the interest rate but can Visit us at www.mhhe.com/bm7e Net present value is present value plus any immediate cash flow: Brealey−Meyers: Principles of Corporate Finance, Seventh Edition 26 PART I I Value Present Value and the Opportunity Cost of Capital © The McGraw−Hill Companies, 2003 Value increase stockholders’ wealth The way to so is to invest in assets having positive net present values There are several institutional arrangements which help to ensure that managers pay close attention to the value of the firm: Visit us at www.mhhe.com/bm7e • Managers’ actions are subject to the scrutiny of the board of directors • Shirkers are likely to find that they are ousted by more energetic managers This competition may arise within the firm, but poorly performing companies are also more likely to be taken over That sort of takeover typically brings in a fresh management team • Managers are spurred on by incentive schemes, such as stock options, which pay off big if shareholders gain but are valueless if they not Managers who focus on shareholder value need not neglect their wider obligations to the community Managers play fair by employees, customers, and suppliers partly because they know that it is for the common good, but partly because they know that their firm’s most valuable asset is its reputation Of course, ethical issues arise in financial management and, whenever unscrupulous managers abuse their position, we all trust each other a little less FURTHER READING The pioneering works on the net present value rule are: I Fisher: The Theory of Interest, Augustus M Kelley, Publishers New York, 1965 Reprinted from the 1930 edition J Hirshleifer: “On the Theory of Optimal Investment Decision,” Journal of Political Economy, 66:329–352 (August 1958) For a more rigorous textbook treatment of the subject, we suggest: E F Fama and M H Miller: The Theory of Finance, Holt, Rinehart and Winston New York, 1972 If you would like to dig deeper into the question of how managers can be motivated to maximize shareholder wealth, we suggest: 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) QUIZ C0 is the initial cash flow on an investment, and C1 is the cash flow at the end of one year The symbol r is the discount rate a Is C0 usually positive or negative? b What is the formula for the present value of the investment? c What is the formula for the net present value? d The symbol r is often termed the opportunity cost of capital Why? e If the investment is risk-free, what is the appropriate measure of r? If the present value of $150 paid at the end of one year is $130, what is the one-year discount factor? What is the discount rate? Calculate the one-year discount factor DF1 for discount rates of (a) 10 percent, (b) 20 percent, and (c) 30 percent Brealey−Meyers: Principles of Corporate Finance, Seventh Edition I Value Present Value and the Opportunity Cost of Capital © The McGraw−Hill Companies, 2003 CHAPTER Present Value and the Opportunity Cost of Capital 27 A merchant pays $100,000 for a load of grain and is certain that it can be resold at the end of one year for $132,000 a What is the return on this investment? b If this return is lower than the rate of interest, does the investment have a positive or a negative NPV? c If the rate of interest is 10 percent, what is the PV of the investment? d What is the NPV? What is the net present value rule? What is the rate of return rule? Do the two rules give the same answer? Define the opportunity cost of capital How in principle would you find the opportunity cost of capital for a risk-free asset? For a risky asset? We can imagine the financial manager doing several things on behalf of the firm’s stockholders For example, the manager might: a Make shareholders as wealthy as possible by investing in real assets with positive NPVs b Modify the firm’s investment plan to help shareholders achieve a particular time pattern of consumption c Choose high- or low-risk assets to match shareholders’ risk preferences d Help balance shareholders’ checkbooks But in well-functioning capital markets, shareholders will vote for only one of these goals Which one? Why? Why would one expect managers to act in shareholders’ interests? Give some reasons 10 After the Salomon Brothers bidding scandal, the aggregate value of the company’s stock dropped by far more than it paid in fines and settlements of lawsuits Why? Write down the formulas for an investment’s NPV and rate of return Prove that NPV is positive only if the rate of return exceeds the opportunity cost of capital What is the net present value of a firm’s investment in a U.S Treasury security yielding percent and maturing in one year? Hint: What is the opportunity cost of capital? Ignore taxes PRACTICE QUESTIONS A parcel of land costs $500,000 For an additional $800,000 you can build a motel on the property The land and motel should be worth $1,500,000 next year Suppose that common stocks with the same risk as this investment offer a 10 percent expected return Would you construct the motel? Why or why not? Calculate the NPV and rate of return for each of the following investments The opportunity cost of capital is 20 percent for all four investments Investment Initial Cash Flow, C0 Cash Flow in Year 1, C1 Ϫ10,000 Ϫ5,000 Ϫ5,000 Ϫ2,000 ϩ18,000 ϩ9,000 ϩ5,700 ϩ4,000 EXCEL Visit us at www.mhhe.com/bm7e Look back to the numerical example graphed in Figure 2.1 Suppose the interest rate is 20 percent What would the ant (A) and grasshopper (G) do? Would they invest in the office building? Would they borrow or lend? Suppose each starts with $100 How much and when would each consume? Brealey−Meyers: Principles of Corporate Finance, Seventh Edition 28 I Value Present Value and the Opportunity Cost of Capital © The McGraw−Hill Companies, 2003 PART I Value a Which investment is most valuable? b Suppose each investment would require use of the same parcel of land Therefore you can take only one Which one? Hint: What is the firm’s objective: to earn a high rate of return or to increase firm value? In Section 2.1, we analyzed the possible construction of an office building on a plot of land appraised at $50,000 We concluded that this investment had a positive NPV of $7,143 at a discount rate of 12 percent Suppose E Coli Associates, a firm of genetic engineers, offers to purchase the land for $60,000, $30,000 paid immediately and $30,000 after one year United States government securities maturing in one year yield percent a Assume E Coli is sure to pay the second $30,000 installment Should you take its offer or start on the office building? Explain b Suppose you are not sure E Coli will pay You observe that other investors demand a 10 percent return on their loans to E Coli Assume that the other investors have correctly assessed the risks that E Coli will not be able to pay Should you accept E Coli’s offer? Visit us at www.mhhe.com/bm7e Explain why the discount rate equals the opportunity cost of capital EXCEL Norman Gerrymander has just received a $2 million bequest How should he invest it? There are four immediate alternatives a Investment in one-year U.S government securities yielding percent b A loan to Norman’s nephew Gerald, who has for years aspired to open a big Cajun restaurant in Duluth Gerald had arranged a one-year bank loan for $900,000, at 10 percent, but asks for a loan from Norman at percent c Investment in the stock market The expected rate of return is 12 percent d Investment in local real estate, which Norman judges is about as risky as the stock market The opportunity at hand would cost $1 million and is forecasted to be worth $1.1 million after one year Which of these investments have positive NPVs? Which would you advise Norman to take? Show that your answers to Practice Question are consistent with the rate of return rule for investment decisions Take another look at investment opportunity (d) in Practice Question Suppose a bank offers Norman a $600,000 personal loan at percent (Norman is a long-time customer of the bank and has an excellent credit history.) Suppose Norman borrows the money, invests $1 million in real estate opportunity (d) and puts the rest of his money in opportunity (c), the stock market Is this a smart move? Explain 10 Respond to the following comments a “My company’s cost of capital is the rate we pay to the bank when we borrow money.” b “Net present value is just theory It has no practical relevance We maximize profits That’s what shareholders really want.” c “It’s no good just telling me to maximize my stock price I can easily take a short view and maximize today’s price What I would prefer is to keep it on a gently rising trend.” 11 Ms Smith is retired and depends on her investments for retirement income Mr Jones is a young executive who wants to save for the future They are both stockholders in Airbus, which is investing over $12 billion to develop the A380, a new super-jumbo airliner This investment’s payoff is many years in the future Assume the investment is positive-NPV for Mr Jones Explain why it should also be positive-NPV for Ms Smith 12 Answer this question by drawing graphs like Figure 2.1 Casper Milktoast has $200,000 available to support consumption in periods (now) and (next year) He Brealey−Meyers: Principles of Corporate Finance, Seventh Edition I Value Present Value and the Opportunity Cost of Capital © The McGraw−Hill Companies, 2003 CHAPTER Present Value and the Opportunity Cost of Capital 29 wants to consume exactly the same amount in each period The interest rate is percent There is no risk a How much should he invest, and how much can he consume in each period? b Suppose Casper is given an opportunity to invest up to $200,000 at 10 percent riskfree The interest rate stays at percent What should he do, and how much can he consume in each period? c What is the NPV of the opportunity in (b)? 13 We said that maximizing value makes sense only if we assume well-functioning capital markets What does “well-functioning” mean? Can you think of circumstances in which maximizing value would not be in all shareholders’ interests? 14 Why is a reputation for honesty and fair business practice important to the financial value of the corporation? CHALLENGE QUESTIONS In Figure 2.2, the sloping line represents the opportunities for investment in the capital market and the solid curved line represents the opportunities for investment in plant and machinery The company’s only asset at present is $2.6 million in cash a What is the interest rate? b How much should the company invest in plant and machinery? c How much will this investment be worth next year? d What is the average rate of return on the investment? e What is the marginal rate of return? f What is the PV of this investment? g What is the NPV of this investment? h What is the total PV of the company? i How much will the individual consume today? j How much will he or she consume tomorrow? FIGURE 2.2 Dollars, year 1, millions See Challenge Question Owner's preferred consumption pattern 3.75 1.6 2.6 Dollars, year 0, millions Visit us at www.mhhe.com/bm7e It is sometimes argued that the NPV criterion is appropriate for corporations but not for governments First, governments must consider the time preferences of the community as a whole rather than those of a few wealthy investors Second, governments must have a longer horizon than individuals, for governments are the guardians of future generations What you think? Brealey−Meyers: Principles of Corporate Finance, Seventh Edition 30 I Value © The McGraw−Hill Companies, 2003 Present Value and the Opportunity Cost of Capital PART I Value Draw a figure like Figure 2.1 to represent the following situation a A firm starts out with $10 million in cash b The rate of interest r is 10 percent c To maximize NPV the firm invests today $6 million in real assets This leaves $4 million which can be paid out to the shareholders d The NPV of the investment is $2 million When you have finished, answer the following questions: e How much cash is the firm going to receive in year from its investment? f What is the marginal return from the firm’s investment? g What is the PV of the shareholders’ investment after the firm has announced its investment plan? h Suppose shareholders want to spend $6 million today How can they this? i How much will they then have to spend next year? Show this on your drawing For an outlay of $8 million you can purchase a tanker load of bucolic acid delivered in Rotterdam one year hence Unfortunately the net cash flow from selling the tanker load will be very sensitive to the growth rate of the world economy: Normal Boom $8 million Visit us at www.mhhe.com/bm7e Slump $12 million $16 million a What is the expected cash flow? Assume the three outcomes for the economy are equally likely b What is the expected rate of return on the investment in the project? c One share of stock Z is selling for $10 The stock has the following payoffs after one year: Slump Normal Boom $8 $12 $16 Calculate the expected rate of return offered by stock Z Explain why this is the opportunity cost of capital for your bucolic acid project d Calculate the project’s NPV Is the project a good investment? Explain why EXCEL In real life the future health of the economy cannot be reduced to three equally probable states like slump, normal, and boom But we’ll keep that simplification for one more example Your company has identified two more projects, B and C Each will require a $5 million outlay immediately The possible payoffs at year are, in millions: Slump B C Normal Boom 5.5 You have identified the possible payoffs to investors in three stocks, X, Y, and Z: Payoff at Year Current Price per Share X Y Z Slump Normal Boom 95.65 40 10 80 40 110 44 12 140 48 16 Brealey−Meyers: Principles of Corporate Finance, Seventh Edition I Value Present Value and the Opportunity Cost of Capital © The McGraw−Hill Companies, 2003 CHAPTER Present Value and the Opportunity Cost of Capital 31 Visit us at www.mhhe.com/bm7e a What are the expected cash inflows of projects B and C? b What are the expected rates of return offered by stocks X, Y, and Z? c What are the opportunity costs of capital for projects B and C? Hint: Calculate the percentage differences, slump versus normal and boom versus normal, for stocks X, Y, and Z Match up to the percentage differences in B’s and C’s payoffs d What are the NPVs of projects B and C? e Suppose B and C are launched and $5 million is invested in each How much will they add to the total market value of your company’s shares? ... “Economics and Ethics: The Case of Salomon Brothers,” Journal of Applied Corporate Finance (Summer 19 92) , pp 23 ? ?28 Brealey−Meyers: Principles of Corporate Finance, Seventh Edition I Value Present Value... opportunity cost of capital Brealey−Meyers: Principles of Corporate Finance, Seventh Edition I Value Present Value and the Opportunity Cost of Capital © The McGraw−Hill Companies, 20 03 CHAPTER Present... of imperfect markets, we shall, like an economist in a shipwreck, simply assume our life jacket and swim safely to shore 21 Brealey−Meyers: Principles of Corporate Finance, Seventh Edition 22