1 NEW YORK UNIVERSITY FINANCIAL ECONOMICS II Spring 2003 Franklin Allen and Douglas Gale Topic 1: What is Corporate Finance? Readings: A Ph. D. textbook that provides basic coverage of some of the main topics is: J. A. de Matos. Theoretical Foundations of Corporate Finance, Princeton: Princeton University Press, 2002). There are many MBA textbooks. A very good one is R.A. Brealey and S.C. Myers, Principles of Corporate Finance, 7th edition (New York: McGraw Hill, 2002). 1.0 Introduction Corporate finance is concerned with how firms should make investment and financing decisions. It is at the heart of most MBA programs. In recent years it has also become an important part of financial economics. In this course we will cover the subject at an advanced level by first developing the economic tools that are used in the subject and then applying them. In this first part of the course we will start by briefly outlining what corporate finance focuses on. We will do this by outlining the coverage of a typical MBA course. As a comparison of the two books above will show, this is somewhat different from what is usually studied in Ph. D. courses. These usually cover a subset of what MBA courses 2 cover. This is unfortunate as many interesting topics with important research questions are left out. It is important that you read an MBA textbook. I would suggest Brealey and Myers as it introduced the current way in which MBA courses are taught. It is quite readable and should take only two or three days to finish. It is perhaps helpful to start with a brief historical account of where corporate finance comes from. The railroad companies in the US began to use discounting techniques to make investment decisions. Irving Fisher?s book on the Theory of Interest was quite influential. However, the corporate finance that was taught in business schools before the Second World War was still very much based on the law. Arthur Stone Dewing?s classic book on Corporate Finance which was originally written in the 1920?s essentially described various financing instruments and legal precedents. After the war books began to move more towards an accounting and economics based approach. Jack Hirshleifer?s 1970 book was quite influential in making the subject more economics based. Brealey and Myers was the first book when it was published in the late 1970?s was the first to properly incorporate the modern foundations of corporate finance which are Fisher?s separation theory, the Gordon Growth model, the Modigliani-Miller theorems, the Capital Asset Pricing Model and efficient markets. In what follows we will start with firm?s investment decisions and then consider the financing aspects. 3 1.1 Investment Decisions Objective Function of the Corporation Motivation Example 1 Suppose you are at a GM shareholders' meeting. Three of the shareholders there have very different ideas about what the firm should do. Old lady: Wants money now. Wants GM to invest in large cars since this would yield a quick profit. Little Boy's trust Wants money a long way in the future. Wants GM to invest in fund representative building electric cars. Pension fund Wants money in the medium term. Thinks there will be a very representative serious oil crisis some time in that period. Recommends that GM build small cars. What should GM do? We will see how to answer this question by looking at how an individual should make investment decisions. Once we see that we can see how a corporation should make investment decisions. Example Bill Ross has inherited $1M. He grew up in Europe and has developed a real aversion to work, which he completely detests. He therefore plans to use his inheritance to finance himself for the rest of his life. For simplicity we'll divide his life into two periods, youth and old age. Also, we're going to assume that there is only one financial institution, a bank, which lends and borrows at a rate of 20%, so that for every dollar deposited in youth $1.20 is received in old age. 4 Bank Alone Assuming this bank is the only opportunity open to Bill, what can he do? (i) He could go on a fantastic trip around the world, spend the whole $1M, and then live in poverty with nothing for his old age. (ii) He could spend $0.5M in his youth, have a moderate lifestyle, put $0.5M in the bank, and still have $0.6M for his old age. (iii) He could put all his money in the bank for his old age and spend nothing in his youth, so that he can take an even better trip around the world in his old age. In this case he gets (0, $1.2M). (iv) If we consider all the other possibilities, we get a straight line between (i) and (iii). He can thus consume anywhere on the straight line between $1M in youth and $1.2M in old age. Analytically we have C OA = 1.2M - 1.2 C Y 5 Projects Alone We're next going to look at the case where there is no bank and there are only productive opportunities or projects that allow him to transfer wealth from his youth to his old age. Bill fancies himself as an entrepreneur and sits down to work out what investments he can make. He ranks them in terms of profitability with the most profitable being first and the least profitable last. Project A Bill is a wine lover. He estimates that a small vineyard that has recently come on the market will cost him $50,000 now and will yield him $200,000 for his old age. This is the best project he can think of. Hence, if he invests just $50,000 in this project and consumes $950,000 now, he can still consume $200,000 in his old age. Project B Bill is also a gourmet. The next best project he can think of is to run a restaurant in the town he lives in. He reckons for a $100,000 outlay now he can get $140,000 in his old 6 age. If he just undertakes this and project A, then he can consume $850,000 now and $340,000 later on. Project C and so on There are a number of other projects he thinks of. We can trace out a curve to approximate these, e.g., see above. With projects alone he can consume anywhere along the curve. Projects and the Bank We now consider what he can do if we take account of both his projects and the possibility of borrowing and lending at the bank. Project A Suppose he just undertakes the first project, A. He has $950,000 now and $200,000 later on--what can he do? (i) He could simply consume $950,000 now and $200,000 later on without going to the bank. (ii) Alternatively, he can use all the money he receives to have a marvelous time. He has $950,000 now and $200,000 later on, which he can use to repay a loan that he spends now. How much can he borrow to repay with the $200,000 later on; i.e., what is the present value of $200,000 at 20%? PV(200,000 OA at 20%) = 200,000 = 166,666 1.20 Hence, Total possible in consumption youth = 950,000 + 166,666 = $1.1167M 7 (iii) Alternatively he can plan to spend it all next period. Total in old age = 1.2 x 950,000 + 200,000 = $1,340,000 As before, we can go on doing this until we trace out a straight-line budget constraint as before. The equation for this line is C OA = 1.34M - 1.2 C Y The slope is again - 1.2 since the interest rate is 20%. You can see that this follows from the structure of the problem since all values in Old Age are multiplied by 1.20 compared to their values in Youth. Project B Now suppose he undertakes the first and second projects, A and B, so that he produces at A + B. We can go through the same calculations again and get another line representing his consumption possibilities. 8 In this case, Intercept on C OA axis = 1.2 x 850,000 + 340,000 = 1.36 M. Hence, analytically the budget constraint is given by C OA = 1.36 M - 1.2 C Y We can see that by undertaking the first project he can push out the line representing his possible consumption, similarly when he undertakes the second project, and so on. If he prefers more money to less, he is better off if his budget constraint is pushed out further since this allows him to consume more in both periods. Hence no matter what his preferences are, he is better off with a budget constraint that is farther out. To see this we can represent preferences in this diagram by an indifference curve. This is the locus of combinations of C OA and C Y such that he is indifferent. 9 We can represent differences in preferences for consumption in old age and youth by differences in the shape of the indifference curves. Suppose, for example, somebody has a strong preference for consumption in old age. Then her indifference curves will look something like this: Her curves are flat for the following reason. Since she is a miser a small reduction in consumption in old age must be compensated for by a large increase in youth to make her indifferent. 10 Somebody who prefers consumption in his youth, who we shall call a spender, will have the type of indifference curves below. They are steep because a large reduction in consumption in old age can be compensated for by a small increase in youth to make him indifferent. Now if we put budget constraints on these diagrams we can see that pushing a budget constraint out makes both better off. 11 Hence no matter what Bill Ross' preferences are, he must be made better off if the budget constraint is pushed out. Clearly the best that he can do is therefore to go on doing projects until he can push out his budget constraint no farther. This is true no matter what his preferences are. The crucial point here is that the level of investment he should undertake does not depend on his preferences. This implies that his consumption and production decisions are separate. If you have $100 now and the interest rate is 10% per year, then you can invest the $100 and get $110 in a year's time. The future value of $100 in 1 year's time at 10% is $110. In general C 1 = (1 + r)PV FV formula Another way of saying the same thing is that the present value of $110 in 1 year's time if the interest rate is 10% is $100. In general PV = C 1 PV formula _____ 1+ r 12 OPP = - Slope = 1 + r ADJ OP =(1 +r)ADJ FV FORMULA ADJ = OP PV FORMULA 1+ r Hence if we have a triangle on the budget constraint in the diagram, the vertical is a future value and the horizontal is the present value. Now let's look at the examples. Miser - Lends 13 Spender - Borrows Maximization of NPV What we're going to show next is that pushing out the budget line is equivalent to the maximization of NPV. 14 The thing to remember is that vertical distances are future values; horizontal distances are PV's. What is XV? It is the return to the investment. What therefore is YZ? It's the PV of the project. What's YW? It's the cost. Thus, what is WZ? It's the NPV of the project since NPV = PV - Cost. Hence the distance between the intercept on the production possibilities curve and the intercept on the budget constraint is NPV. Hence, making this as large as possible allows a person to consume more in both periods, and she should do it. Pushing the line out as far as possible is thus equivalent to making the distance WZ as large as possible and hence is equivalent to maximizing NPV. One important thing to notice from the diagram is that NPV is a monetary measure of how much better off Bill Ross is from undertaking the investment. It measures the increase in his wealth from the project. NPV is a measure of wealth creation. The other important thing here is that the discount rate used to find the NPV is the opportunity cost of capital. If Bill Ross doesn't do the project the best alternative use of his money is to put it in the bank. We use this best alternative rate to discount so we can find out which is the best thing to do. Rate of Return Another way of looking at the problem of what the person should do is in terms of the rate of return. Consider Project A. The rate of return, R, this project earns is given by 1 + R = 200,000 = 4 50,000 Hence, R = 3 or 300%. 15 Slope = - 0.2/0.05 = - 4 = -(1+R) M Graphically we can represent 1 + R by the slope of the line between A and W: With project B the rate of return is given by 1 + R = 140,000 = 1.4 100,000 R = 0.4 or 40%. Graphically, 1+R is again the slope of the line between B and A. A Slope = -0.14/0.1 = -1.4 = -(1+R) .2M 16 - (1+R) Slope = -1.2 Projects to the right have steeper slope and so greater return In the more general case where we have the curve representing the production possibilities, the rate of return is given by the slope of the curve. Intuitively, it is worthwhile undertaking a project if the rate of return on it is above the rate of interest at which you can borrow or lend at the bank. We can then see that this is equivalent to the rule we have just derived. 17 We therefore have two ways of choosing the optimal amount of investment and we have seen these are equivalent. 1. Net Present Value Invest so as to maximize the NPV of the investment. This is the difference between the discounted present value of the future income and the amount of the initial investment. 2. Rate of Return Rule Invest up to the point at which the rate of return on the investment is equal to the rate of return on alternative investments (in our case this was the bank). Rules for Managers of Corporations We have derived these as the rules for an individual to follow when choosing his investments in real assets. But are they relevant for the type of firm we are interested in where (i) management and control are separated; (ii) there are many shareholders who may be very different? To answer this question, we go back to our example. Here and in fact throughout Part II we will be assuming that firms are all equity financed. Thus when we talk about borrowing and lending this refers to shareholders borrowing and lending rather than 18 corporations borrowing and lending. We consider firms? borrowing decisions later in the course. Bill Ross has been thinking a bit about the implementation of these projects and decides they involve more work than he first thought. He therefore decides to hire managers to implement the investment in real assets. In order to ensure that they pursue his interests all he has to do is to tell them to maximize the NPV of the firm, and this will ensure that he can be as well off as possible. The issue of how to get managers to maximize NPV is a large part of what corporate governance is concerned with. The important point to note here is: The decision on how to allocate his consumption between youth and old age is independent of the need to maximize the NPV of the firm. No matter whether he has preferences 1 or 2, he will produce at the point that maximizes NPV. With preferences 1 he consumes at D. With preferences 2 he consumes at E. Thus ownership and control can be separated. It is only necessary for the owner to tell 19 the manager to maximize NPV; the owner doesn't need to give a detailed description of how to run the firm. The fact that it doesn't matter what Bill Ross' preferences are as far as the production decision is concerned has very important implications if there is more than one shareholder. Suppose, that in his father's will, the terms under which Bill Ross inherits, actually say that the inheritance "is to be divided equally among his children." The $1M figure was based on the assumption that Bill Ross was the only child. In actual fact it turns out that the father had another brother, Rex, by a former liaison. His inheritance therefore drops to 0.5M. Should they change the operation of the firm that Bill Ross has set up? No. Since the NPV rule we derived was independent of the owner's preferences, it follows that both Bill and Rex are content to leave the firm the way it is. Why is this? What is the situation they face? The production possibilities curve is now half what it was before. 20 Thus even with separate ownership and control and diverse ownership it is the case that it is in the interest of the owners to maximize NPV (or equivalently to use the rate of return rule). The argument is similar for more than two shareholders. All shareholders agree the firm should maximize NPV. Solution to Original Puzzle What the firm should do is maximize NPV. It should accept any of the projects that has a positive NPV. The old lady only cares about consumption now. What this means is that she can borrow and then use shares to repay the loan, or equivalently she can sell them. She is the ultimate spender. Similarly the little boy can deposit profits in the bank. He is the ultimate miser. 21 They agree on the optimal investment policy for the firm. What GM should do is to maximize NPV. The formal statement of all of this is this following. Fisher?s Separation Theorem Provided capital markets are perfect and complete then the firm?s investment decision can be separated from its owner?s consumption decisions. The firm will maximize the welfare of each shareholder if it maximizes NPV. We shall cover what exactly is meant by ?capital markets are perfect and complete? in greater detail later on in the course. Briefly though perfect capital markets require no transaction costs, symmetric information and they are perfectly competitive. Complete markets require that it is possible to vary consumption in every state independently. There are no predetermined ratios of consumption in any state. 1.2 Implementing the NPV Rule Now that we have developed a criterion for making capital budgeting decisions, the next question is how we can implement this in practice. To see this it will be helpful to consider the following example. Motivation Example 2 The Pierpont company is making a decision on whether to build a small plant to make musical instruments. The plant and equipment will cost 1 million. It will last for five years and will have no salvage value at the end of that time. The costs of running the plant are expected to be 100,000 per year. The revenues from selling the instruments are expected to be 375,000 per year. All cash flows occur at the end of the year. The plant and equipment would be depreciated using straight line depreciation. The relevant tax rate is 30 percent. The opportunity cost of capital for the project is 10 percent. The projected income statement for the project is as follows. 22 Revenues 375,000 Operating Expenses -100,000 275,000 Depreciation -200,000 Taxable Income 75,000 Taxes -22,500 Net Income 52,500 Should the plant be built? Since net income is positive each year the project appears attractive. But this ignores a number of factors. The first is that net income is not what is available to be paid out to shareholders. If our aim in capital budgeting is to create shareholder value it's what is available to shareholders which is cash flows that we must focus on in order to implement the NPV rule. Rule 1 Cash flow after taxes, not net income, is the proper basis for capital budgeting analysis. The first thing that we must therefore do is find the cash flow (or "free cash flow" as it is sometimes called). The crucial point in our example is that depreciation is not paid out to anybody it is an accounting charge not a cash flow. We must therefore add it back to net income to get cash flow. Revenues 375,000 Operating Expenses -100,000 275,000 Depreciation -200,000 Taxable Income 75,000 Taxes -22,500 Net Income 52,500 Add back Depreciation +200,000 Cash flow years 1-5 252,500 23 Note that although depreciation is not itself a cash flow, it does have an effect on cash flows. We are not simply subtracting and adding back $200,000. We subtract the $200,000 before tax and add it back after tax. There is thus a tax effect - the depreciation generates a tax shield. If you reduce taxable income by $200,000 it follows you reduce taxes by 0.30 x $200,000 so there is a tax shield of $60,000. The project generates a cash flow of $252,500 a year for five years. Is this enough to offset the original $1 million investment? In implementing the NPV rule we clearly need to take account of the fact that interest could have been earned on the original investment. Rule 2 The timing of cash flows is critical. Date: 0 1 2 3 4 5 Cash flows -1M 252,500 252,500 252,500 252,500 252,500 Taking into account what is actually available to investors gives a very different answer than just relying on net income figures. The interest that could be earned on the money invested means that in fact this is not a profitable project. If the firm undertook it, the decision would actually have destroyed shareholder value and the stock price would have dropped. 42,826- = 1 1. 252,500 + 1 1. 252,500 + 1 1. 252,500 + 1 1. 252,500 + 1.1 252,500 +1M - = NPV 5432 24 The investment project in Motivation Example 2 was a particularly simple one. The cash flows were easy to identify. This is not always the case. The crucial principle in identifying cash flows is summarized in the following. Rule 3 Only incremental cash flows are analyzed (those which occur on the margin because we invest in the project). This rule has a number of components. (i) Include all incidental effects. Include all externalities on other parts of the business. (ii) Do not forget working capital requirements. Working capital is the money you need to fund day-to-day operations of the firm. It is the money to fund inventories, accounts receivable and so forth. Working capital (or equivalently net working capital as it is sometimes referred to) is defined as current assets less current liabilities. Any increase in working capital must be funded, i.e. it is a negative cash flow. Any decrease in working capital releases money, i.e. it is a positive cash flow. (iii) Forget sunk costs. Sunk costs are expenditures which have already been made. These are irreversible and should not be included in the cash flows. There's nothing you can do about them--bygones are bygones. (e.g. R&D) (iv) Include opportunity costs. If a firm already owns land which it is considering using in a project, it should take into account the fact that it could sell the land, 25 raise cash and invest the money if it does not go ahead with the project. Thus there is an opportunity cost to the land. (v) Be careful with allocated costs such as overhead. The crucial issue here is whether items such as overhead will go up because the project is undertaken. If overhead does go up then the change is an incremental cash flow. If it stays the same then there is no incremental cash flow. Motivation Example 2 highlights the importance of accounting for corporate finance. Good investment decisions require good information about the cash flows that are generated by the project under consideration. This requires a thorough knowledge of accounting. Motivation Example 2 also had constant cash flows. In reality, of course, forecasting cash flows. This is a crucial aspect of corporate finance but receives little attention. Rule 4 Be consistent in the treatment of inflation The first thing is to clarify the distinction between nominal and real. Nominal: The actual number of dollars and actual interest rates Real: What would have happened in the absence of inflation: )rate inflation + (1 tdateat flow cash Nominal = tdateat flow cash Real t 26 The important point with nominal and real is that, in the context of capital budgeting, they are two ways of thinking about the same thing. You must be consistent and stick with one or the other. Either discount nominal cash flows at a nominal discount rate, or discount real cash flows at a real discount rate. Provided you do this, it doesn't matter whether you work in real or nominal terms. Usually in the U.S., Europe and Japan people deal in nominal terms since this is the form in which the data is presented. However, in high inflation countries such as most Latin American countries until recently it's often easier to work in real terms since you usually have a much better feel for the numbers and pick up errors more quickly. For example, if inflation was 20% per year and an entry level car now costs ?1 million, how much would it cost in five years time? Would it be $2 million or $2.5 million. Is either of these figures unreasonable? It's difficult to tell. In fact it would be around $2.5 million. What about in ten year's time? Would it be $5 million or $6 million? In fact it would be about $6.2 million. If you work in real terms you might pick up more easily what is reasonable. It becomes difficult to pick out mistakes if the magnitudes are unfamiliar. 1.3 Risk and Investment Decisions When undertaking investments there are many different kinds of risk involved. Examples are business risk, political risk and foreign exchange risk to name a few. In the previous sections when we were deriving the NPV rule we had made the simplification that we could represent the capital markets by a bank. This has meant that we have so far been rate Inflation + 1 ratediscount Nominal + 1 = ratediscount Real+ 1 27 unable to explicitly discuss risk because our alternative has always been putting money in the bank, i.e. it was effectively safe. Implicitly we were assuming everything was the same risk. In practice, of course, the capital markets are much more than just banks they consist of the stock market, options and futures markets and so on. If we extend our notion of capital markets to include these other possibilities we can start to deal with risk in a more satisfactory way. Let's start once again with a motivation example. Motivation Example 3 Suppose Toyota was thinking of investing in a project in the refrigerator industry. What should it use as its cost of capital? Should it use its own cost of capital in the auto industry (say 15%) or should it use the cost of capital in the refrigerator industry (say 20%)? It is tempting to argue that it should use its own cost of capital from the auto industry. If it uses 15% many more projects will seem attractive than if it uses 20%. This would be incorrect though. Remember that cost of capital is short for opportunity cost of capital. The crucial point here is summarized in the following. Rule 5 Risk must be compensated. The riskier a project's cash flows become, the higher the rate of return which will be required. The notion of opportunity cost is that investors could be investing in some alternative investment. If there are different degrees of risk we clearly have to allow for this by ensuring that when we consider the best available alternative it has the same risk as our project. 28 When deciding on an opportunity cost we must find a stock or other security which has the same risk as our project. Otherwise we will have a discount rate which doesn't properly take account of the risk we are bearing. Hence in our Motivation Example 3, Toyota should use as its discount rate the opportunity cost of capital in the refrigerator industry which is 20%. Otherwise it will not be being properly compensated for the risk it is bearing. If it accepted projects which looked good at 15% but not at 20% it would be destroying shareholder value. The model of risk that is usually advocated in the corporate finance literature is the Sharpe-Lintner Capital Asset Pricing Model or CAPM for short. The opportunity cost of capital for discounting is now given by Motivation Example 4A Consider the following two investments. (i) A lone prospector intends to search for gold in the Rockies and is issuing 100 shares to finance his expenses. The evidence suggests that if he strikes gold he will hit it big and the payoff on the project will be $100. However, the probability of this is only 10 percent. There is a 90 percent chance he will find no gold in which case the payoff on the project will be $0. Hence the expected payoff is $10. (ii) Another investment is 100 shares of an electric utility. If the economy does well a lot of electricity will be used, the utility's profits will be high and its stock will yield a gross payoff of $15. The probability of this happening is 50 percent. The other possibility is that the economy does badly and not much electricity is used. In this case the payoff on the firm's 29 stock is $5. The probability of this happening is 50 percent so the expected payoff is again $10. Both of these investments have the same expected return. Which of them is more risky in a financial sense? Motivation Example 4B Suppose T-bills are yielding 4%. Is it ever worthwhile investing in a risky stock yielding a total return (i.e. including dividends and capital gains) of 3%? The CAPM which is the model that underlies the answers to these questions is r = r F + β(r M - r F ) where r F - risk free rate (e.g., T-bill rate) r M - return on market portfolio (e.g., a value-weighted portfolio of all stocks on the NYSE) β = Measure of risk = Cov (Stock, Market portfolio) Var (Market portfolio) Notice that what's important in the measure of risk is covariance with the market portfolio. You can see from this why we get the results that we do in the motivation examples. In Motivation Example 4A the gold prospecting is an example where β = 0 and the electric utility example is one where β > 0 so the gold prospecting has less risk. In Motivation Example 4B β < 0 and it would be worth holding the stocks. Understanding why covariances matter is the core concept in understanding risk. 30 1.4 The Advantages of NPV as an Investment Criterion Now that the way in which the NPV criterion operates has been demonstrated, it is necessary to explain why it has advantages over the rate of return rule or in its more general form the internal rate of return rule or IRR for short and other traditional criteria. To fix ideas consider the following. Motivation Example 5 Consider a project with the following cash flows: C 0 C 1 C 2 C 3 -925 +1000 +1400 -1500 Initial Clean-up Investment Costs Internal Rate of Return = 4.6% Opportunity Cost of Capital = 10% Should we accept this project? The natural answer seems to be no because the rate of return on the project is 4.6%. But the actual answer is yes since if you work it out, NPV = 14. Had you rejected it, you would have lost an opportunity to make money. The explanation of this puzzle is that if you use rate of return without taking great care, you get the wrong answer. In the one period case we considered before, the one period rate of return R was given by 31 1 + R = Payoff => 1 + R = C 1 => C 0 + C 1 = 0 __________ ___ ______ Investment -C 0 1 + R In the more general case with more than one period it is not entirely clear what is meant by the rate of return, so instead we use the more general concept of IRR. What is the IRR? The IRR extends the last form given above for the rate of return. It is the rate you discount at such that the discounted cash flow (DCF) is zero. The DCF is a function of the rate, i, and the cash flows: T T 2 21 0 )i1( C ... )i1( C i1 C C)i(DCF + ++ + + + += The IRR is the value of i such that DCF = 0, i.e.: 0 )IRR1( C ... )IRR1( C IRR1 C C)IRR(DCF T T 2 21 0 = + ++ + + + += Let us continue with our motivation example i = 0%: DCF = -925 + 1000 + 1400 - 1500 = -25 < 0 i = 10%: DCF = -925 + 1000 + 1400 - 1500 = 14 > 0 ____ ____ ____ 1.1 1.1 2 1.1 3 i = 30% DCF = -925 + 1000 + 1400 - 1500 = -10 < 0 ____ ____ ____ 1.3 1.3 2 1.3 3 We thus have the following situation 32 IRR is much more difficult to use than NPV. There are a number of other problems which we won?t go into here. These are covered in detail in MBA courses.