loans

Uncertainty in Capital Budgeting, Debt, and Equity

admin — Fri, 23 Oct 2009 20:20:59 +0000

We now turn to the problem of selecting projects under uncertainty. Your task is to compute present values with imperfect knowledge about future outcomes. Your principal tool in this task will be the payoff table (or state table), which assigns probabilities to the project value in each possible future value-relevant scenario. For example, a ﬂoppy disk factory may depend on computer sales (say, low, medium, or high), whether ﬂoppy disks have become obsolete (yes or no), whether the economy is in a recession or expansion, and how much the oil price (the major cost factor) will be. Creating the appropriate state table is the manager’s task— judging how the business will perform depending on the state of these most relevant variables. Clearly, it is not an easy task even to think of what the key variables are, to determine the probabilities under which these variables will take on one or another value. Assessing how your own project will respond to them is an even harder task—but it is an inevitable one. If you want to understand the value of your project, you must understand what the project’s key value drivers are and how the project will respond to these value drivers. Fortunately, for many projects, it is usually not necessary to describe possible outcomes in the most minute detail— just a dozen or so scenarios may be able to cover the most important information. Moreover, these state tables will also allow you to explain what a loan (also called debt or leverage) and levered ownership (also called levered equity ) are, and how they differ.

Risk-Averse Investors Have Demanded Higher Expected Rates

admin — Sat, 10 Oct 2009 20:17:31 +0000

We have assumed that investors are risk-neutral—indiﬀerent between two loans that have the same expected rate of return. As we have already mentioned, in the real world, risk-averse investors would demand and expect to receive a little bit more for the risky loan. Would you rather invest into a bond that is known to pay oﬀ 5% (for example, a U.S. government bond), or would you rather invest in a bond that is “merely” expected to pay oﬀ 5% (such as my 6.63% bond)? Like most lenders, you are likely to be better oﬀ if you know exactly how much you will receive, rather than live with the uncertainty of my situation. Thus, as a risk-averse investor, you would probably ask me not only for the higher promised interest rate of 6.63%, which only gets you to an expected interest rate of 5%, but an even higher promise in order to get you more than 6.63%. For example, you might demand 6.75%, in which case you would expect to earn not just 5%, but a little more. The extra 12 basis points is called a risk premium, and it is an interest component required above and beyond the time premium (i.e., what the U.S. Treasury Department pays for use of money over time) and above and beyond the default premium (i.e., what the promised interest has to be for you to just expect to receive the same rate of return as what the government oﬀers).
Recapping, we know that 5% is the time-value of money that you can earn in interest from the Treasury. You also know that 1.63% is the extra default premium that I must promise you, a risk-neutral lender, to allow you to expect to earn 5%, given that repayment is not guaranteed. Finally, if you are not risk-neutral but risk-averse, I may have to pay even more than 6.63%, although we do not know exactly how much.
If you want, you could think of further interest decompositions. It could even be that the time-premium is itself determined by other factors (such as your preference between consuming today and consuming next year, the inﬂation rate, taxes, or other issues, that we are brushing over). Then there would be a liquidity premium, an extra interest rate that a lender would demand if the bond could not easily be sold—resale is much easier with Treasury bonds.
We can preview the relative importance of these components for you in the context of corporate bonds. The highest-quality bonds are called investment-grade. A typical such bond may promise about 6% per annum, 150 to 200 basis points above the equivalent Treasury. The probability of default would be small—less than 3% in total over a ten-year horizon (0.3% per annum). When an investment-grade bond does default, it still returns about 75% of what it promised. For such bonds, the risk premium would be small—a reasonable estimate would be that only about 10 to 20 basis points of the 200 basis point spread is the risk premium. The quoted interest rate of 6% per annum therefore would reﬂect ﬁrst the time premium, then the default premium, and only then a small risk premium. (In fact, the liquidity premium would probably be more important than the risk premium.) For low-quality corporate bonds, however, the risk premium can be important. Ed Altman has been collecting corporate bond statistics since the 1970s. In an average year, about 3.5% to 5.5% of low-grade corporate bonds defaulted. But in recessions, the default rate shot up to 10% per year, and in booms it dropped to 1.5% per year. The average value of a bond after default was only about 40 cents on the dollar, though it was as low 25 cents in recessions and as high as 50 cents in booms. Altman then computes that the most risky corporate bonds promised a spread of about 5%/year above the 10-Year Treasury bond, but ultimately delivered a spread of only about 2.2%/year. 280 points are therefore the default premium. The remaining 220 basis points contain both the liquidity premium and the risk premium—perhaps in roughly equal parts.

Random Variables and Expected Values

admin — Sat, 03 Oct 2009 20:09:02 +0000

The most important statistical concept is the expected value, which is most often just a fancy phrase for mean or average. The only necessary clariﬁcation is that we use “means” and “averages” for past outcomes and “expected value” for future outcomes.
For example, say you toss a coin, which can come up with either heads or tails and with equal probability. You receive $1 if the coin comes up heads and $2 if the coin comes up tails. Because you know that there is a 50% chance of $1 and a 50% chance of $2, the expected value of each coin toss is $1.50—repeated inﬁnitely often, the mean will be exactly $1.50. Of course, exactly $1.50 will never come up—the expected value does not need to be a possible realization of a single coin toss.
Statisticians have invented the concept of random variables to make it easier to work with uncertainty. A random variable is a variable whose value (i.e., outcome) has not yet been determined. In the coin toss example, we can deﬁne a random variable named c (for “coin toss outcome”) that takes the value $1 with 50% probability and the value $2 with 50% probability. The expected value of c is $1.50. To distinguish a random variable from an ordinary non-random variable, we use a tilde over the variable. To denote the expected value, we use the notation E . So, in this bet, E ( c ) = 50% · $1 + 50% · $2 = $1.50 Expected Value(of Coin Toss) = Prob ( Heads ) · $1 + Prob ( Tails ) · $2 .
After the coin has been tossed, the actual outcome c could, e.g., be c = $2 , and c is no longer a random variable. Also, if you are certain about the outcome, perhaps because there is only one possible outcome, then the actual realization and the expected value are the same. The random variable is then really just an ordinary non-random variable. Is the expected outcome of the coin toss a random variable? No: we know the expected outcome is $1.50 even before we toss the coin. The expected value is known, the uncertain outcome is not. The expected value is an ordinary non-random variable; the outcome is a random variable. Is the outcome of the coin throw after it has come down heads a random variable? No: we know what it is (heads), so it is not a random variable.

An Introduction to Statistics

admin — Sat, 26 Sep 2009 20:07:09 +0000

Statistics has a reputation of being the most painful of the foundation sciences for ﬁnance—but we absolutely need it to describe an uncertain future. Fortunately, although statistics can be a diffcult subject, if you have ever placed a bet in the past, chances are that you already have a good intuitive grasp of what you need. In fact, I had already sneaked the term “expected” into previous posts, even though we only now ﬁrm up your knowledge of this important statistical concept.

Annualized Rates of Return

admin — Sat, 19 Sep 2009 20:06:07 +0000

Time-varying rates of return create a new complication, that is best explained by an analogy. Is a car traveling 258,720 yards in 93 minutes fast or slow? It is not easy to say, because you are used to thinking in “miles per sixty minutes,” not in “yards per ninety-three minutes.” It makes sense to translate speeds into miles per hour for the purpose of comparing speeds. You can even do this for sprinters, who cannot run a whole hour. Speeds are just a standard measure of the rate of accumulation of distance per unit of time.
The same issue applies to rates of return: a rate of return of 58.6% over 8.32 years is notas easy to compare to other rates of return as a rate of return per year. So, most rates of return are quoted as average annualized rates. Of course, when you compute such an average annualized rate of return, you do not mean that the investment earned the same annualized rate of return of, say, 5.7% each year—just as the car need not have traveled at 94.8 mph (258,720 yards in 93 minutes) each instant. The average annualized rate of return is just a convenient unit of measurement for the rate at which money accumulates, a “sort-of-average measure of performance.”
So, if you were earning a total three-year holding return of 173% over the three year period, what would your average annualized rate of return be? The answer is not 173%/3 ≈ 57.7%,
because if you earned 57.7% per year, you would have ended up with (1 + 57.7%) · (1 + 57.7%) · (1 + 57.7%) − 1 = 287%, not 173%. This incorrect answer of 57.7% ignores the compounded interest on the interest that you would earn after the ﬁrst year and second year. Instead, you need to ﬁnd a single hypothetical rate of return which, if you received it each and every year, would give you a three-year rate of return of 173%.

All Inﬂows or just All Outﬂows

admin — Tue, 15 Sep 2009 17:22:33 +0000

Now, the same argument applies to dividends: in the end, all earnings must be paid out (i.e., as dividends). This does not need to occur at the same time: your earnings can grow today, and your dividends can be zero or be shrinking today. In our earlier example, ﬁrm G could be a slow dividend payer or a fast dividend payer. It could pay $100 now, $150 next year and $250 in two years. Or, it could reinvest the money, effectively on your behalf, (at the same 10%, of course), and then pay one big lump sum dividend of $100 • (1 + 10%) + $150 • (1 + 10%) + $250 = $536 at the end of period 2. The dividend payout policy does not affect G’s value today. The important point is that the net present value of your total earnings and your total dividends must both be equal to the price of the ﬁrm in our perfect world—or you would get something for nothing or lose something for nothing.
This simple insight is the basis of the “Modigliani-Miller” (M&M) theorems, which won two Nobel prizes in economics. Remember, though, that the “perfect market” assumption is important—the value of the ﬁrm is only the discounted value of all future dividends or all future earnings if markets are not too far from perfect. This is reasonable enough an assumption for large company stocks traded in the United States, but not necessarily the case for small, privately held ﬁrms. You should also realize that over any limited time horizon, neither dividends nor earnings may represent value well—dividends can be zero for a while, earnings can be negative, and the ﬁrm can still have tremendous and positive value.
There is an important corollary. If General Electric is about to win or has just had some great luck, having won a large defense contract (like the equivalent of a lottery), shouldn’t you purchase GE stock to participate in the windfall? Or, if Wal-Mart managers do a great job and have put together a great ﬁrm, shouldn’t you purchase Wal-Mart stock to participate in this windfall? The answer is that you cannot. The old shareholders of Wal-Mart are no dummies. They know the capabilities of Wal-Mart and how it will translate into cash ﬂows. Why should they give you, a potential new shareholder, a special bargain for something that you contributed nothing to? Just providing more investment funds is not a big contribution—after all, there are millions of other investors equally willing to provide funds at the appropriately higher price. It is competition—among investors for providing funds and among ﬁrms for obtaining funds— that determines the expected rate of return that investors receive and the cost of capital that ﬁrms pay. There is actually a more general lesson here. Economics tells us that you must have a scarce resource if you want to earn above-normal proﬁts. Whatever is abundant and/or provided by many will not be tremendously proﬁtable.

IT REALLY HELPS IF YOU CAN MAINTAIN SOME PERSPECTIVE

admin — Sat, 29 Aug 2009 20:01:03 +0000

“To understand what the outside of an aquarium looks like, it is better not to be a fish.”
André Malraux
Back in 1974, when I was working as a junior analyst on Wall Street, I used to circulate a weekly tongue-in-cheek stock market report among my fellow employees. The newsletter was mostly satire, poking fun at some of the idiosyncrasies and absurdities of Wall Street. In the fall of 1974 the Dow Jones Industrial Average was trading below 600, trading volume was running at around 6 million shares, and on most days you could have organized a good racketball tournament on the floor of the New York Stock Exchange and not annoyed anybody because nothing much was going on down there anyway. Things were so slow that a major investment magazine ran a cover story entitled: “This Is Not Just a Bear Market. This Is the Way Things Are Going to Be from Now On.” (The experts were wrong, of course.) During lunch, we would sit around and lazily watch the ticker tape move across the top of our quote machines, that is, when it moved at all. In those days, the tape moved in fits and starts; a couple of trades would show up, then the tape would just sit there, and not move for 10 or 20 seconds, and then another solitary trade would be reported. Sometimes the tape would stop for such a prolonged period of time that we would tap the side of the computer screen, as if we were tapping the side of a pinball or videogame, trying to get the tape moving again.
On some days the trades were so few and far between we were able to sit around and comment at length on each trade that appeared on the tape before the next one appeared. This got me to thinking about the potential for a television program in which a group of analysts just sat around and commented on the New York Stock Exchange ticker tape all day long.
My friends got a big laugh out of that one. A few days later I published my weekly stock market “report” in which I imagined what it would be like if Howard Cosell, Frank Gifford, and “Dandy” Don Meredith, the hosts of ABC-TV’s Monday Night Football, were to host a live daily television program direct from the New York Stock Exchange.
As I envisioned it, Howard Cosell and Frank Gifford would be sitting in a booth high above the New York Stock Exchange trading floor, much as political commentators sit above the floor of a political convention, watching a huge ticker tape and providing a trade-by-trade commentary on the day’s stock market action.
Meanwhile, Don Meredith, a former Dallas Cowboys’ quarterback, would serve as the sideline commentator, roaming the floor of the NYSE, elbowing his way through the mass of traders and looking for expert analysis and inside scoops. What a laugh, right? Little did I know.
There’s nothing wrong with minute-by-minute analysis of the financial markets and the fact that so much market analysis and commentary is so short-term-oriented. There are many ways to skin the proverbial stock market cat, and many approaches to the market that can yield profitable results.
And, there is no use complaining about it. In the age of the Internet and instant information, when complete access to the floor of the New York Stock Exchange is available, you cannot expect that all of this will not be put to use. You can question whether it really matters what the stock market does on any given day, or during any given hour, and you can wonder if much of the short-term commentary you hear day in and day out is of much real value. (You can wonder, for example, how it is possible for a guest to sit there, on live television, and respond to question after question from viewers calling on the telephone, asking about a series of random stocks. How can this “expert” possibly provide a thoughtful, informed response on every single question?)
You can wonder about all of this, but you can’t fight it, and besides, there is a market for this type of information. Plenty of investors apparently find it useful or there would not be such a wide audience for CNBC and stock message boards. Short-term trading, based on instant analysis, is a perfectly acceptable way to approach the stock market. Just ask any trader.
But it is not the only way. And the problem is since so much of the mainstream media has become fixated on this ultra-short-term approach to investing, there is a tendency to forget that there are other approaches that do not make you feel guilty if you leave your quote machine or turn off the financial television station for 10 minutes. You can, if you wish, be made aware of every uptick and downtick of the market, all day, every day. You can know about every analyst upgrade and downgrade and why any stock is moving on any given day. You can know all of the important earnings estimates, down to the last penny; you will also know the “whisper number”; you will know if the company that has just reported earnings managed to beat the official estimate, the “whisper number”, or both; and you can even hang around after the close to see if the lemmings are frantically buying or selling in after-hours trading, based on the burning issue of the moment, which in all probability will be replaced the next day by another, completely unrelated burning issue of the moment. You can put yourself through this madness, if you like. But there is another way to deal with the stock market. You can decide to take a step back from the precipice of urgent microanalysis and deal with the stock market only from a vantage point that provides some perspective.
This vantage point involves looking for stocks that are showing signs that something significant is changing—for the better—on a long-term basis. You can look at neglected stocks that have fallen so far out of favor that you have to begin to remind yourself that this is a business, not just a piece of paper for Wall Street to play games with, and that if certain Telltale Signs are popping up, there is a good possibility that somebody will step in and force the stock market to value this neglected stock at its proper value as a business.
In this blog, you will learn how to spot some of the Telltale Signs that will enable you to buy these out-of-favor stocks with confidence. We will show you how to determine when a formerly sleepy, seemingly uninteresting stock may be about to emerge as a huge winner. In short, we have arrived at a fork in the stock market road— this blog will take you on a trip down the road less traveled. And once you’ve been down this road, you will never look at the frantic three-ring circus of urgent day-to-day stock market commentary and “expert” analysis in quite the same way.