Financial poster

Let us expand on this insight that projects may not have unique values. Have you ever heard someone say “it’s only worth what people are willing to pay for it” and someone else that “it’s worth much more than it’s being sold for”? Who is correct? Are there any good deals? The answer is that both are correct and neither is correct. The first claim is really meaningful only to the extent that markets are perfect: if a market is perfect, items are indeed worth exactly what buyers are willing to pay for them. The second claim is really (sort of) meaningful only to the extent that markets are imperfect: if a market is imperfect, items have no unique value. Different people can place different values on the item, and you may consider an item worth much more than what it was sold for.
In finance, we often “conveniently” assume perfect markets. Although not perfectly accurate, this is often reasonably justifiable. For example, take the market for trading shares of stock in PepsiCo. It definitely appears to be a competitive market, i.e., a situation in which there are many competing buyers and sellers, so that no single buyer or seller can influence the price. There are lots of potential buyers willing to purchase the shares for the same price (or maybe just a tiny bit less), and lots of potential sellers willing to sell you shares for the same price (or maybe just a tiny bit more). A “perfect market” is a stricter requirement than a “competitive market” assumption. If a market is perfect, then it is also competitive, but not vice-versa. (For example, a competitive market can exist even in the presence of opinions and taxes.) For our discussion, we hope you can further assume that taxes are not distorting rates of return in a way that makes the PepsiCo shares’ rates of return to a seller any higher or lower than the equivalent rates of return to a buyer, so that taxes are not distorting holding decisions. (This assumption may be a little, but probably not too far off from reality.) Moreover, few active traders in the market have inside information, so objective information differences should not be too bad either. Everyone should roughly agree to what shares can be sold for tomorrow—which defines value today. Finally, the transaction costs of trading shares on the New York Stock Exchange (NYSE) are very low. There are no costs of having to find out the proper price of PepsiCo shares (it is posted by the NYSE), and there are no costs to searching for a buyer or seller. So, the market for PepsiCo shares may indeed be reasonably close to perfect.
Such perfect markets reduce buyers’ and sellers’ concerns that one deal is better than another—. that buying is better than selling, or vice-versa. For a more concrete example, consider gasoline and imagine that you do not yet know when and where on your road trip you will need to pump more gas. Unlike shares of stock, gas is not the same good everywhere: gas in one location can be more valuable than gas in another location (as anyone who has ever run out of gas can confirm). But, in populated areas, the market for gasoline is pretty competitive and close to perfect—there are many buyers (drivers) and sellers (gas stations). This makes it very likely that the first gas station you see will have a reasonable, fair price. If you drive by the first gas station and it advertises a price of $1.50 per gallon, it is unlikely that you will find another gas station offering the same gas for $1 per gallon or $2 per gallon within a couple of miles. Chances are that “the price is fair,” or this particular gas station would probably have disappeared by now. (The same applies of course in many financial markets, such as large company stocks, Treasury bonds, or certain types of mortgages.) As long as the market is very competitive, or better yet perfect, most deals are likely to be fair deals. Some shopping around may help a tiny bit, but an extreme amount of shopping would likely cost more in time and effort than what it could save.
But there is an important conceptual twist here: Paying what something is worth does not necessarily mean that you are paying what you personally value the good for. Even in competitive perfect markets, there can be many different types of buyers and sellers. It is only the marginal buyer and the marginal seller who end up trading at their “reservation values,” where they are exactly indifferent between participating and not participating—but if you are not marginal, a market will allow you to make yourself better off. For example, if you are running out of gas and you are bad at pushing two-ton vehicles, you might very well be willing to pay a lot more for gas than even $10 per gallon—and fortunately all you need to pay is the market price of $1.50 per gallon! The difference between what you personally value a good for and what you pay for it is called your “surplus.” So, even though everyone may be paying what the good is worth in a perfect market, most buyers and sellers can come away being better off.
Unfortunately, not every good is traded in a perfect market. Let us consider selling a house. What is the value of the house? What if the house is in a very remote part of the country, if potential buyers are sporadic, if alternative houses with the same characteristics are rare, and if the government imposes a 50% transfer fee? Now the value of the house depends on the luck of the draw (how many potential buyers are in the vicinity and see the ad, whether a potential buyer wants to live in exactly this kind of house, and so on), the urgency of the seller (perhaps whether the seller has the luxury to turn down a lowball first offer), and the identity of the seller (the current owner does not need to pay the government transfer fee, so he may value the house more than a potential buyer). So, it is only easy to determine the value of a good if the market is perfect. Because the market for many houses is not even close to perfect, the values of such houses are not unique.
Similarly, not all financial markets are close to perfect. Transaction costs, information differences, special taxes, or the unique power of the seller or market can play a role even in some financial markets. For example, many corporate bonds are traded primarily over-the-counter, meaning that you must call some individual at the brokerage house, who may play the role of the only easy clearinghouse for these particular bonds and who will try to gauge your expertise while negotiating a price with you. You could easily end up paying a lot more for this bond than what you could then sell it for one minute later.
Of course, you should not kid yourself: no market, financial or otherwise, is ever “perfectly perfect.” The usefulness of the perfect market concept is not that you should believe that it actually exists in the real world. Instead, it is to get you to think about how close to perfect a given market actually is. The range in which possible values lie depends on the degree to which you believe the market is not perfect. For example, if you know that taxes or transaction costs can represent at most 2–3% of the value of a project, then you know that even if value is not absolutely unique, it is pretty close to unique—possible values sit in a fairly tight range. On the other hand, if you believe that there are few potential buyers for your house, but that some will purchase the house at much higher prices than others, then it will depend on your financial situation whether you will accept or decline a buyer’s low-ball offer.
In sum, when someone claims that a stock or firm is really worth more than he or she is selling it for, there are only a small number of explanations: First, there may be pure kindheartedness toward any buyer or a desire by a seller to lose wealth; this happens so rarely that we just ignore this. Second, the seller may not have access to a perfect market to sell the goods. This may make the seller accept a low amount of money for the good, so depending on how you look at this, the good may be sold for more or less than you think it is worth. Third, the seller may be committing a conceptual mistake. The good is worth neither more nor less than what it is being sold for, but exactly how much it is being sold for. Fourth, the seller may be lying and is using this claim as a sales tactic.

In a perfect market, the value of the project depends only on the project, and not on you personally or on your cash position. This is often called the “separation of investments and financing decisions.” You could make investment choices based on the quality of the projects themselves, not based on how you would end up financing them. The NPV formula does not have an input for your identity or wealth—its only inputs are the project’s cash flows and the rate of return on alternative investments.
But if the borrowing and lending rates are not the same, then the value of the project depends An example. on your cash holdings. For example, assume that you can lend money (invest cash) at 3%, and borrow money (receive cash) at 7%. What is the present value of a project that invests $1,000 today and returns $1,050 next period?
• If you have $1,000 and your alternative is to invest your money in the bank, you will only get $1,030 from the bank. You should take this project to earn $20 more than you could earn from the bank.
• If you do not have the $1,000, you will have to borrow $1,000 from the bank to receive $1,050 from the project. But because you will have to pay the bank $1,070, you will lose $20 net. You should not take the project.
The proper project decision now depends on how much cash you have. The separation between your project choice and your financial position has broken down. Taking your current cash holdings into account when making investment choices of course makes capital budgeting decisions more difficult. In this example, it is fairly easy—but think about projects that have cash inflows and outflows in the future, and how decisions could interact with your own wealth positions in the future. Equally important, in imperfect markets, the project value is no longer unique, either. In our example, it could be anything between $19.42 ($1,050 discounted at 3%) and −$18.69 ($1,050 discounted at 7%).

A perfect market is defined by the following assumptions:
No Differences in Information Everyone holds the same opinion. How can this assumption be violated? Here is one example. If your bank believes that there is a 50% chance that you will go bankrupt and default, and you believe that there is only a 0.1% chance, then your bank will lend you money only if you pay a much higher expected interest rate than it will pay you if you deposited your money with it.
This is why our perfect markets assumptions includes one that everyone has the same information and agrees on what it means. (It does not mean that there is no uncertainty, however. The important point in a perfect market is that everyone interprets the uncertainty identically.)
A Deep Market You can easily find a buyer or a seller. How could this assumption be violated? Say there is only one bank that you can do business with. This bank will exploit its monopoly power. It will charge you a higher interest rate if you want to borrow money from it than it will pay you if you want to deposit your money with it—and you will have no good alternative. (There is one nitpick qualification: if a project is worth more if it is owned or financed by a particular type—e.g., if a golf range is owned by a golf pro—then there must be a large number of this type of owner.)
This is why our perfect markets assumptions includes one that there are infinitely many buyers and sellers.
No Transaction Costs You can trade without paying any transaction costs. How can this assumption be violated? If it costs $1,000 to process the paperwork involved in a loan, you will incur this cost only if you need to borrow, but not if you want to save. This will make your effective borrowing interest rate higher than your effective savings interest rate. This is why our perfect markets assumptions includes one that there are no transaction costs.
No Taxes There are no tax advantages or disadvantages to buying or selling securities. Specifically, there are no asymmetric tax treatments to the seller divesting or to the buyer purchasing. How can this be violated? If you have to pay taxes on interest earned, but cannot deduct taxes on interest paid, your de facto savings rate will be lower than your borrowing rate.
This is why our perfect markets assumptions includes one that there are no taxes. We will soon tackle each of these issues in detail. However, the effect of violating any of these assumptions is really the same. Any violation that breaks the equality between the borrowing and the savings rate also breaks the link between value and one unique price (or cost). In fact, the value of a project may not even have meaning in imperfect markets—a project may not have one unique value, but any from among a range of possible values.