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Does this mean that it does not matter how much cash you hold? Of course not. The marginal value of liquidity declines as you hold increasing amounts of cash. When you have only a small proportion of your assets in cash, a little extra can be extremely useful; when you have a substantial holding, any additional liquidity is not worth much. Therefore, as financial manager you want to hold cash balances up to the point where the marginal value of the liquidity is equal to the value of the interest forgone.

If that seems more easily said than done, you may be comforted to know that production managers must make a similar trade-off. Ask yourself why firms carry inventories of raw materials. They are not obliged to do so; they could simply buy materials day by day, as needed. But then they would pay higher prices for ordering in small lots, and they would risk production delays if the materials were not delivered on time. That is why they order more than the firm’s immediate needs.11

But there is a cost to holding inventories. Interest is lost on the money that is tied up in inventories, storage must be paid for, and often there is spoilage and deterioration. Therefore production managers try to strike a sensible balance between the costs of holding too little inventory and those of holding too much.

It is exactly the same with cash. Cash is just another material that you require to carry on production. If you keep too small a proportion of your funds in the bank, you will need to make repeated sales of securities every time you want to pay your bills. On the other hand, if you keep excessive cash in the bank, you are losing interest.

The Inventory Decision

Let us look at what economists have had to say about managing inventories and then see whether some of these ideas may also help us to manage cash balances. Here is a simple inventory problem.

Everyman’s Bookstore experiences a steady demand for Principles of Corporate Finance from customers who find that it makes a serviceable doorstop. There are two costs to holding an inventory of the book. First there is the carrying cost. This includes the cost of the capital that is tied up in the inventory, the cost of the shelf space, and so on. The second type of cost is the order cost. Each order involves a fixed handling expense and delivery charge.

These two costs are the kernel of the inventory problem. An increase in order size increases the average number of books in inventory, and therefore the carrying cost rises. However, as the store increases its order size, the number of orders falls, so that the order costs decline. The trick is to strike a sensible balance between these two costs. When carrying costs are high, you should hold a smaller inventory and replenish it more often. When order costs are high, you should hold a larger inventory and place orders less frequently.

Some numbers may help to illustrate. Suppose that the bookstore sells 100 copies of the book a year. Suppose also that the carrying cost of inventory works out at $4 per book and that each order placed with the publisher involves a fixed order cost of $2. The upward sloping line in Figure 31.3 shows that carrying costs increase in proportion to order size. The effect of order size on order costs is de-

11Not much more in many manufacturing operations. “Just-in-time” assembly systems provide for a continuous stream of parts deliveries, with no more than two or three hours’ worth of parts inventory on hand. Financial managers likewise strive for just-in-time cash management systems, in which no cash lies idle anywhere in the company’s business. This ideal is never quite reached because of the costs and delays discussed in this chapter. Large corporations get close, however.

bills. On the other hand, if the firm incurs high costs in selling securities, you should hold larger cash balances.

The Cash Management Trade-off

Baumol’s model of cash balances is unrealistic in one important respect: It assumes that the firm is steadily using up its cash inventory. But that is not what usually happens. In some weeks the firm may collect some large unpaid bills and therefore receive a net inflow of cash. In other weeks it may pay its suppliers and so incur a net outflow of cash. Some of these cash flows can be forecasted with confidence; in other cases the amount of the flow or its timing is uncertain.

Economists and management scientists have developed a variety of more elaborate and realistic models that allow for the possibility of both cash inflows and outflows.14 But no model will ever succeed in capturing all the intricacies of the firm’s cash requirements or provide a substitute for the judgment of the cash manager. The importance of Baumol’s model and its many offspring is that they all highlight the basic trade-off that the cash manager needs to make between the fixed costs of selling securities and the carrying costs of holding cash balances. Since there are economies of scale in buying or selling securities, the firm should wait and place a sufficiently large order rather than place a series of smaller orders.

Baumol’s model helps us understand why small and medium-sized firms hold significant cash balances. But for very large firms, the transaction costs of buying and selling securities become trivial compared with the opportunity cost of holding idle cash balances.

Suppose that the interest rate is 8 percent per year, or roughly 8/365 .022 percent per day. Then the daily interest earned by $1 million is .00022 1,000,000 $220. Even at a cost of $50 per transaction, which is generously high, it pays to buy Treasury bills today and sell them tomorrow rather than to leave $1 million idle overnight.

A corporation with $1 billion of annual sales has an average daily cash flow of $1,000,000,000/365, about $2.7 million. Firms of this size end up buying or selling securities once a day, every day, unless by chance they have only a small positive cash balance at the end of the day.

Why do such firms hold any significant amounts of cash? There are basically two reasons. First, cash may be left in non-interest-bearing accounts to compensate banks for the services they provide. Second, large corporations may have literally hundreds of accounts with dozens of different banks. It is often better to leave idle cash in some of these accounts than to monitor each account daily and make daily transfers between them.

One major reason for the proliferation of bank accounts is decentralized management. You cannot give a subsidiary operating autonomy without giving its managers the right to spend and receive cash.

Good cash management nevertheless implies some degree of centralization. You cannot maintain your desired inventory of cash if all the subsidiaries in the group are responsible for their own private pools of cash. And you certainly want to avoid situations in which one subsidiary is investing its spare cash at 8 percent

14For example, the problem of cash management when inflows and outflows are unpredictable is analyzed in M. H. Miller and D. Orr, “A Model of the Demand for Money by Firms,” Quarterly Journal of Economics 80 (August 1966), pp. 413–435. The Miller–Orr model is described in the Principles of Corporate Finance Web page.

Term Capital Management (LTCM), came close to collapse.16 Fearful that LTCM would be forced to liquidate its huge positions, investors shrank from securities that could not be converted easily into cash. The spread between the yield on commercial paper and Treasury bills rose to about 120 basis points (1.20 percent), almost four times its level at the beginning of the year.

Calculating the Yield on Money-Market Investments

Many money-market investments are pure discount securities. This means that they don’t pay interest. The return consists of the difference between the amount you pay and the amount you receive at maturity. Unfortunately, it is no good trying to persuade the Internal Revenue Service that this difference represents capital gain. The IRS is wise to that one and will tax your return as ordinary income.

Interest rates on money-market investments are often quoted on a discount basis. For example, suppose that six-month bills are issued at a discount of 5 percent. This is rather a complicated way of saying that the price of a six-month bill is 100 (6/12) 5 $97.50. Therefore, for every $97.5 that you invest today, you receive $100 at the end of six months. The return over six months is 2.5/97.5 .0256, or 2.56 percent. This is equivalent to an annual yield of 5.12 percent simple interest or 5.19 percent if interest is compounded annually. Note that the return is always higher than the discount. When you read that an investment is selling at a discount of 5 percent, it is very easy to slip into the mistake of thinking that this is its return.17

The International Money Market

In Chapter 24 we pointed out that there are two main markets for dollar bonds. There is the domestic market in the United States and there is an international market. Similarly, in this chapter we shall see that in addition to the domestic money market, there is also an international market for short-term dollar investments. Since this market is based largely in Europe, it has traditionally been known as the eurodollar market. However, now that the European single currency has been called the euro, the term “eurodollar” is potentially confusing and we will just refer to “international dollars.”

An international dollar is not some strange bank note; it is simply a dollar deposit in a bank outside the United States. For example, suppose that an American oil company buys crude oil from an Arab sheik and pays for it with a $1 million check drawn on Chase Manhattan Bank. The sheik then deposits the check into his account at Barclays Bank in London. As a result, Barclays has an asset in the form of a $1 million credit in its account with Chase Manhattan. It also has an offsetting liability in the form of a dollar deposit. That dollar deposit is placed in Europe; it is, therefore, an international dollar deposit.18

16Hedge funds specialize in making positive investments in securities that are believed to be undervalued, while selling short those that appear overvalued. The story of LTCM is told in R. Lowenstein, When Genius Failed: The Rise and Fall of Long Term Capital Management, Random House, New York, 2000; and N. Dunbar, Inventing Money: The Story of Long Term Capital Management and the Legends behind It, John Wiley, New York, 2000.

17To confuse things even more, dealers in the money market often quote rates as if there were only 360 days in a year. So a discount of 5 percent on a bill maturing in 182 days translates into a price of 100 5 (182/360) 97.47 percent.

18The sheik could equally well deposit the check with the London branch of a U.S. bank or a Japanese bank. He would still have made an international dollar deposit.

U.S. Treasury Bills

The first item in Table 31.1 is U.S. Treasury bills. These are usually issued weekly and mature in four weeks, three months, or six months.20 Sales are by auction. You can enter a competitive bid and take your chance of receiving an allotment at your bid price. Alternatively, if you want to be sure of getting your bills, you can enter a noncompetitive bid. Noncompetitive bids are filled at the average price of the successful competitive bids. You don’t have to participate in the auction to invest in Treasury bills. There is also an excellent secondary market in which billions of dollars of bills are bought and sold every day.

Federal Agency Securities

Agencies of the federal government such as the Federal Home Loan Bank (FHLB) and the Federal National Mortgage Association (“Fannie Mae”) borrow both short and long term. The short-term debt consists of discount notes, which are similar to Treasury bills. They are very actively traded and are often held by corporations. Their yields are slightly above those on comparable Treasury securities. One reason for the slightly higher yields is that agency debt is not quite as marketable as Treasury issues.

Another is that most agency debt is backed not by the “full faith and credit” of the U.S. government but only by the agency itself.21 Most investors do not believe that the U.S. government would allow one of its agencies to default, but in 2000 their faith and the price of agency debt both took a knock when a senior Treasury official reminded Congress that the government did not guarantee the debt. Soothing noises from the Treasury subsequently helped to reassure investors.

Short-Term Tax-Exempts

Short-term notes are also issued by municipalities, states, and agencies such as state universities and school districts.22 These are slightly more risky than Treasury bills and not as easy to buy or sell.23 Nevertheless they have one particular attrac- tion—the interest is not subject to federal income tax.24

Pretax yields on tax-exempts are substantially lower than those on comparable taxed securities. But if your company pays tax at the standard 35 percent corporate rate, the lower gross yield of the municipals may be more than offset by the savings in tax.

Tax-exempt issues also include variable-rate demand bonds (VRDBs). These are long-term securities, whose interest payments are linked to the level of short-term interest rates. Whenever the interest rate is reset, investors have the right to sell the bonds back to the issuer for their face value. This ensures that on these reset dates the price of the bonds cannot be less than their face value. Therefore, although

20So-called three-month bills actually mature 91 days after issue, and six-month bills mature 182 days after issue.

21The exception is Ginnie Mae, whose debt is guaranteed by the U.S. government.

22Some of these notes are general obligations of the issuer; others are revenue securities, and in these cases payments are made from rent receipts or other user charges.

23Defaults on tax-exempts are rare but not unknown. For example, in 1983 the municipal utility Washington Public Power Supply System (unfortunately known as WPPSS) defaulted on $2.25 billion of bonds. The 1994 default of Orange County is described in Section 13.4.

24This advantage is partly offset by the fact that Treasury securities are free of state and local taxes.

VRDBs are long-term bonds, their prices are very stable and they compete with short-term tax-exempt notes as a home for spare cash.

Bank Time Deposits and Certificates of Deposit

If you make a time deposit with a bank, you are lending money to the bank for a fixed period. If you need the money before maturity, the bank will usually allow you to withdraw it but will exact a penalty in the form of a reduced rate of interest.

In the 1960s banks introduced the negotiable certificate of deposit (CD) for time deposits of $1 million or more. In this case, when the bank borrows, it issues a certificate of deposit, which is simply evidence of a time deposit with that bank. If a lender needs the money before maturity, it can sell the CD to another investor. When the loan matures, the new owner of the CD presents it to the bank and receives payment.

In recent years doubts about the creditworthiness of some banks have caused the secondary market in CDs to become less active, so that CDs are now much more like large non-negotiable time deposits.25

Instead of depositing dollars with a bank in the United States, a corporation can deposit them overseas with a foreign bank or the foreign branch of a U.S. bank. These deposits pay a fixed rate of interest, and either they are for a fixed term that may vary from one day to several years or they are for an undefined term but may be called at one or more days’ notice. Since a time deposit is an illiquid investment, the London branches of the major banks also issue negotiable international dollar CDs.

Commercial Paper

We described commercial paper in the last chapter so we will not discuss it here beyond reminding you that it is short-term debt that is issued on a regular basis by both financial and nonfinancial companies. Commercial paper is popular with both industrial companies and money-market mutual funds as a parking place for short-term cash.

Bankers’ Acceptances

In the next chapter we will explain how bankers’ acceptances (BAs) may be used to finance exports or imports. An acceptance begins life as a written demand for the bank to pay a given sum at a future date. The bank then agrees to this demand by writing “accepted” on it. Once accepted, the draft becomes the bank’s IOU and is a negotiable security that can be bought or sold through money-market dealers. Acceptances by the large U.S. banks generally mature in one to six months and involve very low credit risk.

Repurchase Agreements

Repurchase agreements, or repos, are effectively secured loans to a government security dealer. They work as follows: The investor buys part of the dealer’s holding of Treasury securities and simultaneously arranges to sell them back again at a later date at a specified higher price. The borrower (the dealer) is said to have entered into a repo; the lender (who buys the securities) is said to have a reverse repo.

25Some CDs are not negotiable at all and are therefore identical to time deposits. For example, banks may sell low-value non-negotiable CDs to individuals.

Repos sometimes run for several months, but more frequently they are just overnight (24-hour) agreements. No other domestic money-market investment offers such liquidity. Corporations can treat overnight repos almost as if they were interest-bearing demand deposits.

Suppose that you decide to invest cash in repos for several days or weeks. You don’t want to keep renegotiating agreements every day. One solution is to enter into an open repo with a security dealer. In this case there is no fixed maturity to the agreement; either side is free to withdraw at one day’s notice. Alternatively, you may arrange with your bank to transfer any excess cash automatically into repos.

For many years repos appeared to be not only very liquid instruments but also very safe.26 This reputation took a knock in 1982 when two money-market dealers went bankrupt. Each case involved heavy use of repos. One dealer, Drysdale Securities, had been in existence for only three months and had total capital of $20 million. However, it went bankrupt, owing Chase Bank $250 million. It’s not easy to run up debts that fast, but Drysdale did it.

31.5 FLOATING-RATE PREFERRED STOCK—AN ALTERNATIVE TO MONEY-MARKET INVESTMENTS

There is no law preventing firms from making short-term investments in long-term securities. If a firm has $1 million set aside for an income tax payment, it could buy a long-term bond on January 1 and sell it on April 15, when the taxes must be paid. However, the danger in this strategy is obvious. What happens if bond prices fall by 10 percent between January and April? There you are, with a $1 million liability to the Internal Revenue Service, bonds worth only $900,000, and a very red face. Of course, bond prices could also go up, but why take the chance? Corporate treasurers entrusted with excess funds for short-term investment are naturally averse to the price volatility of long-term bonds.

We saw earlier how municipalities devised variable-rate demand bonds, which investors could periodically sell back to the issuer. The prices of these bonds are nearly immune to fluctuations in interest rates. In addition, the interest on municipal loans has the attraction of being tax-exempt. So a municipal variable-rate demand bond offers a safe, tax-free, short-term haven for your $1 million of cash.

Common stock and preferred stock also have an interesting tax advantage for corporations, since firms pay tax on only 30 percent of dividends received from other corporations. For each $1 of dividends received, the firm gets to keep 1 .30

.35 $.895. Thus the effective tax rate is only 10.5 percent. This is higher than the zero tax rate on the interest from municipal debt but much lower than the rate that the company pays on other debt interest.

Suppose you consider putting that $1 million in some other corporation’s preferred shares.27 The 10.5 percent tax rate is very tempting. On the other hand,

26To reduce the risk of repos, it is common to value the security at less than its market value. This difference is known as a haircut.

27Preferred shares are usually better short-term investments for a corporation than common shares. The preferred shares’ expected return is virtually all dividends; most common shares are expected to generate capital gains, too. The corporate tax on capital gains is usually 35 percent. Corporations therefore have a strong incentive to like dividends and dislike capital gains.