The Baumol Model The Baumol Model is based on the Economic Order Quantity (EOQ)
The Baumol Model The Baumol Model is based on the Economic Order Quantity (EOQ)
model developed for inventory management. 2 We will see it applied to inventory in Chapter 20. Applied to the management of cash, the EOQ model determines the amount of cash that minimizes the sum of the holding cost and transactions cost. The holding cost includes the costs
2 William J. Baumol, “The Transactions Demand for Cash: An Inventory Theoretic Approach,” Quarterly Journal of Economics (November 1952).
Management of Cash and Marketable Securities
of administration (keeping track of the cash) and the opportunity cost of not investing the cash elsewhere. The transaction cost is the cost of getting more cash—either through selling marketable securities or through borrowing. The economic order quantity is the level of cash infusion (from selling marketable securities or borrowing) that mini- mizes the total cost associated with cash.
Suppose each time our cash balance is zero we generate $100,000 (borrowing or selling securities). Further suppose that our opportunity cost for holding cash is 5%—we could have invested the cash in some- thing that earns 5% instead of holding it. Our holding costs are the product of the average cash balance and the opportunity cost. If we start with $0 cash and end up with $100,000 after an infusion, our average cash balance is = $50,000, so our holding cost is:
0.05 $100,000 ------------------------- = $2,500
Holding cost =
If we did not hold $50,000 of cash on average, we could have earned $2,500 by investing it.
Now suppose we need $1,000,000 cash for transactions over a given period. If we need $1,000,000 in total and we get $100,000 cash at a time, we need to make 10 transactions during the period. If it costs us $200 every time we make a cash infusion our transactions cost is $2,000:
$1,000,000 Transaction cost = $200 per transaction ----------------------------------------------------------------- $100,000 per transaction
↑ Cost per transaction Number of transactions = $200(10) = $2,000
The total cost associated with cash is the sum of the holding cost and the transactions cost:
Total cost = $2,500 + 2,000 = $4,500
Will cash infusions of $100,000 at a time produce the lowest cost of getting cash? We can’t control the cash needed for transactions purposes or the cost per transaction. But we can control how many cash infusions we make. And that number affects both the holding cost and the trans- actions cost.
MANAGING WORKING CAPITAL
The holding cost is a function of the amount of the cash infusion: With larger cash infusions, we hold more cash. Holding more cash, we have a greater opportunity cost to holding it. The transactions cost is also
a function of the amount of cash infusion: The larger the cash infusion, the fewer the transactions, and therefore the lower our transactions costs. Let’s use these considerations and what we know about economic order quantity to determine the minimum cost of cash. If we get cash in the amount of Q at the beginning of a period and wait until the cash balance is zero before we get more cash, the average cash balance over the period is Q/2. The cost of holding cash during this period is determined by the average cash balance, Q/2, and the opportu- nity cost of holding the cash, k:
Holding cost = -----
But each time we get cash, we have to make a transaction. If we demand a total of S dollars of cash each period, we end up making S/Q transactions per period. If it costs K to make a transaction, the transac- tions cost for the period is:
S Transactions cost = K -----
Putting the holding cost and the transaction cost together, the total cost associated with the cash balance is:
Total cost = Holding cost + Transaction cost = k Q ----- + K ----- S
The total cost associated with any given level of inventory ordering Q is:
Total cost = k ----- + K -----
To calculate the minimum total cost with respect to the amount of inventory we get each time, we:
1. Calculate the first derivative of the total cost equation with respect to Q.
Management of Cash and Marketable Securities
2. Set this first derivative equal to zero.
3. Solve for Q. The first derivative of the total cost with respect to Q (where “d” indi-
cates “change”) is:
---------------------------------- ( d Total cost )
--- k = S – -------- K
dQ ()
Setting the first derivative equal to zero:
--- k 0 S = – -------- K
Solving for the level of Q that minimizes the total cost, Q*,
Q* = ----------------------------------------------------------------------------------------------------------------------------- ( 2 Cost per transaction ) Total demand for cash ( )
Opportunity cost of holding cash or,
Q* = 2 ----------- KS k
What does this mean? If we look at the relations among Q* and K, S, and k in this equation, we see that:
■ The larger the cost per transaction, K, the greater the amount of cash, Q*, infused in a single transaction—the larger the transaction cost, the fewer transactions we make.
■ The larger the demand for cash, S, the larger the amount of cash, Q*, infused in a single transaction. ■ The larger the opportunity cost of holding cash, k, the smaller the amount of cash, Q*, infused in a single transaction.
In our example, K = $200 per transaction, S = $1,000,000, k = 5%, and
Q* = --------------------------------------------------------- ( 2 $200 ) $1,000,000 ( ) = $89,443
MANAGING WORKING CAPITAL
If every time we need a cash infusion, we get $89,443, the costs associated with cash will be minimized. We can check our work by looking at the total costs of cash for lev- els of Q on either side of Q* = $89,443. If Q = $100,000,
Total cost = $2,500 + $2,000 = $4,500
as we saw before. If Q = $50,000:
--------------------- $50,000
Total costs = 0.05
If Q = $89,443,
$1,000,000 Total costs = 0.05 --------------------- + $200 ------------------------------
We can see in Exhibit 19.3 that the minimum of the total cost curve is at
a cash infusion level of $89,443, which corresponds to a total cost of $4,472. If the level of cash infusion is less than or more than $89,443, the cost of cash will be higher.
EXHIBIT 19.3 Costs of Cash for Different Levels of Cash Infusions
Management of Cash and Marketable Securities
The EOQ model can be applied to any time framework—whether the period is a year, a month, a week, or any other unit of time. It is only necessary to make sure that all the elements that depend on the unit of time—the holding costs, k, and transactions demand, S—are in that same unit of time.
The economic order quantity model can be modified to suit the cir- cumstances of different cash situations. For example, the EOQ model for cash can be modified to include a safety stock—a balance of cash for precautionary purposes. The safety stock is a level of cash balance that acts as a cushion in case our cash needs are suddenly greater than expected.
Parts
» Financial Management and Analysis
» SECURITIES MARKETS The primary function of a securities market—whether or not it has a
» Stock Exchanges Stock exchanges are formal organizations, approved and regulated by
» Stock Market Indicators Stock market indicators have come to perform a variety of functions,
» Efficient Markets Investors do not like risk and they must be compensated for taking on
» THE FEDERAL RESERVE SYSTEM The United States has a central monetary authority known as the Fed-
» The Fed and the Money Supply Financial managers and investors are interested in the supply and
» Deposit Institutions Traditionally, the United States has had several types of deposit institu-
» Investment Banking The primary market involves the distribution to investors of newly
» Interest Rates and Yields Because bonds are traded in the secondary market, the price of the bond
» The Risk Premium Market participants talk of interest rates on non-Treasury securities as
» OPTIONS An option is a contract in which the writer of the option grants the
» Buying Call Options The purchase of a call option creates a position referred to as a long call
» Buying Put Options The buying of a put option creates a financial position referred to as a
» CAP AND FLOOR AGREEMENTS There are agreements available in the financial market whereby one
» I n assessing a company’s current and future cash flows, the financial
» Depreciation for Tax Purposes For accounting purposes, a firm can select a method of depreciation
» Capital Gains We tend to use the term “capital gain” loosely to mean an increase in the
» Current assets (also referred to as circulating capital and working
» Noncurrent Assets Noncurrent assets are assets that are not current assets; that is, it is not
» Deferred Taxes Along with long-term liabilities, the analyst may encounter another
» THE INCOME STATEMENT An income statement is a summary of the revenues and expenses of a
» THE STATEMENT OF CASH FLOWS The statement of cash flows is a summary over a period of time of a
» T he notion that money has a time value is one of the most basic con-
» DETERMINING THE PRESENT VALUE Now that we understand how to compute future values, let’s work the
» Shortcuts: Annuities There are valuation problems that require us to evaluate a series of level
» THE CALCULATION OF INTEREST RATES
» T here are a number of factors that affect a stock’s price and its value to
» Dividend Valuation Model If dividends are constant forever, the value of a share of stock is the
» Returns on Common Stock As we saw in the preceding section, the value of a stock is the present
» Straight Coupon Bond Suppose you are considering investing in a straight coupon bond that:
» Returns on Bonds If you invest in a bond, you realize a return from the interest it pays (if
» Coupon Bonds The present value of a bond is its current market price, which is the dis-
» Callable Bonds Some bonds have a feature, referred to as a call feature, that allows the
» RISK Whenever you make a financing or investment decision, there is some
» Financial Risk When we refer to the cash flow risk of a security, we expand our con-
» Reinvestment Rate Risk Another type of risk is the uncertainty associated with reinvesting cash
» Interest Rate Risk Interest rate risk is the sensitivity of the change in an asset’s value to
» Currency Risk In assessing the attractiveness of an investment, we estimated future cash
» 5 (Continued) Portfolio of Investment C and Investment D
» Portfolio Size and Risk What we have seen for a portfolio with two assets can be extended to
» I n Chapters 8 through 10, we discussed and practiced techniques for
» The Cost of Debt Because Congress allows you to deduct from your taxable income the
» The Cost of Common Stock The cost of common stock is the cost of raising one more dollar of com-
» INTEGRATIVE EXAMPLE: ESTIMATING THE COST OF CAPITAL FOR DUPONT
» CAPITAL BUDGETING Because a firm must continually evaluate possible investments, capital
» Investment Cash Flows When we consider the cash flows of an investment we must also consider
» Asset Disposition At the end of the useful life of an asset, the firm may be able to sell it or
» Change in Expenses When a firm takes on a new project, the costs associated with it will
» Putting It All Together Here’s what we need to put together to calculate the change in the firm’s
» The Analysis To determine the relevant cash flows to evaluate this expansion, let’s
» The Problem The new equipment costs $300,000 and is expected to have a useful life of
» T he value of a firm today is the present value of all its future cash
» Payback Period The payback period for a project is the length of time it takes to get your
» Discounted Payback Period The discounted payback period is the time needed to pay back the origi-
» Net Present Value If offered an investment that costs $5,000 today and promises to pay
» Net Present Value Decision Rule
» Profitability Index The profitability index (PI) is the ratio of the present value of change in
» Stand-Alone versus Market Risk If we have some idea of the uncertainty associated with a project’s
» Sensitivity Analysis Estimates of cash flows are based on assumptions about the economy,
» Simulation Analysis Sensitivity analysis becomes unmanageable if we change several factors
» Options on Real Assets The valuation of stock options is rather complex, but with the assis-
» OVERVIEW OF DEBT OBLIGATIONS In a debt obligation, the borrower receives money in exchange for a
» Repayment Schedule Term loans are usually repaid in installments either monthly, quarterly,
» Interest In the United States, interest is typically paid twice a year at six month
» Debt Retirement By the maturity date of the bond, the issuer must pay off the entire par
» Rating Systems In all systems the term high grade means low default risk, or conversely,
» S uppose you buy a new car that costs $20,000 and you pay cash for it.
» Limited Liability The corporate form of doing business is attractive to owners of a busi-
» Stock Ownership We can classify a corporation according to whether its shares of stock
» Voting Rights Common shareholders are generally granted rights to
» Corporate Democracy Corporate democracy gives owners of the corporation a say in how to
» Methods of Repurchasing Stock
» Dividends Although a firm’s board of directors declares a dividend on its preferred
» Sinking Funds Because there is no legal obligation to pay the preferred dividend and
» DEBT VERSUS EQUITY The combination of debt and equity used to finance a firm’s projects is
» CAPITAL STRUCTURE AND TAXES We’ve seen how the use of debt financing increases the risk to owners;
» Interest Tax Shield An interesting element introduced into the capital structure decision is
» Unused Tax Shields The value of a tax shield depends on whether the firm can use an interest
» PUTTING IT ALL TOGETHER As a firm increases the relative use of debt in the capital structure, its
» A s we saw in Part Three, managers base decisions about investing in
» CASH MANAGEMENT Cash flows out of a firm as it pays for the goods and services it pur-
» The Baumol Model The Baumol Model is based on the Economic Order Quantity (EOQ)
» The Miller-Orr Model The Baumol Model assumes that cash is used uniformly throughout the
» The Check Clearing Process The process of receiving cash from customers involves several time-
» RECEIVABLES MANAGEMENT When a firm allows customers to pay for goods and services at a later
» Captive Finance Subsidiaries Some firms choose to form a wholly-owned subsidiary—a corporation
» The Economic Order Quantity Model The Economic Order Quantity (EOQ) model helps us determine what
» Just-in-Time Inventory The goal of the just-in-time (JIT) inventory model is to cut down on the
» Monitoring Inventory Management We can monitor inventory by looking at financial ratios in much the
» Add-on-interest Another way of stating interest is with add-on interest, where the total
» Trade Credit Trade credit is granted by a supplier to a customer purchasing goods or
» Commercial Paper Commercial paper is an unsecured promissory note with a fixed matu-
» Types of Inventory Financing There are several different types of loan arrangements that involve
» SPECIALIZED COLLATERALIZED BORROWING ARRANGEMENT FOR FINANCIAL INSTITUTIONS
» RATIOS AND THEIR CLASSIFICATION
» RETURN-ON-INVESTMENT RATIOS Return-on-investment ratios compare measures of benefits, such as earn-
» The Du Pont System The returns on investment ratios give us a “bottom line” on the perfor-
» LIQUIDITY Liquidity reflects the ability of a firm to meet its short-term obligations
» PROFITABILITY RATIOS We have seen that liquidity ratios tell us about a firm’s ability to meet its
» Using a Benchmark To interpret a firm’s financial ratios we need to compare them with the
» INTEGRATIVE EXAMPLE: FINANCIAL ANALYSIS OF WAL-MART STORES 6
» Dilutive Securities For a company having securities that are dilutive—meaning they could
» ANALYSTS’ FORECASTS There are many financial services firms offering projections on different
» PRICE-EARNINGS RATIO Many investors are interested in how the earnings are valued by the mar-
» FREE CASH FLOW Cash flows without any adjustment may be misleading because they do
» NET FREE CASH FLOW There are many variations in the calculation of cash flows that are used
» Using Cash Flow Information The analysis of cash flows provides information that can be used along
» THE GLOBAL ECONOMY Many countries export a substantial portion of the goods and services
» FOREIGN CURRENCY Doing business outside of one’s own country requires dealing with the cur-
» The Euro The European Union consists of 15 European member countries that
» Global Equity Market In 1985, Euromoney surveyed several firms that either listed stock on a
» Currency Swaps When issuing bonds in another country where the bonds are not denom-
» Currency Option Contracts In contrast to a forward or futures contract, an option gives the option
» A s an alternative to the issuance of a corporate bond, a corporation
» WHAT RATING AGENCIES LOOK AT IN RATING ASSET-BACKED SECURITIES
» Third-Party Guarantees Perhaps the easiest form of credit enhancement to understand is insur-
» EXAMPLE OF AN ACTUAL STRUCTURED FINANCE TRANSACTION
» Accounting for Capital Leases
» FEDERAL INCOME TAX REQUIREMENTS FOR TRUE LEASE TRANSACTIONS
» Direct Cash Flow from Leasing When a firm elects to lease an asset rather than borrow money to pur-
» S tructured financing is a debt obligation that is backed by the value of
» CREDIT IMPACT OBJECTIVE While the sponsor or sponsors of a project financing ideally would pre-
» A business that maximizes its owners’ wealth allocates its resources
» Budgeting In budgeting, we bring together analyses of cash flows, projected income
» Taxes and Transaction Costs The Black-Scholes option pricing model ignores taxes and transaction
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