Effective Cost of Borrowing The effective cost of borrowing is the cost of financing, considering both
Effective Cost of Borrowing The effective cost of borrowing is the cost of financing, considering both
direct and indirect costs. This effective cost is the cost of funds for a given period, the duration of time over which interest is paid and the end of which compounding (if there is compounding) is calculated. For example, if we borrow $1,000 today and must repay it plus $50 after three months, the period is three months and the cost of funds expressed in percent is $50/$1,000 = 5% for the period of the loan. Suppose we borrow $1,000 today and must repay it at the end of the year, plus 5% each quarter, with interest compounded at the end of each quarter. The “period” is three months and the amount repaid after one year is $1,000 compounded four periods at 5% per period or $1,000
× (1 + 0.05) 4 = $1,215.51. To compare alternative forms of financing that may have different
terms, including different periods, we convert the effective cost of financing into a common unit of time—by convention, one year. Return- ing to our last example, suppose we use this same financing arrange- ment throughout a year. At the end of the first three months we borrow the amount we owe—the $1,050—for three more months. At the end of the second three months, we owe $1,050 plus the interest on $1,050:
Amount owed = $1,050 + (0.05)$1,050 = $1,102.50 Borrowing once again for three more months, at the end of the second
three-month period we owe $1,102.50(1.05) = $1,157.63. Borrowing again for the last three months, at the end of the year we owe $1,157.63 (1.05) = $1,215.51.
If we borrow $1,000 for one year and pay 5% interest every three months, we pay $1,215.51 − $1,000.00 = $215.51 interest. Comparing the $215.51 interest with the amount we borrowed, the effective cost over the year is:
Effective cost of borrowing = -------------------------- = 0.2155 or 21.55% per year
By stepping through this example with interest compounded every three months, we see the effect of compounding: 5% for three months compounded over one year translates into 21.55% for one year. We can look at this another way by combining our compounding into one step:
Interest = $1,000 1.05 ( ) 1.05 ( ) 1.05 ( ) 1.05 ( ) – $1,000
Balance due after one year
Principal
MANAGING WORKING CAPITAL
The effective annual rate (EAR) on the borrowing is the ratio of the interest paid in one year to the principal, the amount borrowed:
interest EAR = -----------------------
principal
Substituting the interest on the borrowing for a year,
4 EAR = ------------------------------------------------------------------------ $1,000 1 ( + 0.05 ) – $1,000
which we can break into two fractions,
4 EAR = ----------------------------------------------- $1,000 1 ( + 0.05 ) – ------------------ $1,000
$1,000 Simplifying the fractions, we arrive at the formula for the effective
annual rate: EAR = (1 + 0.05) 4 − 1 = 0.2155 or 21.55% per year Designating the rate per compounding period r and the number of
compounding periods within a year t, we have in general terms:
(21-1) Now let’s see why the effective cost, as expressed by EAR, is the true
EAR = (1 + r) t −1
cost of borrowing. Annual Percentage Rate
The costs of borrowing are often stated on an annualized basis by mul- tiplying the rate per compounding period by the number of compound- ing periods in a year. This is done partly because of custom and partly to simplify matters. The annual percentage rate (APR) is the annualized cost of financing (or lending, if you are on the other side of the transac- tion) without considering the compounding of interest. The APR is the product of the rate per period, r, and the number of periods in a year, t:
(21-2) This APR is also referred to as the nominal rate or the stated rate. If
APR = r ×t
$50 interest is paid every three months on a loan of $1,000, the APR is 5% times 4 = 20%.
Management of Short-Term Financing
The APR is simple to compute, but it is not very useful for compar- ing costs of alternative financing arrangements since it ignores com- pounding. For example, if 1% interest is paid each month, the APR is:
APR = 0.01(12) = 0.1200 or 12% per year
But each month this loan’s effective annual cost with compounding is: EAR = (1 + 0.01) 12 − 1 = 0.1268 or 12.68% per year The APR understates the effective cost of financing if interest is com-
pounded each period during the year. The costs of short-term financing, however, are not always straight- forward. The costs of short-term financing may be direct, such as inter- est or commitment fees, or indirect, such as discount interest and com- pensating balances (we explain these terms later in the chapter). Managers must understand how to calculate the cost of financing for the alternative ways in which these costs may be stated so that we can compare them. In the remainder of this section, we demonstrate how to calculate EAR for a variety of loans.
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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