Internal Rate of Return Decision Rule The internal rate of return is a yield—what we earn, on average, per
Internal Rate of Return Decision Rule The internal rate of return is a yield—what we earn, on average, per
year. How do we use it to decide which investment, if any, to choose? Let’s revisit Investments A and B and the IRRs we just calculated for each. If, for similar risk investments, owners earn 10% per year, then both A and B are attractive. They both yield more than the rate owners require for the level of risk of these two investments:
2 Your calculator does not arrive at the solution directly. Your calculator’s program uses trial and error also—and keeps you waiting as it tries different discount rates.
LONG-TERM INVESTMENT DECISIONS
Investment IRR
Cost of Capital
A 28.65% per year 10% per year B 22.79%
The decision rule for the internal rate of return is to invest in a project if it provides a return greater than the cost of capital. The cost of capital, in the context of the IRR, is a hurdle rate—the minimum acceptable rate of return.
If ... this means that ... and you ...
IRR > cost of capital the investment is expected to should accept the project. return more than required
IRR < cost of capital the investment is expected to should reject the project. return less than required
IRR = cost of capital the investment is expected to should be indifferent return what is required
between accepting or rejecting the project.
The IRR and Mutually Exclusive Projects What if we were forced to choose between projects A and B because they are mutually exclusive? A has a higher IRR than B—so at first glance we might want to accept A. But wait! What about the NPV of A and B? What does the NPV tell us to do?
Investment IRR
NPV
A 28.65% $516,315 B 22.79% $552,620
If we use the higher IRR, it tells us to go with A. If we use the higher NPV, we go with B. Which is correct? If 10% is the cost of capital we used to determine both NPVs and we choose A, we will be foregoing value in the amount of $552,620 − $516,315 = $36,305. Therefore, we should choose B, the one with the higher NPV.
In this example, if for both A and B the cost of capital were differ- ent, say 25%, we would calculate different NPVs and come to a differ- ent conclusion. In this case:
Investment IRR
NPV
A 28.65%
B 22.79% −$67,520
Capital Budgeting Techniques
Investment A still has a positive NPV, since its IRR > 25%, but B has a negative NPV, since its IRR < 25%.
When evaluating mutually exclusive projects, the one with the high- est IRR may not be the one with the best NPV. The IRR may give a dif- ferent decision than NPV when evaluating mutually exclusive projects because of the reinvestment assumption:
■ NPV assumes cash flows are reinvested at the cost of capital. ■ IRR assumes cash flows are reinvested at the internal rate of return.
This reinvestment assumption may lead to different decisions in choosing among mutually exclusive projects when any of the following factors apply:
■ The timing of the cash flows is different among the projects, ■ There are scale differences (that is, very different cash flow amounts),
or ■ The projects have different useful lives.
Let’s see the effect of the timing of cash flows in choosing between two projects: Investment A’s cash flows are received sooner than B’s. Part of the return on each investment comes from the reinvestment of its cash inflows. And in the case of A, there is more return from the rein- vestment of cash inflows. The question is “What do you do with the cash inflows when you get them?” We generally assume that if you receive cash inflows, you’ll reinvest those cash flows in other assets.
Now we turn to the reinvestment rate assumption in choosing between these projects. Suppose we can reasonably expect to earn only the cost of capital on our investments. Then, for projects with an IRR above the cost of capital, we would be overstating the return on the investment using the IRR. Consider Investment A once again. If the best you can do is reinvest each of the $400,000 cash flows at 10%, these cash flows are worth $2,442,040:
Future value of Investment A’s cash flows each invested at 10%
future value annuity factor = $400,000
N = 5 and r = 10% = $400,000 6.1051 ( ) = $2,442,040
Investing $1,000,000 at the end of 2000 produces a value of $2,442,040 at the end of 2005 (cash flows plus the earnings on these cash flows at 10%). This means that if the best you can do is reinvest cash flows at 10%, then you earn not the IRR of 28.65%, but rather 19.55%:
LONG-TERM INVESTMENT DECISIONS
FV = PV 1 + r n ( ) $2,442,040 5 = $1,000,000 1 ( + r )
r = 19.55%
If we evaluate projects on the basis of their IRR, we may select one that does not maximize value.
Remember that the NPV calculation assumes reinvestment at the cost of capital. If the reinvestment rate is assumed to be the project’s cost of capital, we would evaluate projects on the basis of the NPV and select the one that maximizes owners’ wealth.
The IRR and Capital Rationing What if there is capital rationing? Suppose Investments A and B are independent projects. Independent projects means that the acceptance of one does not prevent the acceptance of the other. And suppose the capital budget is limited to $1,000,000. We are therefore forced to choose between A or B. If we select the one with the highest IRR, we choose A. But A is expected to increase wealth less than B. Ranking investments on the basis of their IRRs may not maximize wealth.
We can see this dilemma in Exhibit 13.3. The discount rate at which A’s NPV is $0.00—A’s IRR—28.65%, where A’s profile crosses the hori- zontal axis. Likewise, B’s IRR is 22.79%. The discount rate at which A’s and B’s profiles cross is the crossover rate, 12.07%. For discount rates less than 12.07%, B has the higher NPV. For discount rates greater than 12.07%, A has the higher NPV. If you choose A because it has a higher IRR, and if A’s cost of capital is more than 12.07%, you have not cho- sen the project that produces the greatest value.
Suppose you evaluate four independent projects characterized by the following data:
Project Investment Outlay
If there is no capital rationing, you would spend $20 million since all four have positive NPVs. And we would expect owners’ wealth to increase by $1,900,000, the sum of the NPVs.
But suppose the capital budget is limited to $10 million. If you select projects on the basis of their IRRs, you would choose projects L, M, and
Capital Budgeting Techniques
N. But is this optimal in the sense of maximizing owners’ wealth? Let’s look at the value added from different investment strategies:
Investment
Amount of Total
Selection
Investment NPV
$10,000,000 $900,000 Selection based on highest NPVs
Selection based on highest IRRs
L, M, and N
10,000,000 1,000,000 We can increase the owners’ wealth more with Project O than with the
combined investment in Projects L, M, and N. Therefore, when there is capital rationing, selecting investments on the basis of IRR rankings is not consistent with maximizing wealth.
The source of the problem in the case of capital rationing is that the IRR is a percentage, not a dollar amount. Because of this, we cannot determine how to distribute the capital budget to maximize wealth because the investment or group of investments producing the highest yield does not mean they are the ones that produce the greatest wealth.
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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