MEASUREMENT OF PROJECT RISK The financial decision-maker needs to measure risk to incorporate it into
MEASUREMENT OF PROJECT RISK The financial decision-maker needs to measure risk to incorporate it into
the capital budgeting decision. We next look at several methods of evalu- ating risk, focusing first on stand-alone risk and then on market risk.
Measuring a Project’s Stand-Alone Risk We will first look at a project’s stand alone risk.
Statistical Measures of Cash Flow Risk We will look at three statistical measures used to evaluate the risk asso- ciated with a project’s possible outcomes: the range, the standard devia- tion, and the coefficient of variation. Let’s demonstrate each using new products as examples. Based on experience with our firm’s current prod- uct lines and the market research for new Product A, we can estimate that it may generate one of three different cash flows in its first year, depending on economic conditions:
Economic Condition Cash Flow
Looking at this table we can see there is more than one possible out- come. There are three possible outcomes, each representing a possible cash flow, and its probability of occurring. Product A’s three possible cash flows are represented graphically in Exhibit 14.1. Looking at this graph, we see that there is some chance of getting a −$1,000 cash flow and some chance of getting a +$10,000 cash flow, though the most likely possibility (the one with the greatest probability) is a +$5,000 cash flow.
But to get an idea of Product A’s risk, we need to know a bit more. The more spread out the possible outcomes, the greater the degree of uncertainty (the risk) of what is expected in the future. We refer to the degree to which future outcomes are “spread out” as dispersion. In gen- eral, the greater the dispersion, the greater the risk.
There are several measures we could use to describe the dispersion of future outcomes. We will focus on the range, the standard deviation, and the coefficient of variation.
The Range The range is a statistical measure representing how far apart are the two extreme outcomes of the probability distribution. The range is calculated as the difference between the best and the worst possible outcomes:
LONG-TERM INVESTMENT DECISIONS
Range = Best possible outcome − Worst possible outcome For Product A, the range of possible outcomes is $10,000 − (−$1,000) =
$11,000. The larger the range, the farther apart are the two extreme possible outcomes and therefore, the greater the risk.
The Standard Deviation Though easy to calculate, the range doesn’t tell us anything about the likelihood of the possible cash flows at or between the extremes. In financial decision-making, we are interested in not just the extreme outcomes, but all the possible outcomes.
One way to characterize the dispersion of all possible future out- comes is to look at how the outcomes differ from one another. This would require looking at the differences among all possible outcomes and trying to summarize these differences in a usable measure.
An alternative to this is to look at how each possible future outcome differs from a single value, comparing each possible outcome with this one value. A common approach is to use a measure of central location of a probability distribution, the expected value.
Let’s use N to designate the number of possible future outcomes, x n to indicate the nth possible outcome, p n to indicate the probability of the nth outcome occurring, and E(x) to indicate the expected outcome. The expected cash flow is the weighted average of the cash flows, where the weights are the probabilities:
E(x) = x 1 p 1 + x 2 p 2 + x 3 p 3 +...+ x n p n + ... + x N p N
EXHIBIT 14.1 Probability Distribution for Product A’s Cash Flow
Capital Budgeting and Risk
EXHIBIT 14.2 Calculation of the Standard Deviation of the
Possible Cash Flows of Product A Economic
Cash Conditions Flow Probability x n p n x n – E(x) (x – E(x)) 2 n p n (x n – E(x)) 2
Boom $10,000 0.20 $2,000 $5,800 33,640,000 6,728,000 Normal
5,000 0.50 2,500 800 640,000 320,000 Recession
−1,000 0.30 −300 −5,200 27,040,000 9,112,000 E(x) =
σ 2 ( x) = 15,160,000 Standard deviation = σ ( x) = 15,160,000 = $3,894
or, using summation notation,
Ex () =
The standard deviation is a measure of how each possible outcome deviates—that is, differs—from the expected value. The standard devia- tion provides information about the dispersion of possible outcomes because it provides information on the distance each outcome is from the expected value and the likelihood the outcome will occur. The stan- dard deviation is:
σx () =
p n [ x n – Ex ∑ 2 () ]
The calculation of the standard deviation is shown in Exhibit 14.2. As you can see, it is necessary to calculate the expected value before cal- culating the standard deviation. The standard deviation of Product A’s future cash flows is $3,894.
The standard deviation is a statistical measure of dispersion of the possible outcomes about the expected outcome. The larger the standard deviation, the greater the dispersion and, hence, the greater the risk.
Let’s look at another example. Suppose the possible cash flows and their corresponding probabilities in the first year for Product B are:
LONG-TERM INVESTMENT DECISIONS
Cash Flow Probability
5 Expected value and standard deviation calculated similar to that of
Product A is shown in Exhibit 14.2. We can describe the probability dis- tribution with several measures:
■ The expected value is $7,000. ■ The most likely outcome—the one that has the highest probability of
occurring—is $7,000. ■ The range of possible outcomes is $10,000 − 4,000 = $6,000. ■ The standard deviation of the possible outcomes is $1,449.
Let’s compare the risk associated with Product B’s cash flows with the risk of still another project, Product C, which has the following pos- sible cash flows:
Cash Flow Probability
2 Describing the possible outcomes for Product C (which you can
determine on your own applying what we did for Products A and B), ■ The expected value is $7,000.
■ The most likely outcome is $7,000. ■ The range of possible outcomes is $6,000. ■ The standard deviation of the possible outcome is $1,183.
Capital Budgeting and Risk
EXHIBIT 14.3 Probability Distributions of Product B and Product C
Both B and C have the same most likely outcome, the same expected value, and the same range of possible outcomes. But the standard devia- tion of the cash flows for C is less than it is for B. This confirms what we see when comparing the probability distributions of Product C, as shown in Exhibit 14.3—the distribution of possible outcomes of Prod- uct C are less disperse than that of Product B.
The Coefficient of Variation The standard deviation provides a useful mea- sure of dispersion. It is a measure of how widely dispersed the possible outcomes are from the expected value. However, we cannot compare standard deviations of different projects’ cash flows if they have differ- ent expected values. To see this, consider the possible cash flows from Product D:
Cash Flow Probability
5 We can describe the probability distribution of Product D’s possible
cash flows:
LONG-TERM INVESTMENT DECISIONS
■ The expected value is $70,000. ■ The most likely outcome is $70,000. ■ The range of possible outcomes is $60,000. ■ The standard deviation of the possible outcomes is $14,491.
Is Product D riskier than Product B? Product D’s standard deviation is larger, but so is its expected value. Because Product B’s and Product D’s cash flows are of different sizes, comparing their standard deviations is meaningless without somehow adjusting for the scale of cash flows.
We can do that with the coefficient of variation, which translates the standard deviation of different probability distributions (because their scales differ) so that they can be compared.
The coefficient of variation for a probability distribution is the ratio of its standard deviation to its expected value:
Coefficient of variation = σx ------------ ()
Ex () Calculating the coefficient of variation for each of the four prod-
ucts’ probability distributions in our examples,
Coefficient of Product
Expected
Standard
Value Range
0.2070 Comparing coefficients of variation among these products, we see that: ■ Product A is the riskiest.
■ Product C is least risky. ■ Products B and D have identical risk.
Risk can be expressed statistically in terms of measures such as the range, the standard deviation, and the coefficient of variation. Now that we know how to calculate and apply these statistical measures, all we need are the probability distributions of the project’s future cash flows so we can apply these statistical tools to evaluate a project’s risk.
Where do we get these probability distributions? From research, judg- ment, and experience. We can use sensitivity analysis or simulation analy- sis to get an idea of a project’s possible future cash flows and their risk.
Capital Budgeting and Risk
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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