Sensitivity Analysis Estimates of cash flows are based on assumptions about the economy,
Sensitivity Analysis Estimates of cash flows are based on assumptions about the economy,
competitors, consumer tastes and preferences, construction costs, and taxes, among a host of other possible assumptions. One of the first things managers must consider about these estimates is how sensitive they are to these assumptions. For example, if we only sell 2 million units instead of 3 million units in the first year, is the project still profit- able? Or, if Congress increases the tax rates, will the project still be attractive?
We can analyze the sensitivity of cash flows to change in the assumptions by reestimating the cash flows for different scenarios. Sen- sitivity analysis, also called scenario analysis, is a method of looking at the possible outcomes, given a change in one of the factors in the analy- sis. Sometimes we refer to this as “what if” analysis—“what if this changes,” “what if that changes,” and so on.
To see how sensitivity analysis works, let’s look at the Williams 5 &
10 cash flows we determined in Chapter 12, where the detailed calcula- tions were shown in Exhibit 12.4 of that chapter. The net cash flow for each year is:
Year Net Cash Flow
+460,946 Now let’s play with the assumptions. Suppose that the tax rate is
not known with certainty, but instead the tax rate may be 20%, 30%, or 40%. The tax rate that we assume affects all the following factors:
■ The expected tax on the sale of the building and equipment in the last year; ■ The cash outflow for taxes from the change in revenues and expenses; and ■ The cash inflow from the depreciation tax shield.
Each different tax assumption changes the project’s net cash flows as follows:
LONG-TERM INVESTMENT DECISIONS
Net Cash Flow
Year Tax rate = 20% Tax rate = 30% Tax rate = 40%
+489,987 We can see that the value of this project, hence any decision made based
on this value, is sensitive to what we assume will be the tax rate. We could take each of the “what if” tax rate assumptions and re- calculate the value of the investment.
If the ... the net present value using tax rate is ...
a cost of capital of 5% is ...
But when we do this, we have to be careful—the net present value requires discounting the cash flows at a rate that reflects risk—but that is what we are trying to figure out! So we shouldn’t be using the net present value method in evaluating a project’s risk in our sensitivity analysis.
An alternative is to recalculate the internal rate of return under each “what if” scenario.
If the ... the internal tax rate is ... rate of return will be ...
16.32% And this illustrates one of the attractions of using the internal rate
of return to evaluate projects. Despite its drawbacks in the case of mutually exclusive projects and in capital rationing, as pointed out in Chapter 13, the internal rate of return is more suitable to use in assess- ing a project’s attractiveness under different scenarios and, hence, that
Capital Budgeting and Risk
project’s risk. Why? Because the net present value approach requires us to use a cost of capital to arrive at a project’s value, but the cost of cap- ital is what we set out to determine! We would be caught in a vicious circle if we used the net present value approach in sensitivity analysis. But the internal rate of return method does not require a cost of capital; instead, we can look at the possible internal rates of return of a project and use this information to measure a project’s risk.
If we can specify the probability distribution for tax rates, we can put sensitivity analysis together with the statistical measures of risk. Suppose that in the analysis of the Williams project it is most likely that tax rates be 30%, though there is a slight probability that tax rates will
be lowered and a chance that tax rates will be increased. More specifi- cally, suppose the probability distribution of future tax rates and, hence the project’s internal rate of return, is:
that the and hence the internal Probability is ... tax rate will be ... rate of return will be ...
Applying the calculations for the statistical measures of risk to this distribution,
Expected internal rate of return = 17.433% Standard deviation of possible internal rates of return = 1.148% Coefficient of variation
= 0.066 We could then judge whether the project’s expected return is suffi-
cient considering its risk (as measured by the standard deviation). We could also use these statistical measures to compare this project with other projects under consideration.
Sensitivity analysis illustrates the effects of changes in assumptions. But because sensitivity analysis focuses only on one change at a time, it is not very realistic. We know that not one, but many factors can change throughout the life of a project. In the case of the Williams project, there are a number of assumptions built into the analysis that are based on uncertainty, including the sales prices of the building and equipment in five years and the entrance of competitors no sooner than five years. And you can use your imagination and envision any new product and the attendant uncertainties including the economy, the firm’s competi- tors, and the price and supply of raw materials and labor.
LONG-TERM INVESTMENT DECISIONS
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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