Options on Real Assets The valuation of stock options is rather complex, but with the assis-
Options on Real Assets The valuation of stock options is rather complex, but with the assis-
tance of some well-accepted models such as the Black-Scholes model, we can estimate the value of an option. For example, in the Black-Scholes option pricing model discussed in Appendix A, there are five factors that are important in the valuation of an option: 6
1. The value of the underlying asset, P
2. The exercise price or strike price of the option, E
3. The risk free rate of interest, r
4. The volatility of the value of the underlying asset, σ
5. The time remaining to the expiration of the option, T In Chapter 9 we examine the relation between each of these factors
and the value of a stock option. Our focus here is to map these factors onto a real asset option. Like other options, real options may be a call option (the option to buy an asset), a put option (the option to sell an asset), or a compound option (an option on an option). And, like other options, real options may be a European option (an option that can only
be exercised on the expiration date) or an American option (an option that can be exercised at any time on or before the expiration date). In general terms, the relation between the factors that affect the value of a stock option and those that affect a real option correspond as follows:
6 Fischer Black and Myron Scholes, “The Pricing of Options and Corporate Liabili- ties,” Journal of Political Economy (May/June 1973), pp. 637–659.
Capital Budgeting and Risk
Parameter Option on a Stock Option on a Real Asset
X The stock’s price The present value of cash flows from the investment opportunity S
The exercise price of the The present value of the delayed capital option
expenditure or future cost savings r
The risk-free rate of interest The risk-free rate of interest
s Volatility of value of the Uncertainty of the project’s cash flows underlying asset t
The time to maturity The project’s useful life Of course, the factors that correspond to a specific option can be
better described when we examine the particular option. Consider the option to abandon. In this case, the underlying asset is continuing oper- ations and so the value of the underlying asset is the present value of the cash flows associated with the asset. The strike price or exercise price for this option is the exit value or salvage value of the asset. A number of common real options are described in Exhibit 14.5.
EXHIBIT 14.5 Examples of Real Options
Option Type*
Value of Underlying Asset
Exercise Price
To abandon American The present value of the The exit or salvage put
cash flows from the
value
abandoned assets
To defer an American The present value of The deferred invest- investment
call
completed project’s net
ment outlay
operating cash flows
To abandon Compound The present value of the The investment outlay during
necessary for the next construction
option
completed project’s cash
stage To contract
flows
European The present value of The costs of rescaling the scale
the project of a project To expand
put
potential cost savings
European The present value of The additional invest- call
incremental net operating
ment outlay
cash flows
To switch inputs American The present value of the The cost of retooling or outputs
put incremental cash flows from production or distri- the best alternative use
bution *A put option is an option to sell the underlying asset; a call option is an option to
buy the underlying asset. An American option is one that can be exercised at any time up to and including the expiration date; a European option is one that can only be exercised at the expiration date.
LONG-TERM INVESTMENT DECISIONS
Identifying the options associated with an investment opportunity is the first step. The second step is to value these options. Consider an investment opportunity to defer an investment. This investment oppor- tunity is similar to what a firm experiences in their investment in research and development: An expenditure or series of expenditures are made in research and development and then sometime in the future, depending on the results of the research and development, the actions of competitors, and the approval of regulators, the firm can then decide whether to go ahead with the investment opportunity.
Real Options: An Example Let’s put some numbers to the analysis of a project with a real option.
Suppose that research and development is $2 million initially and $2 million more for each of the next three years. And suppose that at the end of the fourth year the firm has an option to either go ahead with the product or simply abandon it. If the firm goes ahead with the develop- ment of the product, this will require an investment of $100 million at the end of the fourth year. To make the analysis simpler, let’s assume that we can sell the investment in the product to another party—that is,
cash out—at the end of the fourth year for $120 million. 7 And, because we know that all of this is uncertain, let’s attach probabilities of this being a marketable product and, hence, one that the firm is able to cash out. Let’s assume that there is a 60% chance that the firm can cash out for $120 million and a 40% change that the firm cannot cash out at all (and will, therefore, not make the investment).
Given this scenario, it means that: ■ If the R&D is successful and the firm is able to cash out, the value at
the end of the fourth period is $120 million – $100 million = $20 million.
■ If the R&D is not successful and the firm is not able to cash out, the value at the end of the fourth period is $0.
Before we can value the project with or without the option, we need to estimate the cost of capital. The cost of capital is the sum of the risk- free rate of interest and the risk premium. 8 The risk premium is deter- mined relative to the market’s risk premium. Suppose the risk-free rate
7 We are simplifying this example. More realistically, we would estimate future cash flows from the successful project beyond the fourth year and discount these to the
end of the fourth year—and then use this value in place of the $120 million. 8 To be consistent with the Black-Scholes option-pricing model, we’ll use continuous-
ly compounded cost of capital throughout our example.
Capital Budgeting and Risk
of interest is 5%, the market risk premium is 4%, and the volatility is 5 times that of the market. If the market’s volatility (i.e., the standard deviation of expected cash flows) is 15%, the cost of capital is: 9
Cost of capital = Risk-free rate of interest + Risk premium = 5% + ( 5 4% ) = 25%
Using a continuously compounded discount rate of 25%, the present value of the research and development costs is –$5.72 million:
in millions 0 1 2 3
Research and development –$2.00 –$2.00 –$2.00 –$2.00 Present value of research and development –$2.00 –$1.56 –$1.21 –$0.94 Total present value of R&D
Putting the R&D together with the value of the investment four years from today,
$20 million NPV = – $5.720 million + ( 0.60 ) ------------------------------ ( 4 0.25 ) + [ ( 0.40 ) $0 ( ) ]
= – $5.720 million + 4.415 million = – $1.305 million This NPV represents the cost to the firm if the firm makes the decision
today to commit to both the R&D and the investment at the end of the fourth year.
Using the traditional capital budgeting NPV technique, this suggests that we should reject the project because its net present value is less than $0. But wait—we have not considered the valuable option of the deferred investment because the firm can wait until the end of the fourth year to decide on the investment.
We can see the value of the option by estimating how much value the option itself adds to the project. First, we estimate the parameters of the option pricing model. Then we see how the value of the option, when considered along with the present value of the cost of acquiring the option (that is, the present value of the research and development), can make an unattractive project into an attractive project.
9 This means that the volatility of the project’s cash flows are 5(15%) = 75%. This is the estimate of volatility that we include in the valuation of the project’s option.
LONG-TERM INVESTMENT DECISIONS
The value of the underlying asset is the discounted value of the probability-weighted possible outcomes:
Value of the underlying asset = 0.6 $120 million --------------------------------- + [ ( 0.40 ) $0 ( ) ] e ( 4 0.25 )
= $26.487 million
Therefore, the value of the parameters in the option valuation are as fol- lows:
Value of the underlying asset $26.487 million Strike price
$100.000 million Risk-free rate of interest
Number of periods to exercise 4 Using the Black-Scholes option pricing formula, the value of this
option is $7.774 million. Therefore, the value of the project is:
Project NPV = Present value of the R&D + Value of the option
= – $5.72 million + 7.774 million Project NPV = $2.054 million
Another way of looking at this is to estimate the value-added of the deferral option:
Value-added of the option = Project NPV Static NPV – = $2.054 million – ( – 1.305 million ) Value-added of the option = $0.749 million
Hence, the project has a positive NPV considering the valuable option to defer investment.
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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