Implied volatility

Deep in	Deep out of
the money	the money	Strike
		price

8.11 Summary and Conclusions

This chapter developed the put-call parity formula, relat-The pricing of both American calls on dividend-payinging the prices of European calls to those of European puts,stocks and American puts cannot be derived from Euro-and used it to generate insights into minimum call values,pean call pricing formulas because it is sometimes optimalpremature exercise policy for American calls, and the rel-to exercise these securities prematurely. This chapter usedative valuation of American and European calls. The put-the binomial method to show how to price these more com-call parity formula also provided insights into corporateplicated types of options.

securities and portfolio insurance.This chapter also discussed a number of issues relating

This chapter also applied the results on derivative secu-to the implementation of the theory, including (1) the esti-rities valuation from Chapter 7 to price options, using twomation of volatility and its relation to the concept of an im-approaches: the binomial approach and the Black-Scholesplied volatility, (2) extending the pricing formulas to com-approach. The results on European call pricing with theseplex underlying securities, and (3) the known empiricaltwo approaches can be extended to European puts. Thebiases in option pricing formulas. Despite a few biases input-call parity formula provides a method for translatingthe Black-Scholes option pricing formula, it appearsthe pricing results with these models into pricing results forthatthe formulas work reasonably well when properlyEuropean puts.implemented.

Key Concepts

Result 8.1:	(The put-call parity formula.) If no	Result 8.2:	It never pays to exercise an American call
	dividends are paid to holders of the		option prematurely on a stock that pays no
	underlying stock prior to expiration, then,		dividends before expiration.
	assuming no arbitrage	Result 8.3:	An investor does not capture the full value
			of an American call option by exercising
	c pS PV(K)
	000		between ex-dividend or (in the case of a
	That is, a long position in a call and a short		bond option) ex-coupon dates.
	position in a put sells for the current stock
		Result 8.4:	If the underlying stock pays no dividends
	price less the strike price discounted at the
			before expiration, then the no-arbitrage
	risk-free rate.
			value of American and European call
			options with the same features are the same.

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Chapter 8

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293

Result 8.5:	(Put-callparityformulageneralized.)	frictionless markets, and has a constant
	c pS PV(K) PV(div). The	variance, then, for a constant risk-free rate,
	000
	difference between the no-arbitrage values	the value of a European call option on that
	of a European call and a European put with	stock with a strike price of Kand Tyears to
	the same features is the current price of the	expiration is given by
	stock less the sum of the present value of
		cSN(d) PV(K)N(d T)
	the strike price and the present value of all	0011
	dividends to expiration.	where
Result 8.6:	It is possible to view equity as a call option
		lnS/PV(K) T
		0
	on the assets of the firm and to view risky	d
		1 T2
	corporate debt as riskless debt worth PV(K)
	plus a short position in a put option on the	The Greek letter is the annualized standard
	assets of the firm ( p) with a strike price	deviation of the natural logarithm of the
	0
	of K.	stock return, ln( ) represents the natural
Result 8.7:	(The binomial formula.) The value of a	logarithm, and N(z) is the probability that a
	European call option with a strike price of	normally distributed variable with a mean
	Kand Nperiods to expiration on a stock	of zero and variance of 1 is less than z.
	with no dividends to expiration and a	Result 8.9:As the volatility of the stock price
	current value of Sis	increases, the values of both put and call
	0
	N	options written on the stock increase.
	1N!
		Result 8.10:An American call (put) option should not
	c
	0r)N
	(1 j!(Nj)!
	fj0
		be prematurely exercised if the forward
	jN jmax[0, jdN jS	price of the underlying asset at expiration,
	(1 )uK]
	0
		discounted back to the present at the
	where
		risk-free rate, either equals or exceeds
	rfrisk-free return per period	(is less than) the current price of the
	risk-neutral probability of an up	underlying asset. As a consequence, if one
	move	is certain that over the life of the option this
	uratio of the stock price to the prior	will be the case, American and European
	stock price given that the up state	options should sell for the same price if
	has occurred over a binomial step	there is no arbitrage.
	dratio of the stock price to the prior	Result 8.11:If the domestic interest rate is greater (less)
	stock price given that the down	than the foreign interest rate, the American
	state has occurred over a binomial	option to buy (sell) domestic currency in
	step	exchange for foreign currency should sell
Result 8.8:	(The Black-Scholes formula.) If a stock that	for the same price as the European option to
	pays no dividends before the expiration of	do the same.
	an option has a return that is lognormally
	distributed, can be continuously traded in

Key Terms

American option258	ex-dividend value277
Black-Scholes formula279	exercise commencement date	259
compound option269	implied volatility282
continuous-time models278	portfolio insurance269
cum-dividend value277	pseudo-American value279
delta284	put-call parity formula261
discrete models278	smile effect291
European option258	volatility279
ex-dividend date266

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294Part IIValuing Financial Assets

Exercises

8.1.	You hold an American call option with a $30 strike	described above? Express your answer
8.2.	price on a stock that sells at $35. The option sellsfor $5 one year before expiration. Compare thecash flows at expiration from (1) exercising the option now and putting the $5 proceeds in a bankaccount until the expiration date and (2) holding onto the option until expiration, selling short the stock, and placing the $35 you receive into thesame bank account. Combine the Black-Scholes formula with the put-call parity formula to derive the Black-Scholesformula for European puts.	algebraically as a function of dfrom the Black- 1 Scholes model. 8.9.The present price of an equity share of Strategy Inc. is $50. The stock follows a binomial process where each period the stock either goes up 10 percent or down 10 percent. Compute the fair market value of an American put option on Strategy Inc. stock with a strike price of $50 and two periods to expiration. Assume Strategy Inc. pays no dividends over the next two periods. The risk-free rate is 2 percent per period.
8.3.8.4.8.5.8.6.8.7.8.8.	Intel stock has a volatility of .25 and a price of$60 a share. AEuropean call option on Intel stock with a strike price of $65 and an expiration time ofone year has a price of $10. Using the Black-ScholesModel, describe how you would construct an arbitrage portfolio, assuming that the present valueof the strike price is $56. Would the arbitrage portfolio increase or decrease its position in Intel stock if shortly thereafter the stock price of Intel roseto $62 a share? Take the partial derivative of the Black-Scholes value of a call option with respect to the underlyingsecurity’s price, S.Show that this derivative is 0 positive and equal to N(d). Hint:First show that 1 SN (d) PV(K)N (d T)equals zero by 011 using the fact that the derivative of Nwith respect 1 to d, N (d) equals . 112 2exp( .5d) 1 Take the partial derivative of the Black-Scholes value of a call option with respect to the volatilityparameter. Show that this derivative is positive andequal to S TN (d). 01 K If PV(K),take the partial derivative of (1r)T f the Black-Scholes value of a call option withrespect to the interest rate r. Show that this f derivative is positive and equal to T PV(K)N(d T )/(1r). 1f Suppose you observe a European call option on astock that is priced at less than the value of S PV(K) PV(div). What type of transaction 0 should you execute to achieve arbitrage? (Be specific with respect to amounts and avoid using puts in this arbitrage.) Consider a position of two purchased calls (AT&T,three months, K30) and one written put (AT&T,three months, K30). What position in AT&T stock will show the same sensitivity to price changes in AT&Tstock as the option position	8.10.Steady Corp. has a share value of $50. At-the- money American call options on Steady Corp. with nine months to expiration are trading at $3. Sure Corp. also has a share value of $50. At-the-money American call options on Sure Corp. with nine months to expiration are trading at $3. Suddenly, a merger is announced. Each share in both corporations is exchanged for one share in the combined corporation, “Sure and Steady.” After the merger, options formerly on one share of either Sure Corp. or Steady Corp. were converted to options on one share of Sure and Steady. The only change is the difference in the underlying asset. Analyze the likely impact of the merger on the values of the two options before and after the merger. Extend this analysis to the effect of mergers on the equity of firms with debt financing. 8.11.FSAis a privately held firm. As an analyst trying to determine the value of FSA’s common stock and bonds, you have estimated the market value of the firm’s assets to be $1 million and the standard deviation of the asset return to be .3. The debt of FSA, which consists of zero-coupon bank loans, will come due one year from now at its face value of $1 million. Assuming that the risk-free rate is 5 percent, use the Black-Scholes Model to estimate the value of the firm’s equity and debt. 8.12.In the chapter’s opening vignette, Chrysler Corporation argued that there was little risk in the government guarantee of Chrysler’s debt because Chrysler also was offering a senior claim of Chrysler’s assets to the government. In light of this, Chrysler’s warrants appear to have been a free gift to the U.S. government that should have been returned to Chrysler in 1983. Evaluate this argument. 8.13.Describe what happens to the amount of stock held in the tracking portfolio for a call (put) as the stock price goes up (down). Hint:Prove this by looking at delta.

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Chapter 8

Options

295

8.14.Callable bonds appear to have market values thatThe risk-free rate is 12 percent from date 0 to date

are determined as if the issuing corporation1 and 15 percent from date 1 to date 2. AEuropean

optimally exercises the call option implicit in thecall on this stock (1)expires in period 2 and (2)has

bond. You know, however, that these options tenda strike price of $8.

to get exercised past the optimal point. Write up a(a)Calculate the risk-neutral probabilities implied

nontechnical presentation for your boss, theby the binomial tree.

portfolio manager, explaining why arbitrage exists(b)Calculate the payoffs of the call option at each

and how to take advantage of it with thisof three nodes at date 2.

investment opportunity.(c)Compute the value of the call at date 0.8.15.The following tree diagram outlines the price of a8.16.Anondividend-paying stock has a current price of

stock over the next two periods:$30 and a volatility of 20 percent per year.

(a)Use the Black-Scholes equation to value a

European call option on the stock above with a Date:012strike price of $28 and time to maturity of three

months.

30

(b)Without performing calculations, state whether

this price would be higher if the call were

20

American. Why?

12.5010(c)Suppose the stock pays dividends. Would

otherwise identical American and European

options likely have the same value? Why?

8

6

References and Additional Readings

Black, Fischer. “The Pricing of Commodity Contracts.”

Journal of Financial Economics3, nos. 1/2 (1976),

pp. 167–79.

Black, Fischer, and Myron Scholes. “The Pricing of

Options and Corporate Liabilities.” Journal of

Political Economy81 (May–June 1973),

pp.637–59.

Cox, John C.; Stephen A. Ross; and Mark Rubinstein.

“Option Pricing: ASimplified Approach.” Journal of

Financial Economics7 (Sept. 1979), pp. 229–63.

Cox, John C., and Mark Rubinstein. Options Markets.

Englewood Cliffs, NJ: Prentice-Hall, 1985.

Galai, Dan, and Ronald Masulis. “The Option Pricing

Model and the Risk Factor of Stock.” Journal of

Financial Economics3, nos. 1/2 (1976), pp. 53–81.Garman, Mark, and Steven Kohlhagen. “Foreign

Currency Option Values.” Journal of International

Money and Finance2, no. 3 (1983), pp. 231–37.

Geske, Robert. “The Valuation of Compound Options.”

Journal of Financial Economics 7, no. 1 (1979),

pp.63–82.

Geske, Robert, and Herb Johnson. “The American Put

Option Valued Analytically.” Journal of Finance39,

no. 5 (1984), pp. 1511–24.

Grabbe, J. O. “The Pricing of Call and Put Options on

Foreign Exchange.” Journal of International Money

and Finance2, no. 3 (1983), pp. 239–53.

Hull, John C. Options, Futures, and Other Derivatives.3d

ed. Upper Saddle River, NJ: Prentice-Hall, 1997.

MacBeth, James D., and Larry J. Merville. “An Empirical

Examination of the Black-Scholes Call Option

Pricing Model.” Journal of Finance34, no. 5 (1979),

pp. 1173–86.

Merton, Robert C. “Theory of Rational Option Pricing.”

Bell Journal of Economics and Management Science

4 (Spring 1973), pp. 141–83.

Ramaswamy, Krishna, and Suresh Sundaresan. “The

Valuation of Options on Futures Contracts.” Journal

of Finance40, no. 5 (1985), pp. 1319–40.

Rendelman, Richard J., Jr., and Brit J. Bartter. “Two-State

Option Pricing.” Journal of Finance34 (Dec. 1979),

pp. 1093–1110.

Rubinstein, Mark. “Nonparametric Tests of Alternative

Option Pricing Models Using All Reported Trades

and Quotes on the 30 Most Active CBOE Option

Classes from August 23, 1976 through August 31,

1978.” Journal of Finance40, no. 2 (1985),

pp.455–80.

Rubinstein, Mark. “Presidential Address: Implied

Binomial Trees.” Journal of Finance4, no. 3 (1994),

pp. 771–818.

Smith, Clifford. “Option Pricing: AReview.” Journal of

Financial Economics3, nos. 1/2 (1976), pp. 3–51.

Grinblatt608Titman: Financial	II. Valuing Financial Assets	8. Options	© The McGraw608Hill
Markets and Corporate			Companies, 2002
Strategy, Second Edition

296Part IIValuing Financial Assets

Stoll, Hans. “The Relationship Between Put and Call———. “Valuation of American Call Options on

Option Prices.” Journal of Finance24, no. 5 (1969),Dividend-Paying Stocks: Empirical Tests.” Journal of

pp. 801–824.Financial Economics10, no. 1 (1982), pp. 29–58.

Whaley, Robert. “On the Valuation of American Call

Options on Stocks with Known Dividends.” Journal

of Financial Economics9, no. 2 (1981), pp. 207–11.

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Chapter 8Options		297
PRACTICALINSIGHTSFORPART	II

Allocating Capital forReal Investment

•Mean-variance analysis can help determine the risk

implications of product mixes, mergers and

acquisitions, and carve-outs. This requires thinking

about the mix of real assets as a portfolio. (Section 4.6)•Theories to value real assets identify the types of risk

that determine discount rates. Most valuation problems

will use either the CAPM or APT, which identify

market risk and factor risk, respectively, as the relevant

risk attributes. (Sections 5.8, 6.10)

•An investment’s covariance with other investments is a

more important determinant of its discount rate than is

the variance of the investment’s return. (Section 5.7)•The CAPM and the APTboth suggest that the rate of

return required to induce investors to hold an

investment is determined by how the investment’s

return covaries with well-diversified portfolios.

However, existing evidence suggests that most of the

well-diversified portfolios that have been traditionally

used, either in a single factor or a multiple factor

implementation, do a poor job of explaining the

historical returns of common stocks. While multifactor

models do better than single factor models, all model

implementations (to varying degrees) have difficulty

explaining the historical returns of investments with

extreme size, market-to-book ratios, and momentum.

These shortcoming need to be accounted for when

allocating capital to real investments that fit into these

anomalous categories. (Sections 5.11, 6.12)

Financing the Firm

•When issuing debt or equity, the CAPM and APTcan

provide guidelines about whether the issue is priced

fairly. (Sections 5.8, 6.10)

•Because equity can be viewed as a call option on the

assets of the firm when there is risky debt financing, the

equity of firms with debt is riskier than the equity of

firms with no debt. (Sections 8.3, 8.8).

•Derivatives valuation theory can be used to value risky

debt and equity in relation to one another (Section 8.3)Knowing Whetherand How to Hedge Risk

•Portfolio mathematics can enable the investor to

understand the risk attributes of any mix of real assets,

financial assets, and liabilities. (Section 4.6)

•Forward currency rates can be inferred from domestic

and foreign interest rates. (Section 7.2)

Allocating Funds forFinancial Investments

•Portfolios generally dominate individual securities as

desirable investment positions. (Section 5.2)

•Per dollar invested, leveraged positions are riskier than

unleveraged positions. (Section 4.7)

•There is a unique optimal risky portfolio when a risk-

free asset exists. The task of an investor is to identify

this portfolio. (Section 5.4)

•Mean-Variance Analysis is frequently used as a tool for

allocating funds between broad-based portfolios.

Because of estimation problems, mean-variance

analysis is difficult to use for determining allocations

between individual securities. (Section 5.6)

•If the CAPM is true, the optimal portfolio to hold is a

broad-based market index. (Section 5.8)

•If the APTis true, the optimal portfolio to hold is a

weighted average of the factor portfolios. (Section 6.10)

Since derivatives are priced relative to other

•

investments, opinions about cash flows do not matter

when determining their values. With perfect tracking

possible here, mastery of the theories is essential if one

wants to earn arbitrage profits from these investments.

(Section 7.3)

•Apparent arbitrage profits, if they exist, must arise from

market frictions. Hence, to obtain arbitrage profits from

derivative investments means that one must be more

clever than competitors at overcoming the frictions that

allow apparent arbitrage to exist. (Section 7.6)

•Derivatives can be used to insure a portfolio’s value.

(Section 8.3)

•The somewhat disappointing empirical evidence on the

CAPM and APTmay imply an opportunity for portfolio

managers to beat the S&P500 and other benchmarks

they are measured against. (Sections 5.8, 6.10, 6.13)•Per dollar of investment, call options are riskier than the

underlying asset. (Section 8.8)

•	The fair market values, not the actual market values, determine appropriate ratios for hedging. These are usually computed from the valuation models for derivatives. (Section 8.8)

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298Part IIExclusive Perspective

EXECUTIVEPERSPECTIVE

Myron S. Scholes

For large financial institutions, financial models are criti-cal to their continuing success. Since they are liability aswell as asset managers, models are crucial in pricing andevaluating investment choices and in managing the risk oftheir positions. Indeed, financial models, similar to thosedeveloped in Part II of this text, are in everyday use inthese firms.

The mean-variance model, developed in Chapters 4 and5, is one example of a model that we use in our activities.We use it and stress management technology to optimizethe expected returns on our portfolio subject to risk, con-centration, and liquidity constraints. The mean-varianceapproach has influenced financial institutions in determin-ing risk limits and measuring the sensitivity of their profitand loss to systematic exposures.

The risk-expected return models presented in Part II,such as the CAPM and the APT, represent another set ofuseful tools for money management and portfolio opti-mization. These models have profoundly affected the wayinvestment funds are managed and the way individualsinvest and assess performance. For example, passivelymanaged funds, which generally buy and hold a proxy forthe market portfolio, have grown dramatically, accountingfor more than 20 percent of institutional investment. Thishas occurred, in part, because of academic writings on theCAPM and, in part, because performance evaluation usingthese models has shown that professional money managersas a group do not systematically outperform these alterna-tive investment strategies. Investment banks use both debt

and equity factor models—extremely important tools—todetermine appropriate hedges to mitigate factor risks. Forexample, my former employer, Salomon Brothers, usesfactor models to determine the appropriate hedges for itsequity and debt positions.

All this pales, of course, with the impact of derivativesvaluation models, starting with the Black-Scholes option-pricing model that I developed with Fischer Black in theearly 1970s. Using the option-pricing technology, invest-ment banks have been able to produce products that cus-tomers want. An entire field called financial engineeringhas emerged in recent years to support these developments.Investment banks use option pricing technology to pricesophisticated contracts and to determine the appropriatehedges to mitigate the underlying risks of producing thesecontracts. Without the option-pricing technology, presentedin Chapters 7 and 8, the global financial picture would befar different. In the old world, banks were underwriters,matching those who wanted to buy with those who wantedto offer coarse contracts such as loans, bonds, and stocks.Derivatives have reduced the costs to provide financialservices and products that are more finely tuned to theneeds of investors and corporations around the world.Mr. Scholes is currently a partner in Oak Hill Capital Management, L.P.and Chairman of Oak Hill Platinum Partners, L.P. located in Menlo Park,CAand Rye Brook, NY, respectively. He is also the Frank E. BuckProfessor of Finance Emeritus, Stanford University Graduate School of

Business and a recipient of the 1997 Nobel Prize in Economics.

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PART
III
	Valuing	Real Assets

Part II focused on how to value financial assets in relation to one another. We learned

that the future cash flows of financial assets, like derivatives and common stock,

can be tracked (nearly perfectly or imperfectly) by a portfolio of some other financial

assets. This tracking relationship allowed us to derive risk-expected return equations

like the CAPM and the APT, as well as describe the no-arbitrage price of a derivative,

given the value of its underlying financial asset.

The lessons learned from studying valuation in the financial markets carry over to

the valuation of real assets, such as factories and machines. There is a tight connection

between the theory of financial asset valuation and corporate finance. Although corpo-

rate managers employ a variety of techniques to value and evaluate corporate invest-

ment projects, all these techniques essentially require tracking of the real asset’s cash

flows with a portfolio of financial assets.

The correct application and appropriateness of real asset valuation techniques

largely depend on how well the corporate manager understands the linkage between

these techniques and the principles used to value financial assets in Part II. When these

techniques are viewed as black boxes—formulas that provide cutoff values that the

manager blindly uses to adopt or reject projects—major errors in project assessment

are likely to arise.

The first issue to address when valuing real assets is what to value. By analogy to

our previous discussion of financial assets, we know that we should be evaluating the

future cash flows that are generated from the asset that is being valued. As we will

emphasize in Chapter 9, cash flows and earnings are two different things, and it is the

cash flows, not the earnings, that are the relevant inputs to be used to value the assets.

Hence, the ability to translate projections of accounting numbers into cash flows, also

considered in Chapter 9, is critical. Chapter 9 also devotes considerable space to the

simple mechanics of discounting, which is critical for obtaining the values of future

cash flows with many of the project evaluation techniques discussed in Part III.

Chapter 10 focuses on projects where the future cash flows of the project are known

with certainty. While this is not the typical setting faced by corporate managers, it is

ideal for gaining an understanding of the merits and appropriate application of various

project-evaluation techniques. In this simplified setting, one can perfectly track the

future cash flows of projects with investments in financial assets. We learn from this

setting that two techniques, the Discounted Cash Flow (DCF) and the Internal Rate of

Return (IRR) approaches, can generally be appropriately used to evaluate projects.

However, there are several pitfalls to watch out for, particularly with the Internal Rate

299

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300Part IIIValuing Real Assets

of Return. In many cases, even the Discounted Cash Flow method has to be modified

to fit the constraints imposed on project selection.

Graham and Harvey (2001), in a recent article in the Journal of Financial Eco-

nomicsentitled “The Theory and Practice of Corporate Finance: Evidence from the

Field,” surveyed 392 CFOs on the practices used by their firms to evaluate investments

in real assets. The two most popular techniques were the Discounted Cash Flow and

the Internal Rate of Return approaches. Each was used by about three of four firms in

the survey. Many firms use both techniques to evaluate their real investment projects.

Necessary modifications of the DCFapproach—for example, the Profitability Index

approach—are also used by some firms (12 percent) where situations call for them.

This approach is also analyzed in Chapter 10.

Other project evaluation techniques include the payback method and the account-

ing rate of return method. Chapter 10 also discusses the pitfalls that are likely to arise

if one employs these two techniques to evaluate projects. There was a time when these

techniques were more popular. However, as the practice of corporate finance has

become more sophisticated, these more traditional approaches have given way to the

DCFand the IRRapproaches.

Of course, one typically applies real asset valuation techniques to value risky future

cash flows. This raises a host of issues, discussed in Chapter 11. Here the principle of

tracking is still applied to value real assets and make appropriate decisions about cor-

porate projects. However, in contrast to Chapter 10, the tracking portfolios for risky

projects do not perfectly track the project’s cash flows. Hence, appropriate techniques

are designed to ensure that the tracking error risk carries no risk premium and thus car-

ries no value.

Managers also use other techniques besides DCF, IRR, payback, and accounting

rate of return methods to evaluate projects. For example, the Graham and Harvey sur-

vey reports that about 40 percent of firms use ratio comparison approaches, such as

Price to Earnings multiples, and 27 percent employ real options approaches, which are

based on the derivative valuation techniques presented in Chapters 7 and 8. These

approaches and their proper use are discussed in Chapter 12. This chapter also shows

how these techniques can be used as tools for evaluating strategies as well as capital

expenditures on projects. For example, a major oil firm would not consider in isolation

the opportunity to develop a natural gas field in Thailand. Instead, the firm would be

thinking about the strategic implications of an increased presence in Asia, with the nat-

ural gas field as only one aspect of that strategy. Chapter 12 discusses how to estimate

the value created by these strategic implications and provides broad principles that

apply even to cases where quantitative estimation is difficult.

Finally, Chapter 13 introduces corporate tax deductions for debt financing and dis-

cusses how the financing of a project may affect its value to the firm. This sets the

stage for Part IV, where the focus is chiefly on the optimal financial structure of a

corporation.

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CHAPTER
9
	Discounting	and	Valuation

Learning Objectives

After reading this chapter, you should be able to:

1.Understand what a present value is.

2.Know how to define, compute, and forecast the unlevered cash flows used for

valuation.

3.Compute incremental cash flows for projects.

4.Mechanically compute present values and future values for single cash flows and

specially patterned cash flow streams, like annuities and perpetuities, in both level

and growing forms.

5.Apply the principle of value additivity to simplify present value calculations.

6.Translate interest rates from one compounding frequency into another.

7.Understand the role that opportunity cost plays in the time value of money.

In 1993, the Times Mirror Corporation implemented a new capital allocation system,

developed with the aid of the Boston Consulting Group. This system, known as Times

Mirror Value Management (TMVM), provided a framework for computing the market

values of real investments by discounting cash flows at the cost of capital. The TMVM

system committed Times Mirror to base investment decisions systemwide on the

discounted value of cash flows rather than on an evaluation of accounting numbers.

Corporations create value for their shareholders by making good real investment

decisions. Real investmentsare expenditures that generate cash in the future and,

as opposed to financial investments, like stocks and bonds, are not financial instruments

that trade in the financial markets. Although one typically thinks about expenditures on

plant and equipment as real investment decisions, in reality, almost all corporate deci-

sions, including those involving personnel and marketing, can be viewed as real invest-

ment decisions. For example, hiring a new employee can be viewed as an investment

since the cost of the employee in the initial months exceeds the net benefits he pro-

vides his employer; however, over time, as he acquires skills he provides positive net

benefits. Similarly, when a firm increases its advertising expenditures, it is sacrificing

current profits in the hope of generating more sales and future profits.

301

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302Part IIIValuing Real Assets

One of the major thrusts of this text is that financial managers should use a market-

based approach to value assets, whether valuing financial assets, like stocks and

bonds, or real assets, like factories and machines. To value these real assets, corporate

managers must apply the valuation principles developed in Part II. There, we used port-

folios to track investments and compared the expected returns (or costs) of the track-

ing portfolios to the expected returns (or costs) of the financial assets we wanted to

value. This allowed us to value the tracked investment in relation to its tracking port-

folio. Models such as the CAPM, the APT, and the binomial derivative pricing model

were used to determine relevant tracking portfolios.

The techniques developed in Part III largely piggyback onto these models and prin-

ciples. The chapters in Part III show how to combine the prices available in financial

markets into a single number that managers can compare with investment costs to eval-

uate whether a real investment increases or diminishes a firm’s value. This number is

present value (PV)¹

the which is the market price of a portfolio of traded securities

that tracks the future cash flowsof the proposed project, (the free cash that a project

generates). Essentially, a project creates value for a corporation if the cost of investing

in the project is less than the cost of investing in a portfolio of financial assets that

track the project’s future cash flows.

Thus, the present value measures the worth of a project’s future cash flows at the

present time by looking at the market price of identical, or nearly identical, future cash

flows obtained from investing in the financial markets. To obtain a present value, you

typically discount (a process introduced in Chapter 7) the estimated future cash flows

of a project at the rate of return of the appropriate tracking portfolio of financial assets.

This rate of return is known as the discount rate. As the name implies, discounting

future cash flows to the present generally reduces them. Such discounting is a critical

element of the TMVM system, as described in the opening vignette.

The mechanics of discounting are the focus of this chapter. There are two aspects

to the mechanics of discounting cash flows

•	Understanding how to compute future cash flows and
•	Applying the formulas that derive present values by applying discount rates tofuture cash flows.

In the conclusion to this chapter, we briefly touch on the issue of why we discount to

obtain present values. More insight into this issue, including the issue of which dis-

count rate to use, is explored in the two chapters that follow this one.