12.2Valuing Strategic Options with the Real Options Methodology

The term strategic optionsis an appropriate label for the opportunities that arise from

the ability to alter a project midcourse or to enter into new projects as a result of some

investment. There are two reasons for this. First, strategic options represent strategies

that the firm has an option to pursue only by taking on the earlier project; that is, unless

the firm undertakes the earlier project, there is no possibility of obtaining the cash flows

from the strategic option. Second, strategic options are valued with the same option

pricing methodology developed in Chapter 7 (and applied to options in Chapter 8). This

section analyzes the application of this pricing methodology for the valuation of real

assets.

We indicated in Chapter 7 that a derivative is an investment whose value is deter-

mined by the value of another investment. One example is a stock option, which has

a value determined by the price of the underlying stock. Another example is a forward

contract to purchase copper for a specific price at a specific date in the future. The

techniques used to value derivatives also can be used to value projects in relation to

some underlying financial asset(s). In the following sections, we will illustrate the use

of the real options methodology to value:

•	Amine with no strategic options.
•	Amine with an abandonment option.
•	Vacant land.
•	The option to delay the start of a project.
•	The option to expand capacity.
•	Flexibility in production technology.

Valuing a Mine with No Strategic Options

The valuation of natural resource investments (for example, oil wells and copper mines)

illustrates how to implement the real options approach developed in this chapter. This

subsection focuses on a copper mine. The choice of a mine stems from the unambigu-

ous connection to an underlying asset, a forward contract on a metal, and thepopular-

ity, in practice, of the real options approach among natural resource firms. For example,

the trade literature on energy is filled with articles on strategic options, which have

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Markets and Corporate		Corporate Strategy	Companies, 2002
Strategy, Second Edition

Chapter 12

Allocating Capital and Corporate Strategy

427

been embraced by large diversified companies like Enron ($60 billion market capital-

ization in 2001) as well as smaller independent oil companies like Anadarko ($16 bil-

lion market capitalization in 2001).

This subsection first examines how to use real options techniques to value a cop-

per mine when no strategic options exist. In the absence of strategic options, the

approach to mine valuation is identical to the certainty equivalent method discussed in

Chapter 11.

The cash flows of a copper mine can be tracked by financial assets since the mine’s

value is largely determined by the price of copper. Suppose that some of the copper in

the mine will be extracted at date 1 and the remainder at date 2. If the extraction costs

are known or can be contracted for in advance, then the cash flows from this mine are

contingent only on the price of copper. The date 1 and date 2 cash flows from the mine,

Cand C, respectively, can be expressed as

12

C pQK

1111

C pQK

2222

where

p date 1 copper price

1

p date 2 copper price

2

Q date 1 quantity of copper extracted

1

Q date 2 quantity of copper extracted

2

K date 1 cost of extraction

1

K date 2 cost of extraction

2

Only pand pare assumed to be unknown at the adoption decision time, date 0.

12

Profits from holding a forward contract on copper also are determined only by the

price of copper. Exhibit 12.1 illustrates the cash flows of forward contracts to exchange

Qunits of copper for cash at future date t.⁶

t

It is possible to use the forward prices from copper forward contracts maturing at

dates 1 and 2 to value the copper mine. To see this, note that the respective cash flows

at dates 1 and 2 from operating the mine, pQKand pQK, are exactly the

111222

same as the future cash flows incurred by holding the following tracking portfolio:

1.Aforward contract to purchase Qunits of copper at date 1 at the current

1

forward price of Fper unit, and a second forward contract to purchase Q

12

units of copper at date 2 at the current forward price of Fper unit.

2

2.Arisk-free zero-coupon bond paying FQKin year 1, and a second risk-

111

free zero-coupon bond paying FQKat date 2.

222

Since Fand Frepresent the current forward prices, the contracts have zero value

12

at date 0 and thus item 1 in the tracking portfolio (see above) costs nothing. The pres-

ent value of the uncertain cash flows from the mine equal the present value of the zero-

coupon bonds in item 2. The value of the mine thus equals

FQKFQK

1 1¹2 22

PV

(1r)(1r)²

12

⁶The absence of a cash flow at the initiation of these contracts is another way of saying that the

future exchange price of these contracts is set to a value that makes the contracts have zero present

value.

Grinblatt870Titman: Financial	III. Valuing Real Assets	12. Allocating Capital and	© The McGraw870Hill
Markets and Corporate		Corporate Strategy	Companies, 2002
Strategy, Second Edition

428	Part IIIValuing Real Assets

EXHIBIT12.1

Cash Flows of Forward Contracts to Exchange QUnits of t CopperforCash at Future Date t

Date 0

Date t

Long forward

No cash
	Q t F t	Q t p t
exchanged

Short forward

F = Forward price agreed upon

t

at date 0 (certain)

p = Price of copper at date

t

t (uncertain)

t Q ( p ) = Incremental cash flow

–

t t F

where

r the yield to maturity of zero-coupon bonds maturing at date t

t

(t 1, 2)

FQK the future payment of the zero-coupon bond maturing at date t

ttt

(t 1, 2)

Example 12.1 implements this valuation procedure numerically.

Example 12.1:Valuing a CopperMine

Lincoln Copper Company has a mine that will produce a total of 75,000 pounds of copper:

25,000 pounds of copper at the end of the first year and 50,000 pounds of copper at the

end of the second year.Extraction costs are always $0.10 per pound.The current forward

prices are $0.65 per pound for a one-year contract and $0.60 per pound for a two-year con-

tract.The annually compounded risk-free rates are 5 percent for one-year zero-coupon bonds

and 6 percent for two-year zero-coupon bonds.

What is the present value of the cash flows from the mine, assuming that payments for

the mined copper are received at the end of each year?

Answer:

$.65(25,000)$.10(25,000)$.65(50,000)$.10(50,000)

Mine value

1.05(1.06)²

$35,345

The valuation of the copper mine in Example 12.1 is based on identifying the cost

of a combination of investments traded in the financial market that perfectlytrack the

copper mine’s future cash flows at the end of the first and second years. As Exhibit

12.2 illustrates, the forward contracts (items aand b), in combination with a series of

zero-coupon bonds maturing at two different dates (items cand d), produce future cash

flows (bottom row, two right-hand columns) identical to those of the copper mine. The

Grinblatt872Titman: Financial	III. Valuing Real Assets	12. Allocating Capital and	© The McGraw872Hill
Markets and Corporate		Corporate Strategy	Companies, 2002
Strategy, Second Edition

Chapter 12

Allocating Capital and Corporate Strategy

429

EXHIBIT12.2

Future Cash Flows and Current Costs of CopperMine versus Portfolio of Forward Contracts andZero-CouponBonds

F Year 1 forward price $.65 per pound

1

F Year 2 forward price $.60 per pound

2

	Cost	Cash Flow	Cash Flow
	Beginning of	End of	End of
Investment	First Year	First Year	Second Year

Copper Mine	PVUnknown	25,000(p$.10)	50,000(p$.10)
		1	2

a.Forward contract to buy	$0	25,000(p$.65)	$0
		1
25,000 pounds of copper at
beginning of year 1

b.Forward contract to buy	$0	$0	50,000(p$.60)
			2
50,000 pounds of copper at
beginning of year 2

c.	Buy zero-coupon bonds;	$25,000(.65 .10)	$25,000(.65 .10)	$0
	Maturity year 1	1.05
	Face amount $25,000(.65 .10)

d.Buy zero-coupon bonds;	$50,000(.60.10)	$0	$50,000(.60 .10)
	1.062
Maturity year 2
Face amount $50,000(.60 .10)

Total: abcd	$35,345	25,000(p$.10)	50,000(p$.10)
		1	2

tracking portfolio costs $35,345, which is the value attributed to the identical future

cash flows of the copper mine.⁷