Valuing the Option to Expand Capacity

Perhaps the most important application of the real options approach is assessing the

importance of flexibility in the design of investment projects. In an uncertain environ-

ment, flexibility—such as the ability to take a project already initiated and expand it,

reduce its scale (perhaps liquidating some of its assets), or completely abandon it—is

an option, and each option available enhances the project’s value.

One example of flexibility is the abandonment option seen earlier in this chapter

when we discussed the valuation of a copper mine. There, the mine owner simply

stopped mining copper at no cost. This is probably unrealistic, as flexibility generally

imposes some costs on the firm. For example, scaling down or scaling up the capacity

of a project already started often requires additional cash—for example, severance pay-

ments or shutdown costs with scaling down and additional machinery or employees

with scaling up. It is therefore important to value the option to be flexible and com-

pare it with the cost of acquiring that flexibility. Example 12.6 demonstrates how to

use the binomial approach to value investment projects that have this more complex

flexibility.

Example 12.6:Valuing the Option to Increase a Plant’s Capacity

Acme Industries is considering building a plant.The plant will generate cash flows two years

from now, as described in Exhibit 12.6.The cash flows from the plant will be $200 million

following two good years (point D), $150 million following one good and one bad year (point

E), and $100 million (point F) following two bad years.The initial cost of the plant is $140

million (point A).After one year, however, if the state of the economy looks good, the firm

has the option to double the plant’s capacity by investing another $140 million.

Exhibit 12.7 shows that doubling the plant’s capacity will have the effect of doubling the

cash flows to either $400 million or $300 million in its final year (compare the two point Ds

and points Eand E1 in Exhibits 12.6 and 12.7).Assume a risk-free rate of 5 percent per

year and that $1.00 invested in the market portfolio today yields future values, depending on

the state of the economy, shown by the tree diagram in Exhibit 12.8.The corresponding risk-

neutral probabilities, and 1 , attached to the nodes in the tree have been computed

to be consistent with these market portfolio values and appear next to the branches in the

tree diagram in Exhibit12.8.

Compute the value of building a plant under two scenarios:In scenario 1, the option to

double the plant’s capacity is ignored;in scenario 2, it is not ignored.

Answer:Scenario 1:Applying the risk-neutral probabilities, and 1 ,from Exhibit

12.8 to compute expectations and discounting at the 5 percent per year risk-free rate implies

that the value of the plant at point B(the good node) in Exhibit 12.6 is

Grinblatt892Titman: Financial	III. Valuing Real Assets	12. Allocating Capital and	© The McGraw892Hill
Markets and Corporate		Corporate Strategy	Companies, 2002
Strategy, Second Edition

Chapter 12Allocating Capital and Corporate Strategy	439
EXHIBIT12.6Cash Flows If There Is No Capacity Change at Year1

Year 0 Year 1 Year 2

D $200 million if 2 good years

B

–$140 A	Good
		E $150 million if 1 good year and 1 bad year
million
	C

Bad	F $100 million if 2 bad years

EXHIBIT12.7Cash Flows If Plant Capacity Is Doubled at Good Node in Year1

Year 0 Year 1 Year 2

–$140	D $400 million
million
B

		E1 $300 million
	Good
–$140
million		E2 $150 million
	C

Bad
	F $100 million

(.53)$200 million (.47)$150 million

$168.10 million

1.05

The value of the plant at point C(the bad node) in Exhibit 12.6 is

(.35)$150 million (.65)$100 million

$111.90 million

1.05

The value of the plant at point A(the initial node) is thus

(.5)$168.10 million(.5)$111.90 million

$133.33 million

1.05

which yields a net present value of $6.67 million $133.33 million $140 million.

Grinblatt894Titman: Financial	III. Valuing Real Assets	12. Allocating Capital and	© The McGraw894Hill
Markets and Corporate		Corporate Strategy	Companies, 2002
Strategy, Second Edition

440	Part IIIValuing Real Assets

EXHIBIT12.8

Market Portfolio Payoffs forDetermining Risk-Neutral Probabilities in Example 12.6

Year 0 Year 1 Year 2

 = .53$1.60 if good

$1.30

 = .5
	Good 1 –  = .47	$1.10 if bad

$1.00		 = .35
			$1.10 if good
	1 –  = .5$.80

Bad
	1 –  = .65
		$.70 if bad

Scenario 2:Using the risk-neutral probabilities from Exhibit 12.8, the value of the plant

at point B(the good node) in Exhibit 12.7 is

(.53)$400 million(.47)$300 million

$140 million $196.19 million

1.05

The $140 million appears in this equation because at point B,the firm takes advantage of

the option to double the plant’s capacity by spending an additional $140 million.The point

Cvalue is the same as in scenario 1.Thus, the value of the plant at date 0 is

(.5)$196.19 million(.5)111.90 million

$146.71 million

1.05

which yields a net present value of $6.71 million $146.71 million $140 million.

Ignoring the option to increase the plant’s capacity (scenario 1 in Example 12.6)

results in a $140 million cost that exceeds the present value of its future cash flows

($133.33 million). Thus, a naive forecast of the cash flows of the plant makes it appear

as though building the plant destroys value. However, unless Acme builds the plant at

year 0, it can never take advantage of the option to increase capacity. Scenario 2 in

Example 12.6 shows that this flexibility option enhances the value of building the plant

by more than $13 million, enough to turn an apparent negative NPVproject into a pos-

itive NPVone.