762  Flexibility
There are advantages to using either ROV or DTA, depending on the types 
of risks involved. In theory, ROV is more accurate. But it is not the right ap-
proach in every case. It cannot replace traditional discounted cash flow, be-
cause valuing an option using ROV still depends on knowing the value of the 
underlying assets. Unless the assets have an observable market price, you will 
have to estimate that value using traditional DCF.
Company-wide valuation models rarely take flexibility into account. To ana-
lyze and model flexibility accurately, you must be able to describe the set of spe-
cific decisions managers could make in response to future events and include 
the cash flow implications of those decisions. In valuing a company, flexibility 
therefore becomes relevant only in cases where management responds to spe-
cific events that may change the course of the whole company. For example, to 
value internet or biotech companies with a handful of promising new products 
in development, you could project sales, profit, and investments for the com-
pany as a whole that are conditional on the success of product development.3 
Another example is a company that has built its strategy around buying up 
smaller players and integrating them into a bigger entity, capturing synergies 
along the way. The first acquisitions may not create value in their own right but 
may open opportunities for value creation through further acquisitions.
Flexibility is typically more relevant in the valuation of individual businesses 
and projects, as it mostly concerns detailed decisions related to production, ca-
pacity investment, marketing, research and development, and other factors.
Uncertainty, Flexibility, and Value
To appreciate the value of flexibility and its key value drivers, consider a simple 
example.4 Suppose you are deciding whether to invest $6,000 one year from now 
to produce and distribute a new pharmaceutical drug already under develop-
ment. In the upcoming final development stage, the product will undergo clinical 
tests on patients for one year, for which all investments have already been made. 
These tests involve no future cash flows. The trials could have one of two possible 
outcomes. If the drug proves to be highly effective, it will generate an annual net 
cash inflow of $500 into perpetuity. If it is only somewhat effective, the annual net 
cash inflow will be $100 into perpetuity. These outcomes are equally probable.
Based on this information, the expected future net cash flow is $300, the 
probability-weighted average of the risky outcomes ($500 and $100). To keep it 
simple, we assume that success in developing the new product and the value 
3 See, for example, E. S. Schwartz and M. Moon, “Rational Pricing of Internet Companies,” Financial 
Analysts Journal 56, no. 3 (2000): 62–75; and D. Kellogg and J. Charnes, “Real-Options Valuation for a 
Biotechnology Company,” Financial Analysts Journal 56, no. 3 (2000): 76–84.
4 The example is inspired by A. Dixit and R. Pindyck, Investment under Uncertainty (Princeton, NJ: 
Princeton University Press, 1994), 26.

Uncertainty, Flexibility, and Value  763
of the new product are unrelated to what happens in the overall economy, so 
this risk is fully diversifiable by the company’s investors. Therefore, the beta 
for this product is zero, and the cost of capital equals the risk-free rate—say, 5 
percent. Assuming that the company will realize its first year’s product sales 
immediately upon completing the trials and at the end of each year thereafter, 
the net present value (NPV) of the investment is estimated as follows:
NPV = −
+
=
=
∞
∑
$ ,
.
$
( .
)
$
6 000
1 05
300
1 05
286
1
t
t
To apply the NPV approach, we discount the incremental expected project 
cash flows at the cost of capital. Any prior development expenses are irrel-
evant, because they are sunk costs. Alternatively, if the project is canceled, 
the NPV equals $0. Therefore, management should approve the incremental 
investment of $6,000.
In this example of the NPV decision rule, undertaking development cre-
ates value. But there are more alternatives than deciding today whether to 
invest. Using an approach like the scenario approach described in Chapter 
17, we can rewrite the previous NPV calculation in terms of the probability-
weighted values of the drug, discounted to today:
NPV =
−
+
(
)








+
−
=
∞
∑
0 5
6 000
1 05
500
1 05
0 5
6 000
1 05
1
.
$ ,
.
$
.
.
$ ,
.
t
t
+
(
)








=
+
−
=
=
∞
∑
$
.
. ($ ,
)
. ( $ ,
)
$
100
1 05
0 5 4 286
0 5
3 714
286
1
t
t
Here, the NPV is shown as the weighted average of two distinct results: a 
positive NPV of $4,286 following a favorable trial outcome and a negative NPV 
of –$3,714 for an unfavorable outcome. If the decision to invest can be deferred 
until trial results are known, the project becomes much more attractive. Specifi-
cally, if the drug proves to be less effective, the project can be halted, avoiding 
the negative NPV. You invest only if the drug is highly effective, and the annual 
cash flow of $500 more than compensates for the investment required. In prac-
tice, there would likely be an upfront investment need for the trial, regardless of 
its outcome, but we have abstracted from such costs to keep the example simple.
This flexibility is an option to defer the investment decision. To value the 
option, a contingent NPV approach can be used, working from right to left in 
the payoff tree shown in Exhibit 39.2.
NPV
Max
=
×
−
+
(
)














+
=
∞
∑
0 5
6 000
1 05
500
1 05
0
1
.
$ ,
.
$
.
,
t
t
0 5
6 000
1 05
100
1 05
0 5
1
.
$ ,
.
$
.
,
.
×
−
+
(
)














=
=
∞
∑
Max
0
t
t
($ ,
)
. ( )
$ ,
4 286
0 5 0
2 143
+
=