Step 2: Model Uncertainty Using an Event Tree  Both risks can be modeled 
in a combined event tree (see Exhibit 39.17). For simplicity, we have chosen 
a one-step binomial lattice to describe the evolution of the drug value over 
each three-year period.29 Assuming an annual volatility of 15 percent, we can 
derive the upward and downward movements, u and d, as follows:
u =
=
=
=
=
=
e
e
d
u
T
σ
0 15 3
1 30
1
1
1 30
0 77
.
.
.
.
The probability of an upward movement is 86 percent, and the probability 
of a downward movement is 14 percent.30 The value of a marketable drug 
29 With more nodes, the tree quickly becomes too complex to show in an exhibit, because it does not 
converge in the technological risk. We carried out the analysis with ten nodes and found that doing so 
did not affect the results for this particular example.
EXHIBIT 39.17  Event Tree: R&D Option with Technological and Commercial Risk
$ million
Research phase
Testing phase
Marketing
Value up
Value down
PV6 (Drug) = 7,254
Invest6 
 = 
 (150)
PV3 (Drug) = 5,594 
PV0 (Drug) = 4,314 
Invest0 
 = 
 (100)
Invest3 = (250)
PV3 (Drug) = 3,327
Invest3 
 = (250)
PV6 (Drug) = 4,314 
Invest6 
 = 
 (150)
q = 86%
1 – q = 14%
Stop
Stop
Success
Failure
p = 40%
1 – p = 60%
Value up
Value down
q = 86%
1 – q = 14%
Stop
Success
Failure
p = 15%
1 – p = 85%
Value up
Value down
PV6 (Drug) = 4,314 
Invest6 
 = 
 (150)
PV6 (Drug) = 2,566
Invest6 
 = 
 (150)
q = 86%
1 – q = 14%
Success
Failure
p = 40%
1 – p = 60%
Technological risk event
Commercial risk event
Decision event
Note: PVt (Drug) = present value of marketable drug as of year t 
 
 
 
Investt = investment as of year t 
 
 
 
 
  p = probability of technological success 
 
 
 
 
  q = probability of drug value increase
30 The formula for estimating the upward probability is:
(
)
.
.
.
.
.
1
1 07
0 77
1 30
0 77
0 86
3
+
−
−
=
−
−
=
k
d
u
d
T
where k is the expected return on the asset.
Real-Option Valuation and Decision Tree Analysis  789

790  Flexibility
at the start of the research phase is $4,314 million. At the end of the research 
phase, there are three possible outcomes: success combined with an increase 
in the value of a marketable drug to $5,594 million, success combined with 
a decrease in the value of a marketable drug to $3,327 million, and failure 
leading to a drug value of $0. Following the same logic, there are six possible 
outcomes after the testing phase.
Step 3: Model Flexibility Using a Decision Tree  The logic underlying the 
decision tree including commercial risk (see Exhibit 39.18) is the same as under 
the DTA approach. For example, the payoff at the end of the testing phase in 
the top branch equals Max[($7,254 – $150), 0] = $7,104. The primary difference 
is that the ROV version of the tree recognizes the ability to abandon develop-
ment if the value of a marketable drug drops too much.
Step 4: Estimate Contingent NPV  The commercial risk regarding the drug’s 
future cash flows is not diversifiable,31 so you need to use an ROV approach 
to include it in your valuation. This example uses risk-neutral valuation. 
EXHIBIT 39.18  Decision Tree: R&D Option with Technological and Commercial Risk
$ million
Research phase
Testing phase
Marketing
Technological risk event
Commercial risk event
Decision event
Value up
Value down
NPV3 = 1,936
NPV3 = 1,029
q* = 74%
1 – q* = 26%
NPV6 = 0
NPV6 = 0
NPV0 = 120
NPV6 = 7,104
NPV6 = 4,164
NPV6 = 4,164
NPV6 = 2,416
Success
Failure
p = 40%
1 – p = 60%
Value up
Value down
q* = 74%
1 – q* = 26%
NPV3 = 0 
Success
Failure
p = 15%
1 – p = 85%
Value up
Value down
q* = 74%
1 – q* = 26%
Success
Failure
p = 40%
1 – p = 60%
Note: NPVt = net present value of project as of year t 
 
 
 
q* = binomial (risk-neutral) probability of an increase in marketable drug value 
 
 
 
p = probability of technological success
31 Recall that we assumed the cost of capital for a marketed drug is 7 percent. Given our assumption for 
a risk-free rate of 5 percent, its beta must be different from zero.