Yale School of Management
Emerging Market Finance:
Lecture 10: The Real-Option Approach
to Valuation in Emerging Markets
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Yale School of Management
The Limitations of Simple NPV
Simple NPV-Analysis:
Treat investment as one-off decision:
 Project stays constant; cannot be adapted.
Treat uncertainty as an exogenous factor
Decision Trees and real options
Managers respond to risk-factors:
Integrate strategy and capital budgeting: What is
the value of flexibility and responsiveness?
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Investment under Uncertainty:
The Simple NPV Rule
0
1
120
2
120
...
...
T
120
...
Period
...
Revenue
if Demand
is high
...
Revenue
if Demand
is low
Initial
Investment
I
80
80
...
80
Cost of Capital = 10%
NPV = - I + 100/0.1 = 1000 - I
Invest if I < 1000
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Investment under Uncertainty: Delay
Strategy: Wait one Period
Case 1: I > 800, do not invest if demand is low
0
1
2
...
T
...
Period
0
-I
120
...
120
...
Revenue
if Demand
is high
...
Revenue
if Demand
is low
Demand
0
NPV =
0
0
0.5
1.1
(- I +
120
1.1
...
+
120
1.12
+... ) =
0
1200 - I
2.2
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Yale School of Management
Investment under Uncertainty: Delay (2)
Strategy: Wait one Period
Case 2: I < 800, always invest
0
1
0
-I
2
...
120
...
T
120
...
Period
...
Revenue
if Demand
is high
...
Revenue
if Demand
is low
Demand
0
NPV =
-I
1
1.1
(- I +
80
100
1.1
...
+
100
1.12
+ ... )=
80
1000 - I
1.1
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Yale School of Management
Summary of Strategies
Decision rule
NPV
(1)
Simple NPV
(2)
Delay if I > 800
1000 - I
1200 - I
2.2
Delay if I < 800
1000 - I
1.1
(3)
 Delay is never optimal if I < 800
 Delay is better than investing now if I > 833
 Investment is never optimal if I > 1200
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Comparison of both Strategies
NPV
I > 1200:
Never invest
833 < I < 1200:
Wait; invest if demand is high
I < 833:
Invest now
1000
909
Vertical distance
= value of flexibility
181
0
I
0
800
833 1000
1200
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Yale School of Management
Results of Comparison (1)
1 If 833 < I < 1000
Investment now has positive NPV = 1000 - I
However: Waiting is optimal in order to see how uncertainty over
demand resolves.
 Benefits from waiting: receive information to avoid
loss.
 Costs of waiting: delay of receiving cash flows.
Investment in positive NPV projects is not always optimal:
the flexibility gained from waiting has a positive value.
Note:
Critical point is 833, not 800, why?
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Results of Comparison (2)
2. If 1000 < I < 1200
Investment now has negative NPV.
However: The project should not be abandoned: if
demand turns out high later, it has a positive NPV.
Negative NPV-projects should be delayed,
but not always be dismissed.
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Total NPV and Simple NPV
Incorporating the Value of Flexibility
 The project can be broken down into two components:
 The investment possibility itself
 Has a Simple NPV of 1000-I
 The flexibility of the project from the option to delay investment
 Value of Flexibility is:
=
Max (Value of investment later - Value of investing now, 0)
 Total NPV is the value of the whole project:
Total NPV = Simple NPV + Value of Flexibility
 Investing immediately ignores that option of delay is valuable
 Decisions must be based on total NPV
The value of flexibility is never negative
Total NPV leads always to the correct decision
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Compute the Value of Flexibility
 If I<833, invest now, hence option to delay has no value.
 If 1000>I>833, then:
 Value of investing now = 1000 - I
 Expected value of investing later is (1200-I)/2.2
 Value of flexibility is then:
1200  I
1.2 I  1000
 ( 1000  I ) 
2.2
2.2
So, with I=833, the value of flexibility is zero, with I=1000 it increases
to 91.
 If 1200> I>1000, the value of flexibility is simply (1200-I)/2.2.
 How does this change if the investment becomes more risky?
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How to Use Total NPV
 Assume I=900>833, hence value of flexibility positive.
 Value of following optimal strategy = Total NPV
 Value of investing now = Simple NPV
 Value of flexibility = 80/2.2=36.4
 Should you invest now?
 Investing now gives 1000-900=100,
 Simple NPV =100>0
 Investing later gives:
 Total NPV = Simple NPV
+ Value of Flexibility
= 100
+ 36.4
= 136.4
 Total NPV > Simple NPV, therefore delay!
 Deciding on the basis of Simple NPV ignores that investing now “kills
the option”;
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The Impact of Volatility
 How does the value of flexibility depend on
uncertainty?
 Compare previous case with situation of more
volatile prices:
Revenue (High Demand) = 150
Revenue (Low Demand) = 50
Expected revenue is unchanged ( = 100).
 Volatility is higher.
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Flexibility in a Volatile Environment
Value of
Flexibility
Prices 150/50
250
Prices 120/80
0
I
0
583
833
1000
1200
1500
Flexibility has a higher value in a more volatile environment
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The Option to Abandon
Assume same scenario as before, but no option to delay
Revenue (High Demand) =
120
Revenue (Low Demand) =
80
Investment outlay I
=
1010
If there is no option to delay, NPV=1000-I = -10
 Do not invest!
Assume assets have a scrap value:
 At the end of the period:
scrap value = 910
 After the first period: scrap value = 0
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The Option to Abandon
High revenue state (120):
 PV (Cash Flow) = 1200 > 910
 Continue after period 1!
 Receive: 1200 + 120 in period 1
Low revenue state (80):
 PV (Cash Flows) = 800 < 910
 Divest and abandon project in period 1!
 Receive: 910 + 80 in period 1
PV =
910 + 80
1200  120
0 .5 
0 .5  1050  1010
1.1
1.1
With option to abandon, NPV=40
Invest: Option to abandon makes the project viable.
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Yale School of Management
Flexibility and Project Design
 Many projects have built-in flexibility:
 Options to contract or expand.
 Possibility to abandon if the assets have values outside
the project (secondary market).
 Development opportunities:
 Sequence of models of the same product.
 Oil fields.
 In many cases the project can be designed to be more
flexible:
 Leasing contracts.
 Make or buy decisions.
 Scale versus adaptability.
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