Chapter 11– Structured Risk Management
 Risk Management
 Expected Value of Perfect Control
 Sensitivity Analysis – Robustness – easy to do with Precision
Tree
 Value Added structured approach - Individual random events
 Role of Information
 Expected Value of Imperfect Information
 Bayes Rule and EVII
 Optimal Conditional decision
 Sequential decisions with information delay
 Real Options
Chapter 11
Chelst & Canbolat
Value Added Decision Making
02/28/12
1
Risk Management Theme
 You
cannot manage risk if you do not admit there is
uncertainty
 Managing
uncertainty also includes unrealized upside
potential and not just downside losses
 You
cannot allocate appropriate resources if you do not
quantify the risk or uncertainty
Chapter 11
Chelst & Canbolat
Value Added Decision Making
02/28/12
2
Figure 11.1: Decision tree
Boss Controls automation investment
40.0%
9.9
0
1.9
50% Take
60.0%
16.5
0
8.5
30% Take
40.0%
13.8
0.4
0.8
60.0%
0.6
10
30% Take
FALSE
Low
Automation Investment
-8
Take Rate
5.86
How Much
6.32
High
TRUE
-13
Take Rate
6.32
50% Take
Chapter 11
Chelst & Canbolat
Value Added Decision Making
23
02/28/12
3
Investment in Automation Question: Robustness of Optimal Solution
 The “High”
investment alternative involves a new
technology.
 Management is concerned that the capital equipment estimate
could be off by + 7%.
 There is even more concern regarding the variable cost estimate
that could be off by + 10%
 The
Low investment alternative is well tested and there is
hope that continuous improvement could reduce the
variable cost by 5%.
 Because they did not know, they set the take rate
probabilities at 0.6 and 0.4 respectively. However, there is a
lot of uncertainty regarding this estimated probability.
Chapter 11
Chelst & Canbolat
Value Added Decision Making
02/28/12
4
Investment in Automation
Robustness of Optimal Solution
 Magnitude
of Difference between two solutions
 ($6.32M-$5.86M) = $460,000
 Investment(s)
 How much increase in HIGH Investment fixed cost results in
change in best decision?
 Variable
Cost(s)
 How much would the variable cost for Low Investment have to
decline to make it preferred?
 Probability
of 30% take rate: Increases? Decreases?
 What else and why?
Chapter 11
Chelst & Canbolat
Value Added Decision Making
02/28/12
5
Activate: Precision Tree & Sensitivity Analysis
Output – Separate Worksheets

Sensitivity – one parameter at a time
 One line –Objective function for optimal strategy: A change in
optimal decision is usually bend in line
 Multiple lines – Objective function for each decision. Crossing
lines  change in optimal decision
Chapter 11

Tornado diagram – more variables but less info

Spider Plot – more variables, more info, but limited to no
more than 3 or 4 variables – too cluttered and confusing
Chelst & Canbolat
Value Added Decision Making
02/28/12
6
Review: Figure 10.23: Sensitivity analysis automation
investment – fixed cost of high investment
$13.48 million
7.5
Expected Value
7
6.5
High
Low
6
5.5
-$12.0
-$12.2
-$12.4
-$12.6
-$12.8
-$13.0
-$13.2
-$13.4
-$13.6
-$13.8
-$14.0
5
High Investment
X axis – Fixed cost input as negative value (-13)
Axis would be reversed if cost was stored as (13)
Chapter 11
Chelst & Canbolat
Value Added Decision Making
02/28/12
7
Review: Figure 10.24: Expected value of the optimal
decision for each value of fixed cost of high investment
7.5
Expected Value
7
6.5
6
5.5
-$12.0
-$12.2
-$12.4
-$12.6
-$12.8
-$13.0
-$13.2
-$13.4
-$13.6
-$13.8
-$14.0
5
High Investment
Chapter 11
Chelst & Canbolat
Value Added Decision Making
02/28/12
8
Review: Figure 10.25: Sensitivity analysis
automation investment – low take rate probability
8.5
8
Decision changes when probability
approaches 0.6 (a 50% increase)
Expected Value
7.5
7
6.5
6
High
Low
5.5
5
4.5
0.65
0.60
0.55
0.50
0.45
0.40
0.35
0.30
0.25
0.20
0.15
4
Low Probability
Chapter 11
Chelst & Canbolat
Value Added Decision Making
02/28/12
9
List of Variable Ranges
A.
B.
C.
D.
E.
F.
G.
Chapter 11
Fixed investment: High Investment: ±7% of base
Price: 0 to –10% of base
Variable Cost of Low investment: ± 10 % of base
Variable Cost of High investment: 0 to 5 % of base
Probability of Low Take rate: ± 0.2 absolute
Low take rate (30%): 0 to –10% absolute
Volume: 0 to – 15% of base
Chelst & Canbolat
Value Added Decision Making
02/28/12
10
Precision Tree Sensitivity Analysis
Tornado Diagram Many parameters: unlimited



Chapter 11
Uses Min & Max values specified in the range and
calculates Objective function.
Ranks the analysis in order of their range of impact on
the objective  looks like tornado
Does NOT show changed decisions!!
Chelst & Canbolat
Value Added Decision Making
02/28/12
11
Figure 11.2: Tornado diagram
Boss Controls automation investment
Tornado Graph of Decision Tree
'Automation Investment'
Range of parameter
Prob of Low Take (0.2 to 0.6)
Prob. (D13)
Vehicles (850 K to 1 million)
Vehicles (Mil.) (C10)
Price ($54 to $60)
Price (C4)
Take Rate (C13)
Low take rate (20% to 30%)
High_Investment (D6)
High Invest. ($13 m + 910K)
Low_Invest_VC (C7)
8.5
8
7.5
7
6.5
6
5.5
5
4.5
4
3.5
High_Invest_VC (D7)
Expected Value
Chapter 11
Chelst & Canbolat
Value Added Decision Making
02/28/12
12
Precision Tree Sensitivity Analysis
Spider Diagram practical limit of 4 parameters

More detailed than Tornado but harder to include many
variables.
 X axis – change input (percent)
 Y axis – change in expected value



Chapter 11
Aggregation of many one-way sensitivity analyses but
scaled to a common percentage.
Shows the slope of the impact on the objective function
and non-linearities.
Shows changes in decisions  bends in line graph
Chelst & Canbolat
Value Added Decision Making
02/28/12
13
List of Variable Ranges
Fixed investment: High Investment: ±7% of base
Price: 0 to –10% of base  one sided (lower value)



Probability of Low Take rate: ± 0.2 absolute


Decision does not change except at the very highest value – slight
bend in line at end
Volume: 0 to – 15% of base  one sided (lower value)


Chapter 11
Range of Change in input % from a negative % to 0%
Range of Change in input % from a negative % to 0%
Chelst & Canbolat
Value Added Decision Making
02/28/12
14
Figure 11.3: Spider plot for
Boss Controls automation investment
Spider Graph of Decision Tree 'Automation Investment'
Expected Value of Entire Model
8.5
Decision changes: bend
Expected Value
8
7.5
7
6.5
Prob. (D13)
Vehicles (Mil.) (C10)
Price (C4)
High_Investment (D6)
6
5.5
5
4.5
4
3.5
-60%
-40%
-20%
0%
20%
40%
60%
Change in Input (%)
Chapter 11
Chelst & Canbolat
Value Added Decision Making
02/28/12
15
Manage Risk
Impact of Strategies to Change Risk Profile
 Shift
the risk profile to the right Figure 11-4b.
 add value to all possible outcomes  eliminate altogether an
operating cost in a project.
 Cut
off the downside risk Figure 11-4c
 Move outcomes to some guaranteed level.
 Minimum purchase quantity in a contract
 increase the mean and remove the most disastrous possibilities.
 Insurance cuts off the downside risk (costs money)  leftward
shift in the whole risk profile but reduce the overall expected value
Chapter 11
Chelst & Canbolat
Value Added Decision Making
02/28/12
16
Figure 11.4: Impact of risk management actions on risk profile
Figure a: Baseline
Figure b: Shift to right 
by adding net value (cost
elimination)
Chapter 11
F
Figure c: Chop off left 
eliminate downside risk
Chelst & Canbolat
Value Added Decision Making
02/28/12
17
Change Risk Profile – Manage Risk
 Centrally
concentrate uncertainty: Figure 11-4d
 Risk sharing: sell half of a risky opportunity for a price equal to half
of its expected value
 Reduce
but not eliminate extremely negative
outcomes: Figure 11-4e
 Magnitude reduction” consistent with the way managers view risk
 Probability reduction not as well understood
Chapter 11
Chelst & Canbolat
Value Added Decision Making
02/28/12
18
Figure 11.4: Impact of risk management actions on risk profile
Figure a: Baseline
Figure d: Centralize through Figure e: reduce magnitude of
risk sharing
negative outcome
Chapter 11
Chelst & Canbolat
Value Added Decision Making
02/28/12
19
Make or Buy Decision: Non-strategic (strictly cost)
Decision Context: Manufacture a component yourself or
contract with a supplier to manufacture it.
There is a design for a component but you are not sure when it comes time to
manufacture, that the design will be feasible as is. If not, there will need to be a
quick major redesign of the component. If you manufacture it, you expect that
with the redesign it will cost 8% more than the original estimate. The decision
to make or buy must be made now before you have time to fully check out the
design. The demand for the product is also uncertain. If you sign a contract with
the supplier for a specific piece price, if the current design turns out to be
infeasible, you know the supplier will use the design change as an excuse to
increase the price 15%.
Chapter 11
Chelst & Canbolat
Value Added Decision Making
02/28/12
20
Make or Buy Data: Random Events
Random Events
1. Design Feasibility
Current Design will Work
Need a Major Redesign
2. Demand
Low
Medium
High
Chapter 11
Volume

1.0 million
1.25 million
1.5 million
Chelst & Canbolat
Value Added Decision Making
Prob.
0.4
0.6
Prob.
0.3
0.5
0.2
02/28/12
21
Make or Buy Data: Cost Data
Costs: Make In-House
Facility investment fixed Cost $55M
Variable Cost/ per part
If current design works $100/part
If new Design is needed $108/part
Costs: Buy from Supplier
Facility investment fixed Cost $0
Variable Cost/ per part
If current design works $140/part
If new Design is needed $161/part
Chapter 11
Chelst & Canbolat
Value Added Decision Making
02/28/12
22
Design
Feasibility
Works
Does NOT
Demand
1
1.25
1.5
Probability
0.4
0.6
Premium
Make Costs
100
108
8%
Prob.
0.3
0.5
0.2
Complex calculation
& NOT sum of
values on branches
Buy Costs
140
161
15%
30.0%
1
0.12
155
50.0%
1.25
20.0%
1.5
0.2
180
0.08
205
30.0%
1
0.18
163
Demand
187.3
50.0%
Medium
1.25
20.0%
High
1.5
0.3
190
0.12
217
30.0%
1
0
140
50.0%
1.25
20.0%
1.5
0
175
30.0%
1
0
161
Low
Works
E(X)
40.0%
Demand
177.5
100
Medium
Fixed Costs
Make
55
Buy
0
High
Make
TRUE
55
Current Design
183.38
Low
Minimize Cost
Does NOT work
60.0%
108
Decision
Make or Buy
183.38
Low
Works
40.0%
Demand
171.5
140
Medium
High
Buy
Figure 11.8: Western Co.
make or buy decision
Chapter 11
E(X)
FALSE
0
0
210
Current Design
186.935
60.0%
Low
Demand
197.225
Does NOT work
161
Medium
Chelst & Canbolat
Value Added Decision Making
High
0
50.0%
201.25
1.25
20.0%
0
1.5
02/28/12241.5
23
Structured Risk Management Step: Summary

Within optimal decision
 Identify random paths with large downside risk
 Large values that are negative or poor relative to the best paths
 Probability associated with this sequence is not insignificant
 Assess impact of
 Increasing relative value of that path
 Decreasing the probability of that path
 Brainstorm strategies for making the above happen
 Quantify these alternatives

Chapter 11
Repeat for 2nd best decision
Chelst & Canbolat
Value Added Decision Making
02/28/12
24
Summary of Risk Management Alternatives:
Table 11.4
Factor
Reduce Cost Increase
Linked to Redesign
Optimal
Comments
$730,000 If redesign is needed try
$3.65 M to contain added cost of
manufacturing.
Reduce Risk that
From 0.6 to 0.5 $980,000 Modify design quickly
Design will not Work
to reduce need for
major redesign later.
From 0.6 to 0.3 $4.16 M New Optimal: Use
Supplier
From 0.6 to 0.0 $11.9 M Value of Perfect
Control
Manage Uncertainty of Not
Does not make sense to
Demand
appropriate
reduce total demand to
lower total cost.
Chapter 11
Change
From $8 to $7
From $8 to $3
Chelst & Canbolat
Value Added Decision Making
02/28/12
25
Summary of Risk Management Alternatives
Table 11.4 Continued
Factor
Percentage Price
increase by Supplier
if design does not
work
Supplier Price
Reduction if
Volumes are High
EVPI of Design
Feasibility
Chapter 11
Comments
Optimal
Change
Obtain commitment
$0
From 15% to 14%
$3.5 M from supplier not to
From 15% to 8%
take advantage of
redesign to raise prices
disproportionately.
Negotiate major price
No
Up to $8
Impact reduction for high
reduction in price
volumes.
$2.4 M Test feasibility of
current design
Chelst & Canbolat
Value Added Decision Making
02/28/12
26
New topic: Information Value
 Perfect
Information
 Imperfect Information
Sample Information
Expert Information
Accuracy of test (medical or engineering)
 Delay
Chapter 11
decision until information unfolds Options
Chelst & Canbolat
Value Added Decision Making
02/28/12
27
Information Gathering
 Traditional Approach
– Gather information (surveys, tests,
pilot plant, prototypes) until time or the budget runs out.
 Most information is gathered to validate already made decision.
 New Approach
- Gather information if the cost of gathering
it is less than the gain in expected value.
 Process – Restructure the decision tree to determine the expected
value with the information
 Counterintuitive – How can you determine the value of information
before you have even gathered the information?
Chapter 11
Chelst & Canbolat
Value Added Decision Making
02/28/12
28
Expected Value of Perfect Information: EVPI
 Goal: Determine
the expected value of perfect information
regarding an Uncertainty or Risk – Hire a Clairvoyant –
Prophet Isaiah (Thomas)
 This provides an upper bound on the value of all information
including “imperfect” information.
 If the information never changes the optimal decision
then EVPI = 0.
 Decision Tree Process: Move the random event in question to
the front of the tree “before” the first decision is to be made.
 Recalculate the overall expected value.
 The NET Improvement is the EVPI.
Chapter 11
Chelst & Canbolat
Value Added Decision Making
02/28/12
29
Original Decision Tree – Automation Investment
Boss Controls – Base Tree
50% Take Rate
High
TRUE
-13
Automation Investment
Decision
6.32 (MAX{6.32, 5.86})
23
Low
-8
Chapter 11
0.6
10.0
Take Rate
6.32 (=10*0.6 + 0.8*0.4)
40.0%
0.4
30% Take Rate
0.8
13.8
50% Take Rate
FALSE
60.0%
60.0%
16.5
0
8.5
Take Rate
5.86 (=8.5*0.6 + 1.9*0.4)
0
30% Take Rate 40.0%
1.9
9.9
Chelst & Canbolat
Value Added Decision Making
02/28/12
30
Figure 11.7: EVPI tree for Boss Controls Investment
Take rate event moved to before decision
TRUE
1.9
0.4
1.9
How Much
1.9
FALSE
High
0.8
0
0.8
Low
EVPI = 6.76 - 6.32 = 0.44
Perfect Information
30% Take
40.0%
Take Rate
6.76
FALSE
8.5
How Much
10
TRUE
High
10
Low
50% Take
60.0%
0
8.5
0.6
10
Optimal decision depends on outcome of random event
Chapter 11
Chelst & Canbolat
Value Added Decision Making
02/28/12
31
Expected Value of Perfect Information: Boss
 Base
strategy – High Investment & E(X) = $6.32M
 If
information indicates 30% take rate then “shift” to Low
Investment with profit = $1.9M
 If
information indicates 50% take rate then stay with High
Investment with profit = $10M
 What
is the probability the information will indicate a 30%
take rate? Answer 0.4
 E(X)
with perfect information = 1.9(.4) + 10 (.6) = 6.76
 EVPI
= 6.76 – 6.32 = $0.44M
 E(Perfect
Control) = 10 – 6.32 = $3.86 M  much
more valuable to exert control over uncertainty
Chapter 11
Chelst & Canbolat
Value Added Decision Making
02/28/12
32
Review to contrast EVPC with EVPI
Maximum value of risk management  Expected
Value of Perfect Control:
Not about obtaining information but rather exerting
control over destiny
 Goal: Determine
the value of eliminating Uncertainty or Risk
 This provides an upper bound on the value of risk
management with regard to that uncertainty.
 Process:
 Assign probability of “1” to the best outcome of an uncertain event.
 Recalculate the overall expected value.
 The NET Improvement in expected value is the EVPC.
Chapter 11
Chelst & Canbolat
Value Added Decision Making
02/28/12
33
Review: Expected Value of Perfect Control: Automation Investment
Assign probability of “1” to best outcome
Net Change: $10 – 6.32 = $3.68 million
100%
50%
High
Automation Investment
TRUE
-13
Decision
10 (MAX(10, 8.5))
Take Rate
10 =10*1 + 0.8*0)
0%
30%
13.8
50%
Low
FALSE
-8
Chapter 11
Chelst & Canbolat
Value Added Decision Making
23
100%
16.5
1.0
10.0
0
0.8
0
8.5
Take Rate
8.5=8.5*1.0 + 1.9*0)
0%
0
30%
1.9
9.9
02/28/12
34
2nd example: EVPI – Western Make or Buy
 Base
strategy Make: E(X) = $183.38M
 Uncertainties
Design works or not  Bound on Testing Design (Imperfect)
EVPI = $2.41 M
Demand  Bound on value of surveys (Imperfect)
EVPI = $2.16 M
Both uncertainties
EVPI = $3.16 M
Chapter 11
Chelst & Canbolat
Value Added Decision Making
02/28/12
35
Prob.
Works
0.4
Does NOT
0.6
Premium
Design Feasibility
Make Costs
100
108
8%
Low
Buy Costs
140
161
15%
30.0%
1
Works
40.0%
Demand
177.5
100
Medium
50.0%
High
20.0%
1.25
Demand
1
1.25
1.5
Prob.
0.3
0.5
0.2
Make
TRUE
55
1.5
Current Design
183.38
Low
30.0%
1
Fixed Costs
Make
55
Buy
0
Does NOT work 60.0%
108
0.2
180
0.08
205
0.18
163
Demand
187.3
Medium
50.0%
High
20.0%
1.25
Decision
0.12
155
1.5
0.3
190
0.12
217
Make or Buy
183.38
Low
30.0%
1
Works
40.0%
Demand
171.5
140
Medium
50.0%
1.25
High
Make or Buy
Buy
FALSE
0
20.0%
1.5
Current Design
186.935
Low
30.0%
1
Does NOT work 60.0%
161
0
140
0
175
0
210
0
161
Demand
197.225
Medium
50.0%
High
20.0%
1.25
1.5
0
201.25
0
241.5
Low
Figure 11.9: Make-Buy
EVPI: Design Feasibility
Net Improvement
Make
FALSE
Works
40.0%
183.38-180.98 =
$2.40M
High
Low
Buy
TRUE
0
180
0
205
0.12
30.0%
140
140
Demand
171.5
High
Current Design
0.2
50.0%
175
20.0%
210
175
0.08
210
180.98
Low
Make
Design uncertainty
resolved before decision
TRUE
0
Does NOT
work
60.0%
0
0.18
30.0%
163
163
Demand
187.3
Medium
Decision
High
0.3
50.0%
190
20.0%
217
190
0.12
217
187.3
Low
Buy
FALSE
0
High
Chelst & Canbolat
Value Added Decision Making
0
30.0%
161
161
Demand
197.225
Medium
Chapter 11
0
50.0%
180
20.0%
205
171.5
Medium
Info Design
155
Demand
177.5
Medium
Decision
0
30.0%
155
50.0%
201.25
20.0%
241.5
0
201.25
0
241.5
02/28/12
37
40.0%
155
Current Design
159.8
60.0%
Does NOT work
163
0
155
40.0%
140
Current Design
152.6
60.0%
Does NOT work
161
0.12
140
40.0%
180
Current Design
186
60.0%
Does NOT work
190
0.2
180
Works
Figure 11.10:
Make-Buy
EVPI on Demand
Net Improvement
183.38-181.22 =
$2.16M
FALSE
Make
0
Low
30.0%
0
Decision
152.6
Works
Buy
Info Demand
TRUE
0
Demand
181.22
Works
Make
Medium
50.0%
0
TRUE
0
Decision
186
0
163
0.18
161
0.3
190
0
40.0%
175
175
Current Design
190.75
0
60.0% 201.25
Does NOT work
201
40.0%
0.08
Works
205
205
Current Design
212.2
60.0% 0.12
Does NOT work
217
217
Works
FALSE
Buy
0
Demand uncertainty
resolved before decision
Make
High
20.0%
0
TRUE
0
Decision
212.2
0
40.0%
210
210
Current Design
228.9
0
60.0%
Does NOT work
242 241.5
Works
FALSE
Buy
0
Make
Figure 11.11: Make-Buy Decision
EVPI on Feasibility & Demand
Combined
Net Improvement
183.38-180.22 = $3.16M
Less than the SUM of
$2.16 (Demand EVPI)
+ $2.40 (Feasibility EVPI)
INFO on BOTH events
155
Low
30.0%
140
Buy
Works
40.0%
0
Demand
170.5
TRUE
140
Make
FALSE
180
Medium
50.0%
Decision
0
175
Buy
TRUE
175
Make
TRUE
205
High
20.0%
FALSE
Current Design
180.22
30.0%
210
FALSE
163
161
Buy
Demand
186.7
TRUE
161
Make
TRUE
190
Medium
50.0%
190
Buy
FALSE
201.25
Make
TRUE
217
20.0%
217
Buy
FALSE
241.5
Chelst & Canbolat
Value Added Decision Making
0
210
0
163
0.18
161
0.3
190
0
201.25
0.12
217
Decision
0
Chapter 11
0.08
205
Decision
0
High
0.2
175
Decision
0
0
0
180
205
Buy
Does NOT work 60.0%
0.12
140
Decision
0
Low
0
155
Decision
0
Make
Next slide: Schematic Trees
FALSE
0
241.5
02/28/12
39
Original
Make or Buy Schematic Trees: EVPI
Make or Buy
Design
EVPI Demand = $2.4 M
Demand
Make or Buy
Design
EVPI Design = $2.16M
Design
Design
Chapter 11
Demand
Make or Buy Demand
Demand Make or Buy
Chelst & Canbolat
Value Added Decision Making
EVPI Combined:
Design & Demand
=$3.16M
02/28/12
40
Imperfect Information 
Conditional Decision/ Probabilities
P(Positive)
Invest
P (High | Positive)
 Downstream values and/or probabilities are affected by
an upstream random event
 Decision made AFTER resolution of random event
 Optimal decision path differs depending upon the
outcome of a random event
Chapter 11
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Expected Value of Imperfect Information
Imperfect info  partial resolution of uncertainty
Test or Sample Information
 Few tests, experiments or surveys are perfect.

EVPI is an upper bound on the value of imperfect information.
 EVII – without well documented test reliability:

Conditional probabilities based on judgment
 EVII with Bayes Rule is used primarily in environments
with extensive data on the reliability of tests – both
false positives and false negatives.
 Oil industry – Seismographic data. Test wells
 Medical Applications
 Weather forecasts
Chapter 11
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EVII – without well documented test reliability
 Conditional probabilities based on judgment
 Expert understands the uncertain relationship between test data
(performance, throughput, etc.) or market surveys and subsequent
outcome.
 Can the expert provide a probabilistic range of outcomes that have
accompanied similar test results?
 Understand
concept of conditional probability – experience
with both possible outcomes.
 Need stable process environment – A priori probabilities
are always in a narrow range, for example, of 0.40 to 0.60.
 Not used to forecast rare events
 Problem – people have invalid intuition. Cannot factor in
“a priori” estimates that are updated with imperfect
information.
Chapter 11
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43
Boss Controls: Focus Groups & Imperfect Information
based on Experience
Boss Controls (BC) is gearing up to manufacture an option to be
made available on 1 million new cars world-wide. Initial estimates are
that the take rate for the option could be as low as 30% or as high as
50%. Assume for simplicity sake, these two take rates are equally likely.
Experience with focus groups indicates that for options such as the
one BC is considering, the results will either be Enthusiastic (E) or
Good (G). In the past if the focus groups were Enthusiastic, the take
rate ended up being at the HIGH end 70% time. However, if the focus
groups’ reactions were just good, then 80% of the time the take rate
was at the LOW end. Focus groups have an optimistic bias and tend to
be enthusiastic 80% of the time.
Chapter 11
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EVII & Decision Trees - Experience




Chapter 11
Add an uncertain node at the front of tree to represent
uncertain outcome of focus group
Insert the probabilities that reflect the likelihood of different
responses: Here P(E) = .8 and P(G) = .2
Probability of outcomes (Take rates) are now “Conditional”
probabilities based on past experience (or Bayes Rule)
Insert the “conditional” probabilities into tree and calculate
expected value.
Chelst & Canbolat
Value Added Decision Making
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45
Figure 11.14: Decision tree of EVII for BC automation investment
Expert estimates conditional probabilities
30% Take
FALSE
Low
-8
80.0%
6.52
Imperfect Info
TRUE
High
0
16.5
8.5
30.0%
0.24
13.8
0.8
-13
Conditional
Probabilities
70.0%
0.56
Take Rate
7.24
50% Take
23
10
6.436
30% Take
TRUE
Low
-8
Good
20.0%
1.9
20.0%
0.04
16.5
8.5
3.22
3.22
30% Take
High
FALSE
-13
80.0%
13.8
0
0.8
Take Rate
2.64
50% Take
Chelst & Canbolat
Value Added Decision Making
0.16
9.9
How Much
0
EVII = 6.436 – 6.320 = 0.116
Less than one third of
EVPI was $400,000
80.0%
Take Rate
50% Take
Chapter 11
70.0%
7.24
30% Take
Focus Group
0
1.9
How Much
0
EVII = 6.436 - 6.320= 0.116
9.9
Take Rate
50% Take
Enthusiastic
30.0%
02/28/12
20.0%
0
23
10
46
Conditional Probabilities Consistent
with Original Estimates
A
Priori Probability that Take Rate is 30% - Use Partition
Formula P(A) = P(A|B)P(B) + P(A|B)P(B)
Chapter 11
 P(T=30%)
= P(T=30% | G) P(G) + P(T=30% | E) P(E)
 P(T=30%)
= (3/4)(.4) + (1/3) (.6) = .5 “original estimate”
 P(T=50%)
= P(T=50% | G) P(G) + P(T=50% | E) P(E)
 P(T=50%)
= (1/4)(.4) + (2/3) (.6) = .5 “original estimate”
Chelst & Canbolat
Value Added Decision Making
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Boss Control: Conditional Decision
 If
focus group’s reaction is ENTHUSIASTIC
then HIGH investment in automation
 If focus group’s reaction is GOOD then Low
investment in automation
Chapter 11
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INTUITION?
Bayes’ Rule & Reliable Test
 Rare
Disease – How Rare: 1 in 1,000
 Probability of positive reading for a person with the
disease – test is very reliable

P(Pos.| Disease) = P(P|D) = .99
 Probability
of negative reading for a person without the
disease – 4% false positives

P(Neg. | No Disease) = P(N|Dc) = .96
 Key
Question: P(Disease | Pos) = P(D|P) = ??
 Let Dc = D complement, or D , or No disease
Chapter 11
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Bayes’ Rule & Reliable Test - Results
 Bayes’ Rule (General Formula):

P( B | A) 
P( A | B) * P( B)
P( A | B) * P( B)  P( A | B c ) * P( B c )
 with Bc = B complement or NOT B
 Denominator uses partitioning (all ways that A can occur) to determine P(A)
 Bayes’ Rule (Reliable Test): (Pos = Positive test result)
P( D | Pos) 

Chapter 11
P( Pos | D) * P( D)
P( Pos | D) * P( D)  P( Pos | D c ) * P( D c )
0.99 *
1
1000
1
999
0.99 *
 (1  0.96) *
1000
1000

0.00099
 0.024
0.04095
or 1 in 41
 Intuitive  1000 tested yields 40 false positives (4% error rate) and 1 true
positive
Chelst & Canbolat
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50
Probability Misunderstanding
 People
do NOT know how to integrate prior knowledge
and data accuracy.
 Especially problematic with
 Low probability events and highly accurate test
 Weakly reliable tests
Chapter 11
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Bayesian Posterior (after positive result) Probabilities
Test Accuracy
Assume Positive = Negative
Initial Probability
of Success
.7
.8
.9
.95
.1
0.21
0.31
0.50
0.68
.3
0.50
0.63
0.79
0.89
.4
0.61
0.73
0.86
0.93
.45
0.66
0.77
0.88
0.94
.5
0.70
0.80
0.90
0.95
.6
0.78
0.86
0.93
0.97
.7
0.84
0.90
0.95
0.98
For 0.5, .45, and even 0.40, the final estimates are close to test accuracy.
Column heading close to cell value.
For initial low probability events, test accuracy and final probability are far apart.
Chapter 11
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52
EVII: Make or Buy Decision
 Decision
Context: Manufacture a component yourself or
contract with a supplier to manufacture it.
 Design Reliability is a key concern. Experts initially estimate that the
current design will work with probability of only 0.4.
 However
there is a complex test that can be used to ALMOST
validate or invalidate the design.
 This testing procedure is used in a wide range of situations.
 Looking back at past data over a wide range of initial success estimates
 If the design worked, how often were
 Test results GOOD  almost validates
the test results GOOD?
 P(Test results Good | Design Works) = 0.98
 If the design failed, how often were
 Test Results BAD  almost Invalidates
the test results BAD?
 P(Test results Bad | Design Fails) = 0.94
Chapter 11
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53
EVII - Bayes Rule & Decision Trees





Chapter 11
Add an uncertain node at front of tree to represent
uncertain outcome of test
Use Bayes rule to calculate conditional probabilities.
Use partition rule to calculate the probabilities of the
test results. (These appear in the denominator of the
Bayes Rule equation.)
Green on the next page highlights the test result
probabilities
Yellow on the next page highlights the conditional
probabilities. These vary because they depend upon
the results of the tests.
Chelst & Canbolat
Value Added Decision Making
02/28/12
54
EVII - Bayes Rule & Decision Trees
Activity: calculate conditional probabilities
 Data
 P(Design Works) = P(W)= 0.4
 P(Design Fails)
= P(F) = 0.6
 P(Test Results Good | Design Works) = P(G|W)= 0.98
 P(Test Results Bad | Design Fails)=P(B/F) =0.94
 Activity: Use Bayes Rule to calculate
 P(Design Works | Test Results Good) = P(W|G)= ??
 P(G) = ??
 P(F/ G)= ??
 Precision Tree
 Calculate Bayesian Probabilities by hand and
 Insert all of the initial probabilities upfront
 Insert conditional probabilities downstream.
Chapter 11
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55
Figure 11.12
EVII for Make/Buy: Test Design
183.38 – 181.38=2.0
EVII = $2M and EVPI =$2.4M
Works
Make
FALSE
55
Good
Works
Buy
+ means
collapsed
node
8.4%
161
+
+
Demand
187.3
Demand
171.5
+
Demand
197.23
+
Demand
177.5
+
Demand
187.3
Red
Demand values
are expected
values
Test Design
181.38
Works
Make
TRUE
55
Bad
57.2%
0
1.4%
100
Design
187.16
Fails
98.6%
108
Decision
187.16
Works
Buy
FALSE
0
Chelst & Canbolat
Value Added Decision Making
1.4%
140
Design
196.87
Fails
Chapter 11
91.6%
140
Design
173.66
Fails
EVII Make-Buy
8.4%
108
Decision
173.6609
TRUE
0
+
Demand
177.5
Design
178.32
Fails
42.8%
0
91.6%
100
98.6%
161
+
+
Demand
171.5
Demand
197.23
02/28/12
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Conditional Decision
 If
test results are GOOD then buy from supplier
 Less fear of 15% price increase
 If
test results are BAD then make it yourself
 Concerned over supplier’s opportunity for significant price
increase
Chapter 11
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Activity: Concrete examples of
IMPERFECT Information
 Describe
a context in which a decision can be made after
gathering imperfect information and there is still related
uncertainty.
 Product Development
 Example____________________________________________
 Imperfect Information ________________________
 Decision AFTER ____________________________
 Updated future uncertainties _________________________
 Can you quantify accuracy? _______________________
 Manufacturing
 Example____________________________________________
 Imperfect Information ________________________
 Decision AFTER ____________________________
 Updated future uncertainties _________________________
 Can you quantify accuracy? _____________________________
Chapter 11
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58
Sequential Decisions with
Information in between
 Inability
to predict future accurately  Must make
decisions under uncertainty
 A firm unable to determine level of demand in future or predict
rival’s reaction’s
 Understate some perceived risks in order to obtain approval
 Can
management delay high cost PART of decision until
more knowledge is available
 Partial Investment  Gain Information  Broader scope
of subsequent investment
Chapter 11
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59
Investment Decisions
 Three
important characteristics of Investment Decisions
 Partially or completely irreversible
 Uncertainty over future rewards from the investment
 Assess the probabilities of alternative outcomes
 Leeway about timing of your investment
 Postpone action to get more information about the future
 How
should a firm decide on an investing on a project or a
new facility?
Chapter 11
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60
Real Options
 An
option represents a “Right, but not an Obligation”,
to do something under predefined arrangements
 Buy Option (expand or substitute)
 Put Option (contract or cut back)
 Flexibility
to adapt in response to new information
enhances the investment opportunity’s value by
improving its upside potential
 An approach that offers a positive and radical
reassessment of risk and exploration
 The opportunities to acquire real assetsReal
Options
 Real Options term coined by Stewart Myers (1977)
Chapter 11
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Options Analysis
 Financial
options  Data Availability  Precise models
 Technical options
 Data are less accurate
 One time decisions
 Estimates of values are approximates within bands described by
sensitivity analysis
 Analytical niceties that might lead to greater precision might be a
waste of effort
 To decide whether to do the R&D that will lead to a real option on
a launch of a new product, managers only need to know if the value
of option is greater than the cost to acquire it
Chapter 11
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62
Real Options  Uncertainty
 Conventional Approach
 Minimize Risk
 React to uncertainties
 What is the best choice under the given circumstances?
 Work with predetermined set of decisions
 Real
Options
 Proactive towards uncertainties
 Prepare plans to manage the risks
 Identify parts of the system that have most uncertainty, and try to see
how these situations can be exploited
 Identify new possible paths: change decision tree by adding flexibility
Chapter 11
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63
Table 11.10 Common Real Options
Option
Defer
Stage
Alter
Operating
Scale
Abandon
Switch
Explore
Chapter 11
Description
Project that can be postponed allows
learning more about project outcomes
before making a commitment.
A multi-stage project whose construction
involves a series of cost outlays could be
delayed or killed in a midstream.
A project whose operating scale can be
expanded or contracted according to
market conditions.
Project can be abandoned permanently
when market conditions are worsen
severely and project resources could be
sold or put to other more valuable uses.
The project permits changing its output
mix or producing the same outputs using
different inputs in response to changes in
the price of inputs and outputs.
Start with a pilot or prototype project and
follow-up with a full-scale project if the
pilot or prototype succeeds.
Chelst & Canbolat
Value Added Decision Making
Relevant Application Industries
Real estate development,
farming, paper products,
offshore oil lease
R&D intensive industry such as
pharmaceuticals or other long
development capital intensive
projects
Mining, facilities planning,
fashion apparel, consumer goods
Capital intensive industries
(airline, railroad), new product
introduction, financial services
Any good sought in small
batches or subject to volatile
demand (e.g., consumer
electronics, toys, machine parts)
High production cost areas
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Options  Manufacturing and Product Examples



Design all vehicles to facilitate pricey add-ons for specific market
segments. (Vehicle personalization)
Design a truck such that four-wheel steering is a later option that
can be designed into it.
Production system that can change easily
 Inputs: Dual fuel burners (oil and gas)
 Production lines designed to switch equipment so that they can
produce different products
 Flexible machines – rapid tool changeover

Modular Design:
 Option to upgrade a computer system
 Engines? _______________

Chapter 11
Labor Contract – pay premium for option to reduce workforce or
close plants if necessary (Put Option)
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Remaining Text Examples and Figures
 EVII
and Oil Drilling
 Technology Choice
 Schematic tree
 Decision tree
 Risk Profile
 Contingent
Contract
 Negotiations – 2 perspectives
 Merck’s
Chapter 11
options
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20.0%
700
Amount of Oil
64.5
80.0%
Low
100
High
Figure 11.13: Decision tree
for oil drilling case with
imperfect information
TRUE
-5
Drill
10.5%
0
Strong
Seismic Test
57.1%
-150
Oil
TRUE
-0.5
Drill Result
34.5
42.9%
Dry
0
Decision
34.5
FALSE
Don't Drill
0
0.045
-5.5
Test Results
4.23
TRUE
-5
Drill
21.0%
0
Inconclusive
14.3%
-150
Drill Result
4.5
85.7%
Dry
0
Decision
4.5
FALSE
Don't Drill
0
Drill
Weak
68.5%
0
FALSE
-5
Amount of Oil
64.5
+
0.18
-5.5
0
-0.5
1.5%
-150
Oil
Drill Result
-4.5
98.5%
Dry
0
Amount of Oil
64.5
+
0
-5.5
Decision
-0.5
Don't Drill
TRUE
0
0.685
-0.5
Seismic Test
4.225
20.0%
700
Amount of Oil
65.0
80.0%
Low
100
High
Oil
Drill
Don't Test
Chapter 11
0.048
-55.5
0
-0.5
Oil
Oil Drilling
0.012
544.5
FALSE
0
TRUE
-5
10.0%
-150
Drill Result
2.0
90.0%
Dry
0
0
545
0
-55
0
-5
Decision
2.0
Chelst
Don't
Drill
0
&FALSE
Canbolat
0
Value Added Decision Making0
02/28/12
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Figure 11.15: Schematic tree for
technology development example
Chapter 11
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Figure 11.16:
Decision
Tree for
Omega case
Chapter 11
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Figure 11.17: Cumulative risk profile for
technology development case - Omega
1
Cumulative Probability
0.8
0.6
Tech. Y & Prot.
Tech. Z
0.4
0.2
0
15
20
25
30
35
40
45
50
Total Cost (Millions Dollars)
Chapter 11
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Figure 11.18: Contingent Contract
Total sales from perspectives of Biotech and BSG
a) BioTech perspective
Chapter 11
b) BSG perspective
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Figure 11.19: Merck’s options and major
uncertainties in Project Gama
Chapter 11
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