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Chapter 13.
Tool Kit for Real Options
WACC=
14%
Risk-free rate =
6%
Initial cost of project=
$50
DCF Analysis
Expected annual cash flows (in millions):
Probability
Cash Flow
Prob. x CF
25%
$33
$8.25
50%
$25
$12.50
25%
$5
$1.25
Expected CF =
$22.00
Time Line
Year
0
1
2
3
Expected CF
($50)
$22.00
$22.00
$22.00
NPV =
$1.08
Figure 13-1
DCF and Decision Tree Analysis for the Investment Timing Option
(Millions of Dollars)
Part 1. Scenario Analysis: Proceed with Project Today
Future Cash Flows
NPV of this
Probability
Now: Year 0
Year 1
Year 2
Year 3
Probability
x NPV
S
$33
$33
$33
$26.61
0.25
$6.65
High
-$50
Average
$25
$25
$25
$8.04
0.50
$4.02
Low
$5
$5
$5
-$38.39
0.25
-$9.60
1.00
Expected value of NPVs =
$1.08
$24.02
22.32
THE INVESTMENT TIMING OPTION: AN ILLUSTRATION
(Section 13.2)
Murphy Systems is considering a project that will create a new type of hand-held device for connecting to the Internet.
The cost of the project is $50 million, but the future cash flows are uncertain.
Murphy estimates a 25% probability that
the new Internet device will be very popular in which case the project will generate cash flows of $30 million each year
for three years.
There is a 50% probability generating cash flows of $25 million each year for three years.
Unfortunately, there is a 25% chance that the Internet device will not be popular, which means that the project will
generate only $5 million per year in cash flows.
The cost of capital for this project is 14%.
Scenario
c
Standard Deviation
a
=
Coefficient of Variation
b
=
0.25
0.25
0.50

Part 2. Decision Tree Analysis: Implement in One Year Only if Optimal
Future Cash Flows
NPV of this
Probability
Now: Year 0
Year 1
Year 2
Year 3
Year 4
Probability
x NPV
S
-$50
$33
$33
$33
$23.35
0.25
$5.84
High
Wait
Average
-$50
$25
$25
$25
$7.05
0.50
$3.53
Low
$0
$0
$0
$0
$0.00
0.25
$0.00
1.00
Expected value of NPVs =
$9.36
$8.57
0.92
Notes:
Figure 13-2
Sensitivity Analysis for the Investment Timing Option Decision Tree
(Millions of Dollars)
Future Cash Flows
NPV of this
Probability
Now: Year 0
Year 1
Year 2
Year 3
Year 4
Probability
x NPV
S
-$50
$33
$33
$33
$20.04
0.25
$5.01
High
Average
-$50
$25
$25
$25
$3.74
0.50
$1.87
Low
$0
$0
$0
$0
$0.00
0.25
$0.00
1.00
Expected value of NPVs =
$6.88
$7.75
1.13
Part 2. Sensitivity Analysis of NPV to Changes in the Cost of Capital Used to Discount Cost and Cash Flows
Cost of Capital Used to Discount the Year 1 Cost
$6.88
3.0%
4.0%
5.0%
6.0%
7.0%
8.0%
9.0%
8.0%
$13.11
$13.46
$13.80
$14.14
$14.47
$14.79
$15.11
9.0%
$11.78
$12.13
$12.47
$12.81
$13.14
$13.47
$13.78
10.0%
$10.50
$10.85
$11.20
$11.53
$11.86
$12.19
$12.51
11.0%
$9.27
$9.62
$9.97
$10.30
$10.64
$10.96
$11.28
12.0%
$8.09
$8.44
$8.78
$9.12
$9.45
$9.78
$10.09
13.0%
$6.95
$7.30
$7.64
$7.98
$8.31
$8.64
$8.95
14.0%
$5.85
$6.20
$6.54
$6.88
$7.21
$7.54
$7.85
15.0%
$4.79
$5.14
$5.48
$5.82
$6.15
$6.48
$6.79
16.0%
$3.77
$4.12
$4.46
$4.80
$5.13
$5.45
$5.77
17.0%
$2.78
$3.13
$3.47
$3.81
$4.14
$4.46
$4.78
18.0%
$1.83
$2.18
$2.52
$2.86
$3.19
$3.51

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