4/11/2010
Chapter 25.
Tool Kit for Real Options
WACC=
14%
Riskfree 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
T ime Line
Year
0
1
2
3
Expected CF
($50)
$22.00
$22.00
$22.00
NPV =
$1.08
Figure 251
DCF and Decision Tree Analysis for the Investment Timing Option
(Millions of Dollars)
Part 1. Scenario Analysis: Proceed with Project T oday
Future Cash Flows
NPV of this
Probability
Data for
Now: Year 0
Year 1
Year 2
Year 3
Probability
x NPV
Std Deviation
$33
$33
$33
$26.61
0.25
$6.65
163
High
$50
Average
$25
$25
$25
$8.04
0.50
$4.02
24
Low
$5
$5
$5
$38.39
0.25
$9.60
389
1.00
577
=Variance of PV
Expected value of NPVs =
$1.08
$24.02
22.32
Part 2. DecisionT ree Analysis: Implement in One Year Only If Optimal
Future Cash Flows
NPV of this
Probability
Data for
Now: Year 0
Year 1
Year 2
Year 3
Year 4
Probability
x NPV
Std Deviation
$50
$33
$33
$33
$23.35
0.25
$5.84
49
High
Wait
Average
$50
$25
$25
$25
$7.05
0.50
$3.53
3
Low
$0
$0
$0
$0
$0.00
0.25
$0.00
22
1.00
73
=Variance of PV
Expected value of NPVs =
$9.36
$8.57
0.92
Notes:
Figure 252
Sensitivity Analysis for the Investment Timing Option Decision Tree
(Millions of Dollars)
Future Cash Flows
NPV of this
Probability
Data for
Now: Year 0
Year 1
Year 2
Year 3
Year 4
Probability
x NPV
Std Deviation
$50
$33
$33
$33
$20.04
0.25
$5.01
43
High
Average
$50
$25
$25
$25
$3.74
0.50
$1.87
5
Low
$0
$0
$0
$0
$0.00
0.25
$0.00
12
1.00
60
=Variance of PV
Expected value of NPVs =
$6.88
$7.75
1.13
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
$3.83
Notes:
Real Option Analysis
Figure 253
Estimating the Input for "Stock Price" in the Option Analysis
of the Investment Timing Option (Millions of Dollars)
Future Cash Flows
PV of this
Probability
Data for
Now: Year 0
Year 1
Year 2
Year 3
Year 4
Probability
x PV
Std Deviation
$33
$33
$33
$67.21
0.25
$16.80
125
High
Average
$25
$25
$25
$50.91
0.50
$25.46
19
Low
$5
$5
$5
$10.18
0.25
$2.55
300
1.00
444
=Variance of PV
Expected value of PVs =
$44.80
$21.07
0.47
Notes:
Figure 254
Estimating the Input for "Stock Return Variance" in the Option Analysis
of the Investment Timing Option (Millions of Dollars)
Part 1. Find the Value and Risk of Future Cash Flows at the T ime the Option Expires
PV in Year 1
Future Cash Flows
for this
Probability
Data for
Now: Year 0
Year 1
Year 2
Year 3
Year 4
Probability
Std Deviation
$33
$33
$33
$76.61
0.25
$19.15
163
High
Average
$25
$25
$25
$58.04
0.50
$29.02
24
Low
$5
$5
$5
$11.61
0.25
$2.90
389
1.00
577
=Variance of PV
$51.08
$24.02
0.47
Part 2. Direct Method: Use the Scenarios to Directly Estimate the Variance of the Project's Return
Probabilit y
Data for
Probabilit y
Std Deviation
$76.61
71.0%
0.25
17.8%
8.1%
High
$44.80
Average
$58.04
29.5%
0.50
14.8%
1.2%
Low
$11.61
74.1%
0.25
18.5%
19.4%
1.00
Expected return =
14.0%
28.7%
=Variance of PV
53.6%
28.7%
Part 3. Indirect Method: Use the Scenarios to Indirectly Estimate the Variance of the Project's Return
$51.08
$24.02
Coefficient of variation (CV) =
0.47
T ime (in years) until the option expires (t) =
1.00
20.0%
Notes:
Figure 255
Estimating the Value of the of the Investment Timing Option Using
a Standard Financial Option (Millions of Dollars)
Part 1. Find the Value of a Call Option Using the BlackScholes Model
Real Option
Riskfree interest rate
=
6%
t =
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 Spring '12
 Jason
 Finance, Standard Deviation, Variance, Net Present Value, Probability theory, Fut ure Cash Flows

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