Transcript Slide 1

Real Options Analysis
Office Tower Building
Portfolio Presentation
Fall 2008
ESD.71
Professor: Richard de Neufville
Presented by: Charbel Rizk
1
Introduction
• Application of Real Options in construction field
• Time between design and completion relatively long
• Large Investment, expected long life cycle
• Office Building Tower – Based on real projects
• 2 types of offices:
o For Investor’s Use
o For Sale
• Project completion around 2000
•Lack of space in 2006
www.manenterprise.com
2
Objective & Procedure
Analyze project based on tools and method learned in class:
•Identify main uncertainties in design:
o Investor’s Office requirement
o Market Demand (Offices, Stores)
- For simplicity considered only Investor’s office demand
• Identify different scenarios: -Low; -Medium; -High
• Find possible (feasible) options to be added:
o Original: Fixed, deterministic design
o Re-buy Option
o Option to Add Floors
• Evaluate all designs
o Evaluation based on expected monetary value
o Two stages decision analysis
o Lattice decision analysis
3
Summary of Designs
• Fixed design: (3 floors for investor’s use)
o 7 Floors office tower
o 4 Floors for sale
• Flexible contract: (2, or 3, or 4 floors for investor’s use)
o 7 Floors office tower
o 3 Floors for sale
o 2 Other floors for sale with option to Re-buy
•Flexible design: (2, or 3, or 4 floors for investor’s use)
o Start with 6 floors office tower
o 4 Floors for sale
o Option to add 1 or 2 Floors
o Maximum number of floors is higher due to lower risk
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Assumptions (Simplifying) & Expected Demand
• Floors to be sold will be sold upon completion
• Time for execution 1 year
• Construction cost paid at t=0
• r=10%
• i=2%
• Assumed Cost of not having when required based on lost
opportunities
• Benefits are not included (Since using incremental NPV’s)
• Area per floor= 220m2
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General & Particular Costs
• General, defined per unit applicable to all designs
- Construction Cost
- Maintenance
- Running & Fees(Power, Ventilating, etc…)
- Cost of Lacking space
• Particular, unit rate differs or not applicable to all designs
- Permit cost
- Option Cost
a) Allow for Re-buy option in contract
b) Allow for adding floors (thicker columns, etc…)
- Strike price
a) Re-buying floor/s
b) Adding floor/s
6
Two Stages Decision Analysis
•Probabilities are shown below
Year 0
(Actual)
2
Sc Bet Yrs
0&5
Year 5
(Forecast)
Prob(0->5)
Low
2
0.15
Medium
3
0.4
High
4
0.45
Sc Bet Yrs
5 & 10
Year 10
(Forecast)
Prob(5->10)
/Year(0->5)
Low
Medium
High
Low
Medium
High
Low
Medium
High
2
2
3
3
4
4
4
4
4
0.6
0.3
0.1
0.15
0.4
0.45
0.05
0.25
0.7
•Flexible contract or design : Add option to change decision
Year 5
Year 5
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Two Stages Decision Analysis (Cont.)
Fixed Design
Design Type
• NPV calculation for each end node
•ENPV calculation
•Pruning based on maximize ENPV
EV At 5
Year 5
High
High
High
Medium
Medium
Medium
Low
Low
Low
Action at year 5
Not Applicable
Not Applicable
Not Applicable
Not Applicable
Not Applicable
Not Applicable
Not Applicable
Not Applicable
Not Applicable
Year 10
Low
Medium
High
Low
Medium
High
Low
Medium
High
Status
Low - Low
Low- Medium
Low - High
Probability
0.09
0.045
0.015
Best Decision
Can't Do antg
Can't Do antg
Can't Do antg
Fixed Design
Value
-2,227,429
-2,227,429
-1,938,965
Medium - Low
Medium - Medium
Medium - High
0.06
0.16
0.18
Can't Do antg
Can't Do antg
Can't Do antg
-1,938,965
-2,227,429
-2,227,429
High - Low
High - Medium
High - High
0.0225
0.1125
0.315
Can't Do antg
Can't Do antg
Can't Do antg
-2,227,429
-2,227,429
-2,227,429
Decide if
Possible
@5
Options
-2,227,429
-2,227,429 -2,227,429
-2,227,429
-1,938,965
-2,227,429 -2,184,159 -2,205,794
-2,227,429
-2,227,429
-2,227,429 -2,198,583
-1,938,965
Expected V.
-2,205,794
Best Decision
Do Nothing
Do Nothing
Do Nothing
Flexible Contract
Value
Expected V.
-1,067,182
-1,067,182
-1,355,645
Re-Buy 1 Fl
Re-Buy 1 Fl
Re-Buy 1 Fl
-1,337,283
-1,625,747
-1,625,747
Re-Buy 1 Fl
Re-Buy 1 Fl
Re-Buy 1 Fl
-1,625,747
-1,625,747
-1,625,747
-1,528,981
Decsision
@ Year 5
If Scenario
EV
@0
If Design
Type
Nothing
To
Chose
-2,205,794
Best Decision
Do Nothing
Do Nothing
Do Nothing
Flexible Design
Value
-1,143,182
-1,143,182
-1,431,645
Add 1 Floor
Add 1 Floor
Add 1 Floor
-296,796
-585,260
-585,260
Add 2 Floors
Add 2 Floors
Add 2 Floors
-550,411
-550,411
-550,411
Expected V.
-640,285
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Two Stages Decision Analysis (Cont.)
Best Strategy & VARG:
At t=0 choose flexible design
a) If demand during first period Was high => Add 2 Floors
b) If demand during first period was Medium => Add 2 Floors
c) If demand during first period was Low => Don’t Add Floors
VARG Chart
1.2
1
Probabilities
0.8
Fixed Design
Flexible Contract
0.6
Flexible Design
EV Fixed Design
0.4
EV Flexible Contract
EV Flexible Design
0.2
0
-2,500.00
-2,000.00
-1,500.00
-1,000.00
-500.00
0.00
Values in 1,000$
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Lattice Decision Analysis
• Determine: u, d, & p using:
- Maximum Value= S u u => u= Sqrt(Max/S)
- Minimum Value= S d d => d= Sqrt(Min/S)
- Most Likely= p2 * (S u u ) + 2*p*(1-p)*(S u d) + (1-p)2 * (S d d)
• Results:
-u= 1.4142
- d= 1.0000
- p= 0.8494
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Lattice Decision Analysis (Cont.)
• Resulting outcome & probability lattice:
P=0
2.00
Outcome Lattice
P=1(5 Yrs) P=2 (10 Yrs) P=3(15 Yrs) P=4(20 Yrs) P=5(25Yrs)
2.83
4.00
5.66
8.00
11.31
2.00
2.83
4.00
5.66
8.00
2.00
2.83
4.00
5.66
2.00
2.83
4.00
2.00
2.83
2.00
P=0
1.00
Probability Lattice
P=1(5 Yrs) P=2 (10 Yrs) P=3(15 Yrs) P=4(20 Yrs) P=5(25Yrs)
0.85
0.72
0.61
0.52
0.44
0.15
0.26
0.33
0.37
0.39
0.02
0.06
0.10
0.14
0.00
0.01
0.02
0.00
0.00
0.00
• Probability distribution function:
PDF for Lattice
c-1
c-2
c-3
c-4
c-5
c-6
Outcome
Prob
11.31
8.00
5.66
4.00
2.83
2.00
0.44
0.39
0.14
0.02
0.00
0.00
Rank
5.00
4.00
3.00
2.00
1.00
0.00
0.45
0.40
0.35
0.30
0.25
0.20
0.15
0.10
0.05
0.00
-0.050.00
Probability
Data for PDF:
5.00
10.00
15.00
20.00
Outcome
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Lattice Decision Analysis (Cont.)
• Option evaluation:
- Prepare cash flow per state & stage for each design
- Find ENPV for each design:
ENPV = Cash Flow Lattice * Probability Lattice
Flexible Design Cash Flow in 1,000 of $ Expanded (Taking All 4 Floors)
P=0
Cash Flow (566.00)
Flexibility
2 Floors Added
Dynamic programming
approach
P=1
P=2
P=3
(4469.67) (4687.05) (7689.60)
(6082.43) (7332.96) (7689.60)
(9978.88) (12030.50)
(16371.40)
P=4
(7689.60)
(7689.60)
(7689.60)
(12030.50)
(16371.40)
P=5
(7689.60)
(7689.60)
(7689.60)
(7689.60)
(12030.50)
(16371.40)
Flexible Design ENPV in 1,000 of $ Expanded (Taking All 4 Floors)
P=0
P=1
P=2
P=3
P=4
ENPV (Cash Flow) (9376.07) (13617.63) (14267.18) (15428.91) (12464.23)
Flexibility
(17410.70) (17360.39) (15428.91) (12464.23)
2 Floors Added
(23231.25) (20213.55) (12464.23)
Dynamic programming
(27715.82) (17210.94)
approach
(24247.20)
P=5
(7689.60)
(7689.60)
(7689.60)
(7689.60)
(12030.50)
(16371.40)
- Decison Lattice (Strategy):
Excercise CALL
OPTION ?
P=0
Add 2 Fl.
P=1
Add 2 Fl.
Don't Add
P=2
Add 2 Fl.
Add 2 Fl.
Don't Add
P=3
Add 2 Fl.
Add 2 Fl.
Add 2 Fl.
Don't Add
P=4
Add 2 Fl.
Add 2 Fl.
Add 2 Fl.
Don't Add
Don't Add
P=5
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Lattice Decision Analysis (Cont.)
• VARG For Lattice:
- Enumeration of all paths (5 periods 2 decisions => 32 Paths)
- Calculate PV for each path
- Find probabilities and prepare cumulative distribution
5 up
4 up 1 Down
3 up 2 Down
2 up 3 Down
1 up 4 Down
5 Down
EPV
P
P(PATH)
-621.1716915
-619.4651603
-283.0459493
-59.32895678
-6.114694908
-0.252082597
0.39177081
0.40377568
0.16645936
0.03431202
0.00353634
0.00014579
0.39177081
0.08075514
0.01664594
0.0034312
0.00070727
0.00014579
ENUMERATION OF PATHS WITHOUT CLOSING OPTION
(1585.55)
(1585.55)
(1585.55)
(1729.10)
(1729.10)
(1729.10)
(1585.55)
(1585.55)
(1729.10)
(1729.10)
(1585.55)
(1729.10)
(1729.10)
(1729.10)
(1457.13)
(1729.10)
(1729.10)
(1729.10)
(1457.13)
(1729.10) (1729.10) (1729.10) (1729.10) (1729.10) (1729.10)
(1729.10) (1729.10) (1729.10) (1729.10) (1729.10) (1729.10)
(1729.10)
13
Conclusions
• Demand variance was small and still:
- Based on decision trees: Flexible design was best alternative
- Based on lattice analysis: Option value above $ 1 M
• All values are not accurate, they are upper & lower bounds only
• Designers should take uncertainty into consideration, especially
with the availability of all new tools
• Discussion in this paper is based on NPV analysis only
• Other tools metrics can also be taken into consideration for
example:
- Benefit to cost ratio
- Payback period
- Risks
- Range of outcomes (maximum, minimum)
14
Thank you For Your Time
Comments?
Questions?
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