Value of Flexibility
Dr. Richard de Neufville
Professor of Engineering Systems and
Civil and Environmental Engineering
Massachusetts Institute of Technology
Garage Case – Flexible Design / RdN ©
Value of Flexibility
an introduction
using a spreadsheet analysis
of a multi-story parking garage
Developed from
“Valuing Options by Spreadsheet: Parking
Garage Case Example,”
ASCE J. of Infrastructure Systems, 2006
R. de Neufville, S. Scholtes, and T. Wang
Garage Case – Flexible Design / RdN ©
Intended “Take-Aways”
y Design for fixed objective (mission or
specifications) is engineering base case
y Recognizing variability => different design
(because of system non-linearities)
y Recognizing flexibility => even better design
(it avoids costs, expands only as needed)
Garage Case – Flexible Design / RdN ©
Value at Risk and Gain
y Value at Risk and Gain (VARG)
recognizes fundamental reality:
value of any design can only be known
probabilistically
y Because of inevitable uncertainty in
Future demands on system
4 Future performance of technology
4 Many other market, political factors
4
Garage Case – Flexible Design / RdN ©
Value at Risk and Gain Definition
y Value at Risk definition:
A loss that will not be exceeded at some
specified confidence level
4 “We are p percent certain that we will not lose
more than V dollars for this project.”
4
y Value at Gain similar – on the upside
y VARG easy to see on cumulative
probability distribution (see next figure)
Garage Case – Flexible Design / RdN ©
Cumulative Probability
CDF
100%
80%
60%
40%
20%
0%
-400
-200
0
200
NPVA
NPVB NPV
90%VAR for NPVB
10% Probability
400
600
90% VAR for NPVA
y Look at distribution of NPV of designs A, B:
90% VARisk for NPVA,B are -$91, $102
4 20% VAGain for NPVA is around $210
4
Garage Case – Flexible Design / RdN ©
Notes
y Cumulative distribution function (CDF)
shows the probability that the value of a
variable is < or = to quantity on x axis
y VARG can be found on the CDF curve:
90% VARisk => 10% probability the value is
less or equal
4 NPV corresponding to the 10% CDF is 90%
VARisk
4 NPV for 90% CDF is 10% Value at Gain
4
Garage Case – Flexible Design / RdN ©
VAR and Flexibility
y VAR is a common financial concept
y It stresses downside losses, risks
y However, designers also need to look at
upside potential: “Value of Gain”
y Flexible design provides value by both:
Decreasing downside risk
4 Increasing upside potential
4 See next figure
4
Garage Case – Flexible Design / RdN ©
Sources of value for flexibility
Cut downside ; Expand Upside
Cumulative Probability
Expand upside potential
Original
distribution
Distribution with
flexibility
Cut downside risks
Value
Garage Case – Flexible Design / RdN ©
Excel Analysis Sequence to
illustrate value of flexibility
1: Examine situation without flexibility
4
This is Base case design
2: Introduce variability (simulation)
=> a different design (in general)
3: Introduce flexibility
=> a even different and better design
Garage Case – Flexible Design / RdN ©
Parking Garage Case
y Garage in area where population expands
y Actual demand is necessarily uncertain
y Design Opportunity: Stronger structure
enables future addition of floor(s) (flexibility)
4 Requires extra features (bigger columns, etc)
4 May cost less !!! Because can build smaller
4
y Design issue: is flexibility worthwhile?
Garage Case – Flexible Design / RdN ©
Parking Garage Case details
y Demand
At start is for 750 spaces
4 Over next 10 years is expected to rise exponentially
by another 750 spaces
4 After year 10 may be 250 more spaces
4 could be 50% off the projections, either way;
4 Annual volatility for growth is 10%
4
y Average annual revenue/space used = $10,000
y The discount rate is taken to be 12%
Garage Case – Flexible Design / RdN ©
Parking Garage details (Cont)
y Costs
4 annual operating costs (staff, cleaning, etc.) =
$2,000 /year/space available
(note: spaces used is often < spaces available)
4 Annual lease of the land = $3.6 Million
4 construction cost = $16,000/space + 10% for
each level above the ground level
y Site can accommodate 200 cars per level
Garage Case – Flexible Design / RdN ©
Step 1: Set up base case
Demand growth as predicted, no variability
Year
Demand
Capacity
Revenue
Recurring Costs
Operating cost
Land leasing cost
Cash flow
Discounted Cash Flow
Present value of cash flow
Capacity costs for up to two levels
Capacity costs for levels above 2
Net present value
0
$3,600,000
1
2
3
750
893
1,015
1,200
1,200
1,200
$7,500,000 $8,930,000 $10,150,000
$2,400,000
$3,600,000
$1,500,000
$1,339,286
$2,400,000
$3,600,000
$2,930,000
$2,335,778
$2,400,000
$3,600,000
$4,150,000
$2,953,888
19
20
1,688
1,696
1,200
1,200
$12,000,000 $12,000,000
$2,400,000
$3,600,000
$6,000,000
$696,641
$2,400,000
$3,600,000
$6,000,000
$622,001
$32,574,736
$6,400,000
$16,336,320
$6,238,416
Garage Case – Flexible Design / RdN ©
Optimal design for base case
(no uncertainty) is 6 floors
10
5
0
2
3
4
5
6
7
8
9
-5
-10
-15
NUMBER OF LEVELS
TRADITIONAL NPV
Garage Case – Flexible Design / RdN ©
Step 2: Simulate uncertainty
Lower demand => Loss
600
Higher demand => Gain limited by garage size
5-floor design
500
Frequency
Sim ulated Mean
400
6-floor design
300
Determ inistic
Result
200
100
0
-17.8 -15.6 -13.5 -11.3
-9.2
-7.0
-4.9
-2.7
-0.6
1.6
3.7
5.9
8.0
Garage Case – Flexible Design / RdN ©
NPV Cumulative Distributions
Compare Actual (5 Fl) with unrealistic fixed 6 Fl design
1
0.9
Probability
0.8
0.7
0.6
CDF for Result of
0.5
Simulation Analysis (5-
0.4
floor)
Implied CDF for
0.3
Result of
0.2
Deterministic NPV
A
0.1
0
-20
-15
-10
-5
0
5
l i (6 fl
10
Garage Case – Flexible Design / RdN ©
)
Recognizing uncertainty =>
different design: 5 floors
10
5
0
2
3
4
5
6
7
8
9
-5
-10
-15
NUMBER OF LEVELS
TRADITIONAL NPV
RECOGNIZING UNCERTAINTY
Garage Case – Flexible Design / RdN ©
Step 3: Introduce flexibility into
design (expand when needed)
Year
Demand
Capacity
Decision on expansion
Extra capacity
Revenue
Recurring Costs
Operating cost
Land leasing cost
Expansion cost
Cash flow
Discounted Cash Flow
Present value of cash flow
Capacity cost for up to two levels
Capacity costs for levels above 2
Price for the option
Net present value
0
1
820
800
$8,000,000
2
3
924
1,044
800
1,200
expand
400
$8,000,000 $10,440,000
$1,600,000
$3,600,000 $3,600,000
$2,400,000
$3,600,000
$3,200,000
$3,600,000
$3,200,000
$3,600,000
$4,440,000
$3,160,304
$8,390,000
$974,136
$9,200,000
$953,734
$1,600,000
$3,600,000
$8,944,320
$2,800,000 -$6,144,320
$2,500,000 -$4,898,214
19
1,519
1,600
20
1,647
1,600
$15,190,000 $16,000,000
$30,270,287
$6,400,000
$7,392,000
$689,600
$12,878,287
Including Flexibility => Another, better design:
4 Fl with stronger structure enabling expansion
Garage Case – Flexible Design / RdN ©
Summary of design results
from different perspectives
Perspective
Deterministic
Recognizing Uncertainty
Simulation
No
Yes
Option Embedded
No
No
Incorporating Flexibilty
Yes
Yes
Design
6 levels
5 levels
4 levels with strengthened
structure
Estimated Expected NPV
$6,238,416
$3,536,474
$10,517,140
Why is the optimal design much better when
we design with flexibility?
Garage Case – Flexible Design / RdN ©
Sources of value for flexibility:
1) Minimize exposure to downside risk
1
0.9
Probability
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
-20
-15
-10
-5
5-Floor Design
0
5
10
4-Floor Design
Garage Case – Flexible Design / RdN ©
Sources of value for flexibility:
2) Maximize potential for upside gain
100.0%
90.0%
Mean for NPV
without Flexibility
80.0%
CDF for NPV
with Flexibility
Probability
70.0%
60.0%
50.0%
40.0%
CDF for NPV
without Flexibility
30.0%
Mean for NPV
with Flexibility
20.0%
10.0%
0.0%
-20
-15
-10
-5
0
5
10
15
20
25
30
35
Garage Case – Flexible Design / RdN ©
Comparison of designs
with and without flexibility
Design
Initial Investment
Expected NPV
Minimum Value
Maximum Value
Design with Flexibility Thinking Design without Flexibility thinking
(4 levels, strengthened structure)
(5 levels)
$18,081,600
$21,651,200
$10,517,140
$3,536,474
-$13,138,168
-$18,024,062
$29,790,838
$8,316,602
Comparison
Better with options
Better with options
Better with options
Better with options
Wow! Everything is better! How did it happen?
Root cause: change the framing of design problem
From: focus on a (mythical) forecast or set of specs
To: managing (realistic) uncertainties by flexibility
Garage Case – Flexible Design / RdN ©
Summary
y Flexibility Adds great value
y Sources of value for flexibility
4
Cut downside risk; Expand upside potential
y VARG chart is a neat way to represent the
sources of value for flexibility
y Spreadsheet with simulation is a powerful
tool for estimating value of flexibility
Garage Case – Flexible Design / RdN ©