Flexibility in Real Estate
Project Development
Prof. Richard de Neufville
Michel-Alexandre Cardin
Engineering Systems Division
MIT
Cover Story
• Case investigates two general questions in
real estate development strategy:
– Is it worth investing upfront to acquire particular
infrastructures (e.g. a park, utilities, etc.)?
– Is flexibility in expansion timing worthwhile?
• Particular instance studied:
– Development of apartment units around a park
2 May 2007
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2 of 31
Apartment Development Project
• Development of apartment units around a
park
– Five phases, 24 months each, start in 2007
– All units 1000 SF each
– Market value represents NPV (at 9% discount
rate) of all revenues once phase is completed
Phase
I
II
III
IV
V
Total
Type
APT
APT
APT
APT
APT
2 May 2007
SF
50,000
80,000
90,000
110,000
100,000
430,000
Units Net Acreage
50
1.15
80
1.84
90
2.07
110
2.53
100
2.30
430
9.87
Start
1/07
1/08
1/09
1/10
1/11
Completion
1/09
1/10
1/11
1/12
1/13
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Static Case
• Key Assumptions
– Deterministic forecast for market value of built property
currently evaluated at $350/SF -- increases at 2.5% per
year
– Deterministic forecast for development costs currently
evaluated at $220/SF -- increase with inflation at 2.5%
per year
– Development of all phases in a row benefits from cost
reductions of 2.5% due to economies of scale
– Discount rate for market value of built apartment property
(rV) is 9%, and for construction costs (rC) is 6%, close to
currently prevailing risk-free rate
2 May 2007
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Static Case
• Market value of built property and
development cost models
$620
$570
$520
$470
$420
$370
$320
$270
$220
$170
2007
2012
2017
2022
2027
Year
Value per Square Foot
2 May 2007
Dev't Cost per Square Foot
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Static Case
• Assumptions:
– Park area is about 50,000 SF (1 acre) and costs
$1M to develop along with the five development
phases.
– Cost is distributed to each phase as $200,000
each.
– Land acquisition costs $15M, paid when phase I
begins
– Infrastructure development, which includes site
grading, paving, utilities, and landscaping is
estimated at $29/SF
2 May 2007
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Static Case
• Pro Forma Discounted Cash Flow (DCF)
model
Year
Period
Built property value per SF ($)
Dev't cost per SF ($)
Phase I value
Phase I dev't cost
Phase II value
Phase II dev't cost
Phase III value
Phase III dev't cost
Phase IV value
Phase IV dev't cost
Phase V value
Phase V dev't cost
Acquisition cost
Infrastructure cost
Park development cost
Value of built property
Total cost
Net value
PV of built property
PV total cost
NPV
Return over initial cost (incl.
discount rate)
2007
0
$350
$220
$0
$10,725,000
$0
$0
$0
$0
$0
$0
$0
$0
$15,000,000
$1,426,911
$195,000
$0
$27,346,911
-$27,346,911
$115,903,253
$112,740,379
$3,162,873
2 May 2007
2008
1
$359
$226
$0
$0
$0
$17,589,000
$0
$0
$0
$0
$0
$0
$0
$2,340,134
$199,875
$0
$20,129,009
-$20,129,009
2009
2
$368
$231
$18,385,938
$0
$0
$0
$0
$20,282,316
$0
$0
$0
$0
$0
$2,698,467
$204,872
$18,385,938
$23,185,655
-$4,799,717
2010
3
$377
$237
$0
$0
$30,152,938
$0
$0
$0
$0
$25,409,234
$0
$0
$0
$3,380,580
$209,994
$30,152,938
$28,999,808
$1,153,130
2011
4
$386
$243
$0
$0
$0
$0
$34,770,106
$0
$0
$0
$0
$23,676,787
$0
$3,150,086
$215,244
$34,770,106
$27,042,116
$7,727,990
2012
5
$396
$249
$0
$0
$0
$0
$0
$0
$43,559,216
$0
$0
$0
$0
$0
$0
$43,559,216
$0
$43,559,216
2013
6
$406
$255
$0
$0
$0
$0
$0
$0
$0
$0
$40,589,270
$0
$0
$0
$0
$40,589,270
$0
$40,589,270
12%
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No Pre-Investment in Park
• Value At Risk and Gain curve (VARG curve)
100%
90%
80%
70%
60%
50%
40%
30%
20%
10%
0%
$3.10
$3.12
$3.14
$3.16
$3.18
$3.20
Millions
NPV ($)
Static NPV
2 May 2007
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With Pre-Investment in Park
• Value At Risk and Gain curve (VARG curve)
2 May 2007
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Case Recognizing Uncertainty
• Recognize reality of uncertainty
– Only around market value of built property
– Initial value within ± 50% of projection
– Annual growth factor also ± 50% of projection
– 15% volatility around each annual growth value
– Otherwise same DCF model
• Use Monte Carlo: 2000 simulations each
– Easy, routine - no special program
2 May 2007
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Case Recognizing Uncertainty
• Example of Uncertain Market Value Pattern
$620
$520
$420
$320
$220
$120
$20
2007
2012
2017
2022
2027
Year
Projected Value per Square Foot
Realized Value per Square Foot
2 May 2007
Projected Dev't Cost per Square Foot
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Case Recognizing Uncertainty
• NPV distribution for 2000 simulations
4.5%
4.0%
3.5%
3.0%
2.5%
2.0%
1.5%
1.0%
0.5%
$86.1
$80.1
$74.1
$68.1
$62.1
$56.1
$50.1
$44.1
$38.1
$32.1
$26.1
$20.1
$14.1
$8.2
$2.2
-$3.8
-$9.8
-$15.8
-$21.8
-$27.8
-$33.8
-$39.8
-$45.8
-$51.8
-$57.8
0.0%
NPV (MILLIONS $)
2 May 2007
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Case Recognizing Uncertainty
• Observations
– Expected NPV is $3.17M, compared to $3.16M
for static case
• Relatively similar due to unconstrained nature of
problem
• Situation different from parking garage
– Now deal with a distribution of outcomes rather
than single value
• Expected NPV (ENPV) rather than NPV
2 May 2007
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Case Recognizing Uncertainty
• Value At Risk and Gain curve (VARG curve)
100%
90%
80%
70%
60%
50%
40%
30%
20%
10%
-$80.0
-$60.0
-$40.0
-$20.0
0%
$0.0
$20.0
$40.0
$60.0
$80.0 $100.0
Millions
NPV ($)
VARG
2 May 2007
ENPV
Static NPV
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Flexible Case
• Sources of flexibility
– Develop park upfront all at once for $1M
• Increases market value of built property by 10% ONLY
when market value was increasing in previous year
– Expand at strategic times
• When market value of built property is 50% higher
than development cost
– Abandon
• At year 20, when phase is undeveloped
2 May 2007
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Flexible Case
• If recognize uncertainty, what are possible
outcomes from managerial perspective?
$620
$620
$520
$520
$420
$420
$320
$320
VS.
$220
$120
$220
$120
$20
2007
2012
2017
2022
2027
$20
2007
2012
Year
Projected Value per Square Foot
Realized Value per Square Foot
2 May 2007
2022
2027
Year
Projected Dev't Cost per Square Foot
Value > Cost all time
2017
Projected Value per Square Foot
Realized Value per Square Foot
Projected Dev't Cost per Square Foot
Value < Cost most times
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Flexible Case
• Positive NPV Scenario
Year
Develop? Abandon? Wait?
Dev't value criteria
Phase I value
Phase I abandonment value
Phase I dev't cost
Develop? Abandon? Wait?
Dev't value criteria
Phase II value
Phase II abandonment value
Phase II dev't cost
Develop? Abandon? Wait?
Dev't value criteria
Phase III value
Phase III abandonment value
Phase III dev't cost
Develop? Abandon? Wait?
Dev't value criteria
Phase IV value
Phase IV abandonment value
Phase IV dev't cost
Develop? Abandon? Wait?
Dev't value criteria
Phase V value
Phase V abandonment value
Phase V dev't cost
Phase(s) completed
Project abandoned?
Acquisition cost
Infrastructure cost
Park development cost
Value of built property
Total cost
Net value
PV of built property
PV total cost
NPV
Return over initial cost (incl. discount
rate)
2 May 2007
2007
Develop
$7,200,000
$0
$0
$11,000,000
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
2008
2009
2010
2011
2012
2013
2014
$0
$0
$0
$0
$0
$23,276,250
$0
$0
Develop
$18,751,000
$0
$0
$18,491,000
Wait
$21,094,875
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$38,233,990
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$44,531,643
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
Wait
$8,602,270
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
Phase I
$15,000,000
$1,463,499
$1,000,000
$0
$28,463,499
-$28,463,499
$139,603,060
$112,442,848
$27,160,211
$0
$0
$0
$0
$0
$0
Develop
$17,481,349
$0
$0
$21,322,434
Wait
$21,366,093
$0
$0
$0
$0
$2,460,141
$0
$23,276,250
$20,951,141
$2,325,109
$0
$0
$0
Phase I
$0
$2,836,850
$0
$0
$24,159,285
-$24,159,285
Develop
$25,859,464
$0
$0
$26,712,272
Wait
$23,508,604
$0
$0
$0
Phase II
$0
$0
$0
$0
$0
$59,004,637
$0
$0
$0
$0
$0
$0
Develop
$24,588,622
$0
$0
$24,890,981
Phase III
$0
$0
$0
$0
Phase IV
$0
$52,649,235
$0
$0
Phase V
$0
$3,553,943
$0
$38,233,990
$30,266,215
$7,967,775
$0
$3,311,629
$0
$44,531,643
$28,202,609
$16,329,033
$0
$0
$0
$59,004,637
$0
$59,004,637
$0
$0
$0
$52,649,235
$0
$52,649,235
95%
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Flexible Case
• Positive NPV Scenario
Year
2007
Develop? Abandon? Wait?
Develop
Dev't value criteria
$7,200,000
Phase I value
$0
Phase I abandonment value
$0
Phase I dev't cost
$11,000,000
Develop? Abandon? Wait?
Dev't value criteria
Phase II value
$0
Phase II abandonment value
$0
Phase II dev't cost
$0
Develop? Abandon? Wait?
Dev't value criteria
Phase III value
$0
Phase III abandonment value
$0
Phase III dev't cost
$0
Develop? Abandon? Wait?
Dev't value criteria
Phase IV value
$0
Phase IV abandonment value
$0
Phase IV dev't cost
$0
$920
Develop? Abandon? Wait?
$820
Dev't value criteria
Phase V value
$0
$720
Phase V abandonment value
$0
$620
Phase V dev't cost
$0
Phase(s) completed
$520
Project abandoned?
$420
Acquisition cost
$15,000,000
Infrastructure cost
$1,463,499
$320
Park development cost
$1,000,000
$220
Value of built property
$0
$120
Total cost
$28,463,499
Net value
-$28,463,499
$20
PV of2012
built property 2017
$139,603,060
2007
2022
2027
PV total cost
$112,442,848
Year
NPV
$27,160,211
Projected Value
per Square
Projected
Dev't Cost per Square Foot
Return
overFoot
initial cost (incl.
discount
95%
Realized Value
per Square Foot
rate)
2 May 2007
2008
2009
2010
2011
2012
2013
2014
$0
$0
$0
$0
$0
$23,276,250
$0
$0
Develop
$18,751,000
$0
$0
$18,491,000
Wait
$21,094,875
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$38,233,990
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$44,531,643
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
Wait
$8,602,270
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
Phase I
$0
$0
$0
$0
$0
$0
Develop
$17,481,349
$0
$0
$21,322,434
Wait
$21,366,093
$0
$0
$0
$0
$2,460,141
$0
$23,276,250
$20,951,141
$2,325,109
$0
$0
$0
Phase I
$0
$2,836,850
$0
$0
$24,159,285
-$24,159,285
Develop
$25,859,464
$0
$0
$26,712,272
Wait
$23,508,604
$0
$0
$0
Phase II
$0
$0
$0
$0
$0
$59,004,637
$0
$0
$0
$0
$0
$0
Develop
$24,588,622
$0
$0
$24,890,981
Phase III
$0
$0
$0
$0
Phase IV
$0
$52,649,235
$0
$0
Phase V
$0
$3,553,943
$0
$38,233,990
$30,266,215
$7,967,775
$0
$3,311,629
$0
$44,531,643
$28,202,609
$16,329,033
$0
$0
$0
$59,004,637
$0
$59,004,637
$0
$0
$0
$52,649,235
$0
$52,649,235
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Flexible Case
• Negative NPV Scenario
Year
Develop? Abandon? Wait?
Dev't value criteria
Phase I value
Phase I abandonment value
Phase I dev't cost
Develop? Abandon? Wait?
Dev't value criteria
Phase II value
Phase II abandonment value
Phase II dev't cost
Develop? Abandon? Wait?
Dev't value criteria
Phase III value
Phase III abandonment value
Phase III dev't cost
Develop? Abandon? Wait?
Dev't value criteria
Phase IV value
Phase IV abandonment value
Phase IV dev't cost
Develop? Abandon? Wait?
Dev't value criteria
Phase V value
Phase V abandonment value
Phase V dev't cost
Phase(s) completed
Project abandoned?
Acquisition cost
Infrastructure cost
Park development cost
Value of built property
Total cost
Net value
PV of built property
PV total cost
NPV
2 May 2007
2007
Wait
$2,500,000
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
2021
Develop
$7,817,520
$0
$0
$15,542,712
Wait
$12,508,032
$0
$0
$0
Wait
$14,071,536
$0
$0
$0
Wait
$17,198,544
$0
$0
$0
Wait
$15,635,040
$0
$0
$0
$0 $21,194,607
$0
$2,067,885
$0
$1,412,974
$0
$0
$0 $40,218,178
$0 -$40,218,178
$6,413,958
$17,788,539
-$11,374,581
2022
2023
2024
2025
2026
2027
$0
$0
$0
$0
$0
$23,695,280
$0
$0
Wait
$11,785,149
$0
$0
$0
Wait
$13,258,292
$0
$0
$0
Wait
$16,204,579
$0
$0
$0
Wait
$14,731,436
$0
$0
$0
Phase I
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
Wait
$6,601,009
$0
$0
$0
Wait
$7,426,135
$0
$0
$0
Wait
$9,076,387
$0
$0
$0
Wait
$8,251,261
$0
$0
$0
Phase I
Wait
$5,958,301
$0
$0
$0
Wait
$6,703,088
$0
$0
$0
Wait
$8,192,663
$0
$0
$0
Wait
$7,447,876
$0
$0
$0
Phase I
Wait
$12,838,556
$0
$0
$0
Wait
$14,443,376
$0
$0
$0
Wait
$17,653,015
$0
$0
$0
Wait
$16,048,195
$0
$0
$0
Phase I
$0
$0
$0
$23,695,280
$0
$23,695,280
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
Abandon
$5,854,494
$0
$2,498,636
$0
Abandon
$6,586,305
$0
$0
$0
Abandon
$8,049,929
$0
$0
$0
Abandon
$7,318,117
$0
$0
$0
Phase I
Abandoned
$0
$0
$0
$2,498,636
$0
$2,498,636
Wait
$11,698,569
$0
$0
$0
Wait
$13,160,890
$0
$0
$0
Wait
$16,085,532
$0
$0
$0
Wait
$14,623,211
$0
$0
$0
$0
$0
$0
$0
$0
$0
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Flexible Case
• Negative NPV Scenario
Year
2007
2021
Develop? Abandon? Wait?
Wait
Develop
Dev't value criteria
$2,500,000
$7,817,520
Phase I value
$0
$0
Phase I abandonment value
$0
$0
Phase I dev't cost
$0 $15,542,712
Develop? Abandon? Wait?
Wait
Dev't value criteria
$12,508,032
Phase II value
$0
$0
Phase II abandonment value
$0
$0
Phase II dev't cost
$0
$0
Develop? Abandon? Wait?
Wait
Dev't value criteria
$14,071,536
Phase III value
$0
$0
Phase III abandonment value
$0
$0
Phase III dev't cost
$0
$0
Develop? Abandon? Wait?
Wait
Dev't value criteria
$17,198,544
$620
Phase IV value
$0
$0
Phase IV abandonment value
$0
$0
$520
Phase IV dev't cost
$0
$0
Develop? Abandon? Wait?
Wait
$420
Dev't value criteria
$15,635,040
Phase V value
$0
$0
Phase V abandonment value
$0
$0
$320
Phase V dev't cost
$0
$0
Phase(s) completed
$220
Project abandoned?
Acquisition cost
$0 $21,194,607
$120
Infrastructure cost
$0
$2,067,885
Park development cost
$0
$1,412,974
Value of built property
$0
$0
$20
Total 2012
cost
$40,218,178
2007
2017
2022$0
2027
Net value
$0 -$40,218,178
Year
PV of built property
$6,413,958
Projected Value
Square
Projected$17,788,539
Dev't Cost per Square Foot
PV per
total
cost Foot
Realized Value
per Square Foot
NPV
-$11,374,581
2 May 2007
2022
2023
2024
2025
2026
2027
$0
$0
$0
$0
$0
$23,695,280
$0
$0
Wait
$11,785,149
$0
$0
$0
Wait
$13,258,292
$0
$0
$0
Wait
$16,204,579
$0
$0
$0
Wait
$14,731,436
$0
$0
$0
Phase I
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
Wait
$6,601,009
$0
$0
$0
Wait
$7,426,135
$0
$0
$0
Wait
$9,076,387
$0
$0
$0
Wait
$8,251,261
$0
$0
$0
Phase I
Wait
$5,958,301
$0
$0
$0
Wait
$6,703,088
$0
$0
$0
Wait
$8,192,663
$0
$0
$0
Wait
$7,447,876
$0
$0
$0
Phase I
Wait
$12,838,556
$0
$0
$0
Wait
$14,443,376
$0
$0
$0
Wait
$17,653,015
$0
$0
$0
Wait
$16,048,195
$0
$0
$0
Phase I
$0
$0
$0
$23,695,280
$0
$23,695,280
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
Abandon
$5,854,494
$0
$2,498,636
$0
Abandon
$6,586,305
$0
$0
$0
Abandon
$8,049,929
$0
$0
$0
Abandon
$7,318,117
$0
$0
$0
Phase I
Abandoned
$0
$0
$0
$2,498,636
$0
$2,498,636
Wait
$11,698,569
$0
$0
$0
Wait
$13,160,890
$0
$0
$0
Wait
$16,085,532
$0
$0
$0
Wait
$14,623,211
$0
$0
$0
$0
$0
$0
$0
$0
$0
Richard de Neufville / Michel-Alexandre Cardin ©
Draft Presentation for MIT Center for Real Estate
20 of 31
Flexible Case
• NPV distribution for 2000 simulations
30.0%
No investment
scenarios
25.0%
20.0%
15.0%
10.0%
5.0%
$90.5
$85.1
$79.7
$74.3
$68.9
$63.4
$58.0
$52.6
$47.2
$41.8
$36.4
$31.0
$25.6
$20.2
$14.8
$9.4
$4.0
-$1.5
-$6.9
-$12.3
-$17.7
-$23.1
-$28.5
-$33.9
-$39.3
0.0%
NPV (MILLIONS $)
2 May 2007
Richard de Neufville / Michel-Alexandre Cardin ©
Draft Presentation for MIT Center for Real Estate
21 of 31
Flexible Case
• Value At Risk and Gain curve (VARG curve)
100%
90%
80%
70%
60%
50%
40%
30%
20%
10%
-$80.0 -$60.0 -$40.0 -$20.0
0%
$0.0
$20.0
$40.0
$60.0
$80.0
$100.0 $120.0
Millions
NPV ($)
VARG Flexible Case
VARG Inflexible Case
2 May 2007
ENPV Flexible Case
ENPV Inflexible Case
Static NPV
Richard de Neufville / Michel-Alexandre Cardin ©
Draft Presentation for MIT Center for Real Estate
22 of 31
Flexible Case
• Value At Risk and Gain curve (VARG curve)
100%
90%
80%
70%
60%
50%
40%
30%
20%
10%
-$80.0 -$60.0 -$40.0 -$20.0
0%
$0.0
$20.0
$40.0
NPV ($)
VARG Flexible Case
VARG Inflexible Case
2 May 2007
ENPV Flexible Case
ENPV Inflexible Case
$60.0
$100.0 $120.0
Increased
upside
Millions
opportunities
$80.0
Static NPV
Richard de Neufville / Michel-Alexandre Cardin ©
Draft Presentation for MIT Center for Real Estate
23 of 31
Results
• About distribution
– Downside reduced, upside increased
• Increased Expected NPV = ENPV
• Consequences of recognizing uncertainty
– sometimes wait
– sometimes do not invest
– sometimes abandon after starting the project
• Sudden jump near zero NPV
– Scenarios where do not invest compared to
scenarios where profit is barely made over initial
costs
2 May 2007
Richard de Neufville / Michel-Alexandre Cardin ©
Draft Presentation for MIT Center for Real Estate
24 of 31
Results
• Static, “certain” case: no pre-investment in park
NPV = $3.16M
• Inflexible case: no pre-investment in park
ENPV = $3.17M
• Flexible case: pre-investment and timing flexibilities
ENPV = $15.67M
• Value of flexibility due to combination of strategic
timing and pre-investment in park:
E[VFlexibility] = MAX(0,E[NPVFlex.]-E[NPVInflex.])
= $12.5M
2 May 2007
Richard de Neufville / Michel-Alexandre Cardin ©
Draft Presentation for MIT Center for Real Estate
25 of 31
Results
• Other valuation attributes, in Millions $:
Expected initial investment
Expected NPV
Minimum NPV
Maximum NPV
DR)
2 May 2007
Inflexible
$27.35
$3.17
-$60.56
$77.91
12%
Flexible
$21.35
$15.67
-$42.94
$94.19
73%
Richard de Neufville / Michel-Alexandre Cardin ©
Draft Presentation for MIT Center for Real Estate
Better?
Flex. Better
Flex. Better
Flex. Better
Flex. Better
Flex. Better
26 of 31
Results
• Static, “certain” case: with pre-investment in park
NPV = $14.69M
• Inflexible case: with pre-investment in park
ENPV = $10.21M
• Flexible case: pre-investment and timing flexibilities
ENPV = $15.67M
• Value of flexibility due to strategic timing:
E[VFlexibility] = $(15.67 – 10.21)M = $5.46M
– Deduced value of pre-investment in park:
$12.5M - $5.5M = $7.0M
2 May 2007
Richard de Neufville / Michel-Alexandre Cardin ©
Draft Presentation for MIT Center for Real Estate
27 of 31
Results
• Other valuation attributes, in Millions $:
Expected initial investment
Expected NPV
Minimum NPV
Maximum NPV
Return over initial cost (incl.
DR)
2 May 2007
Inflexible
$28.13
$10.21
-$57.79
$95.46
Flexible
$21.35
$15.67
-$42.94
$94.19
Better?
Flex. Better
Flex. Better
Flex. Better
Inflex. Better
36%
73%
Flex. Better
Richard de Neufville / Michel-Alexandre Cardin ©
Draft Presentation for MIT Center for Real Estate
28 of 31
Take-Aways
• Easy method to deal with uncertainty
– No special software required
• Important to recognize uncertainty
– It’s reality!
• Recognizing uncertainty leads to flexible
design and management
• Improve expected NPV and other desirable
attributes
2 May 2007
Richard de Neufville / Michel-Alexandre Cardin ©
Draft Presentation for MIT Center for Real Estate
29 of 31
Questions/Comments?