Risk adjusted asset valuation using a probabilistic approach with
optimized asking rents and resale timing options
by
Sarwesh Paradkar
BTech & MTech Mechanical Engineering, 2009
Indian Institute of Technology Bombay
Submitted to the Program in Real Estate Development in Conjunction with the Center for
Real Estate in Partial Fulfillment of the Requirements for the Degree of Master of Science
in Real Estate Development
at the
MASSACHUSETTS iNSTITUTE
0OF T ECHN 0L 0 G Y
Massachusetts Institute of Technology
SEP 16 2013
September 2013
©2013 Sarwesh Paradkar
All rights reserved
LIBRARIES
The author hereby grants to MIT permission to reproduce and to distribute publicly paper and
electronic copies of this thesis document in whole or in part in any medium now known or
hereafter created.
Signature of Author:
Center for Real Estate
July 30, 2013
Certified by:
David Geltner
or of Real Estate Finance
Thesis Supervisor
Accepted by:
Interdepartmental D
David Geltner
air, MSRED Committee,
reW O4a-m in Real Estate Development
1
Risk adjusted asset valuation using a probabilistic approach with optimized asking rents and
resale timing options
by
Sarwesh Paradkar
BTech & Mtech Mechanical Engineering, 2009
Indian Institute of Technology Bombay
Submitted to the Program in Real Estate Development in Conjunction with the Center for
Real Estate on July 30t , 2013 in Partial Fulfillment of the Requirements for the Degree of
Master of Science in Real Estate Development
ABSTRACT
The model developed here provides an enhancement of the traditional DCF asset acquisition
valuation template, in Excel. It provides a relatively transparent and user-friendly yet flexible
risk-adjusted valuation of a subject individual acquisition, structured to consider the asset either
as a core asset or a value-add asset.
This study applies a basic stock flow model of space market dynamics to address the question
of covariance among input variables. The model is designed with optional probabilistic inputs
and historical data for the local space market (employment, rents, net rentable area, occupied
space, new completions, vacancy and absorption) and the asset market (cap rates history) to
produce a 15-year forecast for the relevant space and asset market for the subject property. An
optional optimal rent module in the model uses the forecasted cap rates and consequent
opportunity cost of capital to arrive at optimal asking rents for the subject property. The existing
rent roll is combined with the future rents and vacancies along with asset level projections of
operating costs and capital expenditures to arrive at the cash flow projections. Renewal
probability and probability to lease up are major differentiating factors between the core and
value add asset.
The model also enables the user to optionally consider how flexibility in resale timing can
improve the overall return performance from a probabilistic perspective. The output of the model
includes an apprehension of the entire going-in risk return relationship, depicted relative to a
relevant security market line generated by the input risk free interest rate and the opportunity
cost of capital in the relevant asset market.
Key words: Probabilistic, risk adjusted valuation, forecast, optimal rent, flexibility, renewal
probability, probability to lease up
Thesis Supervisor: David Geltner
Title: Professor of Real Estate Finance
ACKNOWLEDGEMENTS
I would like to thank Jacques Gordon, Global Head of Research & Strategy at MIT/CRE Industry
Partner firm LaSalle Investment Management for providing me with the opportunity to work with
LaSalle on this thesis, and helping me with his valuable guidance. I also would like to thank
Nathan Kane, Vice President at LaSalle Investment Management and his team for providing the
data required to calibrate the model.
I would like to thank Professor David Geltner from the MIT Center for Real Estate for advising
me on the thesis and for providing his invaluable insight on the topic. Throughout this thesis
experience and all the previous courses I have taken with him, he has been a source of
knowledge and inspiration for me. His book, Commercial Real Estate Analysis and Investment
has been a great source of reference for developing the financial model used in this thesis.
I would like to thank Lisa Thoma, Associate Director at the MIT Center for Real Estate and my
classmate Ryan Butler for helping me network with LaSalle Investment Management and set up
the first meeting with Jacques Gordon, where the idea of this thesis was generated.
Last but not the least, I would like to thank my mother, Sujata Paradkar for encouraging me to
go for my second post graduation and attend the Real Estate Program at MIT.
3
TABLE OF CONTENTS
A b s tra ct..................................................... .......................................................
In tro d u ctio n ...................................... . ..........................................
.. 2
5
A snapshot of the excel template is attached after the introduction.
4
The substance and content of this thesis consists of an Excel model template. In this narrative
written component we only present a brief introduction to the model.
INTRODUCTION
The discounted cash flow (DCF) pro-forma has been the classical work horse for estimating
property value and analyzing individual asset investment acquisition decisions for over a
generation now in the professional real estate world. But with the recent experiences in the
Financial Crisis of 2008, many prudent investment managers are seeking to upgrade this trusty
work horse a bit. As commercial property market data has become richer and more available,
there is a desire to incorporate local market data into the cash flow projections for the subject
asset. And there is growing interest in explicitly recognizing and somehow accounting for risk
and uncertainty in the forecasted future values, within the DCF valuation framework, effectively
to examine the investment's likely IRR outcome probability distribution. This initiative in
acquisition DCF modeling complements growing academic interest in places like the MIT Center
for Real Estate in using basic economic and engineering systems models to improve real estate
and infrastructure investment decision making. Analytical tools such as optimal search and risk
simulation models can help decision makers understand and quantify the value of flexibility in
real estate investment. For acquisitions of existing properties such flexibility prominently
includes the ability of the investor (landlord) to choose optimal asking rents and vacancy
management for the asset, and/or to choose the timing of asset resale (reversion). The present
thesis consists of an original Excel model (DCF 2.0), which aims to reflect and incorporate all of
these considerations and enhancements in a tool that is user-friendly and relatively transparent,
a "new generation" valuation model.
The model developed here provides a risk-adjusted valuation of a subject individual acquisition,
structured to consider the asset either as a "core" asset (stabilized leased-up) or a "value-add"
asset (substantial vacancy initially). Acquisition managers have been interested in
understanding if they are sufficiently compensated for the lease up risk involved in making a
relatively high return, high vacancy value add asset acquisition against a lower return, lower
vacancy core asset acquisition, and this model should help in such understanding.
Users of risk simulation in DCF valuation have also been concerned to adequately reflect not
only the individual uncertainty surrounding individual variables of interest (such as rents and
vacancy), but also the correlation or covariance between the individual variables. This study
applies a basic stock flow model of space market dynamics (of the type first introduced into the
real estate literature by Wheaton) to address the covariance question. The model is designed
with optional probabilistic inputs, so that the user does not have to employ uncertainty where
s/he does not wish to. But the model is set up to facilitate calibration of the uncertainty inputs
based on historical data for the local space market (employment, rents, net rentable area,
occupied space, new completions, vacancy and absorption) and the asset market (cap rates
history). The model uses the historical data to produce a 15-year forecast for the relevant space
and asset market for the subject property. If the user invokes the optional "optimal rent" module
in the model, then the forecasted cap rates and consequent opportunity cost of capital are used
to arrive at optimal asking rents for the subject property. The existing rent roll is combined with
the future rents and vacancies along with asset level projections of operating costs and capital
expenditures to arrive at the cash flow projections. Renewal probability and probability to lease
up are major differentiating factors between the core and value add asset.
The model also enables the user to optionally consider how flexibility in resale timing can
improve the overall return performance from a probabilistic perspective. The output of the model
5
includes not just a single valuation number, but an apprehension of the entire going-in risk
return relationship, depicted relative to a relevant security market line generated by the input
risk free interest rate and the opportunity cost of capital in the relevant asset market.
Rnme nf the
-
-
specific features of the model incli d (hi it nrp nnt limited to) the following:
Use of a stock-flow model of the local real estate market to reflect the relationships
between the various space market variables.
Linkage of the space market replacement rent (long-run equilibrium rent) to the asset
market via the cap rate, and explicit forecasting of cap rates based on user input (such
as bond yields or empirical cap rate histories allowing explicit incorporation of cyclicality
in the asset market).
Optional explicit modeling of optimal asking rent and lease-up timing.
Optional consideration of a valuation mean reversion based decision rule for strategic
resale timing to improve reversion value and lifetime IRR result.
Explicit comparison of ex ante core asset investment risk/return performance with that of
corresponding or otherwise similar value-add asset.
Optional valuation based on direct capitalization and DCF analysis.
For further instructions on using the model, the user should refer to the "Index" worksheet of the
accompanying Microsoft Excel File "DCF 2.0". In the same package is a "NO SIM" version
labeled "DCF NO SIM" which can be used for calibrating the parameters so that long run times
are avoided at calibration stage. The full model including the simulations (activated by
"recalculation" - such as F9 on a PC) can take up to 3-4 minutes to run on a laptop. The "NO
SIM" version runs instantaneously but produces only one future forecast or scenario. (The
simulation runs 2000 randomly generated "trials.) The NO SIM file can therefore be used to
"play around" with input parameters, particularly for the uncertainty inputs (such as volatilities),
to see what the future space and asset market (cap rate) forecasts look like (based on graphical
output). When the user is satisfied with the input parameters, then the full simulation model can
be invoked to generate the implied ex post performance probability outcome distributions for the
subject investment. The passwords for opening the files in read only format and editable format
are "sujata" and "psujata" respectively.
This model was invited for a presentation and received wide appreciation at the Global Planning
Session of LaSalle Investment Management, Chicago, July 22-23, 2013, attended by the Global
CEO, and heads of Europe, Asia and North America.
6
.
11111
-
- -
-
-
..................................
..........................................................
..........................................................
.....................
.......
F71ndex
Sheet Name
Information
This sheet summarizes the goal of this financial model and the interpretation of the results obtained.
used to calibrate this model. The overall architecture of the model is also presented in this sheet.
1
It also presents the major sources of data
Enter the historic data for gross rent, cap rates, net rentable area, occupied stock, absorption, completions, vacancy and employment for the
period under consideration in this sheet. The data has to be recorded on a quarterly basis for 94 quarters. This data is used in the different
modules of the model for future projection.
2
Control Panel
3
Enter the different parameter values to be used as input to the different modules of this model. The user can change the specified inputs based
on the market under consideration. Note that, it is possible to enter uncertainty into the parameters and exogenous variables, but that such
uncertainty input is optional. Further instructions are provided on the sheet.
This is the forecasting module of this financial model. It uses the stock flow appraoch to connect and co-vary the rent, vacancy, occupied stock,
net rentable area and new completions using the sensitivity and trigger parameters entered by the user in the control panel. A forecast for 60
quarters in the future is generated by this model. The forecast generated is used by the down stream modules for risk assessment.
4
This is the simulation for the forecasting model. Depending on choice, the user can view how the different components of the forecast vary
with
over time. If the uncertainty is activated in the control panel, the relationships between the variables would be dynamic and would change
every run of the simulation. The user can choose a particular quarter in the future to see how the different components vary across trials in the
same cross section in time.
This is an add on module to the forecasting module. It uses the forecasted cap rates, rent, vacancy and gross absorption data from the market
to calculate an optimal rent which the land lord would settle for depending on the market conditions. The optimal search algortihm embedded
in this module reflects the amount of uncertainty or volatility in the forecasted rents. The optimal decision is based on maximizing the present
value of the property. The higher the volaitlity, higher is the optimal asking rent, optimal long term vacancy and the maximum building value.
5
6
7
This module creates an asset level occupancy and rent for the core asset under consideration. The module considers four possibilties namely,
already occupied, renewed, new lease and vacant. Depending on this, the rents, occupancy levels, costs and final net operating income and 5
year hold IRR ai tmtd
8
This module creates an asset level occupancy and rent for the value add asset under consideration. The value add asset has a considerable
switches in the control panel. The module
larger vacancy than the core asset. The amount of vacancy can be asjusted using the level
considers four possibilties namely, already occupied, renewed, new lease and vacant. Depending on this, the rents, occupancy levels, costs
and final net operating income and 5 year hold IRR is estimated.
9
This module presents an option for the user to have the asset holding period flexible between 5 and 15 years. The HOLD/SELL decision is
taken based on the ex post knowledge of the investor. The reversion price is compared with the current expected value based on a long term
growth trajectory plus a premium to trigger the resale under the prediction of a future mean reversion.
10
This is the simulation of the 5 year hold IRRs for both the core and value add asset. Simulations for both, the fixed holding period and the
flexible holding period. The higher the uncertainty activated in the control panel, the more valuable is the felxibility in holding periods. This
module allows the user to look at the statistical parameters of the distribution of the IRRs over 2000 trials.
11
his sheet summarizes the risk return relationship for the core and value add assets for both the fixed 5 year hold and for the fisxible holding
>eriod between 5 and 10 years. The ex ante risk is measured in terms of the Treynor ratios. The user input risk free rate of interest and the
>pportunity cost of capital (with a unit risk) are used to generate the security market line.
.......
~~~~~~
..............................................
........................................................
"""""""""""....
MEER""
"
Intent
The intent of this model is to develop a risk adjusted asset valuation model for a single core and value add asset using a probabilistic
abpproach combined with optimized asking rents and selling options.
Strategy
Market Forecast
The strategy adopted is to use the historical data for the local space market (employment, rent, occupied space, net rentable area, new
completions, vacancy, and absorption) and asset market (cap rates history) in order to produce a 15 year forecast of the relevant space
and asset market for the subject property, We then use the rent roll data for the asset under consideration to project cash flows for the
Sn
specific subject asset. We assume the asset to be almost 100% occupied for the core investment and the same asset 50% occupied foryDa
the value add investment. Renewal probability and expected time to lease up are major inputs differentiating the two types of assets.
Source
Cycle
In the present example, the rent, occupied space, net rentable area, new completions, vacancy and absorption is obtained from CBRE.
Employment data isobtained from the New York Labor Department. The cap rate data is obtained by assuming Moody's BAA bond
ratings as an unbiased estimator.
Developer
CP Ras
Sarwesh Paradkar under the guidance of Professor David Geltner.
Cyt
Academic Reference
Commercial Real Estate Analysis and Investments (Third Edition) - David Geltner
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if the user has better parameter
estimates,
sWe
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parameters in the control panel.
1988131 29
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300
2!250
21200
1
50
1.100
50
0IRoAs
250
25.00%
20.00%
15.00%
10.00%
* 5.00%
200
* 150
0*
100
UL
S0.00%
. -5.0004.%
50
0
o*
\Go
IRR Core Asset
450
400
S350
0 300
250
200
50
0
)b
ev
Co.
0'.<b, .
p.
l
Bound
8.23%
8.65%
9.07%
9.49%
9.90%
10.32%
10.74%
11.16%
11.58%
12.00%
12.41%
12.83%
13.25%
13.67%
14.09%
14.51%
14.92%
15.34%
15.76%
16.18%
16.60%
IRR Core
Count
1
6
12
29
60
99
186
316
480
694
914
1169
1403
1609
1773
1866
1940
1977
1989
1999
2000
~1.
,*
IRR VA Asset with flex
IRR Core Asset with flex
Frequency
1
5
6
17
31
39
87
130
164
214
220
255
234
206
164
93
74
37
12
10
1
Bound
10.43%
11.95%
13.48%
15.00%
16.53%
18.05%
19.58%
21.10%
22.63%
24.15%
25.68%
27.20%
28.73%
30.25%
31.78%
33.30%
34.83%
36.35%
37.88%
39.40%
40.93%
IRR VA
Count
1
4
17
48
138
268
393
507
697
898
1098
1250
1364
1496
1624
1753
1857
1935
1974
1992
2000
10.00%
1S00'
20.00%,
S-15.00%
-20.00%
-25.00%
Core Inflex
15.00%
10.00% 4
.11111111.
UL 100
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
o
IRR VA Asset
350
300
250
* 200
150
100
50
0
150
0
VAO Ao
-&0%-
-10.00%
Frequency
1
3
13
31
90
130
125
114
190
201
200
152
114
132
128
129
104
78
39
18
8
IRR Core flex
Bound
Count
Frequencyl
-4.87%
1
1
-3.03%
3
2
-1.19%
13
10
0.65%
17
4
2.48%
20
3
4.32%
20
0
6.16%
20
0
8.00%
20
0
9.83%
20
0
11.67%
31
11
13.51%
63
32
15.35%
165
102
17.18%
334
169
19.02%
571
237
20.86%
907
336
22.70%
1324
417
24.53%
1650
326
26.37%
1841
191
28.21%
1950
109
30.05%
1995
45
31.88%
2000
5
5.00%
0.00%
-
%
10.00%
(9
-10.00%
-15.00%
>-20.00%
-25.00% i
-30.00%
VA Inflex
IRR VA flex
Bound
Count
Frequency
-1.91%
1
1
0.27%
4
3
2.45%
10
6
4.63%
16
6
6.80%
24
8
8.98%
32
8
11.16%
41
9
13.34%
42
1
15.51%
48
6
17.69%
64
16
19.87%
141
77
22.05%
295
154
24.22%
548
253
26.40%
870
322
28.58%
1197
327
30.75%
1474
277
32.93%
1709
235
35.11%
1883
174
37.29%
1958
75
39.46%
1989
31
41.64%
2000
11
S.45O%
p
35.00%
30.00%
a
-
-
-
25.00%
The security market line (SML) in the adjoining graph is generated using the risk free rate of interest and the
ex ante opportunity cost of capital having a risk of 1 unit. The SML is used to price the assets under the
'
20.00%
-
-
-
-
-
-
-
-
-
-
-
-
-
-
assumption that the risk premium per unit of risk equals the market price of risk.
-SML
60OCore Asset Inflex
u
15.00%.-
--
-
-..
VA Asset Inflex
emaCore Asset Flex
aftnVAAsset Flex
10.00%
5.00%
0.00%
0
0.01
0.05
0.04
0.03
0.02
0.07
0.06
Risk
Risk-free Asset
Retum
Risk
Treyncr atia
1.50%
0.00%
OCC
7.00%
1.00%
Flexible
Inflexible
Core Asset VA Asset Core Asset VA Asset
12.51%
1.33%
25.43%
6.11%
20.91%
4.35%
27.09%
5.75%
8.28
3.91
4.46
4.45