D Gimpelevich SERM Paper (JPIF)

Simulation-based excess returnmodel for real estate development

A practical Monte Carlo simulation-basedmethod for quantitative risk management andproject valuation for real estate developmentprojects illustrated with a high-rise office

development case study

David GimpelevichMid-Market Securities LLC, New York, New York, USA

Abstract

Purpose – An acute need exists for a practical quantitative risk management-based real estateinvestment underwriting methodology that clearly helps guide decision making and addresses theshortcomings of discounted cash flow (DCF) modeling by evaluating the full range of probableoutcomes. This paper seeks to address this issue.

Design/methodology/approach – The simulation-based excess return model (SERM) is an originalmethodology developed based on an application of Monte Carlo simulation to project risk assessmentcombined with the widely practiced DCF modeling. A case study is provided where results of themodeling are compared with traditional DCF risk models and with prior projects with knownoutcomes.

Findings – This paper lays out a practical method for stochastic quantitative risk managementmodeling for real estate development projects and illustrates that for identical projects risk-adjustedreturns derived with the use of SERM may differ significantly from returns provided by traditionaldiscounted cash flow analysis. SERM corrects serious shortcomings in the DCF methodology byincorporating stochastic tools for the measurement of the universe of outcomes. It further serves tocondense the results of Monte Carlo simulations into a simplified metric that can guide practitionersand which is easily communicational to decision makers for making project funding decisions.

Practical implications – SERM offers a simple, practical decision-making method for underwritingprojects that addresses the limitations of the prevailing methodologies via: stochastic assessment ofthe range of outcomes; interdependence of input variables; and objective risk premium metrics.

Originality/value – This paper presents an original methodology for making project-fundingdecisions for real estate development projects that is based on Monte Carlo simulation combined withDCF analysis. The methodology presented here will have value for real estate developers, investors,project underwriters, and lenders looking for a practical and objective method for project valuationand risk management than is offered by traditional DCF analysis. A review of literature did not revealanalogous methodologies for risk management.

Keywords Monte Carlo simulation, Underwriting, Real estate, Risk management, Modelling,Return on investment

Paper type Technical paper

I. IntroductionReal estate development is a risky endeavor. Some projects generate outsizedreturns while others languish or else entirely erase investment capital. It is also an

The current issue and full text archive of this journal is available at

www.emeraldinsight.com/1463-578X.htm

Simulation-basedexcess return

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Received June 2010Accepted October 2010

Journal of Property Investment &Finance

Vol. 29 No. 2, 2011pp. 115-144

q Emerald Group Publishing Limited1463-578X

DOI 10.1108/14635781111112765

area of investment management that has historically seen slow adoption of financialrisk modeling by practitioners. Too often, developers operating with their ownfunds proceed with projects with little more than back-of-the-envelope calculationsbased on intuition and developers’ yield or return on cost metrics. Since institutionaland private equity investors have become more active in funding developmentprojects, many developers have adopted discounted cash flow (DCF) as theirprimary risk management methodology, often augmented by multi-point sensitivityanalysis. A few practitioners, recognizing the limitations of DCF, have exploredstochastic methods and real options in their search for more optimal quantitativerisk management methods. However, these methodologies are sufficiently complexin their applications to restrict their usefulness for a majority of practitioners.Furthermore, they often fail to provide a clear go/no-go decision signal whenemployed.

While a number of papers address stochastic methods in real estate asset valuationand non-real estate related project evaluation, research did not reveal any analogousquantitative risk management models or methodologies specifically for use in realestate development, nor did research reveal a useful method for applying the results ofMonte Carlo simulations to practical decision making.

In this paper we formulate a methodology for development of a stochastic modelthat represents a reasonable approximation of reality for development projects andcombining it with DCF in such a way as to generate a clear decision signal for thepractitioner. This paper will have value for real estate developers, investors, projectunderwriters, and lenders looking for a practical and objective method for projectvaluation and risk management than is offered by traditional DCF analysis. SERM isequally applicable to development of all product types; however, this paper onlyaddresses SERM as it applies to ground-up development of office projects.

Limitations of DCFThe limitations of the DCF method have been extensively documented. Baroni et al.(2006), as well as Atherton et al. (n.d.) and Young (2007), for instance, discuss thechallenges of proper identification of discount rates, future rent and expense levelsand terminal value estimates. Selection of these values can be in fact sufficientlyarbitrary as to make results of DCF analysis to be essentially meaningless. Manypractitioners, for instance, will estimate rents, expenses, and the exit capitalizationrate, with perhaps two or three sensitivity scenarios, and solve for the internal rateof return (IRR), looking for a set number as decision-making guideline, usually onthe order of 20 percent, derived from a wide-sample average. However, the selectedIRR hurdle often bears no relationship with the actual risks inherent in theparticular project under consideration. Risk depends on the variability of incomethat the developed property can be expected to generate and variability of themarket value at completion.

Too frequently the decision to proceed is based on nothing more than an intuitionthat the income necessary to clear the hurdle can be achieved at the time the project iscompleted, making it no more rigorous than a decision made on the basis of intuitionalone. Finally, even when input variables are rigorously selected, DCF can onlygenerate point estimates of returns, which, by ignoring the full range of probableoutcomes necessarily tend to distort the picture used for decision-making.

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Prior applications of stochastic methodologies to real estate investmentsA number of papers have addressed application of Monte Carlo methods to real estateinvestments. Many have focused on the problem of asset valuation, including Baroniet al. (2006) and Young (2007). Atherton et al. (n.d.) examine, using a Monte Carlosimulation tool for development profitability analysis. In this paper we build on theirwork to formulate a decision-making methodology.

All of papers examined by the author use the mean valuation as the expected valueof an asset or a project and use probability measures to represent the risk. Knowing theprobability of achieving a certain outcome, however, is not sufficient to make adecision to proceed. What is needed is a way to weigh expected returns in the contextof specific project risk.

II. The simulation-based excess return modelExisting tools for evaluation of simulated results concentrate on the probability ofmissing expected returns. As such they provide valuable information, but the questionwhether this probability is excessive or acceptable remains with the practitioner’sjudgment, rendering an objective determination of project feasibility impossible. Whatis needed is an objective way to determine what return is sufficient to compensate forthe risk taken in undertaking a project. Risk is generally defined in terms of volatilityof returns. Finance professionals have long used the Sharpe ratio in order to measurerelative performance of portfolios with the returns of a market benchmark. The Sharperatio, however, suffers from two significant limitations, one of which is general and theother specific to the practice of real estate investment. The first limitation is the fact theSharpe ratio defines volatility in terms of the standard deviation of returns, whichincludes both the undesirable, downside volatility as well as the desirable, upsidevolatility. As such, it produces a distorted metric. The second limitation is that theSharpe ratio measures relative volatility with an index, or relative risk, whereas a realestate practitioner is generally concerned with absolute risk, both because direct realestate investments are essentially not diversifiable and because sponsor compensationmetrics are based on absolute measures.

The first limitation of the Sharpe ratio has been addressed by Satchell and Pedersen(2002) in formulating the Sortino ratio, which expresses risk as only the downside tailof the distribution of returns. The Sortino ratio also incidentally eliminates the secondlimitation of the Sharpe method by substituting a target rate of returns for the actualmarket returns. As with the Sharpe ratio, the higher values of the Sortino ratio signifygreater returns per unit of risk.

Having addressed the key limitations of the Sharpe ratio, however, the Sortino ratiostill only allows comparison of projects to one another and does not offer an objectivemetric of sufficiency of returns for a given project. Here we submit theSimulation-Based Excess Return Model (SERM), a methodology to address thisproblem.

Since the Sortino and Sharpe ratios have been developed to measure risk-adjustedperformance for investment managers in the equity markets, they take as theirfoundation volatility of actual portfolio and index returns. We apply an analogousmethodology to the universe of simulated outcomes.

First we express the downside risk DR in terms of net present value NPVdiscounted the project’s weighted average cost of capital WACC. We use NPV as a


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measure of returns because during simulation a large proportion of iterations produceundefined values for internal rate of return. In other words, downside risk is heredefined as the semi-standard deviation of returns expressed as NPV divided by meanNPV:

DR ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiR 0

21NPV 2f NPVð ÞdNPV

q

NPVð1Þ

where NPV is the simulated net present value of returns as discounted by the weightedaverage cost of capital for the project.

Next, we determine the mean expected internal rate of return MEIRR. We cancalculate the MEIRR from the mean investment and gains from the simulation andknown effective project duration. Effective project duration is not equal to calendarduration because project cash flows are asymmetric, and is defined as the durationover which the known mean investment and gain amounts would produce a knownIRR. A good value for the known IRR is generally the risk-free rate, and meaninvestments and gains discounted by the risk-free rate are simulated for the purpose.The MEIRR can be calculated based on this effective project duration.

We use IRR as a component of SERM because it offers an objective measuresimulated returns given all cash flows and is the equivalent to the actual equityinvestment return measured by the Sharpe and Sortino ratios. In addition, it is widelyunderstood and accepted by the practitioners. Naturally, in practice the size of theprofit and loss projection needs to be taken into account even when the MEIRR appearsattractive.

Given the MEIRR, we can calculate the mean return per unit of risk by dividingMEIRR by DR. we can then discount the MEIRR by the resulting metric to obtain therisk adjusted return for the project. Finally, we adjust the resulting value for the timevalue of money by subtracting from it the risk-free rate to arrive at excess risk-adjustedreturn ERR, resulting in the following formulation:

SERM ¼E r½ �

E r½ �DR2 rf ð2Þ

where E[r] is the mean expected internal rate of return (IRR) for the project derivedfrom simulation; DR is the simulated downside risk for the project; and is the risk-freerate.

Equation (2) reduced to its normal form is the definition of the excess risk-adjustedreturn under the SERM:

SERM ¼E r½ �

E r½ �DR2 rf : ð3Þ

In other words, SERM adjusts the expected return by the ratio of the expected returnand downside risk that is derived from simulation and measures the excess of thisadjusted return over the risk-free rate.

Once the ERR is obtained, it becomes possible to derive the required rate of returnMAR for the given project, by computing the rate of return at ERR ¼ 0, as follows:

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MAR ¼ffiffiffiffiffiffiffiffiffiffiffiffiffirf DRj j

p: ð4Þ

SERM MAR offers a useful metric to demonstrate the appropriate level of risk for thegiven project expressed in familiar terms. Care should be taken when applying theSERM MAR as a shortcut hurdle rate to other projects with potentially differentcharacteristics because they may face vastly different probable outcomes.

Additional metricsWhile the single-number ERR is a useful decision-making metric of the risk/returnprofile of a project, it does not address every aspect of the risk continuum for thepractitioner. An informed decision to undertake a project requires additionalinformation from the simulation, such as:

. Probability of loss, defined as the probably that the WACC-discounted NPV isless than zero.

. Median expected NPV, defined as the median NPV from simulation multiplied bythe probability of loss.

. Probability of clearing an IRR hurdle is an additional metric that is useful forpractitioners working with equity partners, enabling a practitioner tounderstand the probability to delivering promised return levels to investors.

. Mean expected loss in the event that the project is unsuccessful.

Risk-free rateThe most appropriate risk-free rate to use for SERM analysis is the interest rate paidby the Treasury obligation of a similar maturity to the development project, less anadjustment factor to back out the interest rate risk premium inherent in the Treasurysecurity’s interest rate:

rf ¼ rfT 2 rrp ð5Þ

where rP is the risk-free rate for the project; rfT is the US Treasury rate for an obligationof an equivalent term; and is the interest rate risk premium adjustment factor.

Discount rate: WACCBecause the purpose of the SERM analysis is to determine risk premium, it woulddistort results if a risk premium were also included in the discount rate. Therefore thediscount rate for SERM is determined as follows:

rP ¼ LTVð ÞrD þ 1 2 LTVð ÞrE ð6Þ

where rP is the weighted average cost of capital WACC for the project; rD is theeffective construction period interest rate of the debt portion of the total cost; rE is thebreak-even equity IRR applied to the equity portion of the total cost; and LTV is theloan to value ratio for the construction loan.

A normal profit for the developer needs to be included in the break-even IRR toensure that the developer’s overhead is at least covered. This is best implemented inthe form of a developer’s fee incorporated into the project cost model, or alternatively inthe form of a predetermined markup to the project break-even IRR. Issues with themarkup method include the fact that the normal profit fluctuates with the total return,


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thus putting overhead coverage at risk, as well as the potentially arbitrary nature ofthe predetermined markup that can undermine the objectivity of the SERM analysis.

It is imperative to use realistic component rates of return when constructing theWACC. Assuming the standard development capital structure prevailing in the UnitesStates where land acquisition is financed by developer’s equity and construction isfinanced by a combination of investor equity and construction debt, for instance wouldproduce a structure as follows. The rate of return on debt can be approximated byusing the nominal interest rate on the construction loan. The rate of return on theinvestor’s equity can be approximated by the preferred rate demanded by the investorplus a variable component that depends on the actual return based on the payoutwaterfall for the project, making the WACC an output variable of the simulation. Forsimplicity’s sake it is possible to state the investor’s equity rate of return equals theinvestor’s stated required rate or return. Finally, the developer’s minimal required rateof return should be incorporated in the WACC. This rate may represent the holdingcost of the development parcel, opportunity cost of capital, or even zero in some cases.

Interdependence of input variablesThe following variables are commonly assessed in simulation of outcomes in the caseof office development. Variables for other product types may vary; however, analysisof other product types is outside the scope of this paper.

. General inflation. General inflation can be expressed as the average inflationfrom time T0 to the time of project stabilization TS.

. Market vacancy. The market vacancy of most interest is the vacancy at the timeof project stabilization TS. It may be possible to instead model vacancy as theendpoint of a Brownian-motion series from T0 to TS, but it is not clear that theadded complexity of modeling is justified by the potential enhancement inherentin this methodology as only the terminal value is of interest and the range ofterminal values is empirically derived.

. Starting occupancy and stabilization period. Starting occupancy at completion ofa project and the duration of the stabilization period (TD-TS) are functions ofmarket vacancy.

. Market rent. The market rent of interest is the rent at the of project stabilizationTS. While there is evidence that market rents follow a Brownian random walkover time, a simplification of modeling a range of static rents at the time ofstabilization is possible because interim rent flows between time zero andstabilization are not required.

. Rent escalation. Rent escalation from the time of project stabilization TS to thetime of disposition TD is best expressed as a spread above general inflation inorder to capture the close interrelationship between these variables.

. Hard (construction) cost inflation. Hard cost inflation from time T0 to thecommencement of construction (TC) is best expressed as a spread above generalinflation in order to capture the close interrelationship between these variables.

. Construction loan interest rate. Construction loan interest rate is best expressedas a spread above general inflation in order to capture the close interrelationshipbetween these variables.

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. Direct capitalization rate. Direct capitalization rate of interest is the rate at TD is avariable that is exogenous to the model as it primarily depends onmacroeconomic factors and macro-level investment allocation decisions.

. Construction period duration (TS-TC).

. Actual rate of return on invested equity (rE). Because real estate developmentinvestment agreements frequently employ a waterfall payout schedule, the exactcost of equity depends on the profitability of the project, making the WACC adependent variable in computing the developer’s return. When analysis isperformed from the developer’s perspective rather than the investor’sperspective, the variability of the cost of capital should be modeled as adependent input variable, whereas in the converse case it may be treated as afixed quantity.

For practitioners it is intuitively obvious that market rent levels, rent escalations, newproject vacancy levels, and stabilization period durations, and possibly hard costescalation, are all dependent on the supply and demand for new space, for whichMarket Vacancy can stand as a proxy. The statistical analysis of this relationship ispresented in the case study in this paper.

There is a further relationship among general inflation, hard cost inflation,construction loan interest rates, and the direct capitalization rate.

To add complexity, hard cost inflation and the direct capitalization rate are alsosomewhat correlated with supply and demand for new space as proxied by marketvacancy, but are also dependent on outside factors such as global demand for steel,relative demand for real estate as an asset class, and risk premiums demanded by realestate investors. For a simplified practical implementation, these variables can betreated as independent.

Construction period duration is an independent variable as it relates toproject-specific considerations such as entitlement risk; however, it also exhibits adependency on market conditions, insofar as few practitioners would contemplate orhave the financing for launching new construction in the face of elevated vacancies[1].

The use of interdependent input variables in a simulation context is essentially anapplication of the familiar scenario-based sensitivity analysis extended to a continuumif a large number of intermediate scenarios that extends sensitivity analysis withstatistical and probabilistic analysis tools.

1. Derivation. The relationship among the interdependent variables can beapproximated by the following empirically-derived relationships by using curve fittingmethodologies.

With the exception of new project vacancy, all variables can be derived fromcommercially available sources. Expert estimates of the spread need to be used inpractice because there is little available hard data about vacancy for new projects vsgeneral market vacancy. In selecting data observations for curve fitting the historicalperiod needs to be sufficiently long to capture at least one and for preference multiplereal estate cycles.

It is not expected that the relationships among the variables will hold universallytrue for all MSA, submarket and product type permutations, and in the absence ofcommercially available data sources practitioners will need to perform their own curvefitting exercises to obtain valid relationships.


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2. Additional variables. The following independent variables can be additionallysimulated in special circumstances:

. Project size, for cases where the size of the project developed depends on marketor regulatory variables.

. Environmental and municipal fees.

. Construction commencement date, including modeling of potential delaysresulting from subpar vacancy and rent for the particular simulation instance, aswell as for project delays due to construction or regulatory issues.

These can be dependent on the outcome of entitlement processes such as zoningchanges, density limits, height limits, etc. Modeling regulatory outcomes may requireintroducing a binary variable (1 for approval, 0 for disapproval) with a probabilitydistribution based on prior experience for the market in question.

III. Comparison of SERM with common methodologiesSERM vs “pure” DCFWhile DCF, which has in recent years gained wide acceptance among the moresophisticated developers, is a significant improvement on the older underwritingpractices such as developer’s yield and return on cost, it lacks the ability to accuratelyassess the risk/return profile of a project, forcing the practitioner to rely on rules ofthumb for determination of risk premium.

The key difference between “pure” DCF and SERM is that SERM essentially adjuststhe universe of outcomes from reliance of discount rates to serve as proxy for risk byadding stochastic methods.

SERM vs “naked” simulationMonte Carlo simulation is widely acknowledged to overcome the static limitation ofDCF; however, prevailing implementations of simulation practices suffer from anumber of limitations:

. They treat all input variables as mutually independent despite the fact there areclose interrelationships among them, and thereby producing skewed results.

. While they output a range of return outcomes, they offer no guidance as towhether sufficient risk premium is being generated by a project to justify(continued) investment.

SERM vs real optionsReal options have been recently introduced into the real estate developmentunderwriters’ toolkit. While this approach hold considerable promise, it is not yetpractical for use because:

. Problem setup for real options is highly complex and in the absence of standard“cookbooks” can be highly error-prone.

. No public data are available regarding periodic volatility of returns.

. Real options still produce point estimates of returns and offer no information onthe statistical risk metrics of returns.

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LimitationsThe SERM methodology as described here is intended for modeling individualdevelopment projects indented for disposition on completion rather than portfolios ofprojects or investment performance of existing assets. With additional research it maybe feasible to extend the methodology beyond the current application.

Quality of results produced necessarily depends on the quality and completeness ofinput assumptions. For instance, if the probability spread used for vacancy and rent isexceedingly optimistic, the model will fail to account for the probability of extrememovements and will produce skewed results. The financial crisis of 2008 hasdemonstrated that extreme ends of a probability spectrum must be included in anyinvestment model of significant duration lest the impact of extreme outcomes overstatethe return expectation.

IV. Practical implementationModeling environmentSERM relies on modeling using commercially available spreadsheet software with anda commercially available simulation engine. No purpose-designed commercial toolsexist at present to automate the creation of the model suitable for SERM analysis.

Interpretation of simulation results for decision makingA zero-value SERM ERR return for a project indicates that the forecast returns areexactly equal to the risk inherent in the project, and effectively a zero NPV. A greaterthan zero-value ERR indicates a positive NPV for the project, while a negative ERRimplies a negative NPV.

Further research and applicationsThe SERM methodology as described in this paper is limited to individualdevelopment project investment decisions. With additional theoretical work, the SERMconcept may be possible to expend to portfolios of development project investments,individual and portfolio investments in stabilized real assets, and potentially outside ofreal estate in the areas of investment where stochastic methods may improve thequality of discounted cash flow modeling such as private equity-financed mergers andacquisitions. The author welcomes opportunities to collaborate with practitioners inextending the research into such fields.

V. Case study: high-rise office developmentThe following case study for a high-rise office development in the financial district ofSan Francisco, California is based on an amalgam of characteristics of several realprojects and conditions, costs, and prices prevailing during the second quarter of 2010.

Project descriptionA development project sponsor owns a 0.41 acre parcel of land in the financial districtof San Francisco with a fully-leased structure much smaller than permitted by currentzoning regulations. The property is unencumbered by debt and generates $525,000annually in free cash flow. Current zoning allows structures with floor area ratio up to26:1 for a maximum net rentable area of 461,760 square feet. According to brokers’opinion, the parcel’s market value is approximately $31.00 per square foot of FAR, or


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approximately $14,315,000. The sponsor has commissioned a preliminary design studyfor construction of an office building and obtained cost estimates with expectedescalations. The design study suggests a concrete-framed 32-story tower with a grossarea 572,831 square feet with retail space at street level. Construction costs areestimated to be $170.50 per gross foot in 2010 and are expected to escalate at 100 basispoints above prevailing inflation which is currently running at 2 percent annually. Theproject is expected to take approximately 6.5 years to complete, at which point theaverage full-service gross rent for the office portion of this building is expected reach$51.95 which is an annual average escalation of 6 percent from the current potentialaverage rent of $39.00. Annual step rent is expected to be 1.5 percent. Table I detailsthe building and rental structure of the project. Lease terms and market-ratecommissions are outlined in Table II. The sponsor believes that the project can befinanced at the start of the construction phase with an interest-only mini-permanentloan of 65 percent of the terminal project value at a 6.5 percent interest rate. Themini-perm instrument can remain in place through construction and stabilizationphases and be released upon final disposition of the project, which the sponsor intendsto effect upon stabilization. The sponsor expects based on recent averages and trendsthat the project will fetch a disposition value based on price direct capitalization rate of6.0 percent.

DCF analysisA project budget and schedule constructed based above parameters, as presented inTables III and IV and Figure 1. Table V summarizes forecast returns for the project.Because the sponsor uses an internal hurdle rate of 20.00 percent, this project is likelyto be approved.

Static sensitivity analysis of varying key inputs by 10 percent in unfavorabledirections reveals a generally acceptable level of risk, as illustrated in Table VI, withnone of the scenarios indicating a direct financial loss.

Based on the DCF analysis, this project is likely to be approved to proceed.

Simulation parametersKey drivers of financial performance of development projects of this type areunderstood to include the vacancy rate for the product type, construction cost, debtinterest rate, exit capitalization rate, market rent and project duration. Other costdrivers such as entitlement, legal and architecture and engineering are generallypredictable at the outset of projects and as such do not require simulation. Relativesensitivity of results to input variables within their respective ranges was analyzedwith the use of a Tornado chart presented in Figure 2, confirming that rent, schedule,construction loan interest rate and exit capitalization rate offer the largest impact toprofitability necessitating particularly careful attention to modeling their behavior forsimulation[2].

Market rent is generally assumed to be a function of vacancy. Additionally, itassumed that construction cost is also related to vacancy insofar as it is a function ofeconomic growth. These hypotheses were tested using publicly available sourceswherever possible. Where public data were not available, information was gatheredthrough private interviews with market practitioners. Sources not explicitly citedremain anonymous by request. A strong relationship between market vacancy and

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model

125

rents was empirically demonstrated, as was an anecdotal relationship betweenvacancy and construction costs. Costs of funds, loan rates and capitalization rates werefound to be related to spot inflation, but not to historic inflation patterns and notrelated to vacancy. Tenant Improvement costs, which may be reasonably assumed tobe tied to construction costs, were found to have no clear relationship to either becauseonce prevailing rates are established for a given market they tend to follow apredictable appreciation pattern tied to inflation. In practice, these costs bear somerelationship to relative market power of landlords and tenants but fluctuations aroundthe mean appear to be self-canceling.

Identifying statistical patterns in the independent drivers and their relationshipswith the dependent drivers comprised the bulk of the work in compiling this case studyand, while the resulting patterns may possible to generalize across US real estatemarkets, the specific curve shapes and interrelationships will be specific to eachmarket, and quite possibly submarket, so caution should be used in their applications.

Primary driversMarket rent. Figure 3 details the history of market vacancy and average Class A officerent for the financial district of San Francisco from 1980 through 2009[3]. In order totest the hypothesis that rent is a function of vacancy, rent was expressed in terms ofconstant dollars according to three different metrics: the gross domestic product (GDP)deflator, consumer price index, and the producer price index for real estate. Rents werefound to be relatively weakly tied with the CPI, with the correlation coefficient of20.47, while correlations with the GDP deflator and PPI were nearly identical at 20.54and 20.55 respectively. The sparseness of the PPI data set of only 23 samplessuggested the use of the GDP deflator data for developing a regression. Linearregression analysis results in slope m ¼ 2122:09 with intercept y ¼ 55:95. The dataand regression charts are presented in Table VII and Figure 4.

The regression alone is not sufficient to present a complete picture of therelationship of vacancy and rents because sponsors and are reluctant to initiate – andlenders reluctant to fund – new construction projects at times when vacancies areelevated. In order to reflect this condition, commencement of construction is delayed ifthe simulated vacancy is above average according to the assumption that for everypercentage point of difference between simulated vacancy and average vacancyconstruction will be delayed by 1.75 years. This assumption was based on thehistorical pattern of reversion to the mean observed in Figure 3. However, as vividlydemonstrated by the financial crisis of 2008, vacancy rates can also plunge afterconstruction has been substantially complete[4]. This eventuality is modeled with asecond independent variable for vacancy at completion. The complete picture of the

Office Retail

Term, years 5 5Average escalation (%) 2.50 2.50Commission basis 121,528,045 2,198,206Commission rate (%) 7.0 6.0Total commissions 8,506,963 131,892Commissions PSF ($) 18.98 9.81

Table II.Lease structures andcommissions

JPIF29,2

126

Pro

ject

star

t7/

1/20

10A

vg

infl

atio

n2.

0%P

roje

cten

d12

/1/2

016

Con

stru

ctio

nd

elay

(mon

ths)

–S

tart

ing

occu

pan

cyR

even

ues

2010

$/u

nit

Un

its

2010

$to

tal

Esc

alat

ion

Esc

alat

ed$

Sta

rtD

ura

tion

En

d(%

)In

-pla

cen

etre

nt

525,

000

0.0%

525,

000

7/1/

2010

258/

1/20

1210

0O

ccu

pan

cy6/

1/20

1518

12/1

/201

6O

ffice

ren

t39

.00

448,

200

17,4

79,8

006.

0%23

,283

,871

6/1/

2015

1812

/1/2

016

70R

etai

lre

nt

23.9

413

,450

322,

000

6.0%

428,

918

6/1/

2015

17/

1/20

1550

Ad

dit

ion

alre

nt

692,

000

6.0%

921,

775

6/1/

2015

612

/1/2

015

100

Ste

pre

nt

1.5%

627,

928

6/1/

2015

1812

/1/2

016

70L

ess:

offi

ceg

ener

alv

acan

cy5.

00%

(924

,690

)6.

0%(1

,231

,728

)6/

1/20

1518

12/1

/201

610

0L

ess:

pro

per

tyta

x1.

20%

(1,5

48,6

06)

6/1/

2015

1812

/1/2

016

100

Les

s:in

sura

nce

2.00

461,

650

(923

,300

)2.

0%(1

,017

,795

)6/

1/20

1518

12/1

/201

610

0L

ess:

oper

atin

gex

pen

se9.

2546

1,65

0(4

,270

,263

)2.

0%(4

,707

,303

)6/

1/20

1518

12/1

/201

610

0

Net

oper

atin

gin

com

e12

,375

,548

16,7

57,0

60

Tas

k20

10$/

un

itU

nit

s20

10$

tota

lE

scal

atio

nE

scal

ated

$S

tart

Du

rati

onE

nd

Acq

uis

itio

np

has

e7/

1/20

101

8/1/

2010

Lan

d31

.00

461,

760

14,3

14,5

600.

0%14

,314

,560

7/1/

2010

18/

1/20

10T

itle

insu

ran

ce25

0,00

00.

0%25

0,00

07/

1/20

101

8/1/

2010

Leg

alex

pen

ses

350,

000

0.0%

350,

000

7/1/

2010

18/

1/20

10

En

titl

emen

tp

has

e8/

1/20

1036

8/1/

2013

Tra

nsf

erab

led

evel

opm

ent

rig

hts

7,50

0,00

00.

0%7.

500,

000

8/1/

2010

62/

1/20

11A

rch

itec

ture

and

eng

inee

rin

g4,

500,

000

2.0%

4,50

7,57

58/

1/20

1024

8/1/

2012

En

titl

emen

tap

pro

val

250,

000

2.0%

250,

421

8/1/

2010

368/

1/20

13F

ees

and

per

mit

s47

5,00

00.

0%47

5,00

08/

13/2

010

248/

13/2

012

(continued

)

Table III.Budget and cash flow

forecast


model

127

Con

stru

ctio

np

has

e8/

1/20

1234

6/1/

2015

Imp

act

fees

12,5

00,0

002.

0%13

,027

,598

8/1/

2012

19/

1/20

12D

emol

itio

n52

5,00

02.

0%55

8,10

28/

1/20

132

10/1

/201

3C

onst

ruct

ion

155.

0057

2,83

188

,788

,728

3.0%

97,7

55,3

1110

/1/2

013

184/

1/20

15C

omm

issi

onin

g40

0,00

02.

0%43

9,48

14/

1/20

152

6/1/

2015

Pro

per

tyta

xes

1.20

1,29

1,23

92.

0%1,

345,

740

8/1/

2012

346/

1/20

15A

rtw

ork

887,

887

2.0%

946,

999

10/1

/201

318

4/1/

2015

Insu

ran

ce42

5,00

02.

0%44

2,93

88/

1/20

1234

6/1/

2015

Sec

uri

tysy

stem

s20

0,00

02.

0%21

9,74

14/

1/20

152

6/1/

2015

Sta

bil

izat

ion

ph

ase

8/1/

2013

2610

/1/2

015

Ten

ant

spac

ep

lan

nin

g10

0,00

02.

0%10

9,87

04/

1/20

156

10/1

/201

5L

egal

exp

ense

s65

0,00

02.

0%71

4,15

74/

1/20

156

10/1

/201

5M

ark

etin

gan

dP

R1,

500,

000

2.0%

1,59

4,57

88/

1/20

1324

8/1/

2015

Ten

ant

imp

rov

emen

ts–

offi

ce60

.00

373,

500

22,4

10,0

002.

0%24

,621

,932

4/1/

2015

610

/1/2

015

Lea

sin

gco

mm

issi

ons

–of

fice

17.1

037

3,50

06,

386,

396

8,50

6,96

312

/3/2

014

66/

3/20

15T

enan

tim

pro

vem

ents

–re

tail

40.0

010

,950

438,

000

2.0%

481,

232

4/1/

2015

610

/1/2

015

Lea

sin

gco

mm

issi

ons

–re

tail

9.04

10,9

5099

,015

131,

892

12/3

/201

43

3/3/

2015

Mis

cell

aneo

us

leas

ing

350,

000

2.0%

384,

546

4/1/

2015

610

/1/2

015

Ad

min

istr

atio

n7/

1/20

1063

10/1

/201

5G

ener

alan

dad

min

istr

ativ

e3,

500,

000

2.0%

3,50

0,00

07/

1/20

1063

10/1

/201

5D

evel

opm

ent

fee

2.50

3,64

1,90

74,

000,

352

7/1/

2010

6310

/1/2

015

Pro

ject

con

tin

gen

cy3.

004,

595,

288

5,02

5,42

27/

1/20

1063

10/1

/201

5

Inte

rest

-on

lyd

ebt

serv

ice

6.50

22,2

58,7

6722

,258

,767

Tot

alex

pen

ses

198,

586,

786

213,

713,

177

(continued

)

Table III.

JPIF29,2

128

Con

stru

ctio

nfi

nan

cin

gM

ini-

per

mlo

an65

.00

114,

613,

213

124,

445,

367

8/1/

2012

19/

1/20

12L

ess:

len

der

fees

0.50

(573

,066

.06)

(622

,227

)8/

1/20

121

9/1/

2012

Net

bor

row

ing

114,

040,

147

123,

823,

140

8/1/

2012

19/

1/20

12L

oan

run

nin

gb

alan

ceD

isp

osit

ion

12/1

/201

61

1/1/

2017

Rev

ersi

onv

alu

eC

apra

te6.

0027

0,53

4,32

912

/1/2

016

11/

1/20

17L

ess;

dis

pos

itio

nex

pen

ses

0.35

(946

,870

)12

/1/2

016

11/

1/20

17N

etre

ver

sion

269,

587,

459

12/1

/201

61

1/1/

2017

Deb

tre

tire

men

t(1

24,4

45,3

67)

12/1

/201

61

1/1/

2017

Yie

ldIR

RR

OE

Pro

fit

Cas

hfl

owb

efor

ele

ver

age

8.48

16.5

5%70

.62%

120,

792,

536

Cas

hfl

owb

efor

ein

com

eta

xes

7.60

22.5

1%12

3.06

%97

,911

,543

Table III.


model

129

Per

iod

01

23

45

67

Yea

ren

din

g7/

31/2

011

7/31

/201

27/

31/2

013

7/31

/201

47/

31/2

015

7/31

/201

67/

31/2

017

Con

stru

ctio

nd

elay

(mon

ths)

Rev

enu

esIn

-pla

cen

etre

nt

525,

000

525,

000

1,45

8–

––

–O

ccu

pan

cyO

ffice

ren

t–

––

–17

,074

,839

21,8

09,2

26R

etai

lre

nt

––

––

428,

918

428,

918

Ad

dit

ion

alre

nt

––

––

921,

775

921,

775

Ste

pre

nt

––

––

–27

6,38

3L

ess:

offi

ceg

ener

alv

acan

cy–

––

–(1

,231

,728

)(1

,231

,728

)(1

,231

,728

)L

ess:

pro

per

tyta

x–

––

–(1

,548

,606

)(1

,548

,606

)(1

,548

,606

)L

ess:

insu

ran

ce–

––

–(1

,017

,795

)(1

,017

,795

)(1

,017

,795

)L

ess:

oper

atin

gex

pen

se–

––

–(4

,707

,303

)(4

,707

,303

)(4

,707

,303

)

Net

oper

atin

gin

com

e52

5,00

052

5,00

01,

458

–9,

920,

100

14,9

30,8

7016

,757

,060

Tas

k

Acq

uis

itio

np

has

eL

and

14,3

14,5

60–

––

––

–T

itle

insu

ran

ce25

0,00

0–

––

––

–L

egal

exp

ense

s35

0,00

0–

––

––

–E

nti

tlem

ent

ph

ase

––

––

––

–T

ran

sfer

able

dev

elop

men

tri

gh

ts7,

500,

000

––

––

––

Arc

hit

ectu

rean

den

gin

eeri

ng

2,26

3,11

32,

238,

244

6,21

7–

––

–E

nti

tlem

ent

app

rov

al84

,012

83,0

8983

,089

231

––

–F

ees

and

per

mit

s23

0,62

123

5,86

28,

517

––

––

Con

stru

ctio

np

has

e–

––

––

––

Imp

act

fees

––

13,0

27,5

98–

––

–D

emol

itio

n–

––

558,

102

––

–C

onst

ruct

ion

––

–54

,149

,651

43,6

05,6

60–

–C

omm

issi

onin

g–

––

–43

9,48

1–

–P

rop

erty

tax

es–

–49

0,83

148

5,43

736

9,47

2–

–A

rtw

ork

––

–52

4,57

242

2,42

7–

–In

sura

nce

––

161,

553

159,

777

121,

608

––

(continued

)

Table IV.Budget and cash flowforecast

JPIF29,2

130

Per

iod

01

23

45

67

Yea

ren

din

g7/

31/2

011

7/31

/201

27/

31/2

013

7/31

/201

47/

31/2

015

7/31

/201

67/

31/2

017

Sec

uri

tysy

stem

s–

––

–21

9,74

1–

–S

tab

iliz

atio

np

has

e–

––

––

––

Ten

ant

spac

ep

lan

nin

g–

––

–72

,646

37,2

74–

Leg

alex

pen

ses

––

––

472,

202

241,

955

–M

ark

etin

gan

dP

R–

––

800,

588

791,

790

2,19

9–

Ten

nan

tim

pro

vem

ents

–of

fice

––

––

16,2

80,0

758,

341,

857

–L

easi

ng

com

mis

sion

s–

offi

ce–

––

–8,

506,

963

––

Ten

ant

imp

rov

emen

ts–

reta

il–

––

–31

8,19

216

3,04

0–

Lea

sin

gco

mm

issi

ons

–re

tail

––

––

131,

892

––

Mis

cell

aneo

us

leas

ing

––

––

254,

263

130,

283

–A

dm

inis

trat

ion

––

––

––

–G

ener

alan

dad

min

istr

ativ

e67

6,69

267

6,69

267

6,69

267

6,69

267

6,69

211

6,54

1–

Dev

elop

men

tfe

e81

,361

80,8

4736

1,36

21,

433,

876

1,81

7,07

822

5.82

7–

Pro

ject

con

tin

gen

cy97

1,61

897

1,61

897

1,61

897

1,61

897

1,61

816

7,33

4–

Inte

rest

-on

lyd

ebt

serv

ice

––

1,97

7,12

34,

502,

006

7,69

0,68

98,

088,

949

–T

otal

exp

ense

s14

,914

,560

11,8

07,4

174,

286,

352

17,7

64,6

0064

,262

,550

83,1

62,4

8917

,515

,210

–C

onst

ruct

ion

fin

anci

ng

Min

i-p

erm

loan

Les

s:le

nd

erfe

es–

–(6

22,2

27)

––

––

Net

bor

row

ing

––

30,4

17.2

7338

,844

,354

49,0

56,6

706,

127,

070

–L

oan

run

nin

gb

alan

ce–

–30

,417

,273

69,2

61,6

2711

8,31

8,29

712

4,44

5,36

7–

Dis

pos

itio

nR

ever

sion

val

ue

Les

s;d

isp

osit

ion

exp

ense

sN

etre

ver

sion

––

––

––

269,

587,

459

Deb

tre

tire

men

t–

––

––

–(1

24,4

45,3

67)

Cas

hfl

owb

efor

ele

ver

age

(14,

914,

560)

(11,

282,

417)

(3,7

61,3

52)

(15,

786,

018)

(59,

760,

544)

(65,

551,

700)

5,50

4,60

928

6,34

4,51

8C

ash

flow

bef

ore

inco

me

tax

es(1

4,91

4,56

0)(1

1,28

2,41

7)(3

,761

,352

)12

,031

,905

(25,

418.

196)

(24,

185,

719)

3,54

2,73

016

1,89

9,15

2

Table IV.


model

131

Yield IRR ROE(%) (%) (%) Profit

Cash flow before leverage 8.48 16.55 70.62 120,792,536Cash flow before income taxes 7.60 22.51 123.06 97,911,543

Table V.Summary of expectedreturns

Figure 1.Project schedule

Yield IRR ROE(%) (%) (%) Profit

Rent StatConstruction cost Stat 8.48 16.55 70.62 120,792,536 Before leverageCap rate Stat 7.60 22.51 123.06 97,911,543 Before income taxesRent 210%Construction cost Stat 7.26 11.23 43.90 75,449,929 Before leverageCap rate Stat 6.50 14.39 65.07 52,650,356 Before income taxesRent StatConstruction cost þ10% 7.98 14.62 59.39 107,913,698 Before leverageCap rate Stat 7.15 19.82 99.70 83,849,959 Before income taxesRent StatConstruction cost Stat 8.48 13.81 56.29 96,284,586 Before leverageCap rate þ10% 7.60 18.52 92.26 73,403,592 Before income taxesRent 210%Construction cost 210% 7.75 13.30 54.79 88,328,767 Before leverageCap rate þ10% 6.94 17.60 87.34 66,711,941 Before income taxes

Table VI.Sensitivity analysis

JPIF29,2

132

effect of its elevated condition includes more than impact to rent because both thestarting occupancy at project completion and the duration of the stabilization phase arealso negatively affected. The extension of the stabilization phase may be assumed tofollow the same pattern as the postponement of constriction. Modeling startingoccupancy proved more challenging because hard data were scarce and the slopeprecipitous. A reasonable approximation of reality was achieved with a formulationwhere starting occupancy:

So ¼ MIN Max So; 1 2 MIN LN 100 MIN Vacancy; Avg:Vacancy� ��

11=100; 000; 100%� ��

ðC1Þ

where Max So is a constant limiting the largest starting occupancy to that deemedpossible by the sponsor. In this model, Max So ¼ 80 percent.

Figure 3.San Francisco CBD class

office rent and vacancy1980-2011

Figure 2.Tornado analysis


model

133

Vac

ancy

rate

Yea

r(%

)

Av

erag

ere

nt,

nom

inal

GD

Pd

eflat

ora

GD

Pd

eflat

or,

2009

dol

lars

Av

erag

ere

nt,

2009

dol

lars

CP

IbC

PI

defl

ator

in19

80d

olla

rsC

PI

defl

ator

in20

09d

olla

rsR

ent

in20

09C

PI

dol

lars

PP

Ic

PP

Iin

2009

dol

lars

Ren

tin

2009

PP

Id

olla

rs

1980

1.00

2354

.043

181.

792

41.8

113

.510

012

6.1

2919

814.

0031

59.1

1917

3.20

653

.69

10.3

101.

103

125.

009

38.7

519

825.

7035

62.7

2616

7.45

558

.61

6.2

102.

165

123.

969

43.3

919

835.

9037

65.2

0716

3.65

60.5

53.

210

3.19

712

2.96

945

.519

8410

.10

3267

.655

160.

032

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39.0

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157.

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923

44.9

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6.29

512

0.02

634

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1987

13.9

030

73.1

9615

2.26

445

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2578

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145.

3236

.33

4.8

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4211

7.14

229

.29

110.

814

7.68

536

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1990

10.2

026

.89

81.5

914

1.60

238

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5.4

110.

474

116.

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31.2

411

3.1

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84.4

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8.22

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86.3

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31.2

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26.6

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1.4

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1995

6.20

25.0

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129.

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32.5

2.8

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1.64

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126.

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4.92

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5.40

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7.42

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5.88

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3.18

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1.96

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6.35

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517

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1.77

945

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418

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95.5

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Table VII.Rent vs vacancy inconstant dollars

JPIF29,2

134

Interviews with experienced leasing agents established that asking and contact rentsfor new construction projects tend to be 5-15 percent greater than average. This caseassumes a constant 10 percent premium for new construction beyond the average.Because of low materiality, retail and additional rents were assumed to maintain aconstant ratio to with office rents and an unchanging starting occupancy andstabilization period.

Market vacancy. Statistical analysis of the population of vacancy values returnsresults and histogram are presented in Figure 5.

The observed population for this variable lends itself well for modeling with asimulated Beta distribution and reasonably well for a triangular set to producemeaningful results.

Average inflation. As further described above, rent and construction costparameters were modeled in constant dollars, making it necessary to predict theinflation from initiation to the commencement of construction at which point costs maybe locked in. Other costs and revenues are also affected by inflation. Because near-termexpenses and revenues are affected in a relatively minor way and interim values ofinflation are not material for this analysis we can model a single average inflation over

Figure 4.Rent vs vacancy

regression

Figure 5.Market vacancy


model

135

the life of the project. As a reasonable proxy to the interim period of the project weselected a five-year moving average inflation expressed as a rate of change of the GDPdeflator. Figure 6 demonstrates the data, statistical analysis and histogram for thefive-year moving average inflation. Since no mode value was found, the mean of 2.63percent was selected as the peak value for simulation using triangular distribution.

Construction cost. Unfortunately, no publicly available historical statistics forfluctuation in local construction costs were identified. Furthermore, nationalconstruction costs as measured by PPI Construction correlated very poorly withlocal metrics available, with the highest correlation coefficient obtained not exceeding0.104. In the absence of statistical data, interviews were conducted with generalcontractors with a significant history of operating in the area. The interviews yieldedinformation that construction costs depend broadly on cost of labor and materials, thelatter being impacted by global construction demand. This is particularly true in thecase of the cost of steel. Labor cost can be expected to be correlated with local buildingdemand, which in turn is driven by market vacancy. Because this particular project isexpected to be built on a concrete frame, the price of steel becomes less relevant andlocal variables assume primacy in determining a relationship with outside factors.Interviews with contractors yielded no information regarding absolute cost levels ofconstruction but did suggest that relative change in costs is correlated with marketvacancy in a relationship that can be represented a linear relationship with the slopem ¼ 20:57971 and intercept y ¼ 0:088 as presented in Figure 7.

Loan interest. Public information about construction loan terms has been as difficultto find as it was for construction costs. Lending agents interviewed indicated that

Figure 6.Inflation

JPIF29,2

136

construction loans are generally priced 300-400 basis points above prime. An averagespread of 350 bps was selected as a benchmark for the model. Prime rates from 1947 to2009 and statistical analysis of resulting interest rates are presented in Figure 8.

Capitalization rate. Direct capitalization rates for San Francisco office propertieshave only been recorded in a publicly available way since 1999, offering a limiteddataset for ascertaining long-term patterns. However, the San Francisco cap ratesappear to closely track the national office cap rate trends as derived inChandrashekaran, 2000 for the period of 1985 to 1999, making it possible to extendthe series by 15 data points for a more statistically significant picture. The resultingrange of average cap rates is presented in Figure 9. One issue with the available sampleis the fact that the largest and the smallest values in the dataset, 3.93 percent and 10.20percent, represent single deals made during the top and bottom of the marketrespectively. These two points were therefore treated as outliers and eliminated themfrom the analysis.

Plotting cap rates against their spot market interest rate and spot GDP inflation rateresulted in poor correlation with the prime rate and, interestingly, a negativecorrelation with the spot inflation that becomes progressively smaller with the use of alonger moving average of rates. Since modeling spot inflation rates is outside the scopeof the model here, cap rates can be treated as an independently simulated variablefollowing a triangular distribution[5]. Figure 9 summarizes the statistics of the cap ratespread used.

Interviews with real estate agents in experienced in the San Francisco marketyielded information that new construction project when sold command pricesrepresented by cap rates in the lower ranges of the spread around the average value.The price premium was described as ranging between 100 and 150 basis points belowthe average value. A median value of 125 basis points below average was selected for

Figure 7.Construction cost


model

137

Figure 8.Loan interest

JPIF29,2

138

Figure 9.Cap rates

Term RateTreasury rate (years) (%)

Short term 5 2.08Intermediate term 10 3.25Long term 20 3.97

Table VIII.Treasury rates

Value Min Mode MaxIndependent drivers (%) Distribution (%) (%) (%)

Market vacancy 10.78 Triangular 1.00 9.90 22.10Average inflation 3.06 Triangular 1.60 2.63 5.25Prime rate 8.58 Triangular 1.75 4.50 21.50Exit cap rate 6.30 Triangular 4.40 6.20 8.40

Table IX.Independent simulation

drivers


model

139

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Table X.Simulation results

JPIF29,2

140

use in the model. We have further elected to set a lower bound of 4.40 percent as thelowest observed cap rate excepting a single outlier.

Risk-free rate. Because the duration of the project is not fixed, and in fact was foundin simulation to vary between six and 19 years, the normal practice of selecting a singleTreasury rate as a proxy for the risk-free rate is inappropriate. The effective risk-freerate for the project is extrapolated from the available five-, ten- and 20-year Treasuryrates and is calculated based on the duration of the project in each iteration of thesimulation. The spot Treasury rates used in this case are presented in Table VIII.

Simulation analysisThe independent drivers thus selected for the simulation are market vacancy, averageinflation, prime rate and capitalization rate. Distributions, distribution modelingparameters and median simulated results are summarized in Table IX.

The simulation was run with 10,000 iterations, with the statistical results presentedin Table X[6]. As we can see, the median hurdle NPV result is negative, implying thatthe project as planned is unlikely to meet its profitability objectives. In fact, theprobability of doing so is only 33.39 percent. The probable shortfall in covering theweighted average cost of capital is 48.78 percent, but since the median return for thismetric is positive, the implication is that the project will at least not generate a cashloss for the sponsor. These may or may not be poor odds for the risk tolerance of aparticular sponsor, but they do not offer any information as to whether the size of theexpected profit justifies this level of risk. For the risk-adjusted return metric, we mustturn to SERM analysis.

SERM analysis and recommendationApplying SERM analysis to the results of the simulation, as presented in Table XI, weobtain the excess return metric ERR of -2.85 percent, which is a clear indication that therange of returns for this project does not justify the risk. In fact, once we solve for therequired rate of return MAR, we obtain a discount rate of 79.44 percent, indicating thatthe project’s viability is some distance from break-even.

Clearly, the returns from this project as presented do not justify the risks taken,barring significant mitigation of the primary risk factors such as the exit cap rate andrent and occupancy levels.

VI. ConclusionsThe SERM corrects serious shortcomings in the DCF methodology for evaluating riskin real estate development projects by incorporating stochastic tools for the

%

Downside risk (DR) 2,211.66Return per unit of risk 0.012080Risk-adjusted return 0.000032

Excess return above R-F rate (SERM ERR) 22.85365SERM required rate of return (SERM MAR) 79.44

Table XI.SERM analysis summary


model

141

measurement of the universe of outcomes. It further serves to condense the output ofMonte Carlo simulations into a simple metric that can generally understood andapplied by practitioners for making decisions concerning funding projects.Additionally, key profitability drivers are identified to be market vacancy,capitalization rate and construction debt interest, with rent, construction cost andproject schedule being functions of market vacancy.

Notes

1. Modeling variable durations of the phases of a project using spreadsheet software can bechallenging. An acceptable approximation is the use of the Microsoft Excel XNPV functionthat computes NPVs for cash flows that do not follow a regular periodic pattern. However,such a model at best an approximation because it only captures the changes due to the timevalue of money and does nothing to account for additional debt service expenses that occurbecause of extended construction and stabilization periods. An alternative method, detailedin the case study to be published, utilizes a complex algorithm for adjusting calendar cashflows based on variable project duration.

2. Tornado analysis was performed with the use of the Dartmouth Sensitivity Toolkit,available at http://mba.tuck.dartmouth.edu/toolkit/index.html

3. Figure 3 data and chart courtesy of the San Francisco office of Cornish & Carey Commercial.

4. This is not the only extraordinary risk that may impact outcomes. For instance, the currenttenant may terminate early, or adverse market conditions may manifest themselves duringearly stages of construction. Such eventualities would be analogous to the delay ofconstruction commencement but without the attendant extension of cash flow. Themateriality of the interim cash flows would dictate whether such a case would requireinclusion in simulation. Additionally, the entitlement period here assumed to be fixed may infact vary, requiring an additional delay factor.

5. See above for information on the use of triangular vs beta distribution.

6. Simulation for the case study was performed with the use of ExcelSim2003 (Mayes, 2003), aMicrosoft Excel add-in simulation engine intended for academic use. The specificcharacteristic of this engine necessitated the use of triangular distributions in simulation ofhighly skewed sample populations. Analysis of the data suggests that in practicalapplication a more accurate picture may be obtained with the use of Beta distributions inpreference; nevertheless, triangular distributions offered sufficient accuracy for the purposesof this paper.

References

Atherton, E., French, N. and Gabrielli, L. (n.d.), “Decision theory and real estate development:a note on uncertainty”, working paper, unpublished.

Baroni, M., Barthelemy, F. and Mokrane, M. (2006), “Monte Carlo simulations versus DCF in realestate portfolio valuation”, ESSEC Working Papers DR 06002, ESSEC Research Center,ESSEC Business School, Cergy-Pontoise.

Chandrashekaran, V. (2000), “The predictability of real estate capitalization rates”, available at:http://homepage.mac.com/mikero1/MSY/articlesPDF/CapRates.pdf

Mayes, T.R. (2003), ExcelSim 2003 Simulation Engine, Department of Finance, MetropolitanState College of Denver, Denver, CO, available at: http://clem.mscd.edu/,mayest/../ExcelSim%202003%20Documentation.pdf/

JPIF29,2

142

Satchell, S.E. and Pedersen, C.S. (2002), “On the foundation of performance measures underasymmetric returns”, available at: www.sortino.com/htm/satchell.pdf

Young, M.S. (2007), “Real-time valuation: breathing new life into moribund DCF modeling”,Journal of Real Estate Practice and Education, Vol. 10 No. 1, pp. 25-40.

Further reading

Akalu, M.M. and Turner, R. (2002), “A Monte Carlo comparison between the free cash flow anddiscounted cash flow approaches”, Tinbergen Institute Discussion Paper, TI 2002-083/1,Tinbergen Institute, Rotterdam.

Barman, B. and Nash, K.E. (2007), “A streamlined real options model for real estatedevelopment”, MSRED thesis, Massachusetts Institute of Technology, Cambridge, MA.

Breidenbach, M., Mueller, G.R. and Schulte, K.-W. (2006), “Determining real estate betas formarkets and property types to set better investment hurdle rates”, Journal of Real EstatePortfolio Management, Vol. 12 No. 1, pp. 73-80.

Brotman, B.A. (2010), “The impact of market conditions using appraisal models”, Journal ofProperty Investment & Finance, Vol. 28 No. 3, pp. 237-42.

Brown, R.J. (2006), “Sins of the IRR”, Journal of Real Estate Portfolio Management, Vol. 12 No. 1,pp. 195-200.

Chaplin, R. (2000), “Predicting real estate rents: walking backwards into the future”, Journal ofProperty Investment & Finance, Vol. 18 No. 3, pp. 352-70.

Comeau, J. (2009), “Incorporating uncertainty into discounted cash flow equity”, available at:www.cob.calpoly.edu/media/files/econ/Top-Senior-Project-F2009.pdf

Damodaran, A. (2008), “The promise and peril of real options”, working paper, Stern School ofBusiness, Greenwich Village, NY.

de Neufville, R., Scholtes, S. and Wang, T. (2006), “Valuing options by spreadsheet: parkinggarage case example”, ASCE Journal of Infrastructure Systems, Vol. 12 No. 2, pp. 107-11.

Fekete, I. and Katona, T. (2003), “Modelling the fulfilment of the real estate utilisation plan for2002 by Monte-Carlo simulation”, working paper, Matav Rt (Hungarian Telecom),Budapest.

French, N. (2006), “Value and worth: probability analysis”, Journal of Property Investment& Finance, Vol. 24 No. 4, pp. 374-80.

French, N. and Gabrielli, L. (2005), “Discounted cash flow: accounting for uncertainty”, Journal ofProperty Investment & Finance, Vol. 23 No. 1, pp. 75-89.

Geltner, D.M., Miller, N.G., Clayton, J. and Eichholtz, P. (2007), Commercial Real Estate Analysis& Investments, 2nd ed., Thompson South-Western, Mason, OH.

Greig, W.D. and Young, M.S. (1991), “New measures of future property performance and risk”,Real Estate Review, Vol. 21 No. 1, Spring.

Hengels, A. (2005), “Creating a large practical model using real options to evaluate large-scalereal estate development projects”, MSRED thesis, MIT Center for Real Estate, Cambridge,MA.

Hoesli, M., Jani, E. and Bender, A. (2006), “Monte Carlo simulations for real estate valuation”,Journal of Property Investment & Finance, Vol. 24 No. 2, pp. 102-22.

Holtan, M. (2002), “Using simulation to calculate the NPV of a project”, 2002, available at: www.investmentscience.com/Content/howtoArticles/simulation.pdf

Hudson-Wilson, S. (Ed.) (2000), Modern Real Estate Portfolio Management, Frank J. FabozziAssociates, New Hope, PA.


model

143

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Corresponding authorDavid Gimpelevich can be contacted at: [email protected]

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