Real Options Analysis in Valuation

of Commercial Project: A Case Study

Ketty Vijay Parthasarathy* and R Madhumathi**

Case study analysis is used to examine the application of real options in

valuing a commercial real estate mall project. Comparison of valuations
using traditional discounted cash flow model with Black-Scholes, Binomial
and Samuelson-McKean option models brings out the relevance of real
option analysis in project decisions. Real options analysis is pertinent when
market prices increase the strategic value of real estate development
projects by incorporating fluctuations in volatility and providing project
flexibility in its operations. The developers with varied project alternatives
are able to execute the most desirable alternative using real options
analysis. In real estate, land held by the developer tends to have a
perpetuity value and it is at the discretion of the developer to execute
possible options based on prevalent market conditions. Samuelson-McKean
model that values the project as a perpetual American call option has
computed the premium value of the commercial project as Rs. 154.08 mn,
thus giving a strategic return of 85% to the developers.

Introduction
Construction is considered to be an essential component of a country’s development with
its linkages to various other industries like cement, steel, bricks, etc. It is considered to be
the second largest economic activity next to agriculture and has generated employment to
about 33 million people in India in 2008. Growth of construction has followed the trend
of economic growth rate of the country and construction as a percentage of GDP has increased
from 8.0% in fiscal year 2006 to 8.5% in fiscal year 2008. Construction industry in India
is highly fragmented and the number of unorganized players in the industry that work on
subcontracting basis is large. Construction projects can be materialized through the number
of smaller contracts which mainly depend upon size of the project and diversified nature
of activities to be carried out in the project and as a result, subcontracting is a common
phenomenon in the construction industry (Indian Brand Equity Foundation (IBEF), 2009a).
* Research Scholar, Department of Management Studies, Indian Institute of Technology Madras, Chennai
600036, India. E-mail: vijay.2307@yahoo.com
** Associate Professor, Department of Management Studies, Indian Institute of Technology Madras, Chennai
600036, India. E-mail: rmm@iitm.ac.in

Real Options
© 2010 Analysis
IUP. All RightsinReserved.
Valuation of Commercial Project: A Case Study 7
 It is classified into three sub segments namely infrastructure, industry and real estate.
Infrastructure segment involves construction projects in different sectors like road, rail, port,
irrigation and power. Industrial construction segment caters to expansion projects from
various manufacturing sectors. Real estate construction segment involves development of
vacant land and can be subdivided into residential and commercial projects such as malls
and multiplexes.
Real estate has shown upheavals in its growth in the Indian economy but has appealed
as an investment opportunity for domestic as well as foreign investors. Liberalized Foreign
Direct Investments (FDI) of 100% in the construction business cleared the path towards
foreign investment for development of commercial and residential real estate sectors and
has encouraged several large financial and private equity players to launch exclusive funds
targeting the Indian real estate sector (Ministry of Commerce and Industry, Government of
India, 2005). Almost 80% of real estate developed in India is residential space, the rest
comprising of commercial construction for offices, shopping malls, hotels and hospitals.
The real estate sector has grown at 35% in 2008 and is estimated to be worth
Rs. 675 bn and is expected to grow at 30% annually till 2018 attracting foreign investments
worth Rs. 1.35 tn. This growth has been mainly attributed to the off-shoring business,
including high-end technology consulting, call centers and software businesses. The
Information Technology (IT) and Information Technology Engineering Services (ITES) sectors
are estimated to require 150 million sq ft of office space across urban India by 2010 (Indian
Brand Equity Foundation (IBEF), 2009b).
The profitability of real estate projects varies across different segments with complex
technology savvy projects fetching higher profit margins for developers as compared to that
of low technology projects like residential blocks for middle income group. Real estate
development projects are subject to volatility of land prices and interest rate fluctuations
has affected the developers’ profitability. The traditional models have not been able to
incorporate these crucial factors into the project evaluation decisions. Real options analysis
provides developers the value of flexibility that is absent in traditional discounted models.
This flexibility could increase the strategic value of the projects hence providing developers
with varied choice like the option to exercise, delay, abandon etc.
Project developers need to evaluate the value of construction with respect to changes
in underlying land value. This involves a comparison of construction cost not with historical
land acquisition cost but with volatile market value of land. Another useful decision that
the developer needs to arrive at the time of initiation of project is the percentage of
development needed to initiate a project. This helps the developer to minimize the cost
in relation to the saleable value of the project. A developer also needs to know if the present
market scenario is suitable for the development immediately or delay the development
program. Since land development projects do not have any time limit for implementation,
any project evaluation tool ought to incorporate the ability of the developers to delay the
project till a favorable market price occurs. The evaluation of cash flows as well as a

8 The IUP Journal of Infrastructure, Vol. VIII, Nos. 1 & 2, 2010

quantitative and qualitative assessment of costs and benefits from the real estate project
helps the developers to view project proposals from a broader perspective. Further, the
determination of specific real estate project risk and computation of opportunity cost of
capital would help developers to set their return targets and evaluate their decisions to wait
or immediately implement the project.

Literature Review
Sirmans (1997) suggested that the traditional Discounted Cash Flow (DCF) model may be
insufficient for evaluating real estate projects supporting previous critiques of DCF analysis
(Hayes and Abernathy, 1980; and Hodder and Riggs, 1985) that questioned the selection of
discount rates and the inability of DCF analysis to include options in the valuation of a project.
Leslie and Michaels (1997) discuss cases for applying options to any strategic situation and
its benefits. Chan and Hemantha (2000) discuss application of real option analysis to
engineering economics indicating its advantages on a broader perspective. The importance
of flexibility for corporate real estate portfolios has been highlighted by Gibson (2001). The
drawback of DCF to capture future value of flexibility under uncertainty has been overcome
by real option analysis having managerial implication (Mun, 2002; and Brach, 2003). Greden
and Glicksman (2005) developed real options methodology that could be used by real estate
professional’s decisions on flexibility in conversion to office and non-office space.
Real option analysis in real estate development as a call option has varied applications
like development options (Shilling et al., 1985), option to wait to develop, i.e., delay option
(Titman, 1985), option to convert agricultural to urban land i.e., conversion option (Capozza
and Sick, 1989), option to convert land for urban usage (Capozza and Schwann, 1990), owners
of undeveloped real estate having implied options to delay or abandon a development
(Williams, 1991) and examining 1214 condominium developments in Vancouver, Canada
between 1979 to 1998 providing unambiguous support for the existence of a call option
in the ability to delay irreversible investment (Bulan et al., 2002).
Quigg (1993), Patel et al. (2001) and Yamazaki (2001) worked towards empirical testing
of option premium in real estate favoring the application of real option theory in land prices.
Quigg (1995) presented a method of valuing the option to wait to develop land as perpetual
American options exceeding the value of expected rents for a building at the decision date.
Yao and Pretorius (2004) considered Samuelson-Mckean (1965) Methodology that can be
applied to perpetual American call option to determine the theoretical critical value of the
underlying asset at which it is optimal to build and also the critical benefit-cost ratio
indicating as to how much the built property value must be greater than its construction
cost to trigger immediate optimal development. Oppenheimer (2002) discuss about the
review of conditions and methods that have been proposed for applying real option models
in real estate valuations. Rocha et al. (2007) examined the application of real options analysis
through a case study for housing investment in Rio de Janerio indicating proposed values
for managerial flexibilities and improved risk management by identifying the optimal strategy
(simultaneous vs. sequential) and timing for construction phases.

Real Options Analysis in Valuation of Commercial Project: A Case Study 9

Methodology
A commercial project to construct a mall which was slated to start in 2010 and to be made
operational by 2012 has been selected for application of real options analysis. Data for
the case study was collected from a reputed real estate firm Jones Lang LaSalle Meghraj
(JLLM) operating in Chennai (India). Besides the well known Black-Scholes and binomial
option models, the research methodology used Samuelson-McKean (1965) option model
that can be applied to perpetual American call option to evaluate the project.
The Black-Scholes (1973) formula for the option prices of a European call option on
a non-dividend-paying stock is stated as:

c  S0 N(d1 )  Ke rT N(d2 ) ...(1)

where,

d1  [ln( S0 / K )  (r   2 / 2)T ] /  T
d2  [ln( S0 / K )  (r   2 / 2)T ] /  T  d1   T

The binomial option price developed by Cox et al. (1979) is given by:

C  e rT  pCu  (1  p)Cd  ...(2)

where p   e  d  /  u  d 
rT

The value for call option (land) value using Samuelson-McKean (1965) methodology
is:

C  ( S * K )( S / S*) ...(3)

S*  K /(  1)

  (  r   2 / 2  ((r     2 / 2)2  2r 2 )1/ 2 ) /  2

where S is the current value of underlying land value (built property); K is the strike price
(construction cost excluding land cost); S* is the critical (hurdle) value of underlying land
at and above which it is optimal to immediately exercise the option (develop the land);
 is the elasticity of option.
The case analysis has been carried out in the year 2008 assuming the developers had
to make decisions regarding project investment by 2009.  is the payout ratio or dividend
yield i.e., rental value of the built property. The rental value for the project is 12% for
Chennai; rf is the risk-free rate which is 4.55% as one year RBI’s T-bill for March 2009,
 is the volatility or standard deviation of (unlevered) return individual built properties,
not just systematic or non-diversifiable risk includes idiosyncratic risk. The value of volatility

10 The IUP Journal of Infrastructure, Vol. VIII, Nos. 1 & 2, 2010

for real estate is 15% per year as collected through a telephonic survey of real estate
developers in Chennai.
The option risk as a multiple of underlying asset (land) risk is directly proportional to
option elasticity. This holds both for volatility (total risk) and beta or covariance (systematic
risk). The average risk premium of commercial industry in India is 4.46% for the year
2008. The risk premium of the land (RP) and opportunity cost of the capital (expected
total return) for land [E(r)] is:

Risk Premium (Land ) [RP ]   * Risk Premium (Property ) ...(4)

[E(r )]  rf  RP ...(5)

The traditional Net Present Value (NPV) and Internal Rate Of Return (IRR) analysis that
are most frequently used as a basic tool for evaluating real estate projects have built in
limitations such as non inclusion of volatility estimates and inability for inclusion of options
for flexibility in project implementation. Further, the NPV calculated is not a strategic return
that considers the volatility in prices of the land. The strategic or expanded NPV as defined
by Trigeorgis (2000) is given as:

Expanded ( Strategic ) NPV  Passive NPV  Option Premium ...(6)

Case Description for Commercial Project

The commercial mall project’s area schedule, construction schedule and cash flow
expectations are given below.

Area Schedule
The net area of the plot is given to be 43,560 sq ft and the ground coverage is assumed
to be 50% of the net area turning out to be 21,780 sq ft. The total permissible and
built up area is given to be 108,900 sq ft with phase I (2008) area to be 54,450 sq ft
and phase II (2009) area to be 54,450 sq ft. The base rent per sq ft turns out to be
Rs. 35.

Construction Schedule
The real estate firm has scheduled to start the construction of mall in 2010 and is to be
made operational by 2012. The construction is evenly distributed across both the phases
namely phase I (2010) and phase II (2011). It is assumed that the escalation in construction
costs turns out to be 5% of Rs. 2,200 per sq ft in phase I (2010) to Rs. 2,310 per sq ft
in phase II (2011). The total construction costs is estimated at Rs. 245.5 mn with break up
being Rs. 119.7 mn in phase I (2010) and Rs. 125.7 mn in phase II (2011).

Benefits from Project Implementation

The revenues for the project flow from rental, security deposit and other means such as car
parking rent and event management revenues.

Real Options Analysis in Valuation of Commercial Project: A Case Study 11

 Total number of car parks as per the construction design is 218. It is assumed that at
least 50% of car parks (109) would be used by visitors. The car park rent is estimated at
Rs. 10 per hour and it is assumed that cars are parked for at least 10 hours a day and 25
days a month. Hence the total revenue generated per month is estimated to be Rs. 272,250
and total annual collections are Rs. 3.2 mn.
The project intends to conduct a minimum of five events a month with an assumption
that an event lasts for two days. Every event is estimated to cost about Rs. 15,000. The revenue
generated through event management is estimated at Rs. 150,000 per month and
Rs. 1.8 mn per year.
Together benefits from other means are expected to result in a total revenue generation
of Rs. 5 mn.

Cash Flow Analysis

Cash flow analysis evaluates the costs and benefits quantitatively for the project.

Cash Inflows
The major inflows for the commercial mall project are the rental inflows, security deposit
inflows and the revenue generated by other means. The project is expected to have inflows
from 2011 up to 2019. The assumption taken into consideration in computation of cash
flows is that the rent, security deposit and other revenues increase by 15% every three years.
The rental inflows for leasable area of 108,900 sq ft are Rs. 45.7 mn (2011-2013),
Rs. 52.5 mn (2014-2016) and Rs. 60.4 mn (2017-2019). The security deposit inflows are
computed as Rs. 22.8 mn (2011), Rs. 3.4 mn (2014) and Rs. 3.9 mn (2017). The revenue
generated by other means are Rs. 5.06 mn (2011-2013), Rs. 5.8 mn (2014-2016) and
Rs. 6.7 mn (2017-2019).

Cash Outflows
The major cash outflows for the project are construction costs followed by marketing
and legal costs and property tax. It is assumed that the marketing and legal costs as
a percentage of construction costs are 3.5% whereas the property tax is approximately
6% of rental inflows.
The construction cost is estimated to be Rs. 245 mn with break up being Rs. 119 mn
in phase I (2010) and Rs. 125 mn in phase II (2011). The marketing and legal costs end
up being Rs. 4.1 mn for phase I (2009) and Rs. 4.4 mn for phase II (2010). The property
tax is assumed to be Rs. 2.7 mn (2011-2013), Rs. 3.1 mn (2014-2016) and Rs. 3.6 mn
(2017-2019).

Case Analysis for Commercial Project

The developers used NPV and IRR discounted cash flow models for the evaluation of the
project and these were substantiated with their cost of capital as 15%.

12 The IUP Journal of Infrastructure, Vol. VIII, Nos. 1 & 2, 2010

Net Present Value
The NPV for the project (Appendix A) is Rs. 181.9 mn with payback period being seven
years. The IRR for the project is 24% which is higher than the average rate of return of
the commercial real estate industry being 4.46% for the year 2008. In commercial real estate
industry, Kirloskar proprietary limited had the highest Return on Investment (ROI) value of
32.45% and G Varadan limited the lowest value of –11.1% during the year 2008.

Option Valuation
The call option price using Black-Scholes is Rs. 120.2 mn and for binomial Rs. 119.58 mn
indicating the strategic component that incorporates the market volatility to be positive and
high for the project. The lower value of binomial model signifies that it is not optimal to
exercise earlier behaving more like European option with optimal feasibility being at the
end of the option expiry.
The land premium estimated using the Samuelson-McKean perpetual option pricing
methodology (Table 1) is Rs. 154.08 mn which is higher than that of the value estimated
using other option models. Since land has a value for development without any time limit,
perpetuity model can evaluate the development project better than that of financial option
pricing models such as Black-Scholes and binomial trees. Since the land is with the real
estate developer and as a developer they have a right to develop the project without any
time limit this can be viewed as a perpetuity development option.

Table 1: Samuelson-McKean Model for the Commercial Project

Parameter
Parameters Value
Representation
Value of call option (Land) (Rs. in mn) C 154.08
Critical value of the underlying asset (Rs. in mn) S* 273.88
Average return risk premium of underlying asset (%) RP (S) 4.46
Option elasticity  8.12
Expected return risk premium in land investment (%) RP 36.20
Opportunity cost of capital for land (expected total return) (%) E[R] 40.76
Critical benefit-cost ratio (S*/K) 1.14
Optimal land value fraction at development (%) (S*– K)/S* 12.00
Current land value fraction (%) C/S 39.08
Optimal immediate exercise Yes/No Yes
Total strategic return (%) (C + NPV)/S 85.22

The limitations of Black-Scholes model is that it is applicable only for European options
whereas binomial model can be used for valuing an European and American option that
can be exercised on any date before maturity if early exercise is optimal. This time limit
has been overcome by Samuelson-McKean model that can be applied to perpetual

Real Options Analysis in Valuation of Commercial Project: A Case Study 13

American call option on a dividend-paying underlying asset (land) that has its applications
for land options.
The critical value of the underlying land for immediate development is Rs. 273.88 mn,
i.e., the market value of completed property must be worth at least this amount (Table 1).
In 2008, the underlying land value is Rs. 394.24 mn, wherein the critical value is way below
the underlying land value clearly indicating that it is optimal to exercise immediately rather
than delaying the construction of mall.
The optimal land value fraction considered at development is 12% which is the risk related
expected return. Current land value fraction is 39% which represents the premium to be
paid for development rights to market value. Commercial project’s average risk premium
is 4.46% for the year 2008. The option elasticity (option risk) is 8.12 for the project. At
this risk level, the risk premium desired for the land is 36.2% which in turn is further used
to compute the expected rate of return as 40.76% for the project. Immediate development
is expected to yield a higher return considering the likely change in market price of the
underlying land value. The total strategic return from the project is 85.22%.
The strategic NPV computed using real option analysis is given in Table 2. Incorporating
flexibility of market prices to evaluate a project highlights the project benefits.

Table 2: Strategic NPV for Commercial Project

Strategic NPV (Rs. in mn)
NPV (Rs. in mn) Samuelson-McKean
Black-Scholes Model Binomial Model
Model
181.9 302.1 301.48 335.98

Critical benefit to cost ratio (S*/K) is 1.14 representing the ratio of built property
value in relation to construction cost (Figure 1). The market value being more than its
construction cost by the critical benefit cost ratio indicates the risk related return for
the developer.

Figure 1: Commercial Project (Call Option) Value

(S*/K)

14 The IUP Journal of Infrastructure, Vol. VIII, Nos. 1 & 2, 2010

Risk Analysis for the Black-Scholes and Binomial Model
Risk measures of delta, gamma, vega, theta and rho for the option valuation were evaluated
as given in Table 3.
Table 3: Risk Analysis for the Black-Scholes and Binomial Model
Call Delta Gamma Theta Rho Vega
Risk Analysis
Rs. Per Rs. Per Rs. Per Day Per % Per %
Black-Scholes 120.2 0.89 9.50E-05 –0.086 2.29 2.18
Binomial 119.58 0.99 6.45E-05 –0.03 2.72 0.04

Delta is defined as the rate of change of the option price with respect to the price
of the underlying asset. The delta value for Black-Scholes is 0.89 indicates the option price
changes by 89% for a 1% change in underlying land value and binomial value of 0.99
indicates the option price changes by 99% to a 1% change in underlying land value.

c
 ...(7)
S
From Figure 2, it is evident that as project value increases the call value sensitivity of
the project increases. As the duration of the project nears option expiry date, its development
the value of delta increases to a maximum of 0.4. The sensitivity of the call value in relation
to land price is relatively less.
Figure 2: Delta Value for Commercial Project

Gamma is the rate of change of option price with respect to the price of the underlying
land value. It is the second partial derivative call option price with respect to land value.
If the gamma is small, delta changes slowly and adjustments to keep a risk neutral position
need not be managed by the developers. However, if gamma is large, delta is highly
sensitive to land value and become a risky investment proposal for the developers.

Real Options Analysis in Valuation of Commercial Project: A Case Study 15

The gamma for the Black-Scholes model is 9.5E-05 and binomial is 6.45E-05 indicating
that delta changes slowly and changes needed to make the project delta neutral need
not be frequent.

 2c
 ...(8)
S 2

When the project value increases the value of gamma increases (Figure 3). Gamma
is high when market rates move away from the cost of construction of the project. The
value of gamma is very low at the start of the project (two months) and then increases
gradually as project implementation date nears.

Figure 3: Gamma Value for Commercial Project

Theta is the rate of change of option price with respect to the passage of time with
all other factors remaining the same. Theta is negative for a call option because as time
to maturity decreases, the option tends to become less valuable. It is measured as “per
calendar day” (theta is divided by 365) or “per trading day” (theta is divided by 252).
The value of theta for Black-Scholes is –0.086 per calendar day indicating that the call
option price decreases by Rs. 31.39 mn per annum (i.e., call option price of Rs. 120.2
mn decreases to Rs. 88.81 mn per annum) and for binomial it is –0.03 per calendar day
indicating that the call option price decreases by Rs. 10.95 mn per annum (i.e., call option
price of Rs. 119.58 mn decreases to Rs. 108.63 mn per annum).
For a European call option on an asset (i.e., underlying land value) paying a dividend
at rate q (i.e., rental yield of 12%for the project) it can be shown from the Black-Scholes
formula that:

S0 N' (d1 ) e qT
 (call )  -  qS0 N(d1 )e qT  rKe  rT N(d2 ) ...(9)
2 T

16 The IUP Journal of Infrastructure, Vol. VIII, Nos. 1 & 2, 2010

where,

d1  [ln( S0 / K )  (r   2 / 2)T ] /  T
d2  [ln( S0 / K )  (r   2 / 2)T ] /  T  d1   T

1  x2 / 2
and, N' ( x )  e (Cumulative normal distribution function)
2

The project value between Rs. 250 mn and Rs. 300 mn (Figure 4) shows a minimal of
theta value. Beyond the project value of Rs. 300 mn, the theta value increases gradually.
The theta value is high at the beginning of the project and as the duration of the project
increases theta remains constant.
Figure 4: Theta Value for Commercial Project

Vega is the rate of change of option price with respect to the volatility of the underlying
land value. If vega is high, the value is sensitive to small changes in volatility and low vega
value indicates that the volatility changes have little impact on the option price. The vega
for the Black-Scholes model is 2.18% indicating that volatility change increases the call
option price by Rs. 2.62 mn and binomial is 0.04% indicating that volatility change increases
the call option price by Rs. 0.047 mn.

c
 ...(10)


The project is insensitive to volatility changes when market prices go beyond

Rs. 400 mn (Figure 5). When the time to implementation of the project nears the option
expiry of one year the vega value increases to 80%.

Real Options Analysis in Valuation of Commercial Project: A Case Study 17

 Figure 5: Vega Value for Commercial Project

Rho is the rate of change of option price with respect to the interest rate changes.
It measures the sensitivity of the call value of a project to interest rates. The rho value
for Black-Scholes model is 2.29% and 2.72% for binomial indicating that 1% increase
in the risk free rate (i.e., from 4.55% RBI’s T-Bill to 5.55%) increases the option value
by 2.29 times for Black-Scholes (call option price increases by Rs. 2.75 mn) and 2.72 times
for binomial (call option price increases by Rs. 3.25 mn).

c
rho ( call ) = ...(11)
r

Rho value is insignificant at the beginning of the project and increases gradually to
0.5% as well as project value Rs. 450 mn as it approaches option expiry date (Figure 6).

Figure 6: Rho Value for Commercial Project

Note: In the graph 200 represents 200 basis points (2%).

18 The IUP Journal of Infrastructure, Vol. VIII, Nos. 1 & 2, 2010

Risk Analysis for the Samuelson-McKean Model
Risk analysis with respect to increase in volatility, risk free rate and value of the underlying
land value by 10% was computed (Appendix B).

Variation Volatility
Variation in volatility had a significant impact on the critical benefit to cost ratio
(Figure 7). Any increase in volatility beyond 35% increased the call premium value of land.
Increase in the volatility reduced the opportunity cost of capital for the project
(Figure 8).
Figure 7: Variation with Critical Benefit/Cost Ratio

60%

50%

40%

30%

20%

10%

1.14 1.24 1.5 1.84 2.25

S*/K

Figure 8: Variation with OCC

60%

50%

40%

30%

20%

10%

0%
13.5 15.5 19.5 30.4 45

Opportunity Cost of Capital for Land (%)

Variation in Risk Free Rate

Variation in the risk free rate had a significant impact on the critical benefit to cost ratio
(Figure 9). Variation in risk free rate did not influence the call premium value of land.
Increase in the risk free rate reduced opportunity cost of capital for land (Figure 10).

Real Options Analysis in Valuation of Commercial Project: A Case Study 19

 Figure 9: Variation with Critical Benefit/Cost Ratio

9%
8%
7%
6%
5%
4%
3%
2%
1%
0%
1.14 1.16 1.18 1.21 1.24
S*/K

Figure 10: Variation with OCC

10%
9%
8%
7%
6%
5%
4%
3%
2%
1%
0%
35 37 39 41 44 45

Opportunity Cost of Capital for Land (%)

Variation in Underlying Land Value

Underlying land value remained constant to changes in critical benefit to cost ratio and
opportunity cost of capital. Increase in the underlying land value increased the call premium
value of land.

Conclusion
Real option analysis by incorporating the fluctuations in volatility and providing the option
of flexibility gives the developers a useful evaluation tool for their project decisions. The
land held by the developer tends to have a perpetuity value and it is at the discretion of
the developer to execute various options depending on prevalent market conditions.
Samuelson-McKean model values the project as a perpetual American call option indicating
its edge over other models which is constrained by time limit as reflected by its high
premium value and total strategic return. The current land value fraction dependent on

20 The IUP Journal of Infrastructure, Vol. VIII, Nos. 1 & 2, 2010

the current market price represents the premium to be paid for development rights is 39.08%
which is comparatively less than the opportunity cost of capital representing expected total
return being 40.76%, indicating that the developer has option for further time delay to achieve
the expected total return but since still the difference being minimal it does not stop the
developer from immediate exercise. Risk analysis indicated that a vega of 2.18% could increase
the call option price by Rs. 2.62 mn and rho of 2.72% increase the call option price by
Rs. 3.25 mn. The project is very vulnerable to underlying land prices and interest rate changes
in the market. Total strategic return of 85% from the project justifies the scope for the developers
to implement the project as per schedule.

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22 The IUP Journal of Infrastructure, Vol. VIII, Nos. 1 & 2, 2010

 Appendix A
NPV for Commercial Project
Year 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019
Lease Rent Rs. per sq ft 35 35 35 40.25 40.25 40.25 46.29 46.29 46.29
per month
Lease Rent Rs. per sq ft 420 420 420 483 483 483 555.45 555.45 555.45
per annum
Leasable Area (sq ft) 108,900
Hence Lease Rent 45.73 45.73 45.73 52.59 52.59 52.59 60.48 60.48 60.48
Value of Underlying Land 430.98
Div. Yield (2012-2019) (%) 11 11 12 12 12 14 14 14
Security Deposit in Months six
Absorption Lease Portion 100%
Rent Escalation and 15% Eve ry
Deposit Increase Three Years
Cash Flow (Rs. in mn)
Lease Rentals 45.73 45.73 45.73 52.59 52.59 52.59 60.48 60.48 60.48

Real Options Analysis in Valuation of Commercial Project: A Case Study

Security Deposit 22.86 3.43 3.94
Rental Inflow 45.73 45.73 45.73 52.59 52.59 52.59 60.48 60.48 60.48
Gross Cash Flows 68.6 45.73 45.73 56.02 52.59 52.59 64.43 60.48 60.48
Perpetuity Rate 10%
Cost of Capital 15%
Cash Flow Statement
Inflows
Rental Inflow 45.73 45.73 45.73 52.59 52.59 52.59 60.48 60.48 60.48
Security Deposit Inflow 22.86 3.43 3.94

23
24
Appendix A (cont.)
NPV for Commercial Project
Year 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019
Other Revenues 5.06 5.06 5.06 5.82 5.82 5.82 6.7 6.7 6.7
Gross Inflows 73.67 50.8 50.8 61.85 58.42 58.42 71.13 67.18 67.18
Outflows 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019
Construction Costs –119.79 –125.77
Marketing, Legal Costs, etc., as
a Percentage of Construction 3.5% –4.19 –4.40
Costs
Property Tax (Approx 6% 6% –3 –2.74 –2.74 –3.15 –3.15 –3.15 –3.62 –3.62 –3.62
of Rental Inflows)
Gross Outflows –123.98 –130.18 –2.74 –2.74 –2.74 –3.15 –3.15 –3.15 –3.62 –3.62 –3.62
(Excluding Security Deposit)
Net Cash Flows –123.98 –130.18 70.92 48.06 48.06 58.70 55.26 55.26 67.50 63.56 63.56
Perpetuity Cash Flows –123.98 –130.18 70.92 48.06 48.06 58.70 55.26 55.26 67.50 63.56 699.16
Excluding Security Deposit –123.98 –130.18 48 48.06 48.06 55.26 55.26 55.26 63.56 63.56 699.16

The IUP Journal of Infrastructure, Vol. VIII, Nos. 1 & 2, 2010

 Appendix B

Comparative Table Indicating Risk Analysis for Samuelson-McKean Model

with Increase in Parameters by 10%
Input Values Parameter Value Inc.in ( ) Inc.in (rf) Inc. in (S)
Underlying asset (built property)
() 15 16.5 15 15
volatility (%)
Underlying asset (built property)
() 12 12 12 12
current yield (%)
Risk free interest rate (%) (rf ) 4.55 4.55 4.95 4.55
Underlying asset (built property)
(S) 394.24 394.24 394.24 433.66
current market value (Rs. in mn)
Construction cost exclusive
(K) 240.15 240.15 240.15 240.15
of land (Rs. in mn)
Average return risk premium
RP(S) 4.46 4.46 4.46 4.46
of underlying asset (%)
Output Values
Value of call option
C 154.08 154.08 154.08 193.51
(Land) (Rs. in mn)
Critical value of the underlying
S* 273.88 280.49 275.32 273.88
asset (Rs. in mn)
Option elasticity () 8.12 6.95 7.83 8.12
Expected return risk premium
RP 36.2 31.01 34.92 36.2
in land investment (%)
Opportunity cost of capital for
E(r) 40.76 35.56 39.87 40.76
land (Expected total return) (%)
Critical benefit-cost ratio (S*/K) 1.14 1.17 1.15 1.14
Optimal land value fraction at
(S*–K)/S* 12 14 13 12
development (%)
Current land value fraction (%) (C/S) 39.08 39.08 39.08 44.62
Optimal immediate exercise
Yes/No Yes Yes Yes Yes
(development)

Reference # 27J-2010-03/06-01-01

Real Options Analysis in Valuation of Commercial Project: A Case Study 25

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