This Version: 30 March 2003

Valuation of Rental Commercial Retail Properties: Tenant Management and Real Options Takeaki Kariya Research Center for Financial Engineering KIER, Kyoto University [email protected] www.kier.kyoto-u.ac.jp/fe Yasuyuki Kato KIER, Kyoto University Nomura Securities Co. Ltd. Tomonori Uchiyama Nomura Securities Co. Ltd. Takashi Suwabe Nomura Securities Co. Ltd.

This paper formulates a tenant management problem for a commercial retail real estate such as shopping center , provides an analytical framework for deriving the probability distribution of the sum of a discounted cash flow stochastically generated through the tenant management and finds an optimal strategy for tenant-replacement management and lease agreement structure on rent. More specifically, we formulate the problem of valuing the net present value of future net revenues from a commercial retail property with tenant management and provide a valuation model for management decision making. The revenues fluctuate with market rent variations and management processes. In our framework a property manager is required to choose an optimal mix of fixed rent and variable rent linked to sales of tenant’s business, and one of two tenant-replacement rules for return and risk enhancement. By Monte Carlo simulation we give an optimal strategy for this problem. This is a joint research with the Applied Financial Engineering Division of Nomura SecuritiesGroup at KIER.

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1 Issues and objectives of this paper Three objectives In this paper we consider a tenant management problem, specifically a problem on how to create value under various uncertainties from a commercial retail property such as a shopping center. The first objective is to provide an analytical framework for this problem. The tenant management problem can be regarded as a combination of formulating rules for replacing tenants and structuring lease agreements that create value. Hence the valuation framework is based on the type of tenant-replacement rules, the rental contract structure, and a dynamic analytical model for quantitatively determining the present value of future rent cash flows, which we call dynamic discounted cash flow (DDCF) model that takes into account differences in tenant-replacement rules and the structures of the lease agreements on fixed and variable rents. Once the formulation is made, a commercial property can be valued using a Monte Carlo simulation. Hence, the management problem can be regarded as a problem of valuing retail property under a specific business model. The second objective of this paper is to find optimal combinations of tenant-replacement rules and lease agreement structures through a comparative analysis of alternative lease agreement structures and tenant-replacement rules. It should be noted that under uncertainties the present value of a property, a business project or even a corporation is first expressed as a DDCF probability distribution, since DDCF-based values are subject to stochastic variations over a time horizon in the future. The mean of the probability distribution is typically known as the DCF expected value of the property. However, a large mean is not preferred just because it is large, if the risk of deviation from the mean is also large. In other words the decision-making framework is based on possible trade-off between risk and return. Accordingly, this approach is different from one in which an objective function is set up and dynamic programming is applied to optimize the mean. In our analysis, we optimize tenant-replacement rules in terms of the risk-return relationship. A new Law for Land Lease and House Lease in Japan took effect in 2000. New deregulatory provisions increase the value of the various real options. The new 2000 law is no exception, and under the new House Lease Law, lessors can have a real option in the form of a contractual right to replace lessees. This paper attempts to value this real option from the perspective of retail property management companies. The value of this option is the difference between the value of the option when it is used most effectively and the value when retail property without tenant-replacement rights is used. With a tenant-replacement option, a percentage(variable) rent option is created. Under the old Law for Land Lease and House Lease, no provisions existed for tenant-replacement rights, which made it risky and thereby difficult to use percentage-of-sales rental contracts. With a tenant-replacement option, however, property management companies are able to actively use such lease agreements and add value. The third objective of this paper is to conduct a policy assessment of the new House Lease Law. Perspe ctives and studies on commercial property management The key aspects of commercial property management include: (1) Property management (narrowly defined), and 2

(2) Tenant management Property management concerns the physical structures, the technical functions of the buildings, and other tangible aspects of the property so as to protect the potential value of the property, attract tenants, and thereby increase cash flows. Tenant management, by contrast, concerns the combinations of tenants, the structure of the lease agreements, and other intangible aspects that also affect the value of a property. Research in both of these areas is still fairly nascent and not much data are available, which suggests that further research needs to be done. In general, property management in the broad sense encompasses both aspects noted above. The management issue we analyze in this paper concerns the basic concept (business model) for the management of commercial property, tenant location, tenant selection, and the structure of lease agreements for making these possible. The management objective is to increase the brand value of the property rentals and to seek to achieve long-term stability in DDCF value. Doing so requires tenant selection, particularly in the management of shopping centers and other commercial retail properties. A well-known study of the relationship between regional shopping center rental rates and retail sales is Wheaton and Torto (1995), which found that rental rates increased more rapidly than retail sales did between 1968 and 1993. Chun, Eppli and Shilling (1999), meanwhile, build on models developed by Benjamin, Boyle and Sirmans (1993) and Miceli and Sirmans (1995), but treat base rents and percentage rents as functions of sales, distinguish between fixed and percentage leases, and incorporate lagged effects. Whereas these studies analyzed the relationship between rents and sales for various retail formats from a macro supply-demand perspective, this paper deals with the micro-level management issues for owners of shopping centers and other commercial retail properties, provides a framework for analyzing future cash flows, and analyzes lease agreement structures and tenant selection through simulations. Structure of this paper This paper is structured as follows: Section 2Perspectives on retail property rental Section 3Formulation of an analytical framework Section 4Development of our model Section 5Valuation using Monte Carlo simulation Section 6Tenant replacement costs Section 7Tenant-replacement costs and optimal weightings for percentage rents Section 8Conclusion In section 2, as retail property management the issues of tenant selection and lease agreement structure are discussed. In essence, the issue for retail property managers can be thought of as developing common incentives with tenants to create value, given a certain business model. In section 3, we develop one contract structure that provides common incentives by combining fixed and percentage rents. We frame the tenant selection issue by focusing on sales as they relate to ability to attract and retain customers, specifically by establishing a rule by which tenants that are unable to meet certain sales conditions within the contract period are replaced. This rule can be 3

regarded as a way to maintain the value of the retail property and build brand value. We also analyze the value of a right given to the tenant at the start of the contract to extend the contract for a certain period. In section 4, we develop a specific analytical model based on uncertainties that cause real estate values to fluctuate, specifically: 1) Uncertainties of variation in market rental rates 2) Uncertainties of variation in tenants’ sales The market rental rate determines each fixed rental rate for each contract period, and is generally related to economic conditions as well as the development trends and competitive characteristics of the region in which the property is located. In this paper, however, we assume a log DD (discrete time diffusion) process for an analytical simplicity. Likewise, we assume a log DD process of the same type for the change in tenants’ sales. For the drift of the models, though, we assume an exponential smoothing model that gradually changes in response to changes in its own previous trend, to take into account the non-Markovian characteristics of the actual changes. As strategies for dealing with uncertainties that property managers actually face, these two models forms a basis for describing tenant-replacement rules and contract structures that combine fixed and percentage rents. A large number of Monte Carlo simulations are presented in Section 5 to analyze the characteristics, analytical capability, and phenomenon descriptive capability of the model for comparing two tenant-replacement rules for an optimal mix of fixed and variable rents for each rule. Specifically, we establish three cases [5-1] The core case of fixed rents and no tenant-replacement provisions [5-2] A mix of fixed and percentage rents, and no tenant-replacement provisions [5-3] A mix of fixed and percentage rents, and full tenant-replacement provisions The comparison is based on the risk and return of the probability distribution of the DDCF values. As cases involving sales-based tenant-replacement rules, we then look at [5-4] A mix of fixed and percentage rents, and (I) tenant-replacement rules based on the average change in sales, and (II) tenant-replacement rules based on the level of sales We compare the results for these four cases, with a volatility for the sales process of 20%. In addition, we test [5-5] Case 5-4, but with a volatility for the sales process of 10%

2

Perspectives on retail property rental

The category of retail property we consider below is shopping centers. The tenant management issues can be specified as follows: (1) The business concept of the shopping center, and a business portfolio of tenants and their locative allocation in the shopping center (2) Tenant selection, given a certain business portfolio and tenant locations, and lease agreement structures The first issue above concerns the desired customer segment for the shopping center; the positioning of the shopping center, in terms of grade, function, and regional role, as part of the core 4

business model; and the determination of a business portfolio of tenants for the business model and their locations. This issue is a difficult one that has much to do with whether a shopping center management business is successful. The most typical type of mall in the United States features high-end department stores, with spacious sales floors; Sears, J.C. Penney, and other general department stores that feature inexpensive household goods and cater to the middle class; specialty footwear and clothing stores; and McDonald’s and other food establishments. This retail arrangement stems from a business concept, and may be attractive to consumers. Through the location of the types of businesses and the selection of tenants attractive to the target customer segment, the objective is to bring in customers again and again, have them stay for long periods and spend money, and generate externalities for the other tenants in terms of profits. We do not consider how to make an optimal combination of different businesses of tenants and their locations in this paper. Our objective is the second issue and providing a framework for defining the problem and a cash flow valuation model. Specifically, we address issues concerning the structure of the lease agreements and the change of tenants based on sales, on the assumption that the management company has the right to ask tenants to leave. Hence, we 1) Use a combination of fixed and percentage rents for the lease agreement, and 2) Consider tenants’ sales growth rates and variability of sales as tenant characteristics The partial use of percentage rents is important in that they can provide common incentives for the property management company and the tenants, and encourage both of them to be interested in how well the tenants do. In addition, strong sales mean a strong ability to attract customers, a factor that leads to externalities also benefits the businesses of other tenants. Sales data are readily available. The structure of the lease agreement may differ depending on the type of tenant’s business, as it relates to the business concept of the shopping center, and on the positioning of the tenants. Coffee shops, for instance, may not have particularly significant sales or much variability in sales, but are still an important type of retail business for shopping centers because of their ability to draw customer traffic. A portfolio consisting of such tenants and those in businesses with relatively significant sales and variability of sales can be put together to match the desired business concept. For structuring lease agreements, an analytical framework for considering the choices of combinations of fixed and percentage rents for different types of businesses is needed. In this paper, we provide such an analytical framework and a specific model, and quantitatively compare DDCF probability distributions for the results of simulations involving different combinations of fixed and percentage rents. The second issue involves the valuation of shopping center properties as a probability distribution of the DDCF value when tenants are replaced on the basis of sales, given lease agreements that combine fixed and percentage rents. In this context, sales are a basis for tenant replacements, but the choice of rules represents an issue. The objective function for risk and return should be optimized for the rules on tenant combinations and replacement, but in the simulations in this paper, we compare rules based on the change in sales and those based on the level of sales, and 5

propose the latter type of rule from the perspective of risk and return.

3

Formulation of an analytical framework

We assume the lease agreements are for three years and, for simplicity sake, also assume that they include provisions that prohibit tenants from getting out of their leases before the term is up. The property management companies have the right to ask tenants to leave at the leases end. The time frame for our valuation analysis is 30 years, broken down into 10 three-year contract periods (k = 1, 2 ,L ,10 ). The current time period is denoted 0, and we derive the probability distribution of income capitalization values using DDCF for each monthly period ( n = 1, 2 , L,360 ). In the second contract period, for instance, the months that are analyzed are n = 37 ,38 ,L ,72 . To annualize the time frame, we set h = 1 12 . For instance, the time frame from month 0 to month n can be expressed in years as nh. The discount rate for future cash flows is expressed as an annualized rate. The retail property has I spaces for lease, i = 1,L, I . Each space is occupied by a tenant with a specific type of business. For simplicity it is assumed that a tenant is found on vacancy. The method proposed by Kariya, Ohara and Honkawa (2002) can be applied to the case where there are stochastic vacancy periods after tenants leave. (1) Structure of the lease agreements We assume lease agreements for each contract period that combine fixed and percentage rents.. The percentage-rent portion is based on monthly sales, and is assumed to be paid at the end of each month. Specifically, the per-3.3 m2 rent for the ith space (for a specific type of business) and the nth month can be expressed as X in (k ) ≡ X i ( k , m( k ) )

( n = 36( k − 1) + m( k ) : 1 ≤ m( k ) ≤ 36 )

This rent can be further expressed as ~ ~ (3.1) X in (k ) = (1 − αi ) X i f (k ) + αi βi × Sin (k )

[

]

The left-hand side represents the rent received for the ith space and the nth month of the kth contract period. On the right-hand side, (1 − αi ) represents the proportion of the rent for the kth ~ contract period that is fixed and αi represents the proportion of the rent that is tied to sales βi Sin . ~ Hence, in (3.1), the rent is expressed as a sum of a fixed rent for the kth contract period, X i f ( k ) , ~ ~ ~ ~ and a rent that is tied to sales in the nth month, Sin ≡ Si ( k , m( k ) ) . Contract sales Sin ≡ S in ( k ) are defined in the lease agreement to reflect the differing levels of sales for different types of businesses and the actual variability of tenants’ sales Sin (k ) . We provide the formulation later on. ~ ~ The initially determined fixed rent for the contract term is expressed as X i f ( k ) = X i 12 ( k −1) where ~ ~ X in ≡ X i ( k , m( k )) is the market rent at time n, with n = 36( k − 1) + m( k )) . The dependence on the type of business i with parameter{(αi , βi ) : i = 1, L , I } in (3.1) is 6

related to variability of sales. When αi = 0 , i.e. ~ ~ (3.2) X in (k ) = X i f ( k ) = X i 36( k −1 ) , it applies to a typical fixed-rent agreement, with each fixed rent constant for three years determined at each contract time. ~ We first take the case of k = 1 to consider contract sales Sin (k ) and percentage rents based on the contract sales. The rent at time n = 1 (the end of the first month) is ~ ~ X i 1 (1) = (1 − αi ) X i f (1) + αi [ βi S i1 (1)] (3.3) ~ ~ X i f (1) = X i 0 ~ X i 0 is the market rent at time 0 adjusted for the type of business, and is fixed for 36 months. ~ Si 1 (1) is a random variable at time n = 1. The term X i 1 (1) on the left-hand side is also a random variable at time n = 1. If we denote sales of a tenant at time n as Sin , and the annual variation in sales between time n–1 and n as 1 (3.4) rin = log( S in Sin −1 ) ( h = 1 12) , h then the actual level of sales can be expressed as the identity (3.5)

Sin = Sin −1 exp( rin h) .

When n = 1 , Sin is observable, but Si 0 is not, and hence neither is rin . However, when n ≥ 2 then rin is observable. Management’s required amount of sales at n = 1 is ~ ~ ~ (3.6) Si 1 = X i f (1) = X i 0 and the initial rent after the tenant takes occupancy at time 0 is ~ (3.7) X i 1 (1) = (1 − αi + αi βi ) X i 0 This amount is the required rent for the first month at time 0. The important point in this expression is that the management company’s required rent for the first month, even when tied 100% to sales ~ with αi = 1, βi = 1, is nothing more than fixed rent Χio . In this sense, contract sales are ~ rationally indexed to actual sales. Also, when αi = 0 , then the fixed rent is Χio , but it should be noted that when 0 < αi < 1, 0 < βi < 1 in (3.7), the rent mix X i1 (1) is smaller than the market ~ fixed rent X i 0 , a difference that could be considered the cost of obtaining the right to ask the tenant to vacate under a percentage-rent arrangement. The cost in percentage is one minus (3.8)

δi = 1 − αi + αi βi ,

whereby given δi , the hyperbolic curve for ( αi , βi ) is determined. Contract sales when n = 2 with observable ri 2 are defined as

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(3.9)

~ ~ ~ Si 2 = S i1 exp( ri 2 h) = X io exp( ri 2 h) .

~ ~ The rent in this case is X i 2 (1) = (1 − αi ) X i f (1) + αi [ βi Si 2 ] . Similarly, if contract sales with ~ ~ observable rin are defined as Sin = Sin −1 exp( rin h) , then the rent at time n with 36 ≥ n ≥ 3 is given by ~ ~ X in (1) = (1 − αi ) X i f (1) + αi [ βi S in ] . This is nothing more than equation (3.1) with k ＝１. For the kth contract period as well, the rent for a tenant that continues to lease space and is not asked to vacate starting in the k–1th contract period is given by (3.1). But in the case of a new tenant that takes occupancy at the end of n = 36( k − 1) , the fixed-rent portion is the market rent at ~ ~ time 36( k − 1) , i.e., X i f ( k ) = X i 36 ( k −1) . The percentage rent at time 36( k − 1) + 1 is based on ~ ~ contract sales, as in (3.6), with S i12 ( k −1) +1 = X i f (k ) and ~ （3.10） X i 36 ( k −1 )+1 ( k ) = [1 − αi + αi βi ] X i 36( k −1 ) . From time n ≥ 36( k − 1) + 2 onward, the rent is defined in equation (3.1) based on contract sales as expressed in (3.6). (2) Tenant-replacement rules The importance of tenant management lies in increasing the DDCF value of the property by putting in tenants with the ability to attract customers so that the tenants benefit mutually from externalities. The active replacement of tenants is one way to do so. A practical indicator for the ability to attract and retain shoppers is sales. We express a tenant-replacement rule for the end of a contract period based on sales for that period as (3.11)

F ( S i 36 ( k −1) +1 , L , Si 36 k ) ≥ 0 ( k = 1, L, K )

Specifically, the rule that the average change in sales in the past two years, through six months prior to the end of the kth contract period (which factors in the tenant’s vacancy preparation period and seasonal variations in sales), can be expressed as 1 36 k −6 (3.12) ri ( k ) = rij ≥ c( k ) ∑ 24 j =36 ( k −1) + 7 When the change in sales under such a lease agreement is negative, it is rational to demand that the average profitability be at least a certain level, since the rent could be below the required fixed rent. Another possible rule is that the amount of contract sales six months prior to the end of the contract period be at least a certain level, as follows: ~ ~ 36 k − 6 (3.13) S j 36 k −6 ( k ) = Si 36 (k −1) +1 exp( ∑ j = 36( k −1 )+ 2 rij h ) ≥ c( k ) . A third criterion uses the average of contract sales, as expressed below:

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(3.14)

~ ~ 36 k −6 Si 36 k −6 ( k ) = Si 36( k −1 )+1 exp( ∑ j =36 ( k −1 )+ 2 rij h) ≥ D( k ) .

(3) Expected values Given the above lease agreement structure and tenant-replacement rules, the DDCF value of future cash flows is K

（3.15）

Vi = ∑Vi ( k ) k =1

The DDCF value of future cash flows from the ith tenant for the kth contract period is （3.16）

Vi ( k ) =

∑ [(1 − α ) X nk

n = nk −1 +1

~f

i

i

]

~ (k ) + αi [ βiU in ( k )] Ai D( n)

Also, D(n ) is the discount rate for cash flows at time n and Ai is the size of space i in 3.3 ~ m2 , and U in (k ) represents the tenant’s sales for the k th period, and as noted earlier regarding the first contract,

~ ~ U in (1) ≡ Sin (1) . For the second contract period onward, a change in tenants is a possibility, and so to distinguish between tenants that stay and those that leave, we designate the following: （3.17）

 1 if Li (k ) =  0

~ ~ Fk ( S36( k −1) +1 , L , S36k ) > 0 otherwise

Based on this function, contract sales for the ith tenant for the kth contract period are ~ ~ ~ (3.18) U in ( k ) = U in ( k −1) Li ( k − 1) + Sin ( k )[1 − Li ( k −1)] When Li ( k ) = 1 , this equation expresses the sales of a tenant that stays from the k − 1 th contract ~ period. In other words, whereas n > 36( k − 1) , U in ( k −1) relates to percentage rents that are extended from the k th period, given that the agreement is extended from the k − 1 th period to the k th period. (4) Contract extension option The tenant-replacement rules and the possibility of being forced out with a contract period of only three years are tough conditions for tenants, given the upfront investments they make in their businesses and the relocation costs. Tenants may also face sudden, unfavorable changes in their business environments. Strict property management, however, serves to improve property values, from the perspectives discussed in section 2. One solution would be to give tenants the right to buy an option to extend their lease agreements for one contract period. With this option, tenants could continue for another contract period, even if they do not meet the conditions in (3.11). The value of this option corresponds to the property management company’s opportunity loss. In the case of a

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tenant that does not purchase such an option at time n = 0 for the first contract period, we get for equation (3.16) Vi (1) + Vi ( 2) where Vi (2) represents earnings stemming from the replacement rules in (3.17) and (3.18). If the tenant stays for a second contract period, the total present value for the first contract period is Vi (1) , but without a return to the rent level for a new tenant at the start of the second contract period, the contract sales process for the tenant follows a path that starts from time 0. If we express ~ this path for the second contract period as S in (1) (n ≥ 37) , the total present value for the second contract period is Vi * ( 2) =

72

∑ [(1 − α ) X

~f

i

i

~ ( 2) + αi βi S in (1)] Ai D( n)

n =37

The risk of earnings opportunity losses (payoff) for the management company can be expressed as W = [Vi (1) + Vi (2) − Vi (1) − Vi * ( 2)] + 72 ~ ~ ~ = { ∑ αi βi [ Sin (1) Li (1) + Sin (2)(1 − Li (1)) − Sin (1)] Ai D( n)}+ n =37

72 ~ ~ = { ∑ αi βi [ Sin ( 2) − Sin (1)](1 − Li (1)) Ai D(n )}+ n =37

~ Here a + = max ( a, 0) . In addition, S in (2) represents a new tenant’s contract sales for the ~ second contract period, and Sin (1) represents contract sales for a tenant that renewed after the first contract period. The fair value of the payoff at time 0 under no-arbitrage conditions is the expected value of W, E0 [W ] , which is an insurance premium that the property management company asks to give the tenant the right to stay for the second term.

4

Formulation of our model

An actual analysis using the framework provided in section 3 requires ;(1) A model for market rents, since the fixed rent determined at the start of each contract period is the market rate at that time; and(2) A model for the variability of sales for each type of tenant business. We formulate these models below. (1) A model for market rents The following log DD process is used as our market rent model (Kariya and Liu,2002): ~ ~ (4.1) X in = X in −1 exp µXin −1 h + γ Xin−1 hε~Xin

[

]

~ where drift µXin −1 and volatility γ Xin−1 may depend on past values of X in and ε~Xin ~ iid N(0,1). For the drift µXin−1 for market rents, we use an exponential smoothing model, whicht is non-Markovian,

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µXin−1

(4.2)

 X~in−1  = φxi log  ~  + (1 − φXi )µXin−2 .  X in− 2 

The model may depend on the tenant’s type of business i, which we omit below. This smoothing parameter φX indicates the extent to which new information on rent changes ~ ~ ~ log[ X n −1 X n −2 ] is discounted and reflected in the rent level X n . A small smoothing parameter φX means that the monthly changes are slowly discounted. To express the dependence on the type ~ ~ ~ of business, we use X in = λi X n . The rent is adjusted for the type of business by λi , and X n represents the level of market rent. Figure 4-1 shows the sample path for the parameters in our base case. Figure 4–1. Sample paths

Note: 50 sample paths generated with the following diameters: initial drift

X 0 = 1（

2

¥/t 3.3m ）, and smoothing parameter

φX = 0.2 .

µX 0 = 0% , volatility γ X = 5% , initial market rent

(2) A model for the variability of sales The contract sales process defined by (3.9) is modeled by modeling the rate of return rin ; rin = µin −1 h + γ i hεin . Accordingly, the log DD model for the contract sales process in (3.9) is ~ ~ (4.3) Sin ( k ) = Sin −1 ( k ) exp µin−1 h + γ i hε~in ,

[

]

~ where µin −1 and γ i depend on past values of Sin and ε~Xin ~ iid N(0,1). Here as in the case of the model for rent variation, the drift µin is described by an exponential smoothing model:

(4.4)

µ in−1

~  S in−1 ( k )  = φ i log ~  + (1 − φi )µ in−2 ( ) S k  in−2  = φi rin−1h + (1 − φi ) µ in−2

And volatility γ i is assumed to be a constant. The volatility of sales is set to be greater than the 11

volatility of market rents. (3) The discount rate D( n) represents the present value of ¥1 at time n in the future, which can be expressed as (4.5)

D ( n) = ( 1 + r ( n) )− nh

where r0 (n ) is the spot rate (annualized) for the period nh determined by the term structure of interest rates. From the perspective of the arbitrage pricing theory, it is natural to use a discount rate based on spot rates given by the term structure of interest rates, which is given at 0. In this case, the discount rate differs depending on the timing of the cash flows. The discount rate used in the traditional static DCF valuation model is the exogenous cap rate r* (a constant regardless of the timing of the cash flows) that reflects the complex risks associated with the uncertain profitability of real estate investments and thus includes a risk premium in addition to risk-free rate. (4.6)

r0 (n ) = r *

Accordingly, in the case of an exogenous cap rate, a frequent subject of debate is how the cap rate is determined. There should be a variety of expected values, given that there are a variety of investors using a variety of cap rates. From a DDCF perspective, even in the case of a flat term structure of interest rates as in (4.6), the interest rate used is risk-free rate with no risk premium. Risk is derived directly from the probability distribution of DDCF values. In this paper, we use a constant term structure of interest rates and continuously compounded rates.

5

Valuation using Monte Carlo simulation

We use Monte Carlo simulation to derive the distribution of DDCF values of a commercial retail ~ ~ ~ property. Let X in = λi X n , where λi represents a rent adjustment for the type of business, X n is the market rent, and the process is as described by the log DD process in（4.1）. Below, we consider the case in which λi = 1 . As a base case, we use the following basic parameters for the market rent process: (5.1)

initial drift µX 0 = 0% , volatility γ X = 5% , initial market rent X 0 = 1 （¥/3.3m2）, and smoothing parameter φX = 0.2

Unless otherwise noted, we use these base-case parameters. For the sales process in (4.3), we use the following basic parameters with the variation in sales greater than the variation in rent: (5.2) initial drift μ＝0, smoothing parameter φ＝0.2, and volatility γ＝0.2 12

We also simply outline the case in which sales volatility is 10%. The expected value of a retail space is the product of the mean of the distribution and the size of the space. Our analysis here does not address the issue of choosing between risk and return in the case of multiple tenants (tenant portfolio). Combinations of tenant-replacement rules and lease agreement structures In the following simulation, we consider lease agreement structures and tenant management in terms of: [5-1] A contract with a fixed rent only (α = 0 ) and no replacement of tenants [5-2] The inclusion of a percentage rent (α > 0 ), but no replacement of tenants [5-3] A percentage rent and 100% replacement of tenants each period [5-4] The inclusion of a percentage rent (α > 0 ), with the following types of rules for tenant replacements: (I) Average sales growth rate (ASGR) (II) Sales Level of two years and six months later after the contract [5-5] The same case as [5-4] but with sales volatility of 10% Each distribution is based on 100,000 paths. Case [5-1] is based on the old House Lease Law, and all the other cases are based on the new House Lease Law of 2000 in Japan. [5-1] Fixed rent and no replacement of tenants (old House Lease Law) With αi = 0 , i.e. no percentage rent and a fixed rent only, we analyze the DDCF distribution. The uncertainty in deriving the DDCF distribution for the property is the risk of variation in market rents, which determine the initial rent for each contract period. (a) First, we consider changes in the DDCF value distribution corresponding to changes in the volatility γ X of market rent process. Table 5-1 (a) and Figure 5-1 (a) show the different DDCF distributions in response to changes in the volatility γ X , which is most sensitive to the DDCF property values. Figure 5-1 (a) shows the density function and the distribution function. From the table and figure, it is evident that changes in γ X have a significant impact on the forms of DDCF distribution. Specifically, when γ X increases, we observe the following. 1) The expected value of the distribution is relatively stable up to about 5%, but the standard deviation rises sharply. 2) The skewness and kurtosis increase, skewing the distribution to the right. For a change in rent of up to about 5% annualized, the distributions have somewhat thick tails, but are similar to symmetrical normal distributions. 3) As risk measures, the minimum, the bottom 5%, and the bottom 10% consistently decrease, and the risk increases substantially. 4) As evident from the graphs of the distribution function, the distribution changes at around 311.2

13

in response to changes in γ X , and the probability below that is roughly 0.46. In addition, the maximum and the upper percentage groups increase, making the structure a high-risk, high-return one. The basic statistics of the DDCF distribution for the base case (5.1) are summarized; (5.3) Average 316.8 Standard deviation 48.94 Negative semi-deviation 31.77 Minimum 174.2 Bottom 5% 245.4 Bottom 10% 258.3 The criteria for valuing the real option obtained as a result of the transition from the old House Lease Law to the new one are the average and negative semi-deviation. (b) Next, consider changes in the initial drift µ0 from the base case. As Table 5-1 (b) shows, the distribution shifts to the right as µ0 increases, and the standard deviation also increases, albeit slightly. Also as µ0 increases, the probability for larger DDCF values gets larger. This trend is related to the setting of γ X = 0.05 , but there is no indication of a significant change in the shape of the distribution. Also, the minimum and the lower percentage quantile increase, and the risk decreases. (c) Finally, consider changes in the drift smoothing parameter φX . When φX is 0, the drift stays at its initial value (0 in the base case), and as φX approaches 1, the change in the drift becomes volatile. Perhaps because γ X = 0.05 , the shape of the distribution did not change that much, as shown in Table 5-1(c) and Figure 5-1(c). In sum, when the volatility of market rents is about 5%, the DDCF value distribution does not depend significantly on the values for φX and µX 0 , and is roughly similar to a normal distribution although in general terms not a normal distribution. Table 5-1(a). Dependence of property values on γ χ

1 2 5 10 20

Semi- Skewness Kurtosis Minimum Average Standard Semideviation deviation deviation2

311.2 311.8 316.8 336.7 429.9

9.44 19.05 48.94 110.48 352.22

6.57 13.02 31.77 64.64 154.15

10.20 16.09 31.77 52.26 78.90

0.11 0.25 0.61 1.35 4.92

2.993 3.114 3.729 6.482 79.396

273.6 243.9 174.2 108.8 61.4

Bottom 5%

296.0 282.0 245.4 198.4 139.7

Bottom 10%

299.2 288.1 258.3 218.4 164.9

Median

311.0 311.0 312.1 316.7 330.7

Top 10%

323.5 336.7 381.2 479.6 790.8

Top 5%

Maximum

327.0 352.2 344.5 413.0 404.1 656.1 543.0 1382.5 1043.7 15736.9

Note: Property values corresponding to γ values of 1，2，5，10，and 20%, with φ＝0.2，μ0＝0%，and X0＝1.

Table 5-1(b). Dependence of property values on μ µ

0 1 2 5 10 20 50

Semi- Skewness Kurtosis Minimum Average Standard Semideviation deviation deviation2

317.1 318.1 319.4 322.9 329.9 343.7 388.8

49.16 49.23 49.44 50.13 51.29 53.62 61.77

31.90 31.93 32.09 32.55 33.36 34.80 40.15

31.75 31.15 30.56 28.96 25.86 20.39 8.90

0.616 0.614 0.612 0.599 0.607 0.619 0.608

3.730 3.667 3.704 3.604 3.772 3.754 3.722

174.4 167.3 164.3 182.7 178.1 189.0 204.6

Bottom 5%

245.6 246.4 247.1 249.6 254.7 265.6 298.6

Bottom 10%

258.4 259.3 260.4 263.0 268.4 279.7 314.8

Median

312.3 313.3 314.6 318.0 325.1 338.6 383.0

Top 10%

381.8 382.8 384.4 389.4 397.6 414.3 469.7

Top 5%

405.1 406.4 407.8 412.9 421.6 439.3 499.2

Maximum

665.3 606.9 654.0 613.2 753.9 710.4 794.8

Note: Property values corresponding to μ= 0~50%, with φ＝0.2，γ＝5%， and X0＝1.

Table 5-1(c). Dependence of property values on φ

14

φ

0.0 0.2 0.4 0.5 0.6 0.8 1.0

Semi- Skewness Kurtosis Minimum Average Standard Semideviation deviation deviation2

317.1 318.1 319.4 322.9 329.9 343.7 388.8

49.16 49.23 49.44 50.13 51.29 53.62 61.77

31.90 31.93 32.09 32.55 33.36 34.80 40.15

31.75 31.15 30.56 28.96 25.86 20.39 8.90

0.616 0.614 0.612 0.599 0.607 0.619 0.608

3.730 3.667 3.704 3.604 3.772 3.754 3.722

174.4 167.3 164.3 182.7 178.1 189.0 204.6

Bottom 5%

245.6 246.4 247.1 249.6 254.7 265.6 298.6

Bottom 10%

258.4 259.3 260.4 263.0 268.4 279.7 314.8

Median

312.3 313.3 314.6 318.0 325.1 338.6 383.0

Top 10%

381.8 382.8 384.4 389.4 397.6 414.3 469.7

Top 5%

405.1 406.4 407.8 412.9 421.6 439.3 499.2

Maximum

665.3 606.9 654.0 613.2 753.9 710.4 794.8

Note: Property values corresponding to φ values of 0，0.2，0.4，0.5，0.6，0.8，and 1, with γ＝5%，μ0＝0%，and X0＝1.

Figure 5-1(a1). Dependence of property values on γ

Figure 5-1(b1). Dependence of property values on μ

Figure 5-1(c1). Dependence of property values on φ

15

[5–2] Mix of fixed and percentage rents, but no replacement of tenants Next, let us consider the case involving variable rents. The sales process is similar to the market rent process, and the changes in the shape of the distribution in response to changes in the parameters are similar. Hence, we omit an analysis of this case, but present some results with percentage rents. This case, however, involves risk since tenants are not replaced, and can thus be considered an extension of cases based on the old House Lease Law. The base case for the market rent process is (5.1). The base case for the sales process is as in (5.2), with μ＝0, φ＝0.2, and γ＝0.2, and the assumption that sales variation risk is greater than market rent variation risk. We analyzed the following three cases: β = 0.713 . This case corresponds to the case where the expected value of the DDCF distributions with the fixed (market) rent derived from 100,000 trials is the same as the expected value of the DDCF Distribution with percentage rent (the contract sales portion) (Table 5-2(a), Figure 5-2(a)) (b) Changes in the percentage-rent weighting β and α , with δ = 0.9 and the rent discounted in exchange for the right to ask the tenant to leave (Table 5-2(b), Figure 5-2(b)) (c) β = 1 (Table 5-2(c), Figure 5-2(c)) (a)

From the tables, the following are evident. In all the cases above, the use of percentage rents leads to an increase in the standard deviation of the distribution. The correlation coefficient for the values of the fixed-rent portion and the percentage-rent portion is a very low –0.005. Such a result is significant for property management companies in terms of reducing market rent risk, but the benefits are not all that great since the variation in percentage rents is substantial. To take a specific example, Table 5-2(a) corresponds to the case of a fixed average and the use of a percentage rent. If we increase the weighting α of this percentage rent, the standard deviation naturally increases, but the skewness and kurtosis also increase significantly. Among the key indicators for downside risk, the bottom 5% and 10% quantiles decline consistently, and the downward semi-deviation increases consistently, indicating an increase in risk. Accordingly, this case is not a desirable one for the property management company. Table 5-2(b) is for the case in which the initial rent is at a 10% discount to the market rate, and β changes in response to changes in α. In terms of the relationship between the mean and the standard deviation, this case is not better for the property management company than the one in (a). The values for the bottom 5% and 10% are lower than in case (a), and the risk is significant. For the case in Table 5-2(c), we depart from the initial fixed rent and determine the percentage rent based on α%. Compared with the case in which α＝0 (fixed rent only), an increase in α leads to an increase in the mean and standard deviation, and is thus a high-risk, high-return structure. However, among the key indicators for downside risk, the bottom 5% and 10% both increase when α = 0.1 ,0.2 , compared with when α=0, and hence the risk declines. Similarly, the downward semi-deviation② (the normalized expected value in the case of a fixed rent only) declines, 16

indicating a decline in the risk. Accordingly, in this case the property management company has the possibility of increasing earnings by applying tenant-replacement rules. Figure 5–2(c) illustrates the distribution function, but the actual distribution function for α = 0.1 ,0.2 is further to the right than in the case when α=0, and hence the probabilities are better(the DDCF distributions with α = 0.1 ,0.2 are stochastically larger). In this sense, a 20% weight for percentage rent could be considered appropriate, even without tenant replacement, as long as the variation in sales is in line with our assumption . However, this assumes that a good choice of tenant is made in the first place. Table 5-2(a). Change in the DDCF distribution with percentage rents ( β = 0.713 ) Semi- Skewness Kurtosis Minimum Average Standard Semideviation deviation deviation2

α

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

317.0 317.0 317.0 317.0 317.0 317.0 317.0 317.0 317.0 317.0 317.0

β

Note:

49.04 52.65 69.46 92.53 118.25 145.23 172.87 200.90 229.18 257.62 286.19

31.83 32.78 37.85 45.13 53.97 63.93 74.67 85.92 97.54 109.41 121.46

31.74 32.70 37.76 45.03 53.87 63.83 74.56 85.82 97.44 109.31 121.35

0.615 1.224 3.126 4.344 4.912 5.176 5.304 5.367 5.398 5.412 5.416

3.734 10.102 39.519 62.048 73.205 78.513 81.113 82.417 83.064 83.364 83.474

Bottom 5%

173.1 172.9 162.2 151.3 140.4 124.9 106.8 88.8 70.7 52.6 29.4

245.4 243.9 235.1 223.0 208.5 192.1 174.1 154.6 134.0 112.4 90.0

Bottom 10%

258.4 256.7 248.1 236.2 221.9 205.8 188.3 169.6 150.0 129.8 109.2

Median

312.3 310.9 305.6 297.8 289.0 280.0 270.8 262.0 253.5 245.3 237.2

Top 10%

381.1 383.4 394.8 412.3 436.0 461.2 487.7 514.7 542.5 570.8 598.8

Top 5%

Maximum

404.5 680.3 409.2 1424.5 432.4 2587.8 470.8 3751.1 514.1 4914.4 560.3 6077.7 607.3 7241.0 654.6 8404.4 701.8 9567.7 749.8 10731.0 798.0 11894.3

is chosen so that the average real estate value is constant.

Table 5-2(b). Change in DDCF distribution with percentage rents ( δ = 0.9 ) Semi- Skewness Kurtosis Minimum Average Standard Semideviation deviation deviation2

α

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

285.3 298.0 310.8 323.6 336.3 349.1 361.8 374.6 387.4 400.1

β

Note:

44.13 56.19 87.38 124.03 162.48 201.71 241.33 281.18 321.18 361.28

28.64 32.85 43.15 56.28 71.04 86.74 102.99 119.57 136.37 153.33

50.43 45.47 47.24 51.66 57.57 64.39 71.82 79.66 87.78 96.11

0.615 2.171 4.224 4.956 5.223 5.332 5.381 5.404 5.413 5.416

is chosen so that the discount rate

δ

3.734 23.602 59.732 74.081 79.455 81.699 82.713 83.184 83.395 83.474 is 0.9; no

Bottom 5%

155.8 157.7 149.8 142.0 127.0 110.3 93.6 77.0 60.3 37.1

β

220.8 225.8 220.5 211.0 198.5 184.0 167.9 150.6 132.4 113.6

results in

Bottom 10%

232.5 237.9 233.4 224.6 213.1 199.8 185.4 170.0 154.0 137.9

Median

281.0 290.4 293.1 293.9 294.3 294.6 295.4 296.5 298.0 299.5

Top 10%

343.0 364.8 401.5 448.0 497.2 548.0 599.5 651.3 703.8 755.9

Top 5%

364.0 393.8 455.9 530.5 608.6 687.8 767.4 846.6 927.1 1007.3

α = 0 , and so this case is omitted.

Maximum

612.3 1877.3 3519.6 5161.8 6804.0 8446.3 10088.5 11730.7 13372.9 15015.2

Table 5-2(c). Change in DDCF distribution with percentage rents ( β = 1 ) Semi- Skewness Kurtosis Minimum Average Standard Semideviation deviation deviation2

α

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Note:

317.0 329.7 342.5 355.2 368.0 380.8 393.5 406.3 419.1 431.8 444.6

β

49.04 59.72 89.43 125.29 163.30 202.25 241.69 281.41 321.31 361.32 401.42

31.83 35.61 45.35 57.92 72.22 87.56 103.54 119.92 136.57 153.40 170.36

31.74 28.00 29.78 33.79 39.22 45.64 52.78 60.41 68.40 76.63 85.04

0.615 1.880 3.955 4.811 5.144 5.289 5.357 5.390 5.406 5.414 5.416

3.734 19.170 54.635 71.185 77.868 80.804 82.200 82.894 83.242 83.408 83.474

173.1 176.1 168.2 160.4 148.5 131.8 115.2 98.5 81.8 65.1 41.3

Bottom 5%

245.4 251.1 246.5 237.9 226.5 212.8 197.5 181.0 163.3 145.1 126.2

Bottom 10%

258.4 264.5 260.7 252.8 242.2 229.7 215.8 201.0 185.3 169.4 153.2

Median

312.3 322.0 325.3 326.4 326.8 327.0 327.8 328.6 329.6 331.2 332.7

Top 10%

381.1 402.1 437.1 482.0 530.4 580.8 631.4 683.5 735.2 787.5 839.9

Top 5%

404.5 432.4 490.6 563.8 641.1 720.4 799.3 879.1 958.7 1038.9 1119.3

Maximum

680.3 1903.5 3545.7 5187.9 6830.2 8472.4 10114.6 11756.8 13399.1 15041.3 16683.5

is set to 1.

17

Figure 5-2. Sample paths for sales

Figure 5-2(a). Change in DDCF distribution with percentage rents ( β = 0.709 )

Figure 5-2(b). Change in DDCF distribution with percentage rents ( δ = 0.9 )

18

Figure 5-2(c). Change in DDCF distribution with percentage rents ( β ＝1)

[5–3] Mix of fixed and percentage rents and 100% replacement of tenants each period We next consider the use of percentage rents and active replacement of tenants. We provide our simulation results for the most extreme case, in which all tenants are replaced at the end of each contract period, with all other conditions the same as in the previous case. (a) β = 0.709 (Table 5-3 (a), Figure 5-3 (a)) (b) δ = 0.9 , β changed (Table 5-3 (b), Figure 5-3 (b)) (c) β = 1 (Table 5-3 (c), Figure 5-3 (c)) Unlike in the previous case, when we increase the weight of the percentage rent, the standard deviation is significantly smaller even though the mean increases, since the replacement of tenants at each contract period leads to a divergence in rent and sales paths and a reversion to original fixed-rent levels. Downside risks also increase. However, in cases (a) and (b), the mean declines by more than in the case of a fixed rent only. In case (c), however, both α and the mean increases, and risk declines since the minimum, the bottom 5%, and the bottom 10% increase. In addition, in case (c), the minimum is slightly lower than in the case of a fixed rent only (α=0), even when the percentage rent weight is 100%, but is almost the same. The values for the lower percentage quantiles also increase, corresponding to a decline in risk. In this sense, this case is a noteworthy one, and these are observed in Figures 5-3(a)(b)(c). In comparing cases 5-2(c) and 5-3(c), we can make several points. When the new House Lease Law does not apply, the use of percentage rents is very risky as long as the original tenant stays. The increase in risk is greater than the increase in return. On the other hand, when the new House Lease Law can be fully utilized and tenants are replaced each contract period, the return can be increased while holding down the risk. Accordingly, the use of tenant-replacement rules to select high-sales tenants can increase the average property value and at the same time minimize risk. We look at this in section 5-4.

19

Table 5-3(a). Change in DDCF distribution with percentage rents ( β ＝0.713) Semi- Skewness Kurtosis Minimum Average Standard Semideviation deviation deviation2

α

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

317.0 308.6 300.3 292.0 283.6 275.3 267.0 258.6 250.3 242.0 233.6

49.04 47.77 46.57 45.42 44.35 43.34 42.41 41.57 40.81 40.15 39.58

31.83 31.01 30.22 29.48 28.78 28.13 27.52 26.97 26.47 26.03 25.65

β is set at 0.709．

Note:

31.74 36.16 40.98 46.20 51.81 57.77 64.07 70.67 77.54 84.64 91.95

0.615 0.614 0.614 0.614 0.615 0.615 0.616 0.618 0.619 0.622 0.625

3.734 3.735 3.737 3.739 3.742 3.746 3.751 3.757 3.764 3.771 3.779

173.1 169.4 165.7 162.0 158.3 154.0 147.7 141.1 134.1 127.1 120.1

Bottom 5%

245.4 238.8 232.3 225.6 218.9 212.1 205.0 197.9 190.7 183.4 175.9

Bottom 10%

Median

258.4 251.6 244.7 237.7 230.7 223.6 216.4 209.1 201.6 194.1 186.4

312.3 304.0 295.9 287.6 279.3 271.1 262.9 254.7 246.4 238.0 229.7

Top 10%

381.1 371.3 361.4 351.6 341.9 332.3 322.7 313.3 303.9 294.7 285.5

Top 5%

404.5 393.8 383.3 372.8 362.6 352.6 342.6 332.9 323.4 313.9 304.4

Maximum

680.3 671.5 662.7 654.0 645.2 636.4 627.6 618.8 610.1 601.3 592.5

Table 5-3(b). Change in DDCF distribution with percentage rents (δ＝0.9) Semi- Skewness Kurtosis Minimum Average Standard Semideviation deviation deviation2

α

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

285.3 286.3 287.4 288.5 289.6 290.6 291.7 292.8 293.8 294.9

β

Note:

44.13 44.35 44.69 45.14 45.70 46.36 47.12 47.98 48.93 49.96

28.64 28.79 29.01 29.30 29.65 30.08 30.57 31.11 31.72 32.38

50.43 49.74 49.13 48.60 48.14 47.75 47.43 47.17 46.98 46.86

0.615 0.614 0.614 0.615 0.615 0.617 0.618 0.620 0.622 0.625

is chosen so that the discount rate

δ

3.734 3.736 3.739 3.743 3.747 3.753 3.759 3.766 3.773 3.779 is 0.9; no

155.8 157.6 159.4 161.2 161.5 160.1 158.1 155.9 153.8 151.7

β

Bottom 5%

220.8 221.6 222.2 222.6 222.8 222.9 222.9 222.7 222.4 222.1 results in

Bottom 10%

Median

232.5 233.4 234.0 234.6 235.0 235.4 235.6 235.6 235.5 235.3

281.0 282.1 283.1 284.1 285.1 286.2 287.2 288.1 289.1 290.0

Top 10%

343.0 344.6 346.0 347.8 349.6 351.6 353.7 355.9 358.1 360.4

Top 5%

364.0 365.4 367.0 368.9 371.1 373.4 376.0 378.7 381.5 384.3

α = 0 , and so this case is omitted.

Maximum

612.3 627.4 642.4 657.5 672.6 687.7 702.7 717.8 732.9 748.0

Table 5-3(c). Change in DDCF distribution with percentage rents ( β ＝1) Semi- Skewness Kurtosis Minimum Average Standard Semideviation deviation deviation2

α

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Note:

317.0 318.0 319.1 320.2 321.3 322.3 323.4 324.5 325.5 326.6 327.7

β

49.04 49.25 49.57 49.99 50.51 51.13 51.83 52.63 53.51 54.47 55.51

31.83 31.97 32.17 32.45 32.78 33.17 33.63 34.14 34.70 35.31 35.97

31.74 31.23 30.80 30.44 30.14 29.91 29.75 29.64 29.60 29.61 29.67

0.615 0.614 0.614 0.615 0.615 0.616 0.617 0.619 0.621 0.623 0.625

3.734 3.736 3.738 3.742 3.745 3.750 3.755 3.761 3.767 3.773 3.779

173.1 174.9 176.7 178.5 180.1 178.7 177.1 174.9 172.8 170.7 168.5

Bottom 5%

245.4 246.1 246.8 247.2 247.6 247.7 247.7 247.6 247.4 247.1 246.7

Bottom 10%

Median

258.4 259.2 259.9 260.5 261.0 261.4 261.6 261.8 261.7 261.6 261.5

312.3 313.3 314.3 315.4 316.4 317.4 318.5 319.4 320.3 321.3 322.3

Top 10%

381.1 382.7 384.2 385.9 387.7 389.5 391.5 393.7 395.9 398.1 400.5

Top 5%

404.5 405.8 407.3 409.2 411.3 413.6 415.9 418.6 421.3 424.2 427.0

Maximum

680.3 695.4 710.5 725.5 740.6 755.7 770.8 785.8 800.9 816.0 831.1

is set to 1.

Figure 5-3. Sample paths at the time tenant replacement adopted

20

Figure 5-3(a). Distribution of property values as a result of tenant management ( β ＝0.709)

Figure 5-3(b). Distribution of property values as a result of tenant management (δ＝0.9)

Figure 5-3(c). Distribution of property values as a result of tenant management ( β ＝1)

21

[5–4] Mix of fixed and percentage rents, and use of tenant-replacement rules In this section, we analyze cases of tenant management using tenant-replacement rules. In the case of a weighting of 50% for percentage rents, we set α = 0.5, β = 1 . Specifically, we analyze how tenant management—based on two types of tenant-replacement rules, (I) average change in sales and (II) level of contract sales—affects the DDCF distribution of property values. The parameters are the same as in the previous section. (I) Average sales growth rate tenant-replacement rule (ASG-TR rule) Table 5-4I(a) shows the results of our property valuation simulation with two-year average sales growth rate(ASG) as the tenant-replacement rule. In addition, Table 5-4I(b) shows the proportions of contract extensions at the end of each contract period. We denote the threshold value c(k) for the average change in sales in (3.12) as c. When c = −0.4 , the most relaxed criterion in this analysis, the probability of contract extension at the end of each contract period is about 90%, as shown in Table 5-4I(b). As a result, the shape of the distribution is almost the same as the one in the case in which the ASG-TR rule is not used (Table 5-2(c)). As c is increased and approaches 0, the probability of contract extension declines. Accordingly, the standard deviation of the distribution also declines. By contrast, the mean and the median increase as c approaches –0.1 (low risk, high return). This could be said to be the result of replacing tenants with ASG likely to be on the decline. In this zone, the shape of the distribution narrows and shifts overall to the right, a situation that approaches one preferable for a property management company that aims for earnings while avoiding risk. When c is greater than 0, the mean and the median decline. With the given parameters, the optimal case is when c=0. Given the sales process parameters and the ASGTR rule in this case, the contract extension probability is about 75% when c = −0.1 , 50% when c = 0 , and 25% when c = 0.1 . In addition, as shown in Table 5-4I(b), there are no evident differences in contract extension probabilities when the contract is renewed for 10 three-year periods. In other words, even renewing tenants with high ASG as of the end of the previous contract period have ASG three years later that is about the same as that of new tenants. The reason is that it is difficult to sustain high ASG for an extended period. In any case, when the proportion is 50% each period, it is probably not desirable to have a change in tenants. Compared with the old House Lease Law, the value of the option under the new House Lease Law with a 50% percentage rent contract and a tenant-replacement rule of c = −0.1 is 400.6− 316.8＝83.8, which is quite significant. In addition, the risk is quite minimal, in terms of lower semi-deviation②. Another effect of tenant rebalancing is a decline in the correlation between fixed and percentage rents. The correlation coefficients between market and percentage rents based on various criteria are shown in Table 5-4I(c). As c increases and the probability of contract extension declines, the correlation coefficient increases. Since lease agreements with new tenants are based on market rents, repeated signing of new contracts leads to percentage rents that are also strongly affected by market rents.

22

Table 5-4I (a). ASG-TR rule Semi- Skewness Kurtosis Minimum Average Standard Semideviation deviation deviation2

c

-0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.5 Note:

382.2 388.1 399.8 400.8 377.3 351.2 334.3 326.2 323.3 322.6 β is

199.08 87.16 44.66 196.81 85.91 40.48 187.53 80.69 30.44 162.00 68.14 20.57 114.83 52.49 19.52 74.88 42.00 23.04 58.91 36.84 26.87 53.69 34.54 29.14 51.95 33.66 29.93 51.49 33.43 30.10 set at 1; c is annualized.

4.547 49.594 4.616 50.980 4.947 58.197 5.817 82.270 6.841 141.216 3.336 52.813 1.122 8.523 0.688 4.014 0.627 3.766 0.605 3.654

Bottom 5%

144.8 144.8 154.4 175.8 181.5 177.1 172.2 172.2 172.2 172.2

214.1 221.1 240.4 263.7 266.6 259.3 252.5 248.8 247.9 247.6

Bottom 10%

231.7 239.0 259.1 281.0 282.9 274.4 266.8 262.6 261.3 261.1

Median

329.1 336.6 353.3 364.7 356.9 340.7 327.6 320.6 318.1 317.6

Top 10%

Top 5%

580.8 581.4 576.7 541.2 481.7 436.3 410.0 396.7 391.9 390.7

Maximum

719.0 718.7 708.3 651.0 544.2 473.1 437.9 422.1 415.8 414.4

5557.7 5557.7 5557.7 5557.7 5116.1 3160.5 1312.7 755.8 721.4 646.2

Table 5-4I (b). Contract extension probabilities with the ASG-TR rule ｃ

-0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.5

1 99.7% 97.9% 91.1% 75.0% 49.7% 24.8% 8.7% 2.0% 0.3% 0.0%

2 99.7% 97.8% 91.1% 74.9% 50.0% 24.9% 8.9% 2.2% 0.4% 0.0%

3 99.7% 97.9% 91.2% 75.1% 50.2% 25.3% 8.9% 2.1% 0.3% 0.0%

4 99.6% 97.8% 91.1% 74.8% 49.9% 24.9% 8.8% 2.2% 0.3% 0.0%

5 99.7% 97.9% 91.4% 75.2% 49.8% 25.0% 8.9% 2.1% 0.3% 0.0%

6 99.6% 97.8% 91.1% 75.1% 49.9% 25.0% 8.8% 2.1% 0.3% 0.0%

7 99.7% 97.9% 91.3% 75.2% 50.0% 25.2% 8.8% 2.1% 0.3% 0.0%

8 99.7% 97.9% 91.4% 75.1% 49.9% 24.8% 8.9% 2.1% 0.3% 0.0%

9 99.6% 97.8% 91.2% 75.1% 49.8% 24.9% 8.8% 2.1% 0.3% 0.0%

Note: c is annualized; the column headers 1-9 represent three-year contract periods.

Table 5-4I (c). Correlation between fixed and percentage rents with the ASGR rule ｃ -0.4 Correlation -0.003

-0.3 0.007

-0.2 0.045

-0.1 0.125

0.0 0.252

0.1 0.457

0.2 0.677

0.3 0.819

0.4 0.885

0.5 0.907

Note: c is annualized

Figure 5-4 I. Sample paths by K values

Note: The natural log of sales is used to make it easier to distinguish sales trends and tenant replacements for different values of c for the same sample path.

23

Table 5-4I (a). DDCF distribution with ASG-TR rule

(II) Sales Level tenant-replacement rule (SL-TR rule) Table 5-4II(a) shows the simulation results for the DDCF distribution in the case of a tenant-replacement rule (3.13) based on the level of contract sales two years and six months later, which we call SL-TR rule. The threshold value for the rule in (3.13) is denoted by c. In addition, Table 5-4II(b) shows the contract extension probabilities at the end of each contract period. As in the case of the sales growth replacement rule, the contract extension probabilities decline as the criteria become stricter (increase) (Table 5-4II(b)). However, unlike in the case of the ASG-TR rule, the contract extension probabilities increase as time passes. It should be obvious that the sales of tenants that have strong business and have their contracts renewed have higher sales than new tenants do. When c=1 and tenants are required to maintain the sales level at the time they took occupancy, about 50% of the tenants are able to satisfy this criterion at the end of the first contract period. This proportion increases steadily, to about 60% by the second contract period and to 77.6% by the ninth contract period. The shape of the distribution changes as a result of changes in the contract extension probability related to changes in criteria. When c=1, the standard deviation of the distribution is large, but the mean and the median increase and the distribution overall shifts to the right, while the downside risk diminishes. The values for the lower 5% and 10% quantiles are larger in the case of SL-TR rule with c = 1 than in the case of ASG-TR rule with c = −0.1 . That the SL-TR rule is better is also evident from the decline in the lower semi-deviation②. Compared with the results for the fixed-rent base case (5.3), the mean is much higher; the minimum and the values for the lower quantiles 5% and 10% are higher; the lower semi-deviation ② is lower; and the downside risk is smaller. In this sense, the value of the option stemming from the new House Lease Law is very high (439.4−316．8＝122.6) and the lower semi-deviation② quite small.

24

Table 5-4II (a). DDCF Distribution with the SL-TR rule Semi- Skewness Kurtosis Minimum Average Standard Semideviation deviation deviation2

c

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 Note:

384.4 399.2 417.5 433.6 438.4 427.1 405.3 381.1 361.0 347.0 β is

195.23 83.67 39.23 190.68 80.15 27.92 190.62 79.73 19.54 193.52 81.95 16.29 195.84 85.00 18.23 194.15 85.30 22.37 184.99 79.61 25.85 167.65 68.79 28.01 145.66 57.43 29.13 124.42 48.76 29.67 set at 1; c is annualized.

4.468 45.893 4.649 49.015 4.864 56.860 4.792 55.416 4.615 52.350 4.637 53.864 4.944 61.755 5.681 82.054 6.247 94.099 7.037 124.495

Bottom 5%

154.4 173.9 176.6 176.6 174.5 174.5 174.5 174.5 174.5 174.5

226.6 248.5 266.2 275.6 269.2 257.6 251.5 249.1 248.1 247.7

Bottom 10%

242.0 263.2 282.0 293.7 290.6 276.9 267.9 263.8 262.3 261.7

Median

Top 10%

329.4 345.2 364.4 381.2 388.3 380.1 357.5 336.2 325.6 320.8

Top 5%

579.0 585.1 601.7 621.5 629.9 616.0 581.8 535.5 484.0 441.2

Maximum

718.0 724.3 743.3 762.2 771.0 753.6 714.0 654.5 584.8 524.1

5607.3 5607.3 6394.1 6394.1 6394.1 6394.1 6394.1 6394.1 5607.3 5607.3

Table 5-4II (b). Contract extension probabilities with the SL-TR rule 1 100.0% 99.7% 93.6% 74.5% 49.5% 28.9% 15.5% 7.8% 3.8% 1.9%

ｃ

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 Note:

β

2 99.9% 96.7% 88.0% 78.0% 61.7% 41.4% 24.2% 13.1% 6.7% 3.4%

3 99.5% 95.1% 89.4% 81.2% 67.2% 48.3% 30.4% 17.3% 9.3% 4.9%

4 98.9% 94.8% 90.3% 82.9% 70.7% 53.0% 35.4% 20.9% 11.7% 6.4%

5 98.5% 95.0% 91.0% 84.4% 72.8% 56.4% 38.8% 24.0% 13.9% 7.8%

6 98.2% 95.2% 91.6% 85.4% 74.6% 59.0% 41.9% 26.8% 16.1% 9.3%

7 98.0% 95.5% 92.2% 86.2% 76.1% 61.2% 44.2% 29.1% 18.1% 10.9%

8 98.0% 95.6% 92.4% 86.9% 77.0% 62.4% 46.0% 31.3% 19.8% 12.2%

9 97.9% 95.9% 92.8% 87.1% 77.6% 63.6% 47.9% 33.1% 21.5% 13.6%

is set at 1; c is annualized; the column headers 1-9 represent three-year contract periods.

Table 5-4II (c). Correlation between fixed and percentage rents with the SLR rule ｃ

Correlation

0.2 0.006

0.4 0.024

0.6 0.043

0.8 0.069

1.0 0.113

1.2 0.171

1.4 0.227

1.6 0.274

1.8 0.314

2.0 0.348

Note: c is annualized

Figure 5-4II. Sample paths

Note: The natural log of sales is used to make it easier to distinguish sales trends and tenant replacements for different values of K for the same sample path.

25

Figure 5-4II (a). Distribution of DDCF values with the SL-TR rule

[5-5] Sales volatility γ of 10% (I) ASG-TR rule When Sales volatility γ is 10%, Table 5-5I(a) shows the characteristics of the DDCF value distribution with ASG-TR rule, and Figure 5-5I(b) illustrates the distribution. The return and downside risk are optimal when the threshold value c = –0.1 or 0. Compared with the case in which c = 0 and the fixed rent base case, the average is higher (337.2) and the minimum is lower, but the mean and the values for the lower percentage points are higher, resulting in overall smaller downside risk. In addition, as shown in Table 5-5I(b), the contract extension probabilities are about the same as in the case when sales volatility is 20% (Table 5-4I(b)), and tenant replacement occurs when the proportion is 50%. Table 5-5I(a). Characteristics of value distribution with ASG-TR rule c

Semi- Skewness Kurtosis Minimum Bottom Average Standard Semideviation deviation deviation2 5%

-0.4 327.5 -0.3 327.5 -0.2 328.4 -0.1 339.0 0.0 337.2 0.1 322.8 0.2 318.5 0.3 318.2 0.4 318.2 0.5 318.2 Note: β is

64.55 39.12 32.72 64.55 39.12 32.72 64.31 38.98 32.08 61.11 37.27 24.67 54.56 34.86 23.56 50.65 32.88 29.46 49.69 32.26 31.35 49.61 32.22 31.47 49.61 32.21 31.47 49.61 32.21 31.47 set at 1; c is annualized.

1.135 1.135 1.136 1.121 0.771 0.611 0.610 0.609 0.609 0.609

5.719 5.718 5.733 5.891 4.524 3.694 3.681 3.680 3.681 3.681

163.0 163.0 163.0 180.0 168.9 151.6 151.6 151.6 151.6 151.6

241.8 241.8 242.9 256.8 259.2 249.0 246.1 245.9 245.9 245.9

Bottom 10%

255.9 255.9 257.0 270.7 273.2 262.3 259.2 259.0 259.0 259.0

Median

317.9 317.9 318.9 330.5 331.5 318.0 313.7 313.5 313.5 313.5

Top 10%

411.0 411.0 411.6 417.2 408.0 389.4 384.0 383.6 383.6 383.6

Top 5%

446.0 446.0 446.5 450.4 434.9 413.5 407.3 406.7 406.7 406.7

Maximum

921.4 921.4 921.4 921.4 913.8 639.7 613.7 613.7 613.7 613.7

26

Table 5-5I(b). Contract extension probabilities with ASG-TR rule ｃ

-0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.5

1 100.0% 100.0% 99.7% 91.0% 49.7% 8.9% 0.3% 0.0% 0.0% 0.0%

2 100.0% 100.0% 99.6% 91.1% 49.7% 8.7% 0.4% 0.0% 0.0% 0.0%

3 100.0% 100.0% 99.6% 91.0% 50.1% 9.1% 0.4% 0.0% 0.0% 0.0%

4 100.0% 100.0% 99.6% 91.0% 49.9% 8.7% 0.3% 0.0% 0.0% 0.0%

5 100.0% 100.0% 99.7% 91.2% 50.3% 9.0% 0.3% 0.0% 0.0% 0.0%

6 100.0% 100.0% 99.6% 91.2% 50.2% 8.9% 0.4% 0.0% 0.0% 0.0%

7 100.0% 100.0% 99.7% 91.1% 50.0% 9.0% 0.4% 0.0% 0.0% 0.0%

8 100.0% 100.0% 99.7% 91.2% 49.8% 8.8% 0.3% 0.0% 0.0% 0.0%

9 100.0% 100.0% 99.6% 90.9% 50.0% 8.6% 0.3% 0.0% 0.0% 0.0%

Note: c is annualized; the column headers 1-9 represent three-year contract periods.

Figure 5-5I(a). Distribution of property values with ASG-TR rule

(II) SL-TR rule On the other hand, the use of the SL-TR rule corresponds to the case in which sales volatility is 20%. As shown in Table 5-5II(a), overall optimization is achieved when the threshold value c = 0.8 or 1, and results in a case that is better than the fixed-rent base case (5.3) as well as case (I), because of the higher return and lower downside risk. The contract extension probabilities in Table 5-5II(b) are little different from those in Table 5-4II(b), and show a consistent increase. Table 5-5II(a). DDCF Distribution with SL-TR rule c

Semi- Skewness Kurtosis Minimum Bottom Average Standard Semideviation deviation deviation2 5%

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 Note:

327.9 64.86 39.22 32.59 330.0 63.26 37.72 29.80 337.4 60.14 35.49 23.52 348.4 59.26 35.83 19.03 354.1 64.23 41.24 22.37 343.5 69.02 43.81 28.48 330.0 64.52 38.90 30.86 323.1 58.17 35.07 31.29 320.3 53.90 33.35 31.34 319.2 51.79 32.70 31.35 β is set at 1; c is annualized.

1.163 1.250 1.334 1.207 0.836 0.842 1.087 1.144 1.013 0.885

6.037 6.351 6.894 6.718 5.501 4.739 5.296 5.798 5.386 5.045

158.0 174.2 177.4 175.3 172.6 172.6 172.6 172.6 172.6 172.6

242.3 248.4 260.8 269.8 258.4 248.8 246.6 246.2 246.2 246.2

Bottom 10%

256.1 261.0 272.9 284.2 276.9 262.6 259.5 259.1 259.1 259.1

Median

318.2 319.5 327.1 339.8 349.3 336.3 317.8 314.2 313.7 313.6

Top 10%

411.2 411.4 414.0 423.0 433.6 432.1 417.8 399.1 388.4 385.0

Top 5%

447.6 447.8 449.4 456.5 465.7 464.3 450.5 433.7 417.8 410.4

Maximum

1189.6 1189.6 1189.6 1189.6 1189.6 1189.6 1029.0 1029.0 861.6 840.8

27

Table 5-5II(b) Contract extension probabilities with SL-TR rule 1 100.0% 100.0% 99.9% 91.0% 50.2% 14.0% 2.3% 0.3% 0.0% 0.0%

ｃ

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 Note:

β

2 100.0% 100.0% 97.9% 86.1% 62.1% 24.2% 5.3% 0.9% 0.1% 0.0%

3 100.0% 99.8% 96.2% 87.4% 66.6% 31.0% 8.8% 1.9% 0.3% 0.1%

4 100.0% 99.5% 95.6% 88.2% 69.1% 36.2% 12.3% 3.4% 0.8% 0.2%

5 100.0% 99.1% 95.6% 88.8% 71.0% 40.2% 15.7% 5.2% 1.5% 0.4%

6 100.0% 98.9% 95.6% 89.2% 72.3% 43.0% 18.7% 6.8% 2.3% 0.7%

7 100.0% 98.6% 95.7% 89.4% 73.1% 45.3% 21.2% 8.6% 3.2% 1.2%

8 99.9% 98.5% 95.8% 89.5% 73.8% 47.4% 23.7% 10.4% 4.3% 1.7%

9 99.9% 98.4% 95.9% 89.7% 74.2% 48.7% 25.8% 12.0% 5.4% 2.3%

is set at 1; c is annualized; the column headers 1-9 represent three-year contract periods.

Figure 5-5II(b). DDCF Distribution with SLR rule

6

Tenant replacement costs

Our discussion so far has ignored tenant replacement costs, which include space renovation costs ~ and layout modification costs. The space renovation costs associated with tenant turnover Ci ( k ) can be expressed as a function of market rents at the time the contract is signed. We specify it as ~ ~ Ci ( k ) = A + BX i 36 ( k −1) , which is a linear function of market rents at the time the contract is signed. For instance, when A = 0 and B = 12, the costs incurred by the property management company when there is a change in tenants are the equivalent of one year’s worth of market rent. Table 6-1 I(a) shows the characteristics of the value distribution in the case of ASG-TR rule and values of A = 0 and B = 6 for the cost function, i.e., costs equal to six months’ worth of market rent. Table 6-1 I(ｂ) shows the results for the same case but with a value of B = 12. Table 6-1 II(a) and (b) show the results for the same pair of cases but with SL-TR rule. Figures 6-1 I and II show the expected values and risk (here, we use lower semi-deviation②) for different replacement rules and costs. Whichever rule is used, the higher the value of c and the greater the frequency of tenant turnover, the more the expected property value is affected by costs and declines, indicating greater 28

downside risk than in the case in which tenant-replacement costs are ignored. The tables indicate that when the replacement costs are the equivalent of one year’s worth of market rent, it is possible to increase the expected property value and minimize the downside risk by using tenant-replacement rules. Also, as Figure 6-1 I (a) shows, when the replacement costs reach the equivalent of two years’ worth of market rent and a ASG-TR rule is used, the expected property value effectively does not increase as a result of the adoption of the replacement rule. However, it is evident that when a SL-TR rule is used, it is still possible to increase the expected property value, even when the replacement costs amount to three years’ worth of market rent. This point indicates that even when the replacement costs are high, the active replacement of tenants with weak sales leads to an increase in the property value. Table 6-1I(a). DDCF value distribution with ASG-TR rule and A = 0, B = 6 months c

Standard deviation

Average

-0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.5

382.2 387.6 397.8 394.7 364.9 332.9 312.5 302.7 299.4 298.6

β

Note:

197.74 195.77 186.79 162.37 112.52 72.44 56.14 50.12 47.99 47.38

SemiSemiSkewness deviation deviation2

87.22 86.06 80.97 68.37 52.24 40.83 34.86 32.09 31.02 30.73

44.60 40.76 31.46 23.20 24.71 31.24 37.59 41.20 42.40 42.64

4.503 4.594 4.954 6.214 5.743 2.997 1.130 0.730 0.641 0.616

Kurtosis

58.736 60.914 70.833 114.343 89.926 42.717 8.171 4.206 3.792 3.697

Minimum

132.7 132.7 154.1 157.1 165.1 163.4 161.7 159.6 159.6 159.6

Bottom 5%

214.1 220.6 238.0 257.1 254.6 243.7 235.0 231.0 229.9 229.7

Bottom 10%

231.6 238.7 257.0 274.7 271.1 258.2 248.4 243.7 242.3 242.1

Median

329.3 335.8 350.7 358.0 343.8 322.2 305.8 297.5 294.8 294.2

Top 10%

582.6 583.6 577.8 536.3 470.9 416.7 384.0 368.1 362.3 360.7

Top 5%

723.4 723.7 712.4 644.4 532.8 454.8 412.2 392.7 385.8 383.8

Maximum

8295.8 8295.8 8295.8 8295.8 4159.8 2588.4 1369.7 699.9 688.9 598.9

is set at 1; c is annualized

Table 6-1I(b). DDCF value distribution with ASG-TR rule and A = 0, B = 1 year c

-0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.5

Note:

Average

382.2 387.1 395.7 388.7 352.9 315.0 290.8 279.4 275.7 274.8

β

Standard deviation

197.75 195.85 187.16 163.32 113.52 72.15 53.99 46.72 44.11 43.38

SemiSemiSkewness deviation deviation2

87.22 86.06 81.06 68.77 52.48 40.13 33.13 29.74 28.46 28.11

44.64 41.00 32.45 26.09 30.77 41.28 50.89 56.13 57.83 58.17

4.503 4.593 4.944 6.165 5.713 3.133 1.253 0.782 0.658 0.620

Kurtosis

58.728 60.853 70.468 112.461 88.512 44.705 9.261 4.457 3.857 3.707

Minimum

132.7 132.7 150.6 152.1 156.6 154.1 150.6 147.7 147.7 147.7

Bottom 5%

214.0 220.3 236.2 250.6 242.4 227.7 217.3 213.1 212.0 211.8

Bottom 10%

231.5 238.2 255.0 268.3 258.9 241.8 230.0 224.7 223.3 223.1

Median

329.2 335.1 348.1 351.3 331.1 303.9 283.9 274.3 271.3 270.7

Top 10%

582.6 583.2 576.4 532.2 459.7 397.9 358.9 340.4 333.5 331.7

Top 5%

723.4 723.7 711.3 641.4 523.0 436.6 386.6 363.4 355.1 352.9

Maximum

8295.8 8295.8 8295.8 8295.8 4159.8 2585.8 1355.5 673.0 666.2 558.6

is set at 1; c is annualized.

Table 6-1II(a). DDCF value distribution with SL-TR rule and A = 0, B = 6 months α

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Note:

Average

β

362.5 377.6 396.6 414.5 422.3 415.1 397.0 375.9 358.2 345.3

Standard deviation

197.29 192.58 190.95 192.26 193.44 190.42 179.80 162.27 142.33 121.14

SemiSemiSkewness deviation deviation2

83.44 79.38 78.28 79.58 81.31 80.74 75.23 65.49 55.44 47.54

52.02 38.60 27.28 20.74 20.31 23.20 26.10 28.04 29.07 29.57

4.901 5.134 5.177 5.089 5.012 5.046 5.301 6.020 7.262 7.873

Kurtosis

58.794 63.266 64.092 62.133 60.960 62.620 70.888 93.918 140.323 162.849

Minimum

145.6 169.0 180.8 182.3 176.2 172.9 172.9 172.9 172.9 172.9

Bottom 5%

206.4 229.8 250.2 263.8 263.5 256.1 251.5 249.2 248.2 247.8

Bottom 10%

221.0 243.9 264.7 280.2 283.1 274.5 267.1 263.8 262.1 261.5

Median

306.7 322.6 342.6 361.2 370.9 367.3 351.2 334.8 325.2 320.9

Top 10%

557.0 562.5 578.5 597.9 606.6 595.0 563.8 519.5 472.5 434.9

Top 5%

694.8 700.5 716.6 738.4 746.1 730.4 689.4 633.6 572.1 514.8

Maximum

6594.3 6594.3 6594.3 6594.3 6594.3 6594.3 6594.3 6594.3 6594.3 5955.3

is set at 1; c is annualized.

Table 6-1II(b). Characteristics of value distribution with SL-TR rule and A = 0, B = 1 year α

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Average

339.0 354.7 374.8 394.6 405.5 402.1 387.9 370.1 354.6 343.2

Standard deviation

196.73 191.70 189.59 190.12 190.08 185.74 174.38 156.96 137.73 117.39

SemiSemiSkewness deviation deviation2

82.65 78.20 76.59 77.05 77.54 76.00 70.61 61.90 53.08 46.12

66.80 51.52 37.22 26.87 23.11 24.34 26.56 28.21 29.13 29.59

4.941 5.197 5.269 5.226 5.219 5.329 5.639 6.405 7.694 8.263

Kurtosis

59.443 64.351 65.731 64.564 64.659 67.980 78.271 104.450 155.729 178.982

Minimum

130.6 157.6 173.2 179.6 174.4 172.9 172.9 172.9 172.9 172.9

Bottom 5%

185.9 211.1 234.0 252.0 257.8 254.4 251.0 249.1 248.1 247.8

Bottom 10%

199.4 223.9 247.0 266.0 275.0 271.6 266.2 263.5 262.1 261.5

Median

282.6 298.8 319.5 339.9 352.4 353.5 344.1 332.0 324.5 320.6

Top 10%

532.4 538.1 554.7 574.5 583.7 573.2 543.4 501.5 458.9 427.9

Top 5%

670.3 675.8 692.3 714.3 723.9 708.0 668.3 613.6 553.7 500.5

Maximum

6570.1 6570.1 6570.1 6570.1 6570.1 6570.1 6570.1 6570.1 6570.1 5934.5

29

Note:

β

is set at 1; c is annualized.

Figure 6-1 I(a). DDCF expected property values and risk with ASG-TR rule

Notes: α is set at 0.5 and β at 1; c is annualized; the graph shows plots of the expected property values and risk (negative semi-deviation②) when the value of B in the replacement cost function is 0, 6, 12, 24, and 36 months; the points in the graph represent the replacement threshold value c.

Figure 6-1 I(b). DDCF expected property values and risk with SL-TR rule

Notes: α is set at 0.5 and β at 1; c is annualized; the graph shows plots of the expected property values and risk (negative semi-deviation②) when the value

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of B in the replacement cost function is 0, 6, 12, 24, and 36 months; the points in the graph represent the replacement threshold value c.

7 Tenant-replacement costs and optimal weights for percentage rents We next consider the optimal weights for percentage rents given certain tenant-replacement costs. Figure 7-1 I shows changes in the DDCF distribution as a result of changes in weights for percentage rents and replacement criteria, with the use of a ASG-TR rule. Lower semi-deviation② is used as the risk criterion, a replacement cost of 24 months’ worth of market rent is used, and β is set at 1. The red solid lines in the figure show the different distributions of property values when the replacement criterion c is fixed but the weight for percentage rent αi is changed. The blue dotted lines in the figure show the different DDCF distributions when the weight for percentage rent αi is fixed but the replacement criterion c is changed. The graph shows the aggregate characteristics of the possible DDCF value distributions with a ASG-TR rule. As with the efficient frontier in Markowitz portfolio theory, there are combinations of possible tenant management strategies that can offer the same return with lower risk (in this case, lower semi-deviation②) or higher returns with the same risk. For instance, the bold black line in Figure 7-1 I represents the frontier of such combinations of strategies when the replacement criterion c is set at –0.2 and the weight for the percentage rent changes from 0% to 100%. In addition, a replacement criterion c of –0.2 and a 20% weighting for the percentage rent results in the maximum property value per unit of risk (average expected value of 346.78/negative semi-deviation② of 26.68). Figure 7-1 II shows the results for the same case but with a SL-TR rule. In this case, a replacement criterion c of 0.6 and a 35% weight for the percentage rent results in the maximum property value per unit of risk (average expected value of 382.58/lower semi-deviation② of 24.26). The average expected value is higher and the risk is lower than in the previous case (with a ASG-TR rule). It is difficult to generalize about the optimal strategy, since factors that need to be considered include the impact of property managers on risk and return, and the relationship of the property in question with other properties owned by the property management company. The results of this section, however, indicate that property managers can choose from among the possible tenant management strategies those that lead to optimal property value distributions for them. Figure 7-1I. Combinations of tenant management strategies with ASG-TR rule

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Notes: The graph plots the distributions of expected value and risk (negative semi-deviation②) when the replacement threshold value c or the weighting for percentage rent ái is changed; for the replacement cost function, a replacement cost of 24 months’ worth of market rent is used, and βis set at 1; the red solid lines show the different distributions of property values when the replacement criterion c is fixed but the weighting for percentage rent ái is changed. The blue dotted lines in the figure show the different distributions of property values when the weighting for percentage rentá i is fixed but the replacement criterion c is changed; the bold black line represents the frontier of such combinations of strategies when the replacement criterion c is set at –0.2 and the weighting for the percentage rent changes from 0% to 100%, with the optimal weighting resulting in the maximum property value per unit of risk being 20%

Figure 7-2II. Combinations of tenant management strategies with SL-TR rule

Notes: The graph plots the distributions of expected value and risk (negative semi-deviation②) when the replacement threshold value c or the weighting for percentage rent αi is changed; for the replacement cost function, a replacement cost of 24 months’ worth of market rent is used, and â is set at 1; the red solid lines show the different distributions of property values when the replacement criterion c is fixed but the weighting for percentage rentαi is changed. The blue dotted lines in the figure show the different distributions of property values when the weighting for percentage rentαi is fixed but the replacement criterion c is changed; the bold black line represents the frontier of such combinations of strategies when the replacement criterion c is set at 0.6 and the weighting for the percentage rent changes from 0% to 100%, with the optimal weighting resulting in the maximum property value per unit of risk being 35%

8 Conclusion In this paper, we formulated the retail property management issue in terms of the structure of the tenant lease agreement and rules for replacing tenants, and proposed a framework and 32

methodology for assessing the expected property value and risk based on different DDCF (dynamic discounted cash flow) probability distributions for the property value stemming from different lease structures and tenant-replacement rules. Our simulation results based on the assumptions of our model indicate that active tenant management through the use of percentage rents and appropriate tenant-replacement rules changes the shape of the probability distributions of property values and lead to the generation of firm value. In particular, we found that the optimal weighting for percentage rent can be derived by setting realistic parameters and using optimal tenant-replacement rules. A financial engineering-based real options methodology demonstrates the effectiveness of a tenant management strategy in creating firm value. Moreover, the results of our analysis show that the tenant-replacement options made possible by the new House Lease Law are of very significant value.

References Benjamin, John D., Glenn W. Boyle, and C.F. Sirmans. 1992. “Price Discrimination in Shopping Center Lease,” Journal of Urban Economics, 32, 299-317.

Chun, Eppli and Shilling. 1999. “A Simulation Analysis of the Relationship between Retail Sales and Shopping Center Rents.” Working paper. Kariya, T., Oohara. Y. and Honkawa ,H. 2002. “A Dynamic Discounted Cash Flow Model for Valuation of an Office Building” Kariya, Takeaki.and Liu , R.Y. 2002. Asset Pricing Discrete Time Approach Kluwer Academic Publishers. Miceli, Thomas J. and C.F. Sirmans. 1995. “Contracting with Spatial Externalities and Agency Problems: The Case of Retail Leases,” Regional Science and Urban Economics 25, 355-372. Wheaton, W C. and Raymond G. T. 1995. “Retail Sales and Retail Real Estate,” Real Estate Finance, 12, 22-31.

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