TY - JOUR
AU - Yildirim,, Yildiray
AB - Abstract The capital structure irrelevance argument of Modigliani and Miller (1958) implies that the use of debt or leases should have no impact on firm values. This classical argument leaves out several important considerations crucial for the result, in particular, counterparty credit risk. We re-examine the capital structure problem for firms that can utilize debt and leases in the presence of counterparty risk. Our numerical and empirical estimates show a negative term structure of lease rates that steepens as a function of counterparty risk. Moreover, we document numerical evidence for the complementary relationship between debt and leases in the presence of counterparty risk. 1. Introduction One area of considerable interest in finance concerns the potential trade-off between leases and debt. At the most fundamental level, the capital structure irrelevance argument of Modigliani and Miller (1958) implies that the use of debt or leases should have no impact on firm values. In support of this position, numerous studies have presented theoretical models that assume the substitutability of debt and leases.1 Empirically, these models have considerable support.2 While many studies discuss the substitutability of debt and leases, the theoretical and empirical evidence is not conclusive. For example, in an early empirical study, Ang and Peterson (1984) posit a leasing puzzle after finding a positive (or complementary) relation between debt and leases.3 On the theoretical front, Lewis and Schallheim (1992) and Eisfeldt and Rampini (2009) develop models that imply that debt and leases may in fact be complementary. In Lewis and Schallheim (1992), complementarity arises from incentives inherent in the treatment of tax shields associated with debt and depreciation. In contrast, Eisfeldt and Rampini (2009) motivate their complementary view of debt and leases based on the heterogeneity of agency costs associated with firms with varying credit constraints. More recently, Schallheim, Wells, and Whitby (2013) empirically test the complementary versus substitutability of debt and leases using data on sale-and-leaseback transactions. Their analysis demonstrates that a substantial number of firms (approximately 42% of their sample) appear to exhibit a complementary relation between debt and leasing. As is evident from this brief synopsis of the literature, the debate over whether debt and leases are substitutes or complements remains unsettled. Thus, in this paper, we re-examine the trade-off between leasing and debt usage to develop a theoretical model that provides new insights into the conditions that lead to the substitutability versus complementarity views of leases and debt. We propose a structural model based on the work developed by Leland and Toft (1996) and Agarwal et al. (2011) to effectively link landlord and tenant capital structures to the problem of determining the competitive lease rate. Similar to Leland and Toft (1996), we analyze the endogenous default problem by deriving the equilibrium lease rates given the default boundaries for the tenant and landlord. Our model significantly expands the model and analysis presented in Agarwal et al. (2011) by incorporating the non-trivial interactions of credit-risky tenants and landlords. To the best of our knowledge, this is the first attempt at recognizing the duel causality of capital structure decisions from both parties to a contract that endogenously determine the contracting price. In our discussion, we first determine the equilibrium lease rate (by equating the service flows of the leased asset to the lease payments) when the landlord can default but the tenant is risk-free. Next, we relate this rate to the equilibrium lease rate when both the landlord and tenant can default, which requires updating the landlord and tenant default boundaries. Identifying these boundaries leads to an in-depth discussion on the capital structure of each firm, which directly extends the analysis in Leland and Toft (1996) to include leases. As a result, our analysis provides direct insights into conditions that should prevail when leases and debt are observed as either substitutes or complements. The motivation for our model arises from the observation that a firm’s capital structure decisions can have significant impact on its financial and operational contracts. As an example, consider the events on April 16, 2009 when General Growth Properties made history as one of the largest real estate Chapter 11 bankruptcy filings.4 At the time, General Growth owned or managed over 200 shopping malls with balance sheet assets listed at over $29 billion. While creditors of General Growth were naturally concerned about the prospects of losses arising from the bankruptcy filing, tenants in General Growth malls that had secured leaseholds, which should have made them immune to problems associated with the lessor’s bankruptcy, also expressed concern about the impact that the bankruptcy filing would have on their leasehold positions.5 Similarly, Kulikowski (2012) notes that the near bankruptcy and eventual privatization of Quiznos in 2012 along with bankruptcy filings of other high profile franchise operators during the financial crisis raised awareness of franchisee exposure to capital structure decisions of their franchisors. Kulikowski (2012) quotes franchise lawyer Jeff Fabian as pointing out that “a franchisor’s bankruptcy can significantly impact the success or failure of a franchisee’s operations. From loss of supply of branded inventory, to loss of affiliation with the franchisor’s trademark entirely, to loss of operational support, to customer confusion or defection as a result of less-than-flattering headlines, franchisor’s bankruptcies can have real and long-term effects for the businesses of their franchisees.”6 As these examples demonstrate, tenants in properties where the owner faces financial stress are now discovering the risk that their leases may be terminated as a result of the default or bankruptcy of their landlord.7 Furthermore, Sullivan and Kimball (2009) note that lenders often require standard subordination, nondisturbance, and attornment (SNDA) agreements in leases as a condition of obtaining financing. These seemingly benign SNDA agreements provide lenders (or purchases at foreclosure) with significant rights with respect to the treatment of tenants and leases. For example, a standard lender initiated SNDA may limit the lender’s liability in the event of foreclosure to complete lease contracted tenant improvements, or restrict or eliminate any purchase or renewal options specified in the lease.8 Our model is related to the growing recognition in the literature of the role that relationships among and between a firm’s stakeholders can have on shaping a firm’s financial decisions. For example, Titman (1984) and Maksimovic and Titman (1991) consider how a firm’s capital structure can impact the types of contracts the firm has with its customers. This stream of literature recognizes that when a firm has an interdependent relation with another firm (e.g., a unique product that requires investments that might decline in value if the firm liquidates), then the firm may make capital structure decisions in order to maximize the value of these relations. Similarly, another line in the literature recognizes how firm capital structure decisions can impact management–labor relations. For example, Bronars and Deere (1991), Dasgupta and Sengupta (1993), and Hennessy and Livdan (2009) note that a firm’s management can affect their bargaining power over labor unions by altering the firm’s debt level to reduce the amount of surplus available to stakeholders. In addition, research using similar logic considers the role that capital structure decisions have on the firm’s supply chain relationships (e.g., Kale and Shahrur, 2007; Matsa, 2010; Chu, 2012). To preview our results, our numerical and empirical estimates show a negative term structure of lease rates that steepens as a function of counterparty risk. Specifically, we identify how tenants are compensated (penalized) in the form of lower (higher) lease rates for increasingly (decreasingly) risky financing decisions made by the landlord. Additionally, we obtain a striking, yet consistent, contrast to previous studies in that debt and leases complement each other when the capital structures of both the landlord and the tenant are considered in the leasing problem. This finding is consistent with the conclusion obtained by Lewis and Schallheim (1992) in their one-period leasing model. Finally, our numerical implementation also facilitates an examination into the impact of changes in government tax policies upon lease rates. Specifically, we illustrate how differing tax environments can compensate (penalize) counterparties of the lease agreement through the lease rate. Using property level and loan level information on mortgages contained in commercial mortgage-backed securities (CMBS), we empirically test several of the model’s predictions. We make use of the ability to identify properties that are leased by single-tenants in order to isolate the impact of tenant capital structure on lease rates. By searching on tenant names, we identify publicly traded tenants with publicly available financial statements at the time of the lease. Thus, we are able to verify the prediction that lease rates are negatively related to tenant and landlord capital structures. In particular, we find that a 1% increase in the tenant’s debt/asset ratio decreases the observed lease rate by 0.94%. We further document that lease maturity has a differential impact on lease rates based on the lessor’s risk, as predicted by the model. The remainder of the paper is organized as follows. Section 2 summarizes the existing literature on lease valuation. Section 3 presents the setting for determining lease rates. Section 4 describes the capital structure setup and Section 5 presents the endogenous decision rules to derive the optimal bankruptcy triggers for each firm. Section 6 presents a numerical implementation of the leasing model and discusses the comparative statics to assess the impact of relevant parameters on the term structure of lease rates. In Section 7, we present empirical evidence supporting the model’s predictions and Section 8 concludes. 2. Literature Review In this section, we survey the literature regarding the complex relationship between debt and leases. Additionally, we also discuss related literature about lease rate determination, and how a correct lease contract valuation model can be related to a firm’s leasing policy. As we mentioned earlier, the theory of corporate leasing policy dates back to the analysis of Modigliani and Miller (1958) where frictionless markets and no-arbitrage assumptions ruled out the importance of capital structure decisions to maximizing firm value. Of course, frictions do exist and complicate the capital structure decisions for firms. In particular, a firm deciding between leasing and debt is presented with a number of differing tax incentives that confound the decision-making process. In this paper, we analyze the relationship between debt and leases using the debt-to-lease displacement ratio methodology developed by Ang and Peterson (1984), who use this ratio to characterize the relationship as either a complement or substitute.9 This method for analyzing the degree that debt and leases act as complement or substitute assets is extensively used in the literature (e.g., see Smith and Wakeman, 1985b; Sharpe and Nguyen, 1995; Graham, Lemmon, and Schallheim, 1998; Eisfeldt and Rampini, 2009). A number of empirical studies support the conclusion that debt and leases are interchangeable. For example, Bayliss and Diltz (1986) conduct a survey of bank loan officers, presenting them with firms who use varying lease obligations and measure their willingness to make loans to these firms. They quantitatively determine that $1 of leases can substitute $0.85 of debt. In addition, Marston and Harris (1988) find that $1 of leasing displaces approximately $0.60 of non-leasing debt. More recently, Beattie, Goodacre, and Thomson (2000) use UK data to find that £1 of leasing displaces £0.23 of non-lease debt. In a more comprehensive study, Yan (2006) uses a simultaneous-equation approach to examine the problem of debt or lease use. While utilizing a general method of moments model to estimate parameters, Yan (2006) rejects the hypothesis that debt and leases are complements, but cannot reject the substitutability hypothesis. Additionally, Yan (2006) also finds that the degree of substitutability is greater for firms that pay no dividends (have more asymmetric information), firms that have more investment opportunities (have higher agency costs from underinvestment), and firms that have higher marginal tax rates limiting the value of transferring tax shields. On the other hand, several studies show that debt and leases can act as complements. For example, Lewis and Schallheim (1992) propose a tax-based model that allows for low tax paying firms to sell excess tax shields to firms that place a much higher value on these tax deductions. By selling redundant tax shields, the lessee is motivated to increase its proportion of debt relative to an otherwise identical firm that does not use leasing. Eisfeldt and Rampini (2009) also support the complementary view by focusing on the repossession advantage of leasing to more financially constrained firms. However, the agency costs of leasing due to the separation of ownership and control of the leased assets counterbalance this effect. The net advantage accruing to lessors allows them to offer leases to more credit-constrained firms who will then choose to lease more of their capital than less constrained firms. As a result, debt and leases can be complements. Additionally, several empirical studies find evidence showing how debt and leases can act as complements. In particular, debt and leases seem to be positively associated in the data. For example, Bowman (1980) observes a positive relationship between relative levels of debt and leases. Additionally, Ang and Peterson (1984) propose the so-called “leasing puzzle” and, in doing so, demonstrate a positive correlation between leasing and debt. Both of these findings demonstrate a complementary relationship between debt and leases. As the above discussion demonstrates, no wide consensus exists regarding the precise relationship between leases and debt. One possible reason is that the lease contract is not correctly valued and the lease rate is not well determined. For example, traditional models of lease rates, beginning with Lewis and Schallheim (1992) and Grenadier (1996), have long recognized the importance of tenant default and hence tenant credit risk.10 However, as noted above, leases are not one-sided contracts but rather specify rights and responsibilities of the tenant and the landlord. For example, the typical commercial real-estate lease specifies not only the amount of rent owed by the tenant but also the landlord’s responsibilities in providing services associated with the contracted space. As a result, the typical lease creates the possibility that either party to the contract might default exposing the landlord and the tenant to counterparty risk. In a recent paper, Agarwal et al. (2011) focus on the tenant’s default risk and its effect on the tenant’s capital structure, assuming the landlord is default free. Their model is based on the framework originally proposed by Leland and Toft (1996) and examines the interaction of lessee financial decisions and lease rates. Our paper extends this framework to incorporate both lessor and lessee default risks into the term structure of lease rates as well as its endogenous effect on both tenant and landlord capital structures. Our paper is also related to the works of correlated default modeling (e.g., Duffie and Singleton, 1999; Zhou, 2001; Das et al., 2007; Yu, 2007; Duffie et al., 2009) and counterparty credit risk modeling (e.g., Jarrow and Yu, 2001). However, none of these works consider lease rate term structure modeling and the implied joint capital structure decisions. In contrast, our paper demonstrates how capital structure decisions can endogenously impact other firms. In addition, our paper contributes to the research on correlated defaults in that the correlated default probability and lessor and tenant capital structures can be endogenously determined, while previous research is either based on reduced-form models or exogenous structural models. The advantage of our model is its flexibility in capturing the credit risk interactions between landlord and tenant. Our model also can explain the phenomenon of credit contagion given the large amount of real-estate leases utilized by firms (e.g., Jorion and Zhang, 2009). 3. Determination of Lease Rates We begin by defining a simple market environment for the purchase of space that fully captures the basic features of the commercial real-estate leasing market. For ease of exposition, we describe the setting in terms of the traditional office leasing market but recognize that our model is easily generalizable to other property types (e.g., retail and industrial) as well as other assets that are commonly leased (e.g., commercial aircraft and computer equipment). The office building owner (the landlord) holds the property in a firm financed with debt and equity. For the moment, we assume that the landlord and tenant capital structures are exogenously given in order to derive equations giving the equilibrium lease rates. Later, in Section 5, we relax this assumption by solving for the endogenous default boundary conditions that implicitly recognizes the trade-off between debt and leases. We assume the property’s future service flows are given by: dSBDSBD=μSdt+σSdWS. (1) where SBD represents the service flow before depreciation, μS is the drift rate of the service flow process, σS is the volatility of this process, and dWS is the standard Brownian Motion under physical measure ℙ ⁠. On the other hand, if we reflect the economic (not accounting) depreciation of the leased asset in the drift rate of the service flow process (denoted by q), we can write the service-flow process after depreciation, SAD, as: dSADSAD=(μS−q)dt+σSdWS. (2) Without loss of generality, we assume that debt is in the form of a traditional mortgage secured by the property, and the mortgage is senior to any leasehold. Thus, the landlord is a credit-risk lessor. Additionally, we assume a default-free asset exists that pays a continuous interest rate r. The landlord leases the property to a firm (the tenant). Our goal is to find the equilibrium lease rate for a credit-risk tenant. In order to reach this goal, we first consider the problem of finding the equilibrium lease rate assuming a risk-free lessee. Since this case is not the most relevant to our empirical tests but is useful for derivation purposes for the general case, we present it in the Appendix. We denote the periodic rent payment on a t-period lease contract between a credit-risk (R) lessor and a risk-free (N) lessee as rRNt and the rental payment on a lease originated between a credit-risk (R) lessor and a credit-risk (R) lessee as rRRt ⁠. Subscripts T, L that appear in notation to follow generally refer to tenant and landlord, respectively. We now examine the lease contract assuming a credit-risk tenant. The present value of a lease with maturity t to a risk-free tenant is rRNt(1−e−rtr) ⁠.11 When both landlord and tenant have credit risk, we must calculate the present value of the lease rate rRRt from origination to the tenant default time u, and the recovery of the remaining lease rentals from time u to maturity time t. Under these conditions, we can express the value of the default-risky lease as: ∫0te−rurRRt(1−FT(u;VT,VT,B))du+∫0te−rτρRtRT,RRt−ufT(u;VT,VT,B)du  (3) where FT(u;VT,VT,B) is the tenant’s cumulative default probability up to time u under measure ℙ˜, fT(u;VT,VT,B) is the tenant’s instantaneous default probability under measure ℙ˜ at time u, and ρRt is the tenant’s recovery rate. RT,RRt−u is the present value of the remaining lease payments, and it can be expressed as rRRt(1−e−r(t−u)r) ⁠. The first term in Equation (3) represents the expected discounted lease payment flows from 0 to u. The second term represents the expected discounted value of the remaining lease payments after default. Following the arguments in Grenadier (1996) that any two methods of selling an asset’s service flow for t-years must have the same value, and combining the equation for a risky lessor and risk-free tenant (A.4) with Equation (3), we obtain rRNt(1−e−rtr)=∫0te−rurRRt(1−FT(u;VT,VT,B))du+∫0te−ruρRtRT,RRt−ufT(u;VT,VT,B)du. (4) Thus, we can express the relationship between the lease rates with a maturity of t as: rRRt=rRNt[1−e−rt(1−e−rt)−(1−ρRt)(GT(t)−FT(t)e−rt)], (5) where GT(t):=∫0te−rufT(u;VT,VT,B)du. (6) Equation (5) shows the relation between the risky lease rate and the risk-free lease rate. The denominator represents the discount factor associated with a risky lease, and the numerator is the discount factor associated with a risk-free lease. The first part of denominator is the default-free discount factor that is the same as the numerator. The second part is the loss rate (1−ρRt) times a difference of discounted default probabilities; a positive quantity.12 From this equation, when the lessee’s default probability increases, implying (GT(t)−FT(t)e−rt) increases, the value of the denominator decreases. Hence, the risky lease rate increases to compensate for the increase in default probability. In addition, when the expected recovery rate increases, the lessor recovers more when the lessee defaults, and thus, the risky lease rate decreases, all else being equal. 4. Capital Structure By extending Agarwal et al. (2011), we incorporate the effects of lease credit risk on both the landlord and tenant capital structure in order to determine its net effects on the equilibrium term structure of lease rates.13 The underlying framework for our landlord and tenant capital structures is the continuous time structural model of Leland and Toft (1996). In this section and in Section 5, we adapt the Leland and Toft (1996) approach for both the landlord and the tenant to accommodate the lease agreement between both parties. Following Merton (1974), Black and Cox (1976), Brennan and Schwartz (1978), and Leland and Toft (1996), we assume the landlord has productive assets, one of which is the leased asset delivering service flows described in Equation (1). The un-leveraged value of the landlord’s firm (VL) follows a continuous diffusion process with constant proportional volatility σVL ⁠: dVLVL=(μVL(t)−δVL)dt+σVLdWVL, (7) where μVL(t) denotes the landlord’s total expected rate of return on asset VL, δVL is the landlord’s constant fraction of value paid out to all security holders, and dWVL is the increment of a standard Brownian motion under the physical measure ℙ ⁠.14 We assume the landlord’s capital structure is composed of debt and equity. Consider a single debt issue with maturity t, having periodic coupon (⁠ cL(t) ⁠) and principal (⁠ pL(t) ⁠) payments. Upon bankruptcy, the bondholder forecloses on the debt and recovers a fraction ρL,D(t) of the firm’s net asset value of V˜L,B ⁠, where V˜L,B equals the net asset value after bankruptcy costs plus the present value of lessor’s recovery lease payments at the time of default. In other words, ρL,D(t) is the bondholder’s recovery rate for a debt with maturity t. Thus, we can write the value of risky debt as: dL(VL;VL,B,t)=∫0te−rucL(t)(1−FL(u;VL,VL,B))du+pL(t)e−rt(1−FL(t;VL,VL,B))+∫0te−ruρL,D(t)V˜L,BfL(u;VL,VL,B)du. (8) If the firm does not declare bankruptcy, then the first term on the right-hand side of Equation (8) represents the present value of coupon payments, and the second term represents the present value of the principal payment, respectively. The third term represents the present value of the net asset value accruing to the debt holders if bankruptcy occurs. Thus, we can rewrite Equation (8) as: dL(VL;VL,B,t)=cL(t)r(1−e−rt)−cL(t)r(GL(t)−FL(t)e−rt)+e−rtpL(t)(1−FL(t))+∫0te−ruρL,D(t)V˜L,BfL(u;VL,VL,B)du. We assume that when landlord defaults, he receives an automatic liquidation stay from the bankruptcy court. Given this assumption, we have: V˜L,B=(1−αL)VL,B  (9) where αL is the proportion of firm value loss when landlord firm goes bankrupt, and Equation (9) is consistent with the ordinary trade-off theory of optimal capital structure theory. As with the landlord, we assume the tenant firm has productive assets whose un-leveraged value VT follows a continuous diffusion process dVTVT=(μVT(t)−δVT)dt+σVTdWVT. (10) We assume that the tenant’s capital structure consists of leases, debt, and equity.15 Suppose the tenant firm writes an operating lease contract maturing at time t for an additional asset. The lease contract value l(VT;VT,B,t) is equal to expression (3), that is, l(VT;VT,B,t)=∫0te−rurRRt(1−FT(u;VT,VT,B))du+∫0te−rτρRtRT,RRt−ufT(u;VT,VT,B)du. (11) For describing the tenant’s debt, we follow the notation used for the landlord above. More specifically, for a single debt issue with maturity t, having periodic coupon (⁠ cT(t) ⁠) and principal (⁠ pT(t) ⁠) payments, we can write the value of the tenant’s risky debt as: dT(VT;VT,B,t)=∫0te−rucT(t)(1−FT(u;VT,VT,B))du+pT(t)e−rt(1−FT(t;VT,VT,B))+∫0te−ruρT,D(t)V˜T,BfT(u;VT,VT,B)du, (12) with analogous definitions (to the landlord case) for all quantities in the expression above. Note that Leland and Toft (1996) and Agarwal et al. (2011) follow similar notation to describe a firm’s capital structure. In the next section, we illustrate how the Leland and Toft (1996) endogenous default boundaries for both the landlord and tenant can be determined within our setting. 5. Determining the Endogenous Default Boundaries As in Leland and Toft (1996), we adopt a stationary debt structure for both tenant and landlord. As such, we consider an environment where each firm continuously sells a constant amount of new debt with maturity of T years from issuance, which it will redeem at par upon maturity (if no default has occurred).16 Let Ti,D, i=T, L denote the debt maturity for the tenant and landlord, respectively. More specifically, we let Pi, i=T, L denote the total principal amount of outstanding debt for tenant and landlord, respectively, and let pi=Pi/Ti,D denote the amount of new debt issued per year. Similarly, the total coupon payment for tenant and landlord, respectively, is Ci, i=T, L per year with constant coupon ci=Ci/Ti,D ⁠. We begin by describing the tenant’s endogenous default boundary followed by the landlord’s endogenous default boundary. For the tenant, the net asset value upon bankruptcy takes the form V˜T,B=(1−αT)VT,B−ρRΩR(1−e−r(TL−τT)r), (13) where τT is the tenant default time, ρR is the recovery rate for lease payments (to the landlord) upon tenant default, and ΩR is the total lease payment per year and rRRTL=ΩR/TL is the constant lease rate.17 The first term is the asset value after bankruptcy costs and the second term represents the cash flow recovered by the landlord when the tenant defaults. Following the derivation of Equation (17) in Agarwal et al. (2011), we note that the tenant’s endogenous bankruptcy boundary appears as VT,B∗=QT,B∗1+αTxT−(1−αT)K2TT,D, (14) where QT,B∗=ΩRr(K1TL−K2TL)−K3−K4+M−(PT−CTr)K1TT,D−(CTr)K2TT,D (15) with the distinguishing feature that, within our current analysis, the total lease payments per year ΩR is dependent upon the landlord’s optimal bankruptcy boundary VL,B ⁠, which is not present in the corresponding lease rate in Agarwal et al. (2011).18 Indeed, the lease rate rRRTL is a function of the landlord’s bankruptcy boundary VL,B ⁠. Thus, in this section, we identify the endogenous, optimal bankruptcy boundary VL,B∗ (and hence the endogenous capital structure) for the landlord that is inserted into Equations (A.4) and (5) in order to determine the lease rate rRRTL ⁠. Similar to the tenant, we assume the landlord trades off the tax benefits and the bankruptcy costs of debt financing. Since we incorporate lease financing into the capital structure decision, the tax deductibility benefit of the landlord equals the interest expense on the debt and the depreciation expense of the leased asset. Following Leland (1994), the total firm value of the landlord (⁠ vL(VL;VL,B) ⁠) equals the un-leveraged firm value plus the tax benefit of debt and lease financing minus the bankruptcy cost during the observation period: vL(VL;VL,B)=VL+TaxL(CLr+Depr)(1−(VL,BVL)xL)−(αLVL,B+ damage by default)(VL,BVL)xL  (16) where VL is the un-leveraged firm value, Dep is the depreciation, and xL is defined in the Appendix. The second term in Equation (16) represents the tax-benefits associated with interest rate expense and depreciation expense given that the landlord does not default. The third term in Equation (16) is the bankruptcy cost given that the landlord defaults and includes bankruptcy costs documented by Warner (1977) and the damage compensation19 to the tenant for the landlord’s default. To model the periodic depreciation expense Dep we assume the leased asset is linearly depreciated and the landlord has a stationary lease structure; thus, the total depreciation expense for the life of the leased asset (⁠ TLife ⁠) is E˜[∫0TLifeSBD(u)e−rudu−∫0TLifeSAD(u)e−rudu] ⁠. If we amortize the total expense to a periodic expense, the periodic expense Dep is E˜[r×(∫0TLifeSBD(u)e−rudu−∫0TLifeSAD(u)e−rudu)] because Dep/r is the total life-long depreciation expense. In this setting, Equation (16) is consistent with traditional capital structure trade-off theory that assumes the tax-shield benefit has a positive effect on firm value while bankruptcy costs have a negative effect. We apply the smoothing-pasting condition in Leland and Toft (1996) and solve for the endogenous default boundary, VL,B ⁠. Let20 ∂EL(VL;VL,B,TL,D)∂VL|VL=VL,B=0 (17) By solving Equation (17), we find the endogenous bankruptcy boundary as: VL,B∗=QL,B∗1+αLxL−(1−αL)B, (18) where QL,B∗=(CL/r)(A/(rTL,D)−B)−APL/(rTL,D)−(TaxL(CL+Dep)/r+ damage by default)xL, (19) and A and B are defined in the Appendix and coincide with the same identifications established in Leland and Toft (1996). We then simultaneously solve for the landlord and tenant optimal bankruptcy levels (and resulting capital structures) by Equations (18) and (14). 6. Numerical Implementation In this section, we discuss a numerical implementation of our model. The construction of our model facilitates a separation of the interdependency between the landlord’s and tenant’s capital structure in determining the competitive lease rate. We divide the numerical implementation into three parts21: Find the optimal endogenous bankruptcy boundary for the landlord VL,B* ⁠. Use VL,B* to calculate, respectively: (a) the risky landlord and risk-less tenant lease rate rRN via Equation (A.4), (b) the risky landlord and risky tenant lease rate rRR via Equation (5), (c) the tenant’s optimal endogenous boundary VT,B* via Equation (14). Use the optimal boundaries VL,B* and VT,B* to calculate the tenant and landlord debt and equity values. Table I presents the base case parameters used in the analysis to follow. Our base case parameters match those in the literature allowing for comparison of our results with previous studies.22Table II reports the numerical analysis. Figure 1 shows the relationships between the landlord’s default probability and the equilibrium lease term structure (Panels A and B), the landlord’s default probability and tenant’s capital structure (debt/firm value) (Panel C), and the tenant’s debt maturity and its default probability (Panel D). Specifically, we consider three cases of tenant debt: short-term (⁠ TT,D=5 years), medium-term (⁠ TT,D=10 years), and long-term (⁠ TT,D=20 years) across short- and medium-term lease maturities (⁠ TL=5,10 ⁠), assuming the landlord’s debt maturity remains fixed at 5 years. Later, we relax this assumption and consider the effect of the landlord moving from short-term debt (5 years) to medium-term debt (10 years). In Figure 1, the results are based on the optimal endogenous default boundaries for the landlord and tenant. As will be noted below, the interactive effects of tenant and landlord default probabilities with lease rates are non-linear and depend upon the lease term (5 or 10 years). Figure 1. View largeDownload slide The impact of landlord default probability on lease rate-term structure. Figure 1. View largeDownload slide The impact of landlord default probability on lease rate-term structure. Table I. Initial parameter values Base case parameters match those in the literature allowing for comparison of our results with previous studies; see for example, Agarwal et al. (2011). Base case parameters Market parameters Landlord parameters r 0.075 μVL 0.05 TaxL, TaxT 0.35 σVL 0.06 μS 0.06 VL(0) 100 σS 0.2 Cost of bankruptcy 0.5 q 0.05 Default recovery 0.62 S0 1 Market price of risk δ 0.83 Tenant parameters μVT 0.05 σVT 0.2 δVT 0.06 VT(0) 100 Cost of bankruptcy 0.5 Default recovery 0.62 Base case parameters Market parameters Landlord parameters r 0.075 μVL 0.05 TaxL, TaxT 0.35 σVL 0.06 μS 0.06 VL(0) 100 σS 0.2 Cost of bankruptcy 0.5 q 0.05 Default recovery 0.62 S0 1 Market price of risk δ 0.83 Tenant parameters μVT 0.05 σVT 0.2 δVT 0.06 VT(0) 100 Cost of bankruptcy 0.5 Default recovery 0.62 View Large Table I. Initial parameter values Base case parameters match those in the literature allowing for comparison of our results with previous studies; see for example, Agarwal et al. (2011). Base case parameters Market parameters Landlord parameters r 0.075 μVL 0.05 TaxL, TaxT 0.35 σVL 0.06 μS 0.06 VL(0) 100 σS 0.2 Cost of bankruptcy 0.5 q 0.05 Default recovery 0.62 S0 1 Market price of risk δ 0.83 Tenant parameters μVT 0.05 σVT 0.2 δVT 0.06 VT(0) 100 Cost of bankruptcy 0.5 Default recovery 0.62 Base case parameters Market parameters Landlord parameters r 0.075 μVL 0.05 TaxL, TaxT 0.35 σVL 0.06 μS 0.06 VL(0) 100 σS 0.2 Cost of bankruptcy 0.5 q 0.05 Default recovery 0.62 S0 1 Market price of risk δ 0.83 Tenant parameters μVT 0.05 σVT 0.2 δVT 0.06 VT(0) 100 Cost of bankruptcy 0.5 Default recovery 0.62 View Large Table II. The impact of landlord default probability on lease rate-term structure Table II examines the relationship between the lease-term structure and the probability of default on the landlord’s debt. Table I reports the base case model parameters. The Principal and Coupon Window used in the implementation: P=[0.5,100] using 0.5 as the principal step size, C=[(0.01)P,(0.1)P] with 0.01 as the coupon step size. The first and second columns are the endogenous landlord bankruptcy boundary and the landlord’s default on debt probability (not scaled by 100), that is, ℙVL(0)=100[VL(τL)≤TL,D] ⁠. The third and fourth columns are the endogenous tenant bankruptcy boundary and the tenant’s default on debt probability (not scaled by 100), that is, ℙVT(0)=100[VT(τT)≤TT,D] ⁠. The fifth and sixth columns are the risky landlord, risk-free tenant lease rates. The seventh–tenth columns make up the tenant’s optimal capital structure. Specifically, the seventh and eight columns are the optimal Principal and Coupon for the tenant firm. The ninth column is the optimal tenant firm value and the tenth column is the optimal leverage ratio for the tenant firm. Columns 11 and 12 make up the landlord’s optimal capital structure. Note that, in each block, the italicized third row indicates the optimal capital structure for the landlord and tenant firms when TL,D=5 ⁠. Landlord default Tenant default Lease rates Tenant capital structure Landlord capital structure Boundary Probability Boundary Probability rRN rRR P C Value Debt/value Value Debt/value Lease maturity = 5 years, tenant debt maturity = 5 years 20 0.0010 46.83 0.1499 0.7754 0.7935 46.50 4.19 126.4834 0.3749 193.05 0.3663 30 0.0167 46.63 0.1499 0.7754 0.7935 46.50 4.19 126.4837 0.3749 186.05 0.3929 43.84 0.1163 46.57 0.1492 0.7693 0.7871 46.50 4.19 126.3739 0.3753 110.96 0.4769 60 0.3600 46.47 0.1480 0.7121 0.7284 47.00 4.23 125.2764 0.3827 147.58 0.5439 Lease maturity = 5 years, tenant debt maturity = 10 years 20 0.0010 45.67 0.3625 0.7754 0.7913 44.00 3.96 126.1787 0.3467 193.05 0.3663 30 0.0167 45.67 0.3625 0.7754 0.7913 44.00 3.96 126.1789 0.3467 186.05 0.3929 43.84 0.1163 45.56 0.3607 0.7693 0.7849 44.00 3.96 126.0976 0.3472 110.96 0.4769 60 0.3600 45.22 0.3553 0.7121 0.7258 45.00 4.05 125.2830 0.3587 147.58 0.5439 Lease maturity = 5 years, tenant debt maturity = 20 years 20 0.0010 49.63 0.6639 0.7754 0.8019 51.00 4.59 126.2204 0.3676 193.05 0.3663 30 0.0167 49.63 0.6639 0.7754 0.8019 51.00 4.59 126.2205 0.3676 186.05 0.3929 43.84 0.1163 49.48 0.6622 0.7693 0.7951 51.00 4.59 126.1682 0.3686 110.96 0.4769 60 0.3600 48.40 0.6495 0.7121 0.7330 51.50 4.64 125.6277 0.3803 147.58 0.5439 Lease maturity = 10 years, tenant debt maturity = 5 years 20 0.0010 48.28 0.1720 0.6387 0.7031 49.00 4.90 140.2134 0.3735 191.92 0.3703 30 0.0167 48.23 0.1713 0.6339 0.6976 49.00 4.90 140.0145 0.3739 184.98 0.3969 43.75 0.1151 48.35 0.1728 0.6011 0.6621 49.50 4.95 138.5962 0.3810 110.95 0.4769 60 0.3600 49.25 0.1855 0.5151 0.5715 51.50 5.15 134.7787 0.4060 146.79 0.5484 Lease maturity = 10 years, tenant debt maturity = 10 years 20 0.0010 47.86 0.3975 0.6387 0.7008 31.50 3.15 134.3939 0.2452 191.92 0.3703 30 0.0167 47.63 0.3939 0.6339 0.6944 31.50 3.15 134.2619 0.2457 184.98 0.3969 43.75 0.1151 47.87 0.3977 0.6011 0.6597 33.50 3.35 133.3225 0.2628 110.95 0.4769 60 0.3600 48.26 0.4040 0.5151 0.5670 38.50 3.85 130.8456 0.3069 146.79 0.5484 Lease maturity = 10 years, tenant debt maturity = 20 years 20 0.0010 50.70 0.6762 0.6387 0.7174 24.50 2.21 130.1120 0.1503 191.92 0.3703 30 0.0167 50.77 0.6769 0.6339 0.7125 25.00 2.25 130.0106 0.1541 184.98 0.3969 43.75 0.1151 49.53 0.6627 0.6011 0.6684 26.50 2.39 129.3810 0.1718 110.95 0.4769 60 0.3600 54.39 0.7160 0.5151 0.5997 38.00 3.80 127.7404 0.2624 146.79 0.5484 Landlord default Tenant default Lease rates Tenant capital structure Landlord capital structure Boundary Probability Boundary Probability rRN rRR P C Value Debt/value Value Debt/value Lease maturity = 5 years, tenant debt maturity = 5 years 20 0.0010 46.83 0.1499 0.7754 0.7935 46.50 4.19 126.4834 0.3749 193.05 0.3663 30 0.0167 46.63 0.1499 0.7754 0.7935 46.50 4.19 126.4837 0.3749 186.05 0.3929 43.84 0.1163 46.57 0.1492 0.7693 0.7871 46.50 4.19 126.3739 0.3753 110.96 0.4769 60 0.3600 46.47 0.1480 0.7121 0.7284 47.00 4.23 125.2764 0.3827 147.58 0.5439 Lease maturity = 5 years, tenant debt maturity = 10 years 20 0.0010 45.67 0.3625 0.7754 0.7913 44.00 3.96 126.1787 0.3467 193.05 0.3663 30 0.0167 45.67 0.3625 0.7754 0.7913 44.00 3.96 126.1789 0.3467 186.05 0.3929 43.84 0.1163 45.56 0.3607 0.7693 0.7849 44.00 3.96 126.0976 0.3472 110.96 0.4769 60 0.3600 45.22 0.3553 0.7121 0.7258 45.00 4.05 125.2830 0.3587 147.58 0.5439 Lease maturity = 5 years, tenant debt maturity = 20 years 20 0.0010 49.63 0.6639 0.7754 0.8019 51.00 4.59 126.2204 0.3676 193.05 0.3663 30 0.0167 49.63 0.6639 0.7754 0.8019 51.00 4.59 126.2205 0.3676 186.05 0.3929 43.84 0.1163 49.48 0.6622 0.7693 0.7951 51.00 4.59 126.1682 0.3686 110.96 0.4769 60 0.3600 48.40 0.6495 0.7121 0.7330 51.50 4.64 125.6277 0.3803 147.58 0.5439 Lease maturity = 10 years, tenant debt maturity = 5 years 20 0.0010 48.28 0.1720 0.6387 0.7031 49.00 4.90 140.2134 0.3735 191.92 0.3703 30 0.0167 48.23 0.1713 0.6339 0.6976 49.00 4.90 140.0145 0.3739 184.98 0.3969 43.75 0.1151 48.35 0.1728 0.6011 0.6621 49.50 4.95 138.5962 0.3810 110.95 0.4769 60 0.3600 49.25 0.1855 0.5151 0.5715 51.50 5.15 134.7787 0.4060 146.79 0.5484 Lease maturity = 10 years, tenant debt maturity = 10 years 20 0.0010 47.86 0.3975 0.6387 0.7008 31.50 3.15 134.3939 0.2452 191.92 0.3703 30 0.0167 47.63 0.3939 0.6339 0.6944 31.50 3.15 134.2619 0.2457 184.98 0.3969 43.75 0.1151 47.87 0.3977 0.6011 0.6597 33.50 3.35 133.3225 0.2628 110.95 0.4769 60 0.3600 48.26 0.4040 0.5151 0.5670 38.50 3.85 130.8456 0.3069 146.79 0.5484 Lease maturity = 10 years, tenant debt maturity = 20 years 20 0.0010 50.70 0.6762 0.6387 0.7174 24.50 2.21 130.1120 0.1503 191.92 0.3703 30 0.0167 50.77 0.6769 0.6339 0.7125 25.00 2.25 130.0106 0.1541 184.98 0.3969 43.75 0.1151 49.53 0.6627 0.6011 0.6684 26.50 2.39 129.3810 0.1718 110.95 0.4769 60 0.3600 54.39 0.7160 0.5151 0.5997 38.00 3.80 127.7404 0.2624 146.79 0.5484 View Large Table II. The impact of landlord default probability on lease rate-term structure Table II examines the relationship between the lease-term structure and the probability of default on the landlord’s debt. Table I reports the base case model parameters. The Principal and Coupon Window used in the implementation: P=[0.5,100] using 0.5 as the principal step size, C=[(0.01)P,(0.1)P] with 0.01 as the coupon step size. The first and second columns are the endogenous landlord bankruptcy boundary and the landlord’s default on debt probability (not scaled by 100), that is, ℙVL(0)=100[VL(τL)≤TL,D] ⁠. The third and fourth columns are the endogenous tenant bankruptcy boundary and the tenant’s default on debt probability (not scaled by 100), that is, ℙVT(0)=100[VT(τT)≤TT,D] ⁠. The fifth and sixth columns are the risky landlord, risk-free tenant lease rates. The seventh–tenth columns make up the tenant’s optimal capital structure. Specifically, the seventh and eight columns are the optimal Principal and Coupon for the tenant firm. The ninth column is the optimal tenant firm value and the tenth column is the optimal leverage ratio for the tenant firm. Columns 11 and 12 make up the landlord’s optimal capital structure. Note that, in each block, the italicized third row indicates the optimal capital structure for the landlord and tenant firms when TL,D=5 ⁠. Landlord default Tenant default Lease rates Tenant capital structure Landlord capital structure Boundary Probability Boundary Probability rRN rRR P C Value Debt/value Value Debt/value Lease maturity = 5 years, tenant debt maturity = 5 years 20 0.0010 46.83 0.1499 0.7754 0.7935 46.50 4.19 126.4834 0.3749 193.05 0.3663 30 0.0167 46.63 0.1499 0.7754 0.7935 46.50 4.19 126.4837 0.3749 186.05 0.3929 43.84 0.1163 46.57 0.1492 0.7693 0.7871 46.50 4.19 126.3739 0.3753 110.96 0.4769 60 0.3600 46.47 0.1480 0.7121 0.7284 47.00 4.23 125.2764 0.3827 147.58 0.5439 Lease maturity = 5 years, tenant debt maturity = 10 years 20 0.0010 45.67 0.3625 0.7754 0.7913 44.00 3.96 126.1787 0.3467 193.05 0.3663 30 0.0167 45.67 0.3625 0.7754 0.7913 44.00 3.96 126.1789 0.3467 186.05 0.3929 43.84 0.1163 45.56 0.3607 0.7693 0.7849 44.00 3.96 126.0976 0.3472 110.96 0.4769 60 0.3600 45.22 0.3553 0.7121 0.7258 45.00 4.05 125.2830 0.3587 147.58 0.5439 Lease maturity = 5 years, tenant debt maturity = 20 years 20 0.0010 49.63 0.6639 0.7754 0.8019 51.00 4.59 126.2204 0.3676 193.05 0.3663 30 0.0167 49.63 0.6639 0.7754 0.8019 51.00 4.59 126.2205 0.3676 186.05 0.3929 43.84 0.1163 49.48 0.6622 0.7693 0.7951 51.00 4.59 126.1682 0.3686 110.96 0.4769 60 0.3600 48.40 0.6495 0.7121 0.7330 51.50 4.64 125.6277 0.3803 147.58 0.5439 Lease maturity = 10 years, tenant debt maturity = 5 years 20 0.0010 48.28 0.1720 0.6387 0.7031 49.00 4.90 140.2134 0.3735 191.92 0.3703 30 0.0167 48.23 0.1713 0.6339 0.6976 49.00 4.90 140.0145 0.3739 184.98 0.3969 43.75 0.1151 48.35 0.1728 0.6011 0.6621 49.50 4.95 138.5962 0.3810 110.95 0.4769 60 0.3600 49.25 0.1855 0.5151 0.5715 51.50 5.15 134.7787 0.4060 146.79 0.5484 Lease maturity = 10 years, tenant debt maturity = 10 years 20 0.0010 47.86 0.3975 0.6387 0.7008 31.50 3.15 134.3939 0.2452 191.92 0.3703 30 0.0167 47.63 0.3939 0.6339 0.6944 31.50 3.15 134.2619 0.2457 184.98 0.3969 43.75 0.1151 47.87 0.3977 0.6011 0.6597 33.50 3.35 133.3225 0.2628 110.95 0.4769 60 0.3600 48.26 0.4040 0.5151 0.5670 38.50 3.85 130.8456 0.3069 146.79 0.5484 Lease maturity = 10 years, tenant debt maturity = 20 years 20 0.0010 50.70 0.6762 0.6387 0.7174 24.50 2.21 130.1120 0.1503 191.92 0.3703 30 0.0167 50.77 0.6769 0.6339 0.7125 25.00 2.25 130.0106 0.1541 184.98 0.3969 43.75 0.1151 49.53 0.6627 0.6011 0.6684 26.50 2.39 129.3810 0.1718 110.95 0.4769 60 0.3600 54.39 0.7160 0.5151 0.5997 38.00 3.80 127.7404 0.2624 146.79 0.5484 Landlord default Tenant default Lease rates Tenant capital structure Landlord capital structure Boundary Probability Boundary Probability rRN rRR P C Value Debt/value Value Debt/value Lease maturity = 5 years, tenant debt maturity = 5 years 20 0.0010 46.83 0.1499 0.7754 0.7935 46.50 4.19 126.4834 0.3749 193.05 0.3663 30 0.0167 46.63 0.1499 0.7754 0.7935 46.50 4.19 126.4837 0.3749 186.05 0.3929 43.84 0.1163 46.57 0.1492 0.7693 0.7871 46.50 4.19 126.3739 0.3753 110.96 0.4769 60 0.3600 46.47 0.1480 0.7121 0.7284 47.00 4.23 125.2764 0.3827 147.58 0.5439 Lease maturity = 5 years, tenant debt maturity = 10 years 20 0.0010 45.67 0.3625 0.7754 0.7913 44.00 3.96 126.1787 0.3467 193.05 0.3663 30 0.0167 45.67 0.3625 0.7754 0.7913 44.00 3.96 126.1789 0.3467 186.05 0.3929 43.84 0.1163 45.56 0.3607 0.7693 0.7849 44.00 3.96 126.0976 0.3472 110.96 0.4769 60 0.3600 45.22 0.3553 0.7121 0.7258 45.00 4.05 125.2830 0.3587 147.58 0.5439 Lease maturity = 5 years, tenant debt maturity = 20 years 20 0.0010 49.63 0.6639 0.7754 0.8019 51.00 4.59 126.2204 0.3676 193.05 0.3663 30 0.0167 49.63 0.6639 0.7754 0.8019 51.00 4.59 126.2205 0.3676 186.05 0.3929 43.84 0.1163 49.48 0.6622 0.7693 0.7951 51.00 4.59 126.1682 0.3686 110.96 0.4769 60 0.3600 48.40 0.6495 0.7121 0.7330 51.50 4.64 125.6277 0.3803 147.58 0.5439 Lease maturity = 10 years, tenant debt maturity = 5 years 20 0.0010 48.28 0.1720 0.6387 0.7031 49.00 4.90 140.2134 0.3735 191.92 0.3703 30 0.0167 48.23 0.1713 0.6339 0.6976 49.00 4.90 140.0145 0.3739 184.98 0.3969 43.75 0.1151 48.35 0.1728 0.6011 0.6621 49.50 4.95 138.5962 0.3810 110.95 0.4769 60 0.3600 49.25 0.1855 0.5151 0.5715 51.50 5.15 134.7787 0.4060 146.79 0.5484 Lease maturity = 10 years, tenant debt maturity = 10 years 20 0.0010 47.86 0.3975 0.6387 0.7008 31.50 3.15 134.3939 0.2452 191.92 0.3703 30 0.0167 47.63 0.3939 0.6339 0.6944 31.50 3.15 134.2619 0.2457 184.98 0.3969 43.75 0.1151 47.87 0.3977 0.6011 0.6597 33.50 3.35 133.3225 0.2628 110.95 0.4769 60 0.3600 48.26 0.4040 0.5151 0.5670 38.50 3.85 130.8456 0.3069 146.79 0.5484 Lease maturity = 10 years, tenant debt maturity = 20 years 20 0.0010 50.70 0.6762 0.6387 0.7174 24.50 2.21 130.1120 0.1503 191.92 0.3703 30 0.0167 50.77 0.6769 0.6339 0.7125 25.00 2.25 130.0106 0.1541 184.98 0.3969 43.75 0.1151 49.53 0.6627 0.6011 0.6684 26.50 2.39 129.3810 0.1718 110.95 0.4769 60 0.3600 54.39 0.7160 0.5151 0.5997 38.00 3.80 127.7404 0.2624 146.79 0.5484 View Large 6.1 Impact of Landlord Default Probability First, we see in Panel A of Figure 1 that as the landlord’s default probability increases, the equilibrium lease rate declines regardless of lease maturity. Comparing the results presented in Panels A and B, we find that the effect of a shift in landlord risk is most evident under the case where the tenant is risk-free and the lease is long term (10 years). In this scenario, the tenant has no default risk and thus the tenant’s capital structure has no impact on the equilibrium lease rate (⁠ rRNTL ⁠). As a result, an increase in landlord default probability from 0.1% to 36% results in a 19.35% decrease in the lease rate (from 0.638 to 0.515). However, as expected, shorter term leases mitigate the impact of landlord credit risk and thus the impact of an increase in counterparty risk is lower. For example, when the lease maturity is only 5 years, the lease rate declines only 8.2% as landlord default probability increases. A similar, but less dramatic effect occurs when the tenant is not risk-free (⁠ rRRTL ⁠). However, the effect is complicated since now the tenant’s capital structure also impacts the lease rate. Thus, as intuition suggests we conclude that tenants face lower equilibrium lease rates as their counter-party’s risk increases and this risk increases with exposure to the landlord through lease maturity. Furthermore, these results confirm that credit contagion can be amplified through long-term off balance sheet contracts. In addition, Panel C shows the endogenous tenant capital structure that results from contracting with a risky landlord. Overall, we observe that the use of leverage increases as the lease counter-party risk increases. For example, when both lease and tenant debt are long term, the tenant’s leverage ratio increases 74.58% (from 0.1503 to 0.2624) in response to an increase in the landlord’s default probability. This phenomenon conforms with intuition that tenants have an increasing preference for debt as landlord riskiness increases. 6.2 Impact of Tenant and Landlord Debt Maturity We now investigate the comparative statics associated with changes in debt maturity. First, we see in Figure 1 Panel D that tenant default probabilities increase with longer debt maturities (rising from 14.9% to 66.2% as maturity increases from 5 to 20 years). Panel E provides insights into the impact on equilibrium lease rates to changes to tenant debt maturity. Comparing lease rates for short-term debt and long-term debt evaluated at the landlord’s optimal endogenous default boundary (and holding all else constant), we see that lease rates are positively related to tenant debt maturity irrespective of the lease maturity date and the landlord default boundary. Additionally from Panel E, the results show that landlords are compensated in the form of higher lease rates for riskier tenant firms; this intuitive phenomenon was also observed in the risk-less landlord case examined by Agarwal et al. (2011). Finally, Panel F illustrates the impact of an increase in tenant debt maturity from 5 to 20 years, recognizing that the tenant’s capital structure also impacts the competitive lease rate. Just as the tenant’s capital structure impacts the competitive lease rate, financing decisions made by the landlord also influence lease rates. To illustrate these effects, Table III compares the landlord and tenant default probabilities and lease rates assuming the landlord issues short- or medium-term debt (5 and 10 years) while the tenant issues short-, medium-, and long-term debt (5, 10, and 20 years). The results clearly demonstrate that, as predicted, long-term debt issuance by the landlord, which effectively increases the landlord’s credit risk, reduces the lease rate, that is, the tenant lease payment is reduced for riskier landlord firms. For example, when the lease is short term (5 years) and the landlord and tenant use short-term debt, the endogenous landlord default boundary is 43.84 with an implied default probability of 11.6%. However, as the landlord’s debt maturity increases to 10 years the endogenous landlord default boundary increases to 47.17 with an implied default probability of 38.7%. This increase of landlord default risk translates into a lower lease rate (0.787 versus 0.781). However, we observe an interesting non-linear phenomenon on lease rates as tenant debt maturity changes. For example, holding landlord debt maturity constant at 10 years, the 5-year maturity lease rate first declines 0.256% (from 0.781 to 0.779) as tenant debt maturity increases from 5 to 10 years and then rises 1.28% (from 0.779 to 0.789) as debt maturity increases to 20 years. As a result, Table III reveals interesting new insights regarding the term structure of lease rates that have been ignored in previous studies that did not consider the endogenous counter-party risks. Table III. The impact of short-term and long-term leases Landlord default Tenant default Leases Boundary Probability Boundary Probability rRN rRR Lease maturity = 5 years, Tenant debt maturity = 5 years Landlord debt maturity = 5 years 43.84 0.1163 46.57 0.1492 0.7693 0.7871 Landlord debt maturity = 10 years 47.17 0.3866 46.52 0.1485 0.7638 0.7814 Lease maturity = 5 years, tenant debt maturity = 10 years Landlord debt maturity = 5 years 43.84 0.1163 45.56 0.3607 0.7693 0.7849 Landlord debt maturity = 10 years 47.17 0.3866 45.45 0.3590 0.7638 0.7790 Lease maturity = 5 years, tenant debt maturity = 20 years Landlord debt maturity = 5 years 43.84 0.1163 49.48 0.6622 0.7693 0.7951 Landlord debt maturity = 10 years 47.17 0.3866 49.34 0.6606 0.7638 0.7890 Lease maturity = 10 years, tenant debt maturity = 5 years Landlord debt maturity = 5 years 43.75 0.1151 48.35 0.1728 0.6011 0.6621 Landlord debt maturity = 10 years 47.05 0.3846 48.65 0.1771 0.5872 0.6484 Lease maturity = 10 years, tenant debt maturity = 10 years Landlord debt maturity = 5 years 43.75 0.1151 47.87 0.3977 0.6011 0.6597 Landlord debt maturity = 10 years 47.05 0.3846 48.11 0.4015 0.5872 0.6456 Lease maturity = 10 years, tenant debt maturity = 20 years Landlord debt maturity = 5 years 43.75 0.1151 49.53 0.6627 0.6011 0.6684 Landlord debt maturity = 10 years 47.05 0.3846 49.33 0.6605 0.5872 0.6519 Landlord default Tenant default Leases Boundary Probability Boundary Probability rRN rRR Lease maturity = 5 years, Tenant debt maturity = 5 years Landlord debt maturity = 5 years 43.84 0.1163 46.57 0.1492 0.7693 0.7871 Landlord debt maturity = 10 years 47.17 0.3866 46.52 0.1485 0.7638 0.7814 Lease maturity = 5 years, tenant debt maturity = 10 years Landlord debt maturity = 5 years 43.84 0.1163 45.56 0.3607 0.7693 0.7849 Landlord debt maturity = 10 years 47.17 0.3866 45.45 0.3590 0.7638 0.7790 Lease maturity = 5 years, tenant debt maturity = 20 years Landlord debt maturity = 5 years 43.84 0.1163 49.48 0.6622 0.7693 0.7951 Landlord debt maturity = 10 years 47.17 0.3866 49.34 0.6606 0.7638 0.7890 Lease maturity = 10 years, tenant debt maturity = 5 years Landlord debt maturity = 5 years 43.75 0.1151 48.35 0.1728 0.6011 0.6621 Landlord debt maturity = 10 years 47.05 0.3846 48.65 0.1771 0.5872 0.6484 Lease maturity = 10 years, tenant debt maturity = 10 years Landlord debt maturity = 5 years 43.75 0.1151 47.87 0.3977 0.6011 0.6597 Landlord debt maturity = 10 years 47.05 0.3846 48.11 0.4015 0.5872 0.6456 Lease maturity = 10 years, tenant debt maturity = 20 years Landlord debt maturity = 5 years 43.75 0.1151 49.53 0.6627 0.6011 0.6684 Landlord debt maturity = 10 years 47.05 0.3846 49.33 0.6605 0.5872 0.6519 View Large Table III. The impact of short-term and long-term leases Landlord default Tenant default Leases Boundary Probability Boundary Probability rRN rRR Lease maturity = 5 years, Tenant debt maturity = 5 years Landlord debt maturity = 5 years 43.84 0.1163 46.57 0.1492 0.7693 0.7871 Landlord debt maturity = 10 years 47.17 0.3866 46.52 0.1485 0.7638 0.7814 Lease maturity = 5 years, tenant debt maturity = 10 years Landlord debt maturity = 5 years 43.84 0.1163 45.56 0.3607 0.7693 0.7849 Landlord debt maturity = 10 years 47.17 0.3866 45.45 0.3590 0.7638 0.7790 Lease maturity = 5 years, tenant debt maturity = 20 years Landlord debt maturity = 5 years 43.84 0.1163 49.48 0.6622 0.7693 0.7951 Landlord debt maturity = 10 years 47.17 0.3866 49.34 0.6606 0.7638 0.7890 Lease maturity = 10 years, tenant debt maturity = 5 years Landlord debt maturity = 5 years 43.75 0.1151 48.35 0.1728 0.6011 0.6621 Landlord debt maturity = 10 years 47.05 0.3846 48.65 0.1771 0.5872 0.6484 Lease maturity = 10 years, tenant debt maturity = 10 years Landlord debt maturity = 5 years 43.75 0.1151 47.87 0.3977 0.6011 0.6597 Landlord debt maturity = 10 years 47.05 0.3846 48.11 0.4015 0.5872 0.6456 Lease maturity = 10 years, tenant debt maturity = 20 years Landlord debt maturity = 5 years 43.75 0.1151 49.53 0.6627 0.6011 0.6684 Landlord debt maturity = 10 years 47.05 0.3846 49.33 0.6605 0.5872 0.6519 Landlord default Tenant default Leases Boundary Probability Boundary Probability rRN rRR Lease maturity = 5 years, Tenant debt maturity = 5 years Landlord debt maturity = 5 years 43.84 0.1163 46.57 0.1492 0.7693 0.7871 Landlord debt maturity = 10 years 47.17 0.3866 46.52 0.1485 0.7638 0.7814 Lease maturity = 5 years, tenant debt maturity = 10 years Landlord debt maturity = 5 years 43.84 0.1163 45.56 0.3607 0.7693 0.7849 Landlord debt maturity = 10 years 47.17 0.3866 45.45 0.3590 0.7638 0.7790 Lease maturity = 5 years, tenant debt maturity = 20 years Landlord debt maturity = 5 years 43.84 0.1163 49.48 0.6622 0.7693 0.7951 Landlord debt maturity = 10 years 47.17 0.3866 49.34 0.6606 0.7638 0.7890 Lease maturity = 10 years, tenant debt maturity = 5 years Landlord debt maturity = 5 years 43.75 0.1151 48.35 0.1728 0.6011 0.6621 Landlord debt maturity = 10 years 47.05 0.3846 48.65 0.1771 0.5872 0.6484 Lease maturity = 10 years, tenant debt maturity = 10 years Landlord debt maturity = 5 years 43.75 0.1151 47.87 0.3977 0.6011 0.6597 Landlord debt maturity = 10 years 47.05 0.3846 48.11 0.4015 0.5872 0.6456 Lease maturity = 10 years, tenant debt maturity = 20 years Landlord debt maturity = 5 years 43.75 0.1151 49.53 0.6627 0.6011 0.6684 Landlord debt maturity = 10 years 47.05 0.3846 49.33 0.6605 0.5872 0.6519 View Large 6.3 Debt and Lease as Complements and Substitutes In this section, we analyze the relationship between debt and leases within our model. To facilitate this discussion, we utilize the methodology of Ang and Peterson (1984). Namely, we consider the debt-to-lease displacement ratio α, as defined as, DRNL=DRL+αLRL, (20) where DRNL is the debt ratio of the firm that does not lease (NL), DRL the debt ratio of a similar firm that does lease (L), and LRL is the lease ratio of the latter firm. When α>0 ⁠, leases are said to reduce debt capacity, that is, debt and leases act as substitutes. Alternatively, when α<0 ⁠, debt and leases are complementary assets. Table IV presents the main results of this section. In this table, we estimate the value of α and interpret the resulting sign.23 In Panel A, we show the interaction between leasing and the default risky firm’s (both landlord and tenant) choice of optimal capital structure for different debt and lease maturities. In the case of a low default risk tenant, we document the complementary nature of debt and leases. For example, with the tenant debt maturity fixed (say, TT,D=5 ⁠), then an increase in the lease maturity from 5 to 10 years decreases the lease rate 15.9% (from 0.7871 to 0.6621), increases in tenant’s default probability 16.1% (from 0.149 to 0.173), increases lease value 31.8% (from 3.2076 to 4.2288), and finally increases the debt value 11.3% (from 47.4267 to 52.7914). The negative debt-to-lease displacement ratio in this case (i.e., α=−1.1095 ⁠) posits the complementary effect. However, when the default probability of the tenant is increased by increasing the debt maturity of the tenant to TT,D=10 and TT,D=20 ⁠, the debt-to-lease displacement ratio turns to be positive (⁠ α=13.4389 and 21.2251, respectively), that is, debt and lease act as substitutes. Table IV. Debt and lease as complements/substitutes Table I reports the base case model parameters. Here, in Table IV, Panel A is the result for default risky landlord and default risky tenant. Panel B is the result for default risk-free landlord and default risky tenant by assuming landlord’s optimal bankruptcy boundary is 0. In each panel, the first column is the endogenous landlord bankruptcy boundary (⁠ VL,B∗ ⁠). The second column is the landlord bankruptcy probability of debt (⁠ λD,L ⁠). The third column is the tenant bankruptcy boundary (⁠ VT,B∗ ⁠). The fourth column tenant’s optimal total firm value (⁠ VT∗ ⁠). The fifth column is the tenant bankruptcy probability of debt (⁠ λD,T ⁠). The sixth column is tenant’s optimal leverage ratio (⁠ (D/V)T∗ ⁠). The seventh column is the lease rate when both landlord and tenant are default risky (rRR). The eighth column is the lease rate only landlord is default risky (rRN). The ninth column is the lease contract value. The tenth column is tenant’s optimal debt value. The eleventh column is the debt-to-lease displacement ratio (α) as lease maturity increases from 5 to 10 years. Panel A: Landlord is default risky; tenant is default risky VL,B∗ λD,L VT,B∗ VT∗ λD,T (D/V)T∗ (%) rRR rRN Lease value Tenant’s debt value α TT,D=5 TL = 5 43.84 0.1163 46.57 126.37 0.149 37.53 0.7871 0.7693 3.2076 47.4267 TL = 10 43.75 0.1151 48.35 138.60 0.173 38.10 0.6621 0.6011 4.2288 52.7914 –1.1095 TT,D = 10 TL = 5 43.84 0.1163 45.56 126.09 0.361 34.72 0.7849 0.7693 3.2076 43.7784 TL = 10 43.75 0.1151 47.87 133.32 0.398 26.28 0.6597 0.6011 4.2288 35.0365 13.4389 TT,D = 20 TL = 5 43.84 0.1163 49.48 126.16 0.662 36.86 0.7951 0.7693 3.2076 51.0822 TL = 10 43.75 0.1151 49.53 129.38 0.663 17.18 0.6684 0.6011 4.2288 32.4485 21.2251 Panel B: Landlord is default risk free; tenant is default risky TT,D=5 TL = 5 0.0000 0.0000 46.6254 126.4833 0.1499 37.49 0.7935 0.7754 3.2330 47.4233 TL = 10 0.0000 0.0000 48.2836 140.2215 0.1720 37.35 0.7034 0.6389 4.4945 52.3744 0.2195 TT,D = 10 TL = 5 0.0000 0.0000 45.6713 126.1786 0.3625 34.67 0.7913 0.7754 3.2330 43.7480 TL = 10 0.0000 0.0000 47.8664 134.3993 0.3977 24.52 0.7011 0.6389 4.4945 32.9559 12.9819 TT,D=20 TL = 5 0.0000 0.0000 49.6297 126.2203 0.6639 36.76 0.8019 0.7754 3.2330 46.3983 TL = 10 0.0000 0.0000 50.7192 130.1154 0.6763 15.02 0.7177 0.6389 4.4945 19.5455 24.3469 Panel A: Landlord is default risky; tenant is default risky VL,B∗ λD,L VT,B∗ VT∗ λD,T (D/V)T∗ (%) rRR rRN Lease value Tenant’s debt value α TT,D=5 TL = 5 43.84 0.1163 46.57 126.37 0.149 37.53 0.7871 0.7693 3.2076 47.4267 TL = 10 43.75 0.1151 48.35 138.60 0.173 38.10 0.6621 0.6011 4.2288 52.7914 –1.1095 TT,D = 10 TL = 5 43.84 0.1163 45.56 126.09 0.361 34.72 0.7849 0.7693 3.2076 43.7784 TL = 10 43.75 0.1151 47.87 133.32 0.398 26.28 0.6597 0.6011 4.2288 35.0365 13.4389 TT,D = 20 TL = 5 43.84 0.1163 49.48 126.16 0.662 36.86 0.7951 0.7693 3.2076 51.0822 TL = 10 43.75 0.1151 49.53 129.38 0.663 17.18 0.6684 0.6011 4.2288 32.4485 21.2251 Panel B: Landlord is default risk free; tenant is default risky TT,D=5 TL = 5 0.0000 0.0000 46.6254 126.4833 0.1499 37.49 0.7935 0.7754 3.2330 47.4233 TL = 10 0.0000 0.0000 48.2836 140.2215 0.1720 37.35 0.7034 0.6389 4.4945 52.3744 0.2195 TT,D = 10 TL = 5 0.0000 0.0000 45.6713 126.1786 0.3625 34.67 0.7913 0.7754 3.2330 43.7480 TL = 10 0.0000 0.0000 47.8664 134.3993 0.3977 24.52 0.7011 0.6389 4.4945 32.9559 12.9819 TT,D=20 TL = 5 0.0000 0.0000 49.6297 126.2203 0.6639 36.76 0.8019 0.7754 3.2330 46.3983 TL = 10 0.0000 0.0000 50.7192 130.1154 0.6763 15.02 0.7177 0.6389 4.4945 19.5455 24.3469 View Large Table IV. Debt and lease as complements/substitutes Table I reports the base case model parameters. Here, in Table IV, Panel A is the result for default risky landlord and default risky tenant. Panel B is the result for default risk-free landlord and default risky tenant by assuming landlord’s optimal bankruptcy boundary is 0. In each panel, the first column is the endogenous landlord bankruptcy boundary (⁠ VL,B∗ ⁠). The second column is the landlord bankruptcy probability of debt (⁠ λD,L ⁠). The third column is the tenant bankruptcy boundary (⁠ VT,B∗ ⁠). The fourth column tenant’s optimal total firm value (⁠ VT∗ ⁠). The fifth column is the tenant bankruptcy probability of debt (⁠ λD,T ⁠). The sixth column is tenant’s optimal leverage ratio (⁠ (D/V)T∗ ⁠). The seventh column is the lease rate when both landlord and tenant are default risky (rRR). The eighth column is the lease rate only landlord is default risky (rRN). The ninth column is the lease contract value. The tenth column is tenant’s optimal debt value. The eleventh column is the debt-to-lease displacement ratio (α) as lease maturity increases from 5 to 10 years. Panel A: Landlord is default risky; tenant is default risky VL,B∗ λD,L VT,B∗ VT∗ λD,T (D/V)T∗ (%) rRR rRN Lease value Tenant’s debt value α TT,D=5 TL = 5 43.84 0.1163 46.57 126.37 0.149 37.53 0.7871 0.7693 3.2076 47.4267 TL = 10 43.75 0.1151 48.35 138.60 0.173 38.10 0.6621 0.6011 4.2288 52.7914 –1.1095 TT,D = 10 TL = 5 43.84 0.1163 45.56 126.09 0.361 34.72 0.7849 0.7693 3.2076 43.7784 TL = 10 43.75 0.1151 47.87 133.32 0.398 26.28 0.6597 0.6011 4.2288 35.0365 13.4389 TT,D = 20 TL = 5 43.84 0.1163 49.48 126.16 0.662 36.86 0.7951 0.7693 3.2076 51.0822 TL = 10 43.75 0.1151 49.53 129.38 0.663 17.18 0.6684 0.6011 4.2288 32.4485 21.2251 Panel B: Landlord is default risk free; tenant is default risky TT,D=5 TL = 5 0.0000 0.0000 46.6254 126.4833 0.1499 37.49 0.7935 0.7754 3.2330 47.4233 TL = 10 0.0000 0.0000 48.2836 140.2215 0.1720 37.35 0.7034 0.6389 4.4945 52.3744 0.2195 TT,D = 10 TL = 5 0.0000 0.0000 45.6713 126.1786 0.3625 34.67 0.7913 0.7754 3.2330 43.7480 TL = 10 0.0000 0.0000 47.8664 134.3993 0.3977 24.52 0.7011 0.6389 4.4945 32.9559 12.9819 TT,D=20 TL = 5 0.0000 0.0000 49.6297 126.2203 0.6639 36.76 0.8019 0.7754 3.2330 46.3983 TL = 10 0.0000 0.0000 50.7192 130.1154 0.6763 15.02 0.7177 0.6389 4.4945 19.5455 24.3469 Panel A: Landlord is default risky; tenant is default risky VL,B∗ λD,L VT,B∗ VT∗ λD,T (D/V)T∗ (%) rRR rRN Lease value Tenant’s debt value α TT,D=5 TL = 5 43.84 0.1163 46.57 126.37 0.149 37.53 0.7871 0.7693 3.2076 47.4267 TL = 10 43.75 0.1151 48.35 138.60 0.173 38.10 0.6621 0.6011 4.2288 52.7914 –1.1095 TT,D = 10 TL = 5 43.84 0.1163 45.56 126.09 0.361 34.72 0.7849 0.7693 3.2076 43.7784 TL = 10 43.75 0.1151 47.87 133.32 0.398 26.28 0.6597 0.6011 4.2288 35.0365 13.4389 TT,D = 20 TL = 5 43.84 0.1163 49.48 126.16 0.662 36.86 0.7951 0.7693 3.2076 51.0822 TL = 10 43.75 0.1151 49.53 129.38 0.663 17.18 0.6684 0.6011 4.2288 32.4485 21.2251 Panel B: Landlord is default risk free; tenant is default risky TT,D=5 TL = 5 0.0000 0.0000 46.6254 126.4833 0.1499 37.49 0.7935 0.7754 3.2330 47.4233 TL = 10 0.0000 0.0000 48.2836 140.2215 0.1720 37.35 0.7034 0.6389 4.4945 52.3744 0.2195 TT,D = 10 TL = 5 0.0000 0.0000 45.6713 126.1786 0.3625 34.67 0.7913 0.7754 3.2330 43.7480 TL = 10 0.0000 0.0000 47.8664 134.3993 0.3977 24.52 0.7011 0.6389 4.4945 32.9559 12.9819 TT,D=20 TL = 5 0.0000 0.0000 49.6297 126.2203 0.6639 36.76 0.8019 0.7754 3.2330 46.3983 TL = 10 0.0000 0.0000 50.7192 130.1154 0.6763 15.02 0.7177 0.6389 4.4945 19.5455 24.3469 View Large The complementary behavior between debt and lease in Panel A is also observed in the one-period analysis conducted by Lewis and Schallheim (1992). However, this effect is absent from the traditional literature that examines the term structure of lease rates. Thus, our analysis not only confirms that the tenant default risk is instrumental to observing this complementary behavior, but also confirms that the findings are valid when the counterparty risk exists. 6.4 The Term Structure of Leases We now consider the lease term structure when tenant and landlord are subject to default risk. Figure 2 highlights the effects of changes in landlord and tenant debt maturities and riskiness on the equilibrium term structure of lease rates. The figure highlights the lease term structure that prevails under assumptions that both the landlord and tenant have short-term (5-year) debt and long-term (10-year) debt. In addition, we highlight the shift in the lease term structure that occurs when the landlord becomes risky. While the lease term structure is downward sloping, Figure 2 reveals two interesting results. First, when moving from a risk-free to a risky landlord the lease term structure becomes steeper, indicating that long-term leases are discounted in the presence of landlord risk. The intuition for the discount is that long-term leases increase tenant exposure to potential landlord default and, in equilibrium, the reduction in rent compensates the tenant for this increase in risk. Second, in the case of risky landlord and tenant, the impact of debt maturity dissipates as the lease term increases (the equilibrium rental rates converge). Notice that for risky landlord and tenant, the rental rate convergence begins approximately after the 10-year lease maturity; for the riskless landlord, convergence begins after the 15-year lease maturity. This phenomenon reflects how lengthening of lease maturities beyond both parties’ debt maturity renders both short- and medium-term debt to be viewed as similar risks. Figure 2. View largeDownload slide Term structure of lease rates. Figure 2. View largeDownload slide Term structure of lease rates. 6.5 Impact of Tenant Default Table V shows the relation between the probability of default on the tenant’s existing debt and the lease-term structure. As before, we examine the lease-term structure when the tenant firm issues short-term debt (5-year), intermediate-term debt (10-year), and long-term debt (20-year). Italicized entries in each block indicate optimal endogenous default boundaries for tenant and landlord. These italicized entries along with the corresponding lease rate are the base case within each block. Within each block, we change the default boundary to highlight the impact of the probability of debt default. For a fixed optimal landlord boundary (⁠ 43.84,43.75 ⁠) and suboptimal tenant boundary (30, 40, 60), we calculate the lease rate rRRTL satisfying Equation (5) via the bisection method. Notice this task is much easier using suboptimal boundaries since the right-hand side of Equation (5) is now independent of rRRTL ⁠. Table V. The impact of tenant default boundary on lease rate-term structure Table I reports the base case model parameters. Here, in Table V, the first column is the endogenous landlord bankruptcy boundary (⁠ VL,B∗ ⁠). The second column is the tenant bankruptcy boundary (⁠ VT,B∗ ⁠). The third row in each block [where block refers to entries corresponding to a (TL,TT,D) pair, TT,D is the maturity of tenant’s debt] is the optimal endogenous boundary found using the landlord’s endogenous boundary in the first column. The third and fourth columns are the default probabilities of debt for both tenant (⁠ λD,T ⁠) and landlord (⁠ λD,L ⁠), respectively. The fifth column is the lease rate implied using the first two columns. Columns 6–10 are repeats of Columns 1–3 using TL = 10. Italicized table entries indicate optimal tenant and landlord boundary values. TL = 5 TL = 10 VL,B∗ VT,B∗ λD,T λD,L rRR VL,B∗ VT,B∗ λD,T λD,L rRR TT,D = 5 TT,D = 5 30 0.7702 30 0.6086 40 0.7760 40 0.6286 43.84 46.57 0.1492 0.1163 0.7871 43.75 48.35 0.1728 0.1151 0.6621 60 0.8487 60 0.7491 TT,D = 10 TT,D = 10 30 0.7702 30 0.6086 40 0.7760 40 0.6286 43.84 45.56 0.3607 0.1163 0.7849 43.75 47.87 0.3977 0.1151 0.6597 60 0.8487 60 0.7491 TT,D = 20 TT,D = 20 30 0.7702 30 0.6086 40 0.7760 40 0.6286 43.84 49.48 0.6622 0.1163 0.7951 43.75 49.53 0.6627 0.1151 0.6684 60 0.8487 60 0.7491 TL = 5 TL = 10 VL,B∗ VT,B∗ λD,T λD,L rRR VL,B∗ VT,B∗ λD,T λD,L rRR TT,D = 5 TT,D = 5 30 0.7702 30 0.6086 40 0.7760 40 0.6286 43.84 46.57 0.1492 0.1163 0.7871 43.75 48.35 0.1728 0.1151 0.6621 60 0.8487 60 0.7491 TT,D = 10 TT,D = 10 30 0.7702 30 0.6086 40 0.7760 40 0.6286 43.84 45.56 0.3607 0.1163 0.7849 43.75 47.87 0.3977 0.1151 0.6597 60 0.8487 60 0.7491 TT,D = 20 TT,D = 20 30 0.7702 30 0.6086 40 0.7760 40 0.6286 43.84 49.48 0.6622 0.1163 0.7951 43.75 49.53 0.6627 0.1151 0.6684 60 0.8487 60 0.7491 View Large Table V. The impact of tenant default boundary on lease rate-term structure Table I reports the base case model parameters. Here, in Table V, the first column is the endogenous landlord bankruptcy boundary (⁠ VL,B∗ ⁠). The second column is the tenant bankruptcy boundary (⁠ VT,B∗ ⁠). The third row in each block [where block refers to entries corresponding to a (TL,TT,D) pair, TT,D is the maturity of tenant’s debt] is the optimal endogenous boundary found using the landlord’s endogenous boundary in the first column. The third and fourth columns are the default probabilities of debt for both tenant (⁠ λD,T ⁠) and landlord (⁠ λD,L ⁠), respectively. The fifth column is the lease rate implied using the first two columns. Columns 6–10 are repeats of Columns 1–3 using TL = 10. Italicized table entries indicate optimal tenant and landlord boundary values. TL = 5 TL = 10 VL,B∗ VT,B∗ λD,T λD,L rRR VL,B∗ VT,B∗ λD,T λD,L rRR TT,D = 5 TT,D = 5 30 0.7702 30 0.6086 40 0.7760 40 0.6286 43.84 46.57 0.1492 0.1163 0.7871 43.75 48.35 0.1728 0.1151 0.6621 60 0.8487 60 0.7491 TT,D = 10 TT,D = 10 30 0.7702 30 0.6086 40 0.7760 40 0.6286 43.84 45.56 0.3607 0.1163 0.7849 43.75 47.87 0.3977 0.1151 0.6597 60 0.8487 60 0.7491 TT,D = 20 TT,D = 20 30 0.7702 30 0.6086 40 0.7760 40 0.6286 43.84 49.48 0.6622 0.1163 0.7951 43.75 49.53 0.6627 0.1151 0.6684 60 0.8487 60 0.7491 TL = 5 TL = 10 VL,B∗ VT,B∗ λD,T λD,L rRR VL,B∗ VT,B∗ λD,T λD,L rRR TT,D = 5 TT,D = 5 30 0.7702 30 0.6086 40 0.7760 40 0.6286 43.84 46.57 0.1492 0.1163 0.7871 43.75 48.35 0.1728 0.1151 0.6621 60 0.8487 60 0.7491 TT,D = 10 TT,D = 10 30 0.7702 30 0.6086 40 0.7760 40 0.6286 43.84 45.56 0.3607 0.1163 0.7849 43.75 47.87 0.3977 0.1151 0.6597 60 0.8487 60 0.7491 TT,D = 20 TT,D = 20 30 0.7702 30 0.6086 40 0.7760 40 0.6286 43.84 49.48 0.6622 0.1163 0.7951 43.75 49.53 0.6627 0.1151 0.6684 60 0.8487 60 0.7491 View Large In Table V, we first notice that the lease rate is increasing in the tenant default boundary. For example, when TL = 5 and TT,D=5 the lease rate increases 10.3% (from 0.770 to 0.849) as the tenant default boundary increases. This is expected since the landlord should be compensated for increased tenant default likelihood.24 6.6 Impact of Taxes and Depreciation Table VI highlights how differences in landlord and tenant tax rates and changes in overall tax policy can affect the equilibrium lease rate. Recall from our model that the lease rate is a function of the landlord and tenant marginal corporate tax rates as well as the tax treatment of economic depreciation (q) as reflected in χ. As noted above, χ = 1 reflects the case that accounting and economic depreciation are equivalent, while χ<1 reflects the condition that the tax deduction accepted with depreciation is less than that of the full economic depreciation. Thus, by varying χ, we can observe how changes in the depreciation schedules associated with the leased asset impact lease rates. Table VI. The impact of taxes and depreciation on lease rate-term structure Table VI highlights how differences in landlord and tenant tax rates as well changes in overall tax policy affect the lease rate. Table I reports the base case model parameters. The assumed tax rates 0.25,0.35,0.4 for the tenant appear as rows and the assumed tax rates for the landlord 0.25,0.35,0.4 appear as columns. Entries of the table are the lease rate for a risky landlord and tenant. Tenant tax rate Landlord tax rate χ=0.5 0 0.25 0.35 0.40 0 0.7890 0.7792 0.7963 0.7450 0.25 0.7920 0.7821 0.7721 0.7478 0.35 0.8067 0.7974 0.7871 0.7618 0.40 0.8294 0.8187 0.8080 0.7817 χ = 1 0 0.7890 0.7695 0.7567 0.7370 0.25 0.7920 0.7723 0.7597 0.7397 0.35 0.8067 0.7873 0.7740 0.7534 0.40 0.8294 0.8082 0.7944 0.7748 χ=1.5 0 0.7890 0.7598 0.7448 0.7291 0.25 0.7920 0.7628 0.7476 0.7317 0.35 0.8067 0.7772 0.7615 0.7461 0.40 0.8294 0.7977 0.7814 0.7662 Tenant tax rate Landlord tax rate χ=0.5 0 0.25 0.35 0.40 0 0.7890 0.7792 0.7963 0.7450 0.25 0.7920 0.7821 0.7721 0.7478 0.35 0.8067 0.7974 0.7871 0.7618 0.40 0.8294 0.8187 0.8080 0.7817 χ = 1 0 0.7890 0.7695 0.7567 0.7370 0.25 0.7920 0.7723 0.7597 0.7397 0.35 0.8067 0.7873 0.7740 0.7534 0.40 0.8294 0.8082 0.7944 0.7748 χ=1.5 0 0.7890 0.7598 0.7448 0.7291 0.25 0.7920 0.7628 0.7476 0.7317 0.35 0.8067 0.7772 0.7615 0.7461 0.40 0.8294 0.7977 0.7814 0.7662 View Large Table VI. The impact of taxes and depreciation on lease rate-term structure Table VI highlights how differences in landlord and tenant tax rates as well changes in overall tax policy affect the lease rate. Table I reports the base case model parameters. The assumed tax rates 0.25,0.35,0.4 for the tenant appear as rows and the assumed tax rates for the landlord 0.25,0.35,0.4 appear as columns. Entries of the table are the lease rate for a risky landlord and tenant. Tenant tax rate Landlord tax rate χ=0.5 0 0.25 0.35 0.40 0 0.7890 0.7792 0.7963 0.7450 0.25 0.7920 0.7821 0.7721 0.7478 0.35 0.8067 0.7974 0.7871 0.7618 0.40 0.8294 0.8187 0.8080 0.7817 χ = 1 0 0.7890 0.7695 0.7567 0.7370 0.25 0.7920 0.7723 0.7597 0.7397 0.35 0.8067 0.7873 0.7740 0.7534 0.40 0.8294 0.8082 0.7944 0.7748 χ=1.5 0 0.7890 0.7598 0.7448 0.7291 0.25 0.7920 0.7628 0.7476 0.7317 0.35 0.8067 0.7772 0.7615 0.7461 0.40 0.8294 0.7977 0.7814 0.7662 Tenant tax rate Landlord tax rate χ=0.5 0 0.25 0.35 0.40 0 0.7890 0.7792 0.7963 0.7450 0.25 0.7920 0.7821 0.7721 0.7478 0.35 0.8067 0.7974 0.7871 0.7618 0.40 0.8294 0.8187 0.8080 0.7817 χ = 1 0 0.7890 0.7695 0.7567 0.7370 0.25 0.7920 0.7723 0.7597 0.7397 0.35 0.8067 0.7873 0.7740 0.7534 0.40 0.8294 0.8082 0.7944 0.7748 χ=1.5 0 0.7890 0.7598 0.7448 0.7291 0.25 0.7920 0.7628 0.7476 0.7317 0.35 0.8067 0.7772 0.7615 0.7461 0.40 0.8294 0.7977 0.7814 0.7662 View Large First, we consider how changes in the tenant’s tax rate affect the lease rate. For a fixed landlord tax rate, the lease rate increases for higher tenant tax rates. For instance, when χ=0.5 ⁠, and the landlord tax rate is 25%, the lease rate increases 4.7% (from 0.782 to 0.819) as the tenant’s tax rate increases from 25% to 40%. This behavior, also observed in Agarwal et al. (2011), results from the incentives that higher tax rates create for the tenant to utilize more debt, which in turn, makes the firm riskier. Similarly, we can observe how changes in the landlord’s tax rate affect the lease rate. The results indicate that for a fixed tenant tax rate, the lease rate decreases for higher landlord tax rates; notice that the lease rates decreases 4.35% (from 0.782 to 0.748) as one moves along the first row of the table (holding tenant tax rate constant at 25%). Once again, the incentive to utilize debt to take advantage of tax shields makes the landlord riskier for which the tenant is compensated in the form of a lower lease rate. However, changes in tax policies normally impact both firms simultaneously. The diagonal elements in each block in Table VI show the impact on the equilibrium lease rate of increasing corporate taxes. Since the increase in corporate taxes alters both the landlord’s and tenant’s incentives to use debt in the same direction, Table VI shows that the equilibrium lease rate remains virtually unchanged as tax rates increase. Thus, our analysis confirms that when both parties to a contract face the same tax environment, changes in tax policies should have no impact on the contract pricing. It is only in cases where changes in tax policy differentially impact one party over another that we should observe changes in the equilibrium contract pricing. Finally, the effect of allowing the landlord to accelerate depreciation of the leased asset (⁠ χ=0.5 to χ=1.5 ⁠) results in lower equilibrium lease rates; compare for example, 0.782 (first row, first column) to 0.763 (seventh row, first column). This phenomenon is expected as tax benefits to the landlord are passed to the tenant in the form of lower equilibrium lease rates. 7. Empirical Analysis In this section, we empirically validate several of the theoretical predictions from our model using a novel dataset of commercial real-estate investments. In order to empirically test these predictions, we assembled a dataset of single-tenant commercial real-estate properties utilizing data from the Trepp Data Feed loan file (Trepp) that comprises information on commercial real-estate loans. Trepp provides data covering over 69,000 loans that underlie CMBS. Trepp reports information about each loan and the property collateralizing the loan including information about the leases and square footage occupied by the property’s largest tenants. Furthermore, each mortgage in the loan file has a series of bond payment dates, referred to as tape dates, that allow us to time stamp the information provided about the loan and property. In addition to providing data about each loan on specific tape dates, Trepp provides information about the property and the property’s tenants at the time the loan is securitized. However, information at the time of loan origination is somewhat limited. Thus, we use information about the loan either at the time it is securitized or from a tape date that occurs within 18 months of origination. Because a large number of loans tracked by Trepp are conduit loans (i.e., mortgages originated to be securitized), the characteristics of the loan at securitization should be a close proxy for the loan’s characteristics at origination. Although Trepp provides information on a large number of commercial mortgages, we apply a series of highly restrictive data screens in order to isolate properties where we can observe both the landlord and tenant capital structure. Since Trepp reports information about the top-three tenants in the property securing the mortgage, we use that information to create a dataset of single-tenant properties. For example, we identified 320 properties in the Trepp database as being “single-tenant” leased after screening all loans for properties that report the top tenant as occupying more than 80% of the total leaseable area with lease terms less than 40 years. We then hand screened each of the tenant names to identify 166 properties where the tenant was either a public company or a subsidiary of a public company at the time of lease origination. By screening for tenants that were public companies at lease origination, we are able to collect information about the tenant’s capital structure (from publicly available financial statements). Trepp also provides the name of the borrower (property owner) for each mortgage. Thus, we examined the name of each property owner for the 166 properties with publicly traded tenants in order to determine whether the property owner was also a publicly traded firm. Consistent with standard practice in commercial real estate, the Trepp borrower name field indicates that the mortgage borrowers were most likely single-entity limited liability corporations. As a result, we assume that each property is held by a single-asset firm allowing us to use the mortgage loan-to-value ratio as a proxy for the landlord’s capital structure. Panel A in Table VII shows the distribution of properties by year of lease origination. We see that over 50% of the observations were originated in 2003 and 2004. Unfortunately, Trepp does not report the actual lease rate paid by the tenant. However, Trepp does report the property net operating income (NOI). Thus, under the assumption that tenants in single-tenant properties are usually responsible for expenses associated with the property, we use the property NOI as a proxy for the lease rent.25 Panel B in Table VII shows the descriptive statistics for the properties in our dataset. We see that landlords have an average capital structure (LTV) ratio of 66% while the tenant capital structure (debt/asset) ratio averages 59%. Furthermore, we see that 64% of the leases are classified as long term (>10 years). In addition, we note that 62% of the properties are classified as “retail,” 19% are industrial property, and 16% are general office buildings. Table VII. Summary characteristics of the single-tenant property sample Table VII reports the descriptive statistics for the commercial real-estate properties identified from commercial real-estate loans that are contained in the Trepp Data Feed file (Trepp). Trepp provides information on loans that underlie CMBS. The data comprise property-level and loan-level characteristics including the loan-to-value (LTV) at origination, the loan contract interest rate less the 10-year constant maturity treasury rate (ri), the mortgage term (T), and the property net operating income (NOI). Our dataset comprises loans on “single-tenant” properties where the tenant is identified as either a public company or a subsidiary of a public company at the time of lease origination. By screening for tenants that were public companies at lease origination, we are able to collect information about the tenant’s capital structure (Debt_Asset ratio) from publicly available financial statements. Panel A: Distribution of properties by year of lease origination Year Frequency Percent 1996 1 0.6 1997 21 12.7 1998 17 10.2 1999 4 2.4 2001 2 1.2 2002 13 7.8 2003 47 28.3 2004 49 29.5 2005 2 1.2 2006 10 6.0 Total 166 100.0 Panel B: Descriptive statistics Landlord: Mean Standard deviation Loan-to-value (LTVi) 65.925 16.677 Interest rate spread (ri) 1.730 0.664 Mortgage term (Ti) 144.584 54.465 Tenant: Lease rate (⁠ NOIi/sf ⁠) 29.320 48.797 Lease term (months) 154.030 81.093 Long-term lease indicator (Longi) 0.639 0.482 Debt/asset ratio at lease origination (⁠ Debt/Asseti ⁠) 58.991 22.392 Property: Building age 13.777 19.709 Industrial property indicator 0.187 0.391 Office property indicator 0.157 0.365 Retail property indicator 0.620 0.487 Other property type 0.036 0.187 Panel A: Distribution of properties by year of lease origination Year Frequency Percent 1996 1 0.6 1997 21 12.7 1998 17 10.2 1999 4 2.4 2001 2 1.2 2002 13 7.8 2003 47 28.3 2004 49 29.5 2005 2 1.2 2006 10 6.0 Total 166 100.0 Panel B: Descriptive statistics Landlord: Mean Standard deviation Loan-to-value (LTVi) 65.925 16.677 Interest rate spread (ri) 1.730 0.664 Mortgage term (Ti) 144.584 54.465 Tenant: Lease rate (⁠ NOIi/sf ⁠) 29.320 48.797 Lease term (months) 154.030 81.093 Long-term lease indicator (Longi) 0.639 0.482 Debt/asset ratio at lease origination (⁠ Debt/Asseti ⁠) 58.991 22.392 Property: Building age 13.777 19.709 Industrial property indicator 0.187 0.391 Office property indicator 0.157 0.365 Retail property indicator 0.620 0.487 Other property type 0.036 0.187 View Large Table VII. Summary characteristics of the single-tenant property sample Table VII reports the descriptive statistics for the commercial real-estate properties identified from commercial real-estate loans that are contained in the Trepp Data Feed file (Trepp). Trepp provides information on loans that underlie CMBS. The data comprise property-level and loan-level characteristics including the loan-to-value (LTV) at origination, the loan contract interest rate less the 10-year constant maturity treasury rate (ri), the mortgage term (T), and the property net operating income (NOI). Our dataset comprises loans on “single-tenant” properties where the tenant is identified as either a public company or a subsidiary of a public company at the time of lease origination. By screening for tenants that were public companies at lease origination, we are able to collect information about the tenant’s capital structure (Debt_Asset ratio) from publicly available financial statements. Panel A: Distribution of properties by year of lease origination Year Frequency Percent 1996 1 0.6 1997 21 12.7 1998 17 10.2 1999 4 2.4 2001 2 1.2 2002 13 7.8 2003 47 28.3 2004 49 29.5 2005 2 1.2 2006 10 6.0 Total 166 100.0 Panel B: Descriptive statistics Landlord: Mean Standard deviation Loan-to-value (LTVi) 65.925 16.677 Interest rate spread (ri) 1.730 0.664 Mortgage term (Ti) 144.584 54.465 Tenant: Lease rate (⁠ NOIi/sf ⁠) 29.320 48.797 Lease term (months) 154.030 81.093 Long-term lease indicator (Longi) 0.639 0.482 Debt/asset ratio at lease origination (⁠ Debt/Asseti ⁠) 58.991 22.392 Property: Building age 13.777 19.709 Industrial property indicator 0.187 0.391 Office property indicator 0.157 0.365 Retail property indicator 0.620 0.487 Other property type 0.036 0.187 Panel A: Distribution of properties by year of lease origination Year Frequency Percent 1996 1 0.6 1997 21 12.7 1998 17 10.2 1999 4 2.4 2001 2 1.2 2002 13 7.8 2003 47 28.3 2004 49 29.5 2005 2 1.2 2006 10 6.0 Total 166 100.0 Panel B: Descriptive statistics Landlord: Mean Standard deviation Loan-to-value (LTVi) 65.925 16.677 Interest rate spread (ri) 1.730 0.664 Mortgage term (Ti) 144.584 54.465 Tenant: Lease rate (⁠ NOIi/sf ⁠) 29.320 48.797 Lease term (months) 154.030 81.093 Long-term lease indicator (Longi) 0.639 0.482 Debt/asset ratio at lease origination (⁠ Debt/Asseti ⁠) 58.991 22.392 Property: Building age 13.777 19.709 Industrial property indicator 0.187 0.391 Office property indicator 0.157 0.365 Retail property indicator 0.620 0.487 Other property type 0.036 0.187 View Large Our theoretical model predicts that the lease rate should be a function of both the landlord’s capital structure (LTV) and the tenant’s capital structure (debt/asset ratio). For example, Figure 2 shows that the impact of an increase in the landlord’s capital structure (reflected by the movement from a risk-free landlord to a risky landlord) will have a greater impact on the lease rate as the lease maturity lengthens. In addition, keeping the endogenous default boundary of landlord fixed at its optimum, the theoretical predictions captured in Table V suggest that an increase in the tenant’s debt-to-asset ratio (reflected in Table V by the increase in λD,T ⁠) will result in a decrease in the lease rate as the lease maturity increases. Furthermore, Table V indicates that as we hold debt and lease maturities constant [as reflected by the increase in the tenant default boundary (DBT)], the lease rate will increase as the tenant’s debt-to-asset ratio increases. On the other hand, in Figure 1, we notice that an increase in landlord default probability will result in an increase in the tenant’s debt-to-asset ratio and a decrease in the lease rate. We regress our proxy for the observed lease rate on measures of the landlord and tenant capital structure prior to the lease origination date. However, we also recognize that the landlord’s capital structure (loan-to-value ratio) is endogenous to the associated mortgage terms and conditions prevailing in the capital markets. Thus, to account for the endogenous relation between loan terms (LTV, interest rate, and term) and NOI, we estimate the following system of equations: LTVi=α0+α1ri+α2Ti+α3NOIi+α4Debt/Asseti+ϵi  (21) Ti=γ0+γ1ri+γ2LTVi+ξi  (22) ri=δ0+δ1LTVi+δ2Ti+δ3rf+ωi  (23) NOIi=β0+β1LTVi+β2(Debt/Asseti)+β3(Longi) +β4(Longi*LTVi)+β5(Longi*Debt/Asseti)+εi  (24) where ri is the mortgage interest rate at origination, Ti is the mortgage term for property i, rf is the 10-year Constant Maturity Treasury rate, Longi is a dummy variable equal to 1 if the lease maturity is greater than 10 years, and zero otherwise, and Debt/Asseti is the tenant firm’s debt–asset ratio at the quarter prior to lease origination.26 Table VIII reports the estimated coefficients. As predicted by our theoretical model, we see that the tenant capital structure has a negative and statistically significant estimated tenant capital structure coefficient. The estimated coefficient indicates that a one-unit increase in the tenant’s capital structure (debt/asset) ratio decreases the lease rate by 0.94 units. We also note that the estimated coefficient for the interaction of the dummy variable for leases that are longer than 10 years with the landlord’s capital structure (Longi*LTVi) is negative and statistically significant. The negative coefficient on the interaction term indicates that increases in landlord debt usage have an even greater effect when leases are long term than when leases are short term. This result is exactly as predicted by the numerical analysis presented in Figure 2 showing an increasing negative relation between lease rates and lease term as landlord risk increases. Table VIII. Three-stage Least Squares (3SLS) Estimation of Landlord and Tenant Capital Structure on Lease Rate Table VIII reports the estimated coefficients for the following system of equations: LTVi=α0+α1ri+α2Ti+α3NOIi+α4Debt/Asseti+ϵi,Ti=γ0+γ1ri+γ2LTVi+ξi,ri=δ0+δ1LTVi+δ2Ti+δ3rf+ωi,NOIi=β0+β1LTVi+β2(Debt/Asseti)+β3(Longi) +β4(Longi*LTVi)+β5(Longi*Debt/Asseti)+εi, where LTVi, ri, rT, and Ti are the mortgage loan-to-value ratio, contract interest rate, the 10-year constant maturity treasury, and mortgage term for property i, respectively; Longi is a dummy variable equal to 1 if the lease maturity is >10 years, and zero otherwise; Debt/Asseti is the tenant’s debt to asset ratio at time of lease origination; and NOIi is a proxy for lease rent and is scaled by the leaseable area. The system is estimated via three-stage lease squares (3SLS). LTV Mortgage term Interest rate NOI rate Intercept 84.439*** 331.528*** 3.303*** 224.520*** Interest rate (r) –1.365 3.674* Mortgage term (T) –0.044*** –0.004 NOI rate –0.137*** Tenant (Debt/Asset) 0.014 –0.944*** Landlord (LTV) –3.180 –0.002 –1.553* 10-Year treasury rate 0.814*** Lease term (Long) 224.911*** LTV * LONG –5.070*** Debt∕Asset * Long 1.154*** System weighted MSE 8.592 Degrees of freedom 638 System weighted Rsq 0.647 LTV Mortgage term Interest rate NOI rate Intercept 84.439*** 331.528*** 3.303*** 224.520*** Interest rate (r) –1.365 3.674* Mortgage term (T) –0.044*** –0.004 NOI rate –0.137*** Tenant (Debt/Asset) 0.014 –0.944*** Landlord (LTV) –3.180 –0.002 –1.553* 10-Year treasury rate 0.814*** Lease term (Long) 224.911*** LTV * LONG –5.070*** Debt∕Asset * Long 1.154*** System weighted MSE 8.592 Degrees of freedom 638 System weighted Rsq 0.647 View Large Table VIII. Three-stage Least Squares (3SLS) Estimation of Landlord and Tenant Capital Structure on Lease Rate Table VIII reports the estimated coefficients for the following system of equations: LTVi=α0+α1ri+α2Ti+α3NOIi+α4Debt/Asseti+ϵi,Ti=γ0+γ1ri+γ2LTVi+ξi,ri=δ0+δ1LTVi+δ2Ti+δ3rf+ωi,NOIi=β0+β1LTVi+β2(Debt/Asseti)+β3(Longi) +β4(Longi*LTVi)+β5(Longi*Debt/Asseti)+εi, where LTVi, ri, rT, and Ti are the mortgage loan-to-value ratio, contract interest rate, the 10-year constant maturity treasury, and mortgage term for property i, respectively; Longi is a dummy variable equal to 1 if the lease maturity is >10 years, and zero otherwise; Debt/Asseti is the tenant’s debt to asset ratio at time of lease origination; and NOIi is a proxy for lease rent and is scaled by the leaseable area. The system is estimated via three-stage lease squares (3SLS). LTV Mortgage term Interest rate NOI rate Intercept 84.439*** 331.528*** 3.303*** 224.520*** Interest rate (r) –1.365 3.674* Mortgage term (T) –0.044*** –0.004 NOI rate –0.137*** Tenant (Debt/Asset) 0.014 –0.944*** Landlord (LTV) –3.180 –0.002 –1.553* 10-Year treasury rate 0.814*** Lease term (Long) 224.911*** LTV * LONG –5.070*** Debt∕Asset * Long 1.154*** System weighted MSE 8.592 Degrees of freedom 638 System weighted Rsq 0.647 LTV Mortgage term Interest rate NOI rate Intercept 84.439*** 331.528*** 3.303*** 224.520*** Interest rate (r) –1.365 3.674* Mortgage term (T) –0.044*** –0.004 NOI rate –0.137*** Tenant (Debt/Asset) 0.014 –0.944*** Landlord (LTV) –3.180 –0.002 –1.553* 10-Year treasury rate 0.814*** Lease term (Long) 224.911*** LTV * LONG –5.070*** Debt∕Asset * Long 1.154*** System weighted MSE 8.592 Degrees of freedom 638 System weighted Rsq 0.647 View Large We also find a positive and statistically significant coefficient for the interaction of the tenant’s capital structure and lease term (Longi∗Debt/Asseti) indicating that long-term leases mitigate the impact of higher tenant debt use. Notice that the statistically significant negative Debt/Asseti coefficient (–0.944) and positive interaction coefficient (1.154) together imply that longer term leases should increase the lease amount at a faster rate than shorter maturity leases in response to an increase in the tenant’s debt default risk (capital structure). This result is observed in Table VIII: If we consider a change in tenant debt maturity from 5 to 20 years and a lease maturity of 5 years, we find △rRR△(Debt/Asset)=0.7951−0.78710.3686−0.3753=−1.94. (25) Comparing this ratio to the change in tenant debt maturity from 5 to 20 years and a lease maturity of 10 years producing △rRR△(Debt/Asset)=0.6684−0.66210.1718−0.3810=−0.03, (26) we see that the rate of change increased (–1.194 to –0.03). Thus, with long-term leases, we find that a one-unit increase in the debt-to-asset ratio of the tenant leads to a smaller decrease in the lease rate. The estimated coefficients for the interaction of long-term leases with tenant capital structure confirm this prediction. 8. Conclusion The depth and length of the 2007–9 financial crisis raised awareness of the implications of counterparty risk arising from capital structure decisions to many contracts once thought immune to such problems. Recent examples that demonstrate how a firm’s capital structure can impact entities that have relationships with it extend well beyond the typical financial contracts discussed in the literature. For example, bankruptcies among franchisors, home builders, and real-estate investors have highlighted that counterparty capital structure is an important risk to understand. Using commercial real estate as the motivating example, we develop a continuous time structural model to consider how the endogenous capital structure decisions of landlords and tenants interact to determine equilibrium lease rates. Thus, we provide a novel mechanism to illustrate the credit contagion that results between tenant and landlord through the lease contract. Our analysis also highlights a little known aspect of how the riskiness of counter-parties to a firm’s off-balance sheet financing tools (such as leases) can impact the firm’s capital structure decisions. As a result, our model illustrates the complexity and associated endogenous relationships that accompany corporate financing decisions. Our numerical analysis provides a number of empirical predictions. First, our model predicts that tenants face lower equilibrium lease rates as their landlord’s risk increases and this risk increases with exposure to the landlord through lease maturity. In addition, the numerical results show that credit contagion can be amplified through long-term off balance sheet contracts. In other words, when the landlord’s credit condition deteriorates, tenant debt default probability increases through the interaction of the lease contract and the firm’s capital structure. Second, our model indicates that tenants have an increasing preference for debt as their landlord riskiness increases. Third, our model confirms the intuitive phenomenon that landlords should be compensated with higher lease rates when renting to riskier firms. Fourth, our model provides the novel prediction that the downward sloping term structure of lease rates should become steeper as the landlord risk increases, indicating that long-term leases are discounted more heavily in the presence of landlord risk. Finally, we show that landlord default risk is instrumental in determining the complementary/substitution behavior between debt and leases. We observe debt and leases acting as complements for low levels of tenant debt when landlord risk is introduced. This numerical evidence gives a rational foundation underlying the complements effect documented in previous studies, for example, Ang and Peterson (1984). Thus, our numerical analysis highlights the importance of considering counterparty default risk when assessing the relationship between debt and leases. In order to verify the veracity of the model, we empirically test the model’s predictions using a dataset of single leased properties with publicly traded tenants. Our empirical analysis confirms the model’s prediction that lease rates are negatively related to tenant and landlord capital structures. Furthermore, our analysis indicates that lease maturity has a differential impact on lease rates based on the lessor’s risk, as predicted by the model. Appendix A.1 The Risky Landlord and the Risk-Free Tenant To derive a full equilibrium lease rate, we first model the case assuming a risk-free lessee and a credit-risk lessor. This scenario resembles the situation where a developer builds and leases an office building to the government. The lessor’s credit risk results from his decisions regarding capital structure and thus a risk-free lessor is a special case where the lessor has no debt. Since the landlord’s ability to provide the contracted service flow may be impacted by default, his default probability is considered in the formulation of the net cost of the lease contract. To begin, we define distributions with respect to the first passage time u to the landlord’s default boundary VL,B from the landlord’s present un-leveraged firm value VL. Accordingly, we let pL(u;VL,VL,B) denote the landlord’s cumulative survival probability and define fL(u;VL,VL,B) to be the probability density function of landlord default. We express the time of landlord default as τL. The landlord’s expected net cost of providing the lease from time 0 until maturity t is the expected present value of the service flows before depreciation minus the tax-shield benefit associated with the depreciation expense before default plus the expected cost claimed by the tenant if the landlord defaults: E~[∫0te−ru[SBD(u)−χLTaxL(SBD(u)−SAD(u))]×1{τL>u}du]+E~[ρLt(∫τLte−ru[SBD(u)−χLTaxL(SBD(u)−SAD(u))]du)×1{τL≤t}]=∫0te−ru[SBD(u)−χLTaxL(SBD(u)−SAD(u))]×pL(u;VL,VL,B)du+∫0te−ru DamageufL(u;VL,VL,B)du, (A.1) where ∫0tSBD(u)e−rudu represents the present value of the service flows before depreciation from time 0 to time t discounted by the risk-free rate under risk-neutral measure ℙ˜ ⁠, and ∫0tSAD(u)e−rudu represents the present value of the service flow after depreciation under the risk-neutral measure ℙ˜ ⁠. E˜(⋅) is the expectation under ℙ˜ ⁠. The difference between these two terms is the depreciation cost of the leased asset from time 0 to t. TaxL is the corporate tax rate for landlord and χL is the depreciation adjustment factor that reconciles the government mandated accounting depreciation to the actual physical depreciation.27 The indicator function 1{τL≤t}=1,0 if τL≤t,0  otherwise, respectively, (A.2) highlights when a default occurs. ρLt denotes the recovery rate of the lease contract upon landlord default that may be a function of the maturity t. Additionally, Damageu refers to the landlord’s cost upon default at time u. The first term in Equation (A.1) is the the expected present value of the service flows before depreciation minus the tax-shield benefit associated with the depreciation expense before default, and the second term is the expected cost claimed by tenants upon landlord default. If the landlord or debtor rejects the lease, we have to consider two scenarios: First, the tenant leaves the leased property and files a claim equal to her loss due to landlord’s default. That loss might be due to the inability to use the leased property or the loss associated with having to temporarily stop its business operation. In the second scenario, the tenant remains in the leased property and the landlord continues to pay the cost of providing the contractual service flow. However, the tenant may be responsible for additional costs, such as power, heat, and trash disposal and thus we can assume that damage is a proportion of the present value of future service flows. We define Damageu in Equation (A.1) to be a percentage of the present value of future service flows from default time u to t Damageu=ρLt∫ute−rv[SBD(v)−χLTaxL(SBD(v)−SAD(v))]dv. (A.3) For simplicity, we assume the recovery rate ρLt is constant and independent of t, that is, ρLt=ρL ⁠. Since the leased property is still in the hands of the landlord, he is responsible for the depreciation expense. Thus, the sum of the two terms in Equation (A.1) is the expected net cost of providing the leased property from the landlord’s perspective, recognizing the tax-shield benefit associated with the depreciation expense. In a competitive market, the expected net cost of the lease exactly equals the present value of the future lease payments if the tenant does not default. Thus, the expected cost of the lease is ∫0trRNte−rudu=rRNt(1−e−rtr) ⁠, where rRNt denotes the operating lease rent with maturity t for a combination of a risky landlord and a risk-free tenant. We can solve for the lease rate rRNt by setting Equation (A.1) equal to rRNt(1−e−rtr) Thus, assuming the asset service flow follows Equation (2), then the lease rate is28: rRNt=r1−e−rt×[(1−χLTaxL)∫0tSBD(0)e(μS−r−δσS)u(1−F(u;VL,VL,B))du+χLTaxL∫0tSAD(0)e(μS−r−q−δσS)u(1−F(u;VL,VL,B))du+ρLt((1−χLTaxL,T)×SBD(0)μS−r−δσS[e(μS−r−δσS)tF(t;VL,VL,B)−∫0te(μS−r−δσS)u fL(u;VL,VL,B)du]+χLTaxLSAD(0)μS−r−q−δσS×[e(μS−r−q−δσS)tF(t;VL,VL,B)×−∫0te(μS−r−q−δσS)ufL(u;VL,VL,B)du])]. where δ denotes the market price of risk for the service value process. F(u;VL,VL,B) is landlord’s cumulative default probability and fL(u;VL,VL,B) is landlord’s default probability. A.2 Numerical Implementation Notes For (i), the numerical implementation is similar to the procedure carried out in Leland and Toft (1996). We begin by solving for the landlord’s endogenous default boundary values (VL,B) for a set of debt contracts characterized by the combination of principal and coupon (PL,CL) taken over the principal range [0.5,100] with steps △PL=0.5 ⁠. As in Leland and Toft (1996), we assume the coupon (CL) is set so that newly issued debt sells at par value (⁠ dL(V;cL,p)|VL=VL(0)=pL ⁠, where pL=PL/TL,D and cL=CL/TL,D ⁠.) We use the bisection method to solve dL = pL in order to obtain CL for a given PL. After obtaining the debt contract pair (PL,CL) ⁠, we then calculate the corresponding endogenous default boundary VL,B ⁠. Once we obtain the set of endogenous default boundaries that correspond to the set of debt principal and coupon contracts, we then select the debt contract (PL,CL) that maximizes the landlord’s value vL(VL;VL,B) ⁠. For (ii), once we determine the landlord’s endogenous boundary VL,B* ⁠, we then calculate the equilibrium lease rate and find the tenant’s optimal capital structure. The numerical method for doing so follows the procedure carried out in Agarwal et al. (2011). Recall that Leland and Toft (1996) demonstrate that a firm’s optimal default boundary VB can be calculated given the debt contract combination (P, C). However, from Equation (14), we see that the tenant’s optimal default boundary VT,B* also depends upon the risky lease rent rRRTL as well as the debt contract. Thus, even if we fix PT, we cannot directly solve for CT satisfying dT(V;VT,B,t)=pT since rRRTL is also unknown.29 It is useful to observe that Equation (5) is equivalent to the requirement that newly issued leases are issued at their “par” value, that is, equal to the expected present value of service flows. Thus, Equation (5) is the natural extension for leases to the condition in Leland and Toft (1996) that requires new debt to be issued at “par” value. As a result, we input into dT(V;VT,B,t)=pT the value rRRTL that satisfies Equation (5). In other words, the numerical task is to find the combination of cT and rRRTL such that both debt and leases equal their par value for a given PT. To complete this numerical task, we must solve a two-dimensional system of nonlinear equations. We utilize the following step-by-step method to approximate this solution. Specify a principal and coupon range: [0.5,100]×[(0.01)P,(0.1)P] ⁠. Fix a pair (P, C) and use the bisection method to solve Equation (5) for rRRTL ⁠.30 With 2., check whether the value of rRRTL also satisfies dT(V;VT,B,t)=pT ⁠. If it does, then the pair CT,rRRTL represents a solution to the two-dimensional system. If not, record this error, increment the coupon by △C ⁠, and repeat the process.31 Continue this process until dT(V;VT,B,t)=pT is satisfied or until CT=(0.1)PT ⁠.32 After implementing this procedure and obtaining PT, CT, and rRRTL ⁠, we can then complete part (ii) by calculating the endogenous tenant default boundary VT,B and capital structure corresponding to the pair (PT,CT) that maximizes the firm value vT(VT;VT,B) ⁠. The endogenous boundary corresponding to this capital structure is the optimal endogenous boundary for the tenant VT,B* ⁠. With this boundary, we then calculate the value of the tenant’s debt and equity and thus completing part (iii) of the numerical scheme. A.3 Derivations A.3.1 Derivation of Lease Rate Recall, δ is the market price of risk for the service value process. In this section, suppose τ is the time of default for the landlord and F is the cumulative distribution function for the landlord default time. We begin with four calculations that will assist in determining the lease rate. Using Fubini’s theorem, we have E˜[∫0te−ruSBD(u)1{τ>u}du]=E˜[∫0te−ruSBD(0)e(μS−δσS−σS22)u+σSW˜S(u)1{τ>u}du]=∫0tSBD(0)e(μS−r−δσS−σS22)u×E˜[eσSW˜S(u)1{τ>u}]du=∫0tSBD(0)e(μS−r−δσS)u×(1−F(u;VL,VL,B))du, where the last line follows by assuming the independence of τ and W˜S(·) since E˜[eσSW˜S(u)1{τ>u}]=eu2σS2×(1−F(u;VL,VL,B)). (A.4) Similarly, E˜[∫0te−ruSAD(u)1{τ>u}du]=E˜[∫0te−ruSAD(0)e(μS−q−δσS−σS22)u+σSW˜S(u)1{τ>u}du]=∫0tSAD(0)e(μS−r−q−δσS−σS22)u×E˜[eσSW˜S(u)1{τ>u}]du=∫0tSAD(0)e(μS−r−q−δσS)u×(1−F(u;VL,VL,B))du  Let n(·) denote the density of the standard normal distribution. Using Fubini’s theorem and the independence of τ and W˜S(·) ⁠, we have E˜[∫τte−rsSBD(s)1{τ≤t}ds]=SBD(0)∫−∞∞∫0t∫ute(μS−r−δσS−σS22)s+σSsxds×fL(u;VL,VL,B)n(x) du dx =SBD(0)∫0t∫ut∫−∞∞e(μS−r−δσS−σS22)s+σSsx×fL(u;VL,VL,B)×12πe−x22dx ds du =SBD(0)∫0t∫ute(μS−r−δσS)sds fL(u;VL,VL,B)du =SBD(0)∫0t1μS−r−δσS(e(μS−r−δσS)t−e(μS−r−δσS)u) fL(u;VL,VL,B)du =SBD(0)μS−r−δσS(e(μS−r−δσS)tF(t;VL,VL,B)−∫0te(μS−r−δσS)u fL(u;VL,VL,B)du), if μS−r−δσS≠0 ⁠. Similarly, if μS−r−q−δσS≠0 ⁠, E˜[∫τte−rsSAD(s)1{τ≤t}ds]=SAD(0)∫−∞∞∫0t∫ute(μS−r−q−δσS−σS22)s+σSsxds×fL(u;VL,VL,B)n(x) du dx =SAD(0)∫0t∫ut∫−∞∞e(μS−r−q−δσS−σS22)s+σSsx×fL(u;VL,VL,B)×12πe−x22dx ds du. =SAD(0)∫0t∫ute(μS−r−q−δσS)sds fL(u;VL,VL,B)du =SAD(0)∫0t1μS−r−q−δσS(e(μS−r−q−δσS)t−e(μS−r−q−δσS)u)×fL(u;VL,VL,B)du =SAD(0)μS−r−q−δσS(e(μS−r−q−δσS)tF(t;VL,VL,B)−∫0te(μS−r−q−δσS)u×fL(u;VL,VL,B)du) Recall from Equation (A.1), the lessor’s expected net cost of providing lease services is E˜[∫0te−ru[SBD(u)−χLTaxL(SBD(u)−SAD(u))]1{τ>u}du]+E˜[ρLt(∫τte−ru[SBD(u)−χLTaxL(SBD(u)−SAD(u))]du)1{τ≤t}], (A.5) where the last term is the damage caused to the tenant, that is, a proportion (perhaps >1) of the future service flows. The four above calculations allow us to resolve this net cost of lease services. Thus, the first term in Equation (A.5) is equal to E˜[∫0te−ru[SBD(u)−χLTaxL(SBD(u)−SAD(u))]1{τ>u}du]=(1−χLTaxL)∫0tSBD(0)e(μS−r−δσS)u×(1−F(u;VL,VL,B))du+χLTaxL∫0tSAD(0)e(μS−r−q−δσS)u×(1−F(u;VL,VL,B))du. (A.6) With regard to the second term in Equation (A.5), we have E˜[ρLt(∫τte−ru[SBD(u)−χLTaxL(SBD(u)−SAD(u))]du)1{τ≤t}]=ρLt((1−χLTaxL)×SBD(0)μS−r−δσS(e(μS−r−δσS)tF(t;VL,VL,B)−∫0te(μS−r−δσS)u fL(u;VL,VL,B)du) +χLTaxLSAD(0)μS−r−q−δσS×(e(μS−r−q−δσS)tF(t;VL,VL,B)−∫0te(μS−r−q−δσS)u×fL(u;VL,VL,B)du)). Now, equating Equation (A.5) with rRNt(1−e−rtr) yields, rRNt(1−e−rtr)=(1−χLTaxL)∫0tSBD(0)e(μS−r−δσS)u×(1−F(u;VL,VL,B))du+χLTaxL∫0tSAD(0)e(μS−r−q−δσS)u×(1−F(u;VL,VL,B))du +ρLt((1−χLTaxL)×SBD(0)μS−r−δσS(e(μS−r−δσS)tF(t;VL,VL,B)−∫0te(μS−r−δσS)u fL(u;VL,VL,B)du) +χLTaxLSAD(0)μS−r−q−δσS×(e(μS−r−q−δσS)tF(t;VL,VL,B)−∫0te(μS−r−q−δσS)u×fL(u;VL,VL,B)du)). Solving the above equation for rRNt yields the risky lessor, risk-free tenant lease rate: rRNt=r1−e−rt×[(1−χLTaxL)×∫0tSBD(0)e(μS−r−δσS)u×(1−F(u;VL,VL,B))du+χLTaxL∫0tSAD(0)e(μS−r−q−δσS)u×(1−F(u;VL,VL,B))du+ρLt((1−χLTaxL)SBD(0)μS−r−δσS×(e(μS−r−δσS)tF(t;VL,VL,B)−∫0te(μS−r−δσS)u fL(u;VL,VL,B)du)+χLTaxLSAD(0)μS−r−q−δσS×[e(μS−r−q−δσS)tF(t;VL,VL,B)−∫0te(μS−r−q−δσS)u×fL(u;VL,VL,B)du])]. (A.7) A.3.2 Definitions of Constants aT:=r−δVT−(σVT2/2)σVT2; aL:=r−δVL−(σVL2/2)σVL2;bT:=ln(VTVT,B); bL:=ln(VLVL,B);zT:=((aTσVT2)2+2rσVT2)1/2σVT2; zL:=((aTσVL2)2+2rσVL2)1/2σVL2;xT:=aT+zT;xL:=aL+zL;A:=2aLe−rTL,DN(aLσVLTL,D)−2zLN(zLσVLTL,D)−2σVLTL,Dn(zLσVLTL,D)+2e−rTL,DσVLTL,Dn(aLσVLTL,D)+(zL−aL); B:=−(2zL+2zLσVL2TL,D)N(zLσVLTL,D)−2σVLTL,Dn(zLσSTL,D)+(zL−aL)+1zLσVL2TL,D;K1T:=A/(rT)K2T:=BK3:=(CT+ΩR)(TaxTr)xT;K4:=(1−ρR)ΩR(1−e−rTL2r);M:=(ΩRrρR)(K1TLTLTT,D−K2TT,D)−(ΩRrρRTL)(K1TL−K2TL), where N(·) is the cumulative standard normal distribution and n(·) is the probability density function of the standard normal distribution. TaxT is the tenant’s corporate tax rate. A.3.3 Calculation for “Damage by Default” Term in Equation (16) The “damage by default” term is the compensation owed to the tenant upon landlord default and is equal to ρLE˜[(∫τLTLe−r(u−TL2)[SBD(u)−χLTaxL(SBD(u)−SAD(u))]du)1{τL≤TL}], where ρL is the recovery rate for lost service flows and δ is the market price of risk parameter. Note that this cost depends upon the endogenous default time for the landlord. To simplify the analysis, we calculate this cost when default occurs at the midpoint of the lease contract. This simplification does not assume that the landlord’s endogenous default time τL is fixed at TL/2 ⁠. Rather, we are simplifying the cost calculation for the landlord. The choice of using the midpoint of the lease contract serves as a means of calculating the average cost incurred by the landlord. Thus, we have damage by default=ρLE˜[∫TL/2TLe−r(u−TL2)[SBD(u)−χLTaxL(SBD(u)du−SAD(u))]du]=ρLerTL2[(1−χLTaxL)SBD(0)μS−r−δσS(e(μS−r−δσS)TL−e(μS−r−δσS)TL2) +SAD(0)μS−r−δσS−qχLTaxL(e(μS−r−δσS−q)TL−e(μS−r−δσS−q)TL2)],   if μS−δσS−q−r≠0. A.4 Debt-to-Lease Displacement Ratio α As in Ang and Peterson (1984), we assume the following equation holds. DRNL=DRL+αLRL, that is,DNLVNL=DLVL+αLVL. (A.8) Recall, when α>0 (respectively, α<0 ⁠), debt and leases act as substitutes (respectively, complements). Consider two firms (1 and 2, respectively) with different lease amounts but where both are similar to a firm that does not lease. Using the above equation, the difference between their debt and lease ratios can be written as (DL1VL1+αL1VL1)−(DL2VL2+αL2VL2)=0. (A.9) Continuing, we have VL2DL1−VL1DL2+α(VL2L1−VL1L2)=0 (A.10) DL1+αL1−VL1VL2(DL2+αL2)=0. (A.11) Solving for α, we find α=−DL1−VL1VL2DL2L1−VL1VL2L2. (A.12) We utilize the above representation of α in our numerical analysis of our model to consider the relationship between debt and leases. Footnotes * We thank Dan Cahoy, Sumit Agarwal, and the seminar participants at the BIFEC conference in Istanbul, Pennsylvania State University and at Rensselaer Polytechnic Institute, and National Taiwan University for their helpful comments and suggestions. 1 For example, Myers, Dill, and Bautista (1976) provide theoretical justification for treating leases and debt as substitutes. Smith and Wakeman (1985a) provide an informal list of characteristics of users and lessors that influence the leasing decision, and argue that the substitutability between debt and leases is affected by these characteristics. Eisfeldt and Rampini (2009) provide a more detailed review. 2 See, for example, Bayliss and Diltz (1986); Marston and Harris (1988); Beattie, Goodacre, and Thomson (2000); Yan (2006); and more recently Agarwal et al. (2011). 3 The characterization of the relationship between debt and leases in Ang and Peterson (1984) is distinct from the economic definition of complementary and substitute assets. 4 See Hudson (2009). 5 See Schaefers (2009). 6 See Kulikowski (2012, p. 1). 7 For example, Sullivan and Kimball (2009) point out that “if the lease was entered into after the landlord’s mortgage (or, as is often the case, the lease provides that it is automatically subordinate to any mortgage), the lender’s foreclosure action would automatically terminate the lease, wiping out the tenant’s right to possession along with its investment in its leasehold improvements.” 8 In addition to risks associated with lessor default and foreclosure on debt, tenants also face the possibility that property owners may file for protection from creditors under the bankruptcy code. If a landlord files for reorganization under Chapter 11 of the bankruptcy code, then the tenant’s lease contract is subject to Sections 365 and 363 of the Bankruptcy Code. These sections allow the bankruptcy trustee to either affirm or reject the lease. As a result, tenants with below market rents could find their leases terminated or property services suspended as part of an overall debt restructuring plan. According to Title 11, Chapter 3, Subchapter IV, Section 365 (h)(1), tenants in a lease rejected by the trustee may retain their rights to occupy the space as defined by the lease, but the landlord is released from providing services required under the lease. The tenant will then have to contract separately for those services and may offset the costs of those services from future rent payments (see Anderson (2014) and Eisenbach (2006)]. However, Eisenbach (2006) further notes that tenants in a sublease do not have protection under Section 365(h)(1) and thus would have no rights to continue occupying the space if the trustee rejects the original lease. Harvey (1966) also discusses the rights of tenants upon landlord breach under California law. 9 See Section 6.3 below for a precise definition of the debt-to-lease displacement ratio. 10 Recent work by Clapham and Gunnelin (2003), Ambrose and Yildirim (2008), and Agarwal et al. (2011) expanded on these models to explicitly incorporate the interaction of tenant credit risk and capital structure on the endogenous determination of lease rates. These models recognize the risk that tenants may default on their lease obligations. 11 See the Appendix for the derivation of rRNt and other notation. 12 Note that (GT(t)−FT(t)e−rt)=∫0te−rufT(u;V,VB)du−∫0te−rtfT(u;V,VB)du=∫0t(e−ru−e−rt)fT(u;V,VB)du>0. 13 For the Tenant’s capital structure incorporating the lease and debt, refer to Section IV of Agarwal et al. (2011). 14 Placing the leased asset inside a firm mirrors the market practice of securitizing real-estate assets in a REIT structure. 15 In an operating lease, the present value of lease expenses is not listed on the debt side of the balance sheet and the operating lease expenses for the future 5 years are only listed as a footnote of the balance sheet. However, in terms of cash flows, the lessee firm will expend lease payments in exchange for the leased asset’s service flows that generate operating cash flows for the firm. Therefore, in terms of cash flows, we treat the present value lease expenses as a part of the lessee firm’s debt side on the balance sheet. 16 In the following, we adopt the notation from Leland and Toft (1996) to describe the stationary debt structure. 17 The reasoning here for leases is the same as in Leland and Toft (1996) for debt. Letting l(VL;VL,B,t) denote the lease contract value with maturity t, the value of all outstanding leases (under our stationary debt and lease structure) is ∫t=0Tl(VL;VL,B,t)dt ⁠. If 1 year passes, the total lease payment owed is approximately the Riemann sum rRRTL△t+⋯+rRRTL△t of (TL/△t) terms. The exact payment is the limit of the Riemann sum equal to rRRTLTL ⁠. Now, set the continuous lease rate as rRRTL:=ΩR/TL ⁠. Thus, ΩR represents the total lease payment per year. 18 The definitions of K1T, K2T ⁠, K3, K4, xT, and M in Equation (14) appear in the Appendix. 19 See the Appendix for a discussion about how this term is calculated for the numerical implementation. 20 Letting Ei,Di, i=T, L denote tenant and landlord aggregate equity and debt value, respectively, we have vL=EL+DL , therefore, EL=vL−DL ⁠. 21 See the Appendix for additional notes regarding the implementation scheme. 22 See, for example, Agarwal et al. (2011). 23 See the Appendix for details about the estimation of α. 24 Note that the lease rates in the rows corresponding to the default boundaries of 30, 40, and 60 of each block do not change (holding lease maturity constant) as tenant debt maturity increases (⁠ TT,D=5,10,20 ⁠). This is due to the fact that once the tenant default boundary is determined, the tenant debt maturity does not enter into Equation (5); the time variable in Equation (5) refers to lease length TL. 25 NOI is defined as gross revenues (rent) less operating expenses and is similar to earnings before interest, taxes, depreciation, and amortization. 26 As noted above, NOI is our proxy for lease rent and is scaled by the leaseable area. We estimate the equations in Equation (24) simultaneously using three-stage least squares instrumenting with the log of building age and property type. Our instruments satisfy the usual exclusion restrictions since CMBS mortgages are underwritten to uniform risk standards regardless of building age or type. 27 See Agarwal et al. (2011). 28 See the Appendix for the proof. 29 The “correct” rRRTL satisfies Equation (5). 30 We note that the functions GT and FT are also functions of rRRTL through VT,B ⁠. 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TI - Capital Structure and the Substitutability versus Complementarity Nature of Leases and Debt
JO - Review of Finance
DO - 10.1093/rof/rfy004
DA - 2019-05-01
UR - https://www.deepdyve.com/lp/oxford-university-press/capital-structure-and-the-substitutability-versus-complementarity-6Y0EkRCPIp
SP - 659
VL - 23
IS - 3
DP - DeepDyve
ER -