RENT PRICING DECISION SUPPORT MATHEMATICAL MODEL FOR FINANCE LEASES UNDER EFFECTIVE RISKS

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1 JOURNL OF ENGINEERING NGEENT ND COPETITIVENESS (JEC) Vol. 5, No., 205, 3- RENT PRICING DECISION SUPPORT THETICL ODEL FOR FINNCE LESES UNDER EFFECTIVE RISKS UDC: 338.5: ]:59.87 Original Scientific Paper asoud RBBNI, Shadab Shisheh GR 2, Zeinab GEINI 2, Haed RFIEI 2, ahdi DOLTKHH 2 Departent of Industrial Engineering, College of Engineering, University of Tehran, Tehran, Iran E-ail: rabani@ut.ac.ir 2 Departent of Industrial Engineering, College of Engineering, University of Tehran, Tehran, Iran Paper received: ; Paper accepted: Nowadays, leasing has becoe an increasingly iportant and popular ethod for euipent acuisition. But, because of the rent pricing difficulties and soe risks that affect the lessor and lessee's decision aking, there are any people that still tend to buy euipent instead of lease it. In this paper we explore how risk can affect the leasing issue support atheatical odel. For this purpose, we consider three types of risk; Credit risk, Transaction risk and Risk based pricing. In particular, our focus was on how to ake decision about rent pricing in a leasing proble with different custoers, various uality levels and different pricing ethods. Finally, the atheatical odel has been solved by Genetic lgorith that is a search heuristic to optiize the proble. This algorith was coded in TLB R202a to provide the best set of results. Keywords: leasing, pricing, transaction risk, risk based pricing, genetic algorith. INTRODUCTION Nowadays, leasing is a good option for firs and copanies to buy expensive services or assets which could be defined as: a process in which a fixed asset is borrowed by an individual or entity in return for certain and periodic payents in a certain period. Leasing is uite siilar to debt, but it brings ore benefits for both the lessee and the lessor copared to debt. For instance, the lessor has to pay less tax and the lessee can buy the asset at the end of the period in soe kinds of leases. nother benefit for the lessor is during bankruptcy procedure because, he could return the leased asset to lessee and break to pay ore oney to hi (Lin et al., 203). In the leasing contract, the period of lease should be specified. Generally, the period of leasing should not be less than a year and ore than 80% of the asset s life tie. Four different types could be considered for leasing; financial lease, operating lease, sale and lease back and leveraged leasing. Each type has its own characteristics. For exaple, in operating lease the lessor is responsible for asset s aintenance while in financial lease it is not the lessor s duty to aintain the asset. Or in leveraged leasing the asset which leased, is often expensive so the lessee is forced to buy it by loan or debt and there are three parties in this kind of leasing. This paper has considered operating lease, because of soe assuptions that has taken into account for odeling. However, in the leasing proble, we have to decide whether to purchase or lease, and this will be possible by considering the rent price. In this issue, any copanies often prefer to lease rather than buy euipent and real estate especially when they need facilities in the short ter or when less than an entire building is reuired (Ghayoot, 2003). In spite of leasing benefits in any circustances, there are soe risks that affect its uality. Soe of the applicable risks associated with financing lease are Credit risk, Interest rate risk, arket risk, Operational risk, Liuidity risk, Transaction risk and Risk based pricing which are briefly described below: Credit risk: When a borrower fails to ake his payents because of the credit lost. Interest rate risk: When an unexpected change in interest rates negatively affect the value of an investent. ISSN (Print) 205 University of Novi Sad, Technical faculty ihajlo Pupin in Zrenjanin, Republic of Serbia vailable online at

2 4 Rabbani et al. arket risk: When an investor experiences losses due to factors that affect the overall perforance of the financial arkets. Operational risk: When a breakdown occurs in internal processes, people or syste. Liuidity risk: When the difficulties of selling an asset arises. Transaction risk: When the exchange rate changes after a transaction agreeent. Risk based pricing: When the differences between the pay back ability of people ake lessee to allocate different interest rates on the sae loan to different people. This paper tries to describe a new leasing proble that is affected by three applicable risks; Credit risk, transaction risk and risk based pricing. any ties exchange rate fluctuations in developing countries ake soe probles for those who acuire an asset. But the transaction risk avoids the to lease that asset. lso, credit risk indicates that soe lessees ay face difficulties and do not be able to pay their lease price to the lessor. So, by considering risk based pricing, the lessor allocates different interest rate to different people i.e. those with higher credit score get a lower interest rate and vice versa. By applying these risks, we generate a atheatical odel that helps the lessor decide on the proper price of each uality level that is defined for the asset, and clarify that which custoer is ualified for these price and level of uality. Hence, we assue that in the early years, depreciation is calculated by Double Declining Balanced ethod (DDB) and fro the year t, the calculating ethod is switched to Straight Line (SL). This assuption can save ore oney for the lesser. The reainder of the paper is organized as follows: Section 2 includes a literature review about leasing, and pricingoriented papers within the context of related risks and their effects on decision aking. Proble description and odel forulation are given is Section 3. Section 4 includes the solution procedure. Experiental results are presented is Section 5 and finally Section 6 includes the conclusion and further study. LITERTURE REVIEW The literature on finance lease odeling under effective risks is liited. ost of the existing studies were published in the last few years. These studies could be classified into three categories. The first category explains this proble theoretically. The advantages and disadvantages of leasing and owning real estate (Ghayoot, 2003) are considered in such studies. lthough, soe surveys has been conducted to illustrate the degree of leasing popularity aong copanies. For exaple, a survey on the leasing practices of Fortune 500_ n annual list published by Fortune agazine that ranks the top 500 U.S. corporations_ firs, was done in 99. The priary focus of this survey is on the analytical issues involving financial leases. In this study, the author has found that ost firs (88%) treat leasing as a financing decision. lso, about half of the firs view leasing as a substitute for debt (Redan and Tanner, 99). In addition, a survey in the UK Capital Econoic Organization in 2002 found that coercial and industrial lessees use their rented space ore efficiently than owner-occupiers, saving 2% per eployee. Jane-Raung Lin et al (202) show that firs are not indifferent between debt and leases and the fir s choices depend on their financial liitations. Firs with ore tangible assets prefer leasing to borrowing. So, it is shown that this kind of firs use ore operational leasing by surveying a saple of 458 firs fro Copustat North erica for the period of 99 to 2005 (Lin et al., 203). In another survey, Redan et al. (ukherjee, 99) has worked on sources of funds to acuire real estate. In this atter they studied uses and evaluation of leases. In this issue, 28 ebers of international association of corporate real estate fro twelve hundred ebers, answered to 23 uestions about their firs. One of the concerns of this survey was the use of leasing by corporations. The ost coon benefits, considered by the anagers were the conservation of cash, and tax benefits were the next one. ost of the firs used NPV ethod for leasing calculation. The alternative approach was ROR (Rate of Return) for the. By surveying the literature, we observe that the ain areas the finance lease can deal with, is the proble of aking decision between lease or buy euipent. In this regard, khatshwa (20) has used the net present value (NPV) to decide whether to lease or purchase euipent. He has considered the effects of inflation rate on the NPV's of odel. Based on the analysis considered in this study, certain conclusions can be ade with considering the effects that inflation, interest rates and project life has on the decision to lease or purchase euipent. It is shown that when the percentage of own euity increases, the NPV or expected profit fro a project will decrease at a constant rate. The analysis also gave further insight on the effect of the loan payback period, the project life and the changes in interest rate on net present value. lso,

3 JOURNL OF ENGINEERING NGEENT ND COPETITIVENESS (JEC) 5 the diagras of the above changes are provided to suarize the results of the analysis. lthough, another study has been done that used the present values ethod after tax to copare the lease versus buy profitability, but the scrap value of the investent was not taken into account. However, for calculating the depreciation, three ethods were exained: declining balance ethod, straight line ethod and realization ethod. Then these ethods were used to calculate the net present value of depreciation and finally to calculate NPV (buy) and NPV (lease). By coparing the the right choice is easily achieved (ho and Virtanen, 98). nother study that has used the NPV ethod was done by Levy and Sarnat (979). They discussed the solution to the practical proble of neutralizing the risk differential induced by lease contracts. nd also, they brought up the lease vs. buy proble. This proble stes of using different euations. The used ethod is NPV because the lease or buy decision is a type of capital budgeting proble reuiring the application of present value techniues and taxes are iportant for aking decision with calculating cash flow before and after tax. Finally, they showed that the correct solution reuires a neutralization of differential financial risk iplicit in the lease against purchase evaluation. The second category gets one or two case studies to ake a coparison between the cash flows of buy and lease to acuire euipent. For exaple, karakiri (988) evaluated the ethod of euipent acuisition by eans of leasing in Nigeria. He considered a case study of photocopy achine to copare the cash flow of lease, buy or rent, and finally he concluded that the break-even point plays an iportant role in aking the right choice between these three options. So that, if the lifetie of the euipent is less than break-even point, a short-ter lease or a onth to onth rental is suggested. If econoic useful life of the euipent is greater than the reuired tie to reach the break-even point, a long-ter finance or a long-ter sales contract should be considered. nd finally, if the cuulative cash cost of the three options is up and down or involves uncertainties, rent or a short-ter lease is suggested. The third category tries to study the financing leasing by odeling (ras et al., 20; andell, 2002; Wheaton, 2000; Rabbani and Keyhanian, 202). In the year 200, a paper was published that considered a copany which leases new products and sells reanufactured versions of the at the end of the lease periods. The authors forulate a profit axiizing odel using the notion of consuer surplus. The resulting proble was solved by a Nelder ead siplex search ethod (ras et al., 20). andell (2002) has studied about calculating fairground rent. He introduced a view of fairground rents, which coes fro Pareto criterion and provided two odels for lessee and lessor and then cobined the to get a better odel and provide a decision rule for the lessor to choose between leasing and selling a piece of ground. In this issue, Wheaton has soe studies but he has concentrated on the rent price in retail leasing with considering both lessor and lessee benefits. So, he showed that revenue percentages and fixed rent vary proportional and positively. odel is proposed where percentage rent gives the correct otivation to lessor, rather than to lessee (Wheaton, 2000). There are soe studies that considered risks in leasing probles. Rabbani and Keyhanian (202) have analyzed credit risk and deand reduction risk in a leasing field. This study developed a atheatical odel by considering anufacturer, lessee and lessor. The odel was evaluated in ters of lessor. ll the paraeters are deterinistic and the lessee would buy the asset at the end of the contract s period. Depreciation is considered in the odel and the calculating ethod is straight line. The leasing gae which solved by Nash Euilibriu is deonstrated with a nuerical exaple. With considering this in ind, we have tried to describe a new leasing situation that is affected by three applicable risks; Credit risk, transaction risk and risk based pricing. any ties exchange rate fluctuations in developing countries ake soe probles for those who acuire an asset. But the transaction risk avoids the to lease that asset. lso, credit risk indicates that soe lessees ay face difficulties and do not be able to pay their lease price to the lessor. So, by considering risk based pricing, the lessor allocates different interest rate to different people i.e. those with higher credit score get a lower interest rate and vice versa. By applying these risks, we generate a atheatical odel that helps the lessor decide on the proper price of each uality level that is defined for the asset, and clarify that which custoer is ualified for these price and level of uality. Hence, we assue that in the early years, depreciation is calculated by Double Declining Balanced ethod (DDB) and fro the year t, the calculating ethod is switched to Straight Line (SL). This assuption can save ore

4 6 Rabbani et al. oney for the lesser. The reainder of the paper is organized as follows: Section 2 includes a literature review about leasing, and pricingoriented papers within the context of related risks and their effects on decision aking. Proble description and odel forulation are given is Section 3. Section 4 includes the solution procedure. Experiental results are presented is Section 5 and finally Section 6 includes the conclusion and further study. PROBLE DEFINITION There are three parties in a leasing proble; Producer, lessor and lessee. The proble is solved fro the point of view of the lessor. The objective of the odel is that the lessee axiizes the rate of return of the product which has the uality level, and then decides on the proper price for each uality level. In other words, the lessor wants to know which price is appropriate for which uality level and which custoer is ualified for these price and level of uality. Finally, this custoer is the one who could iniize the payback period of the capital. Since, any risks threaten this issue, we consider three effective risks in the odel; transaction risk, risk based pricing and credit risk. Nowadays, these risks are so prevalent and also, they restrict the odel region. In this proble, the producer and the lessee are affected by the lessor's decisions because here, the ain decisions are ade by the lessor. These assuptions are considered in this issue;. The values of all paraeters are deterinistic and constant over tie. 2. Each lessee buys the product on the specified arket value in the end of the leasing period. 3. The leasing contract period is long enough (at least 30 years). 4. The depreciation calculating ethod is Double Declining Balance (DDB) at first and switched to straight line after a specified year. 5. The rent price is constant. 6. Interest rate is deterinistic and constant over tie. Index: : Nuber of lessees that indexing with Q : Nuber of uality level of the assets indexing with U : Credit level or validity of the custoers that indexing with u P : Nuber of ethods used by the lessor to pricing the rents. It is indexing with p K : Nuber of the year Paraeters: L p : Euivalent unifor annual value of rent price that pricing by ethod p. O& : Euivalent unifor annual value of aintenance costs of the product with uality level. V p : arket value of the product with uality level that pricing by ethod p. SV : Salvage value at the end of the useful life of the product with uality level. θ p : Payback period of the leased product with uality level that pricing by ethod p. I p : Initial cost or price of the product with uality level. D : ount of annual depreciation of the product with uality level in k th year. T e : Effective rate of tax i u : Interest rate for custoer with credit level u N : Duration of leasing contract p b : The probability that a custoer fails to pay rents in a period. Decision variables: χ p : It is a binary variable. If the purchased product with uality level that pricing by p ethod, is dedicated to the lessee, this variable is eual to one. Otherwise, it is eual to zero. z u : It is a binary variable. If the lessee is in the level u of validity, this variable is eual to one. Otherwise, it is eual to zero. f : Transaction risk ratio is a rando variable with F distribution function. Proposed odel ax P Q θ p= = = χ p ()

5 JOURNL OF ENGINEERING NGEENT ND COPETITIVENESS (JEC) 7 S.t: P Q χ = {,2,..., } (2) p p= = 2 2 B SV ( ) N N N t D = B = D k 2 ( ) N t B SV 2B 2 B SV ( t ) ln( ) ln( ) N 2B B SV ln 2B t = + (4) 2 ln N IR U u= U = i z u u Z u u= = {,2,..., } {,2,..., } { } { } E ( L) = p 0 + ( p ) L, 2,..., p, 2,..., p (7) p p p θ = ( ( + f ) V )(, IR, N ) + ( ( )) ( ) ( & )( ) ( ) p E L T O T D T p e + e e F p p p {,2,..., } {, 2,..., } { 0,} {, 2,..., } x p p {, 2,..., Q} { 0,} {, 2,..., } u {, 2, 3} z u I p (3) (5) (6) (8) (9) In this proble we have two variables. The binary variable x p is to assign products to lessees. nother variable is z u that shows the credit level of the lessees. This variable is used to apply the risk based pricing on the odel. This risk is the process in the financial services industry to allocate different interest rates on the sae loan to different people, depending on their credit score and other factors which illustrate their ability of paying back the loan. Those with worse scores have a higher interest rate; those with better scores have a lower one. The idea of the process is to avoid the tragedy of the coons, which happens if everyone has the sae interest rate. So, custoers are categorized into u levels of validity. Each custoer has a different interest rate according to his credit level. Furtherore each custoer is only in one level, so the su of the z u variables, should be eual to one. The objective function in this proble is axiizing the rate of return of the leased product with uality level and p ethod of pricing for custoer (). Therefore, x p variable is needed, to be sure that if there is not a custoer for a product with uality level and p ethod of

6 8 Rabbani et al. pricing, we will not calculate the rate of return for that. There are nuber of constraints for the ain proble that restrict the solution region. Euation (2) ensures that each custoer can leased only one product with one specified uality level and only one specified pricing ethod. So this ethod is used for all custoers. Depreciation is an iportant issue in calculating rent price and also the present value, because the aount of depreciation is including tax saving for the lessor. To calculate depreciation, a switching odel is used as showed in section (3) of the odel. Due to this saving, an increase in depreciation is desirable. For early years of cash flow, DDB ethod is better because the aount of depreciation is ore than end of the cash flow. But fro point t, calculated in euation (4) of the odel, ethod is switched to straight line (SL) for calculating depreciation. Fro this point calculated depreciation by SL ethod is ore than by DDB. Fro this point onwards, the straight-line ethod for depreciation is calculated. Effective risks Risk based pricing is considered in the proble. So, as showed in euation (5), for calculating euivalent unifor annual value of products, we should use desired interest rate naed as IR. lso, with euation (6) ensure that there is only one interest rate for each custoer. The effect of Transaction Risk is on the arket value of the product. The lessee, due to this risk should pay the specified ratio of euivalent unifor annual value of product s arket value. So, f V (, i, N ) is added to the odel to p u F deterine this risk in calculating. We assue that the contract period (N) is long / P, IR, N enough so the financial factor ( ) tends to IR : P ( + IR ) (, IR, N ) = IR N IR li(, IR, N ) = li = IR N N P N ( + IR ) lso, it could be said that θ =. So, the inverse P of θ, is approxiately euivalent to the internal θ rate of return (IRR) of the financial flow (Rabbani and Keyhanian, 202). This concept explains that the objective function axiizes the IRR of all leasing contracts. To reduce the losses resulting fro Credit Risk, we calculate rent price for each lessee as in euation (7); If the custoer does not pay the rent, L is 0 p and the probability is p. But if the custoer pays the rent L is not zero with probability. p s showed in euation (8), to calculate payback period of the asset, we want to know when the initial value of the product will be covered, without considering tie s effect on the cash flow. So, we have to divide the initial cost of asset to the euivalent unifor annual costs and revenues with considering tax rate. zu and x p are binary variables in this proble (9). p SOLUTION ETHODOLOGY The ajority of the studies that provide a odel for the leasing proble did not solve their odel and focus their attention on strategic and theory of the concept. The only study that tries to solve the proble has used Nelder-ead ethod. In an attept to offer an easily ipleentable ethod that can provide good results for solving our odel, a eta heuristic algorith based on genetic algorith has been suggested. Because our odel is a ulti-diensional proble and the genetic algorith execution techniue is not dependent on the error surface so, it can easily optiize such probles. lso, the nuber of paraeters in the odel is large and G can find a good solution for this kind of odels and iprove it. The initial values of the odel are taken fro Iranian leasing official website (Table ) in which a rent calculating is provided. We choose PEUGOET206 in three levels; type 2, 5 and 6, for analyzing. Calculating transaction risk ratio: The f value, a rando variable with F distribution function, is calculated by using the available data. To calculate index of real rate of exchange (Figure ), we used annual data and following euation;

7 JOURNL OF ENGINEERING NGEENT ND COPETITIVENESS (JEC) 9 CPIW RER= NER CPII RER: Real Exchange Rate CPII: Consuer Price Index of Iran CPIW: Consuer Price Index of World NER: Noinal Exchange Rate Table Exchange rate data (Oladi et al., 2007). Year Noinal Real exchange CPI exchange rate rate Year Noinal Real exchange CPI exchange rate rate Exchange rate(tuan) Year Figure : Real exchange rate plot The value of IP (investent by privet sectors), IG (investent by governent), GDP (gross doestic product) and R (interest rate) are shown in Table 2. Table 2: Investent data (Oladi et al., 2007) IP IG GDP (p) R IP IG GDP (p) R

8 0 Rabbani et al. To calculate index of real rate of exchange we use data in Table 3 and 4, and following euation. 2 β= b + ( big+ br+ bp+ bh ) 0 * IP IP By using Garch ethod to calculateβ, we consider following value for b to b 4. b =0.02, b 2 =0.02, b 3 =0.0, b 4 =0.05 β =0.65 So, we use this value as f, uncertainty of the real exchange rate in our odel. Genetic algorith is an optiization ethod based on the biological analogy of survival of the fittest that used to find true or approxiate solutions to optiization and search probles. These algoriths are categorized as global search heuristics. In contrast to siulated annealing where only one odel is disconcerted and walked through the odel space in genetic algoriths a group of odels is always considered. Through analogies of genetic reproduction, crossover, utation the uality of the average population and the individuals is iproved over several generations. Genetic algorith scan be considered as a special case of the ore general evolutionary algoriths. Figure 2 shows the general genetic algorith flowchart. Start Seed population generate N individuals Scoring: assign fitness to each individual Select two individuals NO Use cross over operator to produce offspring Scoring: assign fitness to off-spring Cross over finished? YES Select one off-spring pply utation operation to produce utated offspring NO YES pply utation operation to produce utated off-spring Terinate? NO YE S utation finished? Scoring: assign fitness to off-spring Finish Figure 2 Genetic algorith flowchart We run the odel and, answer is showed in Tables 3 and 4. In this answer for exaple the first custoer has axiu credit level according to Z u results. So, as expected, the best uality level

9 JOURNL OF ENGINEERING NGEENT ND COPETITIVENESS (JEC) with high pricing ethod is selected. The second custoer has axiu credit level too. Selected uality for this custoer is ediu and the pricing ethod is the second one. For the third custoer, validity is in second level. So, there is about percent probability that the custoer will be failed to pay rents. The ediu uality level is selected and the pricing ethod is the third one. In this run payback period with G ethod is year and the payback period odel is Up to 0 percent error is acceptable in G ethod. Table3: Optiu values for x p x p = p p = p = Z u Table4: Optiu values for z u u u Z u Z u CONCLUTION ND FUTURE STUDY Nowadays, leasing has becoe a coon way for euipent acuisition. But because of the lack of awareness of related risks, wrong decisions are ade by anagers and this decisions cause any conseuences on organization's perforance. This study tries to consider any aspects of leasing proble and its related risks; Credit risk, Transaction risk and Risk based pricing. For this purpose, we have provided a odel that helps how to allocate custoers to uality levels and pricing ethods. In other words, this proble illustrates that without considering related risks, the decisions does not assures the best results. In this study, by using a genetic algorith we solve the proble. For further study, other ethods could be suggested for solving the odel such as Seuential Unconstrained iniization Techniue (SUT) or other eta-heuristic ethods to optiize the odel with a better perforance. lso, there are soe other risks like liuidity risk, operational risk, portfolio risk and etc. that could be considered in odel and study its effects on lessee and lessor's decisions. REFERENCES ho, T., & Virtanen, I. (98). nalysis of lease financing under inflation. The Finnish Journal of Business Econoics 3-98, karakiri, J. B. (998). Euipent leasing: a strategy for technology acuisition in Nigeria. Technovation, 8(5), ras, N., Güllü, R., & Yürülez, S. (20). Optial inventory and pricing policies for reanufacturable leased products. International Journal of Production Econoics, 33(), Ghyoot, V. G. (2003). The Lease v Buy Decision in Real Estate: Theory and Practice. In European Real Estate Society Conference, Helsinki. Levy, H., & Sarnat,. (979). Leasing, borrowing, and financial risk. Financial anageent, 4(4), Lin, J. R., Wang, C. J., Chou, D. W., & Chueh, F. C. (203). Financial constraint and the choice between leasing and debt. International Review of Econoics & Finance, 27, Lin, J. R., Chung H., Hsieh.H., Wu S. (202). The deterinants of interest argins and their effect on bank diversification: Evidence fro sian banks Journal of Financial Stability, 8, andell, S. (2002). Lessor and lessee perspectives on ground lease pricing. Journal of Property Research, 9(2), khatshwa, C. P. (20). The decision to lease or purchase euipent fro an engineering econoics perspective. B.S. Thesis, University of Pretoria. ukherjee, T. K. (99). survey of corporate leasing analysis. Financial anageent, 20(3), Oladi,., Ebrahii,., & basiun, V. (2007). Study of real exchange rate uncertainty on investent of private sector. Journal of Econoic Research of Iran, 2, Rabbani,., & Keyhanian, S. (202)., Introducing the concept of leasing field, tripartite decision aking for it with considering credit risk, and the leasing gae with considering deand reduction risk. In The 8th Int. Conf. Industrial Engineering, Tehran, Iran. Redan,. L., & Tanner, J. R. (99). The financing of corporate real estate: a survey. Journal of Real Estate Research, 6(2), Wheaton, W. C. (2000). Percentage rent in retail leasing: the alignent of landlord tenant interests. Real Estate Econoics, 28(2),