Sale-and-Leaseback Agreements and Enterprise Valuation Author(s): E. Han Kim, Wilbur G. Lewellen and John J. McConnell Source: The Journal of Financial and Quantitative Analysis, Vol. 13, No. 5 (Dec., 1978), pp. 871-883 Published by: Cambridge University Press on behalf of the University of Washington School of Business Administration Stable URL: http://www.jstor.org/stable/2330632 . Accessed: 02/08/2013 15:31 Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at . http://www.jstor.org/page/info/about/policies/terms.jsp . JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org. . Cambridge University Press and University of Washington School of Business Administration are collaborating with JSTOR to digitize, preserve and extend access to The Journal of Financial and Quantitative Analysis. http://www.jstor.org This content downloaded from 141.213.163.35 on Fri, 2 Aug 2013 15:31:54 PM All use subject to JSTOR Terms and Conditions JOURNAL OF FINANCIAL AND QUANTITATIVE ANALYSIS December 1978 SALE-AND-LEASEBACK AGREEMENTS AND ENTERPRISE VALUATION Han Kim, Wilbur G. Lewellen, E. on leasing The literature ment with a selection a variety years, and that and ([11] in lessee of investors of the cash asset purchase has been to the latter result and attendant tax these tual are Systematic thereupon in practice These again institutional is assumed, drive necessarily lessors? the present to parity arrangements with direct with the lease-or-buy matters, Ohio State on the other University, of corporate and asset the tax rates that identical. the borrowing by the lessee The key power? firm, when matched by the augmented borrowing just In a competitive enterprise. that the asset's the present value for expecting material transactions gains leasing of the contrac? purchase (tax-adjusted) and differential power firm in the form through to the asset-user imperfections, the only basis provide as firms are relinquished be passed equal long of the fact with the result will as and lessor for the lessor payments, obligations [12]) a recognition will savings lease and of lessee is created simultaneously of lower to activities trading even in the presence to hold savings?implicitly obligations market, [16], inevitably among potential competition with lease seen ([11] possibilities depreciation lease associated [8], firms indifferent of securities-price-equilibrating and income taxes leverage market will capital firms?will [6], the over prices. conclusion This [3], manage? the terms of leasing of value-maximizing Simply put, and lessor flows decision; ([1], shown that competitive [12]). with the mandates together advanced have however, papers, the stockholders to render decision values have been of recommendations in a transaction-costless contracts be such as on providing concentrated generally for the lease-versus-purchase criterion More recent [18]). has and John J. McConnell* price. costs, to be associated choice. hand, Purdue have been University, examined and Purdue thus far entirely University, in respec? tively. and lessee on the part of lessor firms, Including unequal opportunities of the cor? in the carry-forward and carry-back due to deficiencies provisions of tax shields [14]. porate tax law, to take advantage 871 This content downloaded from 141.213.163.35 on Fri, 2 Aug 2013 15:31:54 PM All use subject to JSTOR Terms and Conditions the context of the acquisition the decision is indeed instead the situation and are currently levered issue whether into of those existing assets. stances certain positive shareholder of any market imperfections thy bondholder" "beggar contractual the legal another firm at an agreed-upon will the assets prearranged alter user the underlying real the parties to the agreement. second-hand market value simply be viewed as funds in exchange independent lies in the a form of essentially a variety is to the advance subject back for continued As such, and production of its any residual to that in return the transaction for a not does of the asset- situation value of enterprise stipulation use, future of supple- the transfer from the user cash earn? operating of the leased regard, on terms, package for a contract the lessor that an automatic assets. assets be only partially is open to negotiation promising are includes priority whereby the lessor firm advances a series value Thus, in arriving be characterized of promised, to the uncertain involved, therefore, at may In flows. depend exchanged. extension cash on the collateral capital as properly of future may well of the lessee claim to the prevailing agreement to supply a schedule between The sale-and-leaseback arrangement firm should The credit be sold assets. willingness whose titles of claims ments plus a financing creditworthiness assets specific will It may or may not correspond of those the lessor's on the general leased at in such circum? origin of the arrangement payments. investment at which the assets The price gain choice to the lessor. acrues that firm has a to be exploited, may contain or group of assets of the lease, Upon termination are Their instrument price, of rental been acquired of the Arrangement firm, nor the distribution (now lessee) ings. effects manipulation. be leased immediately schedule to consider for a particular agreement be shown, there represents of an asset ownership is and where the managerial structure the core provisions, here where the asset-user wealth Nature firm, wherein have previously arrangement capital I. mental in question As will the sale-and-leaseback Although Our intent or tax considerations. a sale-and-leaseback that by the lessee a sale-and-leaseback subset fact or buy. in place, already to enter assets in production, used being whether to lease where the assets structure capital is of additional as much of the the final bar? as buying a but uncertain, lease terminal of the value pay? may in many instances "secured." 872 This content downloaded from 141.213.163.35 on Fri, 2 Aug 2013 15:31:54 PM All use subject to JSTOR Terms and Conditions II. We shall examine ments in the standard adjust situation debt and lease decide ting gregate market value bution of prospective of a firm will manner in which those ants total cash flows are divided such default and may then In a market set? and the ag? [17], apply of the distri? of the regardless operations, among the various two classes a firm with just of securities command in the market a total common stock?will of claim- categories and outstanding?bonds of value V = B + S (1) where B is bankruptcy costs, which happens If, then, to a lessor lease back those proceeds a price V is intact, should of the like? assessments in the absence of any dead-weight of the particular from their unaffected. their of course, which underlie payments to sell decide financial a portion A, under an arrangement total A become available In return, attributes. 2 same assets posture the sale of lease but, be independent the corporation prospects quence V will be investors' of common shares. structure to have been adopted. remain flows will of bankruptcy firm for the price and production holders. prices respective and consequences lihood and S the value of the debt, the market value in these Imbedded prior Should only on the character from its flows a in assets?i.e., operations. will as includ? thereto. Thus, cash its defined obligations, position. Principle depend is of its no are with either of the enterprise or to continue it the Value-Additivity fixed the value ownership prices initially?there Bankruptcy equity arrange? wherein associated maturing negative assume creditors sort, least no costs exceeds commitments, to liquidate either of this are of the firm's have a nominal the firm's occur, where?at markets of the firm or bankruptcy. liquidation in which the value which stockholders of sale-and-leaseback securities and where there voluntary ing its of perfect context income taxes, Effects consequences to new information, immediately corporate Valuation the valuation V is new owner, a new category introduced. obligations its market worth will for immediate whereby it the user In consequence, cash asset those earnings to be V, and distribution In the market, to investment operating (the assets agrees firm's continue of claimant and a terminal of its to securityto the lessor) claims?a value?will se? command of their risk market appraisals determined by prevailing capital 2 the cash flows involved Whatever that assessment, represent factors include The relevant to the maturity of the lease, firm bankruptcy of asset-user the possibility in assets the marketability of the leased 873 This content downloaded from 141.213.163.35 on Fri, 2 Aug 2013 15:31:54 PM All use subject to JSTOR Terms and Conditions a corresponding firm's from the original diversion and stockholders. bondholders the new aggregate where S' and B' however, Since, the revised denote A, their becomes sale-and-leaseback be harmed by the transaction, it S' (3) which, from (2), S' or, that simply, will therefore, + B' asset-sale price cash of the firm which are at least of the transaction, offsets of course, more than V without subjecting L its decision rule Accordingly, + B' its will the present committed for them not to + V L terms will be driven the lessee firm's to this stockholders point, (market) lessee firm, unless the asso? value to the lessor. the lessor of the On the oppo? firm cannot afford to a reduction securityholders to pay in wealth. be that A ? V , and thereby only one execuL In a competitive simultaneously. tion price, A = V , can satisfy both parties L market of capital comprised value-maximizing and-leaseback in order A ? V . The management of a value-maximizing L not accede to a sale-and-leaseback arrangement flows to the pursuant position that + A ? V = V* + V_ = S' L future side wealth the asset-sale + A ? S + B ciated site receive will that requires (4) + B' and debt valuations. Obviously, must occur principle, be equity total + B' + A). of the lessee + B' constituent collective (S' will and shareholders bondholders distribution proceeds claims = V = S' VT L V (2) flow prospects by the value-additivity Hence, of their market value cash enterprises, and in equilibrium and bondholders will sale-and-leaseback the aggregate be unchanged wealth of by the sale- agreement. both the second-hand asset and secondary leasing markets, and any distinctive renewal options?which are attached including supplementary provisions?perhaps to the lease contract. A similar conclusion for new-asset leases is documented 874 This content downloaded from 141.213.163.35 on Fri, 2 Aug 2013 15:31:54 PM All use subject to JSTOR Terms and Conditions in detail in [11]. III. Within that to the stockholders tirely payment or through outstanding of of the asset from (2), V, we have S' (5) if V = A under the press L and, stand shareholders Thus, to the extent of values. In distributed en? cash of the corporation*s previously- wealth position will stockholders + A) exceeds (S' dividend benefit S. the original that +B'+V=S+B L of market competition, + A) - S = B - B' (S' (6) by a "special" Consequently, if the quantity V' + VL are end up with a revised with B'. from the sale-and-leaseback Since, to the lessor of a portion common shares?stockholders + A) and bondholders (S' sale of the lessee?either the repurchase Effects can be a reallocation there however, aggregate, if the proceeds particular, of the Valuation Allocation to gain from the transaction suffer that?bondholders . whenever?and precisely in the market value a diminution of their holdings. As it lessee-firm the lessor ginally are happens, bankruptcy. a priority belonged The reason claim of the bonds flows than B, due to market reaction can only decline a finite long is that the sale-and-leaseback Because and there will is as in which the cash than before, which those involved there as to a segment of the cash to bondholders. no circumstances the transaction ruptcy?in the market value of the sale-and-leaseback, a result of this flows will be smaller. to the altered diverts which ori- of claims, there after be some circumstances?notably bondholder to can be greater restructuring Inevitably, of probability flow prospects to bondholders as then, B' will bank? be less position. 4 when the asset-sale While equation (6) is perhaps most easily interpreted in the form of a cash dividend to stockholders are disbursed payment, proceeds In the latter of share repurchase. as well to the situation it obviously applies can also be identified. the per-share Thus, if the case, price implications at a market price P per firir initially has N common shares outstanding lessee A will be AN=A/P', with the sale proceeds share, the number which can be retired as soon as the where P' is the revised per-share price which will be attained and repurchase sale-and-leaseback Hence, shareplans are announced by the firm. as holder wealth can be expressed + A = NP? . S? + A = P'(N-AN) into (6) and rearranging yields Substituting pt - p = (B - B')/N remain constant, that the market price of the shares will increase, indicating firm's bonds or decrease depending upon whether the market price of the lessee or increases. remains constant, decreases, 875 This content downloaded from 141.213.163.35 on Fri, 2 Aug 2013 15:31:54 PM All use subject to JSTOR Terms and Conditions This phenomenon can be demonstrated flow distributions confronted in a one-period leaseback, by bondholders contract, to bondholder Prior period claims. the lessor's claims are in which, rendered by senior fully the distribution random variable of end-of- Y?is if X ? Y* if X < Y* '7) where X denotes and Y* is the (random) the stipulated amount of bondholder X < Y*. here lessor be owed a prescribed will value terminal the events before of bondholder tribution distribution and this where max(Y*,L+R) strictly and the intent nounced Were that returns of That is, (7). min(Y*,L+R) if max(Y*,L+R) X if X < min(Y*,L+R) subtract? each array. element perhaps the case, of (9) is either flow prospects The associated the asset-sale by the lessee payments cash B in the market as to distribute > X ? min(Y*,L+R) of Y* and L+R, and min(Y*,L+R) the larger Since below to investors lease to that inferior if Y*+L+R > X ? max(Y*,L+R) denotes A milder?and promised dis? if X > Y* + L + R if Y* + L + R > X >, L + R if X < L + R of pre-sale-and-leaseback be priced sarily claims becomes Y*-[X-(L+R)] the post-transaction nates to the random the revised Accordingly, the however, both these seniority, if X ? Y* + L + R of the two quantities. the array (L+R) claim 0 / Y-Y' (9) is Having of bondholders. returns "Bankruptcy," sale-and-leaseback, firm, of course, we find that from (7), (8) Y* X 0 J Y' (8) cash of the lessee value payment L and hold assets. those cash claims. Following lease R of the leased must be satisfied total end-of-period encompasses ing the sale-and- the situation to sale-and-leaseback, to bondholders?a returns first the cash by examining and after before Consider setting. the terms of the lease cash most readily claim soon as zero the smaller or positive, for bondholders B' therefore domi? will the sale-and-leaseback proceeds A to shareholders, neces? plan, is an- firm. more common?circumstance to the lessor had equal the post-sale-and-leaseback would be one in which the standing with bondholder distribution would be if X ? Y* + L + R Y* (10) if X < Y* + L + R [Y*/(Y*+L)](x-R) 876 This content downloaded from 141.213.163.35 on Fri, 2 Aug 2013 15:31:54 PM All use subject to JSTOR Terms and Conditions of bondholder claims. cash that given the leased-asset owner o'f" the assets be shared their gate in any event, by the lessor value R will and all other and the bondholders stated respective claims. residual from (7), (10) Subtracting to the lessor cash end-of-period in proportion if the total claims, accrue are flows as flows legal will to the magnitudes less than those of aggre? we have if X > Y*+L+R if Y*+L+R > X ^ Y* [Y*/(Y*+L)](Y*+L+R-X) if X < Y* {0 (LX+RY*)/(Y*+L) which establishes holders are R portion assets themselves firm's would render cash to the (now) pro-rata but the asset cash terminal flows. payment commitments were completely clear of the leased ownership worse off than before. bondholders the post-sale-and-leaseback context, of all the lessor's claim, still lease for bond? prospects pursuant end-of-period the contractual to bondholder subordinate ones, to the two claimants, of the lessee even if Finally, the post-sale-and-leaseback by the preagreement in bankruptcy, allocation value that again dominated flow distribution In that for bondholders would be just if X :> Y* + R {Y* is which circumstance also inferior the difference ment, since if X < Y* + R X-R before to that prevailing the lease arrange? in the two distributions if X :> Y* + R if Y* + R > X > Y* Y*-(X-R) if X < Y* {0 R as consists, in the two situations values possible bondholders preexisting in their diminution firm bankruptcy. and, holders That therefore claims must be manifest B - B', loss, holders, As long fixed additional as as should whose objective there in the event any possibility the latter of the lessor?the in a reduction wealth may occur? of their for the lessee and sale-and-leaseback in to the fullest shareholder gain of lessee- of the extent of bond? position poorer in the market price (6), involved, to a by the introduction consequent a corresponding in equation payments opportunities can only be increased be engaged is of the lease flow X. by the sale-and-leaseback be subjected is cash end-of-period standing priority will generates established uncertain flow recovery cash the likelihood indeed, firm's of the relative Regardless then, of the lessee for all elements only of nonnegative above, possible maximization. 877 This content downloaded from 141.213.163.35 on Fri, 2 Aug 2013 15:31:54 PM All use subject to JSTOR Terms and Conditions securities. firm's stock? transactions by a management While the analysis case to the multiperiod available is parisons emerge. The lessor's residual on the part elect to buy out the lessor's of recovering obligations their would be based losses ket does on their to the assets claims the overall incurred of bondholders position to the lessor's prior The corporate cern: (1) to be neutral vide of corporate the role (2) cations; income tax?which asset depreciation in its an additional impact source developed in sufficient and [14]) as set of fixed-charge an unfavorable ruptcy An analogous contained in [2]. Two such should be the decision, for the latter's represents a burden influences Accordingly, are are unchanged. also the first of these benefits, the second here. under a lease other lowers tax-subsidy price literature contract borrowing will may pro? has been [12], by a firm of a unquestionably opportunities, the margin of protection of the prerogatives impli? can be seen ([11], The assumption con? gains. it simple?and leasing affect of potential While share that which prevailed far ignored?may quite might and resurrect, leverage is mar? capital schedules. in the recent interpretation the going-concern associated on the firm's it presumably, and its only a synopsis because they chose? bondholders to that to realize de? the firm in hopes conclusions we have thus to leverage obligations effect can occur, inferior of possibilities detail to require outflow on sale-and-leaseback The argument with regard firm in fact of sale-and-leaseback. remains of the transaction. the desirability cash and our valuation presence, market, to pay the lessor this an "option" a perfect Even if this in the absence is between to reorganize company. bondholder decision, Since of seniority could?if Their real-goods be required will dimension to operate value. advantageous a bankrupt thereby the lessee periods. of com? must inevitably the original of the relationship it a series analysis bondholders and continue of the firm?and would not have been Should then-liquidation find circumstances the bondholders however, claims imply a perfect than dismember, rather The one added some point, appraisal not necessarily in certain undermine in subsequent of the firm, and its value at need only be issue, assets?and of the bondholders. on its fixed R?will throughout. fault at pattern of the leased flows in the manner of equations periods of the one-period value of cash sale-and-leaseback, of the relevant ownership framework, extension The distribution and after before distribution possibility in a single-period straightforward. the counterparts to the asset return Considerations Given the claim-priority (13). which are cash above for each identified through claim Further was east to bondholders, formally (7) IV. 878 This content downloaded from 141.213.163.35 on Fri, 2 Aug 2013 15:31:54 PM All use subject to JSTOR Terms and Conditions when bank? for other of equity have creditors. ownership is any lease Thus, commitments will for the lessee, doctrine ceived of the same set cipient of unchanged the lessor from accommodating fits will its quoted tion?and its leaseback taxable bined will the basic un? Indeed, from the transac? tax Debt capacity [11]. effects the compensates incurs. of the sale-and- character the associated they should them to respond will are for symmetrical total cash tax flows lease savings, to the commensurate argument above amortization deductions of lessor for debt tax benefits capacity tax will can again be also firm the among lessors they acquire. impacts without lessee do not recapture and competition com? and lessee would have prevailed to securityholders the by the claimable originally terms that firm then-Jboafc value, A value-maximizing values. security not accept that poten? the lessee match those from the levels may not be so to a lessor, at their sold are charges to augment the profit and tax payments, income, depreciation sold assets' If the assets will act are obtains?the aggregate depreciation if anything When assets Because worth of the lost of asset implications reported so will the "transfer" exactly suffer to the terms not accede thus be unchanged management thereupon induce will of the lessee by the lessor acquired sale-and-leaseback. unchanged, bene? (tax) leverage the latter penalty do not alter earnings. The total lessee. where it the point valuation the lessor relinquishes?but deductions to refrain reach of sale-and-leaseback. against the relevant to accommodate led they are that market capital be encouraged thereupon the re- from the same set emanating In a competitive flows. is involved. neutral, conveniently equivalent enterprise will simply because the tax Although that to the lessor, that firm to reduce enabling 6 If is strenuterms. competition among lessors therefore, the two parties re? intact management will bargain, since Consequently, the securityholders considerations, by a precisely offset to the same degree firm for the leverage does, tial cash will the lessee. the reduction to all in an environment leverage promises, lenders sale-and-leaseback it is operating loans be transferred then, lessee less sacrifice of fixed-charge costs, with higher capacity for the firm, plan which?according attend [13])?will power for the lessor, lessee-firm of transaction benefits debt tax-deductible. this hand, of borrowing enhancement ous, are payments On the other and [7], in subsequent and investment production of the valuation ([5], where interest free an unchanged given a sacrifice and thereby imply a reduction will In short, be applied; and lessor confront the same marginal corporate Assuming that both lessee for are fully tax-deductible The lease payments, of course, income tax rate. identical to the lessor, and taxable the lessee rendering their tax influences as well. 879 This content downloaded from 141.213.163.35 on Fri, 2 Aug 2013 15:31:54 PM All use subject to JSTOR Terms and Conditions transaction equilibrium terms should There may, on the other a purchase the transaction?at from book value?so ferent no mandate that Consequently, It discussion. present third-party participant conceivably offer so, whenever and lessor lessee Whatever distinctly secondary identified the "me-first" Those is are senior by re8 source an implicit imperfectly-protected to shareholders. of such claims option to engage to sell (the original senior all promises advantage precisely claimants, standpoint, of to other that transactions it of) out and distributing pre- creditors, oversight. (the value at least [9]). securityholders provisions of that by selling and ([5], in sale-and-leaseback off a portion lessor), From the latter's via of class inadequacy?of arrangements not contain of sale- or any insti? a general within more accurately, of owners?do they are benefits upon taxes creditors?i.e., existing to those fail borrowing for management to take to a new claimant prise in corporate the opportunity may play, valuation sharesholder in fact, benefits, weakening an opening at hand, resents situation. that a may two parties, exploit which in no way depend made to a firm's a subsequent there will of the at issue of the no-tax tax peculiarities these above, covenants the promises case to frequent Commentary to do with the adequacy?or, phenomena having clude which are of the IRS as flows to the other managements to the fundamental rigidities. whose claims role supplemental and-leaseback If the presence cash properties second- they can. V. tutional that of gain source zero-sum rules and subject seems beyond the needs exploration the with the assets' both complex dif? which is as we have noted, is, The tax in the depreciation-related an additional enlightened are to recognize suffices for them the inherently laxmg If book value. of design or accelerate There be aligned price however, a detailed involved the size, tax deductions. with their in such circumstances, imposed revision. to increase acquisition much less hand market value, A, for the assets price, aggregate the lessor for the clever be possibilities either as of the available ciming, hand, be unaffected. In the rep? the enterfrom under the the proceeds in a transaction-costless 7 To the extent that the lessor is better able to claim those deductions tax-loss taxable income?due carryagainst perhaps to less than fully effective for example?additional net over provisions for lessee firms in loss positions, tax savings may arise [14]. o tax rates, would constiand lessor between lessee Differences obviously, for tax-reducing transactions tute a ready basis [11]. 880 This content downloaded from 141.213.163.35 on Fri, 2 Aug 2013 15:31:54 PM All use subject to JSTOR Terms and Conditions that environment, to sale-and-leaseback lease should option in this regard, payment commitments involved over bondholder priority the leased assets Bondholder to that extent, reap The logical which seeks complementary to maximize to issue attempt bonds to exploit eventually that those From the lender's tive. firm may in the future element of risk holders can be expected loan through a higher they should weak "me-first" interest be no better in response, and is deliberately covenants, protective that market, capital for bearing a latent hoping not necessarily affirma? the debtor adds agreement shareholders to obtain price suffer whether a management a sale-and-leaseback Accordingly, rate of residual must therefore the possibility In a competitive bargain. to their a strategy, The answer to demand compensation ex ante (fair) is as should, perspective, into to the loan. of the original appropriate enter to be accorded must fail of course, deficiencies. ex ante even though the gain. wealth contain The key of the ownership of claim securities question, shareholder be able in bankruptcy of their a corresponding that to the lessor seniority prospects the market price the fact may not by contract conveys cash-recovery will shareholders claims, whenever possible. is clearly, the transfer automatically value. be exercised simply an extra bond? prospective that risk, as part should have to pay an sale-and-leaseback on bonds with weak covenants, option? for example?and off in the long run than with borrowings that are well protected. Such an "indifference" indenture features these the borrower costs, and those will companies and some will tracts strong of sale-and-leaseback hibited in that as part of the price would be remiss pensating debt are costs may well is undertakings. At the time of of indenture the combination addresses Since least. vary across firms, in their covenants of the initial question when such arrangements served We conclude by making full to do so is likely for equity the option. At least are that use some loan con? of the im? not proshareholder of leaseback to have been with bondholders, bargain up to obtain by exercising the ex post instruments. best the option not to follow benefits, some expense. restraining on shareholders circumstance In effect, possibilities. costless Conclusions hand, by the terms of existing interests are that not. VI. pact on the assumption of transaction value on the other Our analysis, select of sale-and-leaseback, to include choose without firm should for which the present rest agreements can be accomplished neither a bond issue, does and sale-and-leaseback provisions In practice, however, view, imbedded and management securityholders the com? in a perfectly-competitive 881 This content downloaded from 141.213.163.35 on Fri, 2 Aug 2013 15:31:54 PM All use subject to JSTOR Terms and Conditions market, capital Whatever fits. taxes and bankruptcy central valuation costs, their point may actually of departure augment?those of market imperfections, effects phenomenon identified the proper sale-and-leaseback not diminish?and then may be the influence actions menon as will here. will We therefore for further, richer and trans? be overlaid necessarily regard bene? on the that pheno9 of the treatments transaction. 9 of the optimal timing of sale-andAmong which would be consideration tech? in a multiperiod the backward optimization leaseback framework, utilizing Solutions to the analogous problem of optimal niques of dynamic programming. bond refunding timing have been formulated by Elton and Gruber [4], Kraus [10], and Pye [15]. 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