A Life Contingency Approach for Physical Assets: Create Volatility to Create Value

Transcription

1 A Life Contingency Approach for Phyical Aet: Create Volatility to Create Value homa Emil Wendling 2011 Enterprie Rik Management Sympoium Society of Actuarie March 14-16, 2011 Copyright 2011 by the Society of Actuarie. All right reerved by the Society of Actuarie. Permiion i granted to make brief excerpt for a publihed review. Permiion i alo granted to make limited number of copie of item in thi monograph for peronal, internal, claroom or other intructional ue, on condition that the foregoing copyright notice i ued o a to give reaonable notice of the Society copyright. hi conent for free limited copying without prior conent of the Society doe not extend to making copie for general ditribution, for advertiing or promotional purpoe, for incluion in new collective work or for reale.

2 Abtract A firm will replace a phyical aet at the end of it ueful life. hi fact demontrate that there i a notion of mortality implicit in the way an enterprie manage it phyical aet. We propoe a theory that there i alo an efficient time, which i random and obervable, to replace a phyical aet. Separate economic and financial model converge on agreement that: 1) there i only one intant in time an aet mut be replaced in order to minimize the preent value cot impact to the enterprie, 2) thi efficient intant i obervable and a function of both the enterprie cot of capital and readily obtainable current calendar year information, and 3) the time to thi efficient intant i random and may be infinite. hrough a policy of coordinating the timing of replacement with thee efficient, obervable intant, lot efficiencie are recovered. Such a policy necearily create volatile, fortuitou, future cah flow, which are dealt with through capital adequacy or rik tranfer, rather than deferral or other form of cheduling for convenience. he efficiency gain and accompanying value creation may be material if the enterprie aet are motly phyical. he potential role of the extended ervice contract to implement uch a policy and to tranfer the reulting uncertain cah flow between entitie i dicued. A broad comparion to prior art capital expenditure planning method i made. Poible tax conequence due to the interaction between efficiency and fortuity are dicued. A policy event-baed lo etimation method uing expert input and imulation i preented for forecating thee long duration expenditure and calculating actuarially ound ervice fee for the aforementioned extended ervice contract. In thi world nothing can be aid to be certain, except death and taxe. Benjamin Franklin to Jean-Baptite Leroy in a letter dated Nov. 13,

3 1 Introduction hi paper predict the exitence of potentially ubtantial economic inefficiencie borne by enterprie that are not detectable through examination of data created by currently configured accounting ytem. It concluion are predicated on aumption about the nature of a function called M(t), which define the ize and timing of cah flow unique to individual phyical aet. Certain gro characteritic of M(t) will be decribed and are imply aumed for the purpoe of building a theoretical argument that could form the bai for an enterprie policy to manage phyical aet. he phyical aet referred to in thi paper are fixed aet that are not expended during operation and are ued to produce revenue. hey do not include cah or inventorie, which might ometime be included under a broader definition. hey comprie the plant, property and equipment line item on the balance heet. hee aet are ometime collectively referred to a plant. Many phyical aet will eventually be replaced with like or imilar aet that perform the ame miion within the plant. he proce of replacing phyical aet when they have reached the end of their ueful live i often referred to a renewal. he value of phyical aet in the economy i vat. Of particular interet in thi paper i capital equipment. According to the U.S. Cenu Bureau 2010 Capital Spending Report, $809.9 billion of capital equipment wa purchaed in the United State in 2008 alone. Much of it will be replaced in the future. Subequent year will probably how increaing level of invetment in capital equipment. For ome enterprie, phyical aet expenditure, including not only repair and replacement, but alo other operating cot, are ignificant when compared to their earning. Efficiency gain in thee expenditure may have a material impact on their market valuation. Oil and ga companie, electrical power producer, public utilitie, tranportation authoritie and manufacturer are all ector that rely heavily on phyical aet and may benefit from a management approach realitically addreing their mortality. Matziorini and Rowley (1993) decribe the magnitude of phyical aet expenditure and ome of the hortcoming in the way they are accounted for on a macroeconomic level. hey focu on repair and replacement expenditure and expre the opinion that thee do not receive much attention in the theory and econometric of invetment, depite their importance. hey alo decribe the effect of the level of aggregation of phyical aet in the accounting of uch expenditure a a reaon they cannot be conitently meaured. For example, i an airplane a ingle phyical aet, or i it compoed of the airframe, engine and interior fitting a eparate aet? Work ha been done attempting to explain the economic reaon for replacement invetment. Einer (1972), Feldtein and Foot (1971), Feldtein (1974) and Foot (1970) have tudied tatitical correlation in empirical data claified into different candidate determinant variable including a firm liquidity, cot of capital, level of ale, level of expanion invetment, level of capacity utilization, buine expectation, rate of change in capital good price, the average age of capital good, tax factor and technology change. Intereting correlation among thee variable were dicovered by thee author and ubequent work 2

4 that cite them have ued their finding to addre the accuracy of macroeconomic meaure, uch a gro fixed capital expenditure or gro fixed capital formation. hee author alo conidered behavioral effect implicit in thee explanatory variable, which we intend to filter out by articulating a purely rational enterprie policy for the replacement of phyical aet. 3

5 2 Economic of Phyical Aet Replacement Regardle of the level of aet aggregation, accountant decribe a phyical aet a having a ueful life. he Financial Accounting Standard Board (FASB) Statement of Financial Accounting Standard No. 5 tate, he eventual expiration of the utility of an aet i not uncertain. However, what doe utility mean in the context of lifepan? If a machine fail due to the failure of a dicrete component, it can alway be repaired (the component can be replaced) to return it to it ueful tate. Indeed, any phyical aet that i an aggregation of component can be repaired indefinitely to maintain it uefulne. A phyical aet that i an aggregation of component never ha to reach the end of it ueful life. It can be immortal with repect to utility. Neverthele, we know companie do replace phyical aet at all level of aggregation, and accountant have ued the concept of utility to repreent thi phenomenon. We will focu on an economic, rather than accounting, undertanding of why phyical aet are eventually replaced. It i ueful to look at the motivation for replacement of phyical aet under mot type of extended ervice contract to gain inight. Such contract provide for either repair or replacement of an aet, uch a capital equipment. If it were le expenive to replace an item of equipment than to repair it, then the party paying for the repair or replacement would naturally prefer to replace it. However, in the cae of mot capital equipment, replacement i uually not an immediate alternative to an expenive repair. Under an extended ervice contract for a home, it i eay to purchae a water heater at the hardware tore a an immediate alternative to an expenive repair. In contrat, in an indutrial etting, it i not o eay, for example, to purchae a locomotive a an immediate alternative to repairing one. he procurement proce from requiition to commiioning can lat year. Even prior to uch a requiition, the deciion to replace a major item of capital equipment i the reult of a lengthy proce, which begin with the gradual (and often delayed) recognition of the economic benefit of replacement and i often deferred due to management incentive and the lack of fund for aet replacement. Capital equipment eldom generate repair cot from a ingle failure cloe to the all-in replacement cot of the equipment. herefore, the repair veru replacement rationale decribed at the beginning of the lat paragraph may hold for home, vehicle or appliance ervice contract, but it ha little application with capital equipment. Repair are triggered when equipment or component fail. Repair cannot be deferred, ince they are required to retore equipment to functionality, which can be critical from the tandpoint of afety, reliability, availability or lot revenue. However, replacement of a phyical aet i deferrable, in favor of continued repair, even though it may not alway be economically efficient to do o. Few action have a powerful an impact on the operating cot of an individual phyical aet a it replacement with a new one. Few action are a expenive. o undertand the reaon for replacement, it i ueful to remember that repair cot uually rie a the aet age. hi i the natural conequence of aging machinery component. At ome threhold of repair cot, a deciion to replace an entire aet may be preferable to one of continuing to pay for riing maintenance cot. We will initially focu only on repair cot, in keeping with our 4

6 ervice contract analogy, but will then how that our model encompa any actual expene and opportunity cot that influence the replacement deciion. 2.1 An Economic Model Let u initially define M(t) only a the variable cot of repair at time t. M(t) i the annual variable repair cot in calendar year t. hee variable cot are the additional cot for an enterprie to repair an item of equipment beyond it fixed cot. Variable cot vary with the frequency of equipment failure, but fixed cot do not. An example of a variable cot of repair i the cot of new component and labor to intall them and i contingent on the occurrence of an equipment failure. An example of fixed cot i the cot of routine, cheduled, preventive maintenance. 1 An enterprie may alo have lower variable cot for a given level of repair becaue of it degree of dependence on fixed cot to accomplih the ame repair, for example, the level of on-the-job training given to it maintenance taff, or the invetment in permanent tool needed to perform maintenance function. We looely define thee difference in variable cot to achieve a given level of repair a an organization marginal cot of repair. We define C a the all-in lo and expene to replace an item of equipment including the cot of the new equipment and intallation, le any alvage recoverie. i the average interreplacement time, or average time between replacement, calculated over many replacement occurring over a long period. Cot X 1 X 2 X Figure 1 C t= + 1 M t=1 ( t) M ( t) M ( t) C 1 2 ime, t and, year 1. Although there i a relationhip between the level of routine, preventive maintenance and the frequency of equipment failure, thi doe not change the fact that preventive maintenance can be regarded a a fixed cot. he quetion of chooing an optimum level of preventive maintenance i eparate from the replacement timing quetion under analyi and i a focu of a field called enterprie aet management (EAM). 5

7 Figure 1 i a conceptual model of average cot familiar to economit. he downward loping dark curve i the average cot of replacement, which decreae with. he upward loping dark curve i the average cot of repair, which increae with. he dotted curve i the total average cot of repair and replacement, which i the um of the two dark curve. Unlike M(t), thee curve repreent average over a long period of time and over a large number of replacement. he formula hown on the graph how the algebraic relationhip of thee curve to M(t), C and. We ue ummation rather than integral becaue M(t) would probably be meaured in dicrete annual amount. he mot important feature of thi graph i that for increaing M(t), the total average cot of repair and replacement (the dotted curve) i minimum at, which correpond to a total average cot of repair and replacement of X. It alo illutrate that if time other than are choen for replacement, total average cot will be higher. he efficient time for replacement i at. Any other replacement time i not efficient. hi figure illutrate the effect of a repair veru replacement policy. If replacement occur before, at 1, then the total average repair and replacement cot will be higher than X, at X 1. hi reult from a urplu of M(t) under M(). If replacement occur after, at 2, then the total average repair and replacement cot will alo be higher than X, at X 2. hi reult from a deficit of M(t) over M(). An efficient repair veru replacement policy may have a material impact on the earning of enterprie that rely heavily on phyical equipment to generate revenue. For example, a power utility with $20 billion in machinery and equipment with an optimal lifepan of 20 year would pay 1/20 th x $20 billion each year in replacement and perhap an additional 15 percent of thi amount in repair, or $1.15 billion. If an inefficient repair veru replacement policy reulted in an additional 10 percent in exce of X in total average repair and replacement cot, then thi would add $115 million to the organization annual operating cot. If earning were on the order of $1 billion, then thi inefficiency could be material to uch an enterprie market valuation. hi i a hypothetical example, and we do not have documented accounting evidence of the inefficiencie predicted by Figure 1. However, the dollar value and the potential lo of efficiency (ee Section 5.1) decribed in the above example are realitic. Figure 1 ha two important implication. Firt, it illutrate the exitence of an optimal inter-replacement time. he econd implication i the caual relationhip between repair and optimal replacement timing, ince the evolution of M(t) determine. hi conceptual model i ueful to illutrate thee two implication, but it doe not take into account time value of money when calculating average of repair and replacement cot, which are really perpetuitie, pread over time. herefore, we cannot ue the principle in Figure 1 to preciely calculate value uch a X, or M(t) evaluated at. 6

8 3 A Financial Model A econd conceptual approach i to think of replacement a an option that hould be exercied at the optimal time,. In thi model, we compare the preent value of M(t) evaluated at in perpetuity, to the preent value of all future repair and replacement cot, reulting from a replacement at, in perpetuity. Repair and replacement are mutually excluive and complementary option. By deciding to not replace a phyical aet today, one i deciding to continue to repair it. By deciding to not continue repair, one i deciding to replace the aet. For a going concern, there i no third excluive option. here i alo no do nothing option with repect to thee two alternative. herefore, the deciion mut be exercied relative to each phyical aet, individually. If the variable cot of repair i increaing, it will cro a certain threhold at time at which the preent value of continued repair at that threhold will exceed the preent value of an immediate replacement with all it attendant future repair and replacement. Optimal replacement occur at thi threhold value of M(t). he two firt term on the right ide of equation 3.1 repreent the preent value at replacement time of a perpetuity (due) of replacement coting C occurring every year. he third term on the right of equation 3.1 repreent the preent value at replacement time of a perpetuity of all repair cot repeating every year. he time value of money i repreented by a dicount rate, i. 3.1 M ( ) i = C + C i (1 + i) + t= 1 i M ( t) v t Multiplying both ide of equation 3.1 by i give 3.2 M ( ) = ic + C (1 + i) + t= 1 M ( t) v t he continued derivation beyond equation 3.2 i provided in the appendix, but for M(t) exhibiting the kind of convexity hown in Figure 1, mot value of typical of capital equipment (i.e., > 10 year), and for typical value of i, the right term of equation 3.2 become very mall, and equation 3.2 can be approximated by: 2 2. he tatement about the approximate nature of thee relationhip can be verified by inerting typical value of aet lifepan and dicount rate and fitting polynomial of different convexitie repreentative of M(t) into equation 3.2 to demontrate the vanihing term in thee approximation. 7

9 3.3 ( ) M ic + C A become very large (i.e., > 75 year), equation 3.3 can be further reduced and approximated by equation M ( ) ic Equation 3.4 i imply the dicount rate multiplied by the all-in cot of replacement and repreent an obervable threhold of increaing M(t) at which the replacement deciion i optimal. he equation become an equality a or i, or both, become large. Equation 3.3 and 3.4 are very handy rule of thumb and are reaonably accurate for replacement deciion for mot type of phyical aet with lifepan longer than 10 year. In equation 3.3, i an a priori etimate of the expected ueful life of the phyical aet. Obtaining uch an etimate i the focu of Section 7.6 of thi paper. Equation 3.4 require no uch etimate of the expected lifepan of the phyical aet but would not be appropriate for hort-lived aet, uch a information technology or vehicle. hi conceptual model ha it own intereting implication. If M(t) never exceed thi threhold, then replacement will never occur. In uch a ituation, there will never be a rational time in which the enterprie hould replace the phyical aet. hi may be the cae for an enterprie with a very low marginal cot of repair. It i alo the cae for many type of aet with low repair cot (relative to replacement), uch a building or concrete tructure, which explain why mot of our dicuion on replacement of phyical aet focue on capital equipment. Since we know little about the function M(t), apart from ome gro characteritic dicued below, it i a boon to our analyi that it can be dropped from our determination of the appropriate aet replacement time. Deciion for the efficient replacement of phyical aet can be baed on a imple trigger that i eaily articulated in policy, or a a contractual performance obligation. If i = 0, then equation 3.2 reduce to equation 3.5: M C t= M ( ) = + ( t) he firt term on the right ide of equation 3.4 equal the average cot of replacement in Figure 1, and the econd term on the right ide of thi equation equal the average cot of repair in Figure 1, both evaluated at the optimal replacement time,. herefore, the financial model decribed in equation 3.1 through 3.4 converge with the economic model decribed in Figure 1, if we ignore the time value of money in both model. he curve in Figure 1 can be adjuted for the time value of money to obtain the ame reult a in equation 3.1 to 3.4, but then Figure 1 would loe it implicity and illutrative 8

10 power a an economit tool for undertanding the minimization of average cot. hi adjutment would alo not affect the two important implication of Figure 1 dicued in Section 2.1. If thi adjutment were graphed, we would notice that M(t) till interect the minimum point of the adjuted average cot of repair and replacement (the dotted curve), jut a it doe in Figure 1. All curve of Figure 1, except for M(t), would move upward and to the right with an increaing (nonzero) dicount rate. We will not create uch graph here but imply note that equation 3.1 to 3.4 provide the correct threhold value of M() becaue of their incluion of the time value of money. Another way to approach thi problem derive from peronal experience. A few year ago, I replaced an old car. It had been in the hop everal time that year for unrelated repair and eemed to continue a trend of increaing cot that had begun a few year earlier. he maintenance cot, I reaoned, were becoming a ignificant fraction of what I would pay annually for a loan on a new car and without all the hale. Of coure, the annual amount of uch an imaginary loan would depend on it term, but the number I had in mind for comparion wa for the longet poible loan, perhap approaching the amount of time I might own the next car. My annual maintenance cot were becoming an ever-increaing proportion of the annual amount that would be paid for thi loan (equation 3.6 below). 3.6 Amount = C a hen, with ome algebra: C = v C (1 + i) = i = C [( 1+ i) 1] i 1 = C i + = ic C Equation 3.10 i the ame reult a in equation 3.3. he peronal experience decribed above i a third, eparate philoophical approach to the problem of aet replacement, but it i mathematically equivalent to the firt two. It alo how that the horizon of the deciion doe not have to be infinite. In other word, the cah flow under conideration only have to be a 9

11 long a the expected lifepan of the replacement aet, not in perpetuity, in order for the trigger expreion in equation 3.10 to be true. For typical aet lifepan, the threhold value of M(t) i mot enitive to etimate of the dicount rate and the all-in replacement cot (which are eaily etimable), le enitive to error in the a priori etimate of lifepan and virtually inenitive to the (unknown) form of the function M(t). 3.1 A Broader Interpretation of M(t) In the above conceptual model, M(t) wa defined a the calendar year variable cot of repair for a phyical aet at time t. hi interpretation i uually conitent with the cope of reponibility in an extended ervice contract. he ervice provider for uch a contract i uually not obliged to replace an item of capital equipment imply becaue a newer, more efficient verion of the ame capital equipment emerge in the market. However, the owner of the aet internalize all economic cot aociated with it and may wih to expand the definition of M(t). A more general interpretation of M(t) would be that it repreent the calendar year cot of holding an old phyical aet. By holding an old phyical aet (intead of replacing it) the enterprie may pay not only for increaing repair, but expected revenue loe due to increaed frequency of downtime of aging equipment, or for the opportunity cot of lower operating expene aociated with new, more technologically advanced replacement equipment. Such opportunity cot can be objectively quantified a aving in operating and routine maintenance cot. Since technology generally improve, thee opportunity cot increae, which i conitent with our aumption of increaing M(t) in our model. For thoe replacement aet that are capitalized, even the opportunity cot of not realizing the tax helter from depreciation of a new aet can be conidered a contituent of M(t). However, depreciation i more complicated in our theory, ince, although thi opportunity cot appear toward the end of the exiting aet life, it i not ever increaing. Neverthele, thi can be dealt with by finding an equivalent etimated level perpetuity amount to erve a a proxy contituent of M(t) and which reflect the impact of the unrealized tax helter of a newly capitalized replacement aet. here are probably potential contituent of M(t) that are impoible to meaure objectively. For example, how doe one put a value on new car mell when making a deciion to buy a new car? In an indutrial etting, thee contituent are, or at leat hould be, elected on a more rational bai. Having the flexibility to explicitly define the contituent of M(t) actually allow elimination of ubjective, even behavioral, contituent that have the potential to contribute to deciion that are irrational with repect to the goal of maximizing enterprie value. An example of thi would be deferral of replacement for the ake of hort-term profitability or an individual bonu. here are probably alo contituent of M(t) that are difficult to quantify, uch a the expected revenue lot due to increaing downtime of an aging phyical aet. hee cot, although difficult to meaure, till exit. Such obtacle are alo preent in traditional capital expenditure planning method often ued in an aet replacement deciion. 10

12 In theory, any calendar year cot of not replacing old equipment that would be conidered under a traditional capital budgeting method could be monitored a a contituent of M(t). Becaue of the increaing prevalence of individual phyical aet accounting ytem, repair cot of individual aet are now being regularly tracked and updated. Such information ytem can eaily be adapted to include current opportunity cot and any other objectively meaurable economic contituent of M(t). Such cot can be monitored by engineer, and the accuracy and documentation of that information could become an increaed focu of their expertie. 3.2 he Random Nature of M(t) In reality, M(t) doe not increae moothly over time a depicted in Figure 1 but poradically a it approache the threhold cot from beneath it. For example, variable repair cot, although increaing in t, are random. Repair cot are fortuitou by virtue of their cauation by random phyical factor, uch a breaking, napping, hort-circuiting, wearing, rupture or fouling. he very propenity of a phyical aet to require repair (a meaure of it quality) i a function of factor beyond the enterprie control. For example, wa the phyical aet produced during a labor trike at the factory? echnology change, reflected a opportunity cot in M(t), i an uncontrolled external factor, which can alo trigger the replacement deciion. he opportunity cot created by unforeeen technology advance i fortuitou and beyond the control of the enterprie puruing a policy of efficiency. Since replacement time are determined by a random M(t) and the optimal replacement time depend on a threhold of M(t), then the time until that threhold i croed i alo random. Becaue the contituent cot of M(t) are fortuitou, efficient replacement cot are alo fortuitou in a ene imilar to the fortuity of death benefit. Repair and replacement, if executed efficiently, are both example of uncheduled maintenance. Any attempt to chedule or plan replacement will generally not be efficient. M(t) increae and approache a threhold from underneath much in the ame way that an aggregate exce of lo treaty attachment point might be approached over time. Meauring M(t) and knowing when it croe the threhold value can be difficult, particularly if we wih to ue equation 3.3 a a contractual trigger for replacement. he ue of moving average of M(t), in order to dampen oberved fluctuation and avoid making premature replacement deciion, can olve thi problem. he perpetuity equation above aumed that replacement are evenly paced apart in time, but the random nature of M(t) invalidate thi aumption. Since inter-replacement time i a random variable, replacement are a tochatic tream of event. he preent value of a tochatic tream of cah flow i not equal to the preent value of a regularly paced (cheduled) tream of cah flow, a wa aumed in our financial model. However, the impact of thi idealization on the accuracy and implication of the equation above i minimal and merely repreent a further refinement of our analyi, which will not be analyzed in thi paper. 11

13 3.3 Ever Increaing M(t) Figure 1 how that M(t) increae and i aumed to never return to a level below M(). hi aumption implifie the financial model decribed in Section 3 and i baed on hitorical experience that all of the o-far mentioned contituent of M(t) generally increae over time. here may be exception to thi. Repair cot, for example, can decreae after a period of high frequency of repair. hi i epecially true for array of identical component that comprie a ingle phyical aet, which can create periodic concentration of repair cot over time. Figure 6 of Section 7.2 illutrate uch a ituation. he repair cot may increae initially before decreaing again to a teady tate level. If the threhold M() i higher than thi teady tate level, then an incorrect replacement deciion may be made. 3.4 he Convexity of M(t) In Figure 1, M(t) i hown to have convexity. hat i, cot eem to increae at an increaing rate over time. hi i largely anecdotal, but there i a theoretical bai for thi. Since mot equipment component follow time to failure ditribution that have an increaing force of mortality over time (i.e., the Weibull ditribution), one would expect an aggregation of uch component to exhibit the ame progreion of repair frequency, thu convexity, a that een at the lower percentile of uch a ditribution. Equipment that require repair at an evenly increaing rate over time would be conidered to be of very poor quality. Unforeeen advance in technology will reult in tep increae of the opportunity cot of holding old phyical aet, which can occur at any time. Such change invalidate the aumption of convex M(t) becaue they can occur with equal probability at any point in the aet life. However, advance in technology that create uch opportunity cot are exceptional event and not regular phenomena that occur over the lifepan of each replacement. he aumption of convexity in M(t), a depicted in Figure 1, i important, ince it mean that mot of the M(t) cot occur late in the life of a phyical aet and therefore are heavily dicounted in equation 3.2. Convexity in M(t) i what help u to drop it from the determination of the approximate replacement threhold value of M(t) in equation he Nature of i By broadening the definition of M(t) in Section 3.1, the trigger for economically optimal replacement of a phyical aet given by equation 3.3 now reemble the uual proce of capital expenditure planning in which the net preent value of all future cot operating old phyical aet are compared to that of new one. Since we now undertand the above equation to be an expreion of the traditional capital budgeting proce in the context of renewal and we are conidering alternative ue of a firm free cah flow, we can conclude that the dicount factor ued in the above perpetuitie i the (real) cot of capital of the entity making the replacement deciion. 12

14 3.6 Summary of Aumption Concerning M(t) he above aumption concerning M(t) were made to create an argument from which to draw ueful concluion. he aumption are ummarized a follow: M(t) i compried of variable repair cot but can alo include opportunity cot, expected lo cot and any other cot that would normally be conidered under a traditional capital budgeting method when making a replacement deciion. M(t) increae and doe not return to a value below the threhold value at which replacement i required, once thi threhold i croed. M(t), although increaing, i random and approache the threhold value requiring replacement, much the ame way in which the attachment point of an aggregate exce of lo treaty i approached. M(t) ha convexity, a depicted in Figure 1. hee idealization broadly decribe the time dependent nature of factor uually conidered in a replacement capital budgeting exercie. hey are not alway true, but experience ha hown they are uually the rule rather than the exception. hee aumption are probably alway true for a large ubet of phyical aet, uch a capital equipment. 3.7 Principle of Phyical Aet Replacement he concluion from the application of imple financial mathematic to the above aumption about the nature of M(t) can be ummarized by the following three principle: 1. here i only one intant in time that an aet mut be replaced in order to minimize the preent value cot impact to the enterprie. 2. hi efficient intant i obervable and a function of both the enterprie cot of capital and readily obtainable current calendar year information. 3. he time to thi efficient intant i random. It may be infinite. he above principle imply that efficient phyical aet replacement i a life contingency problem. he advantage of having an eaily calculable and objective trigger for economically optimal replacement i manifeted by the ability to make prompt deciion that are ruthle with repect to the goal of minimizing the overall net preent value cot impact to the enterprie. A threhold value, baed on readily obervable calendar year information, make it poible to bae contractual replacement obligation on event that cannot be manipulated by either party to uch a contract. he advent of individual phyical aet accounting ytem make it eay to track all type of cot aociated with individual phyical aet and make enforcement of uch a policy or ervice contract feaible. 13

15 4 Comparion With Other Capital Budgeting Method he trigger expreion in equation 3.3 and 3.4 ugget a new way of renewal capital budgeting at the operating level that can be implemented through an enterpriewide policy or contractually. Other capital expenditure deciion-making tool, uch a payback period, internal rate of return (IRR) and net preent value (NPV), are decribed in introductory finance text. Often, the author of thoe text expre a preference for the NPV method. he equivalent annual cot (EAC) method alo incorporate the time value of money and i ued a a mean of comparing invetment with different time horizon, uch a aet lifepan. hee are all excellent tool for evaluating new capital invetment or project. hey are flexible and can be ued to imultaneouly evaluate multiple capital invetment, particularly thoe with a finite horizon. However, in our ituation, the initial capital invetment i a unk cot, and the aet i already on the balance heet generating revenue. Phyical aet renewal i ditinct from initial capital invetment in that there are alway the ame two mutually excluive option (ee beginning of Section 3) under conideration, and timeline of the deciion between thee two option i important. An enterpriewide policy baed on the trigger decribed by equation 3.3 and 3.4 recognize the importance of timeline in the aet replacement deciion. However, other capital budgeting method are ued in a manner conitent with planning for new capital invetment. hee traditional method are purely propective in that they only recognize the time to replace an aet ha arrived but fail to account for the fact that the bet time to replace the aet may have long paed. raditional capital budgeting tool are alo relatively cumberome and haphazard tool. hey depend on the initiative of line manager, mut be created for each project and are ubject to review, econd-gueing and deferral. In the ituation of long-lived aet for a going concern, equation 3.3 and 3.4 reduce the capital budgeting proce to monitoring a predetermined et of current calendar year M(t) contituent and regular comparion to threhold value. Deciion are made by policy. he only input needed in uch a ytem i the continual data entry of calendar year M(t) information, with the deciion itelf being automated. he increaed uage of individual phyical aet accounting ytem make thi a practicable reality today. 14

16 5 Value Impact to an Enterprie 5.1 Meaurability Aet renewal i generally the reult of a traditional capital budgeting proce, and, a we have already noted, planned replacement timing generally i not efficient. However, we cannot etimate the magnitude of that inefficiency for any enterprie imply by examining it financial tatement, or even from detailed exiting accounting data. o the extent that M(t) i not being continuouly monitored and manager are not aware of the threhold indicated by equation 3.3, the efficient replacement policy of Figure 1 will generally not be realized. Although there are now individual phyical aet accounting ytem that can digitally track all kind of cot data at the individual aet level, they are not preently being ued to record all the contituent of M(t) decribed in Section 3.1, hence the loe in efficiency predicted by Figure 1 are not being monitored (continuouly or otherwie). Once M(t) i defined and continuouly monitored, it would be poible to meaure exiting deficit of M(t) over M() and any urplue of M(t) under M() for aet about to be replaced. hi would allow approximation of the preent value cot impact of a policy that aim to eliminate uch deficit and urplue Magnitude Earlier, we ued an example of a power utility that might be experiencing 10 percent exce cot aociated with machinery and equipment. In that example, we referred only to repair and replacement cot, but we now know that the inefficiency affect any operational cot aociated with phyical aet. he following analyi provide ome bai for that 10 percent aumption. In equation 3.2, we equated the calendar year value of M(t) with a et of term at the efficient replacement time : 3.2 M ( ) = ic + C (1 + i) + t= 1 M ( t) v t 15

17 In thi ection, we introduce another interpretation of the term on the right ide of equation 3.2. he um of thee term repreent an equivalent annual level amount in perpetuity, which i minimized at the efficient time. For other value of, the equality in equation 3.2 i not true. In other word, thi equivalent annual amount, let u call it A(), i not equal to M() for value of other than. Equation 3.2 i generalized a follow: 5.1 A( ) = ic + C (1 + i) + t= 1 M ( t) v t Now we can ay that the preent value of an efficient enterprie policy baed on equation 3.2 i equal to M()/i and that the preent value of an (inefficient) enterprie policy baed on equation 5.1 (where i not ) i equal to A()/i. he preent value impact of a tranition from an inefficient policy to an efficient policy would be the difference between the preent value of thee two perpetuitie. We then aume that a firm i uing a five-year payback approach to jutify the replacement of the phyical aet, which correpond to M(t)=0.2C at replacement time and if we let i=4.5 percent, C=1000, and decribe M(t) uing the following polynomial: 3 M t = at + bt + ct + dt + et ( ) Where the coefficient equal: a b c d e One can plot equation 3.2 and 5.1 to how that =22 year, M()=83 and A() =89 at =26 year where M(26)=200. hi repreent about a 7 percent increae in the preent value cot impact due to the inefficient five-year payback replacement policy. Becaue of the extreme convexity of M(t) in thi example, a five-year payback policy that i not prompt, reulting in an additional deferral of only four more year (to =30), would reult in A()=104, which 3. hi i the formula that wa ued for M(t) in Figure 1. 16

18 repreent about a 25 percent increae in the preent value cot impact due to an inefficient replacement policy. If we replace the polynomial ued for M(t) by a traight line (no convexity): 5.3 M ( t) = t Performing the ame calculation baed on equation 3.2 and 5.1, we how that =23 year, M()=90 and A()=121 at =51 year where M(51)=200. hi repreent about a 34 percent increae in the preent value cot impact due to an inefficient replacement policy. Becaue there i no convexity of M(t) in thi example, a policy reulting in additional deferral of a few more year would not reult in a ignificant increae in the preent value cot impact due to an inefficient replacement policy. In thi example, the function ued to model M(t) in equation 5.2 and 5.3 were elected to create reaonable value of at typical value of i and becaue they repreent extreme of convexity in M(t) with which to bracket a range of potential preent value cot impact. Convexity i the one characteritic of M(t) for which we have the leat obtainable information. he value of C i arbitrary. A firm uing a five-year payback approach for aet renewal deciion realize a preent value cot impact that i from 7 percent to 34 percent higher than the efficient level. hi exce would be only for cot aociated with phyical aet that are uceptible to replacement, uch a capital equipment. Since many of the contituent of M(t) are not being continuouly monitored, the five-year payback approach ued in thi example i not likely to be prompt, even with repect to it own benchmark. he 10 percent inefficiency aumption ued in the power utility example i at the lower end of thi range and may be generou. 17

19 6 Infratructure Service Contract (ISC) In enterprie rik management, there i a lack of appropriate rik tranfer mechanim for operational rik. In thi paper, we are uggeting the deliberate creation of volatile, riky cah flow in order to achieve a higher level of operational efficiency. Fortunately, there already exit an intitution for tranferring uch rik. We have mentioned the potential ue of extended ervice contract to implement uch a phyical aet management policy. hi ection erve a an introduction to uch contract for facilitie and infratructure, and intend to provide ome hitorical background on the environment in which the above theory wa conceived. A there are extended ervice contract for home and vehicle, o there are long duration repair and replacement agreement for whole indutrial facilitie and public infratructure. Unlike their home and vehicle counterpart, uch extended warrantie for facilitie and infratructure do not exit a tand-alone product. Rather, they are underwritten in the limited context of non-inurance entitie providing entire railway, water treatment plant, power plant or other large enemble of phyical aet. Contract in which ingle entitie provide integrated engineering, procurement, contruction, operation, routine maintenance, repair and replacement ervice to deliver and run new facilitie and infratructure may have firt come into exitence in the 1980 and poibly much earlier if one include public-private partnerhip for public utility infratructure that date back to the late 19 th century. Companie pecializing in one or more of the above ervice uually mut form conortium to meet the wide cope of reponibilitie required under uch contract. Contract term can be a long a 50 year and entitie providing thee ervice aume mot of the functional role of the owner of the facility. hi integrated uite of ervice, including repair and replacement, i not the uual way to deliver infratructure. In the United State, it applie to le than 1 percent of new facilitie. However, ueful principle regarding planning of capital expenditure and method for projecting loe and expene aociated with repair and replacement obligation have been developed during negotiation among partie eeking to tranfer thee uncertain cah flow. hee principle and method apply to all phyical aet, whether or not covered by uch contract. We refer to the entitie decribed above a ervice provider. hey have a direct contractual relationhip with the facility owner to provide a wide range of ervice including repair and replacement of capital aet. he facility owner i the contract holder and i uually a utility, municipality or tranportation authority. Replacement of phyical aet uually refer to the replacement of a whole item of capital equipment or a tructure, uch a machinery or a building. Service provider are reponible for complete facility maintenance including routine maintenance, repair and replacement of phyical aet. he agreement to provide repair and replacement ervice i a part of a larger offering of ervice and i now often et forth in ditinct article within uch contract. In the pat, thee obligation were informally agreed to and not meticulouly documented. Recently, a thi infratructure delivery method ha gained 18

20 traction in the United State, attorney have attempted to formalize repair and replacement obligation. Spelling out thee obligation ha forced negotiating partie to explicitly conider the economic apect that the contract mut capture for an equitable tranfer of rik and fair pricing. In thi paper, only the long duration repair and replacement obligation under uch contract are referred to a infratructure ervice contract (ISC). hi definition, unique to thi paper, allow u to eparate and focu only on the ervice that are a very near counterpart to home and vehicle extended ervice contract with which they hare many imilaritie. Manufacturer of capital equipment have alo provided extended ervice contract covering repair and replacement aociated with their product. hi i partly in repone to the need of ervice provider who wih to tranfer thee rik and manufacturer willingne to aume uch rik in order to ell capital equipment. A manufacturer will often provide an extended ervice contract, which matche the duration and requirement of the ervice provider contract with facility owner. A with their home and vehicle counterpart, the expoure to rik in ISC varie ignificantly during the contract period, and pro rata earning of ervice fee doe not provide a match between income and liabilitie. In addition, ervice fee are uually not received in proportion to the level of expoure to rik. Unlike their home and vehicle counterpart, earning pattern are not eaily predicted by traditional property and caualty method uing data triangle. here i little hitorical lo data, and the tail for uch coverage can be far longer than thee contract have been in exitence. he entitie that underwrite ISC are not inurance companie. o our knowledge, inurer are not involved in underwriting long duration repair and replacement rik aociated with indutrial and public infratructure. here are everal reaon for thi, which will be dicued later. Facility owner tranfer thee rik to ervice provider. hen ervice provider tranfer ome of thee rik to manufacturer. In both of thee tranaction, the underwriting of repair and replacement loe i alway only a portion of the total ervice rendered. Beyond the ervice provider and manufacturer, there i no further place to tranfer thi rik. 6.1 ypical Feature of the ISC In an ISC, the ervice provider agree to repair or replace phyical aet during the term of the contract. Becaue of the long term of thee contract, a large proportion of the covered capital equipment in a facility may be replaced, perhap multiple time. Repair are an important part of the cope of an ISC, but the majority of loe and expene arie from the contract replacement obligation. he timing of replacement deciion i critical to projecting lo cot for thi coverage. In ome ISC, the language controlling timing of equipment replacement i very precriptive. In other, the ervice provider i eentially a conceionaire (owner) of the facility during the term of the contract, and ince maintenance cot are fully internalized by the ervice provider, the deciion of when to replace an item of capital equipment i left to the ervice provider dicretion. 19

21 Some contract tipulate a required phyical condition of the facility at the end of the contract term. hi can be pecified a a threhold minimum weighted average ueful life of covered facility capital equipment at the end of the contract term, in which etimated equipment replacement cot weight etimate of remaining ueful equipment life, a determined by a facility condition aement. Some contract ue verbal threhold to decribe the minimum required phyical condition of equipment and tructure at the end of the term. If the facility doe not meet thee qualitative decription, then the ervice provider mut make all repair, replacement or cah payment neceary to remedy the deficiencie. he ervice provider uually cannot terminate the contract for convenience, nor modify the ervice fee during the term of the contract. he ervice fee can be automatically indexed for inflation. An indexing formula i uually a pre-negotiated part of the contract, not ubject to modification after the contract i executed. Common indexe ued are a weighted combination of Conumer Price Index (CPI), Employment Cot Index (ECI) and other indexe publihed by the Bureau of Labor Statitic (BLS). A with their automobile and home counterpart, ISC are econdary to hort-term warrantie againt defect in workmanhip provided by the equipment manufacturer (original equipment manufacturer or OEM) or equipment eller. However, thi i mall comfort to the ervice provider who eentially provide a warranty many time longer than the OEM warranty. OEM warrantie for capital equipment can typically lat 18 month from delivery or 12 month from time of ue, whichever come firt. hi period i mall compared to the 10- to 50-year term of ISC. Some contract alo include a negotiated lit of major equipment ubject to replacement obligation. Each item of equipment may have a cap for replacement cot reimburement to the ervice provider, but replacement obligation are limited to thoe item on the lit. Another poible contractual arrangement i to leave the level of aggregation of the phyical aet to the ole dicretion of the contract holder for purpoe of triggering the contract replacement obligation. For example, a contract holder could decide to define the engine of the aircraft mentioned in Section 1 a a ingle aet at the time of determination that the M(t) cot aociated only with that aet have exceeded the threhold value of equation 3.3. he ability to do thi depend on the level of detail with which M(t) i recorded in the enterprie accounting ytem. ISC uually do not have explicit ervice fee. Coverage i often bundled a a part of a larger ervice fee for ongoing operation and maintenance ervice. Fee can be paid a a level monthly amount (ubject only to indexing a decribed above) over the contract term. Alternatively, ome fee payment tructure eparate the ISC (repair and replacement) component from the total ervice fee and try to match fee payment with the expected emergence of loe. he latter payment method implicitly recognize that new infratructure will probably not incur ignificant repair and replacement loe until decade after the beginning of the contract. he contract holder uually requet thi, ince ISC normally do not have proviion for the refund of unearned ervice fee hould the owner decide to cancel the contract prematurely. 20

22 ISC alo exit for older facilitie. hee contract are rikier for ervice provider, ince the condition of the facility i difficult to ae without a cotly inpection that mut be conducted prior to bidding on uch ervice. Unlike ervice contract for new facilitie, thee are uually underwritten only by companie providing complete operation and maintenance ervice for the old facility. Manufacturer will eldom underwrite uncheduled maintenance obligation on old capital equipment that ha been in operation for a while. Level ervice fee are uually charged throughout the life of the contract, indexed for inflation but with no other modification. Becaue the fee aociated with ISC can be high (ranging from $100,000 to $25 million per year), the coniderable time and expene of underwriting, which involve item-by-item etimation of aet replacement cot, i jutified. 6.2 Ditortion on Incentive in ISC he conceptual model of ection 2 and 3 try to approach capital planning aociated with repair and replacement from the rational perpective of the facility owner. Care mut be taken in the contract language to inure that the incentive of the ervice provider enhance and protect the interet of the facility owner Finite erm of ISC he dicuion o far ha focued on an analyi of cah flow in perpetuity. hi may be true for the owner who view the facility a a going concern. However, ISC have finite term, and ervice provider do not expect to continue repair and replacement obligation pat the end of thoe term. In many cae, the contract term i only about a long a, or low multiple of, the average expected life of capital equipment in a facility. he finite planning horizon of the ervice provider could encourage behavior, near the end of a contract term, to defer expenive replacement in favor of continued repair. hee repair may be le cotly to the ervice provider who i planning to leave the facility oon. he owner may be left with a facility that i functional but require a higher level of repair. In other word, at the end of the contract term, the owner may be left with a facility full of old equipment that need replacement Whoe Cot of Capital? In the econd conceptual model of Section 3, we derived a rule that tell u that the optimal time for replacement for mot type of capital equipment i when increaing M(t) croe a threhold proportional to the product of the cot of capital and the all-in cot of replacement (ic). However, if the cot of capital for a contract holder, who iue municipal bond, i about 4.5 percent, the cot of capital for a ervice provider i 7 percent and the cot of capital for a manufacturer who relie motly on equity capital i 10 percent, then there i clearly a mimatch of optimal replacement timing implied by equation 3.3 or 3.4. Entitie with the higher cot of capital will rationally defer replacement deciion, compared to thoe with the lower cot of capital. Unle there i an objective contractual trigger for replacement that explicitly recognize which cot of capital to ue, thi mimatch may have a deleteriou impact on the contract holder interet. 21