Financial Decisions, Summer 006, Aricle Capial Budgeing and Iniial Cash Oulay (ICO) Uncerainy Michael C. Ehrhard and John M. Wachowicz, Jr. * * The Paul and Beverly Casagna Professor of Finance and Professor of Finance, respecively The Universiy of Tennessee Absrac According o recen surveys, mos companies use discouned-cash-flow (DCF) mehods o evaluae capial budgeing decisions. DCF mehods ypically assume ha a projec s iniial cash oulay (ICO) is known wih cerainy. However, many ypes of iniial oulays have subsanial uncerainy, especially hose involving he consrucion of a new faciliy. This risk affecs no only he ICO, bu i also affecs subsequen depreciaion ax shields. A proper capial budgeing analysis should incorporae he addiional risk ha is due o an uncerain ICO. We show ha neiher he ypical pracices employed by corporaions nor wo common echniques advocaed in he finance lieraure, risk-adjused discoun raes and cerainy equivalens, saisfacorily address ICO risk. Sensiiviy analysis is an effecive way o address ICO risk, bu he finance lieraure ofen overlooks he adjusmens needed o saisfacorily address ICO risk wihin a sensiiviy analysis. We fill his gap in he lieraure by showing he impac of ICO risk on he sandard deviaion of a projec s PV. We hen apply sensiiviy analysis wih he appropriae adjusmens in a numerical example o illusrae he impac of ICO risk. I. Inroducion According o surveys, mos companies use discouned-cash-flow (DCF) mehods o evaluae capial budgeing decisions. 1 DCF mehods ypically assume ha a projec s iniial cash oulay (ICO) is known wih cerainy. However, many ypes of iniial oulays have subsanial uncerainy, especially hose involving he consrucion of a new faciliy. In addiion, his risk affecs no only he ICO, bu i also affecs subsequen depreciaion ax shields. A proper capial budgeing analysis should incorporae all of he addiional risk ha is due o an uncerain ICO. Unforunaely, he ypical coningency approach employed by many corporaions does no saisfacorily address ICO risk. The academic lieraure also has no saisfacorily addressed ICO risk. For example, wo common echniques advocaed in he finance lieraure, he use of cerainy equivalens and risk-adjused discoun raes, require oo much subjeciviy o be useful. Sensiiviy analysis is an effecive way o address ICO risk, bu he finance lieraure ofen overlooks he adjusmens needed o saisfacorily address ICO risk wihin a sensiiviy analysis. Following is a more deailed discussion of he praciioner and academic shorcomings relaed o assessing he risk of an uncerain ICO. A recen survey by he CFO Execuive Board indicaes ha companies believe ICO uncerainy is imporan and ha companies ry o address i in heir capial budgeing analyses. Mos 1 For example, see Bierman (1993) or Graham and Harvey (001). See CFO Execuive Board (005).
Financial Decisions, Summer 006, Aricle companies adjus he esimaed iniial cash oulay by adding a coningencies amoun o he original cos esimae. 3 For example, if he esimaed cos of he projec is $10 million, hen he firm migh creae a coningencies accoun equal o $100,000, resuling in a oal adjused iniial cos of $1.1 million, which is used when compuing he projec s ne presen value and inernal rae of reurn. If acual coss exceed he adjused ICO, based eiher upon a dollar basis or a percenage of he adjused ICO, hen many companies require he projec o go hrough a reapproval process. There are wo shorcomings o his pracice. Firs, he rigger for re-approval analysis should be based upon he expeced ne presen value of he projec (given he cos overrun) and no upon a pre-deermined dollar amoun or percenage. For example, a cos overrun of 10 percen migh cause one projec s PV o become very negaive, while i migh have only a small impac on anoher projec s PV. Second, because here is no heoreical basis for esimaing he appropriae amoun ha should be included in he coningencies accoun, he coningencies accoun becomes only an educaed guess. The academic lieraure for assessing risk includes he cerainy equivalen approach, he riskadjused discoun rae approach, and sensiiviy analysis. 4 A cerainy equivalen is he cerain amoun ha one would be willing o ake in lieu of a risky cash flow. For example, consider a coin oss in which you mus pay $100 for heads and $00 for ails. The expeced cos is $150, bu i is very risky. To avoid his risk, you migh be willing o pay a sure $155 raher han ake he risky coin oss, even hough he sure $155 coss more han he expeced $150 cos of he coin oss. Wih respec o ICO risk, one could, in heory, esimae he cerainy equivalen cash ouflow for each uncerain (risky) ICO componen, based on he expeced cash flow and is risk, and use his cerainy equivalen raher han he esimaed ICO when esimaing he projec s PV. 5 oice ha his is very similar o he common pracice described above of increasing he ICO by a coningencies accoun, where he adjused ICO is essenially a cerainy equivalen. In he example above, he adjused cos of $1.1 million is equivalen o a cerainy equivalen for he risky $1 million cos. Unforunaely, here are no heoreical guidelines for esimaing he cerainy equivalens ha would be chosen by he firm s shareholders. In oher words, here is no way o deermine he sure, bu more cosly, cash flow ha a shareholder would be willing o pay in lieu of he risky ICO. An addiional complicaion o he cerainy equivalen approach is ha many iniial oulay componens add o he depreciable basis of he projec. If he depreciable basis of he projec changes due o a change in he ICO, hen he fuure ax-shield benefis due o depreciaion will also change. This means ha he cerainy equivalen becomes he sure amoun you are willing o pay now o avoid he combinaion of a risky cash flow (he ICO) and he presen value of he 3 Some companies use he erm coningencies as a cach-all for many esimaed small coss. In oher words, some companies would raher lis a single accoun called coningencies raher han numerous small accouns. Oher companies use he erm coningencies for unknown coss ha migh occur. I is his second use ha we address. 4 Scenario analysis and simulaion are wo oher echniques o assess risk. We focus upon sensiiviy analysis, bu our adjusmens can easily be exended o scenario analysis and simulaion. 5 If he ICO occurs a some oher ime han zero, hen he cerainy equivalen would be discouned a he risk-free rae.
Financial Decisions, Summer 006, Aricle depreciaion ax shield. This muliple-period spillover effec furher complicaes any realisic use of cerainy equivalens when dealing wih uncerain ICO componens. A second echnique ofen advocaed in he finance lieraure is he use of risk-adjused discoun raes. For example, if wo fuure expeced cash flows have differen degrees of risk, hen a higher (i.e., risk-adjused) discoun rae migh be applied o he riskier cash flow. Similar o he problem wih cerainy equivalens, here is ofen no way o deermine he risk-adjusmen ha would be preferred by shareholders. 6 A second problem is ha he ICO is by definiion assumed o occur a ime zero (or a leas i is assumed o occur one year prior o he cash flow a he end of he projec s firs yea. Even if one were o assume ha he iniial cash flow occurs over some fracion of he projec s firs year, he presen value of a cash flow occurring a shor ime in he fuure is close o he acual value of he cash flow irrespecive of discoun raes. 7 Therefore, he risk-adjused discoun rae echnique does no saisfacorily address ICO risk. In a radiional sensiiviy analysis, he esimaed expeced values of inpu variables are varied one a a ime wih a series of wha if quesions. The original se of esimaes for inpu variables is called he base case. As an inpu variable s esimae is changed from is value, is impac on a projec s performance measures, such as ne presen value (PV) or inernal rae of reurn (IRR), can be deermined. For example, a ypical sensiiviy analysis migh involve changes in he number of unis sold, he price per uni, he cos per uni, ec. As we show in his paper, i is possible for a sensiiviy analysis o capure he impac of ICO risk, bu only if he analysis properly accouns for he muli-year spillover effec due o he depreciaion ax shield. 8 In summary, he ypical corporae pracice of using coningency accouns fails o saisfacorily address ICO risk. The cerainy equivalen approach and he risk-adjused discoun rae approach are inappropriae. Sensiiviy analysis can accommodae ICO risk if he depreciaion ax shield is appropriaely incorporaed, bu exising exbooks do no ariculae his 6 In some circumsances i is possible o make a heoreically correc adjusmen. See Daves and Ehrhard (000). 7 This assumes a reasonable discoun rae (for example, one beween 3% and 5%) is used. 8 Virually all finance exbooks include examples of sensiiviy analysis, bu, o he bes of our knowledge, only a couple even angenially address ICO in a sensiiviy analysis. Those excepions ypically provide a numerical example showing variaion in PV wih respec o changes in several variables, including he ICO. However, heir explanaion and discussion do no explain he impac ha he resuling depreciaion ax shield has on PV and risk. 3
Financial Decisions, Summer 006, Aricle aspec of risk in heir examples. We fill his gap in he lieraure by showing how ICO risk affecs he sandard deviaion of PV. Secion II provides a more deailed discussion of he sources of ICO uncerainy. Secion III explicily idenifies he risk due o he muli-year spillover of he depreciaion ax shield. Secion IV illusraes appropriae sensiiviy analysis wih a numerical example. II. Dealing wih ICO Uncerainy For many capial budgeing analyses, he assumpion of a cerain ICO is valid e.g., he purchase of a cerain piece of equipmen for a fixed price. However, even here, if his equipmen purchase were o require seup and insallaion, hose capialized expenses could be boh sizeable and uncerain a he ime he projec is being evaluaed. In fac, he larger he projec, he more likely i is o involve a hos of uncerain ICO componen coss. In Exhibi 1, we lis some of he common iems included in he acquisiion cos of a firm s major propery, plan, and equipmen (PP&E) accouns. Addiions o one or more of hese accouns would normally be relaed o a ypical invesmen projec s ICO. oice how many of he iems lised under he four major PP&E caegories land, land improvemens, buildings, machinery and equipmen could very well have uncerain esimaes a he ime he projec is being evaluaed. Weaher condiions, for example, could easily affec land sie preparaion coss, building consrucion coss, and insallaion coss of equipmen involved in a consrucion projec. In fac, i is he avoidance of jus his ype of uncerainy ha ofen leads firms o consider leasing (wih is fixed/cerain coss) as opposed o building/purchasing wih is poenial for cos overruns. In addiion, anoher ypical componen of an ICO migh be an invesmen in working capial, such as invenory. The dollar amouns of such iems are unlikely o be known wih cerainy a he projec evaluaion sage, which inroduces uncerainy ino he ICO. I is imporan ha managers be able o correcly assess he risk of a poenial projec, including he risk due o ICO uncerainy. If he risk is oo high, a manager migh well choose o forego a projec, even if he expeced PV is posiive. The resuls of an appropriae risk analysis also allow a manager o idenify any appropriae levels of cos overruns ha should rigger a complee projec re-evaluaion. Armed wih his informaion, a manager can hen decide wheher any esimaes need refining or reviewing, and wheher any are no worh invesigaing furher before deciding on projec accepance/rejecion. Based on his analysis, a manager migh decide o remove he uncerainy surrounding a paricular ICO inpu variable by negoiaing a fixed price for some service or ousourcing some in-house, uncerain cos iem (like equipmen insallaion) so as o make i ino a cerain cos expense. The manager can also idenify he criical levels of cos overruns ha endanger he economic viabiliy of he projec. 4
Financial Decisions, Summer 006, Aricle The following secion idenifies he impac of ICO uncerainy on projec risk. Exhibi 1. Common Iems Included in he Acquisiion Cos of Propery, Plan, and Equipmen Land -- Capializaion of land coss include he following -- all of which are no subjec o ax depreciaion: Purchase price Commissions, permis, or fees paid by he buyer Closing coss Cos of real esae surveys Special assessmens for local improvemens (e.g., such as pavemens, sree lighs, sewers, and drainage sysems) Cos necessary o prepare land for is inended use (e.g., grading, filling, draining, and clearing) Land Improvemens -- Capializaion of land improvemen coss include he following -- all of which are subjec o ax depreciaion: Paving Fencing Landscaping Oudoor lighing Buildings -- Capializaion of building coss include he following -- all of which are subjec o ax depreciaion: Purchase price of an exising building (old or new), or consrucion coss from excavaion o compleion Expenses incurred in remodeling or alering a purchased building o prepare i for is inended use Professional fees (e.g., archiecural, engineering, and legal coss) and consrucion permis Machinery and Equipmen -- Capializaion of machinery and equipmen coss include he following -- all of which are subjec o ax depreciaion: Purchase price Shipping coss (e.g., freigh, impor duies, handling charges and insurance on he equipmen while i is in ransi) Sales, use and oher axes imposed on he purchase Insallaion coss, including special foundaions or plan modificaions Recondiioning (used equipmen) and esing for use (used and new equipmen) 5
Financial Decisions, Summer 006, Aricle III. ICO Uncerainy and Projec Risk: The Impac of he Depreciaion Tax Shield Spillover Consider a projec wih an iniial cash oulay and expeced cash flows a denoed by CF. If he projec lass years and has a cos of capial of r, hen he projec PV is: CF = 1 (1+ PV = - ICO + (1) The iniial cash oulay is comprised of a depreciable Basis and a porion ha migh be nondepreciable, denoed by ondepr: ICO = Basis + ondepr () The cash flow a year is deermined by he projec s expeced earnings before ineres, axes, depreciaion and amorizaion (EBITDA ), is depreciaion (Depr ), he ax rae (T), and he required invesmen (i.e., he change) in working capial (ΔWC ): CF = (EBITDA Depr )(1-T) + Depr - ΔWC (3) This can be rewrien o separae he impac of EBITDA, he depreciaion ax shield benefi, and he change in working capial: CF = (EBITDA )(1-T) + Depr T - ΔWC (4) Le F denoe he depreciaion facor for he h year for an asse placed in service a =0. Le n denoe he depreciaion life of he asse, which may be differen from he projec life. For example, under sraigh line depreciaion, he depreciaion facor is 1/n. The depreciaion facors for he MACRS ax depreciaion mehod are provided by he U.S. Treasury for each asse class. For clariy of exposiion, we assume ha n<= (i.e., he asse is fully depreciaed by he end of he projec life) and ha here is no salvage value. The depreciaion expense a ime is he produc of he basis and he depreciaion facor: Depr = Basis(F ) (5) The projec s PV can be expressed in erms of he projec s ICO, is afer-ax EBITDA, he depreciaion ax shield benefis, he invesmens in working capial, and he projec s cos of capial, r: 9 9 In heory, each source of cash flow (e.g., sales revenue, coss of goods sold, depreciaion, ec.) should be discouned a a rae ha is appropriae for he paricular risk of ha paricular cash flow source. In pracice (and in mos exbooks), all usual projec cash flows are discouned a he projec cos of capial. Therefore, we discoun all of he projec s cash flows a r. For siuaions wih unusual cash flows, see Daves and Ehrhard (003). 6
Financial Decisions, Summer 006, Aricle n EBITDA (1 T) Basis (F )(T) + = 1 (1+ = 1 (1+ = 1 (1+ ΔWC PV = - ondepr - Basis + (6) Grouping erms associaed wih he basis yields: n F (T) EBITDA (1 T) ΔWC PV = - ondepr - Basis 1 + (7) = 1 (1+ = 1 (1+ = 1 (1+ oice he second erm in Equaion (7) shows ha a dollar change in he basis does no cause a dollar change in PV, due o he presen value of he ax savings due o depreciaion. Thus, a dollar change in he basis produces less han a dollar change in PV. The depreciaion ax shield also has an impac on he projec s risk, as measured by is variance. As we show below, he ax shield also affecs risk. Using Equaion (7), he variance of he PV is: σ PV = σ + + ondepr = 1 = 1 = 1 + 1 + 1 + = 1 1 (1+ 1 (1+ = 1 = 1 j n n + 1 F (1+ F (1+ = 1 T T n σ (1+ ΔWC F = 1 = 1 + 1 1 (1+ (1 T) 1 (1+ (1+ T Basis n = 1 + = 1 (1+ (1 T) COV[onDepr, EBITDA ] (1+ σ F T COV[onDepr,ΔWC ] (1 T)σ (1+ COV[EBITDA,ΔWC EBITDA COV[onDepr, Basis] (1 T) COV[Basis,EBITDA ] (1+ COV[Basis,ΔWC ] ] (8) where σ k denoes he variance of he k h source of cash flow and COV denoes he covariance beween he sources of cash flow. To focus upon he relaive conribuions o risk due o he ICO and he operaing cash flows, suppose ha σ ondepr and σ ΔWC, are equal o zero. To simplify he exposiion, suppose ha σ EBITDA is consan for all. Also assume ha all covariances are equal o zero. Under hese 7
Financial Decisions, Summer 006, Aricle simplifying assumpions, projec risk can be wrien as: σ n F 1 PV = 1 T σ Basis + σebitda (1 T) 1 (1 = + = 1 (1+ (9) oice in his simplified example, he summaion in he second erm of Equaion (9) is he presen value facor for an annuiy of periods when discouned a he rae r, denoed by PVIFA,r. Therefore, he risk due o EBITDA is scaled up or down by he presen value facor due o he iming of EBITDA. The longer he life of he projec is, he larger he presen value facor is, and he higher he risk due o EBITDA. Le PVDepr,r denoe he summaion in he firs parenheses above. For he special case of sraigh-line depreciaion over n years (noe ha he deprecaion life n maybe differen from he projec life ), F = (1/n) for n and zero oherwise. For sraigh-line depreciaion, PVDepr,r is equal o T/n muliplied by he presen value facor for an annuiy of n years when discouned a he rae r: PVDepr,r = (T/n) PVIFA n,r. For MACRS depreciaion, here is no simple closed form formula for PVDepr r. Using his noaion, he variance of expeced PV can be wrien: σ ( 1 T PVDeprn,r ) σbasis + (1 T) (PVIFA,r ) EBITDA PV σ = (10) The conribuion of ICO risk has wo componens. The firs is due o he iniial cash flow. The second is due o he ax shield benefi provided by depreciaion; i.e., T(PVDepr,r ). oice ha his ax shield benefi dampens he risk due o he basis. For example, if he basis becomes larger, here is a larger cash ouflow a ime zero, bu here is a larger value of he ax shield benefi. The opposie is rue if he basis urns ou o be smaller han expeced. Equaion 10 provides several insighs. Firs, if an analys simply ignores he ICO risk (which implicily assumes ha σ Basis is zero), Equaion 10 becomes: σ (1 T) (PVIFA PV,r ) σ EBITDA = (11) In his case, he resuling esimae of projec risk will be biased downward wih respec o he rue risk given in Equaion 10. Second, if an analys incorporaes he ICO risk due o he iniial purchase bu ignores he subsequen impac of he depreciaion ax shield generaed by he ICO (which implicily assumes PVDep,r = 0), hen Equaion 10 becomes: σ σbasis + (1 T) (PVIFA PV,r ) σ EBITDA = (1) In his case, he resuling esimae of projec risk will be biased upward wih respec o he rue risk given in Equaion 10. Therefore, o appropriaely incorporae ICO risk, he analys mus 8
Financial Decisions, Summer 006, Aricle explicily consider he depreciaion ax shield benefi. IV. An Illusraive Example of a Modified Sensiiviy Analysis for ICO Uncerainy To illusrae he use of modified sensiiviy analysis as i applies o ICO uncerainy in a capial budgeing analysis, consider he poenial purchase of some equipmen o be used in a projec. The purchase price is known wih cerainy o be $600,000. The equipmen has a useful life of five years and is in he hree-year propery class for MACRS ax-depreciaion purposes. Shipping and insallaion coss are "esimaed" o be $100,000 and $00,000, respecively, and he equipmen has a zero expeced final salvage value, five years from now. o addiional "ne" working capial is needed. The new equipmen will generae esimaed addiional annual ne operaing cash flows, before consideraion of depreciaion and axes, of $300,000 a year for five years. Assuming ha he marginal ax rae equals 40 percen, we can esimae he projec's relevan incremenal cash flows for he "base case." IV.A. The Base Case: e Presen Value Exhibi shows he projec's $900,000 iniial cash ouflow under he "base case." Exhibi. The Expeced Iniial Cash Ouflow Equipmen cos (cerain) = $600,000 + Capialized expendiures: Shipping cos (esimae) = 100,000 Insallaion cos (esimae) = 00,000 = Iniial cash oulay (ICO) = $900,000 = depreciable basis for ax purposes 9
Financial Decisions, Summer 006, Aricle Exhibi 3 shows he expeced he incremenal fuure cash flows. Exhibi 3. Expeced Incremenal Fuure Cash Flows ED OF YEAR (in $000s) 1 3 4 5 e change in operaing revenue, excluding depreciaion 300.00 300.00 300.00 300.00 300.00 e increase in ax depreciaion (99.97) (400.05) (133.9) ( 66.69) -- = e change in income before axes.03 (100.05) 166.71 33.31 300.00 (+) e increase (decrease) in axes (40% rae) (.01) 40.0 (66.68) (93.3) (10.00) = e change in income afer ax.0 ( 60.03) 100.03 139.99 180.00 + e increase in ax depreciaion 99.97 400.05 133.9 66.69 -- = Incremenal ne cash flow for years 1 o 5 99.99 340.0 33.3 06.68 180.00 10
Financial Decisions, Summer 006, Aricle Exhibi 4 combines he ICO from Exhibi wih he annual operaing cash flows from Exhibi 3, resuling in he oal expeced ne incremenal cash flows from he projec. Exhibi 4. Expeced Annual Cash Flows ED OF YEAR (in $000s) Period 0 1 3 4 5 e cash flows ( 900.00) 99.99 340.0 33.3 06.68 180.00 For an esimaed iniial cash oulay of $900,000, he firm expecs o generae ne cash flows of $99,990, $340,00, $33,30, $06,680, and $180,000 over he nex five years. The firm's weighed-average cos of capial is 13 percen. Given his "base case" daa, he ne presen value is $17,90. The ypical capial budgeing response o he projec's posiive ne presen value would be o signal projec accepance. However, given he uncerain esimaes for wo of he hree ICO componens, i.e., shipping and insallaion, we sugges ha he capial budgeing analys should defer an accep/rejec decision unil hose uncerain esimaes and heir muli-year spillover effecs are subjeced o sensiiviy analysis. IV.B. Sensiiviy Analysis Sensiiviy analysis can be applied o our equipmen purchase's uncerain ICO componens o answer a few wha if quesions. Wha if, for example, our $100,000 esimae for shipping cos urns ou o be higher/lower? And, wha if insallaion is higher/lower han he $00,000 we originally hough? To answer hose wha if quesions, we firs perform new PV calculaions in which we change our wo variables of concern (shipping and insallaion) individually by, for example, -30%, -0%, -10%, +10%, +0%, and +30%. oe ha changes in hese variables have muliperiod spillover effecs on depreciaion, which affecs axes and fuure cash flows. Thus, he change in he ICO no only affecs he Year-0 cash flow, bu i also affecs he cash flows in he subsequen years. 11
Financial Decisions, Summer 006, Aricle Exhibi 5 compares he esimaed PVs for he differen levels of ICOs. Exhibi 5. Sensiiviy analysis for he equipmen purchase showing he impac of individual changes in wo iniial cash oulay componens on he projec s ne presen value (PV) in housands of dollars CHAGE I ORIGIAL ISTALLATIO COST -30% -0% -10% Base +10% +0% +30% Resuling PV 58.93 45.7 31.58 17.9 4.5 ( 9.43) (3.09) CHAGE I ORIGIAL SHIPPIG COST -30% -0% -10% Base +10% +0% +30% Resuling PV 38.43 31.53 4.75 17.9 11.08 4.5 (.59) From Exhibi 5, we can see ha if esimaed insallaion cos were o increase by roughly 13 percen or more from he base case, our projec s ne presen value urns negaive. For shipping cos, however, he increase would need o be roughly 8 percen or more before he projec has a negaive ne presen value. The daa conained in Exhibi 5 can also be presened graphically in an PV sensiiviy graph see Exhibi 6. oice he wo sensiiviy lines in he PV sensiiviy graph. The insallaion cos line has he seepes slope. Therefore, PV is more sensiive o equal percenage changes in ha variable han in shipping cos. Based on his informaion, managemen may wan o concenrae more conrol effors on he seemingly more criical insallaion cos variable. I may even wan o ry and negoiae a fixed-cos price conrac for insallaion from a hird pary. 1
Financial Decisions, Summer 006, Aricle Exhibi 6: PV Sensiiviy Graph for he Equipmen Purchase ET PRESET VALUE AT 13% ($OOOs) 60 50 40 30 0 10 0 (10) (0) (30) Insallaion cos Shipping cos -30-0 -10 Base 10 0 30 CHAGE I VARIABLE FROM BASE VALUE (%) One poenial problem wih our sensiiviy analysis, so far, is ha i has looked a sensiiviy one variable a a ime. We can also judge he sensiiviy of PV o simulaneous changes in wo variables by consrucing an PV sensiiviy marix. Exhibi 7 is one such sensiiviy marix ha depics PV resuls for combinaions of changes in our wo inpu esimaes shipping cos and insallaion cos. oe ha a simulaneous cos increase approaching 10 percen for boh shipping and insallaion coss would resul in a negaive ne presen value. 13
Financial Decisions, Summer 006, Aricle Exhibi 7. Sensiiviy marix for he equipmen purchase showing he impac of simulaneous changes in wo iniial cash oulay componens on he projec s ne presen value (PV) in housands of dollars CHAGE I SHIPPIG COST -30% -0% -10% Base +10% +0% +30% CHAGE I ISTALLATIO COST -30% 79.44 7.60 65.77 58.93 5.10 45.7 38.43-0% 65.77 58.93 5.10 45.7 38.43 31.58 4.75-10% 5.10 45.7 38.43 31.58 4.75 17.9 11.08 Base 38.43 31.58 4.75 17.9 11.08 4.5 (.59) +10% 4.75 17.9 11.08 4.5 (.59) (9.43) (16.5) +0% 11.08 4.5 (.59) (9.43) (16.5) (3.09) (9.93) +30% (.59) (9.43) (16.5) (3.09) (9.93) (36.77) (43.60) Sensiiviy analysis, as we have seen, provides useful and easily undersood insighs ino how a projec s PV responds o a change in one (or more) uncerain ICO inpu variables. Thus, he analysis provides insighs ino he risk-reurn rade-off for he projec. Given he risk-reurn profile in Exhibi 7, should he projec be aken? In oher words, is he expeced PV of $17,90 worh he risk of wo simulaneous 30% cos overruns, which would resul in $43,600 loss? Alhough here is no heoreically definiive answer, if he possible loss is small relaive o he size of he company, hen he risk is probably worh aking, given ha he projec has a posiive expeced value. If he loss is so large ha i is a be he company proposiion, hen he board of direcors should make he final decision. Sensiiviy analysis does no provide any absolue rules for deciding wheher or no o accep he projec, bu i does provide some clear guidelines regarding he need for a projec o be reevaluaed. For he projec in his example, a re-approval analysis should be riggered when he combined shipping and insallaion cos overrun is $6,13 or more, since his leads o an expeced negaive PV. 10 In fac, if cos overruns approach $6,13, hen he company s managers should consider possible inervenions ha migh help salvage he value of he projec. 10 A $6,13 combined shipping/insallaion cos overrun corresponds o he region in grey in Exhibi 7 which indicaes negaive PVs. This break-even overrun can be calculaed as: (Base PV)/[1 T(PVDepr n,r )]. 14
Financial Decisions, Summer 006, Aricle V. Summary and Conclusions In a ypical capial budgeing analysis, a projec s iniial cash oulay (ICO) is generally reaed as a single, cerain cash ouflow. However, upon closer inspecion, one or more of he following condiions may hold rue in real life : The ICO may have several cash ouflow componens e.g., land, land improvemens, buildings, machinery and equipmen. Some of he ICO componens may be cerain cash flows and some may be uncerain/risky cash flows. Some ICO componens may be capialized, bu no subjec o ax depreciaion (e.g., land). An ouflow like his is already afer-ax and provides no depreciaion ax-shield benefis ha would affec fuure afer-ax operaing cash inflows. Oher ICO componens may also be capialized, bu would be subjec o ax depreciaion (e.g., land improvemen, buildings, machinery and equipmen). These ouflows will have spillover effecs on fuure operaing cash inflows because of heir depreciaion ax shield. Some ICO componen flows may occur afer ime period zero. Given hese real life complicaing facors involving a projec s ICO, we recommend ha sensiiviy esing be applied o uncerain ICO componens a he projec-evaluaion sage. Based on his sensiiviy esing, he firm can hen beer decide wheher o: a) subjec any ICO componen esimaes o furher refining/review; b) remove any ICO componen uncerainy by negoiaing a fixed price conrac for some service; c) ousource some in-house, uncerain ICO cos iem; or d) accep/rejec he projec based on he currenly available informaion. The firm can also idenify he criical levels of cos overruns ha should rigger a formal re-approval of he projec. 15
Financial Decisions, Summer 006, Aricle References Bierman, Harold, Capial Budgeing in 199: A Survey, Financial Managemen, Auumn, 1993, 4. CFO Execuive Board, Capial Expendiure Re-Approvals, Corporae Execuive Board, April 005. Daves, Phillip, and Michael Ehrhard, Capial Budgeing: The Valuaion of Unusual, Irregular, or Exraordinary Cash Flows, Financial Pracice and Educaion, Vol. 10, o., Fall/Winer 000, 106-114. Graham, John R., and Campbell R. Harvey, The Theory and Pracice of Corporae Finance: Evidence from he Field, Journal of Financial Economics, Vol. 60, o. -3, 001, 187-43. 16