Facility Sustainment and Firm Value: A Case Study Based on Target Corporation

Transcription

1 Facility Sustainment and Firm Value: A Case Study Based on Target Corporation Autor Robert Beac Abstract Tis paper argues tat increasing te level of facility sustainment (maintenance and repair) funding can increase firm value. iger levels of facility sustainment funding reduce te list of maintenance and repair projects and maintain te liquidation value of te firm s facilities. A condition is derived tat establises te minimum probability of financial distress required for firm value to increase as sustainment funding increases. Tis condition is tested wit a case study based on te annual reports of a major retailer, Target Corporation. Te results support te ypotesis. Tis olds even toug adverse externalities tat migt occur from underfunding sustainment ave not been considered. Most firms are responsible for te operation of a number of buildings and oter facilities. In managing tese facilities, tey must make decisions tat can ave a profound impact on uman ealt and te natural environment. For example, consider Leadersip in Energy and Environmental Design (LEED) standards for operation and maintenance of existing buildings. Tese standards apply to a number of operation and maintenance activities including occupant comfort, air quality, and waste management (U.S. Green Building Council, 2008). It is widely accepted tat te decision to adopt LEED standards can reduce te armful ealt and environmental effects from te operation of tese facilities. Tis paper looks at anoter important facility management decision: ow muc to fund facility sustainment. Tis decision can also significantly impact ealt and te environment yet receives little attention in te sustainability and corporate finance literature. As it is used ere, facility sustainment refers to te yearly cost of maintaining a facility in good working order over its expected lifespan. Funding facility sustainment at 00% maximizes te value and usefulness of te facility. Underfunding facility sustainment not only leads to a growing backlog of maintenance and repair projects but can also result in catastropic failures tat lead to severe ealt and environmental consequences. For example, te 2005 explosion at te Britis Petroleum refinery in Texas City, Texas resulted in te deat of fifteen people and pollution of te surrounding neigborood. Tis incident was largely attributed to te inadequate maintenance of production facilities (Lyall, 200). As anoter example, sources of Legionnaires disease, a very serious pulmonary illness, include large central air-conditioning systems tat ave been inadequately maintained. Despite its potential ealt and environmental consequences, many firms and organizations routinely underfund facility

2 Facility Sustainment and Firm Value 233 sustainment since te costs of doing so will be deferred to an unknown point in te future. A recent assessment of te facility sustainment backlog at a major U.S. university was $620 million (Carlson, 2008). Many experts would agree tat tis is probably te typical case rater tan te exception. Te ypotesis of tis paper is tat under certain conditions increasing sustainment funding can increase firm value. In many cases, te liquidation value of facilities tat ave been adequately maintained will be iger tan oterwise and outweig te additional expense of iger sustainment funding. Te model developed ere is based on a tradeoff teory of capital structure tat takes into account te probability of financial distress and incorporates te facility degradation process tat occurs wen sustainment is underfunded. It represents te initial effort in te literature to model te impact of te level of sustainment funding on firm value. It contributes bot to te literature on te tradeoff model of capital structure along te lines proposed by Damodaran (2006) and to te literature on sustainment funding and facility condition as discussed in Coi, Jondrow, Taylor, and Weis (994) and Ottoman, ixon, and Lofgren (999a, 999b). Using a case study based on te financial reports of a major retailer, Target Corporation, it is sown tat tis ypotesis olds in two different versions of te model. Te first is referred to as te finite valuation period model and is based on an expected value model of financial distress similar to tat described in Damodaran (2006). A condition is derived for te probability of financial distress tat must be met for firm value to increase as sustainment funding is increased. It is sown tat for te parameters of te case study, tis condition is met. Witin te framework of tis model, firm value is also calculated at Target s istorical level of sustainment, 5.7%, and at te recommended level of sustainment, 00%. Te results support te ypotesis tat firm value can increase as sustainment funding increases. Te second model is a Monte Carlo simulation. Again Target s istorical funding level of 5.7% and te recommended funding level at 00% are considered. Te Monte Carlo simulation also supports te ypotesis tat firm value can increase as sustainment funding is increased. A Model of Facility Sustainment and Firm Value A version of te backlog projection model is used to model facility sustainment in tis paper. Te backlog projection model predicts te future backlog of maintenance and repair given expected funding. It requires estimates of sustainment cost factors, a metod of measuring facility condition, a model of te facility degradation process, and estimates of degradation rates for different types of facilities. Sustainment cost factors for facilities found on a typical military installation ave been developed by eely and eatammer (99) of te Army s Civil Engineering Researc Laboratory. Tese cost factors are updated annually and are also available from commercial sources suc as te R.S. Means Company or Witestone Researc, bot of wic publis an annual update of facility JOSRE Vol. 3 o. 2 0

3 234 Beac sustainment cost factors for commercial and residential facilities. Te sustainment cost factors for retail stores used in te case study below come from government sources. A facility condition index (FCI) measures te condition of a given facility and weter it meets te standard for te primary use of tat facility. Ottoman, ixon, and Lofgren (999a, 999b) summarize te various approaces to facility condition measures used by academic, government, and commercial planners. Closely related are models of facility degradation. eely, eatammer, and Stirn (99) developed te Army s Maintenance Resource and Prediction Model, a component-based model. Coi, Jondrow, Taylor, and Weis (994) summarize muc of te researc on facility sustainment and facility degradation. Backlog projection models also require a degradation rate. Te degradation rate for te retail stores considered in te case study come from studies conducted by te autor and oters (Beac, Carson, and Keating, 998; and Beac, 2004). Backlog Projection Model Te backlog projection model discussed above defines te relationsip between funding and facility condition. It can be expressed as: C ( )C S F, () t t t t were C t is te cost of facility deficiencies (te backlog of maintenance and repair projects) at te end of year t, is te degradation rate, S t is te required yearly sustainment to maintain te facility in good operating condition, and F t is te level of sustainment funding for year t. (Te year subscripts are retained for S t and F t even toug in te case study discussed below bot are taken as constant.) Tis equation can also be expressed as: C ( )C ( )S, (2) t t t were is te percentage of sustainment funded. Tat is: F t S t. Te firm s sustainment requirement, S t, for a given type of facility is computed using te following equation: St TSFt SCF, (3)

4 Facility Sustainment and Firm Value 235 were S t is te firm s sustainment requirements for year t, TSF t is te total square footage of tat type of facility in year t, and SCF is te sustainment cost factor based on te industry standard for a given type of facility. Finite Valuation Period Model Te finite valuation period model estimates te expected firm value over a finite number of future years. Te estimate of firm value is similar to te approac described in Damodaran (2006). Tis approac assumes tere is a positive probability of financial distress and tat expected firm value over te valuation period is made up of a going concern component and a financial distress component. Tis is expressed in te following equation: V V V, (4) F GC FD were V F, V GC, and V FD represent te expected value of te firm, te expected value of te going concern component, and te expected value of te financial distress component, respectively. Te going concern value is based on te present value of te free cas flow of te firm over te valuation period. Free cas flow is estimated using te following equation: FCF ebit( t ) dep (capex nwc), (5) c were FCF is free cas flow, ebit is earnings before interest and taxes, t c is te corporate tax rate, capex is te yearly capital expenditures, dep is te current year depreciation, and nwc is te yearly cange in net working capital. Te expected going concern value of te firm is estimated by calculating te present value of te free cas flow of te firm over te valuation period times te annual probability tat te firm will not experience financial distress. Tat is: FCF VGC ( ), (6) ( WACC) were FCF is te yearly free cas flow of te firm as defined in Equation 5, is te valuation period, is te annual probability of financial distress, and WACC is te weigted average cost of capital based on te weigted average of te firm s cost of debt and cost of equity. JOSRE Vol. 3 o. 2 0

5 236 Beac By separating out sustainment cost expenses, te going concern value can be expressed in a more convenient form as: FCFadj S t( t c) VGC ( ), (7) ( WACC) were FCF adj is te free cas flow before subtracting out sustainment expenses. Te financial distress value is estimated as te expected liquidation value of te firm s facilities. For liquidation value, we use te plant replacement value (PRV) of te facility adjusted for expected degradation based on te level of sustainment funding. PRV represents te cost of building a similar facility on te current site. It does not include site preparation or te value of te land. In te absence of fire sale effects, te adjusted PRV value represents a conservative estimate of te liquidation value since te market value could easily be muc iger. 2 Te financial distress value can be expressed as: j PRV ( ) S t( ) j ( WACC) V, (8) FD were all variables are as defined above. Given Equations 3 8, te model of firm value can be expressed as: FCFadj S t( t c) VF ( ) ( WACC) j PRV ( ) S t( ) j ( WACC), (9) were V F represents te expected value of te firm given sustainment funding at % and wit an annual probability of financial distress of. Equation 9 states tat expected firm value is te discounted sum of te expected cas flows for eac year in te valuation period. Te Critical Value of Financial Distress Taking te first derivative of Equation 9 wit respect to te percent of sustainment funded,, te following expression is derived:

6 Facility Sustainment and Firm Value 237 dv t c d ( WACC) ( ) j j t ( WACC) F ( )S ( t ) S. (0) It follows for tis to be positive te following must old: ( ) j j ( )( t c). () ( WACC) ( WACC) Solving Equation for, te annual probability of financial distress, te following condition is derived. Condition. Firm value increases as sustainment funding increases if te annual probability of financial distress is greater tan te critical value, c, described by: c ( t c) ( WACC) ( ) j j c ( t ). (2) ( WACC) ( WACC) Te critical value of te probability of financial distress, c, can be interpreted as a measure of te likeliood tat an increase in sustainment funding,, will increase firm value. Tat is, as c decreases, te likeliood tat an increase in will increase firm value will go up for any given valuation period. Te critical value of te probability of financial distress depends on te weigted average cost of capital, WACC, te degradation rate,, and te valuation period,. Te tree propositions below determine te response of te critical value of to canges in tese tree parameters. Proposition. For a valuation period,, te response of te critical value of to a cange in te degradation rate,, is negative. Proposition 2. For a valuation period,, te response of te critical value of to a cange in te weigted average cost of capital, WACC, is positive. JOSRE Vol. 3 o. 2 0

7 238 Beac Proposition 3. As te valuation period,, becomes longer, te critical value of decreases. Te proofs of te tree propositions can be found in Appendix A. Propositions and 2 are consistent wit te intuition tat anyting tat reduces te liquidation value of te firm s facilities will increase te critical value of ; and anyting tat increases te liquidation value of te firm s facilities will decrease te critical value of. In te case of te degradation rate, te greater te degradation rate, te faster facilities degrade and te greater te potential gain if sustainment funding is increased. ence te critical value of goes down as te degradation rate goes up. In te case of te weigted average cost of capital, te greater te weigted average cost of capital, te more free cas flow and te liquidation value of te firm s facility are discounted. At first glance, te impact of increasing te weigted average cost of capital is ambiguous. owever, te liquidation value occurs wen te firm experiences financial distress at te end of te valuation period and ence gets discounted te most. Proposition 2 confirms tat tis effect dominates and te critical value of goes up as te weigted average cost of capital increases. Proposition 3 sows tat it must be te case tat as te valuation period becomes longer, te cumulative effect of te degradation process becomes greater and te critical value of decreases. Case Study Te case study estimates te parameters of te finite valuation period model for a specific example: a major retail firm, Target Corporation. Tis firm was cosen because of te major retailers considered it was te only one tat specifically stated its maintenance and repair costs in its annual reports. Data from te firm s annual reports from 993 troug 2007, available on its website, is te basis for te analysis. Since te primary focus ere is te firm s facility sustainment funding, te analysis is simplified by assuming te firm s property, plant, and equipment is represented by its retail stores. Te loss of generality is minimized in tis case since retail stores represent 95% of te firm s facilities and 85% of te firm s property, plant, and equipment. Tis data is used to estimate te following parameters of te model: TSF Total square footage of te retail floor space; Annual probability of financial distress; istoric level of sustainment funding of te firm as a percentage of requirements; FCF Free cas flow of te firm; R D Cost of debt for te firm; R E Cost of equity for te firm; WACC Te firm s weigted average cost of capital; and t c Te firm s corporate tax rate.

8 Facility Sustainment and Firm Value 239 Exibit Case Study Parameters Parameter Variable Value Total Square Feet (,000 SF) TSF 207,945 Probability of Financial Distress (%) 4.00 Sustainment Funding % 5.70 Free Cas Flow ($million) FCF,62.70 Cost of Debt (%) R D 5.55 Cost of Equity (%) R E 9.39 Weigted Average Cost of Capital (%) WACC 7.64 Corporate Tax Rate (%) t c ote: Parameters based on annual report data of Target Corporation for Exibit 2 Cost Factors and te Degradation Rate Cost Factor Variable Value Sustainment Cost Factor SCF $3.34/SF ew Construction CF $92.2/SF Degradation Rate 8.57% ote: Cost factors and te degradation rate apply to retail stores for 2007, based on industry and DOD sources. In addition to tese parameters, standard cost factors and a degradation rate for retail stores are required. Te cost factors for retail stores used ere come from commercial and government sources. Te degradation rate for retail stores comes from studies conducted by myself and oters as cited above. For retail stores te following cost factors are required: SCF Sustainment cost factor per square foot; CF ew construction cost factor per square foot; and Degradation rate expressed as a percent. Estimating te annual probability of financial distress is central to te analysis and is explained in te following section. Te procedure for estimating te oter parameters is discussed in Appendix B. Te parameter values for te case study are summarized in Exibit. Te cost factors and degradation rate values are listed in Exibit 2. JOSRE Vol. 3 o. 2 0

9 240 Beac Estimating te Probability of Financial Distress Assuming a constant probability of financial distress over time, te market price of te firm s bonds can be used to estimate te probability of financial distress,. Tat is, by adjusting te coupon and principal payments by te annual probability of financial distress, te bond price can be expressed in terms of certainty equivalent cas flows and discounted wit te risk-free interest rate. Given bond prices for te firm s outstanding debt, tis means te probability of financial distress can be estimated using te following equation: 3 t t ƒ ƒ t coupon ( ) facevalue ( ) Bond Price, (3) ( r ) ( r ) were represents te probability of financial distress and r ƒ is an appropriate risk-free interest rate. Using te firm s 0-year-to-maturity bonds, te above equation was solved for eac bond issue and a weigted average computed for te value of te probability of financial distress. Tis metod yields an estimated value for of 4.0%. Firm Value in te Finite Valuation Period Model Testing Condition One Using te values of,, and WACC estimated for te case study, Condition is tested. Critical values of are calculated for 5-, 0-, 5-, 20-, 25-, and 30-year valuation periods. Consistent wit Proposition 3, te longer te valuation period, te smaller te critical value required for an increase in sustainment funding to increase firm value. It is clear from Exibit 3 tat between years 20 and 25, te firm s probability of financial distress of 4% will exceed te critical value and firm value will increase as sustainment funding increases. Exibit 3 also displays te critical values wen te weigted average cost of capital is increased by 25% over te base case. Given Proposition 2, we would expect te critical value of to go up relative to te case study. Te last column displays te critical value wen te degradation rate is increased by 25% over te case study. Given Proposition, we would expect te critical value of to go down relative to te case study. Comparing Firm Value: istorical Funding and 00% Funding Using te model expressed in Equation 9, firm value is calculated for valuation periods of 5, 0, 5, 20, 25, and 30 years for te case were sustainment is funded at 5.7% (te firm s istorical rate) and 00%. Te percentage cange in firm value is calculated in te last column. Tese results are displayed in Exibit 4.

10 Facility Sustainment and Firm Value 24 Exibit 3 Comparison of te Critical Values of for Various Valuation Periods Valuation Period Critical (Base Case) Critical (WACC 9.55%) Critical ( 0.7%) 5 Years 6.3% 6.5% 6.0% 0 Years 8.9% 9.2% 8.5% 5 Years 5.9% 6.2% 5.4% 20 Years 4.2% 4.6% 3.8% 25 Years 3.2% 3.6% 2.8% 30 Years 2.5% 3.0% 2.% otes: Te table compares te critical values of for valuation periods of 5, 0, 5, 20, 25, and 30 years to te base case: probability of financial distress () 4.0%; weigted average cost of capital (WACC ) 7.64%; and degradation rate () 8.57%. Exibit 4 Firm Value based on te Case Study Parameters and Cost Factors wit a 4% Annual Probability of Financial Distress Valuation Period Critical (%) Firm Value at 5.7% Firm Value at 00% % Cange 5 Years 6.3% 7, , % 0 Years 8.9% 2, , % 5 Years 5.9% 5, , % 20 Years 4.2% 7, , % 25 Years 3.2% 8, , % 30 Years 2.5% 8, , % otes: Firm value based on te case study parameters and cost factors wit te annual probability of financial distress,, equal to 4.0%. Te results are for 5-, 0-, 5-, 20-, 25-, and 30-year valuation periods. Firm value is in millions of dollars. In Exibit 5, te parameters are te same as in te case study except te probability of financial distress is assumed to be 5% instead of 4%. Tis exibit illustrates tat for a iger probability of financial distress, it takes a sorter valuation period before an increase in sustainment funding will increase firm value. Monte Carlo Simulation As an alternative approac, a Monte Carlo simulation is developed to calculate te impact of a cange in sustainment funding on firm value. Te simulation is JOSRE Vol. 3 o. 2 0

11 242 Beac Exibit 5 Firm Value based on te Case Study Parameters and Cost Factors wit a 5% Annual Probability of Financial Distress Valuation Period Critical Firm Value at 5.7% Firm Value at 00% % Cange 5 Years 6.3% 8, , % 0 Years 8.9% 3, , % 5 Years 5.9% 6, , % 20 Years 4.2% 8, , % 25 Years 3.2% 9, , % 30 Years 2.5% 9, , % otes: Firm value based on te case study parameters and cost factors wit te annual probability of financial distress,, equal to 5.0%. Te results are for 5-, 0-, 5-, 20-, 25-, and 30-year valuation periods. Firm value is in millions of dollars. based on te probability of financial distress. Random numbers are generated based on tis probability and used to determine a given realization. Using te Monte Carlo simulation, realizations in wic te financial distress occurs in te first year can be considered wit realizations in wic financial distress occurs in a distant future year. Te average of firm value for all of te realizations can ten be used to estimate firm value. Using te parameters estimated above for te case study, te Monte Carlo simulation is run for te following: () sustainment funded at te firm s istorical rate of 5.7% of requirements; and (2) sustainment funded at 00% of requirements. Te Monte Carlo simulations yield te following results. At 5.7% sustainment, firm value is calculated as $4, million. At 00% sustainment, firm value is calculated as $4, million. Firm value increases by 0.78% if sustainment is funded at 00%, wic supports te ypotesis tat fully funding sustainment can increase firm value. Sensitivity Analysis To test te robustness of tis result, sensitivity analysis is performed by canging te values of te annual probability of financial distress, ; te firm s weigted average cost of capital, WACC; and te degradation rate,. Te results of te sensitivity analysis are displayed in Exibit 6. Canges in te parameters WACC,, and are calculated. Eac parameter is increased by 25% and ten decreased by 25%. Te sensitivity analysis indicates tat firm value goes up for an increase in or, and for a decrease in WACC. Firm value decreases for a decrease in or, and for an increase in WACC.

12 Facility Sustainment and Firm Value 243 Exibit 6 Monte Carlo Simulation Sensitivity Parameter Parameter Value Firm Value at 5.7% Firm Value at 00% % Cange 5.00% $4, $4, % 3.00% $4, $4, % 0.7% $4, $4, % 6.43% $4, $4, % WACC 9.55% $2, $2, % WACC 5.73% $6, $7, % otes: Sensitivity of te Monte Carlo simulation to canges in te probability of financial distress (), te degradation rate (), and weigted average cost of capital (WACC ). Increasing and, or decreasing WACC results in an increase in firm value. Decreasing and, or increasing WACC results in a decrease in firm value. Firm value is in millions of dollars. Tese results are consistent wit Propositions and 2 above. Recall tat Proposition states tat as te degradation rate increases, te critical value of decreases. Tis means for any given probability of financial distress, it is more likely tat an increase in sustainment funding will result in an increase in firm value. Proposition 2 says tat as te weigted average cost of capital increases, te critical value of increases. For any given probability of financial distress, it is less likely tat an increase in sustainment funding will result in an increase in firm value. Conclusion Tis paper represents te initial effort to relate te literature on sustainment funding and facility degradation to firm value. It argues tat te level of facility sustainment can be a significant factor in determining firm value for te major retailer considered in te case study. iger levels of sustainment funding reduce te list of maintenance and repair projects and maintain te value of te firm s facilities. Troug te degradation process and te effect of te degradation rate, funding at lower levels of sustainment increases te rate of deterioration and accelerates te decrease in te liquidation value of its assets. Te analysis supports te conclusion tat, at least for some firms, an increase in sustainment funding can result in an increase in firm value. In te finite valuation period model and te Monte Carlo simulation tis is sown to be te true for te major retailer in te case study. Based on te Monte Carlo simulation, gain in firm value from fully funding sustainment in te case study is modest at 0.78%. Tis is due primarily to te low probability of financial distress of 4%. owever, te Monte Carlo sensitivity analysis sows tat at a sligtly iger probability of JOSRE Vol. 3 o. 2 0

13 244 Beac financial distress of 5%, te gain is more substantial at 2.44%. For firms facing more serious financial problems, te probability of financial distress could be muc iger. Using te same metod represented by Equation 3, Damodaran (2006) estimated tat sortly before its bankruptcy proceedings, Global Crossing s probability of financial distress was 3.53%. Weter tese results old for anoter firm depends on te firm s weigted average cost of capital, te firm s annual probability of financial distress, and te degradation rates required for te firm s facilities. If oter major retailers ave te same capital structure as te firm in te case study, it is quite likely tat te results of tis paper also apply. Te increase in firm value ere is due to te increase in te liquidation value of te firm s retail stores. Te additional maintenance and repair expense of funding sustainment at 00% as been taken into account, but oter factors tat could ave a positive impact on free cas flow and te going-concern value of te firm ave not. For example, better maintained stores could ave a positive impact on employee morale and productivity, as well as customer satisfaction. Bot of tese factors would increase firm value even more wen sustainment is funded at 00%. It is interesting to consider tese results from te perspective of te firm s stakeolders. Te increase in firm value comes about from preserving te liquidation value of te firm s assets. Because of te additional maintenance and repair expenses incurred, te cost of tis is a reduction in te ongoing operations value of te firm since its free cas flow is reduced. For tis reason, CEOs and sareolders may find fully funding sustainment is undesirable. Indeed, Graam, arvey, and Rajgopal s (2005) survey found tat 78% of CEOs would sacrifice long-term value for sort-term earnings gains. owever, since it preserves te liquidation value of te firm s assets, debt olders could find fully funding sustainment to be in teir best interest. Since typically it is upper management and sareolders tat ave te final say as to te level of sustainment funding, tis suggests tat it is in te interest of te firm s debt olders to include covenants regarding te level of sustainment funding wen te corporation issues debt. Tese results occur despite te fact tat issues of pollution, ealt treats, and oter adverse externalities tat migt occur from underfunding facility sustainment ave not been taken into consideration. Witin te context of facility sustainment, tis paper illustrates a potentially fruitful approac to considering issues related to green facilities and sustainability. By looking beyond free cas flow, it is clear tat many firm decisions tat ave environmental or social consequences also impact te financial value of te firm. Wen tese effects can be quantified, a clearer financial picture emerges as to teir true benefits and costs. Appendix A Proofs of Propositions Proposition. For a valuation period,, te response of te critical value of to a cange in te degradation rate,, is negative. Tat is:

14 Facility Sustainment and Firm Value 245 c ( t c) ( WACC) ( j )( ) j2 j ( t c) ( WACC) ( ) j j c 2 ( t ) 0. ( WACC) ( WACC) (A) Proof From Equation 2: c ( t c) ( WACC) ( j )( ) j2 j ( t c) ( WACC) ( ) j j c 2 ( t ). (A2) ( WACC) ( WACC) First, note tat since tere are no negative terms in te denominator, it must be positive. By inspection, if, te numerator equals zero. For, bot of te numerator terms in brackets are positive, and, since tese are multiplied by, te numerator must be negative. Proposition 2. For a valuation period,, te response of te critical value of to a cange in te weigted average cost of capital, WACC, is positive. Tat is: JOSRE Vol. 3 o. 2 0

15 246 Beac c WACC ( ) j j ( t c) ( WACC) ( WACC) () ( t c) ( t ) c ( WACC) ( WACC) ( ) j j () () ( t c) () ( WACC) ( WACC) 2 ( ) j j ( t ) c 0. ( WACC) ( WACC) (A3) Proof From Equation 2, and simplifying: ( ) j j j c WACC ( WACC) ( WACC) ( ) j ( WACC) ( WACC) ( ) j j ( WACC) 2 ( t c). (A4) ( WACC) ( t ) c

16 Facility Sustainment and Firm Value 247 To simplify te notation let: j Z ( ). (A5) j Equation A5 as te property tat if k, ten Z k Z. First, note tat since tere are no negative terms in te denominator, it must be positive. Tus, if te numerator is positive, ten Proposition 2 must old. Tat is, if: Z ( WACC) ( WACC) Z ( WACC) ( WACC) 0. (A6) Te proof is by induction. Letting 2 in Equation A6, we get te following terms: 3 Z Z2 2Z ( WACC) ( WACC) ( WACC) 2Z 2 ( WACC) Z 2Z2 Z ( WACC) ( WACC) ( WACC) 4 4 2Z2 Z2 2Z 2Z2 Z. (A7) ( WACC) ( WACC) ( WACC) Since Z 2 Z ; Equation A6 must old for 2. Assume true for and prove tat te additional terms generated for are zero or positive. Expanding Equation A6 for te additional terms generated for : JOSRE Vol. 3 o. 2 0

17 248 Beac Z ( WACC) ( WACC) 2 ( WACC) ( WACC) Z ( WACC) ( WACC) ( )Z 2 ( WACC) ( WACC) () (). (A8) Te denominators for te terms in Equation A8 ave exponents from 3to 2 3. Tat is, ( WACC) j, (A9) were 3 j 3. umerators for te negative terms can be sown to be of te form: ( j 2)Z ( )Z j2. (A0) umerators for te positive terms can be sown to be of te form: ( j 2)Zj2 ( )Z. (A) Since for k, Z k Z, it can be sown tat for eac j: ( j 2)Z ( )Z ( j 2)Z ( )Z. (A2) j2 j2 Tis means tat for eac term te positive numerators are greater tan te negative numerators. Te exceptions is wen j 3, in wic case te positive numerator equals te negative numerator. ence, te inequality in Equation A6 olds and te proposition is true. Proposition 3. As te valuation period,, becomes longer, te critical value of decreases. Tat is:

18 Facility Sustainment and Firm Value 249 c c ( ) j j ( t ) ( WACC) ( t c) ( WACC) ( WACC) ( t c) ( WACC) ( ) j j ( t c) 0. ( WACC) ( WACC) (A3) Proof It is assumed tat is a discrete variable. It is sown tat te critical value of for is less tan te critical value for. From Equation 2: c c ( WACC) Z ( t ) c ( t ) ( WACC) ( WACC) ( t c) ( WACC) Z ( t c). (A4) ( WACC) ( WACC) To simplify notation, let D represent te divisor of te first term in brackets and let D represent te divisor of te second term in brackets. Also, as above, let: j Z ( ), (A5) j JOSRE Vol. 3 o. 2 0

19 250 Beac and note tat Z Z. Given tis notation and finding a common denominator, te following expression is derived. c c ( t ) ( WACC) Z ( t c) ( WACC) ( WACC) ( t c) ( WACC) Z ( t c) ( WACC) ( WACC) {DD }. (A6) Tis simplifies to: Z c c Z c ( WACC) ( WACC) ( t ) ( t ) ( WACC) ( WACC) {D D }. (A7) Tis can also be expressed as: Z ( t ) c ( WACC) ( WACC) Z Z c ( t c) ( t c) ( WACC) ( WACC) {D D }. ( WACC) ( WACC) (A8) Tis furter simplifies to:

20 Facility Sustainment and Firm Value 25 c c Z c ( WACC) ( WACC) ( t ) Z ( t ) ( WACC) ( WACC) {D D } 0. (A9) Since Z is greater tan any Z, Proposition 3 must old. Appendix B Parameter Estimates Total Square Footage: Te total square footage of te firm s retail stores is based on te total square footage reported in te 2007 annual report. In 2007, total square footage (in tousands of square feet) was 207,945. Sustainment Requirement: Te sustainment requirement represents te amount tat sould be funded, based on industry standards, to maintain facilities in good working condition. It is te product of total square footage and te sustainment cost factor. Tat is: S 207,495 SF $3.25/SF $ million, t (B) were SF is in tousands of square feet. Sustainment Funding: Sustainment funding is based on te firm s expenditures for maintenance and repair of property, plant, and equipment. Tis type of information is not necessarily reported in a firm s annual report. owever, for te firm in te case study, maintenance and repair expenditures were reported for Since 85% of property, plant, and equipment is retail stores, 85% of te maintenance and repair expenditure was applied to te retail stores. Te average istorical funding percentage was calculated based on te sustainment requirements for eac of tese years. Te calculated istorical funding is 5.7%. Free Cas Flow: Free cas flow is estimated using te following equation: FCF ebit ( t ) dep (capex nwc), c (B2) were ebit is earnings before interest and taxes, t c is te corporate tax rate, capex is te yearly capital expenditures, dep is te current year depreciation, and nwc is te yearly cange in net working capital. JOSRE Vol. 3 o. 2 0

21 252 Beac Free cas flow was computed by averaging te above variables from te annual returns for Tis was calculated as: FCF $4560 ( ) $,59 ($3,702 $509) $,62, (B3) were all dollar amounts are in millions. Weigted Average Cost of Capital (WACC): WACC is based on te weigted average of te cost of debt and te cost of equity. For te cost of debt, R D,te average yield to maturity of te firm s 0-year bonds is used. Tis is calculated as R D 5.55%. For te cost of equity, R E, te CAPM model is used. Using te interest for te 0-year Treasury bond, r ƒ 4.02%; beta 0.70 (as reported on te Internet for 2007); E(R M ).69% (based on te S&P 500 returns for ). Tis is calculated as R E 9.39%. Debt and equity weigts are in millions of dollars. Debt is based on te firm s 2007 annual report and equity is based on te 2007 market capitalization. WACC is calculated as: $7,090 WACC (5.55%)(.378) $58,027 $40,937 (9.39%) 7.64%, (B4) $58,027 were all dollar amounts are in millions. Endnotes I abstract from oter costs of financial distress to focus on te impact of sustainment funding. Te assumption ere is tese costs are te same for any given level of sustainment funding. 2 Te argument against fire sales is along two lines: () tey mostly occur wen an industry or te overall economy is experiencing a downturn, or (2) wen te assets are specialized and industry specific. Acarya, Barat, and Srinivasan (2007) support te first argument and find no correlation in te second. 3 Damodaran (2006). References Acarya, V.V., S.T. Barat, and A. Srinivasan. Does Industry-Wide Distress Affect Defaulted Firms? Evidence from Creditor Recoveries. Journal of Financial Economics, 2007, 85:3,

22 Facility Sustainment and Firm Value 253 Beac, R. Computing Degradation Rates. Working Paper, R&K Solutions, Roanoke, VA, Beac, R., J. Carson, and K. Keating. Cost Predictions of Facilities: Discussion Paper. Journal of Management in Engineering, 998, 4, Carlson, S. As Campuses Crumble, Budgets are Crunced. Te Cronicle of iger Education, 2008, 37:5, A, A2 A4. Coi, J., J.M. Jondrow, D.G. Taylor, and T.D. Weis. Maintenance of Real Property: an Annotated Bibliograpy. Alexandria, VA: Center for aval Analysis, 994. Damodaran, A. Damodaran on Valuation: Security Analysis for Investment and Corporate Finance. oboken, J: Jon Wiley and Sons, Graam, J.R., C.R. arvey, and S. Rajgopal. Te Economic Implications of Corporate Financial Reporting. Journal of Accounting and Economics, 2005, 40: 3, Lyall, S. In BP s Record, a istory of Boldness and Costly Blunders. Te ew York Times, 7/ 2/ 200. Available at: ttp:// en.wikipedia.org/ wiki/ Texas City Refinery (BP). February 0, 20. eely Jr., E.S. and R. eatammer. Life-cycle Maintenance Cost by Facility Use. Journal of Construction Engineering and Management, 99, 7:2, eely Jr., S. Edgar, R.D. eatammer, and J.R. Stirn. Maintenance Resource Prediction in te Facility Life-Cycle Process. U.S. Army Corps of Engineers Civil Engineering Researc Laboratory Tecnical Report P-9/ 0. Available at: ttp:// cgi-bin/ GetTRDoc?ADADA236424&LocationU2&docGetTRDoc.pdf. 99. Ottoman, G.R., W.B. ixon, and S.T. Lofgren. Budgeting for Facility Maintenance and Repair I: Metods and Models. Journal of Management in Engineering, 999a, 5:4, Budgeting for Facility Maintenance and Repair II: Metods and Models. Journal of Management in Engineering, 999b, 5:4, United States Green Building Council. LEED for Existing Buildings: Operations and Maintenance. Available at: ttps:// Accessed February 0, Te autor expresses gratitude to Ricard Gregory, William Trainor, and te faculty of te Economics and Finance Department at East Tennessee State University, Jonson City, Tennessee, for seminar discussions tat gave sape and direction to tis researc. Robert Beac, East Tennessee State University, Jonson City, T 3764 or beacr@etsu.edu. JOSRE Vol. 3 o. 2 0