205 Depreciaion and Corporae Taxes Chris Hendrickson Carnegie Mellon Universiy Tung Au Carnegie Mellon Universiy 205.1 Depreciaion as Tax Deducion 205.2 Tax Laws and Tax Planning 205.3 Decision Crieria for Projec Selecion 205.4 Inflaion Consideraion 205.5 Afer-Tax Cash Flows 205.6 Evaluaion of Afer-Tax Cash Flows 205.7 Effecs of Various Facors The governmen levies axes on corporaions and individuals o mee is cos of operaions. Regulaions on depreciaion allowances are par of axaion policy. The ax laws promulgaed by he federal governmen profoundly influence capial invesmens underaken by privae corporaions. Economic valuaion of he afer-ax cash flows of an invesmen projec based on projeced ax raes and inflaion effecs provides a raional basis for acceping or rejecing invesmen projecs. 205.1 Depreciaion as Tax Deducion Depreciaion refers o he decline in value of physical asses over heir esimaed useful lives. In he conex of ax liabiliy, depreciaion allowance refers o he amoun allowed as a deducion in compuing axable income, and depreciable life refers o he esimaed useful life over which depreciaion allowances are compued. The depreciaion allowance is a sysemaic allocaion of he cos of a physical asse over ime. A fully depreciaed asse has received depreciaion allowances equal o is original purchase price. The mehods of compuing depreciaion and he esimaed useful lives for various classes of physical asses are specified by governmen regulaions as a par of he ax code, which is subjec o periodic revisions. Differen mehods of compuing depreciaion lead o differen annual depreciaion allowances and hence have differen effecs on axable income and he axes paid. Le P be he purchase cos of an asse, S is esimaed salvage value, and N he depreciable life in years. Le D denoe he depreciable allowance in year, and T denoe he accumulaed depreciaion up o and including year. Then for = 1, 2,, N, T = D + D + + D 1 2 L (205.1) An asse s book value B is simply is hisorical cos less any accumulaed depreciaion. Then B = P -T (205.2)
205-2 The Engineering Handbook, Second Ediion or TABLE 205.1 Modified Acceleraed Cos Reducion Sysem (MACRS) Depreciaion for Personal Propery Recovery Year 3-Year Period 5-Year Period 7-Year Period 10-Year Period 1 33.33 20.00 14.29 10.00 2 44.45 32.00 24.49 18.00 3 14.81 19.20 17.49 14.40 4 7.41 11.52 12.49 11.52 5 11.52 8.93 9.22 6 5.76 8.92 7.37 7 8.93 6.55 8 4.46 6.55 9 6.56 10 6.55 11 3.28 Source: Inernal Revenue Service. 2002. Insrucions for Form 4562 Depreciaion and Amorizaion. U.S. Deparmen of he Treasury, Washingon, DC. B = B -D -1 (205.3) Among he depreciaion mehods accepable under he ax regulaions, he sraigh-line mehod is he simples. Using his mehod, he uniform annual allowance in each year is D = ( P -S)/ N (205.4) Oher accepable mehods, known as acceleraed depreciaion mehods, yield higher depreciaion allowances in he earlier years of an asse and less in he laer years han hose obained by he sraigh-line mehod. Examples of such mehods are sum-of-he-years -digis depreciaion and double-decliningbalance depreciaion [Au and Au, 1992]. For example, he double-declining-balance depreciaion allowance in any year is: D P = 2 1-2/ N N ( ) - 1 (205.5) Under he curren IRS regulaions on depreciaion, known as he Modified Acceleraed Cos Reducion Sysem (MACRS), he esimaed useful life of an asse is deermined by is characerisics ha fi one of he eigh specified caegories. Furhermore, he salvage value S for all caegories is assumed o be zero and all asses wih a life of 10 years or less are assumed o be purchased and sold a mid-year. The MACRS schedules are generally double-declining balance swiching o sraigh-line depreciaion or sraigh-line depreciaion alone for he longer propery life periods. The MACRS depreciaion schedules for 3-, 5-, 7- and 10- year recovery periods are shown in Table 205.1, where each enry in he able is he allowable percenage of he purchase cos depreciaion allowance in ha year. Table 205.2 shows some example asses for he 3- o 10-year recovery schedules. Noe ha he MACRS schedule can be changed a any ime, so accessing up-o-dae informaion for compuing allowable depreciaion amouns is advisable. 205.2 Tax Laws and Tax Planning Capial projecs are long-lived physical asses for which he promulgaion and revisions of ax laws may affec ax liabiliy. For he purpose of planning and evaluaing capial projecs, i is imporan o under-
Depreciaion and Corporae Taxes 205-3 TABLE 205.2 Recovery Period and Examples of Propery Class for MACRS Depreciaion Recovery Period Examples of Depreciable Asses 3 years Qualified ren-o-own propery, race horse 5 years Auomobiles, office equipmen 7 years Office furniure, railroad rack 10 years Vessels, barges, and ugs, frui- or nu-bearing rees or vines Source: Inernal Revenue Service. 2002. Insrucions for Form 4562 Depreciaion and Amorizaion. U.S. Deparmen of he Treasury, Washingon, DC. sand he underlying principles, including adjusmens for he ransiion period afer each revision and for muliyear carry-back or carry-forward of profis and losses. The federal income ax is imporan o business operaions because profis are axed annually a subsanial raes on a graduaed basis. Excep for small businesses, he corporae axes on ordinary income may be esimaed wih sufficien accuracy by using he marginal ax rae. Capial gain, which represens he difference beween he sale price and he book value of an asse, is axed a a rae lower han on ordinary income for privae individuals if i is held longer han a period specified by ax laws. For corporaions in 2003, capial gains are axed a he same rae as oher axable income. Some sae and/or local governmens also levy income axes on corporaions. Generally, such axes are deducible for federal income ax o avoid double axaion. The compuaion of income axes can be simplified by using a combined marginal ax rae o cover he federal, sae, and local income axes. If F is he federal marginal rae on axable income, R is he sae marginal ax rae and X is he combined rae, hen: X = F + R - F R (205.6) Tax planning is an imporan elemen of privae capial invesmen analysis because he economic feasibiliy of a projec is affeced by he axaion of corporae profis. In making esimaes of ax liabiliy, several facors deserve aenion: (1) number of years for reaining he asse, (2) depreciaion mehod used, (3) mehod of financing, including purchase versus lease, (4) capial gain upon he sale of he asse, and (5) effecs of inflaion. Appropriae assumpions should be made o reflec hese facors realisically. 205.3 Decision Crieria for Projec Selecion The economic evaluaion of an invesmen projec is based on he meri of he ne presen value (NPV), which is he algebraic sum of he discouned ne cash flows over he life of he projec o he presen. The discoun rae is he minimum aracive rae of reurn specified by he corporaion. The evaluaion of proposed invesmen projecs is based on NPV crieria, which specify he following: (1) an independen projec should be acceped if he NPV is posiive and rejeced oherwise; and (2) among all accepable projecs ha are muually exclusive, he one wih he highes posiive NPV should be seleced. 205.4 Inflaion Consideraion Consideraion of he effecs of inflaion on economic evaluaion of a capial projec is necessary because axes are based on hen-curren dollars in fuure years. The year in which he useful life of a projec begins is usually used as he baseline of price measuremen and is referred o as he base year. A price index is he raio of he price of a predefined package of goods and service a a given year o he price of he same package in he base year. The common price indices used o measure inflaion include he
205-4 The Engineering Handbook, Second Ediion consumer price index, published by he Deparmen of Labor, and he gross domesic produc price deflaor, compiled by he Deparmen of Commerce. For he purpose of economic evaluaion, i is generally sufficien o projec he fuure inflaion rend by using an average annual inflaion rae j. Le A be he cash flow in year, expressed in erms of baseyear (year 0) dollars, and be he cash flow in year, expressed in erms of hen-curren dollars. Then A A = A ( 1 + j) A = A ( 1 + j) - (205.7) (205.8) In he economic evaluaion of invesmen proposals in an inflaionary environmen, wo approaches may be used o offse he effecs of inflaion. Each approach leads o he same resul if he discoun rae i, excluding inflaion, and he rae i, including inflaion, are relaed as follows: i = ( 1+ i)( 1+ j) - 1 = i + j + ij i = ( i - j)/( 1 + j) (205.9) (205.10) The NPV of an invesmen projec over a planning horizon of n years can be obained by using he consan price approach as follows: n NPV = Â A ( 1 + i ) - = 0 (205.11) Similarly, he NPV obained by using he hen-curren price approach is n NPV = Â A ( 1 + i ) - = 0 (205.12) In some siuaions he prices of cerain key iems affecing he esimaes of fuure incomes and/or coss are expeced o escalae faser han he general inflaion. For such cases he differenial inflaion for hose iems can be included in he esimaion of he cash flows for he projec. 205.5 Afer-Tax Cash Flows The economic performance of a corporaion over ime is measured by he ne cash flows afer ax. Consequenly, afer-ax cash flows are needed for economic evaluaion of an invesmen projec. Since ineres on debs is ax deducible according o he federal ax laws, he mehod of financing an invesmen projec could affec ne profis. Alhough he projeced ne cash flows over he years mus be based on hen-curren dollars for compuing axes, he depreciaion allowances over hose years are no indexed for inflaion under he curren ax laws. I is possible o separae he cash flows of a projec ino an operaing componen and a financing componen for he purpose of evaluaion. Such separaion will provide beer insigh o he ax advanage of borrowing o finance a projec, and he combined effec of he wo is consisen wih he compuaion based on a single combined ne cash flow. The following noaions are inroduced o denoe various iems in year over a planning horizon of n years: A = ne cash flow of operaion (excluding financing cos) before ax A = ne cash flow of financing before ax
Depreciaion and Corporae Taxes 205-5 A = A + A = combined ne cash flow before ax Y = ne cash flow of operaion (excluding financing cos) afer ax Y = ne cash flow of financing afer ax Y = Y + Y = combined ne cash flow afer ax D = annual depreciaion allowance I = annual ineres on he unpaid balance of a loan Q = annual paymen o reduce he unpaid balance of a loan W = annual axable income X = annual marginal income ax rae K = annual income ax Thus, for operaion in year = 0, 1, 2,, n, W K = A - = X W D Y = A -X ( A -D ) (205.13) (205.14) (205.15) For financing in year = 0, 1, 2,, n, I = Q - A Y = A + X I (205.16) (205.17) where he erm X I is referred o as he ax shield because i represens a gain from deb financing due o he deducibiliy of ineres in compuing he income ax. Alernaely, he combined ne cash flows afer ax may be obained direcly by noing ha boh depreciaion allowance and ineres are ax deducible. Then, Y W = -D -I A = A -X ( -D -I ) A (205.18) (205.19) I can be verified ha Equaion (205.19) can also be obained by adding Equaions (205.15) and (205.17), while noing A = A + A and Y = Y + Y. When an asse is sold, capial gains axes mus be paid on he difference beween he sale price and he book value (as calculaed by Equaions (205.1) and (205.2)). If he sale price is less han he book value, a capial loss is incurred. Capial losses can be used o offse capial gains. 205.6 Evaluaion of Afer-Tax Cash Flows For privae corporaions, he decision o inves in a capial projec may have side effecs on he financial decisions of he firm, such as aking ou loans or issuing new sock. These financial decisions will influence he overall equiy-deb mix of he enire corporaion, depending on he size of he projec and he risk involved. Tradiionally, many firms have used an adjused cos of capial, which reflecs he opporuniy cos of capial and he financing side effecs, including ax shields. Thus, only he ne cash from operaion Y obained by Equaion (205.15) is used when he NPV is compued. The afer-ax ne cash flows of a proposed projec are discouned by subsiuing Y for A in Equaion (205.11), using afer-ax adjused
205-6 The Engineering Handbook, Second Ediion cos of capial of he corporaion as he discoun rae. If inflaion is anicipaed, Y can firs be obained in hen-curren dollars and hen subsiued ino Equaion (205.12). The selecion of he projec will be based on he NPV hus obained wihou furher consideraion of ax shields, even if deb financing is involved. This approach, which is based on he adjused cos of capial for discouning, is adequae for small projecs such as equipmen purchase. In recen years anoher approach, which separaes he invesmen and financial decisions of a firm, is someimes used for evaluaion of large capial projecs. In his approach, he ne cash flows of operaion are discouned a a risk-adjused rae reflecing he risk for he class of asses represening he proposed projec, whereas ax shields and oher financial side effecs are discouned a a risk-free rae corresponding o he yield of governmen bonds. An adjused NPV reflecing he combined effecs of boh decisions is hen used as he basis for projec selecion. Deailed discussion of his approach may be found elsewhere [Brealey and Myers, 2000]. 205.7 Effecs of Various Facors Various depreciaion mehods will produce differen effecs on he afer-ax cash flows of an invesmen. Since he acceleraed depreciaion mehods generae larger depreciaion allowances during he early years, he NPV of he afer-ax cash flows using one of he acceleraed depreciaion mehods is expeced o be more favorable han ha obained by using he sraigh-line mehod. If a firm lacks he necessary funds o acquire a physical asse ha is deemed desirable for operaion, i can lease he asse by enering ino a conrac wih anoher pary, which will legally obligae he firm o make paymens for a well-defined period of ime. The paymens for leasing are expenses ha can be deduced in full from he gross revenue in compuing axable income. The purchase-or-lease opions can be compared afer heir respecive NPVs are compued. When an asse is held for more han a required holding period under ax laws, he capial gain is regarded as long-erm capial gain. In a period of inflaion he sale price of an asse in hen-curren dollars increases, bu he book value is no allowed o be indexed o reflec he inflaion. Consequenly, capial gain ax increases wih he surge in sale price resuling from inflaion. Example 205.1 Suppose a ligh, general-purpose ruck is purchased for $25,000 in February. This ruck is expeced o generae a before-ax uniform annual revenue of $7,000 over he nex 6 years, wih no salvage value a he end of 6 years. According o he curren IRS regulaions, his ruck is assigned o a 5- year propery class wih no salvage value afer he depreciaion period. The MACRS schedule in Table 205.1 is used o compue he annual depreciaion allowance. The combined federal and sae income ax rae is 38%. Assuming no inflaion, he afer-ax discoun rae of 8%, based on he adjused cos of capial of he corporaion, is used. Deermine wheher his invesmen proposal should be acceped. Soluion. Using he 5-year recovery period schedule in Table (205.1), he annual depreciaion allowance D is found o be $25,000 muliplied by he allowable percenage depreciaion allowance in each year. We assume ha he ax loss in year 2 may be offse by income elsewhere, so he loss resuls in a ax shield of $380. Tax amouns are rounded o he neares dollar. Period T Capial Invesmen Before-Tax Cash Flow, A Depreciaion Allowance D Taxable Cash Flow A - D Taxes K Afer-Tax Cash Flow Y 0-25,000-25,000 1 7,000 5,000 2,000 760 6,240 2 7,000 8,000-1,000-380 7,380 3 7,000 4,800 2,200 836 6,164 4 7,000 2,880 4,120 1,566 5,434
Depreciaion and Corporae Taxes 205-7 Period T Capial Invesmen Before-Tax Cash Flow, A Depreciaion Allowance D Taxable Cash Flow A - D Taxes K Afer-Tax Cash Flow Y 5 7,000 2,880 4,120 1,566 5,434 6 7,000 1,440 5,560 2,113 4,887 Using he adjused cos of capial approach, he NPV of he afer-ax ne cash flows discouned a 8% is obained by subsiuing Y for A in Equaion (205.11), NPV =- 25 000 + ( 6240)( P F, 8%, 1) + ( 7380)( P F, 8%, 2) + ( 6194)( P F, 8%, 3) + (5434)(P F, 8%, 4) + (5434)(P F, 8%, 5) + (4887)(P F, 8%, 6) = 2794 in which (P F, 8%, ) = 1/(1.08) is he presen worh facor of a fuure amoun discouned a an 8% rae for years. Since NPV = $2,794 is posiive, he proposed invesmen should be acceped. Example 205.2 Consider a proposal for he purchase of a compuer worksaion ha coss $20,000 and has no salvage value a disposal afer 4 years. This invesmen is expeced o generae a before-ax uniform annual revenue of $7,000 in base-year dollars over he nex 4 years. An average annual inflaion rae of 5% is assumed. The MACRS 5-year propery depreciaion schedule is used o compue he annual depreciaion allowance. The combined federal and sae income ax rae is 38%. Based on he adjused cos of capial of he corporaion, he afer-ax discoun rae, including inflaion, is 10%. Deermine wheher his invesmen proposal should be acceped. Soluion. Depreciaion in each year is calculaed by muliplying he 5-year depreciaion percenage in each year by $20,000. This annual depreciaion allowance will no be indexed for inflaion, according o he IRS regulaions. A he end of he 4 years, he compuer has a book value of $3,456 (as calculaed from Equaion 205.1 and 205.2). When he compuer is disposed of wih no salvage value, his amoun would represen a capial loss ha could be used o offse capial gains accumulaed elsewhere in he business. Taxes in year 4 would hen be $3,509 muliplied by he combined marginal ax rae (0.38) less he capial-gain ax shield of $3,456 muliplied by he combined marginal ax rae (0.38). The annual before-ax revenue of $,7000 in base-year dollars mus be expressed in hen-curren dollars before compuing he income axes. From Equaion (205.7), A = ( 7000)( 1 + 0. 05) where = 1 o 4 refers o each of he nex 4 years. The afer-ax cash flow Y for each year can be compued by Equaion (205.15). The sep-by-sep abulaion of he compuaion for each year is shown in he following able. Period T Capial Invesmen Before Tax Cash Flow (Base Year $) A Before Tax Cash Flow (Curren Year $) A Depreciaion D Taxable Income D Capial Loss Taxes K Afer Tax Cash Flow Y 0-20,000-20,000 1 7,000 7,350 4,000 3,350 1,273 6,077 2 7,000 7,718 6,400 1,318 501 7,217 3 7,000 8,013 3,840 4,123 1,586 6,427 4 7,000 8,509 2,304 6,205 3,456 1,045 7,464 A
205-8 The Engineering Handbook, Second Ediion Using he adjused cos of capial approach, he NPV of he afer-ax cash flows discouned a i = 10%, including inflaion, can be obained by subsiuing he value of Y for A in Equaion (205.10) as follows: Since NPV = $1416 is posiive, he invesmen proposal should be acceped. Example 205.3 A developer bough a plo of land for $100,000 and spen $1.6 million o consruc an aparmen building on he sie for a oal price of $1.7 million. The before-ax annual renal income afer he deducion of mainenance expenses is expeced o be $300,000 in he nex 6 years, assuming no inflaion. The developer plans o sell his building a he end of 6 years when he propery is expeced o appreciae o $2.1 million, including land. Suppose he enire cos of consrucion can be depreciaed over 32 years based on he sraigh-line depreciaion mehod, whereas he original cos of land may be reaed as he salvage value a he end. The ax raes are 34% for ordinary income and 28% for capial gain, respecively. Based on he adjused cos of capial, he developer specifies an afer-ax discoun rae of 10%. Soluion. Using Equaion (205.4), he annual depreciaion allowance D over 32 years is found o be $50,000. Noing ha P = 1 700,000 and T = (6) (50 000) = 300,000, he book value of he propery afer 6 years is found from Equaion (205.2) o be $1.4 million. Ignoring he assumpion of mid-year purchase o simplify he calculaion and assuming no inflaion, he afer-ax annual ne income in he nex 6 years is given by Equaion (205.13): The capial gain ax for he propery a he end of 6 years is Using he adjused cos of capial approach, he NPV of afer-ax ne cash flows in he nex 6 years, including he capial gain ax paid a he end of 6 years discouned a 10%, is in which (PΩU, 10%, 6) is he discoun facor o presen a 10% for a uniform series over 6 years, and (PΩF, 10%, 6) is he discoun facor o presen a 10% for a fuure sum a he end of 6 years. Since NPV = $311, 1 98 is posiive, he proposed invesmen should be acceped. Defining Terms NPV =- 20 000 + ( 6077)( 1. 1) + ( 7217)( 1. 1) + ( 6427)( 1. 1) + ( 7464)( 1. 1) = 1416-1 -2-3 -4 Y = 300 000 -( 34%)( 300 000-50 000) = 215 000 ( 28%)( 2 100 000-1 400 000) = 196 000 NPV =- 1 700 000 + ( 215 000)( P U, 10%, 6) + ( 2 100 000-196 000)( P F, 10%, 6) = 311 198 Base year The year used as he baseline of price measuremen of an invesmen projec. Capial gain Difference beween he sale price and he book value of an asse. Depreciable life Esimaed useful life over which depreciaion allowances are compued. Depreciaion Decline in value of physical asses over heir esimaed useful lives.
Depreciaion and Corporae Taxes 205-9 Depreciaion allowance Amoun of depreciaion allowed in a sysemaic allocaion of he cos of a physical asse beween he ime i is acquired and he ime i is disposed of. Ne presen value Algebraic sum of he discouned cash flows over he life of an invesmen projec o he presen. Price index Raio of he price of a predefined package of goods and service a a given year o he price of he same package in he base year. Tax shield Gain from deb financing due o deducibiliy of ineres in compuing he income ax. References Au, T. and Au, T. P. 1992. Engineering Economics for Capial Invesmen Analysis, 2nd ed. Prenice Hall, Englewood Cliffs, NJ. Brealey, R. and Myers, S. 2000. Principles of Corporae Finance, 6h ed. McGraw-Hill, New York. Inernal Revenue Service. 2002. Insrucions for Form 4562 Depreciaion and Amorizaion. U.S. Deparmen of he Treasury, Washingon, DC. Park, Chan S. 2002. Conemporary Engineering Economics, 3rd ed. Prenice Hall, New York. Furher Informaion Up-o-dae informaion on he ax code may be found a websies for individual sae axaion deparmens and he following websies: U.S. Inernal Revenue Service, www.irs.gov Federaion of Tax Adminisraors, www.axaadmin.org