Valuing Businesses:A Teaching Note1I. IntroductionOrganizations andindividuals spendenormous amounts of time andenergyvaluingbusinesses.Investorscreate independentestimatesofa companysworththen comparetheirvaluationwiththemarket price; if themarket priceisbelowtheestimatedvaluetheybuy,believing that the business is undervalued. Underwriters, or those assisting with theunderwriting process, seek to offer securities at a fair price.Investment bankers advise clients onacuisitions, mergers, or divestitures based on their calculations of fair value as compared withthe proposedprice. !ankers assess a business e"pected future cashflows and potentialcollateral value in setting the terms of a loan. #inancial advisors offer fair$value opinions foremployee stock ownership plans and for both ta" and private estate$planning purposes.%his teaching note outlines three fundamental approaches to valuing a business& the 'ost(ethod, )iscounted 'ash #low *)'#+, and ,rice-'haracteristic .atios. /ppraisers sometimesrefer to these as the 'ost, Income, and (arket 'omparison methods, respectively.0mphasis isgiven to discounted cash flow and ratio valuation approaches. II. Cost Method%he cost method to valuation reuires two steps.In the first step, the appraiser estimatesthe cost to replicate or reproduce the assets of a company. In the second step, the appraiserad1usts for intangibles.%he cost approach is typically applied to the total assets of the firm andthus produces a valuation number for the combined debt and euity holders.%he valuation of thefirms euity can then be estimated by subtracting the market value of the debt. )epending onthe nature of the assets and the purpose for the valuation, the following four common variationsof the cost method can be used in step one& !ook, /d1usted /sset, 2iuidation, and .eplacement.%he first step in valuation for these four cost approaches are summarized in %able 3&Table 1 Cost ApproachesBook Adjusted Liuidation !eplace"ent3 !y ,rofessors 4al 4eaton, 5rant (c6ueen, and 7teven %horley from !righam 8oung Universitys (arriott 7choolof (anagement.%he note is based on an earlier note of the same name by 4al 4eaton.Asset#tep 1Co"pan$%alue euals&the 9book: value of assets on the balance sheet *historical cost less depreciation+%he estimated market value of the assets on the balance sheetthe value of the assets if bankruptcy were to occur *bankruptcy causes asset market value decreases+the cost of buildinganother company with the same productive capacity using newer technologyApproachshould be usedi'&book values are close to market values *i.e., recently purchased or formed company+book values are significantly different than market values andmarket values are ascertainablethe purpose is to assess collateral value given that the value of the assets could be affected by bankruptcynewer technology or processes make the older prices non$applicable for the current industry%he !ook approach is simple and easy to use.;hat is the company worth billion, but, due to technological advancement, the same capacity could bebuilt todayfornewer, moreadvancedchipswiththesamecapabilityforB?.Ebillion. %hereproduction cost of B?.E billion would be used to estimate the value of the old plant even thoughthe original cost to build the old plant was higher.%he four cost method approaches to valuation outlined above do not include the value ofacompanysintangibleassets. 'onseuently, 7tepDistoaddorsubtract thevalueof theintangibles. (ost companies have some intangible value that stems frombrand$namerecognition, relationships withclients andcustomers, reputation, e"perienceandknowledge,along with a variety of other values that are not captured in accounting numbers.#or e"ample,the value of 'oke 'ola 'o. has little to do with its land, buildings, and euipment; rather, valueis derived from its world$wide brand recognition.7ome companies with pending legal problemsor unfavorable long$term contracts could have negative intangibles./lthough a complete reviewof thevaluationof intangibles is outsidethe scopeof this teachingnote, onee"ample isinstructive. /n appraiser could estimate the value of a companys brand identity by estimatingthe cost of advertising reuired to build similar brand identity./lso, if the company was recentlysold, the accounting or book value may include intangibles in a goodwill account./lthough thevaluation of intangibles is sub1ective at best, it is a necessarypart of all cost valuationapproaches. 5iven the difficulties and sub1ectivity in valuing numerous tangible and intangible assets,financial professionals and investors should be reluctant to rely solely on the cost method forvaluation.III. (iscounted Cash )lo* ApproachA;arren !uffet, the famous multibillionaire investor, described the discounted cash flowprocesssuccinctlywhenhearticulatedhisinvestment strategy, 98ou1ust want toestimateacompanys cashflows over time, discount thembackandbuyfor less thanthat.:Inthe)iscounted 'ash #low *)'#+ approach, the appraiser estimates the cash flows after all operatinge"penses, ta"es, and necessary investments in working capital and property, plant and euipment.;hat is left is often call the free cash flow meaning the cash available to secure financing frombanks, bondholders, euityinvestors, orothers. %heword9free:indicatescashflowsafterneeded investments to maintain future cash flows and is sometimes dropped. %he forecastedcash flows are discounted at the cost of capital,which reflects the investors reuired rate ofreturn based on the riskiness of the particular business.%he )'# approach not only facilitates in$depth understanding about the company andindustry, but also provides criticalinformation for decision makers about the likely return oninvestment.7pecifically, the price is compared with the present value of future cash inflows todecide if an investment adds value to a company by meeting some minimum reuired rate ofreturn. Iftheinvestment doesnot providethereuiredrateofreturn, thenthesuppliersoffinancingarebetter off allocatingthefunds toother investments. %hus, the)'#approachestimates value as the highest price a willing buyer could pay and still be able to compensate theinvestors for their reuired return on capital.(athematically, the )'# value is&...,+ 3 +* 3 +* 3 *F G+ 3 +* 3 *F G3F GA D 3A ?D 3D ?33 ??++ + +++ +++=r r rFCF Er rFCF ErFCF EVwhere V0 is the value today *time ?+, E0 denotes e"pectations at time ?, FCFt is the free cash flowat time t, and r1, r2, H are the discount rates of the first, second, and so on to all future periods.DOften analysts assume that the discount rate does not change over time so thatr1I r2I r3HUnder this simplifying assumption, the )'# value isD/ppendi" ' is a glossary of valuation terms. JVF C Frttt?33=+=* +,*3+wherethee"pectationsoperatorhasbeendroppedtoavoidnotational clutter. /lthoughthisnotational simplification is used in the remainder of the teaching note, remember that the #'#sare nonetheless only uncertain estimates and therefore risky.%he )'# approach can be used to value the total company *debt and euity+ or to value1ust the euity.%his teaching note illustrates both valuation perspectives.4owever, an appraisermust be careful to maintain consistency between the cash flows *numerator+ and discount rate*denominator+.%hat is, free cash flows available to pay off all contributors of capital should bediscounted at a rate that reflects the average reuired rate of return of those contributors *i.e., a;eighted /verage 'ost of 'apital, ;/'', rate+./lternatively, free cash flows after interest andnet borrowing available to euity investors *#'#e+ should be discounted at the rate reuired bystock holders.7imilarly, consistency must be maintained from a ta" and an inflation perspective.#or e"ample, after$ta" cash flows should be discounted at the after$ta" discount rate and nominalcash flows should be discounted at nominal discount rates.III. A. Total )ir" +,uit$ and (ebt- Valuation%hefollowingbo"provides fivegeneralizedsteps for estimatingfreecashflowforcombined euity and debt investors.#teps 'or 'inding )C) to Value Total Assets$.evenues *3+'osts7tep 3& 0stimate future revenues and operating e"penses *including depreciation+ to find 0arnings !efore Interest and %a"es *0!I%+ for each year.I$0!I%%a"es *D+7tep D& 2ess ta"es *calculated as a percent of 0!I%+ to find Ket Operating ,rofit /fter %a" *KO,/%+ for each year.IL$$LKO,/%Kon$cash costs *A+'apital e"pendituresIncrease in K;'%erminal value7tep A& /dd back non$cash costs *e.g. depreciation+ subtracted in step 3.%hen subtract capital e"penditures and increases in net working capital *K;'+ needed to attain revenue growth forecasts.#or the last year, add the terminal value to the operating cash flow.>I #'#7tep J& )iscount the #'# for each year at the after$ta" cost of capital.7tep >& Use the firms capital structure to calculate the portion of the value that pertains to debt and euity investors./lthough in practice several alternative ways to calculate the free cash flow numbers, they tendto end up with the same result.#or e"ample, instead of adding depreciation and then subtractinggrosscapital e"penditures, onecancombinebothitemsandsubtract netcapital e"penditures*e.g., subtract theincreaseinnetpropertyplant andeuipment onabalancesheet+. Otherappraisers prefer to start with 0!I%)/ instead of 0!I%. 0!I%)/ is 0arnings !efore Interest,%a"es, and )epreciation and /mortization.In this mathematically euivalent approach, the non$cash costs are never subtracted from revenues so they do not have to be added back in.4owever,inthisvariationonfreecashflowcalculation, onedoeshavetoaddintheta"shieldfromdepreciation, calculated as the depreciation costs times the marginal ta" rate.A%he estimated ta"es in the total firm value approach are more than the actual ta"es thatwill be paid since interest payments are not subtracted before calculating ta"es, i.e., the total firmapproach values the assets and ignores financing in terms of calculating the cash flows. %he ta"benefit of ta"$deductible interest payments is accounted for in the calculation of the weightedaverage cost of capital *;/''+&W A C C k t xDAkEAd e= + * + M M 3 , *D+where kd is the reuired rate of return for lenders *i.e., 8%( on similar long term bonds+, ke is thereuired rate of return of stock holders *i.e., output from the 'apital /sset ,ricing (odel+, tx isthe marginal ta" rate, and D/A and E/A represent the firms target proportion of )ebt and 0uityin the firms capital structure. .emember thatD/Aand E/Aare the 9weights: in the weightedaverage cost of capital calculation and must sum to one.A 2etting DEP represent all non$cash costs *i.e., depreciation and amortization+, the euivalence proof is&EBIT*3$tx+ L DEP I *EBITDA N DEP+ *3$tx+ L DEP I EBITDA *3$tx+ L tx DEP.O/ sample;/''calculationcouldbeasfollows& aclient contactsfinancingsourcesabout acuiring a business.%hese sources indicate that because the client company has a capitalstructure of J?P debt *D/A I ?.J+, and is in a fairly safe business, they are willing to accept kd ICP interest on long term loans.,rivate euity investors reuire ke I 3OP return to attract themintotheventure.%hecompanyisinthetxIJ?Pta"bracket. 5iventhisinformation, theaverage cost of funds for this business is CP " *3 $ J?P+ " J?P L 3OP " O?P I 33.>DP. /;/'' of 33.>DP is used for the ne"t e"ample.0"ample 3& 2imited$2ife #irm @aluation/ssumean analyst isvaluinga businesswith one asset,anolder oilwell. .evenuesstarting at BDD million are e"pected to decline as the resources are depleted.7uppose that the oilreserves are sufficient to last five full years./s indicated above, the company is financed withJ?P debt costing CP per year and O?P euity on which investors demand a 3OP return *33.>DPcost of capital+./fter five years, the oil well euipment will be sold./ reasonable estimate forthe salvage value in five years, based on prices in the used euipment market, is BQ million.%able D shows the e"pected free cash flows available to both debt and euity holders for afive$year horizon *all numbers in thousands of dollars+ under some additional assumptions aboute"penses and depreciation.7teps Table . /ear 1 /ear . /ear 0 /ear 1 /ear 2*3+ !e%enues DD,??? D?,OC? 3Q,JAQ 3C,DAE 3E,3EO3 4perating ,5p 3A,AJD 3D,>QC 33,QAA 33,A?E 3?,CDD3 (epreciation J,?>? J,?>? J,?>? J,?>? J,?>?,BIT J,O?C J,?AD A,J>O D,CC? D,A?J*D+ 3 Ta5es 6 178 3,CJA 3,O3A 3,ACD 3,3>D QDDN49AT D,EO> D,J3Q D,?EJ 3,EDC 3,ACD*A+ : (epreciation J,?>? J,?>? J,?>? J,?>? J,?>?3 Cap ,5p 3,A?? 3,A?? 3,A?? 3,A?? 3,A??3 ; N?+ *D>?+ *D>?+ *D>?+ *D>?+4perating Cash )lo* >,EO> >,J3Q >,?EJ J,EDC J,ACDTer"inal Value Q,???)ree Cash )lo* >,EO> >,J3Q >,?EJ J,EDC 3A,ACD7ince revenues are declining, the net working capital *i.e., accounts receivable and inventory lessaccounts payable+ needs arealsodecliningcausingnegativechangeinK;'numbers andEconseuentlycashinflows*i.e., subtractinganegativenumber+. Inflowsfromnet workingcapital are unusual since most business grow over time and growing businesses typically need toadd to inventories and accounts receivable.JIn step J, the free cash flows are discounted and summed to find asset value as follows&V? 3 D A J >E O >3 3 3 > DJ 3 Q3 3 3 > D? E J3 3 3 > DE D C3 3 3 > DA C D3 3 3 > D= + + + +B > ,* . +B > ,* . +B > ,* . +B J ,* . +B 3 A ,* . + I BDJ,???.7tep > involves subtracting the BQ,O?? value of the debt *J?P debt financing+ from the total firmvalue of BDJ,??? for an euity value of B3J,J??.III. B. ,uit$ +4nl$- ValuationOften the value of the stock or euity position in a company is desired rather than theentire firm.@aluing euity using the free cash flow to stockholders is very similar to using thetotal asset valuation discussed above.4owever, there is one critical difference; whereas the priorvaluationreuiredestimatingthecashflowavailabletobothdebtandeuityholders, euityvaluation reuires estimating only free cash flow to euity holders, after debt holders have beenpaidoff. %hefollowingbo"providesgeneralizedstepsforusingdiscountedcashflowstoestimate the value of the euity position of a company.7tep 3 is the same as before but the othersteps for euity valuation differ from the total asset valuation; specifically, interest and principlepayments are deducted./n e"ample is provided following the generalized steps.#teps 'or )inding )C) to Value ,uit$I$0!I% *3+Interest *D+7tep 3&0stimate 0!I%7tep D& 2ess interest payments *calculated as a percent of long term debt+.I$,rofit before ta"%a"es *A+7tep A& 2ess ta".J In the e"ample, the convenient and common simplifying assumption of annual cash flows is made.Obviously, notall revenues are collected and e"penses paid on )ecember A3st of each year..ather, cash flows occur throughout theyear. %he simplifying assumption of annual cash flows typically biases )'# values down because of the 9overdiscounting.: 7witching to uarterly or monthly numbers would reduce the size of the bias. /lternatively, someappraisers use the half$year convention and assume that all cash flows come in the middle of the year *i.e., discountthe first cash flow ?.> years, the second cash flow 3.> years, etc.+CIL$$LR,rofit after ta"Kon$cash costs *J+'apital e"pendituresIncrease in K;'%erminal @alue2oan payments *>+7tep J& /dd back non$cash costs subtracted in step 3.7ubtract capital e"penditures and increases in net working capital./dd the terminal value accruing to euity holders in the final year.7tep >& /dd changes to loan principal *paymentsare negative and new loans are positive+. I #ree 'ash #lowe7tep O& )iscount the #'#e for each year at the after$ta" cost of euity./lternative approaches to valuing euity e"ist in practice and these alternatives produceeuivalent results./n obvious alternative is to discount dividends since #'# to euity holders isvery similar to dividends paid.In fact, given that interest is subtracted and ad1ustments are madefor changes in debt as well as changes in various asset accounts, a uicker way to get the freecash flow to euity numbers may be to simply use forecasted dividends as shown later.0"ample D& 2imited$2ife 0uity @aluation.emember that the company has BQ,O?? of debt at CP which will be assumed by the newbuyer. 7uppose that the debt is scheduled to be paid off over C years at a rate of B3,D?? ofprinciple at the end of each year.%able A illustrates how to find #'#e.7teps Table 0 /ear 1 /ear . /ear 0 /ear 1 /ear 2,BIT J,O?C J,?AD A,J>O D,CC? D,A?J*D+ Interest EOC OED >EO JC? ACJ9ro'it be'ore ta5 A,CJ? A,AO? D,CC? D,J?? 3,QD?*A+ Ta5es 3,>AO 3,AJJ 3,3>D QO? EOCNet Inco"e D,A?J D,?3O 3,EDC 3,JJ? 3,3>D*J+ : (epreciation J,?>? J,?>? J,?>? J,?>? J,?>?3 Cap ,5p 3,A?? 3,A?? 3,A?? 3,A?? 3,A??3 ; N?+ *D>?+ *D>?+ *D>?+ *D>?+*>+ 3 (ebt !epa$"ent 3,D?? 3,D?? 3,D?? 3,D?? 3,D??Cash )lo* J,3?J A,C3O A,>DC A,DJ? D,Q>DTer"inal Value >,J??)C)eJ,3?J A,C3O A,>DC A,DJ? C,A>DIn %able A, ta"es are calculated after interest then subtracted to find Ket Income ratherthan KO,/%./lso note that the interest decreases as debt is paid down./gain, a terminal valueis added to the operating cash flow to get #'#e.%he assets will be salvaged for BQ,??? but, afterpaying the BA,O?? still owed to creditors, B>,J?? is left for euity holders.In step O, the free cashflows are discounted at the cost of euity to find the value of euity, V?e, as follows&QVe?3 D A J >3 ? J3 3 OC 3 O3 3 O> D C3 3 OD J ?3 3 OA > D3 3 O= + + + +B J ,* . +B A ,* . +B A ,* . +B A ,* . +B C ,* . + I B3J,J??.%he euity valuation, 0"ample D, produced the same value of B3J,J?? as the total firmvaluation, 0"ample 3.%his euality is e"pected since both versions the )'# approach made thesame assumptions.In practice, keeping assumptions e"act across the two free cash flow versionsis difficult.In 0"ample D, for simplicity, the e"act mi" of O?-J? euity and debt was maintainedeach year.7uch simplicity is rare in real valuations, and an appraiser must account for varyinglevels of debt.>0"ample A& 5rowing 'ompany 0uity @aluationInstead of a depleting oil well, consider a retailing company where revenues are e"pectedto grow. In 0"ample A, shown in %able J, the companys sales again start at BDD,??? but areforecast to grow at QP for five years and then grow at OP forever./s before, the company has acapital structure of J?P debt and O?P euity, the cost of debt is CP, and the cost of euity is3OP.5iven the companys continuing growth and the unlimited life of corporations, 0uation*3+ obligates an analyst to calculate an infinite number of #'#es.In practice, analysts choose afinite horizon, five years in 0"ample A, and use a terminal value to account for the remainingcash flows.In theory, year$by$year forecasting should be done at least through any unusual *i.e.,growth, merger, etc.+ periods.7teps Table 1 /ear 1 /ear . /ear 0 /ear 1 /ear 2*3+ !e%enues DD,??? DA,QC? DO,3AC DC,JQ3 A3,?>>3 4perating ,5p 3>,JED 3O,COJ 3C,ACD D?,?AE D3,CJ?3 (epreciation 3,QD? D,?QA D,DC3 D,JCO D,E3?,BIT J,O?C >,?DA >,JE> >,QOC O,>?>*D+ 3 Interest EOC CAE Q3D QQ> 3,?CJ9reta5 9ro'it A,CJ? J,3CO J,>OA J,QEA >,JD3*A+ 3 Ta5es 6 178 3,>AO 3,OEJ 3,CD> 3,QCQ D,3OC> /nother way to view the similarity between the total firm and euity valuation methods is to notice that, ultimately,both methods account for the cost of debt.In the total asset method, the cost of debt is included in the discount rate. %he ;/'' includes the CP *less the ta" deduction+ debt holders e"pect on the J?P of the firm they financed.%he euity method accounts for the cost of debt in the cash flows by e"plicitly deducting interest *which lowers ta"es+ and the debt repayment in the cash flows.%hus, the cost of debt is the same in both methods; the euity method accounts for dollar costs of debt in the numerator of 0uation *3+ and the total firm method accounts for the percentage cost of debt in the denominator of 0uation *3+.3?9ro'it a'ter ta5 D,A?J D,>3D D,EAC D,QCJ A,D>A*J+ : (epreciation 3,QD? D,?QA D,DC3 D,JCO D,E3?3 Cap ,5p A,COJ J,D3D J,>Q3 >,??J J,>J?3 ; N D>E DC? D?A*>+ : Ne* (ebt +needed to "aintain debt=euit$ ratio-COJ QJD 3,?DE 3,33Q C3ACash )lo* 3,??C 3,3?? 3,3QC 3,A?> D,?AATer"inal Value D3,>>?)ree Cash )lo*e3,??C 3,3?? 3,3QC 3,A?> DA,>CAKotethat depreciationandcapital e"penditures aregrowingsinceadditional assetsmust bepurchased each year to support the higher sales.%he fifth increase in capital e"penditures dropsto BJ,>J? since fewer year$end additions are needed when sales growth drops from QP down toOP.%he terminal value of the euity needs to be estimated but is often a hard number to pindown. Unlike the limited$life e"ample, the business is growing and the assets will not be soldoff.'onseuently, theterminal value must beestimatedusingagrowingperpetuity formula*sometimesreferredtoasthe5ordon5rowthformula+. %hefollowingestimateofterminalvalue implicitly assumes that the fifth year #'#e will grow at OP forever.. >>? , D3 B?O . 3O .+ ?O . 3 * ?AA , D BO>===g kFCFVeee7tep O reuires that the appraiser discount the cash flows at ke& Ve?3 D A J >? ? C3 3 O3 ? ?3 3 O3 Q C3 3 OA ? >3 3 O> C A3 3 O= + + + +B 3 ,* . +B 3 ,* . +B 3 ,* . +B 3 ,* . +B D A ,* . + I B3J,J??.0"amples D and A were designed to illustrate a key concept of valuation.!oth 0"ample D*depleting oil well+ and 0"ample A *growing retailer+,the euity of the company is valued atB3J,J??. 7houldnt the euity of a growing company with the same capital structure be worthmore than the euity of the declining company< %he answer to this uestion stems from thefundamental notion of creating shareholder value& value is only created if the company can earnmore than its cost of capital.!oth companies only earned their cost of capital in the future, sothe growth of the second company added no incremental value. %hat is, the incremental profits in33later years 1ust compensated investors for the incremental capital e"penditures./ company maygrow rapidly, butifitdoes not earn more than its costof capital, todaysshare priceshouldremain unaffected.%o create value for euity investors, a firm has to have a return on its pro1ectsthat e"ceeds thereuiredreturns of itsinvestors; that ise"ceeds thecost of capital. %hismotivatesacomparisonofthefirmsaccountingreturnoneuity*.O0+andcost ofeuitycapital *ke+ although the standard caveats on accounting numbers apply.%he phrase 9economicvalue added: or 0@/, used by some consulting firms and appraisers, refers to the fundamentalidea that .O0 must be greater than ke to increase shareholder value./ppendi" ! discusses 0@/and the .esidual Income approach to valuation that is based on the principles of 0@/. III. C. Valuation o' ,uit$: (iscounted (i%idends/nalternative waytovaluetheeuityof acompanyis todiscount theforecasteddividends.%his approach is similar to discounting free cash flow to euity holders and is morecommonly used for stable publicly traded companies that pay large dividends. Using the after$ta"profits from0"ample Awithanestimatedpayout ratio*basedonhistorical precedent,company policy, and forecasted growth+, the future cash flows to euity holders *dividends+ canbe forecasted.0"ample J& )iscounted )ividend 0uity @aluationIn0"ampleJ, theQPandtheOPsalesgrowthassumptionsaremaintained. )uringyears of faster growth, moremoneyis neededfor capital e"penditures; alternativelyhigherpayout ratios are e"pectedduringyears of slower growth. %able>shows the companysforecasts with a J?P payout ratio during the first four years and a OJP payout ratio in the fifthyear as capital e"penditures decrease in line with slower growth.Table 2 /ear 1 /ear . /ear 0 /ear 1 /ear 29ro'it a'ter Ta5 D,A?J D,>3D D,EAC D,QCJ A,D>A9a$out !atio ?.J ?.J ?.J ?.J ?.OJ(i%idend QDD 3,??> 3,?Q> 3,3QJ D,?CDTer"inal Value DD,?OCTotal Cash Value QDD 3,??> 3,?Q> 3,3QJ DJ,3>?%he forecasted terminal value is the present value *in the fifth year+ of the e"pected futuredividends.%he terminal value can be thought of as a liuidating dividend or as the value *price+3Dof the euity after five years. %he calculation of the terminal value, using the 5ordon 5rowthmodel is as follows&OC? , DD B?O . 3O .OJ . M ?O . 3 M D>A , AO>===g kDVeewhere the si"th dividend is based on a OP growth in Ket Income and a OJP payout ratio.%o obtain the euity value today, one discounts the cash flows in %able > at the cost ofeuity&Ve?3 D A J >3 3 O? ? >3 3 O? Q >3 3 O3 Q J3 3 O3 > ?3 3 O= + + + +B Q D D* . +B 3 ,* . +B 3 ,* . +B 3 ,* . +B D J ,* . + I B3J,J??./gain, since the same assumptions were used in the )ividend version, the calculation results inthe same value as the %otal #irm and 0uity versions of the )'# approach.%he )iscounted )ividend model can provide misleading information if certainassumptions are not met.7pecifically, if the free cash flows e"ceed the dividend and the value issimplistically determined by discounting the dividend without accounting for the e"tra cash, theeuity will be undervalued. %hat is, if the e"cess free cash flows are invested in securities *shortterm, interest bearinginstruments+theriskinessofthefirmwill decrease*sincemoreoftheassets are low risk securities+ so the appraiser should discount the dividends at a lower rate toreflect the lower risk. %he lower discount rate will result in a higher value than the unad1ustedvalue./lternatively, if free cash flows are less than dividends, then this approach might result inan overvaluation error.If dividends e"ceed free cash flow, then the appraiser must decide wherethe additional funds necessary to make the capital e"penditures come from.If the difference willbefinancedwithdebt, thecashflowstoeuityholdersaremoreleveraged. %heincreasedleverage would likely 1ustify a higher discount rate on the dividends. %he higher discount ratewould then result in a lower value.!oth of these problems can be avoided if the appraiser ensures that the dividend payoutrate e"actly corresponds with the growth assumption. / company which pays out most of itsearnings in dividends cannot grow as rapidly as one that retains more of its earnings./ companythat ismaintainingitsdebt-euityratioanddoesnotseeke"ternal euityfinancingcanonly3Agrow at the sustainable growth rate which is eual to .eturn on !eginning 0uity " *3 $ ,ayout.atio+.III. (. #pecial Considerations in (iscounted Cash )lo*In a merger or acuisition situation, the appropriate value is determined by the way theacuirer will operate the business./ common problem occurs when a privately held company isacuired and the e"penses change dramatically. #or e"ample, family owned businesses have ata" incentive to pay unusually large salaries rather than take cash out of the company in the formof dividends.!y paying large salaries and reporting small profits, the family only pays one layerof ta"es rather than paying ta"es at the business level and again when the dividends are reportedas income. %ocorrectlyvalue the business, the appraiser must reconstruct the forecastedfinancial statements to reflect the salaries that the market would generally pay managers ratherthan the above$market salaries paid to family./nother valuation difference rising in a merger or acuisition stems from synergies.%hemost freuentlycitedreasonfor mergers andacuisitions are synergies suchas increasedrevenues through 1oint$product development and sales, reduced cost through economies of scale,increased growth through greater negotiating power with distribution channels, and a variety ofother revenue$enhancing or cost$reducing opportunities.%o determine the ma"imum possibleprice that could be paid without harming the acuirers share price, sometimes referred to as thewalkaway price, the increased cash flows associated with the synergies should be included in theforecast.IV.9rice=Characteristic !atio Method%he third commonly used valuation approach involves the use of ratios from comparablecompanies or 9comps: with known stock prices. #or e"ample, many investors use ,-0 ratioswhenvaluingstocks. /pproaches tovaluationbasedoncomps aregenericallycalledthe,rice-'haracteristic .atio method.7imilar to the )'# approach, ,rice-'haracteristic .atios canbeused tovalueeitherthe entirefirm *stock plus debt+ or 1ust the euityofthefirm.O %he,rice-'haracteristic .atio method, at first glance, appears to be straightforward since theappraiser does not need to make an e"plicit forecast of cash flows. 4owever, this method isO /ppendi" / discusses in more detail what is meant by valuing the 9total firm.:3Jfraught with hidden difficulties which can result in significant misestimates of value. #or thesereasons, many appraisers will generally start with a )'# approach to valuation and then use avariety of ratios to check whether the )'# approach is producing valuations similar to othercompanies. %he key to the ,rice-'haracteristic .atio method is to first find a set of companies, thecomps, that areverysimilar orcomparabletothebusinessbeingvalued, andhavepubliclytradedstockprices.%heideaofcomparabilityisdiscussedinmoredetail later.Ingeneral,comparable companies should compete in similar markets, have similar capital structures, andhavesimilar total market values. Inthefollowinge"ample, anappraiser is tryingtovalueprivately held 'ompany # and has identified five 'ompanies / to 0, that are both publicly tradedand in the same industry as #.%he appraiser can compute a variety of price-characteristic ratiosfrom the public companies and then apply that ratio to the private company to obtain a value.IV. A. Co"paring 9rice=Characteristic !atios5enerically, some value related number is divided by some characteristic of the companyto compute a price-characteristic ratio. Kormally the appraiser will choose a characteristic thatprovides information about the relative financial health of a company within its industry. Onee"ample that relates to the value of the entire firm *not 1ust the euity+ uses 9enterprise value:*i.e., the value of both the debt and euity+ divided by 0arnings !efore Interest, %a",)epreciation, and /mortization*0!I%)/+. #ore"ample, supposethat the'ompany / had0!I%)/ of BCC,E3? and a market value of B>>?,??? *stock price times the number of sharesoutstanding, plus the market value of debt+.#or simplicity, assume the firm has no debt so theenterprise value of the firmis the price of the euity. %hen'ompany/wouldhave a@alue-0!I%)/, ratio of O.D.7uppose that the other firms in the industry had @alue-0!I%)/ratios as follows&Co"pan$ 9rice=,BIT(A/ O.D! E.>' >.E) C.?0 >.?3>%heappraiserwouldcomparecompanies / through0tothesub1ectcompany,#,andmake ad1ustments for any differences using his-her own 1udgment. %hus, choosing the correctvalue of a ratio is as much an art form as a science since an e"act publicly$traded replica of thetarget companyisnever available. %heappraiser might say, fore"ample, that eventhough'ompanies ! and ) are in the same industry, their earnings are e"pected to grow more rapidlythan # because they are in faster growing regions of the country or have newer products. %hefaster growth would raise the price of their shares compared to current earnings *since currentearnings do not reflect the future potential+ and thus raise the @alue-0!I%)/ ratio compared tothe sub1ect company. %he appraiser might decide that since company 0 is facing litigation, itsstockpriceislow.%hesub1ect company, #,whichisnot facingsuchlitigation, wouldbee"pected to trade at a higher @alue-0!I%)/ ratio./fter e"cluding firms !, ), and 0, becausethey are not truly comparable, the average of the remaining two companies, / and ', is *O.D L>.E+-D I >.Q>./fter calculating this average, suppose the appraiser feels comfortable with a@alue-0!I%)/ ratio of O.? for 'ompany #.Kote that the value is not an e"act average of / and'; rather the appraiser made yet another sub1ective ad1ustment.#or e"ample, the appraiser maybelieve that #s growth opportunities are closer to /s than to 's. Snowing this, the appraisercouldlookat thesub1ect companysfinancial recordstofindits0!I%)/. #orthesakeofdiscussion, assume the 0!I%)/ of the sub1ect company, #, is B3D million.%he appraiser couldthen estimate #s value as B3D million " O I BED million.IV. B. !atio Valuation Considerations/ variety of ratios are commonly used in the ,rice-'haracteristic .atio method, each witha different set of considerations. / fundamental principle in valuation is that assets are worth thepresent value of their future benefits. #or investors, those benefits are usually cash flows andtherefore an asset should sell for the present value of its future cash flows./n appraiser thinkingof using a price-characteristic ratio to value a business must answer the uestion& Under whatcircumstances will the assets of the comparable and sub1ect firms sell for the same multiplenit Value ,arnings 9=, !atio4perating (i%ision B3?? million B3? million 3?#tart up 4perations BD? million *BD million+ n.a.Co"bined 4perations B3D? million BC million 3>7ince divisions do not have separately traded stock prices, the only ratio that is observable forthis company is the combined ,-0 ratio of 3>. If an appraiser were to use the observable ,-0ratio to value the operating division, the value would be estimated as,-0 " 0arnings I 3> " B3? million I B3>? million.3E%his B3>? million is a >?P overvaluation to the actual value of B3?? million./ppraisers mustbe careful to ad1ust for the distortions caused by other subsidiaries when computing the ratios ofthe comparables.Often these conditions will affect all of the comparable companies in e"actlythe same direction since the comparable companies may have similar subsidiaries.#or e"ample,consider theregional telephonecompanies; all haveresidential phoneservicedivisionsandcellular telephone operations.7ince the cellular operations have much greater growth potential,they will raise the observed ,-0s of all of the regional telephone companies.%o use the observed,-0s to value the residential phone service divisions would result in significant overvaluations.Second, since the characteristic used for valuation comes from the accounting system ofthe sub1ect and comparable companies, the accounting systems employed need to be similar.#ore"ample, supposethefollowingtwobusinesses hade"actlythesame operations; however,'ompany /ggressive had a different approach to accounting than 'ompany ,assive./ggressive ,assive7ales B3,??? BQ??'ost of goods sold >?? O??7elling and admin. e"penses 3?? 3??Operating profit J?? D??0"traordinary gain 3?? T,rofit before ta" >?? D??%a"es *J?P+ D?? C?Ket income A?? 3D?0"traordinary gain T O?Ket income after e"traordinary BA?? B3C?%he aggressive company recognizes revenue from installment sales immediately *gain onsale accounting+.#or e"ample, in the 3QQ?s Uero" intentionally attributed most of the price of a1oint sale of copiers with service contracts to the copier since recognition of revenue from theservice contract would be delayed. %he aggressive company capitalized, rather than e"pensed,money spent refurbishing, upgrading, and refitting euipment, delaying their recognition. #ore"ample, inthelate3QQ?s, ;orldcomcapitalizedmoneyspent oncommunicationhardwareupgrades so that the e"pense would not show up on the current years income statement,butratherbespreadoutasdepreciationoverfutureyears.%heaggressivecompanyincludedthenonrecurringgainfromsellingausedwarehouse. %hepoint is, althoughbothcompaniese"periencedthesamethings, theaggressivecompanyreports Ket Incomeof BA??andthe3Cpassive only recognizes B3D?.;hen it comes to net income, 9some dollars are more eual thanothers.: /nalysts sometimes use the phrase 9earnings uality: to indicate how aggressive theaccounting was *uestionable practices lead to low uality earnings+.Third, comparability in size, management philosophy, competitive position, geographicallocation, regulators *if any+, industry environment, customer base, age of assets, marketing andoperational strategies, and a host of other variables may also be necessary. #or e"ample, twosteel manufactures with e"actly the same 0!I%)/ may have very different values.One in Ohiocould have a strong union, declining sales, pending 0,/ litigation, and old euipment.%he othercould be a newly built plant on the coast of !razil with increasing sales.Forth, the financial structure of the firms should also be highly comparable as measuredby a variety of financial ratios such as debt-euity, current, uick, inventory turns, sales-assets,payout, return on sales, return on euity, return on assets, as well as working capital ratios *e.g.working capital-assets, days in receivables, payables period, etc.+.#or e"ample, a company withidentical assets but a different debt levelthan the sub1ect firm should receive a different ,-0multiple.%he levered firm will have higher interest, less total net income but fewer shares andhigher 0,7. 4owever, the levered firm will also have more volatile earnings *higher risk+ andconseuently may receive a lower multiple than the comparable firm with similar assets.Fi!th, consideration should be given to the e"pected growth and risk associated with thecomparable firms. #irms with different levels of growth or risk will have differentprice-characteristic ratios.#or e"ample, %arget, 'ostco, #amily )ollar, and ;al$mart stores areall retail stores and competitors.%he two graphs below plot the firms forward ,-0 ratios againstforecasted sales growth and historical beta *risk+ estimations as of /ugust D??A.3QP/E and Sales GrowthA BCD19202122232425262728298.50% 9.50% 10.50% 11.50%12.50% 13.50% 14.50%5 yr Sales GrowthForward P/EP/E and RiskABDC19202122232425262728290.75 0.85 0.95 1.05 1.15 1.25BetaForward P/E2egend& / I %arget ! I 'ostco ' I #amily )ollar 7tores ) I ;al$martKotice that higher levels of growth correspond with higher ,-0 ratios, whereas higherlevelsofrisk*!eta+correspondwithlower,-0ratios. %hedependencyongrowthandriskmakes sense..egarding growth, the value of one dollar of ;al$marts D??J earnings should bemore than the value of one dollar of %argets D??J earnings since the stockholder has a claim onall future earnings, not 1ust the ne"t years..egarding risk, the value of one of ;al$marts futureearnings shouldbeworthmorethanoneof %argetsearnings because%argetsearningsarediscounted more due to the higher risk.%he point is, when valuing a retail outlet, the appraisershould ask, 9is the sub1ects growth and risk more like ;al$mart or %arget?-,O,.7uch price-operating characteristic ratios are particularly useful in cross bordertransactions in which there may be no comparables within the same country for comparison./nappraiser can compute these ratios for companies throughout the world where prices are knownand then ad1ust for local economic circumstances.V. Conclusion@aluing a company is one of the more difficult problems in finance. @aluation reuiresnot onlyathoroughunderstandingofeconomicandfinancial principles, butalsoathoroughunderstandingof the company, its accountingconventions, the industry, andthe economicenvironment at the time of the appraisal./lthoughthecost approachmayprovideareasonableestimatefor acompanyinacompetitive environment under normal economic circumstances, the value of any company willdepend on its future.#orecasting the future is reuired by both the )'# and price-characteristicratio approaches.In the )'# approach, the appraiser must e"plicitly forecast the cash flows ofthe sub1ect company. In the price-characteristic ratio approach,the appraiser must ad1ust theobserved ratios of comparable companies for differences in the future e"pected cash flows of thesub1ect company and the companies chosen as comparables.DOAppendi5 A:Net ,??? 'ommon 7tock J>,???Net )i5ed Assets A0D2C777 .etained 0arningsE?,???Total Assets A2E7C777 Total Liab. and ,uit$ A2E7C777/ssuming that all of the cash is needed for ongoing operations *i.e., does not include e"tra cashor marketable securities+, then the net workingcapital of this company*inthousands+ isB3C>,??? $ BQ?,??? $ B3>,??? I BC?,???, not B3C>,??? $ BAJ>,??? I $ B3O?,???.%he bank loanis considered part of the capital.%he market value of the debt would be the market value of the BDJ?,??? face$value loanplus the market value of the long term debt with face value of B3??,???.Often, the debt is nottraded and it is not possible to determine market value directly.If the payment terms of the debtinstrumentsareknown, theappraiserwill discount thecashflowsoftheloansat prevailingmarket rates *which depend upon the risk of the debt+ to obtain the market value of the debtDEinstruments.Often, the terms of the debt are not known and appraisers will estimate the marketvalue as book value.#or the U8W 'ompany, suppose that market interest rates have risen slightly since theissuance of the debt and that the debt is now selling at BAA?,???, a B3?,??? discount from itsbook value of BAJ?,???./lso suppose that the U8W 'ompany has 3? thousand shares trading atBDD each./s if often the case, the market euity value of the firm, BDD " 3? thousand shares IBDD?,???, is much greater worth than the book value *common stock plus retained earnings, orB33>,???.+5iven both the debt and euity, the total market value of the company is BAA?,??? LBDD?,??? I B>>?,???. 7o, if an appraiser was using the U8W 'ompany as a comp to find thetotal firm value *debt plus euity+ of a privately held firm, the appraiser would use B>>?,??? inthe numerator of any ,rice- 'haracteristic .atio.DCAppendi5 B:!esidual Inco"e Valuation MethodIn his book, #est !or V$%e, !ennett 7tewart popularized a performance evaluation tool he called 0conomic @alue /dded *0@/+.0@/ measures whether a manager or pro1ect contributes *earnings+ more than it consumes *cost of capital employed+.In terms of the whole firm, 0@/ for period t is&0@/t I *.O/t N ;/''+ M /t$3 ,where .O/t is the .eturn on /ssets *KI-/+ in period t and /t$3 are total /ssets at the end of the prior period..ather than 1ust rewarding profits *.O/t M /t$3+, 0@/ makes managers accountablefor profits relative to the capital they use *;/''t M /t$3+.Kotice that managers can add value *holding the other two factors constant+ by generating higher returns on assets, reducing the cost of capital, or reducing the amount of capital.%he euity version of 0@/ is&0@/t I *.O0t N ke+ M 0t$3 ,where .O0t is .eturn on 0uity *KI-0+ in period t and 0 t$3 is the book value of Owners 0uity at the end of the prior period.,rofessors 0dgar 0dwards, ,hilip !ell, and =ames Ohlson are credited with using the principles behind 0@/ as a forward looking valuation model, not 1ust a backward looking performance measurement tool.%heir valuation model is known as the 0!O approach, after their last names, or the .esidual Income approach.One way to derive the .esidual Income approach is to start with the )iscounted )ividend model&,+ 3 *3=+=ttet eokDV*!3+where the e"pectations operator is not shown to reduce notational clutter.Using a series of the 9clean surplus: accounting relationships, 0t I 0t$3 L KIt $ )t, which states that Owners 0uity DQgrows through retained earnings, and other technical assumptionsQ, one can rewrite euation *!3+as&

( ).+ 3 *,+ 3 *3?33?==++ =++ =ttetttet e t eokEVAEkE k &"EE V*!D+0uation *!D+ points out that a firms value comes from both its e"isting invested capital plus the present value of all the e"pected added value *residual earnings+.0uation *!3+ euates value to the distri'tion of wealth, whereas *!D+ euates value to the cre$tion of wealth, and reminds analysts that the source of stock price increases is not simply a larger dividend or a faster growing dividend; rather, price increases come about by investing in pro1ects with positive net present values.%he .esidual Income approach is not only related to the )'# approach, but also to the ,rice-'omparables approach as well.#or e"ample, the following euation shows that the forward ,-0 ratio depends on a firms ability to add economic value in the future&,33 33?Te ek&"Ek EPSP++= *!A+where P? is the price of stock, Ve?, and T is the number of years that the firm is e"pected to add 9economic value: by having .O0 greater than ke.%hus, a firm can receive a high ,rice-'haracteristic ratio by first, investing in pro1ects that return much more than their cost of capital, and second, earning the economic rents for a long time./lthough this teaching note focuses the three most popular valuation methods& 'ost, )iscounted 'ash #low, and ,rice-'omparables, the .esidual Income can be considered a fourth method that, although relatively unknown, seems to be growing in popularity.#urthermore, the .esidual Income method is related to both the )'# method and the ,rice-'haracteristics methodand highlights the principle that value is created by investing in pro1ects that contribute more than they consume.Q #eltham and Ohlson *9@aluation and 'lean 7urplus /ccounting for Operating and #inancial /ctivities, Conte()or$r* Acconting &ese$rch, 7pring, 3QQ>+ show the relationship between the 0!O valuation model *!D+ and the dividend model *!3+.2ee *9(easuring ;ealth,: CA +$g$,ine- 3QQO+ shows the relationship between 0!O and 0@/.%he original work by 0dwards and !ell can be found in 9The Theor* $nd +e$sre(ent o! Bsiness Inco(e,: *University of 'alifornia ,ress, !erkeley+. A? Appendi5 C:Flossar$ Cost o' CapitalN %he reuired rate of return to satisfy investors given the companyslevel of risk.If the company or pro1ect cannot earn the cost of capital then investors arebetter off investing money elsewhere with similar risk. Cost o' ,uit$$ .euired return rates for euity holders. (C) N *)iscounted 'ash #low model+ @aluation model in which a companys forecastedcash flows are discounted to the present and summed. ,BIT$ *0arnings !efore Interest and %a"es+ .evenues N 0"penses *not including ta"es orinterest+. ,BIT(A N *0arnings !efore Interest, %a"es, )epreciation, and /mortization+ .evenuesN 0"penses *e"cluding interest, ta"es, depreciation, and amortization+. )C) N *#ree 'ash #low+ 'ash flow available to investors *stock and bond holders+ afterinvestments in working capital and fi"ed assets have been made. )C)eN *#ree 'ash #low to euity investors+ 'ash flow available to stockholders afterpaying interest and principle and making investments in working capital and fi"ed assets. FAA9 N 5enerally /ccepted /ccounting ,rinciples. N49ATN *Ket Operating ,rofit /fter %a"+ /n estimate of the companys earnings if ithad no debt. N