A Project Report on 'Capital Budgeting' SUBMITTED TO:SUBMITTED BY: Dr. Yashwant GuptaFarhad Rohilai Professor Class Roll No. - 2496 Himachal Pradesh University Business School.University Roll No. - 2396 (STUDENTS DECLARATION) IherebydeclarethattheprojectreportentitledCAPITALBUDGETINGSubmittedinpartial fulfilment of the requirements for the degree of Masters of Business Administration To Himachal Pradesh University, this is my original work and not submitted For the award of any other degree, diploma, fellowship, or any other similar Title or prizes Place : Shimla FARHAD ROHILAI Date :University Roll No.: 2396 (EXAMINERS CERTIFICATION) The project report of FARHAD ROHILAI on CAPITAL BUDGETING Is approved and is acceptable in quality and form. Internal ExaminerExternal Examiners (Name, qualification and designation)(Name, qualification) (UNIVERSITY STUDY CENTRE CERTIFICATE) This is to certify that the project report entitled CAPITAL BUDGETING Submitted in partial fulfilment oftherequirementsforthedegreeofMastersofBusinessAdministrationofHimachalPradesh UniversityBusinessSchool.FarhadRohilaihasworkedundermysupervisionandguidanceandthat nopartofthisReporthasbeensubmittedfortheawardofanyotherdegree,Diploma,Fellowshipor other similar titles or prizes and that the work has not been published in any journal or magazine. Certified (YASHWANT GUPTA) CONTENTS TOPICS......................................................................................................................PAGE NO. 1. INTRODUCTION........................................................................................ 2.METHODS OF CAPITAL BUDGETING...............................................................A. NET PREST VALUE................................................................................ B.PROFITABILITY INDEX.............................................................................. C.INTERNEL RATE OF RETURN............................................................... D.MODIFIED I.R.R.......................................................................................... E.EQUIVELENT ANNUITY................................................................................. 3.OTHER RELATED CONCEPTS OF CAPITAL BUDGETING................................ 4. A DETAILED UNDERSTANDING OF MAIN TECHNIQUES OF CAPITAL BUDGETING...... 5. CAPITAL BUDGETING: RISK AND UNCERTAINITY.............................................. 6. CAPITAL BUDGETING CASES (PRE-DECIDED)...................................................... A. FALCON AIRLINES INC.......................................................................................... B. PRINCESS CRUISE LINES INC................................................................................ 7. CASE STUDIES (SELF ASSESSMENT)...................................................................... A. WIPRO BPO- NEW PROCESS-- PEPBOYS.............................................................. B.WIPRO BPO- NEW PROCESS-- MSN..................................................................... ........... REFRENCES............................................................................................................... 1. INTRODUCTION: A Perspective from the viewpoint of definitions: Capitalbudgetingistheprocessbywhichthefinancialmanagerdecideswhetherto investinspecificcapitalprojectsorassets.Insomesituations,theprocessmayentailin acquiring assets that are completely new to the firm. In other situations, it may mean replacing an existing obsolete asset to maintain efficiency.

Capitalbudgetmaybedefinedasthefirmsdecisiontoinvestitscurrentfundsmost efficiently in the long-term assets in anticipation if an expected flow of benefits over a series of years. Therefore it involves a current outlay or series of outlay of cash resources in return for an anticipated flow of future benefits. Capital budgeting is the process of identifying, analyzing andselectinginvestmentprojectswhosereturns(cashflow)areexpectedtoextendbeyond one year. Long-terminvestmentsrepresentsizableoutlaysoffundsthatcommitafirmtosome courseofaction.Consequently,thefirmneedsprocedurestoanalyzeandproperlyselectits long-term investments. It must be able to measure cash flows and apply appropriate decision techniques. As time passes, fixed assets may become obsolete or may require an overhaul; at these points, too, financial decisions. Capital budgeting is the process of evaluating and selecting long-term investments that are consistent with the firms goal of maximizing owner wealth. Firms typically make a variety oflong-terminvestments,butthemostcommonforthemanufacturingfirmisinfixedassets, which include property (land), plant, and equipment. These assets, often referred to as earning assets, generally provide the basis for the firms earning power and value. The Meaning Perspective: Capital budgeting (or investment appraisal) is the planning process used to determine whetherfirm'slongterminvestmentssuchasnewmachinery,replacementmachinery,new plants, new products, and research and development projects are worth pursuing. Acapitalexpenditureisanoutlayofcashforaprojectthatisexpectedtoproducea cashinflowoveraperiodoftimeexceedingoneyear.Examplesofprojectsinclude investmentsinproperty,plantandequipment,researchanddevelopmentprojects,large advertising campaigns, or any other project that require a capital expenditure and generates a future cash flow. Capitalexpenditurescanbeverylargeandhaveasignificantimpactonthefinancial performance of the firm, great importance is placed on project selection. This is called Capital budgeting. Nature of Capital Budgeting:Nature of capital budgeting can be explained in brief as under (a) Capital expenditure plans involve a huge investment in fixed assets. (b) Capital expenditure once approved represents long-term investment that cannot be reserved or withdrawn without sustaining a loss. (c) Preparation of coital budget plans involve forecasting of several years profits in advance in order to judge the profitability of projects. It may be asserted here that decision regarding capital investment should be taken very carefully so that the future plans of the company are not affected adversely. Importance of Capital Budgeting Techniques: The key function of the financial management is the selection of the most profitable assortment of capital investment and it is the most important area of decision-making of the financial manger because any action taken by the manger in this area affects the working and the profitability of the firm for many years to come.The key function of the financial management is the selection of the most profitable assortment of capital investment and it is the most important area of decision-making of the financial manger because any action taken by the manger in this area affects the working and the profitability of the firm for many years to come. The need of capital budgeting can be emphasised taking into consideration the very nature of the capital expenditure such as heavy investment in capital projects, long-term implications for the firm, irreversible decisions and complicates of the decision making. Its importance can be illustrated well on the following other grounds:- (1) Indirect Forecast of Sales. The investment in fixed assets is related to future sales of the firm during the life time of the assets purchased. It shows the possibility of expanding the production facilities to cover additional sales shown in the sales budget. Any failure to make the sales forecast accurately would result in over investment or under investment in fixed assets and any erroneous forecast of asset needs may lead the firm to serious economic results. (2) Comparative Study of Alternative Projects Capital budgeting makes a comparative study of the alternative projects for the replacement of assets which are wearing out or are in danger of becoming obsolete so as to make the best possible investment in the replacement of assets. For this purpose, the profitability of each projects is estimated. (3) Timing of Assets-Acquisition. Proper capital budgeting leads to proper timing of assets-acquisition and improvement in quality of assets purchased. It is due to the nature of demand and supply of capital goods. The demand of capital goods does not arise until sales impinge on productive capacity and such situation occur only intermittently. On the other hand, supply of capital goods with their availability is one of the functions of capital budgeting. (4) Cash Forecast. Capital investment requires substantial funds which can only be arranged by making determined efforts to ensure their availability at the right time. Thus it facilitates cash forecast. (5) Worth-Maximization of Shareholders. The impact of long-term capital investment decisions is far reaching. It protects the interests of the shareholders and of the enterprise because it avoids over-investment and under-investment in fixed assets. By selecting the most profitable projects, the management facilitates the wealth maximization of equity share-holders. (6) Other Factors. The following other factors can also be considered for its significance:- (a) It assist in formulating a sound depreciation and assets replacement policy. (b) It may be useful in considering methods of coast reduction. A reduction campaign may necessitate the consideration of purchasing most up-todate and modern equipment. (c) The feasibility of replacing manual work by machinery may be seen from the capital forecast by comparing the manual cost and the capital cost. (d) The capital cost of improving working conditions or safety can be obtained through capital expenditure forecasting. (e) It facilitates the management in making of the long-term plans an assists in the formulation of general policy. (f) It studies the impact of capital investment on the revenue expenditure of the firm such as depreciation, insure and there fixed assets. Kinds of Capital Budgeting Decisions: Capital budgeting refers to the total process of generating, evaluating, selecting, implementing and following up on capital expenditure alternatives. The firm allocates or budgets financial resources to newinvestmentproposals.Basicallythefirmmaybeconfrontedwiththreetypesofcapital decisions: (i) the accept reject decision; (ii) the capital rationing decision; and (iii)the mutually exclusive project accepted. (i)The Accept-Reject Decision This is a fundamental decision in capital budgeting. If the project is accepted, the firm invests in it; if the proposal is rejected, the firm does not invest in it. In general, all those proposals, which yield a rate of return greater than a certain required rate of return or cost of capital is accepted and the rest, are rejected. Under the accept-reject decision, all the independent projects that satisfy the minimum investment criterion should be implemented. (ii)Capital Rationing Decision: In a situation where the firm has unlimited funds, capital budgeting becomes a very simple process in that all independent investment proposals yielding return greater than some predetermined level are accepted. However, this is not the situation prevailing in most of the business firms in the real world. They have a fix capital budget or limitation of availability of funds at a given point of time. A large number of investment proposals compete for these limited funds. The firm must, therefore, ration them. The firm allocates funds to projects in a manner that it maximizes long-run returns. Thus, capital rationing refers to the situation in which the firm has more acceptable investments, requiring a greater amount of finance than is available with the firm. Ranking of the investment projectsisemployed incapitalrationing.Projectscanberankedonthe basisofsomepre- determined criterion such as the rate of return. The project with the highest return is ranked first and the project with the lowest acceptable return last. The projects are ranked in the descending order of the rate of return. It may be noted that only acceptable projects should be ranked and higher Ranked projects till funds are available should be selected for implementation. (iii) Mutually Exclusive Project Decisions Mutually exclusive projects are projects, which compete with other projects in such a way that the acceptance of one will exclude the acceptance of the other projects. The alternatives are mutually exclusive and only one may be chosen. Suppose a company is intending to buy a new folding machine. There are three competing brands, each with different initial investment and operating cost.Thethreemachinesrepresentmutuallyexclusivealternatives,as only oneofthethree machines can be selected. Mutually exclusive investment decisions acquire significance when more than one proposal is acceptable. Then some techniques have to be used to determine the best one. The acceptance of this best alternative automatically eliminates the other alternatives. Criteria for Capital Budgeting Decisions: Potentially, there is a wide array of criteria for selecting projects. Some shareholders may want thefirmtoselectprojectsthatwillshowimmediatesurgesincashinflowothermaywantto emphasizelong-termgrowthwithlittleimportanceonshort-termperformance.Viewedinthis way,itwouldbequitedifficulttosatisfythedifferinginterestsofalltheshareholders. Fortunately, there is a solution. The goal of the firm is to maximize present shareholder value. This goal implies that projects should be undertaken that result in a positive net present value, that is, the present value of the expectedcashinflowlessthepresentvalueoftherequiredcapitalexpenditures.Usingnet presentvalue(NPV)asameasure,capitalbudgetinginvolvesselectionthoseprojectsthat increases the value of the firm because they have a positive NPV. The timing and growth rate of the incoming cash flow is important only to the extent of its impact on NPV. Using NPV as the criterion by with to select projects assumes efficient capital markets so that thefirmhasaccesstowhatevercapitalinneededtopursuethepositiveNPVprojects.In situations where this is not the case, there may be capital rationing and the capital budgeting process becomes more complex. Note that it is not the responsibility of the firm to decide whether to please particular groups of theshareholderswhopreferlongerorshortertermresults.Oncethefirmhasselectedthe projectstomaximizeitsnetpresentvalue,itisuptotheindividualshareholdertousethe capital markets to borrow or lend in order to move the exact timing of their own inflows forward orbackward.Thisideaiscrucialintheprincipal-agentsrelationsthatexistsbetween shareholdersandcorporatemanagers.Eventhougheachmayhavetheirownindividual preferences, the common goal is that of maximizing the present value of the corporation. 2. METHODS OF CAPITAL BUDGETING: There are a number of techniques of capital budgeting. Some of the methods are based on the concept of incremental cash flows from the projects or potential investments. There are some othertechniquesofcapitalbudgetingthatarebasedontheaccountingrulesandaccounting earnings.However, the techniques based on the accounting rules are considered to be improper by the economists.Thehybridandsimplifiedtechniquesofcapitalbudgetingarealsousedin practice.Capitalbudgetingistheprocessofmanagingthelong-termcapitalofafirminthe most profitable way.The prime task of the capital budgeting is to estimate the requirements of capital investment of a business. The capital allocation to various projects depending on their needs and selection of proper project for the business also fall under the canopy of capital budgeting concept. Following are the formal methods used in the Capital Budgeting: Net present valueProfitability indexInternal rate of returnModified Internal Rate of Return, andEquivalent annuity. Thesemethodsusetheincrementalcashflowsfromeachpotentialinvestment,orproject. Techniques based on accounting earnings and accounting rules are sometimes used- though economists consider this to be improper - such as the accounting rate of return, and "return on investment."Simplifiedandhybridmethodsareusedaswell,suchaspaybackperiodand discounted payback period. A. NET PRESENT VALUE: Eachpotentialproject'svalueshouldbeestimatedusingadiscountedcashflow(DCF) valuation, to find its net present value (NPV) - (see Fisher separation theorem). This valuation requiresestimatingthesizeandtimingofalloftheincrementalcashflowsfromtheproject. These futurecash flowsarethendiscountedtodeterminetheirpresentvalue. Thesepresent values are then summed, to get the NPV. The NPV decision rule is to accept all positive NPV projects in an unconstrained environment, or if projects are mutually exclusive, accept the one with the highest NPV. TheNPVisgreatlyaffectedbythediscountrate,soselectingtheproperrate-sometimes called the hurdle rate - is critical to making the right decision. The hurdle rate is the minimum acceptablereturnon aninvestment.Itshouldreflecttheriskinessoftheinvestment,typically measuredbythevolatilityofcashflows,andmusttakeintoaccountthefinancingmix. ManagersmayusemodelssuchastheCAPMortheAPTtoestimateadiscountrate appropriate for each particular project, and use theweighted average cost of capital (WACC) toreflectthefinancingmixselected.Acommonpracticeinchoosingadiscountratefora projectistoapplyaWACCthatappliestotheentirefirm,butahigherdiscountratemaybe more appropriate when a project's risk is higher than the risk of the firm as a whole Formula Each cash inflow/outflow is discounted back to its present value (PV). Then they are summed. Therefore or shortened: Where t - the time of the cash flow N - the total time of the project r-thediscountrate(therateofreturnthatcouldbeearnedonaninvestmentinthe financial markets with similar risk.) Ct-thenetcashflow(theamountofcash)attimet(foreducationalpurposes,C0is commonly placed to the left of the sum to emphasize its role as the initial investment.). The Discount Rate: Therateusedtodiscountfuturecashflowstotheirpresentvaluesisakeyvariableofthis process.Afirm'sweightedaveragecostofcapital(aftertax)isoftenused,butmanypeople believe that it is appropriate to use higher discount rates to adjust for risk for riskier projects. A variablediscountrate withhigherratesappliedtocash flowsoccurringfurther alongthe time span might be used to reflect the yield curve premium for long-term debt. Anotherapproachtochoosingthediscountratefactoristodecidetheratewhichthecapital neededfortheprojectcouldreturnifinvestedinanalternativeventure.If,forexample,the capitalrequiredforProjectAcanearnfivepercentelsewhere,usethisdiscountrateinthe NPVcalculationtoallowadirectcomparisontobemadebetweenProjectAandthe alternative. Related to this concept is to use the firm's Reinvestment Rate. Reinvestment rate canbedefinedastherateofreturnforthefirm'sinvestmentsonaverage.Whenanalyzing projectsinacapitalconstrainedenvironment,itmaybeappropriatetousethereinvestment rateratherthanthefirm'sweightedaveragecostofcapitalasthediscountfactor.Itreflects opportunity cost of investment, rather than the possibly lower cost of capital. NPVvalueobtainedusingvariablediscountrates(iftheyareknown)withtheyearsofthe investmentdurationbetterreflectstherealsituationthanthatcalculatedfromaconstant discountratefortheentireinvestmentduration.Forsomeprofessionalinvestors,their investment funds are committed to target a specified rate of return. In such cases, that rate of returnshouldbeselectedasthediscountratefortheNPVcalculation.Inthisway,adirect comparison can be made between the profitability of the project and the desired rate of return. To some extent, the selection of the discount rate is dependent on the use to which it will be put. If the intent is simply to determine whether a projectwill add value to the company, using thefirm'sweightedaveragecostofcapitalmaybeappropriate.Iftryingtodecidebetween alternative investments in order to maximize the value of the firm, the corporate reinvestment rate would probably be a better choice. Usingvariableratesovertime,ordiscounting"guaranteed"cash flowsdifferent from "at risk" cash flows may be a superior methodology, but is seldom used in practice. Using the discount rate to adjust for risk is often difficult to do in practice (especially internationally), and is really difficult to do well. An alternative to using discount factor to adjust for risk is to explicitly correct the cash flows for the risk elements, then discount at the firm's rate. What NPV Means: NPV is an indicator of how much value an investment or project adds to the value of the firm. With a particular project, if Ct is a positive value, the project is in the status of discounted cash inflow in the time oft. IfCt is a negative value, the project is in the status of discounted cash outflow in the time of t. appropriately risked projects with a positive NPV could be accepted. Thisdoesnotnecessarilymeanthattheyshould be undertakensinceNPVatthecostof capital may not account for opportunity cost, i.e. comparison with other available investments. Infinancialtheory,ifthereisachoicebetweentwomutuallyexclusivealternatives,theone yieldingthehigherNPVshouldbeselected.ThefollowingsumsuptheNPVsinvarious situations. If...It means...Then... NPV > 0 theinvestmentwouldaddvalueto the firm the project may be accepted NPV < 0 the investment would subtract value from the firm the project should be rejected NPV = 0 theinvestmentwouldneithergain nor lose value for the firm Weshouldbeindifferentinthedecision whether to accept or reject the project. Thisprojectaddsnomonetaryvalue.Decision should be based on other criteria, e.g. strategic positioningorotherfactorsnotexplicitly included in the calculation. However, NPV = 0 does not mean that a project is only expected to break even, in the sense of undiscounted profit or loss (earnings). It will show net total positive cash flow and earnings over its life. Example X Corporation must decide whether to introduce a new product line. The new product will have start-up costs, operational costs, and incoming cash flows over six years. This project will have animmediate(t=0)cashoutflowof$100,000(whichmightincludemachinery,andemployee trainingcosts).Othercashoutflowsforyears1-6areexpectedtobe$5,000peryear.Cash inflowsareexpectedtobe$30,000peryearforyears1-6.Allcashflowsareafter-tax,and there are no cash flows expected after year 6. The required rate of return is 10%. The present value (PV) can be calculated for each year: T=0 -$100,000/ 1.100 = -$100,000 PV.T=1 ($30,000 - $5,000) / 1.101 = $22,727 PV.T=2 ($30,000 - $5,000) / 1.102 = $20,661 PV.T=3 ($30,000 - $5,000) / 1.103 = $18,783 PV.T=4 ($30,000 - $5,000) / 1.104 = $17,075 PV.T=5 ($30,000 - $5,000) / 1.105 = $15,523 PV.T=6 ($30,000 - $5,000) / 1.106 = $14,112 PV. The sum of all these present values is the net present value, which equals $8,881. Since the NPV is greater than zero, the corporation should invest in the project. The same example in an Excel formulae: NPV(rate,net_inflow)+initial_investment PV(rate,year_number,yearly_net_inflow) Morerealisticproblemswouldneedtoconsiderotherfactors,generallyincludingthe calculationoftaxes,unevencashflows,andsalvagevaluesaswellastheavailabilityof alternate investment opportunities. Common Pitfalls Ifsome(orall)oftheCthaveanegativevalue,thenparadoxicalresultsarepossible.For example, if the Ct are generally negative late in the project (eg, an industrial or mining project might have clean-up and restoration costs), then an increase in the discount rate can make the project appear more favourable. Some people see this as a problem with NPV. A way to avoid this problem is to include explicit provision for financing any losses after the initial investment, i.e., explicitly calculate the cost of financing such losses. Another common pitfall is to adjust for risk by adding a premium to the discount rate. Whilst a bank might charge a higher rate of interest for a risky project, that does not mean that this is a validapproachtoadjustinganetpresentvalueforrisk,althoughitcanbeareasonable approximationinsomespecificcases.Onereasonsuchanapproachmaynotworkwellcan be seen from the foregoing: if some risk is incurred resulting in some losses, then a discount rate in the NPV will reduce the impact of such losses below their true financial cost. A rigorous approachtoriskrequiresidentifyingandvaluingrisksexplicitly,e.g.byactuarialorMonte Carlo techniques, and explicitly calculating the cost of financing any losses incurred. Yetanotherissuecanresultfromthecompoundingoftheriskpremium.Risacompositeof the risk free rate and the risk premium. As a result, future cash flows are discounted byboth theriskfreerateaswellastheriskpremiumandthiseffectiscompoundedbyeach subsequentcashflow.ThiscompoundingresultsinamuchlowerNPVthanmightbe otherwisecalculated.Thecertaintyequivalentmodelcanbeusedtoaccountfortherisk premium without compounding its effect on present value. FISHER SEPARATION THEOREM TheFisherseparationtheoremineconomicsassertsthattheobjectiveofafirmwillbethe maximizationofitspresentvalue,regardlessofthepreferencesofitsowners.Thetheorem therefore separates management's "productive opportunities" from the entrepreneur's "market opportunities". It was proposed by and is named after the economist Irving Fisher. The Fisher Separation Theorem states that: the firm's investment decision is independent of the preferences of the owner;the investment decision is independent of the financing decision.thevalueofacapitalproject(investment)isindependentofthemixofmethods equity, debt, and/or cash used to finance the project. Fisher showed the above as follows: 1.Thefirmcanmaketheinvestmentdecisioni.e.thechoicebetweenproductive opportunities that maximizes its present value, independent of its owner's investment preferences.2.Thefirmcanthenensurethattheownerachieveshisoptimalpositionintermsof "market opportunities" by funding its investment either with borrowed funds, or internally as appropriate. B. PROFITABILITY INDEX METHOD: Profitability index identifies the relationship of investment to payoff of a proposed project. The ratio is calculated as follows: (PV of future cash flows) / (PV Initial investment) = Profitability Index ProfitabilityIndexisalsoknownasProfitInvestmentRatio,abbreviatedtoP.I.andValue Investment Ratio (V.I.R.). Profitability index is a good tool for ranking projects because it allows you to clearly identify the amount of value created per unit of investment, thus if you are capital constrained you wish to invest in those projects which create value most efficiently first. NotaBene;StatementsbelowthisparagraphyassumethecashflowcalculatedDOESN'T includetheinvestmentmadeintheproject.Whereinvestmentcostsareincludedinthe computedcash flowaPV>0simplyindicatestheprojectcreatesmorevaluethanthecostof capital which is determined by the Weighted Average Cost of Capital (WACC). Aratioofoneislogicallythelowestacceptablemeasureontheindex.Anyvaluelowerthan onewouldindicatethattheproject'sPVislessthantheinitialinvestment.Asvaluesonthe profitability index increase, so does the financial attractiveness of the proposed project. Rules for selection or rejection of a project: If PI > 1 then accept the projectif PI < 1 then reject the project For Example Given: Investment = 40,000 life of the Machine = 5 Years CFAT YearCFAT 1 18000 2 12000 3 10000 49000 56000 Calculate NPV @10% and PI YearCFATPV@10% PV 1180000.90916362 2 120000.827 9924 3 100000.752 7520 490000.683 6147 5 60000.621 3726 Total present value43679 (-) Investment 40000 NPV 3679 PI =43679 / 40000 =1.091 = >1= so accept the project C. INTERNAL RATE OF RETURN: The internal rate of return (IRR) is a capital budgeting metric used by firms to decide whether they should make investments. It is an indicator of the efficiency of an investment, as opposed to net present value (NPV), which indicates value or magnitude. TheIRRistheannualizedeffectivecompoundedreturnratewhichcanbeearnedonthe invested capital, i.e., the yield on the investment. A project is a good investment proposition if its IRR is greater than the rate of return that could be earned by alternate investments (investing in other projects, buying bonds, even putting the money in a bank account). Thus, the IRR should be compared to any alternate costs of capital including an appropriate risk premium. MathematicallytheIRRisdefinedasanydiscountratethatresultsinanetpresentvalueof zero of a series of cash flows. In general, if the IRR is greater than the project's cost of capital, or hurdle rate, the project will add value for the company. Method To find the internal rate of return, find the value(s) of r that satisfies the following equation: Example Internal Rate of Return (IRR) IRR = r, IRR = 17.09% Net Present Value (NPV) Thus using r = IRR = 17.09%, YearCash Flow 0595 139 259 355 419 Graph of NPV as a function of r for the example Problems with using internal rate of return (IRR) Asaninvestmentdecisiontool,thecalculatedIRRshouldnotbeusedtoratemutually exclusive projects, but only to decide whether a single project is worth investing in two mutually exclusive projects.Incaseswhereoneprojecthasahigherinitialinvestmentthanasecondmutuallyexclusive project, the first project may have a lower IRR (expected return), but a higher NPV (increase in shareholders'wealth)andshouldthusbeacceptedoverthesecondproject(assumingno capital constraints). IRR makes no assumptions about the reinvestment of the positive cash flow from a project. As a result, IRR should not be used to compare projects of different duration and with a different overallpatternofcashflows.ModifiedInternalRateofReturn(MIRR)providesabetter indication of a project's efficiency in contributing to the firm's discounted cash flow. TheIRR methodshouldnotbeusedin the usual manner forprojectsthatstartwithan initial positivecashinflow(orinsomeprojectswithlargenegativecashflowsattheend),for examplewhereacustomermakesadepositbeforeaspecificmachineisbuilt,resultingina single positive cash flow followed by a series of negative cash flows (+- - - -). In this case the usual IRR decision rule needs to be reversed. Iftherearemultiplesignchangesintheseriesofcashflows,e.g.(-+-+-),theremaybe multipleIRRsforasingleproject,sothattheIRRdecisionrulemaybeimpossibleto implement.Examplesofthistypeofprojectarestripminesandnuclearpowerplants,where there is usually a large cash outflow at the end of the project. In general, the IRR can be calculated by solving a polynomial equation.Sturm's Theorem can be used to determine if that equation has a unique real solution. Importantly, the IRR equation cannot be solved analytically (i.e. in its general form) but only via iterations. AcriticalshortcomingoftheIRRmethodisthatitiscommonlymisunderstoodtoconveythe actual annual profitability of an investment. However, this is not the case because intermediate cash flows are almost never reinvested at the project's IRR; and, therefore, the actual rate of return(akintotheonethatwouldhavebeenyieldedbystocksorbankdeposits)isalmost certainlygoingtobelower.Accordingly,ameasurecalledModifiedInternalRateofReturn (MIRR) is used, which has an assumed reinvestment rate, usually equal to the project's cost of capital. DespiteastrongacademicpreferenceforNPV,surveysindicatethatexecutivespreferIRR overNPV.Apparently,managersfinditeasiertocompareinvestmentsofdifferentsizesin terms of percentage rates of return than by dollars of NPV. However, NPV remains the "more accurate" reflection of value to the business. IRR, as a measure of investment efficiency may givebetterinsightsincapitalconstrainedsituations.However,whencomparingmutually exclusive projects, NPV is the appropriate measure. In addition if the NPV of one project is higher than another and the other project has a higher IRR, then the cross over point method can be used to solve this dispute. Cross Over Point > IRR = Accept project with higher NPV and if the Cross Over Point < IRR = Accept project with higher IRR D. MODIFIED INTERNAL RATE OF RETURN(MIRR)isafinancialmeasureusedtodeterminetheattractivenessofaninvestment.Itis generallyusedaspartofacapitalbudgetingprocesstorankvariousalternativechoices.As thenameimplies,MIRRisamodificationofthefinancialmeasureInternalRateofReturn (IRR). The main difference is that rather than ignoring the investment rate of the positive cash flow, MIRR makes an explicit assumption about the rate of return of investment of those flows. The modified internal rate of return assumes all positive cash flows are re-invested (usually at theWACC)totheterminalyearoftheproject.Allnegativecashflowsarediscountedand includedintheinitialinvestmentoutlay.MIRRranksprojectefficiencyconsistentwiththe presentworthratio(variantofNPV/DiscountedNegativeCashFlow),consideredthegold standardinmanyfinancetextbooks.(PrinciplesofCorporateFinance,Brealey,Myers,and Allen; or Economic Evaluation and Investment Decision Methods, Stermole and Stermole) Problems with IRR ThereareafewmisconceptionsabouttheIRRcalculation.ThemajoroneisthatIRR automaticallyassumesthatallcashoutflowsfromaninvestmentarereinvestedattheIRR rate. IRR is the "internal rate of return" with "internal" meaning each dollar in an investment. It makes no assumptions about what an investor does with money coming out of an investment. Whether the investor gives it away or puts it in a coffee can, the IRR stays the same. The IRR does, however, reflect reinvestment at the IRR. It does however have a few drawbacks. First, IRR is not made to calculate negative cash flows after the initial investment. If an investment has an outflow of $1,000 in year three and an IRR of 30%, the $1,000 is discounted at 30% per year back to a present value. You would have to put this PV amount in an investment earning 30% per year for the IRR to reflect the true yield. Also,IRRignoresthereinvestmentpotentialofpositivecashflows.Sincemostcapital investmentshaveintermediate(non-terminal)positivecashflows,thefirmwillreinvestthese cash flows. Unless a better number is known, the firm's cost of capital is a reasonable proxy for the return to be expected. Investments with large or early positive cash flows will tend to look far better with IRR than with MIRR for this reason. Toillustrate:afirmhasinvestmentoptionswithreturnsthataregenerallymoderate.An unusually attractive investment opportunity comes up with much higher return. The cash spun off from this latter investment will probably be reinvested at the moderate rate of return rather thaninanother unusuallyhigh-returninvestment.Inthiscase,IRRwilloverstatethevalueof the investment, while MIRR will not. Formula E. EQUIVALENT ANNUAL COST: In finance the equivalent annual cost (EAC) is the cost per year of owning and operating an asset over its entire lifespan. EAC is often used as a decision making tool incapital budgeting when comparing investment projects of unequal life spans. For example if project A has an expected lifetime of 7 years, and project B has an expected lifetime of 11 years it would be improper to simply compare the net present values (NPVs) of the two projects, unless neither project could be repeated. EACiscalculatedbydividingtheNPVofaprojectbythepresentvalueofanannuityfactor. Equivalently, the NPV of the project may be multiplied by the loan repayment factor. EAC= The use of the EAC method implies that the project will be replaced by an identical project A practical example A manager must decide on which machine to purchase: Machine A Investment cost$50,000 Expected lifetime3years Annual maintenance $13,000 Machine B Investment cost $150,000 Expected lifetime8 years Annual maintenance$7,500 The cost of capital is 5%. The EAC for machine A is: ($50,000/A3,5)+$13,000=$31,360 The EAC for machine B is: ($150,000/A8,5)+$7,500=$30,780 Where A is the loan repayment factor for t years and 5% cost of capital. The conclusion is to invest in machine B since it has a lower EAC. Alternative method: The manager calculates the NPV of the machines: MachineAEAC = $85,400/A3,5=$31,360 Machine B EAC = $198,474/A8,5=$30,708 Theresultisthesame,althoughthefirstmethodiseasieritisessentialthattheannual maintenance cost is the same each year. AlternativelythemanagercanusetheNPVmethodundertheassumptionthatthemachines willbereplacedwiththesamecostofinvestmenteachtime.Thisisknownasthechain method since 8 repetitions of machine A are chained together and 3 repetitions of machine B arechainedtogether.SincethetimehorizonusedintheNPVcomparisonmustbesetto24 years (3*8=24) in order to compare projects of equal length, this method can be slightly more complicatedthancalculatingtheEAC.Inaddition,theassumptionofthesamecostof investmentforeachlinkinthechainisessentiallyanassumptionofzeroinflation,soareal interest rate rather than a nominal interest rate is commonly used in the calculations. 3. OTHER RELATED CONCEPTS OF CAPITAL BUDGETING: CAPITAL EXPENDITURE Capitalexpenditures(CAPEXorcapex)areexpenditurescreatingfuturebenefits.Acapital expenditure is incurred when a business spends money either to buy fixed assets or to add to thevalueofanexistingfixedassetwithausefullifethatextendsbeyondthetaxableyear. Capexareusedbyacompanytoacquireorupgradephysicalassetssuchasequipment, property,orindustrialbuildings.Inaccounting,acapitalexpenditureisaddedtoanasset account("capitalized"),thusincreasingtheasset'sbasis(thecostorvalueofanassetas adjustedfortaxpurposes).CapexiscommonlyfoundontheCashFlowStatementas "Investment in Plant Property and Equipment" or something similar in the Investing subsection. For tax purposes, capital expenditures are costs that cannot be deducted in the year in which theyarepaidorincurred,andmustbecapitalized.Thegeneralruleisthatiftheproperty acquiredhasausefullifelongerthanthetaxableyear,thecostmustbecapitalized.The capitalexpenditurecostsarethenamortizedordepreciatedoverthelifeoftheassetin question.Asstatedabove,capitalexpenditurescreateoraddbasistotheassetorproperty, whichonceadjusted,willdeterminetaxliabilityintheeventofsaleortransfer.IntheUS, Internal Revenue Code 263 and 263A deal extensively with capitalization requirements and exceptions. Included in capital expenditures are amounts spent on: 3.acquiring fixed assets4.fixing problems with an asset that existed prior to acquisition5.preparing an asset to be used in business6.legal costs of establishing or maintaining one's right of ownership in a piece of property7.restoring property or adapting it to a new or different use8.starting a new business An ongoing question of the accounting of any company is whether certain expenses should be capitalizedorexpensed.Coststhatareexpensedinaparticularmonthsimplyappear onthe financial statement as a cost that was incurred that month. Costs that are capitalized, however, areamortizedovermultipleyears.Capitalizedexpendituresshowuponthebalancesheet. Mostordinarybusinessexpensesareclearlyeitherexpensableorcapitalizable,butsome expenses could be treated either way, according to the preference of the company. The counterpart of capital expenditure is operational expenditure ("OpEx"). CORPORATE FINANCE Corporate finance is an area of finance dealing with the financial decisions corporations make andthetoolsandanalysisusedtomakethesedecisions.Theprimarygoalofcorporate finance is to maximize corporate value while reducing the firm's financial risks. Although it is in principledifferentfrommanagerialfinancewhichstudiesthefinancialdecisionsofallfirms, ratherthancorporationsalone,themainconceptsinthestudyofcorporatefinanceare applicable to the financial problems of all kinds of firms. The discipline can be divided into long-term and short-term decisions and techniques.Capital investment decisions are long-term choices about which projects receive investment, whether tofinancethatinvestmentwithequityordebt,andwhenorwhethertopaydividendsto shareholders. On the other hand, the short term decisions canbe grouped under the heading "Workingcapitalmanagement".Thissubjectdealswiththeshort-termbalanceofcurrent assets and current liabilities; the focus here is on managing cash,inventories, and short-term borrowing and lending (such as the terms on credit extended to customers). ThetermsCorporatefinanceandCorporatefinancierarealsoassociatedwithinvestment banking. The typical role of an investment banker is to evaluate investment projects for a bank to make investment decisions. PERSONAL FINANCEPersonal finance is the application of the principles of finance to the monetary decisions of an individual or family unit. It addresses the ways inwhich individuals or families obtain,budget, save and spend monetary resources over time, taking into account various financial risks and futurelifeevents.Componentsofpersonalfinancemightincludecheckingandsavings accounts, credit cards and consumer loans, investments in the stock market, retirement plans, social security benefits, insurance policies, and income tax management. Personal financial planning Akeycomponentofpersonalfinanceisfinancialplanning,adynamicprocessthatrequires regular monitoring and reevaluation. In general, it has five steps: 1.Assessment:One'spersonalfinancialsituationcanbeassessedbycompiling simplifiedversionsoffinancialbalancesheetsandincomestatements.Apersonalbalance sheetliststhevaluesofpersonalassets(e.g.,car,house,clothes,stocks,bankaccount), along with personal liabilities (e.g., credit card debt, bank loan, mortgage). A personalincome statement lists personal income and expenses. 2.Settinggoals:Twoexamplesare"retireatage65withapersonalnetworthof $200,000American"and"buyahousein3yearspayingamonthlymortgageservicingcost thatisnomorethan25%ofmygrossincome".Itisnotuncommontohaveseveralgoals, some short term and some long term. Setting financial goals helps direct financial planning. 3.Creatingaplan:Thefinancialplandetailshowtoaccomplishyourgoals.Itcould include,forexample,reducingunnecessaryexpenses,increasingone'semploymentincome, or investing in the stock market. 4.Execution:Executionofone'spersonalfinancialplanoftenrequiresdisciplineand perseverance.Manypeopleobtainassistancefromprofessionalssuchasaccountants, financial planners, investment advisers, and lawyers. 5.Monitoring and reassessment: As time passes, one's personal financial plan must be monitored for possible adjustments or reassessments.Typical goals most adults have are paying off credit card and or student loan debt, retirement, college costs for children, medical expenses, and estate planning. Anoperatingexpense,operatingexpenditure,operationalexpense,operational expenditureorOPEXisanon-goingcostforrunningaproduct,business,orsystem.Its counterpart,acapitalexpenditure(CAPEX),isthecostofdevelopingorprovidingnon-consumable parts for the product or system. For example, the purchase of a photocopier is the CAPEX, and the annual paper and toner cost is the OPEX. For larger systems like businesses, OPEX may also include the cost of workers and facility expenses such as rent and utilities. In business, an operating expense is a day-to-day expense such as sales and administration, or research & development, as opposed to Production, costs, and pricing. In short, this is the moneythebusinessspendsinordertoturninventoryintothroughput.Operatingexpenses also include depreciation of plants and machinery which are used in the production process. On an income statement, "operating expenses" is the sum of a business's operating expenses for a period of time, such as a month or year. Inthroughputaccounting,thecostaccountingaspectofTheoryofConstraints(TOC), operatingexpenseisthemoneyspentturninginventoryintothroughput.InTOC,operating expense is limited to costs that vary strictly with the quantity produced, like raw materials and purchasedcomponents.Everythingelseisafixedcost,includinglabourunlessthereisa regular and significant chance that workers will not work a full-time week when they report on its first day. Inarealestatecontext,operatingexpensesarecostsassociatedwiththeoperationand maintenanceofanincomeproducingproperty.Operatingexpensesincludeaccounting expenseslicensefeesmaintenanceandrepairs,suchassnowremoval,trashremoval, janitorialservice,pestcontrol,andlawncare,advertising,officeexpenses,supplies,attorney fees andlegal fees,utilities,suchastelephoneinsurance,propertymanagement,includinga resident manager, property taxes, travel and vehicle expensesTravel expenses are defined as those incurred in the event of travel required for professional purposes.For this purpose, travel is defined as the simultaneous absence from the residence and from theregularplaceofemployment.Itispromptedbyprofessionalorcompanypurposesand likely does not concern the travellers private life, or concerns it only to a small degree. Travel expensesincludetravelcostsandfares,accommodationexpenses,andso-calledadditional expensesformeals.Fortheself-employed(contractorsandfreelancers),theexpenses constitute business expenses.

4. A DETAILED UNDERSTANDING OF THE MAIN TECHNIQUES OF CAPITAL BUDGETING: Avarietyofmeasureshaveevolvedovertimetoanalyzecapitalbudgetingrequests.The newermethodsusetimevalueofmoneyconcepts.Oldermethods,likethepaybackperiod, have the deficiency of not using time value techniques and will eventually fall by the wayside and be replaced in companies by the newer, superior methods of evaluation. The newer methods have one thing in common: they conduct a test to see if the benefits (i.e., cash inflows) are large enough to repay the company for three things: (1) the cost of the asset, (2)thecostoffinancingtheasset(e.g.,interest),and(3)arateofreturn(calledarisk premium) that compensates the company for potential errors made when estimating cash flows that will occur in the distant future. Let's take a look at the most popular techniques for analyzing a capital budgeting proposal. 1. Net Present Value (NPV) Using the hurdle rate as the required rate of return, thenet present value of an investment is thepresentvalueofthecashinflowsminusthepresentvalueofthecashoutflows.Amore common way of expressing this is to say that the net present value (NPV) is the present value of the benefits (PVB) minus the present value of the costs (PVC) NPV = PVB - PVC By using the hurdle rate as the discount rate, we are conducting a test to see if the project is expected to earn our minimum desired rate of return. Here are our decision rules: If the NPV is:Benefits vs. Costs Should we expect to earn at least our minimum rate of return? Accept the investment? PositiveBenefits > CostsYes, more thanAccept ZeroBenefits = CostsExactly equal toIndifferent NegativeBenefits < CostsNo, less thanReject Very important: Notice that, if the NPV is positive, it says that the company expects to receive benefitsthatarelargeenoughtorepaythecompanyfor(1)theasset'scost,(2)thecostof financing the project, and (3) a rate of return that adequately compensates the company for the risk found in the cash flow estimates. If the NPV is negative, the benefits are not large enough to cover all three of the above, and therefore the project should be rejected. 2. Internal Rate of Return (IRR) The Internal Rate of Return (IRR) is the discount rate that will cause the present value of the benefitstoequalthepresentvalueofthecost.Inotherwords,theIRRisthesituation describedinthemiddlelineoftheabovetable.Weuseatrial-and-errorprocesstofindthis percentage rate. Wegenerallystartbyconductingatestusingthehurdlerate.Thiswilltelluswhetherthe project is expected to earn us more than or less than the hurdle rate. Test Results Interpretation of ResultsNext percentage to be tested? PVB > PVC The project is expected to earn more than the percentage rate used for the test A higher rate PVB < PVC The project is expected to earn less than the percentage rate used for the test A lower rate Itisn'tnecessarytotestinincrementsof onepercent(e.g., 10%, 11%, 12%, etc.).Onceyou have conducted the test using the hurdle rate, compare the PVB and PVC. If the two numbers are relatively close to one another, the IRR is relatively close to the hurdle rate. If the PVB is well away from the PVC, you will need to choose a percentage rate that is well away from the hurdle rate for your second test. We continue the testing until we find a range of values for the IRR. In other words, we need to knowthattheIRRisgreaterthansomepercentagenumberandlessthansomepercentage number(e.g.,greaterthan10%andlessthan15%).Intheinterestofaccuracy,keepthis range to 5% or less, e.g., greater than 12% and less than 13% is ideal, greater than 10% and lessthan15%isO.K.,greaterthan10%andlessthan20%isnotacceptablefortherange. We then set up a proportion and interpolate to find the IRR. Calculation of the IRR Assume that we are evaluating a project that has a cost of $100,000. Using the hurdle rate, we obtain a PVB of $103,000. Comparing the PVB of $103,000 to the PVC of $3,000, this tells us that the project is expected to earn a rate higher than 10%. So we choose a higher rate for our secondtest.Sincethegapbetween$103,000and$100,000issmall(inrelativeterms),we shouldn't have to go far. Let'schoose15%foroursecondtest.Usingthisasourdiscountrate,weobtainaPVBof $98,000. Since the PVB is now less than the PVC, the IRR is less than 15%. We now have our range: the IRR is between 10% and 15%. We are searching for the discount rate that will cause the PVB to equal the PVC. Here is what we know so far: Percentage TestedPVB 10%$103,000 IRR$100,000 15%$ 98,000 Notice that we place the smaller percentage number on top (to simplify the arithmetic later). On the middle row, the IRR is the discount rate that will give us a PVB exactly equal to the PVC of $100,000. Let'scallthedistancebetween10%andtheIRR(above)adistanceofx.Theratioofthis distance to the distance between the outside two numbers (i.e., 10% and 15%) should be the same for both columns. In other words, we can set up a proportion using this: the ratio of the differencebetweenthetoptwonumbersandtheoutsidetwonumbersisthesameforboth columns. That is: x is to 5% as $3,000 is to $5,000. x/ 5% =

$3,000 / $5,000X=$3,000 / $5,000 * 5% X=0.60 * 5% X =3.0% If x is 3.0%, then the IRR is 3% away from 10% and is larger than 10% (since we know that the IRR is between 10% and 15%); therefore, the IRR must be 13.0%. WHICH METHOD IS BETTER: THE NPV OR THE IRR? SurveysshowthattheIRRmethodisthemorepopularofthetwomethods(byasmall margin). However, the NPV is superior to IRR for at least two reasons: 9.The NPV assumes that the cash inflows are reinvested to earn the hurdle rate; the IRR assumesthatthecashinflowsarereinvestedtoearntheIRR.Ofthetwo,theNPV's assumption is more realistic in most situations.2.It is possible for the IRR to have more than one solution. If the cash flows experience a sign change (e.g., positive cash flow in one year, negative in the next), the IRR method willhavemorethanonesolution.Inotherwords,therewillbemorethanone percentagenumberthatwillcausethePVBtoequalthePVC.(Whenthisoccurs,we simply don't use the IRR method to evaluate the project, since no one value of the IRR is theoretically superior to the others.) The NPV method does not have this problem. 3.Modified Internal Rate of Return (MIRR) TheModifiedInternalRateofReturn(MIRR)isanattempttoovercometheabovetwo deficiencies in the IRR method. The cash inflows (which are received at the end of each year) are assumed to be reinvested at the hurdle rate for the remainder of the project's life. Using the hurdle rate, the MIRR technique calculates the present value of the cash outflows (i.e., the PVC), the future value of the cash inflows (to the end of the project's life), and then solves for the discount rate that will equate the PVC and the future value of the benefits. In this way, the two problems mentioned previously are overcome: 1. the cash inflows are assumed to be reinvested at the firm's hurdle rate, and 2. there is only one solution to the technique. Calculation of the MIRR Assumethatweareevaluatingaprojectthathasacost of $30,000,after-taxcashinflowsof $10,000 per year for four years, and a hurdle rate of 10%. Since the cash inflows are assumed to be received at the end of each year, the cash inflows would be reinvested as shown below. Notice that the 1st year's cash inflow is assumed to be reinvested for 3 years, so we multiply it times the future value factor for 10% and year 3 (i.e., 1.331). The2ndyear'scashinflowisassumedtobereinvested for2years,sowemultiplyit time the future value factor for 10% and year 2 (i.e., 1.210). Year 3's cash inflow is invested for 1 year and year 4's cash inflow is received at the end of the 4th year, so it is not available for reinvestment since it coincides with the end of the project's life. YearYears Reinvested Cash Inflow Future Value Factor (at 10%) Future Value 13$10,0001.331$13,310 22$10,0001.210$12,100 31$10,0001.100$11,000 40$10,0001.000$10,000 Total$46,410 Now,theonlyquestionremainingis:IfIinvest$30,000inanaccounttodayandreceivethe equivalent of $46,410 in four years, what rate would be earned on the investment? We can find the MIRR in one of two ways: 1.Thetrial-and-errortechniquethatwasused earlierto find the IRR.Usinganydiscount rate,like10%,takethepresentvalueofthe$46,410receivedfouryearsfromnow. (Thisis$31,699.)Sincethepresentvalueofthebenefits($31,699)islargerthanthe present value of the cost ($30,000), we need to use a higher discount rate, like 12%. At 12%, the present value is $29,494. Since the PVB is now less than the PVC, the MIRR is less than 12%. We now have our range: the MIRR is between 10% and 12%. We are searching for the discount rate that will cause the PVB to equal the PVC. Here is what we know so far: Percentage TestedPVB 10%$31,699 MIRR$30,000 12%$29,494 Onthemiddlerow,theMIRRisthediscountratethatwillgiveusaPVBequaltothe PVC of $30,000. Let's call the distance between 10% and the MIRR (above) a distance ofx. The ratio of thisdistancetothedistancebetweentheoutsidetwonumbers(i.e.,10%and12%) should be the same for both columns. In other words, x / 2% =

$1,699 / $2,205x =$1,699 / $2,205 * 2% x=0.7705 * 2% x=1.54% If x is 1.54%, then the MIRR is 1.54% away from 10% and is larger than 10% (since we know that the MIRR is between 10% and 12%); therefore, the MIRR must be 11.54%. 2.As an easier alternate method, we can solve for the geometric mean return.a.Divide the future value by the present value (i.e., $46,410/$30,000) to get a value of1.547.Noticethatthisisthevaluethat$1.00wouldgrowtoin4yearsif invested at the hurdle rate of 10%.b.Set the result to the 1/n power (where n = 4 years). If you have ay-to-the-x key on your calculator, simply enter 1.547 as the y-value and 0.25 (i.e., 1/4) as the x-value, and solve. The result is 1.1153.c.Subtract 1.0 from the answer and place the answer (0.1153) in percentage form. The answer is the MIRR of 11.53%. 4. Payback Period ThePaybackPeriodistheweakestofthecapitalbudgetingmethodsdiscussedhere.By definition, the payback period is the length of time that it takes to recover your investment. The paybackperiodoftheillustrationimmediatelyaboveis3.0years.(Torecover$30,000atthe rate of $10,000 per year would take 3.0 years.) Other Issues 1.SunkCosts-Coststhathavebeenincurredinthepastandcannotberecovered are not relevant to the analysis. These costs are called sunk costs. The only cash flows that matterarethosethatwillchangeifwedecidetoaccepttheproject.Thesecashflows are called incremental cash flows (or relevant cash flows). 2.Inflation-Withthepassageoftime,inflationwillhaveanimpactonthecashflows (e.g., wage rates will likely increase in the future as a result of inflation). Should the cash flows be adjusted for the impact of inflation? The answer is: You have to be consistent in the relationship between the discount rate and the cash flows.a.If the discount rate includes an inflation premium (as it almost alwayswill), then the cash flows should reflect the impact of inflation as well.b.Ifthecashflowsdonotincludetheimpactofinflation,thentheinflationrate should be deducted from the discount rate. 3.Scale Effect - If we are consideringmutually exclusive proposals and the assets (e.g., machines) cost different amounts, there is a potential bias in favor of accepting the more expensiveasset,simplybecauseofthelargersizeofthepricetag.Forexample,we may consider investing in either:Asset A, which cost $100,000 and has an NPV of $3,000, or Asset B, which cost $300,000 and has an NPV of $3,100. IfwemakeourdecisionbasedsolelyontheNPV'sdollaramount,wewouldchoose assetBsinceithasthehigherNPV.However,perdollarinvested,assetAobviously has the higher return. If the cost of the two assets differ by a considerable amount, we should use the profitability index instead of the NPV to make our decision. Theprofitabilityindex,bydefinition,istheratioofthepresentvalueofthebenefits (PVB)tothepresentvalueofthecost(PVC).Thiswillremovethescaleeffect'sbias. We obviously prefer the asset that has the higher value for the profitability index. 4.Unequal Lives - If we are comparing mutually exclusive proposals and the assets (e.g., machines)havedifferentlives,thereisabiasinfavorofacceptingthelonger-lived asset. To see how to eliminate this bias, read this coverage of replacement chains. 5. Capital Budgeting Uncertainty and Risk: 1.While the risk-adjusted discount rate method provides a means for adjusting the riskiness ofthediscountrate,thecertaintyequivalentmethodadjuststheestimatedvalueofthe uncertain cash flows. The risk-adjusted discount rate method extends the cash flow valuation model under certainty to the uncertainty case as follows: 1(1 )Nttt tXVr==+, where V = value of Capital budgeting project, tX = median or mean of the expected risky cash flow t distribution Xt, rt= the risk adjusted discount rate appropriate to the riskiness of the uncertain cash flows tX, N= the life of the project. Thecertaintyequivalentmethodusestherationalethatgivenariskycashflow,thedecision makerwillevaluatethiscashflowaccordingtoanexpectedutility,theutilityestimatebeing hypothesized to be equal to utility derived from some certain cash flow amount. The decision maker performs this process for each cash flow. The valuation model is as follows: 1(1 )NtttCVi==+, where Ct = certainty equivalent cash flow at period t, i = riskless interest rate. Ct can be expressed as a fraction of the expected value of the cash flow as follows: t t tC X o =, where to = some fractional value. The valuation formula becomes 1(1 )Nt tttXVio==+. Since both models evaluate future uncertain cash flows, they should yield the same value for a given cash flow stream. The present value of each periods cash flows should be the same. (1 ) (1 )t t ttt ttX XPVi Ro= =+ + (1 )(1 )ttttiro+=+ (1/ ) (1/ 1)11(1 ) (1 )11( ) ( )t tt tt ti ir ro o+++ (( + += = (( From the 2 values of r at time t and t + l, the risk-adjusted discount rate rts will be a function of (1) the investors attitude toward risk measured by rt, (2) the risk-free interest rate, and (3) the time period t. 2.a. The risk adjusted discount rate method (RADR) is similar to the NPV. It is defined as thepresentvalueoftheexpectedormeanvalueoffuturecashflowdistributions discountedatadiscountrate,k,whichincludesariskpremiumfortheriskinessofthe cash flows from the project. It is defined by the following equation: 01(1 )NtttXNPV Ik== + b.Thecertaintyequivalentmethod(CE)adjustsforriskdirectlythroughtheexpected value of the cash flow in each period and then discounts these risk adjusted cash flows by the risk free rate of interest, Rf. The formula for this method is given as follows: 01(1 )Nt tttfXNPV IRo== + c.Simulation is a method in which the specific capital budgeting decision is modeled with all uncertain variables being treated as random variables. A detailed discussion of this method is given on pp.520 thru 524. d.Adecisiontreeapproachisusedtoanalyzeinvestmentopportunitiesinvolvinga sequence of decisions over time. A detailed discussion of the method is given in pp.515-520. 3.ThemajordifferencebetweentheRADRandCEmethodsisthattheRADRmethod adjusts for risk in the discount rate while the CE method adjusts the cash flows for risk and then discounts at a risk-free rate of interest. 4.NetpresentvalueandstandarddeviationofNPVareestimatedinperformingcapital budgeting using a probabilistic distribution approach. The mean and standard deviation of the NPV distribution are defined as 01(1 ) (1 )Nt tt NtC SNPV Ik k== + + + 12 221 1 1( )(1 )N N NtNPV t T T ttt T tWW Cov C Ckoo= = = (= + (+ whereCt = uncertain net cash flow in period t, k = risk adjusted discount rate, St = salvage value, I0 = initial outlay, 2 = variance of the cash flow, WT, Wt = discount factors in the Tth and tth periods. Cov(CTCt)isusedtomeasurethecovariabilitybetweenthecashflowintheTthand5th periods. Cov(CTCt) can also be written TtTt, where Tt is the correlation coefficient. Furthermore, we can define equations that can be used to analyzeinvestment proposals in which some of the expected cash flows are closely related (significantly correlated) and others are fairly independent. The standard deviation of NPVs for each case are: 1 1NtttNPVk==+ perfect correlation 12 221 (1 )NtNPVttkoo= (=(= mutually independent If cash flows show less than perfect correlation, this model is inappropriate and the problem mustbehandledwithaseriesofconditionalprobabilitydistributions.InBoninismodel,cash flowamountsareuncertainbutprobabilitiesassociatedwithcashflowsinagivenperiodare assumedtobeknown.Later-periodexpectedcashf1owsayehighlydependentonwhat occursinearliertimeperiods.Jointprobabilitiesarefoundforthevariouscashflowseries. Finally,theNPVforeachcashf1owseriesiscalculatedusingtheconditionalprobabi1ities. These series of NPVs are then multiplied by each joint probability and assumed. The result is the NPV and associated standard deviation for the project as a whole. The decision-tree method of capital budgeting analyzes investment opportunities involving a sequence of decisions over time. Various decision points are defined in relation to subsequent chanceevents.TheNPVforeachdecisionstageiscomputedontheseriesofNPVsand probabilities that branch out or follow the decision point in question. In other words, once the rangeofpossibledecisionsandchanceeventsarelaidoutintree-diagramform,theNPVs associatedwitheachdecisionarecomputedbyworkingbackwardsonthediagramfromthe expected cash flows defined for each path on the diagram. TheoptimaldecisionpathischosenbyselectingthehighestexpectedNPVforthefirst-stage decision. Standard deviations for each first-stage NPV should be computed to determine risksassociatedwitheachdecision.Ifthereisnodominantdecision(e.g.,ifNPVishighest, butsoisstandarddeviation),thedecisionbecomesafunctionoftheriskattitudesof management. BothcapitalbudgetingmethodsdescribeduseexpectedNPVsandriskmeasures associated with the NPVs. In the probability distribution method, risk is defined in terms of the correlation among cash flowsinthevarioustimeperiodsthroughouttheprojectslife.Witheachsubsequenttime period,latercashflowdistributionsareinfluencedbypriorCFdistributions.Thismodel assumes that the CF distributions are known as are the probabilities associated with each flow, andthatonceaninvestmentdecisionismade,themanagementislockedintothatproject decision. In the decision-tree method, there is a sequence of investment decisions whose probability distributionscantakeonseveralvalues.Themanagerdoesnotbecomelockedintoone decision but rather has a range of possible outcomes as a result of a priorchoice from among several alternatives. Cash flows and NPVs are computed for each alternative series of possible decisions. An optimal decision path is chosen by evaluating the NPV and associated standard deviations of that NPV for each of the alternative first-stage decisions. 5.Becausethenumberofrandomvariablesassociatedwithcapitalbudgetingunder uncertainty may be large, it may be impossible to represent these in a model. To simulate thedistributionofNPVorIRR,simulationanalysisexplicitlyusesrangesofvaluesfor inputssuchasmarket,investmentcost,operating,andfixedcostinformation.The managerisbetterabletoincorporatedetailedinformationintothedecisionprocess through simulation methods. Procedure steps: a)Random and deterministic variables are defined. b)Value ranges for random variables are defined. c)Bymeanofarandomnumbergenerator,randomnumbersarechosenforeach random variable. d)From these random numbers, a set of values is created for each random variable. e)For each simulation, a series of cash flows and NPVs is calculated. f)Mean NPV, variance, and standard deviation are calculated from the NPVs from each simulation. g)Sensitivity analysis can be performed if ranges or distributions require change. 6.Thestatisticaldistributionmethodrequiresthattheprobabilitydistributionofcashflows bespecified foreach periodoftheprojects life.Usingtheseprobabilitydistributions,the meanandvarianceoftheprojectsNPVcanbecalculated.Adetaileddiscussionofthis method and examples are presented on pp.509 thru 515 and in Section 13.5.1. 7.Inflationcanintroducebiasintotheaccept/rejectdecisionwhenthecostofcapitalrate contains an element recognizing expected future rates of inflationwhereas the cash flow estimates dont include a similar component. Thereisaneedtoadjustthediscountrateforinflationinthatthenoninflationaryrequired rate of return should be grossed up by the expected rate of inflation. Present prices for physical goods cant be viewed as already accounting for future inflation; hence we need to derive estimates of the impact of future inflation on prices. The need to adjust depreciation levels for inflation is critical, because depreciation is based onthehistoricalcost ofthe asset. Theadjustmentistokeepthefirmstaxshieldinlinewith current price levels so that inflation doesnt have an adverse impact on capital investment. (See also Nelsons 5 propositions in question 6 Chapter 9.) A variety of adjustments can be made to account for inflationary effects. These include the risk-adjusteddiscountrate,thecertaintyequivalentmethod,adjustmentstotheinflation adjustment term used in the risk-adjusted discount rate and the certaintyequivalent methods, solvingfortheoptimallevelofinvestmentgivenanticipatedchangesinpricelevels,and estimating future cash flows by taking inflation into account. 8.Themultiperiodcapitalbudgetingdecisionproblemcanbesolvedbytheproductlife-cycle(PLC)approach,theCapitalAssetPricingModelmethod,orbyusingthemean-variance framework. A products life cycle can be broken up into 4 stages: development, growth, stabilization, and decline.Usingthisframeworkwecanexaminecashflowsassociatedwitheachstageinthe life cycle so that even very-long-term projects becomes easier to analyze. Beyond forecasting future cash flows, the PLC approach aids financial planning in terms of determiningfinancingneedsandtheabilityofthefirmtoimplementgivendividendpolicies. PLC facilitates cash-flow smoothing so as to reduce the firms business risk. FromPLC,riskisembeddedintotheestimatedcashflowsaccordingtowhatstagethe productisin.Intheintroductoryphase,marketacceptanceorrejectionoftheproduct determines what cash flows will follow. During the growth stage cash flows increase, whereas at maturity they level off, and during decline they fall. This sequence can be modeled using a decision-treeformatbyestimatingfuturecashflowsandattachingprobabilitiestothose estimates.NPVscanthenbecomputedalongwithexpectedvariances.Projectsatdifferent life-cycle phases can be combined to smooth the aggregate cash flow stream. TheCAPMcanbeextendedformultiperiodusewithseveralassumptionsconcerning homogeneousexpectationsrelatingtotheinvestmentprojectssuccessandtheassumption that there exists a single price of risk. With perfect capital markets for physical capital, the multi period project can be thought of as a series of single-period projects where the physical capital employed could be sold at its end-of-period market value. The critical point here is whether the one-periodreturnisconsideredfavorable.Ifperfectsecondarymarketsdontexist,expected salvagevalue must be built into the model. Depending on the degree of market imperfection, projects may be rejected on the basis of this revised secondary market value estimate. To the extentthatthecapitalisresalableatperfectmarketprices,thesingle-periodprocedureis viable. 9.BlackandScholesOptionPricingModel(OPM)hasenabledfinancialplannerstouse state-preference models in real-world decision making. The basic model is: 1 1n sst sts sPV VZ= ==, where PV = present value of the project, Vst = current value of a dollar for state s and time t, Zst = present value of cash flow for state s and time t. Thefollowingstepsareinvolvedinsolvingthisequation:Expectedcashflowsandpricesof moneyareformulatedfordifferentpossiblestatesoftheeconomy(i.e.,boom,normal,or recession). The state prices (Vst) are estimated using the OPM. The only changes in the option values formula are that here there is no exercise price and that the payoff is limited to $1. The above equation is solved and the PV obtained is compared with the initial level of investment. If the present value is greater than the investment, the project is accepted. This can be extended to a multiperiod framework. 10.a) Yes, Project A is less risky than Project B, since the coefficient of variation of Project A issmallerthanthatofProjectB. b)NPV(A) = ($15,000)(3.791) $60,000=$56,865$60,000 =$3,135 NPV(B) = ($25,000)(3.791) $80,000 = $94,775 $90,000 = $4,775 If cash flows over time are positively perfectly correlated, then (A) = (.2)($15,000)(3.791) = $11,373 (B) = (.4)($25,000)(3.791) = $37,910 c)Information from (b) can be used to do internal inferences; e.g., Pr. ( $3,135 2($11.373)) = 99.45% Pr. ($4,775 2($37,910)) = 99.45% d)Capitalbudgetingunderuncertaintyisageneralizedcaseofcapitalbudgetingunder certainty; thus basic financial capital budgeting theory and methodology is useful in both cases. 11. 5160020001 ( )ttiNPVER == ++ ( ) 5 10 15%iER = + = 51 2000 521.73 433.68 394.516002000(1343.05 298.31 1 .2811. 5)ttNPV== + + + + ++== + 12. a.E(Ri) = 5 + 1.8(7) = 17.6% b. 2 31000 1000 10002200(1 .176) (1 .176) (1 .176)NPV = + + ++ + + 2200 850.34 723.08 614.8611.72+ + +==

Since the NPV is less than zero, the project should be rejected. c.If net income in the third year is certain, the relevant required rate of return is equal to the risk free rate for the third period. Thus, 3850.34 723.0810002200(1 .05)NPV = + + ++ 2200 850.34 723.08 863.84237.26= + + += Since the NPV is larger than zero, the project would be acceptable. 13. a.Expected cash flow = (.3)(1000) + (.4)(3000) + (.3)(4000) = 300 + 1200 + 1200 = 2700Required rate of return = 5% + 2(10% 5%) = 15% 27002000 347.83(1 .15)NPV = =+ b.NPV = 347.83 = I + 2500(1 .05) + Thus, I = 347.83 + 2427.18 = 2079.35 The initial cost for project B is 2079.35 so that project B has the same NPV as project A. 14. Recall that E(Ri) = Rf + i[E(Rm) Rf]Thus, E(Ri) Rf = i[E(Rm) Rf] E(iXV) .05 = i[E(Rm) .05] E(Rm) = .1 E(Xi) = (400)[.2/(.2 + .1 + 0)] + (600)[.1/(2 + .1 + 0)] = 466.67 Eq.(1): E(iXV) .05 = 466.67V .05 = (.1 .05) E(Rm) = .15 E(Xi) = (400)[.1/(.1 + .2 + .1)] + (600)[.1/(.1 + .2 + .1] + (800)[.1/(.1 + .2 + .1)] = 600 Eq.(2): 600V .05 = (.15 .05) E(Rm) = .20 E(Xi) + 400[0/(0 + .1 + .2 + ] + 600[.1/.3] + 800[.2/.3] = 733.33 Eq.(3): 733.33V .05 = (.20 .15) SolvingforandVinequations(1),(2),and(3)wefindthatV=$6666.67whichisgreater than 6500. Thus, accept the opportunity. 15. ( )( ) 15%ioEXERV= = 1000$6667.15oV = = 1( ) [ ( ) ]1000 6667(.15 .05)333.33.05o m ffEX V ER RCER| = = = 16. a.E(RA) = (.3)(25) + (.4)(15) + (.3)(5) = 15% E(RB) = (.3)(30) + (.4)(15) + (.3)(0) = 15% Var(RA) = (.3)(25 15)2 + (.4)(15 15)2 + (.3)(5 15)2= 30 + 0 + 30 = 60 Var(RB) = (.3)(30 15)2 + (.4)(15 15)2 + (.3)(0 15)2= 6.75 + 0 + 6.75 = 135 Project A has the same expected return as project B, but has a lower variance. Thus, project A is preferred. b.E(Rm) = (.3)(20) + (.4)(10) + (.3)(0) = 10% Var(Rm) = (.3)(20 10)2 + (.4)(0) + (.3)( 10)2 = 30 + 0 + 30 = 60 Project A: C0V(RA, RM) = (.3)(25 15)(20 10) + (.4)(15 15)(10 10)+ (.3)(5 15)(0 10) = 30 + 0 + 30 = 60 601.0060A| = = E(RA) = 7 + 1.00(10 7) = 10.00% Project B: E(Rm) = 10 % COV(RB, Rm) = (.3)(30 15)(20 10) + (.4)(15 15)(10 10)+ (.3)(0 15)(0 10) = 90 901.560A| = = Thus, E(RB) = 7 + 1.5(10 7) = 11.5% 17. a. 11( , )[ ( ) ( ( ) )]mm f fmX RCE EX COV ER R RVarR= 50[450 (.12 .06)] .06.02(450 150) 0.06 5000 the firm's value= = = = b. 10( , )( ) [ ( ) ]mi f m fmXCOV RVER R ER RVarR= + 50 50006 (12 6).026 3 9%= + = += c.It implies a good opportunity for investors to invest in this company. 18. a.Expected Value of Annual Cash Flows: Project L Yr.1 1 CF = (.4)(300) + (.6)(400) = 360 Yr.2 2 CF = (.2)(200) + (.5)(500) + (.3)(700) = 500 Project K Yr. 1 1 CF = (.5)(400) + (.5)(600) = 500 Yr. 2 2 CF = (.3)(400) + (.4)(600) + (.3)(800) = 600 b.1) RADR RL = 6 + 0.9(12 6) = 11.4% Rk = 6 + 1.2(12 6) = 13.2% 1 2360 500323.16 402.90 726.06(1 .114) (1 .114)LNPV = + = + =+ + 1 2500 600441.70 468.23 909.93(1 .132) (1 .132)KNPV = + = + =+ + NOTE: There is no initial investment in this project. Since NPVk > NPVL project K is preferred. 2)CE Project L: 21 2 2(1.06) (1.06)0.95150.9054(1 .114) (1 .114)o o = = = =+ + Project K: 21 2 21.06 (1 .06)0.9364.87681 .132 (1 .132)o o+= = = =+ + 3)CE CAPM ThereisaproblemwithapplyingtheCECAPMformulationforthisprobleminthattheCE-CAPMisaone-periodmodeland/orassumesanannuity.Studentsmighttrytoapplythe formulation on page 222 of the text (in the discussion under equation 8-4) which relies on the initial investment to arrive at an estimate of the COV(X1, Rm). It is restated below: 221[1 ( )( )( )[ ( ) ]](1 )t M o M fo ttfX I ER RVR| o= =+ Since I0 = 0, then V0 is just the PV of Xdiscounted at the Rf rate. 2500 6001005.70(1 .06) (1 .06)KNPV = + =+ + 2360 500784.62(1 .06) (1 .06)LNPV = + =+ + It should be pointed out to the students that an approximation of the CE CAPM formulation for more than one period is given as follows: 21[ ( , ) ][ ( ) ](1 )nt t Mt m M fttfX COVX R ER RNPVRo= =+ If aCOV(X1,Rm)=COV(X2,RM)=50 forbothprojectsisassumed,thentheprojectsNPVs would be as follows: 2[ ( ) ][ ( , )] (50)(.06) .02 150m ft MtMER RCOVX Ro = = Then, 1 2360 150 500 150509.61(1 .06) (1 .06)LNPV = + =+ + 1 2500 150 600 150730.69(1 .06) (1 .06)KNPV = + =+ + 19. a.CE coefficients Project L: 12000.5555360o = = 23000.6000500o = = Project K: 1300.6000500o = = 2400.6670600o = = b.CE Method 1 2200 300188.68 267.00 455.68(1 .06) (1 .06)LNPV = + = + =+ + 1 2300 400283.02 356.00 639.02(1 .06) (1 .06)KNPV = + = + =+ + 20. The certainly equivalent and the RADR methods give the same present value whenever: (1 )(1 )tft tRko+=+ where k represents the risk adjusted discount rate. 21. a. 1 2700 900( ) 500 880.16(1 .10) (1 .10)ENPV = + + =+ + 2 21//41 222[33, 057.53 61, 471.21(200) (300)[ ]] [94528.74(1 .10) (1 .1]$307.450)NPVo= +== ++=+ b. 1 2700 900( ) 500 880.16(1 .10) (1 .10)ENPV = + + =+ + 1 2 200 300[ ](1181.82 247.93429.7.10) (1 105. )NPVo= +== ++ + c.Since the projects have the same expected NPV, the one with the lower amount of risk should be accepted. 22.a.Project: 1 CF = (.1)(4000) + (.8)(6000) + (.1)(8000) = 600021o= 800,000 1 = 894.43 2 CF = (.3)(4000) + (.4)(6000) + (.3)(8000) = 600022o= 2,400,0002 = 1549.19 216000( ) ( ) 10, 000 699.8(1 .08)A BtENPV ENPV== = =+ 1 21 21 2(1 ) (1 )894.43 1549.19

(1 .08) (1 .08) 2156.27NPVAi io oo = ++ += ++ += 2 21/ 2 1 2 1 22 4 31/ 22 4 32 0.5[ ](1 ) (1 ) (1 )800, 000 2, 400, 000 (05)(894.43)(1549.19)(2) [ ](1 .08) (1 .08) (1 .08) 1884.08NPVBi i io o o oo = + ++ + += + ++ + += b.Portfolio 1)A and existing (E): E(NPV)pE+A = E(NPV)E + E(NPV)A

= 10,000 + 699.8 = $10,699.80 pE+A = [(5,000)2 + (2,156.27)2 + 2(5,000)(2,156.27)(0)]1/2= $5,445.13 2)B and existing E(NPV)PE+B = E(NPV)E + E(NPV)B= 10,000 + 699.8= $10,699.8 PE+B = [(5,000)2 + (1,884.08)2 + 2(5,000)(1,884.08)(0.3)]1/2= 5,848.25 c.Project A is preferred since E(NPV)PE+A equals E(NPV)PE+B but PE+A is less than PE+B. 23. Without Phase II: 10 101 13, 000 5, 000( ) 0.3[ ] 0.7[ ] 5, 000 $22, 036.24(1 0.1) (1 0.1)t tt tENPV= == + =+ + With Phase II: 3 731 43 731 4315, 000 10, 000 1( ) (0.7)(0.8)[ [ ] ](1 0.1) (1 0.1) (1 0.1)5, 000 6, 000 1 (0.7)(0.2)[ [ ] ](1 0.1) (1 0.1) (1 0.1)3, 000 (0.3)(0.5)[(1 0.1)t tt tt tt tttENPV= == === ++ + ++ ++ + ++ ++ 7343 731 434, 000 1[ ] ](1 0.1) (1 0.1)3, 000 1, 000 1 (0.3)(0.5)[ [ ] ](1 0.1) (1 0.1) (1 0.1)7, 000 5, 000(1 0.1)26, 981.61ttt tt t== =+ ++ ++ + + += SincetheexpectedNPVwithPhaseIislargerthanthatwithoutittheimplementationoftwo stages is more profitable. 6. CAPITAL BUDGETING CASES (PRE-DECIDED): A. FALCON AIRLINES, INC. As owner of Falcon Airlines, you are considering the purchase of a new de-icing machine. The machine will be used to remove ice from the wings of Falcons planes duringwinter. The newmachinewillcost$98,000,shippingcostsof$2,000,andalsowillrequire$3,000in workingcapitaltosupportthenewmachinesoperation.Theequipmentwillbedepreciated over a 3-year period using MACRS and will have an expected salvage value of $4,000 at the endofitsexpectedeconomiclifeoffouryears.Theannualsavingsassociatedwiththe machineareexpectedtobe$25,000peryearforthenextfouryears.Thecompanywillnot deduct the salvage value from the machines cost when calculating depreciation. The existing de-icing machine is one year old but is not adequate for the companys needs; it can be sold today for $40,000. The equipment was purchased for $60,000 and was being depreciated over a three-year period using the MACRS method. Falcon uses a hurdle rate of 11% for its capital budgeting projects and has a marginal tax rate of 30%. Determine whether you should purchase the new de-icing machine. CHANGE IN DEPRICIATION DETRIMENTS OF CASH INFLOWS Yr. Net Savingsx(1- TR)+ Change inx Tax Rate =Cash Deprec.Inflow 1. $25,000x 0.70+ $6,600x $19,480 2. 25,000x 0.70+ 35,620x 28,186 3. 25,000x 0.70+ 10,360x 20,608 CASH OUTFLOWS (OR INITIAL INVETMENT) Cost of New Assets $98,000 Shipping2,000 Working Capital3,000 Sale Proceeds(40,000) Tax on Sales of Old Assets(see below)(6) Total Cash Outflows (Initial Investment) $62,994 TAX ON SALE OF OLD ASSET Original Cost$60,000 Selling Price$40,000 -Acc. Depreciation 19,980- Book Value40,020 Book Value $40,020Gain (loss) $20 Tax Gain = Gain * Tax rate = ($20) x 30%= ($6) 4. 25,000x 0.70+ 7,400x 19,720 5.0x0+ 0 x0 6.0x0+ 0 x0 7.0x0+ 0 x0 8.0x0+ 0 x0 9.0x0+ 0 x0 10. 0x0+ 0 x0 Does not include the Terminal Cash Flow( Shown below) Of$5,800 TERMINAL CASH INFLOWS (Year 4) Working Capital $3,000 + Salvage value of New Asset 4,000 - Tax on sale of New Asset

Salvage Value of New Asset$4,000 - Book Value 0 Gain/ Loss 4,000 x Tax Rate 30% Tax on salvage Value - 1,200 Total Terminal Cash Inflows $5,800 CASH OUTFLOWSCASH INFLOWS (0)Cost of New Assets $98,000 Shipping 2,000 Working Capital 3,000 Sale Proceeds(40,000) Tax on Sale of Old Assets (6) ----------- P.V.OF COSTS= $62,994 Cash Flowx PVFPVB (1)$19,480x 0.901 =$17,550(2) 28,186 x 0.812 =22,876. (3) 20,608 x 0.731 =15,068 (4) 25,520 x 0.659 =16,811 (5) 0 x0.000 = 0 (6) 0 x0.000 = 0(7) 0 x0.000 = 0(8) 0 x0.000 = 0(9) 0 x0.000 = 0(10) 0 x0.000 = 0 ----------- P.VOF BENEFITS $72,305 SUMMARY OF FINDINGS Net Present Value $9,311 Internal Rate of Return 17.57% Profitability Index =1.15 MODIFIED INTERNAL RATE OF RETURN CASH OUT FLOWSCASH INFLOWS Cost of New Asset $98,000 Shipping $2,000 Working Capital$3,000 Sale Proceeds ($40,000) Tax on Sale of Old Asset($6) ----------- PV of COST=$62,994 Cash FlowxFVF =Future Value (1) 19,480 x1.368 = $26,641 (2) 28,186 x1.232 = $34,728 (3) 20,608 x1.110 = $22,875(4) 25,520 x1.000 = 25,520 (5)0 x 0 =0 (6)0 x 0 =0 (7)0 x 0 =0 (8)0 x 0 =0 (9)0 x 0 =0 (10)0 x 0 =0 -------------- FV of BENEFITS= $1,09,764 INTERPOLATION FOR IRR First Conduct the trail and error calculations to find the proper range of value Discount RatePVB

1763,726 732 I.R.R. 62,9941,269 18 62,457 Then set up the Proportion. X 732 ------= ------- 1% 1,269 Solve for the value of X X = 58% Solve for the Internal Rate of Return Internal Rate of Return=17.57% INTERPOLATION FOR IRR Payback Period CashCashAmount No. of YearOutflowsInflowsOwedYears

1 $62,994 62,9942 19,480 43,514 1 3 28,186 15,328 1 4 20,608 01.74 5 25,523 0060 0 0.0070 0 0.0080 0 0.0090 0 0.00 10 0 0 0.00 Payback Period 2.74Yrs. B. PRINCESS CRUISE LINES, INC. PrincessCruiseLines ownsfivecruiseshipsthat operatecontinuouslyintheCarribean Sea. Asthechieffinancialofficer,youareconsideringthepurchaseofanewmachinetoremove barnacles from the bottom of the ships when they are in dry dock.The new machine will cost $3,300,000,shippingcostsof$18,000,andalsowillrequire$37,000inworkingcapitalto support the new machines operation. The equipment will be depreciated over a 3-year period using MACRS and will have an expected salvage value of $120,000 at the end of its expected economic life of four years. The annual savings associated with the machine are expected to be $1,000,000 per year for the next four years. (The company will not deduct the salvage value from the machines cost when calculating depreciation.) Princesscurrentlyownsamachinewhichwillprovidethissamefunction,butthemachineis old (4 years old) and tends to break down a lot. This machine can be sold today for $160,000. The equipment was purchased four years ago for $2,800,000 and was being depreciated over a three-year period using the MACRS method. Princessusesahurdlerateof8%foritscapitalbudgetingprojects;itsmarginaltaxrateis 40%. Determine whether you should purchase the new barnacle removing machine by conducting a capital budgeting analysis using various measures of profitability. CASH OUTFLOWS (OR INITIAL INVESTMENT) Cost of New Assets$3,300,000 Shipping$18,000 Working Capital$37,000 Sale Proceeds($1,60,000) Tax on sale of Old Assets64,000 Total Cash Outflows(Initial Investment) $32,59,000 TAX ON SALE OF OLD ASSET Original Cost $2,80,000 -Accumulated Dep. 2,80,000 Book Value 0 Selling Price$1,60,000 Book Value0 Gain/ Loss $1,60,000 Tax Gain = Gain * Tax rate = $1,60,000 * 40%=$64,000 CHANGE IN DEPRECIATION DepreciationDepreciationChange on New Assets- on Old Assets= in Dep. Next Year =$11,04,894 -0=$11,04,894 Year2 =$14,76,510 -0=$14,76,510 Year3 =4,91,064 -0=4,91,064 Year4=2,45,532 -0=2,45,532 Year5=0 -0=0Year6=0 -0=0Year7=0 -0=0Year8=0 -0=0Year9=0 -0=0Year10=0 -0=0 DETERMINATION OF CASH INFLOWS

Change in CashYr.Net Savings x(1 TR)+Depreciation x Tax Rate = Inflow 1. $10,00,000x 0.60+ $11,04,894x0.40= 10,41,958 2. 10,00,000x 0.60+ 14,76,510x0.40= 11,90,604 3. 10,00,000x 0.60+4,91,064 x0.40= 7,96,426 4. 10,00,000x 0.60+ 2,45,532x0.40= 6,98,213 5. 0x0+0 x 0=06. 0x0+0 x 0=07. 0x0+0 x 0=08. 0x0+0 x 0=09. 0x0+0 x 0=010. 0x0+0 x 0=0 Does notinclude the Terminal Cash Flows (Shown Below) of $1,09,000 TERMINAL CASH INFLOW YEAR 4 CASH OUTFLOWSCASH INFLOWS (0) Cost of New Asset $33,00,000 Shipping 18,000 Working Capital 37,000 Sale Proceeds (1,60,000) Tax on Sale of Old Assets 64,000

--------------- P.V. OF COSTS = $32,59,000 Cash InflowxPVF=PVB (1) 10,41,958x09.26 = 964776 (2) 11,90,604x0.857 =1020751 (3)7,96,426 x0.794 = 632228 (4)8,07,213 x0.735 = 593326 (5) 0x0=0 (6) 0x0=0 (7) 0x0=0 (8)P.V.OFBENEFITS $32,11,080SUMMARY OF FINDINGS Net Present Value = ($47,920) Internal Rate Return=7.30% Modified Int. Rate of Return =7.60% Profitability Index= 0.99 Payback Period(Yrs)= 3.28 0x0=0 (9) 0x0=0 (10) 0x0=0 -------------- MODIFIED INTERNAL RATE OF RETURN CASH OUTFLOWSCASH INFLOWS Cost of New Assets $33,00,000 Shipping $18,000 Working Capital $37,000 Sale Proceeds($1,60,000) Tax on Sale of Old Asset $64,000 -------------- P.V. OF COSTS= $32,59,000 Cash FlowxFVF= Future Value (1)10,41,958 x1.260 = $13,12,566 (2)11,90,604 x1.166 = 13,88,721 (3)7,96,426 x1.080 =8,60,140 (4)8,07,213 x1.000 =8,07,213 (5)0 x 0 = 0 (6)0 x 0 = 0 (7)0 x 0 = 0 (8)0 x 0 = 0 (9)0 x 0 = 0 (10)0 x 0 = 0 -------------- F.V. OF BENEFITS =$43,68,639 INTERPOLATION FOR IRR First, Conduct the trial-and-error calculations to find the proper range of values. DiscountRate P.V.B. 7 32,79,651 I.R.R.32,59,000 8 32,11,080 Then set up the proportion. X20,651 ----------- = --------------- 1%68,571 Solve for the Value of X X=0.30% Solve for the Internal Rate of Return Internal Rate of Return =7.30% PAYBACK PERIOD Cash Cash AmountNo. of YearOutflowInflowOwedYears 032,59,000 32,59,000 110,41,958 22,17,0421.00 211,90,604 10,26,4381.00 37,96,426 2,30,0131.00 48,07,2130 0.28 5 0 00 6 0 00 7 0 00 8 0 00 9 0 00 10 0 00 Payback Period =3.28Yrs. . 7. CASE STUDIES (SELF ASSESSMENT) A. WIPRO BPO -- NEW PROCESS -- PEPBOYS Wipro-BPOconsideringthepurchaseofanewWorkstations40No.Thesewillcost$67,000, transportation (or freight) of $3,000, and also will require $4,000 in working capital to support thenewprocessoperation.Theequipmentwillbedepreciatedovera3-yearperiodusing MACRSandwillhaveanexpectedsalvagevalueof$1,500attheendofitsexpected economic life of four years. The annual savings associated with the Assets are expected to be $30,000 per year for the next three years and $20,000 in the fourth year. The company will not deduct the salvage value when calculating depreciation. Theexistingworkstationswerealmostwornoutbutcanstillbesoldfor$12,000.The equipmentwaspurchasedthreeyearsearlierfor$50,000andwasbeingdepreciatedovera three-year period using the MACRS method. Wipro-BPO uses a hurdle rate of 12% for its capital budgeting projects and has a marginal tax rate of 30%. ForsettingupthisprocessandforCapitalbudgetingpurposefollowingquestionsare supposed to solved: a.Determinethedepreciationassociatedwiththenewequipment,aswellastheunused depreciation on the old equipment. b.Determinethecashinflows(afterdepreciationandtaxes)associatedwiththenew equipment. c. Determine thecash outflowsassociated with the equipment. Show each of the items that would appear in the T-account. Then showboth the cash inflows and cash outflows in the T-account. d. Determine (1) the net present value, (2) the profitability index, (3) the internal rate of return, and (4)the payback period of the proposed project. Pep-Boys Process Solution. The cash outflows for Wipro-BPO in case of Pep-Boys new workstations are as follows: Cost of new asset$67,000 Freight3,000 Working Capital4,000 Sale Proceeds of the old asset(12,000) Tax on Sale of Old Asset2,490 Present value of the Cash Outflows$64,490 The cash inflows are: Year 1$26,883 Year 230,345 Year 324,108 Year4(includingterminalcashflowsof $5,050.) 20,604 Using the hurdle rate of 12%, the present value of these cash inflows is $78,461. The net present value of the new asset is $13,971. The profitability index is 1.22. The internal rate of return is 22.45%. The payback period is 2.30 years. (Small differences caused by rounding errors are allowable,) B. WIPRO BPO -- NEW PROCESS -- MSN Consideringthepurchaseofanewcomputernetworkforthecompanysofficestaff.The existing computer equipment can be sold for a total of $17,000. The equipment was purchased fouryearsearlierfor$97,000andwasbeingdepreciatedoverafive-yearperiodusingthe MACRS method. The new computer equipment will cost a total of $83,000, require modifications to the buildings electricalwiringof$2,300,andalsowillrequire$3,500inworkingcapitaltosupportthenew equipments operation. The equipment will be depreciated over a 5-year period using MACRS and will have an expected salvage value of $4,500 at the end of its expected economic life of six years. Thecompanywillnotdeductthesalvagevaluewhencalculatingdepreciation.Theannual savingsareexpectedtobe$20,000peryearforeachyearoftheequipmentsexpectedsix year life. Current Recording Studios uses a hurdle rate of 14% for all potential capital budgeting projects and has a marginal tax rate of 35%. Now the Question raised for solving this problem were:

a.Determinethedepreciationassociatedwiththenewequipment,aswellastheunused depreciation on the old equipment. b.Determinethecashinflows(afterdepreciationandtaxes)associatedwiththenew equipment. c. Determine thecash outflowsassociated with the equipment. Show each of the items that would appear in the T-account. Then showboth the cashinflows and cash outflows in the T-account. d. Determine (1) the net present value, (2) the profitability index, (3) the internal rate of return, and (4) the payback period of the proposed project. Solution The cash outflows of the new computer network are: Cost of new asset$83,000 Modifications to wiring2,300 Working Capital3,500 Sale Proceeds of the old asset(17,000) Tax on Sale of Old Asset77 Present value of the Cash Outflows$71,877 The cash inflows are: Year 1$15,067 Year 220,585 Year 318,732 Year 416,433 Year 516,433 Year6(includingterminalcashflowsof $6,425.) 21,157 At 14%, the present value of these cash inflows is $69,592. The net present value of the new computer network is ($2,285). The profitability index is 0.97. The internal rate of return is 12.86%. The payback period is 4.06 years. (Small differences caused by rounding errors are allowable,) .................References................................