BRT Co has developed a new confectionery line that can be sold for $5·00 per box and that

is expected to have continuing popularity for many years. The Finance Director has proposed that investment in the new product should be evaluated over a four-year time-horizon, even though sales would continue after the fourth year, on the grounds that cash flows after four years are too uncertain to be included in the evaluation. The variable and fixed costs (both in current price terms) will depend on sales volume, as follows.

BRT Co has developed a new confectionery line that

The production equipment for the new confectionery line would cost $2 million and an additional initial investment of $750,000 would be needed for working capital. Capital allowances (tax-allowable depreciation) on a 25% reducing balance basis could be claimed on the cost of equipment. Profit tax of 30% per year will be payable one year in arrears. A balancing allowance would be claimed in the fourth year of operation.

The average general level of inflation is expected to be 3% per year and selling price, variable costs, fixed costs and working capital would all experience inflation of this level. BRT Co uses a nominal after-tax cost of capital of 12% to appraise new investment projects.

Required:

(a) Assuming that production only lasts for four years, calculate the net present value of investing in the new product using a nominal terms approach and advise on its financial acceptability (work to the nearest $1,000). (13 marks)

(b) Comment briefly on the proposal to use a four-year time horizon, and calculate and discuss a value that could be placed on after-tax cash flows arising after the fourth year of operation, using a perpetuity approach. Assume, for this part of the question only, that before-tax cash flows and profit tax are constant from year five onwards, and that capital allowances and working capital can be ignored. (5 marks)

答案

(a)NetpresentvalueevaluationofnewconfectioneryinvestmentComment:Theproposedinvestmentinthenewproductisfinanciallyacceptable,astheNPVispositive.Examiner’snote:Includingcapitalallowancetaxbenefitsbysubtractingcapitalallowances,calculatingtaxliabilityandthenaddingbackthecapitalallowancesisalsoacceptable.(b)Theproposaltouseafour-yeartimehorizonThefinancedirectorbelievesthatcashflowsaretoouncertainafterfouryearstobeincludedinthenetpresentvaluecalculation,eventhoughsaleswillcontinuebeyondfouryears.Whileitistruethatuncertaintyincreaseswithprojectlife,cuttingofftheanalysisafterfouryearswillunderestimatethevalueoftheinvestmenttotheextentthatcashflowsafterthecut-offpointareignored.Furthermore,sincethenewconfectionerylineisexpectedtobepopular,cashflowsafteryearfourcouldbesubstantial,increasingtheextentoftheundervaluation.Artificiallyterminatingtheevaluationafterfouryearshasacceleratedtherecoveryofworkingcapitalandhasalsoledtoalargebalancingallowance.Theseincreasedcashflows,whichariseinyearsfourandfiverespectively,willoverestimatethevalueoftheinvestment.ThevalueofcashflowsafterthefourthyearofoperationTheapproachhereshouldbetocalculatethepresentvalueoftheexpectedfuturecashflowsbeyondyearfour.Ifthebefore-taxcashflowsareassumedtobeconstantandiftheone-yeardelayintaxliabilitiesisignored,theyearfourpresentvalueoffuturecashflowsbeyondyearfourcanbeestimatedusingaperpetuityapproach.Ifinflationinyearfiveisignored,theyearfourpresentvalueofcashflowsfromyearfiveonwardswillbe:2,308,000x(1–0·3)/0·12=$13,463,000Theyearzeropresentvalueofthesecashflows=13,463,000x0·636=$8,562,468Ifoneyear’sinflationisincluded:2,308,000x1·03x(1–0·3))/0·12=$13,867,000Theyearzeropresentvalueofthesecashflows=13,867,000x0·636=$8,819,000Althoughthesecalculationsignorethecapitalallowancetaxbenefits(whichwilldecreaseeachyear)andtheincrementalinvestmentinworkingcapital(whichwillincreaseslightlyeachyear),thepresentvalueofcashflowsafteryearfourisstillsubstantial.(c)Examinernote:onlyTHREEwaysofincorporatingriskintoinvestmentappraisalwererequiredtobediscussed.RiskanduncertaintyRiskininvestmentappraisalreferstotheattachmentofprobabilitiestothepossibleoutcomesfromaninvestmentprojectandthereforerepresentsaquantifiedassessmentofthevariabilityofexpectedreturns.Uncertaintycannotbequantifiedbyattachingprobabilitiesandalthoughthetermsareoftenusedinterchangeably,thedifferenceisimportantininvestmentappraisal.SensitivityanalysisThisassessesthesensitivityofprojectNPVtochangesinprojectvariables.ItcalculatestherelativechangeinaprojectvariablerequiredtomaketheNPVzero,ortherelativechangeinNPVforafixedchangeinaprojectvariable.Onlyonevariableisconsideredatatime.Whenthesensitivitiesforeachvariablehavebeencalculated,thekeyorcriticalvariablescanbeidentified.Theseshowwhereassumptionsmayneedtobecheckedandwheremanagerscouldfocustheirattentioninordertoincreasethelikelihoodthattheprojectwilldeliveritscalculatedbenefits.However,sincesensitivityanalysisdoesnotincorporateprobabilities,itcannotbedescribedasawayofincorporatingriskintoinvestmentappraisal,althoughitisoftendescribedassuch.SensitivityanalysisThisassessesthesensitivityofprojectNPVtochangesinprojectvariables.ItcalculatestherelativechangeinaprojectvariablerequiredtomaketheNPVzero,ortherelativechangeinNPVforafixedchangeinaprojectvariable.Onlyonevariableisconsideredatatime.Whenthesensitivitiesforeachvariablehavebeencalculated,thekeyorcriticalvariablescanbeidentified.Theseshowwhereassumptionsmayneedtobecheckedandwheremanagerscouldfocustheirattentioninordertoincreasethelikelihoodthattheprojectwilldeliveritscalculatedbenefits.However,sincesensitivityanalysisdoesnotincorporateprobabilities,itcannotbedescribedasawayofincorporatingriskintoinvestmentappraisal,althoughitisoftendescribedassuch.ProbabilityanalysisThisapproachinvolvesassigningprobabilitiestoeachoutcomeofaninvestmentproject,orassigningprobabilitiestodifferentvaluesofprojectvariables.Therangeofnetpresentvaluesthatcanresultfromaninvestmentprojectisthencalculated,togetherwiththejointprobabilityofeachoutcome.ThenetpresentvaluesandtheirjointprobabilitiescanbeusedtocalculatethemeanoraverageNPV(theexpectedNPVorENPV)whichwouldariseiftheinvestmentprojectcouldberepeatedalargenumberoftimes.Otherusefulinformationthatcouldbeprovidedbytheprobabilityanalysisincludestheworstoutcomeanditsprobability,theprobabilityofanegativeNPV,thebestoutcomeanditsprobability,andthemostlikelyoutcome.Managerscouldthenmakeadecisionontheinvestmentthattookaccountmoreexplicitlyofitsriskprofile.Risk-adjusteddiscountrateItappearstobeintuitivelycorrecttoaddariskpremiumtothe‘normal’discountratetoassessaprojectwithgreaterthannormalrisk.Thetheoreticalapproachherewouldbetousethecapitalassetpricingmodel(CAPM)todetermineaproject-specificdiscountratethatreflectedthesystematicriskofaninvestmentproject.Thiscanbeachievedbyselectingproxycompanieswhosebusinessactivitiesarethesameastheproposedinvestmentproject:removingtheeffectoftheirfinancialriskbyungearingtheirequitybetastogiveanaverageassetbeta;regearingtheassetbetatogiveanequitybetareflectingthefinancialriskoftheinvestingcompany;andusingtheCAPMtocalculateaproject-specificcostofequityfortheinvestmentproject.AdjustedpaybackPaybackcanbeadjustedforrisk,ifuncertaintyisconsideredtobethesameasrisk,byshorteningthepaybackperiod.Thelogichereisthatasuncertainty(risk)increaseswiththelifeoftheinvestmentproject,shorteningthepaybackperiodforaprojectthatisrelativelyriskywillrequireittopaybacksooner,puttingthefocusoncashflowsthataremorecertain(lessrisky)becausetheyarenearerintime.Paybackcanalsobeadjustedforriskbydiscountingfuturecashflowswitharisk-adjusteddiscountrate,i.e.byusingthediscountedpaybackmethod.Thenormalpaybackperiodtargetcanbeappliedtothediscountedcashflows,whichwillhavedecreasedinvalueduetodiscounting,sothattheoveralleffectissimilartoreducingthepaybackperiodwithundiscountedcashflows.

发布时间：2023-01-09