DeterminingtheTargetCashBalanceAppendix27ACopyright?2010bytheMcGraw-HillCompanies,Inc.Allrightsreserved.McGraw-Hill/Irwin
CostsofHoldingCashOpportunityCostsTradingcostsTotalcostofholdingcashC*CostsindollarsofholdingcashSizeofcashbalanceTheinvestmenteforegonewhenholdingcash.Tradingcostsincreasewhenthefirmmustsellsecuritiestomeetcashneeds.
TheBATModelF=ThefixedcostofsellingsecuritiestoraisecashT=ThetotalamountofnewcashneededR=Theopportunitycostofholdingcash,i.e.,theinterestrate.TimeC123C2–Ifwestartwith$C,spendataconstantrateeachperiodandreplaceourcashwith$Cwhenwerunoutofcash,ouraveragecashbalancewillbeC2–Theopportunitycostofholding isC2–C2–×R
TheBATModelTimeCAswetransfer$CeachperiodweincuratradingcostofF.123C2–Thetradingcostis ×F–TC–TCIfweneed$Tintotalovertheplanningperiodwewillpay$F times.
TheBATModelC*SizeofcashbalanceOpportunityCostsTradingcosts
TheBATModelOpportunityCosts=TradingCostsTheoptimalcashbalanceisfoundwheretheopportunitycostsequalsthetradingcosts.MultiplybothsidesbyC
TheMiller-OrrModelThefirmallowsitscashbalancetowanderrandomlybetweenupperandlowercontrollimits.$TimeUCLWhenthecashbalancereachestheuppercontrollimitU,cashisinvestedelsewheretogetustothetargetcashbalanceC.Whenthecashbalancereachesthelowercontrollimit,L,investmentsaresoldtoraisecashtogetusuptothetargetcashbalance.
TheMiller-OrrModelMathGivenL,whichissetbythefirm,theMiller-OrrmodelsolvesforC*andUwheres2isthevarianceofnetdailycashflows.TheaveragecashbalanceintheMiller-Orrmodelis:
ImplicationsoftheMiller-OrrModelTousetheMiller-Orrmodel,themanagermustdofourthings:Setthelowercontrollimitforthecashbalance.Estimatethestandarddeviationofdailycashflows.Determ