EQUATION SHEET Principles Of Finance Final Exam

EQUATION SHEETPrinciples of FinanceFinal ExamFINANCIAL STATEMENT ANALYSISNet cash flow Net income Depreciation and amortizationDuPont equation: ROA Net profit margin Total assets turnover Net incomeSalesDuPont equation: ROE ROA SalesTotal assets Equity multiplierNet incomeTotal assets Pr ofit Total assets marginturnover Net income Sales Total assetsCommon equityEquitymultiplier Total assets Total assets Common equitySalesTHE FINANCIAL ENVIRONMENTNet proceeds from issue Amount of issue – Flotation costs (Amount of issue) x (1 – Flotation costs)Amount of issue Amount needed(Net proceeds) (Other cos ts) (1 Flotation costs)(1 Flotation costs)TIME VALUE OF MONEYLump-sum (single) payments:FV n PV(1 r)PV n 1 FV n FVnn(1 r ) n (1 r ) Annuity payments: n 1 (1 r )n - 1 t PMT(1 r PMT ) FVA nr t 0 n 1 (1 r )n - 1 FVA(DUE )n PMT (1 r ) t (1 r) PMT (1 r) r t 0

1 - 1 n n1 (1 r ) PMT PVA n PMT t r t 1 (1 r) 1 - 1 n 1 (1 r )n PVA(DUE )n PMT (1 r) PMT (1 r) t r(1 r) t 1 Perpetuities:PaymentPMT Interest raterPresent value of a perpetuity PVP Uneven cash flow streams:n 1n-1FV CFn CF1(1 r ) . CFn(1 r )0 CF (1 r )ttt 0 1 1 PV CFn CF1 . CFn 1 n (1 r ) (1 r ) n CF (1 r ) 1ttt 1Interest rates (yields):Periodic rate rPER rStated annual interest rate SIMPLENumber of interest payments per yearm Number of n Number Number of int erest nYRS mint erest periods PER of yearspayments per yearm r SIMPLE Effective EAR r- 1.0 (1 rPER )m - 1.0EAR 1 annual ratem Annual percentage rate APR rPER x mCOST OF MONEYDollar returnYield (Dollar income) (Capital gains) (Dollar income) (Ending value – Beginning value)Dollar returnDollar income Capital gains Beginning valueBeginning valueDollar income (Ending value - Beginning value)Beginning valueRate of return r Risk-free rate Risk premium r rRF RPRate of return r rRF RP rRF [DRP LP MRP] [r* IP] [DRP LP MRP]rTreasury rRF MRP [r* IP] MRPYield on an n-year bondrate Interest rate Interest rate Interest in Year n R R in Year 1 in Year 2 1n2n Rn

Valuation ConceptsGeneral valuation model: Value of V PV of CF CF1 CFn an asset 0(1 r )1(1 r )n n (1 r)CFtt 1tBond Valuation: 1 - 1 1 Bond V INT . INT M INT (1 rd )N M NValue d (1 )1 (1 r d)(1 r d)N rd rd Vd INT(1 YTM )Vd 1INT1(1 YT C)INT . (1 YTM ) . NINTN(1 YT C) Adjust rd, N, and INT if interest ispaid more than once per year.MYTM Yield to maturity(1 YTM )NMYTC Yield to call(1 YT C)NINT V d1 - V d 0rd YTM Bond yield Current Capital gains yieldyieldV d0V d0Stock Valuation:ˆStock V Pˆ D1 value s 0 (1 r )1s ˆD ˆDt (1 rs ) (1 r )t 1tsˆ(1 g) D1rs - grs - gConstant growth stock: P0 D0Nonconstant growth stock: P0 ˆDˆ 2Dˆ n Pˆnˆ Dn (1 gnorm ) ;wherePnrs gnorm(1 rs )1 (1 rs )2(1 rs )nDˆ 1 ˆˆ Pˆ P DDr̂s Stock yield Dividend Capital gains 1 g 1 1 0yieldyield P0 P0P0 gnorm normal, orconstant growth Economic EVA EBIT(1 T) Average cost Invested value addedof fundscapital Risk and Rates of ReturnExpected rate rˆ Pr r Pr r . Pr r 112 2nnof returnn Prriii 1nStandard deviation 2 (r r)ˆ Pr2ii 1i

nVariance 2 (r - r)ˆ Pr2iii 1nEstimated s n r(rt r )2 Pr tr r rn t 1r 1 2 nnt 1n 1Coefficient of variation CV tRisk Return rˆNrˆP w1rˆ1 w 2rˆ2 . w NrˆN w rˆj jj 1N P w1 1 w 2 2 . w N N w j jj 1Return Risk-free return Risk Premium rRF RPRP RPInvestment rInvestment Return - rRFRPM x βInvestmentrRF RPInvestmentrRF (RPM)βInvestmentrRF (rM - rRF)βInvestmentCapital BudgetingEvaluation techniques:Amount of the initial investment that is Number of years just unrecovered at the start of therecovery year Payback before full recovery of original investment Total cash flow generated duringtherecoveryyear Traditional payback—unadjusted cash flows are usedDiscounted payback—discounted cash flows, or present values, are usedNPV CF0 CF0 CF1CFn(1 r)1 (1 r)n CF1CFn(1 IRR)1 (1 IRR)nn (1 r)CFtt 0n t (1 IRR) 0t 0CFtIRR internal rate of returntnMIRR: PV of cash outflows FV of cash inflows(1 MIRR)n TV(1 MIRR)nn; (1 r) t 0COFtt CIF (1 r)tt 0(1 MIRR)nt

Cash Flow EstimationNet cash flow Net income Depreciation Return on capital Return of capitalSupplementaloperating cash flow t Cash revenuest - Cash expensest - Taxest NOIt (1 T) Deprt ( NOIt Deprt ) (1 T) T( Deprt )Cost of Capital Tax savingsAfter-tax component Bondholders' required rd -rd T rd (1-T) YTM(1 – T)cost of debtrate of returnassociated with debtComponent costDpsDps r ps of preferred stock(1F)P0NP 0ˆComponent cost r s rRF (rM -rRF )β s D1 g rˆsof retained earningsP0ˆ1ˆComponent costD re g D1 gof new equityP0 (1 - F)NP Proportion After-tax Proportion Cost of Proportion Cost of WACC of x cost of of preferred x preferred of common x common stock equity equity debt debt stock w dT rdT wps rps ws (rs or re )WACCTotal dollar amount of lower cost of capital of a given type Break PointProportion of this type of capital in the capital structurePlanning and ControlFull capacity sales Sales level Percent of capacity used to generate sales level Operating Breakeven AnalysisSalesTotal operatingTotalTotal revenuescostsvariable costs fixed costs(P Q) QOpBE TOC (V Q)FF P-V Contribution margin FSOpBE FF V Gross profit margin1- P

Degree ofPercentage change in NOI DOL operating leveragePercentage change in salesDOL ΔNOINOI ΔSalesSales ΔEBITEBIT ΔSales Sales ΔEBITEBIT ΔQ Q (Q P) - (Q V)S - VCGross profit (Q P) - (Q V) - FS - VC - FEBITFinancial Breakeven AnalysisEPS Earnings available to common stockholders (EBIT-I)(1-T)-Dps 0Number of common shares outstandingShrsCEBIT FinBE I Dps(1 - T)Degree ofPercent change in EPS DFL financial leveragePercent change in EBITDFL DFL EBITEBIT EBIT - IEBIT - [Financial BEP]EBITEBIT - IDegree of DTL total leverageDTL ΔEPSEPS ΔEBIT EBIT Financial BEP I When there is no preferred stock. ΔEPSEPS ΔSales Sales ΔEBIT ΔEPS EBIT x EPSΔEBIT ΔSalesSales EBIT DOL x DFLGross ProfitEBITGross Profitx EBITEBIT - [Financial BEP]EBIT - [Financial BEP]S - VCQ(P - V) EBIT - I[Q(P - V) - F ]- IWhen there is no preferred stock.Dps(1 - T)

(Q P) - (Q V) - F S - VC - F EBIT Financial Breakeven Analysis ps C Earnings available to common stockholders (EBIT-I)(1-T)-D EPS 0 Number of common shares outstanding Shrs ps FinBE D EBIT I (1 - T) û(36 EPS û(%,7 EBIT Degree of Percent change in EPS DFL financial leverage Percent change in EBIT