Corporate Finance Formula Sheet
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Receivables Turnover=Sales/AR Times Int. Earned=EBIT/interest Accounting veil: not affect stock prices Break Even: Accounting: Q= (FC+D)/P-‐V Total OCF= OCF – addition to NWC-‐capital spending Cash Q= (FC)/P-‐V Can only service op. costs not investment
NI=0 Payback=N NPV<0 IRR=0
OCF=0 Payback=infinity NPV=Co<0 IRR=-‐100%
Financial: Payback=N Q= (FC+OCF*)/P-‐V NPV=0 OCF*=Co/PVAF IRR=r DOL= 1+ (FC/OCF) DOL= degree to which Change project relies on fixed OCF=DOL*%change in Q costs Bond Value= PV(Coupons) + PV(FV) HPR=(P1-‐P0)/P0 SML𝑅! = 𝑅! + 𝑅! − 𝑅! 𝑋𝐵! Does not require companies to apy dividends & have steady growth, base calculations on 2 estimates, explicitly considers risk. Fixed Asset Turnover= sales/net fixed assets Total; Debt Ratio= (Assets-‐Equity)/Assets
Capital Intensity Ratio:Total Assets/Sales (use % of sales approach)
Efficient Market: NPV=0, well organized markets are efficient, investors get what they pay for, firms get exact value. Holding Period Yield: Rate where Co= PV(cash inflows) Price Earnings: P=EPS/R +NPVGO DFL = EBIT/(EBIT-‐Interest) =%change in EPS/%change in EBIT Long Term Debt Ratio = LT Debt/LT Debt+equity
Equity Multiplier: Total Assrts/Total Equity Days Sales in Receivable =365/receivables turnover M&M Proposition 1 𝐸𝐵𝐼𝑇 𝑉! = ! = 𝑉! 𝑅! (𝐶𝑜𝑠𝑡 𝑜𝑓 𝐶𝑎𝑝𝑖𝑡𝑎𝑙) = 𝐸 + 𝐷 Arbitrage Opp when Vl
Cost of equity rises as debt increase Equity Risk=business + financial M&M Proposition 1 with Tax 𝐸𝐵𝐼𝑇 1 − 𝑇 𝑉! = ! 𝑅! 𝐶𝑜𝑠𝑡 𝑜𝑓 𝐶𝑎𝑝𝑖𝑡𝑎𝑙 𝑉! = 𝑉! + 𝑇(𝐷) straight line with slope of Tc. Y intercept of Vu Compound G of Dividends: (𝐷! )!/! − 1 And (1+r)*(1+r)^1/t -‐ 1 M&M Proposition 2 with taxes: 𝐷 𝑅! = 𝑅! + (𝑅! − 𝑅! )(1 − 𝑡) 𝐸 𝐸 = (𝐸𝐵𝐼𝑇 − 𝑅! 𝐷)(1 − 𝑡)/𝑅! CAPM: 𝐸𝑅! = 𝑅! + 𝐸𝑅! − 𝑅! 𝑋𝐵! 𝐷 𝐵! = 𝐵! 𝑋(1 + ) 𝐸 Interval Measure: current assets/avg. daily op. costs
DuPoint ROE = NI/Total Equity =(NI/Assets) X (Total Assets/Total Equity) =(NI/S) X (S/A) X (A/E) =(NI/S) X (S/A) X (1+ D/E) =Profit Margin x total asset turnover x equity multiplier Dividends: Share price cum div = equity/#of sharesw Share price ex div = share price – div Share price =PV(all future divs) Dividend Payout Ratio = Dividends/NI
Cost of Equity Capital=R=(D1/Po) +g = dividend yield +capital gains yield Point of financial leverage Indifference: EPS(with Debt)=EPS(without Debt) EBIT = interest/ 1 – (#shares with debt/#shares without Debt) Nominal Risk Prem=Avg. Nom Return-‐Risk free= arithmetic Real Risk Free Rate= Risk free – avg. infl. Real Risk Prem=Avg Real return-‐ RealRisk Free Dilution: NI increases by ROE x New issue amount New Market share price: use EPS not sale price
Effective Annual Rate: Home 250,000 Downpmt 12500 Loan 237,500 Term 120m APR 13% SEMI ANNUAL COMPOUND EAR (1+6.5%)^2 -‐1 =0.134225 Effective monthly rate (1+EAR)power(1/12) -‐1 Set your calculator to BEG PV =-‐237,500 T=120 R=1.0551 FV=0 THEN COMPUTE PMT = 3462.31 Check: EAR =𝑒 ! − 1
Theoretical Value of a right: 𝑀! − 𝑆 𝑅! = 𝑛 + 1 𝑀! =common share price with rights S=subscription Price N= # of rights required to buy 1 share=#old shares/#of new shares 𝑴𝒆 = 𝑀! − 𝑅! = share price exrights 𝑹𝒆 = (𝑀! − 𝑆)/𝑁 = Ex rights value of a right Funds raised= S*#new shares Dollar Flotation cost= funds raised – net proceeds % Flotation Cost= Dollar FC/Funds Raised
Return on Portfolio: 𝐸𝑅! = 𝑊! ×𝐸𝑅! + (𝑊! ×𝐸𝑅! ) EFN = -‐ pSR + g(A-‐pSR) =A(g)-‐pSR(1+g)-‐CL(g) Exact Fisher Effect: (1+Rnom)=(1+Rreal) x (1+infl)
𝐵! = 𝑊! ×𝐵! + (𝑊! ×𝐵! (= 0))
BASE CASE NPV PV(ATOCF)+(PV(CCATS)+PV(Salvage)+ PV(NWC Recovered)-‐ Co-‐Initial NWC
NWC to total assets = (current assets-‐current liabilities)/total assets NWC Turnover=Sales/NWC OCF Basic = EBIT+D-‐Taxes Private Leverage: OCF Bottom up= NI+D Leverage reduces value of firm OCF TopDown=S-‐Costs-‐Taxes when: OCF Tax Shield= (S-‐C)(1-‐T)+(D*T) 1 − 𝑇! < (1 − 𝑇! )(1 − 𝑇! ) Analysis OCF=[(P-‐V)Q-‐FC) X (1-‐T)]+TD 𝑏 = 𝑝𝑟𝑖𝑣𝑎𝑡𝑒 𝑖𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝑟𝑎𝑡𝑒 C=corporate tax rate Annuity: S=private dividend tax rate Annuity Due=PMT PVAF(1+r) If> then increases !"# !!! ! If = then indifferent PVgrowing Annuity = [1 − ] !!! !!! If B=S then leverage increases PVgrowing perp = PMT/r-‐g firm value P/E =price/EPS Capital Budgeting Alternatives: P Index= PV(cash flows)/Investment > 1 NPV (may lead to wrong dec. when mut. Ex) IRR (IRR>R = accepted) Profit Margin=NI/Sales Payback Ruke ROA=NI/Total Assets Discounted Payback rule Retention ratio= pSR X(1+g) or RE/NI Avg. Accounting Return Std Dev on Calculator: Capital Budgeting: adjust for 2nd F, Mode,0,0,Mode,1,0, data enter, time value? Adjust for risk? alpha, 5 = Provide information & value Reward to Risk= (ERi – Rf)/Betai @equilibrium:RTRA=RTRB=RTRp r^2=portion of total risk that is systematic Growth =b x ROE
Sustainable=(ROE X R)/(1-‐(ROE X R))
Internal Growth: =pSR/(A-‐pSR) ROA X R)/(1-‐(ROA X R)) 𝑾𝑨𝑭𝑪 = (𝑊! ×𝐹𝐶! ) + (𝑊! ×𝐹𝐶! ) Total Amnt raised =Project Cost/1-‐WAFC Capital Structure Weights= MV(Debt)=BondPrice*#bonds/Assets MV(Equity)= Price*#shares/assets MV(PS)=PS Price*#of PS/Assets Unlevered/Levered Borrowing: D/E=0.5, EPS=2.5, i=10% D=0.5E, @ E=2000, D=1000. Total=3000, #shares=3000/20=150, Expected Payoff=EPS(Shares)-‐ (1000*0.1)=375-‐100=275, Expected Payoff=375+100=475 (lender) ! !! Stock Valuation= 𝑝! = ! ! Constant Growth: 𝑝! =
!!! !!
!!!
Supernormal Growth = 𝑝! =
!! (!!!)!
+
𝑃𝑡/ 1 + 𝑟 𝑡 Funds to be Raised = Net Proceeds/1-‐flotation spread MV(Before)=#of old shares * Rights on share price MV(after)=(Total *Me)-‐(#of new shares*S) 0.010551
@Sustainable g, company can increase sales & Assets without selling equity. Debt can increase Calculator to Find IRR Cfi,2ndf, CA,ON,data,ON,2ndf,cash,2ndf,CA Nonconventional Cash flows: use diff between cash flows for each project and use as entries MIRR: Method 1: discount 2nd negative cash flow back to Co Method2: FV all cash flows and add to last negative cash flow.3)use both methods simult. Replacement of equipment: NPV= Net Investment + PV (ATOCF) +PV(net salvage value=salvage of old-‐salvage of new)+PV(CCATS, C=New cost-‐old salvage) Setting Price on a bid: NPV=0=Capital spending+PF(Salvage)+addition/ recovery of NWC+PV(ATOCF)(S-‐ C)(1-‐T) + tax sield on CCA. Then find S and Q.
Avg Account. Return: Avg.NI/Avg Investment(1/2 of Co, need target)
EFN=increase in total assets-‐ addition to RE-‐New Borrowing
Dividend Growth Model: Re=(D1/Po)+g Days Sales in Inventory=365/Inventory Turnover
Approximate: Rnom=Rreal+infl.
Inventory Turn. =COGS/Inv. EAC = PV(Costs)/ PVAF
Equally risky investments=equally risky returns
Homemade leverage: assumption that individuals can lend& borrow at same rate as the firm
NI=0 Payback=N NPV<0 IRR=0
OCF=0 Payback=infinity NPV=Co<0 IRR=-‐100%
Financial: Payback=N Q= (FC+OCF*)/P-‐V NPV=0 OCF*=Co/PVAF IRR=r DOL= 1+ (FC/OCF) DOL= degree to which Change project relies on fixed OCF=DOL*%change in Q costs Bond Value= PV(Coupons) + PV(FV) HPR=(P1-‐P0)/P0 SML𝑅! = 𝑅! + 𝑅! − 𝑅! 𝑋𝐵! Does not require companies to apy dividends & have steady growth, base calculations on 2 estimates, explicitly considers risk. Fixed Asset Turnover= sales/net fixed assets Total; Debt Ratio= (Assets-‐Equity)/Assets
Capital Intensity Ratio:Total Assets/Sales (use % of sales approach)
Efficient Market: NPV=0, well organized markets are efficient, investors get what they pay for, firms get exact value. Holding Period Yield: Rate where Co= PV(cash inflows) Price Earnings: P=EPS/R +NPVGO DFL = EBIT/(EBIT-‐Interest) =%change in EPS/%change in EBIT Long Term Debt Ratio = LT Debt/LT Debt+equity
Equity Multiplier: Total Assrts/Total Equity Days Sales in Receivable =365/receivables turnover M&M Proposition 1 𝐸𝐵𝐼𝑇 𝑉! = ! = 𝑉! 𝑅! (𝐶𝑜𝑠𝑡 𝑜𝑓 𝐶𝑎𝑝𝑖𝑡𝑎𝑙) = 𝐸 + 𝐷 Arbitrage Opp when Vl
Cost of equity rises as debt increase Equity Risk=business + financial M&M Proposition 1 with Tax 𝐸𝐵𝐼𝑇 1 − 𝑇 𝑉! = ! 𝑅! 𝐶𝑜𝑠𝑡 𝑜𝑓 𝐶𝑎𝑝𝑖𝑡𝑎𝑙 𝑉! = 𝑉! + 𝑇(𝐷) straight line with slope of Tc. Y intercept of Vu Compound G of Dividends: (𝐷! )!/! − 1 And (1+r)*(1+r)^1/t -‐ 1 M&M Proposition 2 with taxes: 𝐷 𝑅! = 𝑅! + (𝑅! − 𝑅! )(1 − 𝑡) 𝐸 𝐸 = (𝐸𝐵𝐼𝑇 − 𝑅! 𝐷)(1 − 𝑡)/𝑅! CAPM: 𝐸𝑅! = 𝑅! + 𝐸𝑅! − 𝑅! 𝑋𝐵! 𝐷 𝐵! = 𝐵! 𝑋(1 + ) 𝐸 Interval Measure: current assets/avg. daily op. costs
DuPoint ROE = NI/Total Equity =(NI/Assets) X (Total Assets/Total Equity) =(NI/S) X (S/A) X (A/E) =(NI/S) X (S/A) X (1+ D/E) =Profit Margin x total asset turnover x equity multiplier Dividends: Share price cum div = equity/#of sharesw Share price ex div = share price – div Share price =PV(all future divs) Dividend Payout Ratio = Dividends/NI
Cost of Equity Capital=R=(D1/Po) +g = dividend yield +capital gains yield Point of financial leverage Indifference: EPS(with Debt)=EPS(without Debt) EBIT = interest/ 1 – (#shares with debt/#shares without Debt) Nominal Risk Prem=Avg. Nom Return-‐Risk free= arithmetic Real Risk Free Rate= Risk free – avg. infl. Real Risk Prem=Avg Real return-‐ RealRisk Free Dilution: NI increases by ROE x New issue amount New Market share price: use EPS not sale price
Effective Annual Rate: Home 250,000 Downpmt 12500 Loan 237,500 Term 120m APR 13% SEMI ANNUAL COMPOUND EAR (1+6.5%)^2 -‐1 =0.134225 Effective monthly rate (1+EAR)power(1/12) -‐1 Set your calculator to BEG PV =-‐237,500 T=120 R=1.0551 FV=0 THEN COMPUTE PMT = 3462.31 Check: EAR =𝑒 ! − 1
Theoretical Value of a right: 𝑀! − 𝑆 𝑅! = 𝑛 + 1 𝑀! =common share price with rights S=subscription Price N= # of rights required to buy 1 share=#old shares/#of new shares 𝑴𝒆 = 𝑀! − 𝑅! = share price exrights 𝑹𝒆 = (𝑀! − 𝑆)/𝑁 = Ex rights value of a right Funds raised= S*#new shares Dollar Flotation cost= funds raised – net proceeds % Flotation Cost= Dollar FC/Funds Raised
Return on Portfolio: 𝐸𝑅! = 𝑊! ×𝐸𝑅! + (𝑊! ×𝐸𝑅! ) EFN = -‐ pSR + g(A-‐pSR) =A(g)-‐pSR(1+g)-‐CL(g) Exact Fisher Effect: (1+Rnom)=(1+Rreal) x (1+infl)
𝐵! = 𝑊! ×𝐵! + (𝑊! ×𝐵! (= 0))
BASE CASE NPV PV(ATOCF)+(PV(CCATS)+PV(Salvage)+ PV(NWC Recovered)-‐ Co-‐Initial NWC
NWC to total assets = (current assets-‐current liabilities)/total assets NWC Turnover=Sales/NWC OCF Basic = EBIT+D-‐Taxes Private Leverage: OCF Bottom up= NI+D Leverage reduces value of firm OCF TopDown=S-‐Costs-‐Taxes when: OCF Tax Shield= (S-‐C)(1-‐T)+(D*T) 1 − 𝑇! < (1 − 𝑇! )(1 − 𝑇! ) Analysis OCF=[(P-‐V)Q-‐FC) X (1-‐T)]+TD 𝑏 = 𝑝𝑟𝑖𝑣𝑎𝑡𝑒 𝑖𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝑟𝑎𝑡𝑒 C=corporate tax rate Annuity: S=private dividend tax rate Annuity Due=PMT PVAF(1+r) If> then increases !"# !!! ! If = then indifferent PVgrowing Annuity = [1 − ] !!! !!! If B=S then leverage increases PVgrowing perp = PMT/r-‐g firm value P/E =price/EPS Capital Budgeting Alternatives: P Index= PV(cash flows)/Investment > 1 NPV (may lead to wrong dec. when mut. Ex) IRR (IRR>R = accepted) Profit Margin=NI/Sales Payback Ruke ROA=NI/Total Assets Discounted Payback rule Retention ratio= pSR X(1+g) or RE/NI Avg. Accounting Return Std Dev on Calculator: Capital Budgeting: adjust for 2nd F, Mode,0,0,Mode,1,0, data enter, time value? Adjust for risk? alpha, 5 = Provide information & value Reward to Risk= (ERi – Rf)/Betai @equilibrium:RTRA=RTRB=RTRp r^2=portion of total risk that is systematic Growth =b x ROE
Sustainable=(ROE X R)/(1-‐(ROE X R))
Internal Growth: =pSR/(A-‐pSR) ROA X R)/(1-‐(ROA X R)) 𝑾𝑨𝑭𝑪 = (𝑊! ×𝐹𝐶! ) + (𝑊! ×𝐹𝐶! ) Total Amnt raised =Project Cost/1-‐WAFC Capital Structure Weights= MV(Debt)=BondPrice*#bonds/Assets MV(Equity)= Price*#shares/assets MV(PS)=PS Price*#of PS/Assets Unlevered/Levered Borrowing: D/E=0.5, EPS=2.5, i=10% D=0.5E, @ E=2000, D=1000. Total=3000, #shares=3000/20=150, Expected Payoff=EPS(Shares)-‐ (1000*0.1)=375-‐100=275, Expected Payoff=375+100=475 (lender) ! !! Stock Valuation= 𝑝! = ! ! Constant Growth: 𝑝! =
!!! !!
!!!
Supernormal Growth = 𝑝! =
!! (!!!)!
+
𝑃𝑡/ 1 + 𝑟 𝑡 Funds to be Raised = Net Proceeds/1-‐flotation spread MV(Before)=#of old shares * Rights on share price MV(after)=(Total *Me)-‐(#of new shares*S) 0.010551
@Sustainable g, company can increase sales & Assets without selling equity. Debt can increase Calculator to Find IRR Cfi,2ndf, CA,ON,data,ON,2ndf,cash,2ndf,CA Nonconventional Cash flows: use diff between cash flows for each project and use as entries MIRR: Method 1: discount 2nd negative cash flow back to Co Method2: FV all cash flows and add to last negative cash flow.3)use both methods simult. Replacement of equipment: NPV= Net Investment + PV (ATOCF) +PV(net salvage value=salvage of old-‐salvage of new)+PV(CCATS, C=New cost-‐old salvage) Setting Price on a bid: NPV=0=Capital spending+PF(Salvage)+addition/ recovery of NWC+PV(ATOCF)(S-‐ C)(1-‐T) + tax sield on CCA. Then find S and Q.
Avg Account. Return: Avg.NI/Avg Investment(1/2 of Co, need target)
EFN=increase in total assets-‐ addition to RE-‐New Borrowing
Dividend Growth Model: Re=(D1/Po)+g Days Sales in Inventory=365/Inventory Turnover
Approximate: Rnom=Rreal+infl.
Inventory Turn. =COGS/Inv. EAC = PV(Costs)/ PVAF
Equally risky investments=equally risky returns
Homemade leverage: assumption that individuals can lend& borrow at same rate as the firm
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