Formulas - Corporate Finance

Chapter 2 Accounts Receivable Days = Accounts Receivable / Average Daily Sales Accounts Payable Days = Accounts Payable / Average Daily Sales Cash Ratio = Cash / Current Liabilities Change in Stockholders Equity = Retained Earnings + Net sales of stock Change in Stockholders Equity = Net Income - Dividends + Sales of stock - Repurchases of stock Current Ratio = Current Assets / Current Liabilities Debt to Capital Ratio = Total Debt /( Total Equity + Total Debt) Debt-Equity Ratio = Total Debt / Total Equity Debt-to-Enterprise Value Ratio = Net Debt / (Market Value of Equity + Net Debt) Debt-to-Enterprise Value Ratio = Net Debt / Enterprise Value EBITDA = EBIT + Depreciation and Amortization Enterprise Value = Market Value of Equity + Debt - Debt EPS = Net Income / Shares Outstanding Gross Margin = Gross Profit / Sales Inventory Turnover = Annual Cost of Sales / Inventory Market Value of Equity = Shares outstanding*Market price per share Market-to-Book ratio = Market value of equity / Book Value of Equity Net Debt = Total Debt - Excess Cash & Short-term Investments Net Profit Margin = Net Income / Sales Operating Margin = Operating Income / Sales P/E ratio = Market Capitalization / Net Income P/E ratio = Share price / Earnings per Share Quich Ration = (Cash & Short-term Investments + Accounts Receivable) / Current Liabilities Retained Earnings = Net Income - Dividends ROA = (Net Income + Interest Expense) / Book Value of Assets ROE = Net Income / Book Value of Equity ROIC = EBIT (1 - tax rate) / (Book Value of Equity + Net Debt) ROE = (Net Income / Sales) * (Sales / Total Assets) * (Total Assets / Book Value of Equity) The Balance Sheet Equation = Assets = Liabilities + Shareholders’ Equity Equity Multiplier (book) = Total Assets / Book Value of Equity Equity Multiplier (market) = Total Assets / Market Value of Equity Chapter 3 Expected return of a risky investment = Expected gain at end of year / Initial cost NPV = PV(Benefits) - PV (Costs) NPV = PV(All projects cash flow) NPV (Buy security) = PV (All cash flows paid by the security) - Price (Security) NPV (Sell security) = Price (Security) - PV (All cash flows paid by the security) Price(Security) = PV (All cash flows paid by the security) r_s = rf + (risk premium for investment s) Return = Gain at End of Year / Initial Costs Chapter 4 C (load or annuity payment) = P / ((1/r)*(1-(1/(1+r)^n))) FV = C * (1+r)^n FV_n (cash flow stream) = PV * (1+r)^n FV_n (cash flow) = C*(1+r)*(1+r)*...*(1+r)=C*(1+r)^n FV(annuity) = C/r * (1-(1/(1+r)^n)) * (1+r)^n IRR (growing perpetuity) = (C/P) + g IRR (with two cash flows) = ((FV/P)^(1/n))-1 PV (C in perpetuity) = C/r PV (cash flow stream) = C_0 + C_1/(1+r) + C_2/(1+r)^2 + ... + C_n/(1+r)^n PV (growing perpetuity) = C / (r-g) PV (growing perpetuity) = C / (r-g) * (1-((1+g)/(1+r)^2)) PV (perpetuity) = C/(1+r) + C/(1+r)^2 +C/(1+r)^3 + ... PV (with g) = C / (1+r) + (C*(1+g))/((1+r)^2) + (C*(1+g)^2)/((1+r)^3) + ... PV_n (cash flow) = C / (1 + r)^n PV(annuity of C with interest rate r) = C * 1/r * (1-(1/(1+r)^n)) PV(annuity of C) = P - (P/(1+r)^n) Chapter 5 (1+EAR) = (1+(ARP/k))^k (1+EAR) = e^ARP ARP = ln(1+EAR) Equivalent n-Period Discount Rate = ((1+r)^n) -1 Growth in Purchasing Power = (1+r) / (1+i) Interest Rate (compounding period) = ARP / (k_periods/year) PV = C_n / ( 1+r_n)^n r (real) = (r-i) / (1+i) Chapter 6 CPN = (Coupon Rate * Face Value) / Number of Coupon Payments per Year P = FV / ((1+YTM)^n) P = CPN * (1/y) * (1-(1/(1+y)^n)) + (FV/(1+y)^n) P (coupon bond) = (CPN / 1 + YTM_1) + (CPN /( 1 + YTM_2)^2) + … + ((CPN+FV)/(1+YTM_n)^n) r_n = YTM YTM = ((FV/P)^(1/n))-1 YTM = (FV/P) - 1 Chapter 8 After-Tax Cash Flow from Asset Sale = Sale Price - (t * Gain on Sale) Book Value = Purchase Price - Accumulated Depreciation Free cash flow = (Revenues - Costs - Depreciation) * (1-t) + Depreciation - CapEx - ∆NWC Free cash flow = (Revenues - Costs * (1-t) - CapEx - ∆NWC + t * Depreciation Gain on sales = Sale Price - Book Value Income Tax = EBIT * t Net working capital = Current assets - Current liabilities Net working capital = Cash + Inventory + Receivables - Payables PV(FCF) = FCF / (1+r)^t PV(FCF) = FCF * (1/(1+r)^t) Unlevered Net Income = EBIT * (1-t) Unlevered Net Income = (Revenues - Costs - Depreciation) * (1-t) Chapter 9 Change in earnings = New investment * Return on new investment Div_t (dividend payout rate) = (Earnings / Shares Outstanding) * Dividend Payput Rate Earnings growth rate = Change in earnings / earnings Forward P/E = P_0/EPS_1 Forward P/E = (Div_1/EPS_1)/(r_e-g) Forward P/E = Dividend Payout Rate / (r_e - g) g = Retention rate * return on new investment New investment = Earnings * Retention Rate P_0 (constant growth) = Div / ( r_e - g ) P_0 (constant long-term growth) = (Div_1/(1+r_e)) + (Div_2/(1+r_e)^2) + … + (Div_n/(1+r_e)^n) + (1/(1+r_e)^n) * Div_(n+ P_0 (discounted free cash flow) = (V_0 + Cash_0 - Debt_0) / Shares outstanding_0 P_0 (dividend discount) = (Div_1/(1+r_e)) + (Div_2/(1+r_e)^2) + … + (Div_n/(1+r_e)^n) + (P_n/(1+r_e)^n) P_0 (multiple year) = (Div_1/(1+r_e)) + ((Div_2+P_2)/(1+r_e)^2) P_0 (one year) = (Div_1 + P_1) / (1+r_e) P_0 (total payment model) = PV (future total dividend and repurchases) / Shares outstanding P_n = Div_(n+1)/(r_e-g) r_e = (Div + P_1) / P_0 r_e (constant growth) = (Div_1 / P_0) + g V_0 (continuation) = (FCF_1/(1+r_wacc)) + (FCF_2/(1+r_wacc)^2) + … + ((FCF_n+V_n)/(1+r_wacc)^n) V_0 (discounted free cash flow) = PV (future free casg flow of firm) V_0(enterprise) = FCF/(r_wacc-g_fcf) V_n (continuation) = (FCF_(n+1)/(r_wacc-g_fcf)) V_n (continuation) = ((1+g_fcf)/(r_wacc-g_fcf))*FCF_n Chapter 10 E(R) = sum(Pr.*R) 1 + R_annual = (1+R_q1) * (1+R_q2) * (1+R_q3) * (1+R_q4) Cov(Ri,Rj) = E((Ri-E(Ri)*(Rj-E(Rj)) Cov(Ri,Rj) = (1/(t-1)) * sum(Ri-Ri_average) * (Rj-Rj_average) E (Rp) = E (sum(xi*Ri)) Market Risk Premium = E(R_market) - rf r_i (cost of capital) = rf + β * (E(R_market) - rf) R_p (weighted average) = (x_1*R_1) + (x_2*R_2) + … + (x_n*R_n) R_t+1 = ((Div_t+1 + P_t+1) / P_t) - 1 R(average) = (1/t) * (R_1+R_2+ … +R_t) SD(average) = SD (Individual Risk) / (number_of_observation^0,5) SD(R) = Var(R)^0,5 SD(Rp) arbitrary weights = sum( x * (SD/Ri) * corr(Ri, Rp) ) Sharpe ratio = (E(Rp)-rf)/SD(Rp) Var(R) = E((R-E(R))^2) Var(R) realized returns = (1/(t-1)) * sum( R_t - R_average)^2 Var(Rp) large portfolio = (1/n) * average_variance Var(Rp) two stock = x1^2*Var(R1) + x2^2*Var(R2) + 2*x1*x2*Cov(R1,R2) x_i (portfolio weights) = Value of investment i / total value of portfolio βi^p = (SD(Ri)*corr(Ri,Rp))/SD(Rp) Chapter 12 Effective after tax interest = r*(1-t) Net debt = Debt - Excess cash and short term investments r_u (unlevered) = ((E/(E+B)*r_e)+((D/(E+B)*r_d) r_wacc = ((E/(E+B)*r_e)+((D/(E+B)*r_d*(1-t)) r_wacc = r_u-(D/(E+D))*t*r_d β_u (unlevered) = ((E/(E+B)*β_e)+((D/(E+B)*β_d) Chapter 14 EPS = Earnings / Number of shares MarkV_E = MarkV_A - MarkV_Liabilities r_e = r_u + ((D/E)*(r_u-r_d)) β_e = β_u + ((D/E)*(β_u-β_d)) Chapter 15 Cash flow to investors with leverage = Cash flow to invester with leverage + interest tax shield Interest tax shield = Corporate tax rate * interest payments Market value of debt = PV (future interest payments) PV (Interest Tax Shield) = (t*interest)/rf PV (Interest tax shield) = t * Future Interest payments PV (Interest Tax Shield)_perpetual = D * t r* (effective tax advantage of debt) = ((1-t_i)-(1-t_c)*(1-t_e))/(1-t_i) T_ex* = 1-((1-t_e)/(1-t_i)) V_L = V_U + PV(Interest Tax Shield) V_L = V_U + (r * D) Chapter 16 V_L (agency) = V_U + PV(Interest Tax Shield) - PV(Financial Distress Costs) - PV(Agency Costs of Debt) + PV(Agency Benef V_L (optimal) = V_U + PV(Interest tax shield) - PV(Financial Distress Costs) Chapter 17 Div = 100*rf*(1-t) Div*(1-t) = (P_cum - P_ex)*(1-t_g) P_cum = P_ex + div_0 * ((1-t_d)/(1-t_g)) P_retain = (Div*(1-t_d))/(rf*(1-t_i)) t_d* (effective dividend t) = (t_d-t_g)/(1-t_g) t_retain = 1-(((1-t_c)*(1-t_g))/(1-t_i)) Chapter 18 V0_L = (FCF_1/(1+r_wacc)) + (FCF_2/(1+r_wacc)^2) + … APV (adjusted present value) = V_U + PV(Interest Tax Shield) Dt (debt capacity) = d * Vt_L FCFE (Free Cash Flow to Equity) = FCF - (1-t_c) * Interest payments + net borrowing Net borrowing at date t = D_t - D_(t-1) PV (Interest tax shield) = t_c * k * PV (FCF ) PV(t*int_t) = ((t*int_t)/((1+r_U)^t-1*(1+r_d)) r_wacc (project) = (r_u) - (d) * (t_c) * (r_d) V_L = (1+t*k*((1+r_u)/(1+r_d)))*V_U V_L (interest coverage ratio) = V_U + t_c * k * V_U Vt_L = ((FCF_(t+1) + V_(L_t+1) / (1+r_wacc)) Chapter 19 Sales = Market Size * Market Share * Average Sales Price Raw materials = Market Size * Market Share * Raw Materials per Unit Sales and marketing = Sales * (Sales and Marketing % of Sales) Income tax = Pretax Income * Tax rate After-tax interest expense = (1 - Tax Rate) * (Interest on Debt - Interest on Excess Cash) Net borrowing in year t = Net Debt in Year t - Net Debt in Year_(t-1) New Stockholders’ Equity = Equity Contributions - Expensed Transaction Fees β_U (unlevering beta) = (Equity value / Enterprise value) * β_E + (Net debt value / Enterprise value) * β_D Continuation Enterprise Value at Forecast Horizon = EBITDA at Horizon * EBITDA Multiple at Horizon Enterprise Value in Year T = FCF_t+1 / (r_wacc - g) FCF_t+1 = UNI_T+1 + Depr._T+1 - ∂NWC_T+1 - CapEx_T+1 CapEx_t+1 = Depr._t+1 + g * fixed assets_t FCF_t+1 = (1 + g ) * UNI_t - g * NWC_t - g * Fixed_assets_t V_U_t-1 = (FCF_t + V_U_t) / (1 + r_u) Ts_t-1 = (Interest Tax Shield_t + T_s_t) / (1 + r_d) Cash Multiple = Total Cash Received / Total Cash Invested