Chapter 2: Financial Statements, Taxes & Cash Flow o Affected by i/r, default, inflation, taxability, liquidity Variance of N-stock portfolio , premiums / bond values move inversely with interest r Income = Revenue – Expenses Interest payments are tax deductible (1 - tax rate) x payment Earnings per share = NI/total shares outstanding Variance of equally-weighted N-stock portfolio , Current yield = (Coupon/current price) ≠ YTM Dividend/Share = Total dividends/total shares o. Capital gain yield = (New price – original price)/original price Cash flow from assets = OCF - NCS - ∆ NWC Security i s contributi on to the Effective current yield = EAR = Cash flow to creditors + CF to stockholders volatility of the portfolio CF to creditors = Interest – net new borrowings SD ( R P ) x i SD ( R i ) Corr ( R i , R p ) i CF to stockholders = Dividends – net new equity Bond value (pv) = – Taxes OCF = EBIT + Depreciation Amount Total Fraction of i s of i held Risk of i riskthat is o = PV of coupons + PV of face amount Bottom-up = Net Income + Depreciation + Interest common to P Bonds of similar risk will be priced to yield a similar return Top-down = Sales – Cost - Taxes Unless all stocks in portfolio hv perfect positive correlation of regardless of coupon rate / interest rate decline buy zero, LT Tax Shield = (Sales – cost)(1 – T) + (Depr x T) + ( Interest + T) +1, risk of portfolio < weighted avg volatility of individual stocks Bonds selling at par can have any length of maturity NCS = End net fixed assets – Begin NFA + Depre Diversification unsystematic risks for each stock avged out Longer time to mature greater interest rate risk ∆NWC = Ending NWC – Beginning NWC – x )r f + xE [R p] [R xp] = (1 – x Portfolio with R f asset, E Lower coupon rate greater interest rate risk – – = End (CA CL) Begin (CA-CL) r x (E [R p] – r f ) = + f Zero coupon bonds need to sell more bonds and incur Avg tax rate = Tax/taxable income greater repayment but has yearly cash inflow(in the form of Marginal tax rate = Tax payable on next dollar earned SD[R xp] = interest tax shield of debt) instead of outflow Chapter 3: Ratios P1 – P0 , CF (in) No. of bonds sold x tax Interest payt of zero = ST Solvency rate x interest payment of zero bond Current ratio = Current assets/Current liabilities Efficient portfolio: no way to reduce portfolio volatility w/o CF (out) of cupn bds: No. of bonds x coupon payt x (1 – tax rate) o To creditor – high ratio better, but maybe inefficient cash use lowering expected return; inefficient: possible find another way Holding Period Yield: r of new FV (sale price) & N (holding time) Low ratio - not a bad sign for company with large reserve of Efficient frontier: set of efficient portfolios, those offering Inflation – Fisher Effect (1 + Nominal rate) = (1 + real rate) x (1 + untapped borrowing power highest possible E(R) for given volatility, northwest edge of curve expected inflation rate) Cash ratio = Cash/CL Quick ratio = (CA-Inventory) – CL Long: positive investment Short: negative investment Know Pa, estimate YTM a use it to find P b o Large, slow-moving inventory ST trouble Short sale : sell a stock tt not owned t hen buy tt stock back later o Dirty price – price actually paid to buy NWC to total assets = NWC/TA Short sales volatility of portfolio > volatility of stocks within o Clean price – price ‘quoted’ in mkt Interval measure = CA/Avg daily operating cost / Reward-to-volatility ratio Sharpe ratio = = Dirty price – accrued interest (of coupon) LT Solvency Chapter 8: Stock Valuation Total debt ratio = (TA – TE)/TA Optimal portfolio: Tangent to efficient frontier of risky invest. Stock price = PV of future dividends, R = required return o x% of assets financed by debt, rest by equity Investor will determine how much to invest along the tangent or o Debt-equity ratio = TD/TE = TD ratio/(1- TD ratio) Dividend growth model , the capital market line depending on taste of risk o Equity Multiplier = TA/TE = (TE + TD)/TE = 1 + D/E CAPM = Cost of preferred stock = dividend yield = D 1/P0 LT Debt ratio = LT Debt/(LT Debt + TE) - measure t+1 t / ( R – g ) = P 0 x (1 + g) Pt = D0 x (1 + g) Coverage Ratio (likelihood of default) Required return, R =capital gains yield + dividend yield systematic risk. Beta of a portfolio, Times Interest Earned ratio = EBIT/Interest Dividend yield = D1/P0 Capital gains yield = g Assumptions: buy&sell at competitive mkt prices + borrow/lend Cash coverage = (EBIT + Depre)/Interest Supernormal, Dividend grows steadily aft t periods, at risk-free interest rate; only efficient portfolios are held for a Turnover Ratios given volatility; homogeneous expectations regarding future Inventory turnover = COGS/Inventory demand same efficient portfolio (not possible in real life) Receivables turnover = Credit sales/Acct receiv SML – linear r/s between a stock’s beta and it’s expected return Payable turnover = COGS/Acct payable Chapter 15: Cost of Capital = cost of (equity + debt + pref stock) Days’ sales in ___ = 365 days/___ turnov. Chapter 9: Investment Decisions Cost of equity , Dividend Approach, RE = (D1/P0 ) +g Asset Turnover Ratios Payback period / Discounted payback period NWC turnover = Sales/NWC (RE ) = R f + βE x [E (RM) – R f ] SML Approach, E o (+)tmv, easy to understand, reject (-) NPV Fixed asset turnover = Sales/Net fixed asset Use average of SML and Dividend approach if cannot decide o (-) arb pt, ignore CF aft, +NPV rej. cos too long Total asset turnover = Sales/TA Cost of debt , YTM on bonds / Cost of Pref Stock, R P = D/P0 Avg Accounting Return (Avg NI/Avg Book Value) o Every $1 in TA generate $x in sales + (P/V)(R P ) WACC = (E/V)(RE) + (D/V)(RD)(1 – TC) o (+) easy to calculate, info available Profitability Ratios Tend to accept unprofitable investments w/ risk > than firm o (-) no tmv, bk value, not mkt or cashflow Profit margin = Net income/Sales Reject some +NPV & accept some –NPV projects o Avg bk value = (initial + end)/2 ROE = NI/TE = ROA x EM ROA = Net income/TA Pure play approach – use of WACC tt unique to particular prj IRR (acpt if > required return or WACC) , NPV=0 Market Value Ratios o (-) Nonconventional cash flow & Mutually exclusive projects Avg floatation cost, f A = (E/V) x f E + (D/V) X f D Market-to-book ratio = Mkt value per share ÷ bk value per share o Crossover rate = IRR of NPV (B-A) True cost = Amount needed / (1 – floatation cost%) Price-sales ratio = Price per share/Sales per share o (+) related to NPV, easy to understand Chapter 17: Financial Leverage & Capital Structure Policy PEG ratio = Price-earnings ratio/earnings growth rate Profitability Index (NPV/Initial investment) M&M I: Value of levered firm is equal to unlevered firm Price-earnings ratio = Price/share ÷ earnings/share o > 1 for +NPV, < 1 for – NPV VL = VU > 1.firm’ s capt. struct. irrelevant 2.firm WACC is same Du Pont Identity Chapter 10: Capital Budgeting ( Investment decisions) M&M I - Homemade leverage: borrow & lend on their own ROE = Profit Margin (operating efficiency) x TAT (asset use Pro forma (Sales, VC, FC, Depre, EBIT, T , NI) Since R D < RE, as D/V ↑, WACC↓, V↑ Equity = EBIT/Ru efficiency) x Equity Multiplier (financial leverage) Good prj, NPV NPV > 0 X Sunk cost , √ Opportunity cost, Erosion M&M II: cost of equity, RE = RA + (RA – RD) x (D/E), RA-WACC o (NI/sales) x (sales/assets) x (TA/TE) EAC = NPV cost on annual basis (PMT) 1.Cost of equ rises as debt use increase 2.risk of equ depends on Chapter 4: LT Financial Planning & Growth Aft tax salvage value = S x (1-T) i. Business risk (RA) ii.financial risk [(R A – RD) x (D/E)] NWC returns to the firm at the end (depends on qn) Required return rate on firm’s asset R A, cost of debt R D and D/E Internal growth rate = Chapter 12: Some Lessons from History Solve for R E, calculate WACC -> remains same for diff D/E ratio o b = plowback (retention) ratio RE = RU + (RU – RD) x (D/E), when RU = RE = WACC, interest r > RD Risk premium: excess return required from risky asset over o b = 1- dividend payout ratio M&M I w/ taxes, VL = VU + (TC x D) > 1. debt fin is v advantag, required from risk-free investment (1: Risky asset earn risk o b = addition to retained earnings/NI optimal capital structure is 100% 2.lower WACC w/ more debt premium; reward for bearing risk) (2: Greater potential reward, o Max. growth rate attain with no ext. financing PV of interest tax shield = (TC x D x R D)/RD = TC x D greater the risk 2 2 Sustainable growth rate = M&M II w/ taxes, R E = RA + (RA – RD) x (D/E) x (1 – TC) > same Var(R) = 1/(T – 1) x [(R 1 – Mean) + … + (R T – Mean) ] VU = (EBIT – Taxes )/RU = [EBIT x (1-TC)] /RU VL = VU + TC x D (>Geometric) Arithmetic avg return (R 1 + R2 + … RT)/T o Max. growth rate attain with no ext. equity financing while 1/T E = VL – D, find E/D, find RE using M&MII w/ taxes, find WACC – 1 Geometric avg return [(1 + R1) x (1 + R 2) x … x (1 + R T )] maintaining a constant D/E ratio Static theory: Too much debt increase prob. of fin distress due o What actually earned per year on avg, compounded annually Chapter 5/6: TVM to bankruptcy (optimal: tax benefit of debt = cost of distress) o AAR too high for longer period, GAR too low for shorter t , , PV factor = 1/(1 + r) Chapter 18: Dividends & Dividend Policy Efficient capital mkt : security prices reflect available info Declaration date : declares payment; ex-dividend date : 2 Efficient mkts hypothesis : actual capital mkt are efficient – NPV Rule of 72: Time taken to double $ = 72/r% business days before date of record – buy on day or after no of projects are 0 (mkt value of investment & cost = 0) date of record: holder of stock determined; dividend; Chapter 13: Return, Risk and SML Annuity, = Capital mkt imperfection : Low-payout (personal income tax + Expected return, E(R) = Weighted avg of possible returns floatation cost + dividend restrictions) High-payout (Corp tax + Annuity due = start of each period = Ordinary annuity x (1 + r) Risk premium = Expected return of stock – risk-free rate (R f ) 2 institutional investing requmt + transact. costs + current income) Growing annuity , – Variance, = E[(R E[R]) ] = Clientele effect Payout does not matter assuming equilibrium Perpetuity, Growing perpetuity , = - measures volatility or total risk Standard dev, Residual dividend approach: payout aftr meeting invest. needs Portfolio exp return = weighted returns from each stock and maintain desired D/E ratio (Dividend stability consideration) EAR = APR = Compromise dividend approach: APR/quoted rate = period rate x no. of periods/year Portfolio weights , g Stock repurchase: prefer repurchase (akin a cash dividend Continuous compound , Variance of 2-stock portfolio , program provided no taxes or o ther imperf.) homemade divide. Partial Amortization – Balloon payment (PV of remaining) Stock dividend/stock split: no change in equity (trading range) Chapter 8: Interest Rates & Bonds Dividend policy does not matter – firm reinvest capital > pay Covar. btw returns R1 and R2, Coupon rate (pmt) = Annual coupon/Face value ($1000) higher dividends in the future bt offset of lower PV factor Cov (R (Rx,Ry) = E[ (Rx – E[Rx]) (Ry – E[Ry]) ] = YTM (r) = Rate required in mkt for bond (find r on fin cal.) associated w/ CF Homemade dividends policy w/ perfect mkt o Current Yield + Capital Gains Yield Correl. btw returns R1 & R2,
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