] (3.3) ] (1 + r)t (3.4)


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1 Present value = future value after t periods (3.1) (1 + r) t PV of perpetuity = C = cash payment (3.2) r interest rate Present value of tyear annuity = C [ 1 1 ] (3.3) r r(1 + r) t Future value of annuity of $1 per year = present value of annuity of $1 per year (1 + r) t = [ 1 1 ] (1 + r)t (3.4) r r(1 + r) t = (1 + r)t 1 r 1 + real interest rate = 1 + nominal interest rate (3.5) 1 + inflation rate PV = PV (coupons) + PV (face value) = (coupon annuity factor) + (face value discount factor) (4.1) Rate of return = coupon income + price change (4.2) investment Expected return r DIV 1 + P 1 P 0 (5.1) P 0 P 0 = DIV1 + DIV DIV H +P H (5.2) 1 + r (1 + r) 2 (1 + r) H Stock price = PV (all future dividends per share) (5.3) r = DIV1 + g (5.4) P 0 = dividend yield + growth rate P 0 = DIV1 + DIV DIVH r (1 + r) 2 (1 + r) H (1 + r) H (5.5) P H PV of dividends from Year 1 to horizon PV of stock price at horizon
2 NPV = PV required investment (6.1) Book rate of return = book income (6.2) book assets Equivalent annual cost = present value of costs (6.3) annuity factor Profitability index = net present value (6.4) initial investment Incremental = cash flow cash flow cash flow with project without project (7.1) Total cash flow = cash flow from investment in plant and equipment (7.2) + cash flow from investment in working capital + cash flow from operations Depreciation tax shield = depreciation tax rate (7.3) Taxable income = revenues expenses CCA (7.4) CCA tax shield = CCA tax rate (7.5) fixed costs including depreciation Breakeven level of revenues = additional profit from each additional dollar of sales (8.1) DOL = percentage change in profits (8.2) percentage change in sales DOL = 1 + fixed costs (8.3) profits Percentage return = capital gain + dividend (9.1) initial share price dividend Dividend yield = initial share price (9.2)
3 capital gain Percentage capital gain = initial share price (9.3) 1 + real rate of return = 1 + nominal rate of return (9.4) 1 + inflation rate Variance = probabilityweighted average of squared deviations around the expected return (9.5) Standard deviation = square root of variance (9.6) Variance = sum of squared deviations/(number of observations 1) (9.7) Standard deviation = square root of variance (9.8) Portfolio rate = ( fraction of portfolio rate of return (9.9) of return in first asset on first asset + ( fraction of portfolio rate of return in second asset on second asset) Risk premium on any asset = r r f = β(r m r f ) (10.1) Expected return = riskfree rate + risk premium (10.2) r= r f + β(r m r f ) Value of business = value of portfolio of all the firm s (11.1) debt and equity securities Risk of business = risk of portfolio (11.2) Rate of return on business = rate of return on portfolio (11.3) Investors required return on business investors required return on = (company cost of capital) portfolio (11.4)
4 Company cost of capital = weighted average of debt and equity returns (11.5) r assets = total income (11.6) value of investment = (D r debt) + (E r equity ) = ( D r debt ) + ( E r equity ) V V V Aftertax cost of debt = pretax cost (1 tax rate) (11.7) = r debt (1 T c ) WACC = [ D (1 T c )r debt ] ( + E (11.8) r V V equity ) WACC = [ D (1 T c )r debt ] + ( P r preferred ) + ( E r equity ) (11.9) V V V r preferred = dividend price of preferred (11.10) debt expected expected (15.1) Expected expected return = return + equity return on return on on equity on assets ratio assets debt PV tax shields = annual tax shield = T c (r debt D) = Tc D (15.2) r debt r debt WACC = (1 T c ) r debt ( D ) + r equity ( E ) (15.3) D + E D + E Overall market value if allequity PV tax PV costs of = + value financed shield financial distress (15.4) ROA = net income + interest = sales net income + interest assets assets sales (17.1) asset profit turnover margin
5 ROE = assets sales net income + interest net income equity assets sales net income + interest (17.2) leverage asset profit debt ratio turnover margin burden addition to Required external financing = new investment retained earnings (18.1) = (growth rate assets) addition to retained earnings addition to retained earnings Internal growth rate = (18.2) assets addition to retained earnings Internal growth rate = (18.2) assets Sustainable growth rate = plowback ratio return on equity (18.4) Cash conversion cycle = (inventory period + receivables period) (19.1) accounts payable period Inventory period = average inventory (19.2) Accounts receivable period = average accounts receivable annual sales/365 (19.3) Accounts payable period = average accounts payable (19.4) Inventory period = average inventory (19.5) Receivables period = average accounts receivable annual sales/365 (19.6) Payables period = average accounts payable (19.7)
6 beginning accounts receivable Ending accounts receivable = + sales collections (19.8) 2 annual sales cost per order Economic order quantity = carrying cost (20.1) 2 annual cash outflows cost per sale of securities Initial cash balance = interest rate (20.2) Effective annual rate = ( 1 + discount ) 365/extra days credit 1 (21.1) discounted price Refuse credit: 0 Grant credit: p PV(REV COST) (1 p) PV(COST) (21.2) Profit to seller = initial futures price ultimate market price (26.1) Profit to buyer = ultimate market price initial futures price (26.2)
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