1 Formula Sheet: 1) Present Value Factors Cash Flow Present Value Factor T-period annuity immediate t = 1, 2, …, T T-period annuity due t = 0, 1, …, T-1 Perpetuity t = 1, 2, 3, … Growing T-period annuity immediate t = 1, 2, …, T Growing T-period annuity due t = 0, 1, …, T-1 Growing perpetuity t = 1, 2, 3, … 2) Other Formulas • • • • • • • • • • • • �1 − 1 1 �� � (1+𝑟𝑟)𝑇𝑇 𝑟𝑟 �1 − 1 1+𝑟𝑟 � � 𝑟𝑟 � (1+𝑟𝑟)𝑇𝑇 �1 − (1+𝑔𝑔)𝑇𝑇 1 �� � (1+𝑟𝑟)𝑇𝑇 𝑟𝑟−𝑔𝑔 �1 − 1 𝑟𝑟 (1+𝑔𝑔)𝑇𝑇 1+𝑟𝑟 �� � (1+𝑟𝑟)𝑇𝑇 𝑟𝑟−𝑔𝑔 1 𝑟𝑟−𝑔𝑔 EAR = (1 + 𝑚𝑚𝑟𝑟 )𝑚𝑚 − 1 EAR = 𝑒𝑒 𝑟𝑟 − 1 Duration Modified Duration = Volatility (%) = Dividend Growth Model: 𝑃𝑃0 = 𝑃𝑃0 = 𝐸𝐸𝐸𝐸𝐸𝐸1 ROE = 𝑟𝑟 + 𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃 EPS 𝐷𝐷1 𝑟𝑟−𝑔𝑔 1+YTM Book equity per share 𝐷𝐷 Payout ratio = 𝐸𝐸𝐸𝐸𝐸𝐸 Plowback ratio = 1 − 𝐷𝐷 𝐸𝐸𝐸𝐸𝐸𝐸 g = Plowback ratio × ROE CAPM: 𝑟𝑟 = 𝑟𝑟𝑓𝑓 + 𝛽𝛽(𝑟𝑟𝑚𝑚 − 𝑟𝑟𝑓𝑓 ) Sharpe Ratio = 𝑟𝑟 − 𝑟𝑟𝑓𝑓 𝜎𝜎 Portfolio Variance = 𝑥𝑥12 𝜎𝜎12 + 𝑥𝑥22 𝜎𝜎22 + 2𝑥𝑥1 𝑥𝑥2 𝜎𝜎12 = 𝑥𝑥12 𝜎𝜎12 + 𝑥𝑥22 𝜎𝜎22 + 2𝑥𝑥1 𝑥𝑥2 𝜌𝜌12 𝜎𝜎1 𝜎𝜎2 3) Formulas for project cash flows • Project cash flow = Project operating cash flow – Project capital spending – Change in net working capital • Calculating operating cash flow (OCF): The bottom-up approach: Project net income = EBIT – taxes OCF = Net income + depreciation = EBIT – taxes + depreciation The top-down approach: OCF = Revenue – costs and expenses – taxes The tax shield approach: OCF = (Sales – costs) × (1 – t) + depreciation × t • Net working capital = Inventory + Accounts receivable – Accounts payable
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