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## DISCOUNTED CASH FLOW VALUATION

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**DISCOUNTED CASHFLOW VALUATION**• Discounting the expected cash flow at a risk adjusted discount rate • Discounting a Certainty Equivalent of the cash flow at the risk free rate**DETERMINING THE RISK ADJUSTED DISCOUNT RATE**• Risk–and–Return Models (CAPM) • Expected Return = rf + b*(rm – rf), • whereby (rm – rf) is the equity risk premium • Calculation of b : • Historical regression b, by regressing its ROI against return on the market index • Bottom-up b , by looking at the betas of other public traded companies • Example on Google : • 10 year Treasury Bond is 4.25% • Bottom-up beta for internet companies is 2.25 • Risk premium is 4.09% • Expected return on Google stocks = 4.25% + 2.25*4.09%=13.45%**DETERMINING THE RISK ADJUSTED DISCOUNT RATE**• Proxy Models • Find variables that characterized high return stocks and regressed them • Findings of Fama & French • rj=1.77%-0.11*ln(MVj)+0.35*ln(BVj/MVj) • Expected annual return = (1+rj )12 – 1 • Example : • Market Value = usd 500 • Book Value = usd 300 • rj=1.77%-0.11*ln(500)+0.35*ln(300/500)=0.9076% • Expected annual return = (1+0.009076 )12 – 1=11.45%**DETERMINING THE RISK ADJUSTED DISCOUNT RATE**• Implied Discount Rates • Market Value = Exp CFt+1 / ( radj – gexp ) • Example : • USD 1,000 = USD 100/(radj – 0.03) radj=13.00%**FLAWS OF THE METHODS**• Assumptions of stocks are publicly traded • Assumptions that Market Value used are correct • Calculated returns are for a single period only, but used as a multi period rate • Discounting uses one same discount rate • Negative cash flows discounted will result in increasing value**DETERMINING CERTAINTY EQUIVALENT CASH FLOWS**• Risk-and-Return Models • Cash Flow Haircuts • Cuts are done based on analysts judgment • Risks can be considered twice to this intuitive judgment**CFaR VALUATION**• Define all risks that might have an impact on the cy’s cash flow • Do several cash flow projections with the assumptions of each respective occurring use MONTE CARLO simulation • Use valuation method for every projected cash flow Cash Flow at Risk (CFaR) • Cash flow before risk management vs cash flow after risk management • Difference of value is the gain from risk management • Value the gain**CFaR VALUATION**PV ( of company’s cash flow with hedge plus hedging cost ) --- PV ( of company’s cash flow without hedge plus bankruptcy cost) === Benefit of risk management**Requirements :**• Use EBITDA or operational cash flow excluding interest • Calculate projected Cashflow/EBITDA considering probabilities of occurrence • Use WACC as discount rate • Include risk premium in cost of equity • Include transaction cost of hedging • Include bankruptcy cost