DISCOUNTED CASH FLOW VALUATION

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

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DETERMINING THE RISK ADJUSTED DISCOUNT RATE

Risk–and–Return Models (CAPM)– Expected Return = rf + (rm – rf),

whereby (rm – rf) is the equity risk premium Calculation of :

Historical regression by regressing its ROI against return on the market index

Bottom-up , 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%

• 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%

DETERMINING THE RISK ADJUSTED DISCOUNT RATE

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

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HYBRID MODELSType of Risks Examples Risk Adjustment in

Valuation

Continuous market risk where buying protection is difficult or impossible

Interest rate risk, inflation risk, exposure to economic cyclicality

Adjust the discount rate for risk

Discontinuous market risk, with low likelihood of occurrence but big impact

Political risk, risk of expropriation, terrorism risk

If insurance exists, include premium as cost and adjust cash flow. Otherwise adjust discount rate

Market risk that is contingent on a specific occurrence

Commodity price risk Estimate the option premium to hedge against the risk, include as cost and adjust cash flow

Firm-specific risk Estimation risk, competitive risk, technology risk

If investors are diversified, no adjustments needed. If investors are not diversified use the models for market risk

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 )

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PV ( of company’s cash flow without hedge plus bankruptcy cost)

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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