Discounted Cash Flow

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Discounted Cash Flow Sequential Valuation

• In this class, we will value companies using
  Discounted Cash Flows.
• We will use the Sequential method to determine
  the stock price.
• To do this valuation, we will break the firms
  life into two stages.
• Non-constant growth period
• Constant Growth period.

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Discounted Cash Flow Sequential Valuation

• To value the cash flows during the non-constant
  growth period, we need
• Estimate Cash flow for all years
• Discount cash flow
• Note growth annuity calculation may be helpful
  but can only use if r gt g!
• During the non-constant growth period, the firm
  may go through many different growth cycles.
• Only when the we can assume that growth is stable
  and will remain unchanged, does the non-constant
  growth period end.

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Discounted Cash Flow Sequential Valuation

• Once the non-constant growth ends, the constant
  growth period begins.
• To value the firm during the constant growth
  period, we must calculate a Terminal Value
• Two ways typically calculated
• If can estimate constant growth rate, use
  perpetuity equation.
• Timing is essential here.
• You use the cash flow after one year of the
  constant growth rate.
• This gives the value at the point when growth
  became constant, so the value must be discounted
  to t0.
• If you are unable to estimate constant growth,
  you can use an exit multiple.

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Three Rules for Valuing Cash flows

• Different cashflows have different levels.
• A firm could have different divisions with
  different risk levels.
• Certain cashflows could be certain and others are
  uncertain or risk.
• Example If you know you will have 20,000 of
  depreciation for the next 10 years and the tax
  rate is 30, then the depreciation tax shield is
  a riskless cash flow
• Use risk-adjusted discount rates to value risky
  cash flows
• Use the risk-free discount rate to value riskless
  cashflow

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Three Rules for Valuing Cash flows

• Be consistent in your treatment of inflation
• Use nominal cash flows and a discount rate that
  accounts for inflation.
• Use real cash flows and a discount rate that
  ignores the effect of inflation.
• Consider the timing of the cash flows
• End of the year versus Beginning of the year.
• Best approximation Mid-year discounting.

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Valuation Example Motel

• From the Benninga and Sarig text book, Chapter 3,
  Cash Flow this year is
• Profit After Tax (net income)- 30,203
• Depreciation - 20,000
• Interest Expense (net of tax) 22,496
• Free Cash Flow 72,699
• Change Assumptions from the book
• FCF (excluding depreciation tax shield) grows at
  10 for the next 10 years (the book assumed it
  was constant). This is above the industry
  average.
• After 10 years, growth stabilizes. However, you
  are uncertain what the stable growth rate will
  be.
• You know that similar real estate assets have a
  price to earnings ratio of 8 and you expect the
  same for your hotel in 10 years.

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Valuation Example Motel

• Different Cash flows have different risks. So,
  when you value the cash flow consider different
  risk levels.
• Free Cash Flow 72,699
• Depreciation Tax Shield
• (20,000 x .30304)
• Operating Cash Flow
• (residual)

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Cashflow and Inflation Adjustments

• Is the depreciation tax shield a real or nominal
  cashflow?
• It will not change so it is nominal , so it must
  be discounted using an rate including inflation
  (nominal rate)
• Is it a risky cash flow?
• No, so we use the nominal, riskfree rate.
• Is the cash flow for operations a real or nominal
  cashflow?
• Our estimates do not account for changes that
  occur due to inflation, so it is a real cash flow
  and must be discounted using a real rate.
• Is it a risky cash flow?
• Yes, so we use the real, risky rate.
• Both of these cashflow accrue throughout the
  year, so they are discounted at mid-year.

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Cashflow and Inflation Adjustments

• The terminal value
• Is the terminal cashflow nominal or real?
• If it is based on nominal earnings, then it is
  nominal
• Is it risky? yes,
• so nominal risky rate is used.
• Terminal Value using exit multiple

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Discount Rate

• Real RADR (risky) 20 (given)
• Real Riskfree 7 (given)
• Inflation 3 (given)
• Nominal RADR
• Nominal Riskfree

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Valuing the Firm

• PVA (real operating CF, g10, 20, 10 yrs at
  mid-year)
• PVA (nominal tax shield CF, 10.21, 10 yrs at
  mid-year)
• PV (Terminal Value, 10 yrs, 23.6)
• Firm Value
• Equity Value
• Debt value given in text.

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