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 firm’s life into two stages.– Non-constant growth period– Constant Growth period.

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 > 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.

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

1. 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 t=0.

2. If you are unable to estimate constant growth, you can use an exit multiple.

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

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.

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.

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)

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.

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

Discount Rate

• Real RADR (risky) = 20% (given)

• Real Riskfree = 7% (given)

• Inflation = 3% (given)

• Nominal RADR =

• Nominal Riskfree =

Valuing the Firm

• PVA (real operating CF, g=10%, 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.