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Introduction to
Firm Valuation
Equity vs. Firm Valuation
Value of Equity: The value of the equity stake
in the firm, the value of the common stock for a
publicly traded firm
Value of Firm: The value of all investors who
have claims on the firm
A General Valuation Model
The basic components of the valuation are:
An estimate of the future cash flow stream from
owning the asset
The required rate of return for each period based
upon the riskiness of the asset
The value is then found by discounting each
cash flow by its respective discount rate and
then summing the PV’s (Basically the PV of an
Uneven Cash Flow Stream)
The Formal Model
The value of any asset should then be equal
1  r1 (1  r2 ) 2
(1  rt ) t
(1  rn ) n
 (1  r )
t 1
Applying the general valuation
formula to a firm
The only questions are what to use as the
future cash flows when valuing the firm and
what to use as the interest rate.
We are going to look at discounted cash flow
three models which differ by their choice of
cash flows:
Free Cash Flows to the Firm
Free Cash Flows to Equity
Elements Common to All Models
Choose Cash Flows
Choose discount rate consistent with the cash
Estimate short term growth of cash flows
Estimate long term sustainable growth of
cash flows and when sustainable growth
Cash Flows are assumed to continue forever
Multi-Stage Growth Models
The growth of the cash flows can be broken
down into general stages. The firm may
experience all three or only two of the stages.
High growth
Transition to Stable growth
Stable growth
Actually any path of growth could be assumed
for the short term – the key is that at some
point stable long term growth is assumed.
Two and Three Stage Growth Models
A two stage growth model is characterized by a
period of fast growth followed by a period of
stable growth.
A three stage growth model is characterized by
a period of fast growth followed by a transition
period followed by a period of stable growth.
Stable Growth Period
Once a period of stable growth is reached you can
approximate the terminal (horizon) value of the cash
flows using the constant growth formula.
CFt (1  g )
Generic DCF Valuation Model
Expected Growth
Firm: Growth in
Operating Earnings
Equity: Growth in
Net Income/EPS
Cash flows
Firm: Pre-debt cash
Equity: After debt
cash flows
Firm is in stable growth:
Grows at constant rate
Terminal Value
Firm: Value of Firm
Equity: Value of Equity
Length of Period of High Growth
Discount Rate
Firm:Cost of Capital
Equity: Cost of Equity
The Dividend Discount Model
The value of a share of stock should be the PV
of the dividends you will receive in the future if
you own the stock.
The Formal Model
Allowing the CF in the general valuation
model to be the expected future dividends
the model becomes:
E(D t )
E(D 1 ) E(D 2 )
E(D  )
  
  
1  re (1  re )
(1  re )
(1  re ) 
t 1
Expected Dividend t
(1  re )
Estimating growth rates
Historical Growth Rate
Comparison to analysts forecasted growth
Growth based upon investment policy
Dividends are based upon the amount reinvested
in the firm
g=(retention rate)(ROE)
Stable growth
Stable Growth
When the firm reaches stable growth the
characteristics of the firm also change – this
implies a change in riskiness of the firm and a
change in the cost of equity.
Dividend Growth Model
The model can be changed to account for
firms that are not currently paying a divided
(high growth) but will start paying a dividend
in the future.
You can use a per share or aggregate
measure of dividends – if there are equity
options, warrants etc outstanding it is best to
start with an aggregate estimate.
Free Cash Flow Choices
Free Cash Flow to Equity
The residual cash flow left over after meeting
interest and principal payments and providing
for reinvestment to maintain existing assets.
Free Cash Flow to the Firm
The cash flow from operations that is actually
available for distribution to investors
(stockholders, bondholders and preferred
Free Cash Flow to Equity
Net Income
-Capital Expenditure
-Changes in Net Working Capital
-Principal Repayments
+New Debt Issues
Free Cash Flow to Equity
The Formal Model Again
The value of equity should be equal to:
 (1  r )
t 1
Value of Equity
After forecasting the free cash flows it is then possible
to find the value of operations for the firm.
value of
 Vop 
 (1  r )
t 1
Notice, this depends upon a forecast of future free
cash flow which much like dividends are not certain.
Estimating Inputs
The length of high growth period and rate of
return is the same as for the dividend growth
E(growth) = (Equity Reinvestment Rate)(ROE)
Similarly the growth rate in the stable period
should be based on stable growth
Equity Reinvest = Stable Growth Rate
Stable Period ROE
Dividends v FCFE
If Aggregate Dividends = FCFE then they
produce the same value for the value of equity.
IF FCFE > Dividends and
the $ are reinvested in projects with NPV =0
(fairly priced assets) then the values are close.
The $ are invested in low return projects FCFE
provides higher value of equity.
If FCFE does not equal Dividends
What does the difference tell us?
Which model is appropriate?
Free Cash Flow to the Firm
Net Operating Profit After Taxes
+ depreciation
-Gross Capital Expenditure
-Change in net operating working capital
Free Cash Flow
NOPAT = EBIT(1-Tax Rate)
NOPAT is the amount of profit a firm would earn
if it had no debt and held no financial assets.
Five good uses of FCF
Pay interest to debtholders (cost to firm is
after tax interest expense)
Repay debt
Pay dividend to shareholders
Repurchase stock from shareholders
Buy marketable securities or other
nonoperating assets.
The Formal Model Again
Using Free Cash Flow to the firm, the value
of operations should be equal to:
 (1  WACC )
t 1
Value of Operations
After forecasting the free cash flows it is then possible
to find the value of operations for the firm.
value of
 Vop  
t 1 (1  WACC)
Notice, this depends upon a forecast of future free
cash flow which much like dividends are not certain.
Estimating Inputs
Expected growth during high growth period
g = (Reinvestment Rate)(ROC)
EBIT (1  t )
(Book Value Debt  Book Value Equity)
Remember that the assumption about the Cost
of capital will change as the firm grows
Terminal Value Based on assumptions
concerning long run growth in economy
Firm Value to Equity value
You can take the value of the firm and subtract
the amount of debt to get to the value of
equity. (use the same debt classifications you
used for cost of debt)
The value of equity obtained form the FCFE and
FCFF valuations should be the same if you are
consistent with your assumptions about
financial leverage.
Other things impacting Value
Liabilities on lawsuits
Unfunded Pensions and Health Care Obligations
Deferred Taxes
Firm Characteristics as Growth Changes
High Growth Firms
Stable Growth Firms
tend to
tend to
be above-average risk
be average risk
Dividend pay little or no dividends pay high dividends
Net Cap Ex have high net cap ex
have low net cap ex
earn high ROC
earn ROC
(excess return)
closer to WACC
Leverage have little or no debt
higher leverage
Equity Valuation to per share
An estimate of the value per share can be
found by dividing the value of equity by the
number of outstanding shares.
The value of outstanding options must also
Value Enhancement
Changes in any of the four key inputs will
impact value in all models.
Increases in cash flow
Changes in growth rates
Change in length of growth period
Reduction in cost of capital.
Relative Valuation
You can also value the firm by looking at
multiples of similar firms and benchmarking
Make sure to standardize ratios that you use
across firms