Equity and Firm Valuation

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Equity and Firm Valuation
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Why do we need to understand how to value assets?

• Fact in the end of 1998, Boeings stock price
  was 32.25 and Home Depots was 57.94
• Do these prices reflect the true value of each
  companys stock?
• Moreover, how can we value each of the above two
  companies?
• Value of companys equity
• Value of companys debt

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• Investors need to understand equity and firm
  valuation in order to
• Be able to determine the factors that create
  value for the firm
• Understand the causes of changes in the firms
  stock price from period to period
• Managers also need to understand valuation in
  order to
• Make investment, financing and dividend decisions
  that create value
• Determine the value of the stock or stock options
  that they own

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What is the value of an asset?

• The value of any asset is the PV of the expected
  cash flows on the asset
• Value is determined by
• Magnitude of these cash flows
• Expected growth rate of these cash flows
• Uncertainty associated with receiving these cash
  flows

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How can we use this definition of valuation?

• This definition can be applied to value both real
  and financial assets
• Machinery, Real Estate, Transportation Equipment
• Bonds, Equity, Options, Hybrid securities
  (convertible debt, preferred stock)
• We can also use it to value a firm
• Publicly-traded firms
• Private firms

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What types of assets can we value?

• Assets with guaranteed cash flows
• Discount cash flows by using a risk-free rate
  (e.g. US and some other developed countries
  government securities)
• Assets with uncertain cash flows
• Discount cash flows by adjusting risk-free rate
  for
• Default risk in the case of bonds risk that the
  cash flows will not be delivered
• Equity risk in the case of stocks risk that the
  cash flows can be much lower than expected, but
  can also be much higher

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• Assets with finite lives (certain or uncertain
  cash flows)
• Coupon or zero-coupon bonds
• Investments in real estate, machinery, etc. (at
  the end of their life, the assets lose their
  operating capacity, but may still have some
  value)
• Assets with infinite lives (certain or uncertain
  cash flows)
• Common and preferred stock
• A firm
• Console bonds

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Approaches to valuation

• Discounted Cash Flow (DCF) approach
• We measure the value of an asset (intrinsic
  value) by discounting back expected cash flows at
  a rate that reflects their riskiness

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• Relative (Multiples) Approach
• We value a firm or its equity based on how the
  market values similar or comparable firms and
  their equity
• Price-earnings (P/E) ratios
• Price-book ratios (market-to-book ratio)
• Price-sales (market value per share/revenues per
  share)
• Comparable firms (peer group)
• Select firms with similar cash flow patterns,
  growth potential and risk characteristics
• Use also industry averages

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Equity Valuation

• One way to value equity is to use the DCF
  approach
• According to the DCF approach, the value of
  equity is obtained by discounting expected cash
  flows to equity at the cost of equity
• Cash flows are the residual cash flows to
  stockholders after meeting all expenses, tax
  obligations and interest and principal payments
• The cost of equity (ke) is the return required by
  equity investors to invest in the firm

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• Note that stocks are assets that have an infinite
  life
• Thus, we write

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The Dividend Discount Model (DDM) to value equity

• One approach to equity valuation is to assume
  that the cash flows to stockholders consist only
  of dividends
• Using the DCF approach we obtain the DDM as
  follows

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• If we assume that a stock pays constant dividends
  every year, then the above formula can be easily
  estimated through the PV of a perpetuity
• Value of equity Annual Dividend/ke
• Given that every firm tries to grow the size of
  its operations, we can assume that the firms
  dividends, starting today, will grow at a
  constant rate forever

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• Applying the formula for a growing perpetuity, we
  can rewrite the value of equity for a firm whose
  dividends grow at a constant rate (g) as follows

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• This model is called the Gordon growth model for
  equity valuation
• Expected next periods dividend (Current
  periods dividend) ? (1 g)
• Limitations of the model
• Applied only to companies that pay dividends
• Applied only to companies whose dividends are
  expected to grow at a constant rate forever

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Example 1 Valuing a stock with stable growth
dividends

• Suppose that given the history of dividend
  payments of the Gordon Growth Company, we expect
  that future dividends will grow at 5 annually
  forever. This years dividend per share is 2.50
  and the companys cost of equity has been
  estimated to be 10. What is the companys value
  per share?
• Value per share (2.50 ? 1.05)/(.10 - .05)
  52.50

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At what rate and for how long can a firms
dividends grow?

• A firms dividends cannot grow at a rate higher
  than the nominal rate of growth of the economy
  forever
• In applying the model, the constant growth rate
  must be constrained to be less than or equal to
  the economys nominal growth rate
• Recall Nominal growth rate real growth rate
  inflation rate

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• In the case of the US economy, the nominal growth
  rate in the 1990s was 5
• Use a maximum rate of 5-6 in your calculations
• What if we forecast a companys dividends to grow
  at a rate higher than 5-6 for, lets say, the
  next five years?

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• In this case, the companys stock value is the
  sum of two components
• PV of expected dividends (based on our forecasts)
  during the high dividend growth period
• PV of Terminal price
• Terminal price present value of all future
  dividends beyond the high dividend growth period

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How do we derive the terminal price?

• Suppose we have a forecast of a firms dividends
  for the next 6 years (the high dividend growth
  period) and that the forecasted dividend per
  share for the sixth year is 3
• We may then assume that after the sixth year the
  firms dividends will be growing at a constant
  growth rate of 3 per year
• Our assumption about this rate could be based on
• The companys average dividend growth rate over
  the past few years
• Information about the companys future dividend
  policy

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• The terminal price can be derived from the
  growing perpetuity formula as follows (assuming a
  cost of equity of 8)
• Terminal price (3 ? 1.03)/(.08 - .03)

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Example 2 Valuing a stock with growing dividends

• Assume that you want to value the stock of Fuji,
  Corp. You know that the company paid 0.69
  dividend per share last year
• You forecast that for the next 10 years, the
  companys dividends per share will grow at 25
  per year
• You have also estimated the companys cost of
  equity to be 11
• What is the value of Fuji, Corp. stock today?

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Step 1 Estimate the PV of dividends per share
for the next 10 years
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Step 2 Estimate terminal price (value) of Fuji
stock at end of high-growth period

• We will assume that after period 10, Fujis
  dividend per share will grow at 6 per year
• Given dividend per share in period 10 (6.43), we
  then calculate dividend per share in period 11 as
• 6.43 ? 1.06 6.81

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• The terminal value of Fuji stock in period 10 is
• 6.81/(0.11 0.06) 136.24

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Step 3 Estimate Fujis stock price today

• Fujis stock price is the sum of
• PV of dividends in high-growth period
• PV of terminal price
• In our example, this is
• 14.05 136.24/(1.11)10 62.03

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Another way to value equity

• A broader measure of the value of equity is based
  on the Free Cash Flows to Equity (FCFE)
• FCFE is calculated by subtracting from net income
• Expenses for reinvestment needs
• Net debt payments (Debt repaid New debt issued)

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• Having estimated the FCFE, we can use the DDM as
  discussed above to value stocks
• With free cash flows that are growing at a
  constant rate that is less than the economys
  nominal growth rate
• With free cash flows growing at a rate higher
  than the economys nominal growth rate (estimate
  PV of FCFE during high-growth period and PV of
  terminal value of equity)
• Our estimation of FCFE depends on our assumptions
  about the growth of net income, the firms
  reinvestment needs and the net issues of debt

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Valuing the firm

• In a DCF valuation of the firm, we discount the
  Free Cash Flow to the Firm (FCFF) rather than
  FCFE
• FCFF After-tax operating income Reinvestment
  needs
• Note that FCFF is estimated
• Using the firms income after taxes
• But before interest and principal payments have
  been made to creditors (banks and bondholders)

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• Again, we can assume that FCFF will be growing at
  a constant rate forever
• Alternatively, a firm may be experiencing a
  high-growth period in its income, but we assume
  that eventually it will reach a period of stable
  growth
• In this case, we will use again the tree-step
  process as in the case of stock valuation