Common Stock Valuation

1
Common Stock Valuation

• Timothy R. Mayes, Ph.D.
• FIN 3600 Chapter 14

2
What is Value?

• In general, the value of an asset is the price
  that a willing and able buyer pays to a willing
  and able seller
• Note that if either the buyer or seller is not
  both willing and able, then an offer does not
  establish the value of the asset

3
Several Kinds of Value

• There are several types of value, of which we are
  concerned with four
• Book Value The carrying value on the balance
  sheet of the firms equity (Total Assets less
  Total Liabilities)
• Tangible Book Value Book value minus intangible
  assets (goodwill, patents, etc)
• Market Value - The price of an asset as
  determined in a competitive marketplace
• Intrinsic Value - The present value of the
  expected future cash flows discounted at the
  decision makers required rate of return

4
Determinants of Intrinsic Value

• There are two primary determinants of the
  intrinsic value of an asset to an individual
• The size and timing of the expected future cash
  flows.
• The individuals required rate of return (this is
  determined by a number of other factors such as
  risk/return preferences, returns on competing
  investments, expected inflation, etc.).
• Note that the intrinsic value of an asset can be,
  and often is, different for each individual
  (thats what makes markets work).

5
Common Stock

• A share of common stock represents an ownership
  position in the firm. Typically, the owners are
  entitled to vote on important matters regarding
  the firm, to vote on the membership of the board
  of directors, and (often) to receive dividends.
• In the event of liquidation of the firm, the
  common shareholders will receive a pro-rata share
  of the assets remaining after the creditors
  (including employees) and preferred stockholders
  have been paid off. If the liquidation is
  bankruptcy related, the common shareholders
  typically receive nothing, though it is possible
  that they may receive some small amount.

6
Common Stock Valuation

• As with any other security, the first step in
  valuing common stocks is to determine the
  expected future cash flows.
• Finding the present values of these cash flows
  and adding them together will give us the value
• For a stock, there are two cash flows
• Future dividend payments
• The future selling price

7
Common Stock Valuation An Example

• Assume that you are considering the purchase of a
  stock which will pay dividends of 2 (D1) next
  year, and 2.16 (D2) the following year. After
  receiving the second dividend, you plan on
  selling the stock for 33.33. What is the
  intrinsic value of this stock if your required
  return is 15?

8
Some Notes About Common Stock

• In valuing the common stock, we have made two
  assumptions
• We know the dividends that will be paid in the
  future.
• We know how much you will be able to sell the
  stock for in the future.
• Both of these assumptions are unrealistic,
  especially knowledge of the future selling price.
• Furthermore, suppose that you intend on holding
  on to the stock for twenty years, the
  calculations would be very tedious!

9
Common Stock Some Assumptions

• We cannot value common stock without making some
  simplifying assumptions. These assumptions will
  define the path of the future cash flows so that
  we can derive a present value formula to value
  the cash flows.
• If we make the following assumptions, we can
  derive a simple model for common stock valuation
• Your holding period is infinite (i.e., you will
  never sell the stock so you dont have to worry
  about forecasting a future selling price).
• The dividends will grow at a constant rate
  forever.
• Note that the second assumption allows us to
  predict every future dividend, as long as we know
  the most recent dividend and the growth rate.

10
The Dividend Discount Model (DDM)

• With these assumptions, we can derive a model
  that is variously known as the Dividend Discount
  Model, the Constant Growth Model, or the Gordon
  Model
• This model gives us the present value of an
  infinite stream of dividends that are growing at
  a constant rate.

11
Estimating the DDM Inputs

• The DDM requires us to estimate the dividend
  growth rate and the required rate of return.
• The dividend growth rate can be estimated in
  three ways
• Use the historical growth rate and assume it will
  continue
• Use the equation g br
• Generate your own forecast with whatever method
  seems appropriate
• The required return is often estimated by using
  the CAPM ki krf bi(km krf) or some other
  asset pricing model.

12
The DDM An Example

• Recall our previous example in which the
  dividends were growing at 8 per year, and your
  required return was 15.
• The value of the stock must be (D0 1.85)
• Note that this is exactly the same value that we
  got earlier, but we didnt have to use an assumed
  future selling price.

13
The DDM Extended

• There is no reason that we cant use the DDM at
  any point in time.
• For example, we might want to calculate the price
  that a stock should sell for in two years.
• To do this, we can simply generalize the DDM
• For example, to value a stock at year 2, we
  simply use the dividend for year 3 (D3).

14
The DDM Example (cont.)

• In the earlier example, how did we know that the
  stock would be selling for 33.33 in two years?
• Note that the period 3 dividend must be 8 larger
  than the period 2 dividend, so
• Remember, the value at period 2 is simply the
  present value of D3, D4, D5, , D8

15
What if Growth Isnt Constant?

• The DDM assumes that dividends will grow at a
  constant rate forever, but what if they dont?
• If we assume that growth will eventually be
  constant, then we can modify the DDM.
• Recall that the intrinsic value of the stock is
  the present value of its future cash flows.
  Further, we can use the DDM to determine the
  value of the stock at some future period when
  growth is constant. If we calculate the present
  value of that price and the present value of the
  dividends up to that point, we will have the
  present value of all of the future cash flows.

16
What if Growth Isnt Constant? (cont.)

• Lets take our previous example, but assume that
  the dividend will grow at a rate of 15 per year
  for the next three years before settling down to
  a constant 8 per year. Whats the value of the
  stock now? (Recall that D0 1.85)

17
What if Growth Isnt Constant? (cont.)

• First, note that we can calculate the value of
  the stock at the end of period 3 (using D4)
• Now, find the present values of the future
  selling price and D1, D2, and D3
• So, the value of the stock is 34.09 and we
  didnt even have to assume a constant growth
  rate. Note also that the value is higher than the
  original value because the average growth rate is
  higher.

18
Two-Stage DDM Valuation Model

• The previous example showed one way to value a
  stock with two (or more) growth rates.
  Typically, such a company can be expected to have
  a period of supra-normal growth followed by a
  slower growth rate that we can expect to last for
  a long time.
• In these cases we can use the two-stage DDM

19
Two-Stage DDM Valuation Model (cont.)

• The two-stage growth model is not a complex as it
  seems
• The first term is simply the present value of the
  first N dividends (those before the constant
  growth period)
• The second term is the present value of the
  future stock price.
• So, the model is just a mathematical formulation
  of the methodology that was presented earlier.
  It is nothing more than an equation to calculate
  the present value of a set of cash flows that are
  expected to follow a particular growth pattern in
  the future.

20
Three-Stage DDM Valuation Model

• One improvement that we can make to the two-stage
  DDM is to allow the growth rate to change slowly
  rather than instantaneously.
• The three-stage DDM is given by

21
Other Valuation Methods

• Some companies do not pay dividends, or the
  dividends are unpredictable.
• In these cases we have several other possible
  valuation models
• Earnings Model
• Free Cash Flow Model
• P/E approach
• Price to Sales (P/S)

22
The Earnings Model

• The earnings model separates a companys earnings
  (EPS) into two components
• Current earnings, which are assumed to be
  repeated forever with no growth and 100 payout.
• Growth of earnings which derives from future
  investments.
• If the current earnings are a perpetuity with
  100 payout, then they are worth

23
The Earnings Model (cont.)

• VCE is the value of the stock if the company does
  not grow, but if it does grow in the future its
  value must be higher than VCE so this represents
  the minimum value (assuming profitable growth).
• If the company grows beyond their current EPS by
  reinvesting a portion of their earnings, then the
  value of these growth opportunities is the
  present value of the additional earnings in
  future years.
• The growth in earnings will be equal to the ROE
  times the retention ratio (1 payout ratio)
• Where b retention ratio and r ROE (return on
  equity).

24
The Earnings Model (cont.)

• If the company can maintain this growth rate
  forever, then the present value of their growth
  opportunities is
• Which, since NPV is growing at a constant rate
  can be rewritten as

25
The Earnings Model (cont.)

• The value of the company today must be the sum of
  the value of the company if it doesnt grow and
  the value of the future growth
• Where RE1 is the retained earnings in period 1, r
  is the return on equity, k is the required
  return, and g is the growth rate

26
The Free Cash Flow Model

• Free cash flow is the cash flow thats left over
  after making all required investments in
  operating assets
• Where NOPAT is net operating profit after tax
• Note that the total value of the firm equals the
  value of its debt plus preferred plus common

27
The Free Cash Flow Model (cont.)

• We can find the total value of the firms
  operations (not including non-operating assets),
  by calculating the present value of its future
  free cash flows
• Now, add in the value of its non-operating assets
  to get the total value of the firm

28
The Free Cash Flow Model (cont.)

• Now, to calculate the value of its equity, we
  subtract the value of the firms debt and the
  value of its preferred stock
• Since this is the total value of its equity, we
  divide by the number of shares outstanding to get
  the per share value of the stock.

29
Relative Value Models

• Professional analysts often value stocks relative
  to one another.
• For example, an analyst might say that XYZ is
  undervalued relative to ABC (which is in the same
  industry) because it has a lower P/E ratio, but a
  higher earnings growth rate.
• These models are popular, but they do have
  problems
• Even within an industry, companies are rarely
  perfectly comparable.
• There is no way to know for sure what the
  correct price multiple is.
• There is no easy, linear relationship between
  earnings growth and price multiples (i.e., we
  cant say that because XYZ is growing 2 faster
  that its P/E should be 3 points higher than
  ABCs there are just too many additional
  factors).
• A companys (or industrys) historical multiples
  may not be relevant today due to changes in
  earnings growth over time.

30
The P/E Approach

• As a rule of thumb, or simplified model, analysts
  often assume that a stock is worth some
  justified P/E ratio times the firms expected
  earnings.
• This justified P/E may be based on the industry
  average P/E, the companys own historical P/E, or
  some other P/E that the analyst feels is
  justified.
• To calculate the value of the stock, we merely
  multiply its next years earnings by this
  justified P/E

31
The P/S Approach

• In some cases, companies arent currently earning
  any money and this makes the P/E approach
  impossible to use (because there are no
  earnings).
• In these cases, analysts often estimate the value
  of the stock as some multiple of sales
  (Price/Sales ratio).
• The justified P/S ratio may be based on
  historical P/S for the company, P/S for the
  industry, or some other estimate