5: Valuing Shares

Now, take this expression for P 1 and substitute it back into Equation 5.2:

=

+

+

+

=

+

+

+

P

D

DP

r

r

D

r

DP

r

(1 )

(^0) (1 )(1)(1 )
1
22
1
2
1
1
22
2
We have an expression that says that the price of a share today equals the present value of the
dividends it will pay over the next two years, plus the present value of the selling price in two years. Again
we could ask, what determines the selling price in two years, P 2? By repeating the last two steps over and
over, we can determine the price of a share today, as shown in Equation 5.3:
Eq. 5.3 =
(1+)

• (1+)


• 
  

  (1+)

  
  


• 
  

  (1+)

  
  


• 
  

  (1+)
  P 0 11 22 33 44 55 +...
  D
  r
  D
  r
  D
  r
  D
  r
  D
  r
  The price of a share today equals the present value of the entire dividend stream that the share will
  pay in the future. Now consider the problem that an investor faces if she or he tries to determine whether
  a particular share is overvalued or undervalued. In deciding whether to buy the share, an investor needs
  two inputs to apply Equation 5.3: the projected dividends and the discount rate. Neither input is easy
  to estimate. For a share that already pays a dividend, predicting what the dividend will be over the next
  few quarters is not terribly difficult, but forecasting far out into the future is another matter. For shares
  that currently do not pay a dividend, the problem is even more difficult, because the analyst has to
  estimate when the dividend stream will begin. Likewise, the discount rate, or the rate of return required
  by the market on this share, depends on the share’s risk. We defer a full discussion of how to measure a
  share’s risk and how to translate that into a required rate of return until chapters 6 and 7. For now, we
  focus on the problem of estimating dividends.^4 In most cases, analysts can formulate reasonably accurate
  estimates of dividends in the near future. The real trick is to determine how quickly dividends will grow
  over the long run. Our discussion of share valuation centres on three possible scenarios for dividend
  growth: zero growth, constant growth and variable growth.
  5-2c ZERo GRoWtH
  The simplest approach to dividend valuation, the zero growth model, assumes a constant dividend stream.
  That assumption is not particularly realistic for most companies, but it may be appropriate in some
  special cases. If dividends do not grow, we can write the following equation:
  DD 12 ==DD 3 ==...
  Plugging the constant value D for each dividend payment into Equation 5.3, you can see that the
  valuation formula simply reduces to the equation for the present value of a perpetuity:
  P
  D
  (^0) r

  
  

  In this special case, the formula for valuing ordinary shares is essentially identical to that for valuing
  preferred shares.
  4 For shares that do not pay dividends, analysts can estimate the value of the share either by discounting the free cash flow that the company
  produces or by using a ‘multiples’ approach. Both of these alternatives are described later in this chapter.
  LO5.2
  zero growth model
  The simplest approach to
  share valuation that assumes
  a constant dividend stream
  Holding all other factors
  constant, if investors become
  less risk averse, meaning that
  they are willing to accept lower
  returns when investing in risky
  assets, what would happen to
  share values generally?
  thinking cap
  question