Stock Valuation Common Stock Valuation Features of Common and Preferred Stocks The Stock Market 1. Common Stock Valuation In 1938, John Burr Williams postulated what has become the fundamental theory of valuation :
1. Common Stock Valuation
In 1938, John Burr Williams postulated what has become the fundamental theory of valuation:
The value today of any financial asset equals the present value of all of its future cash flows.
For common stocks, this implies the following (the general case):
D1 P1 D2 P2
P0 = +and P1 = +
(1 + R)1 (1 + R)1(1 + R)1 (1 + R)1
substituting for P1 gives
D1 D2 P2
P0 = + + . Continuing to substitute, we obtain
(1 + R)1 (1 + R)2 (1 + R)2
D1 D2 D3 D4
P0 = + + + + …
(1 + R)1 (1 + R)2 (1 + R)3 (1 + R)4
C/r or, in this case, D1/R.
D1 D2 D3 D0(1+g)1 D0(1+g)2 D0(1+g)3
P0 = + + + … = + + + ...
(1 + R)1 (1 + R)2 (1 + R)3 (1 + R)1 (1 + R)2 (1 + R)3
D0(1 + g) D1
P0 = = .
R - g R- g
= = $
R - g
= = $
R - g
Why does a lower growth rate result in a lower value?
Stock price ($)
D1 = $1
Required return, R, = 12%
Dividend growth rate, g
P0 =present value of dividends in the nonconstant growth period(s)
+ present value of dividends in the “steady state” period.
See Examples in page 223
If a firm is not paying dividend currently and it expects to pay $0.50/share dividend in year 5. Dividend will grow by 10% since then. The required rate of return is 20%. What is the price of the stock today?
the starting point is year 0 while first dividend is in year 5. Let’s ignore the period from year 0 to year 5. Assuming year 5 is a new year 0. What would be the stock price of the new stock in the setup:
P(5) = D(5)+D(5)*(1+g)/(R-g) = 0.5+0.5*1.1/(.2-.1)=6.0
P(0) = P(5)/(1+R)^5 = 6.0/1.2^5=2.41
Go through the next example (figure 8.1, p223)
Go through Table 8.1
Example 2: A company has been growing at a rate of 30% for 3 years and then drops to 10% per year. Its total dividend just paid were $5 million and required rate of return is 20%. If the growth rate remains constant indefinitely, what is the total value of the stock?
The required return, r, can be written as the sum of two things:
R = D1/P0 + g
where D1/P0 is the dividend yield and gis the capital gains yield (which is the same thing
as the growth rate in dividends for the steady growth case).
The right to vote
The right to share proportionally in dividends paid
The right to share proportionally in assets remaining after liabilities have been paid, in event of a liquidation
The preemptive right
Preferences over common stock - dividends, liquidation
Dealers vs. brokers
Multiple market makers