CHAPTER 8 – STOCK VALUATION
Reasons for difficulty in evaluating a share:
1) Promised cash flows are not known in advance
2) Life of the investment is forever as common stock has no maturity
3) No way to observe the rate of return that the market requires
Present Value of FCF (Future Cash Flows) to determine share of stock value:
Po = (D1 + P1) / (1+r)
D = cash dividend paid at the end of the period
Po = Current price of the stock
P1 = Price in one period
R = required return in the market on the investment
Current price of the stock can be written as the PV of the dividends beginning in one period and
extending out forever:
D1/(1+r)^1 + D2/(1+r)^2 + D3/(1+r)^3….
Price of the stock today is = to the present value of all the future dividends.
1) Dividend has a zero growth rate
P0 = D1/(1+r)^1 + D2/(1+r)^2 + D3/(1+r)^3….
Because the dividend is always the same, the stock can be viewed as an ordinary
perpetuity. P0 = D/r
R = Required rate of return
2) Constant growth (The dividend grows at a constant rate) – growing perpetuity
Dt = D0 x (1+g)^t
T = periods in the future
G= growth rate
Only if the growth rate, g, is less than the discount rate, r, use the DIVIDENT GROWTH
P0 = D0 x (1+g)/r-g = D1/r-g
To get the stock price at any point in time use:
Pt = Dt x (1+g)/r-g = Dt+1/r-g
3) The dividend grows at a constant rate after some length of time
If the company is not currently paying dividends and decides to in 4 years one can calculate
the stock price today.
We find out what it will be worth once dividends are paid. Then calculate the PV of that
future price to get todays price.
P4 = D5/r-g
Ex. The stock will be worth 5$ in four years.
To get the current value, discount this back four years.
P0 = 5/ (1+r)^4
SPECIAL CASE: To calculate value of the stock today, do the following:
Changing the Growth Rate
r = (r-g) = D1/P0
r = D1/P0 + g
Dividend Yield = D1/P0
The price a share of preferred stock is the dividend divided by the required return.
Ex. Dividends will be paid 12$ per year beginning in 4 years. To find PV of preferred stock:
Find P3, then P3/(1+r)^3
Rate at which the stock price grows = Capital gains yield
Dividend growth model calculates total return as: r = Dividends yield + Capital gains yield
Companies that don’t pay dividends:
Find benchmark PE Ratio by stock’s price per share to its EPS over the previous year.
PE Ratio = Stock price/share/Earnings per share (EPS)
Price at time t = Pt = Benchmark PE Ratio x EPSt 8.2
Shareholders have the right to hire management/directors to