1. Miss Faith Moono Simwami
Stock Valuation
Chapter 6
Miss Faith Moono Simwami

2. What is a Preferred Stock ?
Preferred Stock is a type of stock that promises a (usually) fixed dividend, but at the discretion of the board of directors.
What is a Preferred Stock ?
Preferred Stock has preference over common stock in the payment of dividends and claims on assets.
Preferred Stock Valuation
This is a perpetuity!
V = DivP / kP
Where : DivP is the dividend on the preferred stock and
kP is the required rate of return.
Preferred Stock. Example
Stock PS has an 8%, $100 par value issue outstanding. The appropriate discount rate is 10%. What is the value of the preferred stock?
DivP = $100 ( 8% ) = $8.00. kP = 10%.
V = DivP / kP = $8.00 / 10% = $80

3. What is a Common stock?
Common stock represents a residual ownership position in the corporation.
Pro rata share of future earnings after all other obligations of the firm (if any remain).
It represent an interest in the ownership of a company. Shares entitle shareholders to dividends but do not guarantee payment of dividend all the time. Shares can also be sold at some future date at a higher price. This allows the shareholder to earn Capital Gains. It is also possible to make capital losses if share prices depreciate. The main cash flow streams from stocks are dividends and capital gains resulting from selling the shares at a higher price.
Dividends may be paid out of the pro rata (proportion) share of earnings.
How to evaluate the Intrinsic Value (P0). of Common stock
Intrinsic Value represents the value of the stock today in the market it is determined through fundamental analysis
A prudent investor will only buy a stock if its market price does not exceed what the investor thinks the stock is worth.
Intrinsic value depends upon several factors:
Estimates of future cash flows
Discount rate
Amount of risk

4. Common Stock Valuation
What cash flows will a shareholder receive when owning shares of common stock?
(1) Future dividends
(2) Future sale of the common stock shares
Dividend Valuation Model
Basic dividend valuation model accounts for the PV of all future dividends
The value of a stock depends on whether the dividend is static (Zero growth); growing from year to year at constant rate or growing at a
non constant rate.
Hence the following models have been developed.

5. Constant Growth Model (Gordon’s model)
Dividend Growth Pattern Assumptions
The dividend valuation model requires the forecast of all future dividends. The following dividend growth rate assumptions simplify the valuation process.
Constant Growth
No Growth (Zero growth);
Growth Phases (growing at a non constant rate).
Constant Growth Model (Gordon’s model)
Assume that dividends grow at a constant rate, g, per period forever.
Given this assumption, the price of common stock equals
D0 = Dividend that the firm just paid
is the dividend paid at the end of year one..
D1 = D0(1 + g)
Required rate of return on equity
Dividend growth rate

6. Constant Growth Model Example
Stock CG has an expected dividend growth rate of 8%. Each share of stock just received an annual $3.24 dividend. The appropriate discount rate is 15%. What is the value of the common stock?
D1 = $3.24 ( ) = $3.50
P0 = D1 / ( kS - g ) = $3.50 / ( ) = $50

7. Zero Growth Model Zero Growth Model Example
The zero growth model assumes that dividends will grow forever at the rate g = 0.
D1: Dividend paid at time 1.
kS: Investor’s required return.
Zero Growth Model Example
Stock ZG has an expected growth rate of 0%. Each share of stock just received an annual $3.24 dividend per share. The appropriate discount rate is 15%. What is the value of the common stock?
D1 = $3.24 ( ) = $3.24
PZG = D1 / ( ke - 0 ) = $3.24 / ( ) = $21.60

8. Non – Constant or Growth Phases Model
This is a model that is applied when growth is not constant
The growth phases model assumes that dividends for each share will grow at two or more different growth rates.
Example 1. A company’s required rate of return is 16% and the dividend growth at a rate of 30% g1 for 3 years and then it dropped to a constant growth rate of 10% g2 thereafter. The most recently paid dividend was D0= K1.82. Find the value of the stock?
Where dividends grow a varying growth rates the following steps are required to solve such a question.
Step 1 Find the PV of the dividend during the period of non constant growth by first finding respective dividends for each year and then discounting those cash flows.
Step 2 Find the price of the stock at the end of the non constant growth period, at which point it has become a constant growth stock and then discount this price back to the present.
Steps 3 Finally add the values found in Step 1 and Step 2 to determine the value of the stock today.

9. Growth Phases Model Example: Time Line Illustration 
D D D D D D6
Growth of g1 = 30% for 3 years
Growth of g2 = 10% to infinity!
The Stock has two phases of growth. The first, 30%, starts at time t=0 for 3 years and is followed by 10% thereafter starting at time t=3. We should view the time line as two separate time lines in the valuation.
Note that the second phase of the growth phases model assumes that dividends will grow at a constant rate g2.

10. Valuing common stock with non-constant growth Example 1:
D1= 1.82(1.30)1 = 2.366
D3= 1.82(1.30)3 = 3.999
P3= D4/ks-g
D4= 3.999(1.10)
D2= 1.82(1.30)2 = 3.076 1 2 3 4
D0 =
...
4.3989
rs = 16%
g = 30%
g = 10%
2.040
2.286
2.562
46.98
53.87 = P0 =
0.10
$73.32 3
4.3989
0.16 - $ P ^
This is the price of the stock at the end of year 3,so we discount back to the present- 3 years back. PV of P3
 Total

11. Growth Phases Model Example2
Stock GP has an expected growth rate of 16% for the first 3 years and 8% thereafter. Each share of stock just received an annual $3.24 dividend per share. The appropriate discount rate is 15%. What is the value of the common stock under this scenario? 
D D D D D D6
Growth of 16% for 3 years
Growth of 8% to infinity!
Stock GP has two phases of growth. The first, 16%, starts at time t=0 for 3 years and is followed by 8% thereafter starting at time t=3. We should view the time line as two separate time lines in the valuation.

12. Growth Phases Model Example

13. Growth Phases Model Example
Determine the annual dividends.
D0 = $3.24 (this has been paid already)
D1 = D0(1 + g1)1 = $3.24(1.16)1 =$3.76
D2 = D0(1 + g1)2 = $3.24(1.16)2 =$4.36
D3 = D0(1 + g1)3 = $3.24(1.16)3 =$5.06
D4 = D3(1 + g2)1 = $5.06(1.08)1 =$5.46

14. Growth Phases Model Example
We determine the PV of cash flows.
PV(D1) = D1(PVIF15%, 1) = $3.76 (0.870) = $3.27
PV(D2) = D2(PVIF15%, 2) = $4.36 (0.756) = $3.30
PV(D3) = D3(PVIF15%, 3) = $5.06 (0.658) = $3.33
P3 = $5.46 / ( ) = $78 [CG Model]
PV(P3) = P3(PVIF15%, 3) = $78 (0.658) = $51.32
Finally, we calculate the intrinsic value by summing all of cash flow present values.
V = $61.22
V =$ $ $ $51.32

15. Determining the Yield on Preferred Stock
Determine the yield for preferred stock with an infinite life. P0 = DivP / kP Solving for kP such that kP = DivP / P0
Preferred Stock Yield Example
Assume that the annual dividend on each share of preferred stock is $10. Each share of preferred stock is currently trading at $100. What is the yield on preferred stock?
kP = $10 / $100.
kP = 10%.

16. Determining the Yield on Common Stock
To Assume this, the constant growth model is appropriate. Determine the yield on the common stock. By rearranging the equation, we can find the required rate of return on equity
Required rate of return on equity
Dividend yield
Capital gains yield
Required rate of return on equity is also called Expected Yield (ke)
Common Stock Yield: Example1
Assume that the expected dividend (D1) on each share of common stock is $3. Each share of common stock is currently trading at $30 and has an expected growth rate of 5%. What is the yield on common stock?
rs = ( $3 / $30 ) + 5%
rs = 10% + 5% = 15%

17. Expected Yield (ke) = (D1/Po) + g Dividend yield = (K5/K20) = 25%
Example 2
A stock originally sold for K20 per share and now sells for K25.The dividend last paid was K5.Find the Dividend yield and capital gains yield and total yield or return?
Expected Yield (ke) = Dividend Yield + Capital Gains Yield
Expected Yield (ke) = (D1/Po) + g
Dividend yield = (K5/K20) = 25%
Capital Gain = K25-K20 = K5
Capital Gains yield = K5/K20 =25%
Total Yield (Ke)= 25%+25% =50%
NOTE. Suppose the stock had a growth rate g of 5% this represent the capital gains yield for such a stock.