1. FI 3300 - Corporate Finance Leng Ling
FINC3131 Business Finance
Chapter 9: Stocks and Their Valuation

2. Learning objectives Compute the price of a preferred stock.
Compute the price of common stock under various assumptions about dividend growth.

3. Preferred stock Hybrid security.
Like bonds, preferred stockholders receive a fixed dividend that must be paid before dividends are paid to common stockholders.
However, companies can omit preferred dividend payments without fear of pushing the firm into bankruptcy.

4. Common Stock Represents ownership Ownership implies control
Stockholders elect directors
Directors elect management
Management’s goal: Maximize the stock price

5. Dividend growth model
Value of a stock is the present value of the future dividends expected to be generated by the stock.

6. FI 3300 - Corporate Finance Leng Ling
Preferred stock
Pays a fixed dividend forever.
Price of preferred stock is simply the present value of a perpetuity.
Required rate of return on preferred stock.
Preferred stock dividend
Price of preferred stock
Required rate of return on preferred stock/ cost of capital for preferred stock

7. FI 3300 - Corporate Finance Leng Ling
Common stock
For common stock, the future cash flows are:
Dividends
Selling price
These cash flows are highly uncertain.
To find the value of common stock, we make assumptions about how dividends evolve in the future. We look at 3 set of assumptions:
Constant dividend stream
Dividends grow at constant rate (constant dividend growth model)
Non-constant dividend growth

8. Constant dividend stream
FI Corporate Finance Leng Ling
Constant dividend stream
Same amount of dividend is paid for ever.
Cash flow stream resembles a perpetuity.
Thus, we value the common stock in the same way as we value the preferred stock.
Common stock price, Pe
Cost of equity capital, re
Common stock dividend
Cost of equity capital or required rate of return on equity

9. Dividends grow at constant rate 1
Assume that dividends grow at a constant rate, g, per period forever.
Given this assumption, the price of common stock equals
Don’t panic.
D1 = D0(1 + g)
D0 = Dividend that the firm just paid
Required rate of return on equity
Dividend growth rate

10. Dividends grow at constant rate 2
Useful properties.
All other things unchanged,
If D0 increases (decreases), Pe increases (decreases).
If g increases (decreases), Pe increases (decreases).
If re increases (decreases), Pe decreases (increases).

11. Dividends grow at constant rate 2
FI Corporate Finance Leng Ling
Dividends grow at constant rate 2
By rearranging the above equation, we can find the required rate of return on equity
For the constant growth model to work, re > g.
Capital gains yield
Required rate of return on equity
Dividend yield

12. Constant growth problems 1
FI Corporate Finance Leng Ling
Constant growth problems 1
Jarrow Company will pay an annual dividend of $3 per share one year from today. The dividend is expected to grow at a constant rate of 7% permanently. The market requires 15% What is the current price of the stock (to 2 decimal places)?
In this question D1 is already given to you.
Verify that Price = $37.5

13. Constant growth problems 2
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Constant growth problems 2
Johnson Foods Inc. just paid a dividend of $10 (i.e., D0 = 10.00). Its dividends are expected to grow at a 4% annual rate forever. If you require a 15% rate of return on investments of this risk level, what is Johnson Foods’s current stock price? (to 2 decimal places)
Straightforward application of price formula.
Verify that price = $94.55

14. Constant growth problems 3
FI Corporate Finance Leng Ling
Constant growth problems 3
The price of a stock in the market is $62. You know that the firm has just paid a dividend of $5 per share (i.e., D0 = 5). The dividend growth rate is expected to be 6 percent forever. What is the investors’ required rate of return for this stock (to 2 decimal places)?
Use re = (D1/P) + g.
Verify that re = 14.55%

15. Constant growth problems 4
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Constant growth problems 4
A firm is expected to pay a dividend of $5.00 on its stock next year. The price of this stock is $40 and the investor’s required rate of return is 20%. The firm’s dividends grow at a constant rate. What is this constant dividend growth rate (g)?
use re = (D1/P) + g
Verify that g = 7.5%

16. Constant growth problems 5
FI Corporate Finance Leng Ling
Constant growth problems 5
In order to use the constant dividend growth model to value a stock it must be true that:
a. The required rate of return is less than the expected dividend growth rate.
b. The expected dividend growth rate is greater than zero.
c. The next dividend (D1) is expected to be greater than $1.00.
d. The expected dividend growth rate is less than the required rate of return.
Which statement is correct?

17. Non-constant dividend growth 1
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Non-constant dividend growth 1
With this assumption, dividends grow at different rates for different periods of time. Eventually, dividends will grow at a constant rate forever.
Time line is very useful for valuing this type of stocks.
To value such stocks, also need the constant growth formula.
Best way to learn is through an example.

18. Non-constant dividend growth 2
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Non-constant dividend growth 2
ABC Co. is expected to pay dividends at the end of the next three years of $2, $3, $3.50, respectively. After three years, the dividend is expected to grow at 5% constant annual rate forever. If the required rate of return on this stock is 15%, what is the current stock price?
Dividends grow at 5% forever
$2.00
$3.00
$3.50
T = 0
T =1
T = 2
T = 3
T = 4

19. FI 3300 - Corporate Finance Leng Ling
What to do?
Use constant growth formula to find stock price at the end of year 3. Call this stock price P3.
Add P3 to dividend received at t=3. This sum is the cash flow for t=3. Find PV of this cash flow.
Find PV of dividends at t=1, t=2.
Current stock price = sum of 2 and 3.

20. Apply the method to find ABC’s stock price
FI Corporate Finance Leng Ling
Apply the method to find ABC’s stock price
P3 = (3.5 x (1.05))/(0.15 – 0.05) = 36.75
At t=3, cash flow is = 40.25
Current stock price, P0

21. If D0 = $2 , r=13% and g = 30% for 3 years before achieving long-run growth of 6%, what is the PV?
Can no longer use just the constant growth model to find stock value.
However, the growth does become constant after 3 years.

22. 1 2 3 4
D0 =
...
4.658
rs = 13%
g = 30%
g = 6%
2.301
2.647
3.045
46.114
= P0 =
0.06
$66.54 3
4.658
0.13 - $ P ^

23. Another type of non-constant growth problem
FI Corporate Finance Leng Ling
Another type of non-constant growth problem
Malcolm Manufacturing, Inc. just paid a $2.00 annual dividend (that is, D0 = 2.00). Investors believe that the firm will grow at 10% annually for the next 2 years and 6% annually forever thereafter. Assuming a required return of 15%, what is the current price of the stock (to 2 decimal places)?
Use timeline to ‘see’ the problem better.
Verify that stock price = $25.29

24. Summary Find the price/ present value of equity securities
Consols, preferred stock are valued using the same techniques.
Common stocks are valued under 3 different assumptions about dividends
Constant dividends
Dividends grow at constant rate
Dividends grow at different rates
Assignment:
self-test question ST-3 ST-4
problems: