1. Stock Valuation

2. One Period Valuation Model
To value a stock, you first find the present discounted value of the expected cash flows.
P0 = Div1/(1 + ke) + P1/(1 + ke) where
P0 = the current price of the stock
Div = the dividend paid at the end of year 1
ke = required return on equity investments
P1 = the price at the end of period one

3. One Period Valuation Model
P0 = Div1/(1 + ke) + P1/(1 + ke)
Let ke = 0.12, Div = 0.16, and P1 = $60.
P0 = 0.16/ $60/1.12
P0 = $ $53.57
P0 = $53.71
If the stock was selling for $53.71 or less, you would purchase it based on this analysis.

4. Generalized Dividend Valuation Model
The one period model can be extended to any number of periods.
P0 = D1/(1+ke)1 + D2/(1+ke)2 +…+ Dn/(1+ke)n + Pn/(1+ke)n
If Pn is far in the future, it will not affect P0
Therefore, the model can be rewritten as:
P0 = S Dt/(1 + ke)t ∞
t=1

5. Generalized Dividend Valuation Model
The model says that the price of a stock is determined only by the present value of the dividends.
If a stock does not currently pay dividends, it is assumed that it will someday after the rapid growth phase of its life cycle is over.
Computing the present value of an infinite stream of dividends can be difficult.
Simplified models have been developed to make the calculations easier.

6. Gordon Growth Model Assumptions:
Dividends continue to grow at a constant rate for an extended period of time.
The growth rate is assumed to be less than the required return on equity, ke.
Gordon demonstrated that if this were not so, in the long run the firm would grow impossibly large.

7. The Gordon Growth Model
Firms try to increase their dividends at a constant rate.
P0 = D0(1+g)1 + D0(1+g)2 +…..+ D0(1+g)∞
(1+ke) (1+ke)2 (1+ke)∞
D0 = the most recent dividend paid
g = the expected growth rate in dividends
ke = the required return on equity investments
The model can be simplified algebraically to read:
P0 = D0(1 + g) D1
(ke – g) (ke – g) =

8. Gordon Model: Example
Find the current price of Coca Cola stock assuming the following:
g = %
D0 = $1.00
ke = 13%.
P0 = D0(1 + g)/ke – g
P0 = $1.00(1.1095)/
P0 = $1.1095/ = $54.12

9. Gordon Model: Conclusions
Theoretically, the best method of stock valuation is the dividend valuation approach.
But, if a firm is not paying dividends or has an erratic growth rate, the simple model will not work.
Consequently, other methods are required.

10. Non-constant Growth Firms typically go through life cycles.
Early in the cycle, their growth is much faster than that of the economy as a whole.
Later in the cycle, their growth matches the economy’s growth.
Finally, their growth is less than the economy’s.
Non-constant or supernormal growth occurs during that part of the life cycle when the firm grows faster than the economy as a whole.

11. Dividend Growth Rates Div($) Normal growth = 8%
Supernormal growth = 30%
Normal growth = 8%
1.15
Zero growth = 0%
Declining growth = -8%
Years

12. Firm Valuation with Non-constant Growth
The value of the firm equals the present value of its expected future dividends.
Process:
Find the present value of the dividends during the period of non-constant growth.
Find the price of the stock at the end of the non-constant growth period and discount this price back to the present.
Add the two components to find the value of the stock, P0.

13. Firm Valuation with Non-constant Growth: Problem
Assume the following:
k = 13.4% (required rate of return
N = 3 (years of supernormal growth)
gs = 30% (rate of growth in supernormal period)
gn = 8% (rate of growth in normal period)
D0 = $1.15 (last dividend paid)
Find the value of the stock.

14. Firm Valuation with Non-constant Growth: Problem
Step 1:
Calculate the dividends expected at the end of each year during the supernormal period.
Dn = Dn-1(1 + gs)
D1 = $1.15(1 + .3) = $1.495
D2 = $1.495(1 + .3) = $1.9435
D3 = $1.9435(1 + .3) = $2.5265

15. Firm Valuation with Non-constant Growth: Problem
Step 2:
Calculate the price of the stock during the normal growth period using the Gordon model.
Calculate the dividend in the fourth period.
Use the constant growth formula to find P3.
D4 = $2.5265( ) = $2.7286
P3 = $2.7286/0.134 – 0.08 = $50.53
If the stockholder sold the stock in period 3, he would receive $ Total cash flow at time 3 equals D3 + P3 = $

16. Firm Valuation with Non-constant Growth: Problem
Step 3:
Discount the cash flows found in steps 1 and 2 and sum the amounts to find the value of the supernormal growth stock.
D1 = $1.4950/(1.134) = $1.3183
D2 = $1.9435/ = $1.5113
D3 = $2.5265/ = $1.7325
P3 = $ / = $34.65
Value of growth stock = $39.21

17. Errors in Valuation Problems with Estimating Growth
Growth can be estimated by computing historical growth rates in dividends, sales, or net profits.
But, this approach fails to consider any changes in the firm or economy that may affect the growth rate.
Competition, for example, will prevent high growth firms from being able to maintain their historical growth rate.
Nevertheless, stock prices of historically high growth firms tend to reflect a continuation of the high growth rate.
As a result, investors receive lower returns than they would by investing in mature firms.

18. Estimating Growth: Table 1
Stock Prices for a Security with D0 = $2.00, ke = 15%,
and Constant Growth Rates as Listed
Growth(%) Price
1 $14.43

19. Errors in Valuation Problems with Estimating Risk
The dividend valuation model requires the analyst to estimate the required return for the firms equity.
However, a share of stock offering a $2 dividend and a 5% growth rate changes with different estimates of the required return.

20. Estimating Risk: Table 2
Stock Prices for a Security with D0 = $2.00, g = 5%,
and Required Returns as Listed
Required Return(%) Price
10 $42.00

21. Errors in Valuation Problems with Forecasting Dividends Conclusion:
Many factors can influence the dividend payout ratio. They include:
The firm’s future growth opportunities
Management’s concern over future cash flows
Conclusion:
Analysts are seldom certain that the stock price projections are accurate.
This is why stock prices fluctuate widely on news reports.

22. Price Earnings Valuation Method
The price earnings ratio (PE) is a widely watched measure of how much the market is willing to pay for $1 of earnings from a firm.
A high PE has two interpretations:
A higher than average PE may mean that the market expects earnings to rise in the future.
A high PE may indicate that the market thinks the firm’s earnings are very low risk and is therefore willing to pay a premium for them.

23. Price Earnings Valuation Method
The PE ratio can be used to estimate the value of a firm’s stock.
Firms in the same industry are expected to have similar PE ratios in the long run.
The value of a firm’s stock can be found by multiplying the average industry PE times the expected earnings per share.
P/E x E = P

24. Price Earnings Model: Example
The average industry PE ratio for restaurants similar to Applebee’s is 23. What is the current price of Applebee’s if earnings per share are projected to be $1.13?
P0 = P/E x E
P x $1.13 = $26.

25. Price Earnings Valuation Method
Advantages:
Useful for valuing privately held firms and firms that do not pay dividends.
Disadvantages:
By using an industry average PE ratio, firm-specific factors that might contribute to a long-term PE ratio above or below the average are ignored.

26. Non-constant Growth Model
The non-constant growth model can be used to estimate the value of a stock that does not pay dividends during its early years, if it is expected to pay dividends in the future.

27. Non-constant Growth Model
Process:
Estimate the following:
when dividend will be paid
the amount of the first dividend
the growth rate during the supernormal period
the length of the supernormal period
the long-run constant growth rate
the rate of return required by investors.
Use the constant growth model to determine the price of the stock after the firm reaches stable growth.
Find all the cash flows, take the present value of each and sum.

28. Setting Security Prices
Stock prices are set by the buyer willing to pay the highest price.
The price is not necessarily the highest price that the stock could get, but it is incrementally greater than what any other buyer is willing to pay.
The market price is set by the buyer who can take best advantage of the asset.

29. Setting Security Prices
Superior information about an asset can increase its value by reducing its risk.
The buyer who has the best information about future cash flows will discount them at a lower interest rate than a buyer who is uncertain.