1. Lahore School of Economics
Capital Markets
Winter Semester 2013
Lahore School of Economics

2. Common Stock Valuation

3. Chapter 10 Common Stock Valuation Learning Objectives
Dividend Growth model
Zero Growth
Constant Growth
Multiple growth model
Intrinsic Value & Market price
Relative Valuation Techniques (P/E,P/S,P/S)
Components of Required Return 2

4. Capital Market Securities
Fixed Income (Bonds)
Treasuries
Agencies
Municipals
Corporates
Equities
Preferred Stock
Common Stock 2

5. Stocks
It is an equity ownership in a corporation, initially issued to raise capital
Points to keep in mind (vs Bonds)
C/F’s are NOT known in advance
Life of stocks is forever – no maturity
Difficult to observe required rate of return for discounting 2

6. Stocks How do we come up with the Price of a Stock?
PV of all future expected C/F’s?
Assumptions will be needed!
Assume a dividend the stock will pay.
Come up with a required rate of return. 2

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

8. Stocks Valuation Formula: Po = E Dn / (1+R)^n
PV of all future dividends…
as a general valuation framework.
Dividends to infinity are still a problem at this stage! 2

9. Stocks Valuation The problem of NO dividends….
This formula assumes the company will pay something at some point in its life to its shareholders.
A Corp where money goes in but nothing comes out doesn’t exist. Or shouldn’t exist! 2

10. Stocks Valuation Special Cases…. of dividends Zero-growth:
Here the dividend is constant, D1=D2=D
So, the value of the stock is a Perpetuity (ordinary),
Po = D/R same as PV = C/r 2

11. Stocks Valuation Suppose a company pays Rs. 10 dividend always.
Example zero-growth
Suppose a company pays Rs. 10 dividend always.
If this policy is forever,…
What’s the stock price if the required return is 20%? 2

12. Stocks Valuation Suppose a company pays Rs. 10 dividend always.
Example zero-growth
Suppose a company pays Rs. 10 dividend always.
If this policy is forever,…
What’s the stock price if the required return is 20%?
Po = 10 / 0.2 = Rs 50 per share 2

13. Stocks Valuation Example:
Zero Growth
Example:
A company pays a dividend of $2 per share, which is not expected to change. Required return is 20%.
What’s the price per share today? 2

14. Stocks Valuation Example:
Zero Growth
Example:
A company pays a dividend of $2 per share, which is not expected to change. Required return is 20%.
What’s the price per share today?
Po = Do / k
2/.2 = 10 2

15. Stocks Valuation Special Cases…. of dividends Constant Growth Model:
Suppose the dividend grows at a constant rate g.
If dividend just paid is Do, then the next D1 is:
D1 = Do x (1+g)
& for 2 periods is:
D2 = Do x (1+g)^2 (FV formula)
D2 = (Do x (1+g)) x (1+g) 2

16. An asset where the C/F’s grow at a constant rate forever.
Stocks Valuation
Growing Perpetuity:
An asset where the C/F’s grow at a constant rate forever.
Po = Do x (1+g) / R-g OR
D1 / R - g (g<R) 2

17. Stocks Valuation Example: Suppose Do = 2.30, R=13%, g=5%.
Whats the price per share? 2

18. Example: Suppose Do = 2.30, R=13%, g=5%. D1 / R - g (g<R)
Stocks Valuation
Example:
Suppose Do = 2.30, R=13%, g=5%.
Whats the price per share?
D1 / R - g (g<R)
2.3 x (1.05) / ( )
2.415 / 0.8 = 30.19 2

19. Stocks Valuation Note:
You can use this to find the stock price at any point in time!
Just find the D for that year,
grow it at (1+g)
& then divide by R-g 2

20. Example: Suppose Do = 2.30, R=13%, g=5%. D6 / R - g (g<R)
Stocks Valuation
Example:
Suppose Do = 2.30, R=13%, g=5%.
What’s the price per share in 5 years?
D6 / R - g (g<R) 2

21. Example: Suppose Do = 2.30, R=13%, g=5%. D6 / R - g (g<R)
Stocks Valuation
Example:
Suppose Do = 2.30, R=13%, g=5%.
What’s the price per share in 5 years?
D6 / R - g (g<R)
2.3 x (1.05)^5 / ( )
2.935x(1.05) / 0.8 = /.08 = 38.53 2

22. Stocks Valuation Example:
Suppose Company T’s next dividend will be $4. Required return is 16%.
Dividend increases by 6% every year.
What’s the price per share today?
& in 4 years? 2

23. Stocks Valuation Example:
Suppose next dividend will be $4. Required return is 16%. Dividend increases by 6% every year.
D1 = 4 , R=16%, g=6%. (since D1 is given, don’t need to grow by g)
What’s the price per share today?
Po = D1 / R - g (g<R)
4/ ( ) = 4/.1 = $40 = Po
What’s the price per share in 4 yrs?
Find D5 first, D1 (1+g)^4 = 4(1.06)^4 = 5.05
5.05/0.1 = = P4 2

24. Stocks Valuation Notice here: P4 = Po (1+g)^4 50.50 = 40 x (1.06)^4
So, Stock price grows at the same constant rate as the Dividend!
P4 is simply D5/(R-g) 2

25. Stocks Valuation Constant growth
Example:
Suppose ODGC pays a dividend of Rs.2 per share which is expected to grow at a constant rate of 7% per year. Investors require a rate of return of 16% given the risk of this stock.
D1 = 2*(1.07) = 2.14 , R=16%, g=7%.
What’s the price per share today?
What’s the price per share in 4 yrs? 2

26. Stocks Valuation Constant growth
Example:
Suppose ODGC pays a dividend of Rs.2 per share which is expected to grow at a constant rate of 7% per year. Investors require a rate of return of 16% given the risk of this stock.
D1 = 2*(1.07) = 2.14 , R=16%, g=7%.
What’s the price per share today?
Po = D1 / R - g (g<R)
2.14/ ( ) = = Po
What’s the price per share in 4 yrs?
Find D5 first, D1 (1+g)^4 = 2.14(1.07)^4 = 2.81
2.81/.09 = Rs = P4 2

27. If rRF = 7%, rM = 12%, and β = 1.2, what is the required rate of return on the firm’s stock?
Use the SML to calculate the required rate of return (ks):
rs = rRF + (rM – rRF)β
= 7% + (12% - 7%)1.2
= 13%

28. If D0 = $2 and g is a constant 6%, find the expected dividend stream for the next 3 years, and their PVs. 1
2.247 2
2.382 3
2.12
rs = 13%
g = 6%
1.8761
1.7599
D0 = 2.00
1.6509

29. What is the stock’s market value?
Using the constant growth model:

30. What is the expected market price of the stock, one year from now?
D1 will have been paid out already. So, P1 is the present value (as of year 1) of D2, D3, D4, etc.
Could also find expected P1 as:

31. Dividend yield Capital gains yield Total return (rs)
What is the expected dividend yield, capital gains yield, and total return during the first year?
Dividend yield
= D1 / P0 = $2.12 / $30.29 = 7.0%
Capital gains yield
= (P1 – P0) / P0
= ($ $30.29) / $30.29 = 6.0%
Total return (rs)
= Dividend Yield + Capital Gains Yield
= 7.0% + 6.0% = 13.0%

32. Components of Required Return
Let’s break down the R, discount rate which we used in the Dividend Discount Model or DDM
Po = D1 / (R-g)
if we rearrange to solve for R….
then…
R-g = D1/Po
R = D1/ Po + g 2

33. Components of Required Return
R = D1/ Po + g
This means TR has 2 components:
D1/Po = Dividend Yield
g = same rate as the increase in stock price
= Capital gains yield 2

34. Components of Required Return
EXAMPLE
R = D1/ Po + g
If a stock is selling for $20 per share. Next dividend will be $1 per share. Dividend will grow by 10% per year forever.
What is the return on this stock? 2

35. Components of Required Return
EXAMPLE
R = D1/ Po + g
If a stock is selling for $20 per share. Next dividend will be $1 per share. Dividend will grow by 10% per year forever.
What is the return on this stock?
R = Div yield + Cap gains yield
= 1/ %
= 5% + 10% = 15% 2

36. Components of Required Return
EXAMPLE
R = D1/ Po + g
A stock’s dividend will grow by 8% per year forever. If the stock is selling for $60 per share and next dividend will be $3 per share.
What is the required return on this stock? 2

37. Components of Required Return
EXAMPLE
R = D1/ Po + g
A stock’s dividend will grow by 8% per year forever. If the stock is selling for $60 per share and next dividend will be $3 per share.
What is the required return on this stock?
R = Div yield (D1/Po) + Cap gains yield (g)
= 3/
= = 13% 2

38. PART II

39. Stocks Valuation
Multiple Growth model
Company grows at a certain high rate first, then slows down to grow at a constant sustainable rate. 2

40. Supernormal growth: What if g = 30% for 3 years before achieving long-run growth of 6%?
Can no longer use just the constant growth model to find stock value.
However, the growth does become constant after 3 years.
Terminal Date (Horizon date): the date when the growth becomes constant. At this date it is no longer necessary to forecast the individual dividends.
Horizon(Terminal value): the value at the horizon date of all dividends expected thereafter.

41. Four steps for applying non constant growth model
Find the PV 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, at which point it has become a constant growth stock.
Discount this price back to the present
Add these two components to find the intrinsic value of the stock.(expected price)

42. Valuing common stock with nonconstant growth1 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 ^

43. Find expected dividend and capital gains yields during the first and fourth years.
Dividend yield (first year)
= $2.60 / $54.11 = 4.81%
Capital gains yield (first year)
= 13.00% % = 8.19%
During nonconstant growth, dividend yield and capital gains yield are not constant, and capital gains yield ≠ g.
After t = 3, the stock has constant growth and dividend yield = 7%, while capital gains yield = 6%.

44. Nonconstant growth: What if g = 0% for 3 years before long-run growth of 6%?1 2 3 4
D0 =
...
2.12
rs = 13%
g = 0%
g = 6%
1.77
1.57
1.39
20.99
= P0 ^
0.06 $
$30.29 P 3
2.12
0.13 = -

45. If the stock was expected to have negative growth (g = -6%), would anyone buy the stock, and what is its value?
The firm still has earnings and pays dividends, even though they may be declining, they still have value.

46. Intrinsic Value & Market Price
Stocks Valuation
Intrinsic Value & Market Price
If IV > Mkt Price = under/over-valued?
IV < Mkt Px = under/over valued? 2

47. Stocks Valuation Multiple growth
Example:
MCB is expanding and is expected to grow at a rate of 20% per year for the next three years. Current dividend is Rs. 2 per share. After this rapid growth, the company is likely to slow down to a normal growth of 7% for the foreseeable future. Required return on this stock is 22%.
D1 = 2*(1.20) = 2.40 , R=22%, G1= 20%, g=7%.
What’s the price per share today? 2

48. Relative Valuation Techniques
P/E = Price to Earnings ratio
P/E = Stock Price / EPS
Gives a idea of what the market is willing to pay for the company’s earnings.
The higher the P/E ratio , the more the market is willing to pay for company’s earnings and vice versa.
A high P/E ratio gives an indication that an investor has high hopes for this stock’s future and has bid up the price , which makes the stock over valued. 2

49. Relative Valuation Techniques
Determinants of P/E ratio:
Po = D1 / k – g
P/E1 = D1/E1 / k – g
The expected dividend payout ratio D1/E1
The required rate of return
The expected growth rate in dividends.
“Other things being equal”

50. Relative Valuation Techniques
P/E ratio and interest rates:
The higher the risk , the lower would be the P/E ratio.
As the investor require a higher required rate of return which eventually reduced the P/E ratio.
The required rate of return is related to interest rates.
When interest rates increases, bonds become more attractive than the stocks.
Therfore, as interest rate rise (decline), other things being equal , P/E ratios should decline (rise).

51. Valuation using the P/E ratio:
Stock price is a product of 2 variables:
EPS
The P/E multiple
Po= Eo * Po/Eo
E1= Eo(1+g)
P1= E1 * P1/E1

52. Forward P/E = Po/E1

53. Relative Valuation Techniques
Price/Book Value:
P/B= Share price/ Book value per share
Price/ Sales ratio:
How much revenue you get per dollar invested.
Price/Sales ratio = Stock price/revenue/share Or
Price/sales ratio= Total market value/ annual sales

54. Economic value added (EVA)
EVA = NOPAT – Annual dollar cost of capital
EVA= NOPAT- after tax dollar cost of capital used to support operations
=EBIT(1-tax rate)-[total net operating capital*(after tax cost of capital)]
EVA measures the extent to which the firm has increased shareholder value
In order to generate positive EVA, a firm has to more than just cover operating costs. It must also provide a return to those who have provided the firm with capital.
EVA takes into account the total cost of capital, which includes the cost of equity.

55. Question
The ABC corporation has on its balance sheet $ 5 million in net operating capital and $ 37 million in net fixed assets. The company’s weighted average cost of capital is 8.5 percent. The company has the following statement:
Sales ` $25,000,000
Operating costs 18,625,000
EBIT 6,375,000
Interest 2,325,000
EBT 4,050,000
Taxes(40%) 1,620,000
Net income 2,430,000
What is ABC’s EVA?

56. In class practice of Ch-10
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