The document discusses stock valuation concepts, including types of stock, methods for determining stock value, and the efficiency of markets. It outlines various valuation approaches such as discounted cash flow models, dividend discount models, and enterprise value calculations, along with factors influencing stock pricing. Additionally, it explores the implications of growth rates and market equilibrium on stock prices, emphasizing the complexity and strategies involved in effective stock valuation.

1. STOCKS & THEIR
VALUATION
CHARAK RAY
LIBRA.CHARAK@GMAIL.COM

2. LEARNING OBJECTIVES
• Features of common stock
• Determining common stock values
• Efficient markets

3. COMMON STOCK: OWNERS, DIRECTORS, AND
MANAGERS
• Represents ownership.
• Ownership implies control.
• Stockholders elect directors.
• Directors hire management.
• Since managers are “agents” of shareholders, their goal should be:
Maximize stock price.

4. VALUES OF A COMMON STOCK
Book Value: Accounting value, Historical value =
Net worth/ shares outstanding
Par Value: Face Value of stock on which dividends
and earnings calculated
Issue Price: Par value or Par value + Premium

5. CONTINUED
 Liquidation Value: Earnings available to share holders after meeting prior
claims like debts on liquidation
 Market Value: Price at which traded in the market
 Real Value/ Intrinsic Value: PV of all future benefits if shares are held.

6. DECISION CRITERIA
If MV > IV – Sell, shares overpriced
If MV < IV, Buy, shares under-priced
Logic
In efficient market, the MV closely reflects IV or
fundamental value.
Larger the difference, the investor would take
position on estimate of IV.

7. CONTINUED
More confidant the investor is about the valuation
model, the decision based on whether share
under-priced/over-priced.
Overpricing / under-pricing called mispricing in
the market.
Rational investors belief, market price would move
towards the IV in a fairly efficient market.

8. COMPLEXITIES IN STOCK VALUATION
Future benefits come from dividend, capital gain and
bonus issue.
In a share, each component is uncertain.
Benefits have to be fairly estimated.
No single tool / method can be appropriate.
All methods used are at best approximations.
Practically, multiple methods used to derive a
reasonably a better estimate.

9. APPROACHES TO VALUATION
Discounted cash flow or PV models:
Dividend discount model : based on cash
distributed to share holders
Free cash flow to equity model: based on cash
available to share holders
Multiplier models: Market multiplier models based on
Ratio of stock price to fundamentals like earnings,
sells, book value etc.

10. CONTINUED…
 Enterprise Value model:
 Market value of outstanding securities – cash, short term Investments
 Common stock Value: Enterprise Value – value of long term liabilities and
preferred stocks.

11. DIVIDEND DISCOUNT MODEL
       









ssss r
D
r
D
r
D
r
D
P
1
...
111
ˆ
3
3
2
2
1
1
0
One whose dividends are expected to
grow forever at a constant rate, g.
Stock Value = PV of Dividends
What is a constant growth stock?

12. FOR A CONSTANT GROWTH STOCK,
 
 
 t
tt gDD
gDD
gDD



1
1
1
2
02
1
01
 
gr
D
gr
gD
P
ss 



 10
0
1ˆ
If g is constant, then:

13. WHAT HAPPENS IF G > RS?
• If rs< g, get negative stock price, which is nonsense.
• We can’t use model unless (1) g  rs and (2) g is expected to be constant
forever. Because g must be a long-term growth rate, it cannot be  rs.
.rrequiresˆ
s
1
0 g
gr
D
P
s




14. ASSUME BETA = 1.2, KRF = 7%, AND RPM = 5%.
WHAT IS THE REQUIRED RATE OF RETURN ON
THE FIRM’S STOCK?
ks = kRF + (RPM)bFirm
= 7% + (5%) (1.2)
= 13%.
Use the SML to calculate ks:

15. D0 WAS $2.00 AND G IS A CONSTANT 6%. FIND
THE EXPECTED DIVIDENDS FOR THE NEXT 3 YEARS,
AND THEIR PVS. RS = 13%.
0 1
2.2472
2
2.3820
3g=6% 4
1.8761
1.7599
1.6508
D0=2.00
13%
2.12

16. WHAT’S THE STOCK’S MARKET VALUE?
D0 = 2.00, RS = 13%, G = 6%.
Constant growth model:
 
gr
D
gr
gD
P
ss 



 10
0
1ˆ
= = $30.29.
0.13 - 0.06
$2.12 $2.12
0.07

17. WHAT IS THE STOCK’S MARKET VALUE ONE YEAR
FROM NOW, P1?
• D1 will have been paid, so expected dividends are D2, D3, D4 and so on. Thus,
^
D2
P1 = rs - g
= $2.2427 = $32.10
0.07

18. FIND THE EXPECTED DIVIDEND YIELD AND CAPITAL
GAINS YIELD DURING THE FIRST YEAR.
Dividend yield = = = 7.0%.
$2.12
$30.29
D1
P0
CG Yield = =
P1 - P0
^
P0
$32.10 - $30.29
$30.29
= 6.0%.

19. FIND THE TOTAL RETURN DURING THE
FIRST YEAR.
• Total return = Dividend yield + Capital gains yield.
• Total return = 7% + 6% = 13%.
• Total return = 13% = rs.
• For constant growth stock:
Capital gains yield = 6% = g.

20. Rearrange model to rate of return form:
.rtoˆ
0
1
s
1
0 g
P
D
gr
D
P
s




Then, rs = $2.12/$30.29 + 0.06
= 0.07 + 0.06 = 13%.
^

21. WHAT WOULD P0 BE IF G = 0?
The dividend stream would be a
perpetuity.
2.00 2.002.00
0 1 2 3rs=13%
P0 = = = $15.38.
PMT
r
$2.00
0.13
^

22. IF WE HAVE SUPERNORMAL GROWTH OF
30% FOR 3 YEARS, THEN A LONG-RUN CONSTANT G
= 6%, WHAT IS P0? R IS STILL 13%.
• Can no longer use constant growth model.
• However, growth becomes constant after 3 years.
^

23. Nonconstant growth followed by constant
growth:
0
2.3009
2.6470
3.0453
46.1135
1 2 3 4rs=13%
54.1067 = P0
g = 30% g = 30% g = 30% g = 6%
D0 = 2.00 2.60 3.38 4.394 4.6576
^
5371.66$
06.013.0
6576.4$
Pˆ
3 



24. WHAT IS THE EXPECTED DIVIDEND YIELD AND
CAPITAL GAINS YIELD AT T = 0? AT T = 4?
Dividend yield = = = 4.8%.
$2.60
$54.11
D1
P0
CG Yield = 13.0% - 4.8% = 8.2%.
At t = 0:
(More…)

25. • During nonconstant growth, dividend yield and capital gains yield are not constant.
• If current growth is greater than g, current capital gains yield is greater than g.
• After t = 3, g = constant = 6%, so the t = 4 capital gains gains yield = 6%.
• Because rs = 13%, the t = 4 dividend yield = 13% - 6% = 7%.

26. IS THE STOCK PRICE BASED ON
SHORT-TERM GROWTH?
• The current stock price is $54.11.
• The PV of dividends beyond year 3 is $46.11 (P3 discounted back to t = 0).
• The percentage of stock price due to “long-term” dividends is:
^
= 85.2%.
$46.11
$54.11

27. SUPPOSE G = 0 FOR T = 1 TO 3, AND THEN G IS
A CONSTANT 6%. WHAT IS P0?
0
1.7699
1.5663
1.3861
20.9895
1 2 3 4
rs=13%
25.7118
g = 0% g = 0% g = 0% g = 6%
2.00 2.00 2.00 2.12
2.12
.
P3
0 07
30.2857 
^
...

28. WHAT IS DIVIDEND YIELD AND CAPITAL GAINS
YIELD AT T = 0 AND AT T = 3?
t = 0:
D1
P0
CGY = 13.0% - 7.8% = 5.2%.
 
2.00
$25.72
7.8%.
t = 3: Now have constant growth with
g = capital gains yield = 6% and
dividend yield = 7%.

29. IF G = -6%, WOULD ANYONE BUY THE STOCK?
IF SO, AT WHAT PRICE?
Firm still has earnings and still pays
dividends, so P0 > 0:
 
gr
D
gr
gD
P
ss 



 10
0
1ˆ
^
= = = $9.89.
$2.00(0.94)
0.13 - (-0.06)
$1.88
0.19

30. WHAT ARE THE ANNUAL DIVIDEND
AND CAPITAL GAINS YIELD?
Capital gains yield = g = -6.0%.
Dividend yield = 13.0% - (-6.0%)
= 19.0%.
Both yields are constant over time, with the
high dividend yield (19%) offsetting the
negative capital gains yield.

31. WHY ARE STOCK PRICES VOLATILE?
gr
D
0
P
s
1

 rs = rRF + (RPM)bi could change.
 Inflation expectations
 Risk aversion
 Company risk
 g could change.
^

32. STOCK VALUE VS. CHANGES IN RS AND G
D1 = $2, rs = 10%, and g = 5%:
P0 = D1 / (rs-g) = $2 / (0.10 - 0.05) = $40.
What if rs or g change?
g g g
rs 4% 5% 6%
9% 40.00 50.00 66.67
10% 33.33 40.00 50.00
11% 28.57 33.33 40.00

33. WHAT IS MARKET EQUILIBRIUM?
In equilibrium, stock prices are stable.
There is no general tendency for
people to buy versus to sell.
The expected price, P, must equal the
actual price, P. In other words, the
fundamental value must be the same as
the price.
(More…)

34. In equilibrium, expected returns must
equal required returns:
rs = D1/P0 + g = rs = rRF + (rM - rRF)b.^

35. HOW IS EQUILIBRIUM ESTABLISHED?
If rs = + g > rs, then P0 is “too low.”
If the price is lower than the fundamental
value, then the stock is a “bargain.”
Buy orders will exceed sell orders, the price
will be bid up, and D1/P0 falls until
D1/P0 + g = rs = rs.
^
^
D1
P0
^

36. FREE CASH FLOW TO EQUITY
•

37. PRICE MULTIPLE APPROACH

38. USING THE STOCK PRICE MULTIPLES TO ESTIMATE
STOCK PRICE
• Analysts often use the P/E multiple (the price per
share divided by the earnings per share) or the P/CF
multiple (price per share divided by cash flow per
share, which is the earnings per share plus the
dividends per share) to value stocks.
• Example:
• Estimate the average P/E ratio of comparable
firms. This is the P/E multiple.
• Multiply this average P/E ratio by the expected
earnings of the company to estimate its stock
price.

39. PRICE MULTIPLE BASED ON DIVIDEND (1/2)
•

40. PRICE MULTIPLE BASED ON DIVIDEND (2/2)

41. P/E BASED ON FUNDAMENTALS
• Firms has payout ratio = 60%
• Required rate of return = 11%
• Expected dividend growth rate = g = 5%
• Firm’s justified P/E ratio = 0.6/0.11-0.05 = 10
• Serves as a benchmark for comparison.
• If the firms actual P/E ratio is16.
• Stock considered to the overvalued
• Based on the formula: P0 = D1/ E1
E1 k-g
Continue…………..

42. FUNDAMENTAL P/E RATIO COMPARISON.
Company Industry Average
D/P ratio 25% 16%
Sales Growth 7.5% 3.9%
Total Debt/Equity 113% 68%

43. WHICH FACTORS SUGGEST A HIGHER FUNDAMENTAL P/E
FOR THE COMPANY.
High D/P ratio suggest a high P/E ratio.
High growth in sales suggest high dividend, high P/E.
High level of debt indicates high risk and higher RoE
which supports lower P/E than industry.
In practice increase in D/E will reduce ‘g’ which dividend
increases
values ‘g’ reduces value.
The phenomenon is called dividend displacement of
earnings.
Continue…………..

44. VALUATION USING COMPARABLES
Year end 2013 2012 2011
Stock holders Eq. 55.6 54.1 52.6
Net revenue 77.3 73.6 70.8
Net income 3.2 1.1 0.40
Net CFO 17.9 15.2 12.2
Stock price 11.4 14.4 12.05
Share outstanding 4.476 3.994 3.823
Continue…………..

45. INDUSTRY RATIO
P/E – 8.6
Price to cash flow – 4.6
Price to sales – 1.4
Price to book value -3.6
2013 2012 2011 Industry Company Avg
P/E 15.9 52.3 115.2 8.6 61.1
P/CF 2.9 3.8 3.8 4.6 3.5
P/S 0.7 0.8 0.7 1.4 0.7
P/B 0.9 1.1 0.9 3.6 1.0
Continue…………..

46.  High P/E of the company may be due to depressed earnings due to high
depreciation, high taxes, high interest etc.
 Calculating P/EBITD would be a better measure as it is unaffected by above
expenses.
 On the whole, low ratios of the company suggest company may be currently under
valued.
Continue…………..

47. USING ENTITY MULTIPLES
• The Entity value (V) is:
• the market value of equity (# shares of stock
multiplied by the price per share)
• plus the value of debt.
• Pick a measure, such as EBITDA, Sales,.
• Calculate the average entity ratio for a sample of
comparable firms. For example,
• V/EBITDA

48. USING ENTITY MULTIPLES (CONTINUED)
• Find the entity value of the firm in question. For
example,
• Multiply the firm’s sales by the V/Sales multiple.
The result is the total value of the firm.
• Subtract the firm’s debt to get the total value of
equity.
• Divide by the number of shares to get the price per
share.

49. EXAMPLE ON ENTERPRISE VALUE
Daniel is a manufacturer of home appliances
the following are the figures:
Stock price 30.00
Shares outstanding 3,00,000
MV of LTD 8,00,000
book value of LTD 11,00,000
book value of total Debt 26,00,000
Cash and marketable security 3,00,000
EBITD 12,00,000
Continue…………..

50. Calculate EV/EBITD .
Book value of TD 26,00,000
Less Book value of LTD 11,00,000
Book value of STD 15,00,000
Assume Mkt. value of STD = Book value of STD
Mkt. value of TD = value of LTD + value of STD
= 8,00,000+ 15,00,000 =23,00,000
Continue…………..

51. Mkt. value of Eq = 30*3,00,000 = 90,00,000
Enterprise Value = Value of Debt + Value of Equity – cash
= 23,00,000 + 90,00,000 - 3,00,000 =
110,00,000
EV/EBITD = 9.2
If the industry avg. is more than 9.2 Daniel is under valued.
Continue…………..

52. EXAMPLE ON ASSET BASED MODEL
Willams optical is a publicly traded firm.
An analyst estimates that MV of net fixed assets is 120%
of Book value.
Liabilities and short term asset market values are close
to their Book value
Shares outstanding 2,000
Following Information is Available
Continue…………..

53. Cash - 10,000 A/P – 5,000
A/R - 20,000 N/P – 30,000
Inv - 50,000 Term loan – 45,000
NFA - 1,20,000 Equity – 1,20,000
TA 2,00,000 2,00,000
Calculate Equity Value per Share
Continue…………..

54. Market value of Assets =
10,000+20,000+50,000+1,20,000 (1.2)=2,24,000
Market value of Liabilities =
5,000+30,000+45,000=80,000
Adjusted Equity value → 2,24,000- 80,000 = 1,44,000
No. of share outstanding = 2,000
Value per share = 72.00
Continue…………..

55. WHAT’S THE EFFICIENT MARKET
HYPOTHESIS (EMH)?
Securities are normally in equilibrium
and are “fairly priced.” One cannot
“beat the market” except through
good luck or inside information.
(More…)

56. PREFERRED STOCK
• Hybrid security.
• Similar to bonds in that preferred stockholders receive a fixed dividend which
must be paid before dividends can be paid on common stock.
• However, unlike bonds, preferred stock dividends can be omitted without fear of
pushing the firm into bankruptcy.

57. WHAT’S THE EXPECTED RETURN ON PREFERRED
STOCK WITH VPS = $50 AND ANNUAL DIVIDEND =
$5?
%.0.1010.0
50$
5$
5$
50$




ps
ps
ps
r
r
V

58. APPENDIX…

59. 1. Weak-form EMH:
Can’t profit by looking at past trends. A
recent decline is no reason to think
stocks will go up (or down) in the future.
Evidence supports weak-form EMH, but
“technical analysis” is still used.

60. 2. Semistrong-form EMH:
All publicly available information is
reflected in stock prices, so it doesn’t
pay to pore over annual reports
looking for undervalued stocks.
Largely true.

61. 3. Strong-form EMH:
All information, even inside
information, is embedded in stock
prices. Not true--insiders can gain
by trading on the basis of insider
information, but that’s illegal.

62. THANK YOU…