Stock and equity evaluation

1. Chapter Four
Common Stocks valuation

2. • Equity market is one of the key sectors of financial markets
where long -term financial instruments are traded.
• The purpose of equity instruments issued by corporations is to raise
funds for the firms. The provider of the funds is granted a residual
claim on the company’s income, and becomes one of the owners of
the firm.
• For market participants equity securities mean holding wealth as well
as a source of new finance, and are of great significance for
savings and investment process in a market economy.
• Within the savings-investment process magnitude of retained
earnings exceeds that of the news stock issues and constitutes the
main source of funds for the firms.
• Equity instruments can be traded publicly and privately.
• Internal equity financing of companies is provided through
retained earnings; whereas the external source of equity is provided
through stock issuance.

3. Fundamental Stock Analysis:
Models of Equity Valuation
Basic Types of Models
Balance Sheet Models
Dividend Discount Models
Price/Earning Ratios
Estimating Growth Rates and
Opportunities

4. Intrinsic Value and Market Price
Intrinsic Value
Self assigned Value
Variety of models are used for estimation
Market Price
Consensus value of all potential traders
Trading Signal
IV > MP Buy
IV < MP Sell or Short Sell
IV = MP Hold or Fairly Priced

5. Common Stock as Residual Ownership
Common stock is quite different than
bonds and preferred stock:
Return is dependent upon success of firm
Provides a residual claim on firm’s assets
Ownership rights to cash flows remaining
after all other claims are paid
Not a contractual obligation and no stated
maturity

6. Difficulty of Estimating
Common Stock Value
The value of a security is the sum of the
present values of its future expected cash
flows. Common stock is difficult to value
because future cash flows are uncertain.
Future common stock dividends are difficult to
forecast accurately.
The future common stock selling price is
difficult to forecast.

7. Valuation of common Stocks
Process of determining the fair market value
of a financial asset on the basis of present
value of the expected cash flows
Three step process:
Estimate the expected cash flows
Determine the appropriate discount rate or
required rates of return to discount the cash flows
Compute the present value of the expected cash
flows in step 1 by discounted them with discunt
rate(s) in step 2

8. Value of Common-Stock
Two forms of expected cash flows from
common stocks:
1. Dividends received over investor’s
stock holding period
2. Price expected to be received when
stock is sold

9. Value of a Common Stock
The intrinsic Value of a common stock
equals PV of cash flows from a stock
which is:
1. PV of an infinite dividend stream OR
2. PV of a finite dividend stream plus PV
of the sale price of the stock

10. Common stock valuation
Common stocks can be valued using:
1. Dividend Discounted model
(DDM)
2. Free cash Flow to Equity
(FCFE) model

11. Dividend Discount Model
If the stock is held for finite period, Value of a
share of common stock is the present value of
all future dividends
If finite holding period there are two types of
expected cash flows
Dividends during the holding period
Expected price at the end of holding period—this
itself is dependent on future dividends

12. Specified/finite Holding Period Model
0
1
1
2
2
1 1 1
V
D
k
D
k
D P
k
N N
N
  

  
( ) ( ) ( )
...
PN = the expected sales price for the stock at
time N
N = the specified number of years the stock is
expected to be held
Vo – is value of stock
K- is RRR

13. Infinite Holding Period
What will be the value of a share of common
stock?
Present value of an infinite stream of anticipated
dividends
Simplified assumptions to simply valuation
model
Zero Growth Model
Constant Growth Model
Two-stage growth model

14. Zero Growth Model
Dividend every year will be the same
Investor anticipates to receive the same
amount dividend per year forever
DPS
Vs = -------------
rcs

15. No Growth Model
V
D
k
o 
Stocks that have earnings and dividends that
are expected to remain constant
Preferred Stock

16. No Growth Model: Example
E1 = D1 = $5.00
k = .15
V0 = $5.00 / .15 = $33.33
V
D
k
o 

17. Constant Growth Model
Assume that firm grows at a stable
growth rate of g per year forever
DPS1
Vs = ---------, where r>g
r - g

18. Constant Growth Model
Vo
D g
k g
o



( )
1
g = constant perpetual growth rate

19. Constant Growth Model: Example
Vo
D g
k g
o



( )
1
E1 = $5.00 b = 40% k = 15%
(1-b) = 60% D1 = $3.00 g = 8%
V0 = 3.00 / (.15 - .08) = $42.86

20. Two-Stage DDM
In general version of the model, two stages
of growth
An initial period of extraordinary growth
After initial period, a period of stable growth
n DPSt Pn
P0 =  ---------- + ---------
t=1 (1+r)t (1 + r)n
DPSn+1
Where Pn = -----------------
(r – gn)

21. Shifting Growth Rate Model
V D
g
k
D g
k g k
o o
t
t
t
T
T
T





 


( )
( )
( )
( )( )
1
1
1
1
1
1
2
2
g1 = first growth rate
g2 = second growth rate
T = number of periods of growth at g1

22. Shifting Growth Rate Model:
Example
D0 = $2.00 g1 = 20% g2 = 5%
k = 15% T = 3 D1 = 2.40
D2 = 2.88 D3 = 3.46 D4 = 3.63
V0 = D1/(1.15) + D2/(1.15)2 + D3/(1.15)3 +
D4 / (.15 - .05) ( (1.15)3
V0 = 2.09 + 2.18 + 2.27 + 23.86 = $30.40

23. Dividend Discount Models:
General Model
V
D
k
o
t
t
t




( )
1
1
V0 = Value of Stock
Dt = Dividend
k = required return

24. Four Basic Inputs
Length of high growth period
Dividends per share each period
Required rate of return by stockholders
each period
Terminal price at the end of high
growth period

25. How do we Estimate Growth
Rate?
If the firm’s dividend growth rate is not
known, it can be estimated using two
ways:
1. geometric mean of past dividend
growth.
2. Retention model

26. How do we Estimate Growth Rate?
1. geometric mean of past dividend.
g = -1
Where
rn …dividend growth rate in nth year
G … dividend growth rate
2. Retention growth model
Most firms pay out some of their net
income as dividends and reinvest, or
retain, the rest.
g = (retention rate) (ROE)
n rn
r
r
r )
1
)...(
3
1
)(
2
1
)(
1
1
( 




27. Estimating Dividend Growth Rates
g ROE b
 
g = growth rate in dividends
ROE = Return on Equity for the firm
b = plowback or retention percentage
rate
(1- dividend payout percentage rate)

28. Example
Ameritech Corporation just paid dividends per share
of $7.04 and dividends are expected to grow 5% a
year forever. The stock has a beta of 0.90 the
market risk premium is 7.5 % and the treasury
bond rate is 6.25%.
a)What is the current value per share, using the
DDM?
b)The stock was trading for $80 per share. What
would the growth rate in dividends have to be to
justify this price?

29. Example: multiple growth rate
Chain Reaction, Inc., has been growing at a
phenomenal rate of 30 percent per year
because of its rapid expansion and explosive
sales. You believe that this growth rate will
last for three more years and that the rate
will then drop to 10 percent per year. The
growth rate then remains at 10 percent
indefinitely. Total dividends just paid were $5
million, and the required return is 20 percent.
Require: what is the total value of the stock?

30. Exercise
The next dividend for the Gordon Growth
Company will be $4 per share. Investors require a
16 percent return on companies such as Gordon.
Gordon’s dividend increases by 6 percent every
year. Based on the dividend growth model, what is
the value of Gordon’s stock today?
Required: What is the value in four years?

31. Price Earnings Ratios
P/E Ratios are a function of two factors
Required Rates of Return (k)
Expected growth in Dividends
Uses
Relative valuation
Extensive Use in industry

32. P/E Ratio: No expected growth
P
E
k
P
E k
0
1
0
1
1


E1 - expected earnings for next year
E1 is equal to D1 under no growth
k - required rate of return

33. P/E Ratio with Constant Growth
P
D
k g
E b
k b ROE
P
E
b
k b ROE
0
1 1
0
1
1
1




 


 
( )
( )
( )
b = retention ration
ROE = Return on Equity

34. Numerical Example: No Growth
E0 = $2.50 g = 0 k = 12.5%
P0 = D/k = $2.50/.125 = $20.00
PE = 1/k = 1/.125 = 8

35. Numerical Example with Growth
b = 60% ROE = 15% (1-b) = 40%
E1 = $2.50 (1 + (.6)(.15)) = $2.73
D1 = $2.73 (1-.6) = $1.09
k = 12.5% g = 9%
P0 = 1.09/(.125-.09) = $31.14
PE = 31.14/2.73 = 11.4
PE = (1 - .60) / (.125 - .09) = 11.4

36. Free Cash Flow to Equity
(FCFE) Valuation Model
The cash flow that the firm can afford
as dividends and contrasted with actual
dividends—may not payout as dividends
The residual cash flow left over after
meeting interest and principal payments
and providing for capital expenditures is
the FCFE

37. FCFE…
FCFE model is suitable under the following
conditions :
the firm is not dividend paying, or
the firm is dividend paying but dividends differ
significantly from the firm’s capacity to pay
dividends,
FCFE =FCFF-Interest exp (1- tax rate) + net
borrowing
Where FCFF … is free cash flow to the firm

38. FCFE ….
FCFE is the cash flow from operations minus
capital expenditures minus payments to (and
plus receipts from) debt-holders.
Computed as:
FCFE = Net Income
+ non cash charges (Income)
- Capital Spending
+ net borrowing

39. Valuing FCFE
The value of equity can be found by discounting
FCFE at the required rate of return on equity (r):
Since FCFE is the cash flow remaining for equity
holders after all other claims have been satisfied,
discounting FCFE by r (the required rate of return
on equity) gives the value of the firm’s equity.
Dividing the total value of equity by the number of
outstanding shares gives the value per share.
1
FCFE
Equity Value
(1 )
t
t
t r






40. Constant-growth FCFE valuation
model
FCFE in any period will be equal to FCFE in the
preceding period times (1 + g):
FCFEt = FCFEt–1 (1 + g).
The value of equity if FCFE is growing at a
constant rate is
The discount rate is r, the required return on
equity. The growth rate (g) is the growth rate
of FCFE.
0
1 FCFE (1 )
FCFE
Equity Value
g
r g r g

 
 

41. Example
Gray Furniture Company earned net income of $350,000
last year. Investment in fixed capital was $200,000,
depreciation was $160,000, and the investment in working
capital was $50,000. Gray is currently operating at its
target debt-to-asset ratio of 40%. Thus, 40% of annual
investments in working capital and fixed capital will be
financed with new borrowings. Shareholders require a
return of 14% on their investment, and the expected
growth rate of the FCFE is 4%. The company has 100,000
outstanding shares.
Required: what is the value of Gray company’s stock?

42. Example 2
Ridgeway Construction has FCFE of $ 2,500,000 and
1 million shares. The firm is currently operating at a
target debt-to-equity ratio of 0.4. The expected
return on the market is 9%, the risk free rate is 4%,
and Ridgeway stock has a beta of 1.5. The expected
growth rate of FCFE is 4.5%.
Required:
A) Calculate the value of Ridgeway stock
B) What is the total value of Ridgeway company

43. Types of Stock Analysis
Technical Analysis - using prices and
volume information to predict
future prices
Weak form efficiency & technical analysis
Fundamental Analysis - using
economic and accounting
information to predict stock prices
Semi strong form efficiency & fundamental analysis

44. • Fundamental analysis is one of the methods of
valuing stocks, which involves the analysis of a
company’s operations to assess its economic prospects.
• It is based on fundamental financial characteristics
(e.g. earnings) about the company and its
corresponding industry that are expected to influence
stock values.
• The analysis is based on financial statements of the
company in order to investigate the earnings, cash
flow, profitability, and financial leverage.
• The fundamental analysis includes analysis of the
major product lines, the economic outlook for the
products (including existing and potential competitors),
and the industries in which the company operates.

45. • This analysis results in projections of earnings growth.
Based on the growth prospects of earnings, the fair value
of the stock using one or more of the equity valuation
models is determined.
• The fair value is based on present value calculations.
• Present value –the current value of a future cash flow.
• It is obtained by discounting future cash flow by
the market –required rate of return.
• There are various models to estimate the fundamental
value of company shares.
• One approach is to estimate expected earnings and then
multiply by expected price/ earnings ratio.
• Another approach is to estimate the value of the assets of
the company.

46. • The estimated fair value is compared to the market price to
determine if the stock is fairly priced in the market, cheap
(a market price below the estimated fair value), or rich
(a market price above the estimated fair value).
• In a perfectly efficient market all securities are always
correctly priced.
• The market price equals to the fundamental value of the
security.
• In a market that is partially inefficient, the market prices
deviate from fundamental value.
• Financial analysts aim to discover the fundamental value
ahead of the rest of the market participants before the
market prices approach the fundamental value in order
to make profits.
• The actions of such profit seeking investors push the

47. Technical Analysis
• The aim of the technical analysis is to identify stocks
that are candidates for purchase or sale, and the
investor can employ technical analysis to define the
time of the purchase or sale.
• Such analysis is used not only for investigation of
common shares, but also in the trading of
commodities, bonds, and futures contracts.
• This analysis can be traced back to the seventeenth
century, where it was applied in Japan to analyze the
trend in the price of rice.
• The father of modern technical analysis is Charles
Dow, a founder of the Wall Street Journal and its first
editor in the period of 1889 -December 1902.

48. • Technical analysis ignores company
fundamental information, focusing instead on
the study of internal stock market
information on price and trading volume of
individual stocks, groups of stocks, and the
overall market, resulting from shifting supply
and demand.
• Technical analysts believe that stock markets
have a dynamic of their own, independent of
outside economic forces.
• Technical analysis – a forecasting method for
asset prices based solely on information about
the past prices.

49. • Technical analysis is aimed to determine past
market trends and patterns from which
predictions of future market behavior are derived.
• It attempts to forecast short-term price
movements.
• The methodology of analysis is based on the belief
that stock market history tends to repeat itself.
• If a certain pattern of prices and volumes has
previously been followed by particular price
movements, it is suggested that a repetition of that
pattern will be followed by similar price
movements.