Chapter 2: Valuation of Stocks and Bonds

1
Chapter 2 Valuation of Stocks and Bonds
2
What is Value?

• In general, the value of an asset is the price
  that a willing and able buyer pays to a willing
  and able seller
• Note that if either the buyer or seller is not
  both willing and able, then an offer does not
  establish the value of the asset

3
Several Kinds of Value

• There are several types of value, of which we are
  concerned with three
• Book Value - The assets historical cost less its
  accumulated depreciation
• Market Value - The price of an asset as
  determined in a competitive marketplace
• Intrinsic Value - The present value of the
  expected future cash flows discounted at the
  decision makers required rate of return

4
Determinants of Intrinsic Value

• There are two primary determinants of the
  intrinsic value of an asset to an individual
• The size and timing of the expected future cash
  flows
• The individuals required rate of return (this is
  determined by a number of other factors such as
  risk/return preferences, returns on competing
  investments, expected inflation, etc.)
• Note that the intrinsic value of an asset can be,
  and often is, different for each individual
  (thats what makes markets work)

5
Chapter 2 Valuation of Stocks and Bonds

• 2.3 Valuation of Preferred Stocks

6
Preferred Stock Features

• Preferred stock differs from common stock because
  it has preference over common stock on payment of
  dividends and in the distribution of corporation
  assets in the event of liquidation.
• Preferred stock is a form of equity from a legal,
  tax, and regulatory standpoint.
• Holders of preferred stock generally have no
  voting privileges.
• However, holders of preferred stock are often
  granted voting and other rights if preferred
  dividends have not been paid for some time.
• Preferred stock have a stated liquidating value.
  
• The cash dividend is described in dollars per
  share.
• A preferred dividend is not like bond interest
• Dividends on preferred stock are either
  cumulative or non-cumulative.
• Dividends not declared on cumulative preferred
  stock are carried forward and must be paid before
  common shareholders can receive anything

7
Features of preferred stock

• A hybrid security
• May be perpetuity or redeemable
• Paid before common dividends.
• Cumulative or Non-cumulative dividends
• Dividends not a liability
• Protective provisions (voting)
• Call provisions sinking funds
• Convertible or Non-convertible
• Usually non-voting and non-participative.
• Priority-lower than debt, higher than stock.

8
Preferred Stock Valuation

• Preferred stocks can usually be valued like a
  perpetuity

9
Example

• Xerox preferred that pays 4.125 dividend per
  year. Suppose our required rate of return on
  Xerox preferred is 9.5

10
Expected Rate of Return on Preferred

• Just adjust the valuation model

11
Example

• If we know the preferred stock price is 40, and
  the preferred dividend is 4.125, the expected
  return is

12
Valuation of redeemable preferred stock

• The value of a preferred stock equals the present
  value of all future dividends

13
Chapter 2 Valuation of Stocks and Bonds

• 2.4 Valuation of Common Stocks

14
Features of common stock

• Residual income and asset claimants
• Unlimited upside
• First to suffer
• Priority
• Debt
• Preferred Stock
• Common Stock
• A firm cannot go bankrupt for not declaring
  dividends
• Dividends and Taxes
• Dividend payments are not considered a business
  expense, therefore, they are not tax deductible
• Dividends received by individuals are taxed as
  ordinary income

15
Features of Common Stock

• The term common stock usually implies the
  shareholder has no special preference either in
  dividends or in bankruptcy.
• Shareholders, however, control the corporation
  through their right to elect the directors. The
  directors in turn hire management to carry out
  their directives.
• Directors are elected at an annual shareholders
  meeting by a vote of the holding of a majority of
  shares present and entitled to vote.

16
Common Stock Features

• Shareholders usually have the following rights
  also
• The right to share proportionally in dividends
  paid.
• The right to share proportionally in assets
  remaining after liabilities and preferred
  shareholders have been paid in a liquidation.
• The right to vote on stockholder matters of great
  importance, such as a merger or new share
  issuance.

17
Common Stock Features

• Dividends
• Dividend payments are at the discretion of the
  BoD.
• Dividends are not a liability of the corporation
  until declared by the BoD.
• Dividends are not tax deductible for the issuing
  corporation.

18
Common Stock Features

• Classes of Stock
• Some firms have more than one class of common
  stock often, the classes are created with
  unequal voting rights.
• Non-voting shares must receive dividends no lower
  than dividends on voting shares.
• A primary reason for creating dual classes of
  stock has to do with control of the firm.

19
Common Stock Valuation

• Just like with bonds, the first step in valuing
  common stocks is to determine the cash flows
• For a stock, there are two
• Dividend payments
• The future selling price
• Again, finding the present values of these cash
  flows and adding them together will give us the
  value

20
Cash flows for stockholders

• If you buy a share of stock, you can receive cash
  in two ways
• The company pays dividends
• You sell your shares, either to another investor
  in the market or back to the company
• As with bonds, the price of the stock is the
  present value of these expected cash flows

21
Common Stock Valuation

• Unlike bonds, valuing common stock is more
  difficult.
• Why?
• The timing and amount of future cash flows is not
  known.
• The life of the investment is essentially
  forever.
• There is no way to observe the rate of return
  that the market requires.

22
Some Notes About Common Stock

• In valuing the common stock, we have to make two
  assumptions
• We know the dividends that will be paid in the
  future
• We know how much you will be able to sell the
  stock for in the future
• Both of these assumptions are unrealistic,
  especially knowledge of the future selling price
• Furthermore, suppose that you intend on holding
  on to the stock for twenty years, the
  calculations would be very tedious!

23
Common Stock Some Assumptions

• We cannot value common stock without making some
  simplifying assumptions
• If we make the following assumptions, we can
  derive a simple model for common stock valuation
• Assume
• Your holding period is infinite (i.e., you will
  never sell the stock)
• The dividends will grow at a constant rate
  forever (this is only one example of assumption
  that simplifies the problem)
• Note that the second assumption allows us to
  predict every future dividend, as long as we know
  the most recent dividend

24
Common Stock Valuation Dividend Discount Model
25
Single-Period Valuation Model

• Suppose you are thinking of purchasing the stock
  of Moore Oil, Inc. and you expect it to pay a 2
  dividend in one year and you believe that you can
  sell the stock for 14 at that time. If you
  require a return of 20 on investments of this
  risk, what is the maximum you would be willing to
  pay?
• Remember, the cash flows to the stockholder is
  simply the dividends received the future sales
  price

26
Single Holding Period

• You expect XYZ stock to pay a 5.50 dividend at
  the end of the year. The stock price is expected
  to be 120 at that time. If you require a 15
  rate of return, what would you pay for the stock
  now?

Ans 109.13
27
What happens if ?

• The price of common stock is expected to grow at
  the rate of g annually ?
• The current price P0 becomes Po(1g) a year
  hence.

28
Example

• The expected dividend per share on the equity
  share of Roadking Limited is Rs 2.00. The
  dividend per share of Roadking Limited has grown
  over the past five years at the rate of 5 per
  year. This growth rate will continue in future.
  Further, the market price of the equity share of
  Roadking Limited, too, is expected to grow at the
  same rate. What is a fair istimate of the
  intrinsic value of the equity share of Roadking
  Limited if the required rate is 15 ?

29
Expected Rate of Return

• What rate of return can the investor expect,
  given the current market price and forecasted
  values of dividend and share price ?
• Kc (D1 / Po) g

30
Multi-period Valuation Model

• The value of a stock today (its current price) is
  in theory equal to the present value of all
  future dividends plus that of the selling price.

31
Multi-period Valuation Model

• But common shares have no maturity period they
  may be expected to bring a dividend stream of
  infinite duration

32
Multi-period Valuation Model

• That was the generalized multi-period valuation
  formula which is general enough to permit any
  dividend pattern constant, rising, declining or
  randomly fluctuating.
• For practical applications, it is helpful to make
  simplifying assumptions about the pattern of
  dividend growth.

33
Commonly used assumptions types

1. The dividend per share remains constant forever,
   implying that the growth rate is nil (THE ZERO
   GROWTH MODEL)
2. The dividend per share grows at a constant rate
   per year forever (THE CONSTANT GROWTH MODEL)
3. The dividend per share grows at a constant rate
   for a finite period, followed by a constant
   normal rate of growth forever thereafter (THE TWO
   STAGE MODEL)
4. The dividend per share, currently growing at an
   above-normal rate, experiences a gradually
   declining rate of growth for a while. Thereafter
   it grows at a constant normal rate (THE H MODEL)

34
Zero Growth Model

• Assuming that the dividend per share remains
  constant year after year, at a value of D, the
  valuation model becomes as that of the perpetual
  preference stock

35
Example

• Suppose stock is expected to pay a 0.50
  dividend every quarter and the required return is
  10 with quarterly compounding. What is the price?

36
Constant Growth model

• Assumes that the dividend per share grows at a
  constant rate (g)

• With a little algebra, this reduces to

37
Example 1

• Suppose Big K, Inc. just paid a dividend of 5.
  It is expected to increase its dividend by 2 per
  year. If the market requires a return of 15 on
  assets of this risk, how much should the stock be
  selling for?

38
Example 2

• Suppose Comolli, Inc. is expected to pay a 2
  dividend in one year. If the dividend is expected
  to grow at 5 per year and the required return is
  20, what is the price?

Ans 13.33
39
Example 3

• Griggs Inc. last dividend (D0) was 2. The
  dividend growth rate (g) is a constant 5. If
  the required return (kc) 10, what is P0?

40
Example 4

• Overton Corp. just paid a 2 dividend. If the
  dividends will grow at a constant rate of 5 in
  the future, what is the stock price in 4 years
  (at t 4) assuming a required rate of return
  10?

41
What drives growth ?

• Most stock valuation models are based on the
  assumption that dividends grow over time.
• What drives this growth ?
• The two major drivers of growth are
• Plough-back or Retention Ratio
• Return on Equity (ROE)
• Growth Retention Ratio x Return on Equity
• Illustration
• Omega limited has an equity (net worth) base of
  100 at the beginning of year 1. It earns a ROE of
  20 . It pays out 40 of its equity earnings and
  ploughs back 60 of its equity earnings

42
Financials of Omega Limited
Year 1 Year 2 Year 3
Beginning Equity
ROE
Equity Earnings
Dividend Payout Ratio
Dividends
Retention Ratio
Retained earnings
What is the growth Rate of Dividend ?
43
Financials of Omega Limited
Year 1 Year 2 Year 3
Beginning Equity 100 112 125.44
ROE 20 20 20
Equity Earnings 20 22.4 25.1
Dividend Payout Ratio 0.40 0.40 0.40
Dividends 8 8.96 10.04
Retention Ratio 0.60 0.60 0.60
Retained earnings 12 13.44 15.06
Growth Rate RE x ROE 0.60 x 20 12
44
What is this growth actually ?

• Sustainable growth rate ROE ? Retention ratio
• Return on equity (ROE) Net income / Equity
• Retention ratio 1 Payout ratio

45
Estimation of Growth

• The growth rate in dividends (g) can be estimated
  in a number of ways.
• Using the companys historical average growth
  rate.
• Using an industry median or average growth rate.
• Using the sustainable growth rate.

46
Two Stage Growth Model

• The simplest extension of the constant growth
  model assumes that the extraordinary growth will
  continue for a finite number of years and
  thereafter the normal growth rate will prevail
  indefinitely.

47
Two Stage Growth Model (contd.)

• The first term on the right hand side of above
  equation is the PV of a growing annuity, and its
  value is equal to

48
Reminder Present Value of a Growing annuity
49
Two Stage Growth Model (contd.)

• The first term on the right hand side of above
  equation is the PV of a growing annuity, and its
  value is equal to

50
Two Stage Growth Model (contd.)

• Hence,

51
Two Stage Growth Model (contd.)

• Since the two-stage growth model assumes that
  the growth rate after n years remains constant at
  g2, Pn will be equal to

52
Two Stage Growth Model (contd.)

• Substituting the above expressions, we have

53
Example

• The current dividend on an equity share of
  Vertigo Limited is Rs 2.00. Vertigo is expected
  to enjoy an above-normal growth rate of 20 for a
  period of 6 years. Thereafter, the growth rate
  will fall and stabilize at 10. Equity investors
  require a return of 15 . What is the intrinsic
  value of the equity share of Vertigo ?

g1 20 , g2 10 , n 6 years, kc 15, D0
Rs 2.00
Ans Rs 79.597
54
Non-constant growth

• Suppose a firm is expected to increase dividends
  by 20 in one year and by 15 in two years. After
  that dividends will increase at a rate of 5 per
  year indefinitely. If the last dividend was 1
  and the required return is 20, what is the price
  of the stock?
• Remember that we have to find the PV of all
  expected future dividends.

55
Non-constant growth solution

• Compute the dividends until growth levels off
• D1 1(1.2) 1.20
• D2 1.20(1.15) 1.38
• D3 1.38(1.05) 1.449
• Find the expected future price (by using the
  final dividend calculation)
• P2 D3 / (k g) 1.449 / (.2 - .05) 9.66
• Find the present value of the expected future
  cash flows
• P0 1.20 / (1.2) (1.38 9.66) / (1.2)2 8.67

56
Non-constant growth

• The Green Shoe Companys last dividend paid (D0)
  was 1.00. Dividends are projected to grow at a
  rate of 7 per year for the next 2 years, 5 per
  year for the 3rd year, and starting with year 4
  they will grow at a constant rate of 4, forever.
  If the required return on the stock is 12, what
  is the price of the stock today?

57
Non-Constant Growth

• At times, a new company may pay no dividends
  early in its life but start paying dividends that
  grow at a constant rate some time in the future.
  
• At other times, a new company may pay small
  dividends initially and, at some point in the
  future, start paying dividends that grow at a
  constant rate.
• However, as always, the value of the stock is the
  present value of all future dividends.
• Many cash flow scenarios are possible in this
  situation.

58
Non-Constant Growth

• Example
• ABC Company does not plan to pay a dividend until
  year 5. ABCs expects the dividend in year five
  to be 1 and dividends in future years to grow at
  a constant rate of 5. If the firms
  risk-adjusted required rate of return is 13,
  what is the value of a share of stock in the
  company today?
• P4 1/(.13 .05) 12.50
• P0 12.50(1.13)-4 7.67

59
Components of Required Return

• Thus far, the discount rate or required rate of
  return has been given to us.
• Later chapters have more to say about this, but
  for now, using the dividend growth model, lets
  analysis the required rate of return
• Rearranging kc r D1/P0 g
• where, D1/P0 the dividend yield g
  the capital gains yield

60
Components of Required Return

• Hence, Total Return on Common Stock has two
  components
• Dividend Yield
• Capital Gains Yield.
• Return Dividend Yield Capital Gains Yield

61
Illustration

• We observe a stock selling for 20 per share.
  The next dividend will be 1 per share. You
  think that the dividend will grow by 10 per
  year more or less indefinitely. What return does
  this stock offer you if this is correct ?
• Return Dividend Yield Capital Gains Yield
• r D1/P0 g
• 1 / 20 0.10
• 0.05
  0.10
• 0.15
• i.e. 15

62
Verification

• We can verify this answer by calculating the
  price in one year P1 , using 15 as the required
  return.
• P1 D1 (1g) / (r g)
• 1 x 1.10 / (0.15 -0.10)
• 22
• 22 is 10 more than 20, so the stock price
  has grown by 10
• If you buy the stock today in 20, itll pay 1
  dividend at the end of the year, and youll gain
  2 by selling it.
• Dividend yield is thus 1 / 20 0.05 i.e. 5
• Capital gains yield is thus 2 /20 0.10 i.e.
  10
• So your Total return would be 5 10 15

63
Impact of growth on Price, Returns and P/E Ratio

• The expected growth rates of the companies differ
  widely.
• Some are expected to remain virtually stagnant or
  grow slowly others are expected to show normal
  growth still others are expected to achieve
  supernormal growth rate.
• Assuming a constant total required return,
  differing expected growth rates mean differing
  stock prices, dividend yields, capital gains
  yields, and P/E ratios.

64
Illustration (contd.)

• Consider three cases of growth rates
• Low growth firm 5
• Normal growth firm 10
• Supernormal growth firm 15
• The expected earnings per share and dividend per
  share of each of the three firms are Rs 3.00 and
  Rs 2.00 respectively. Investors required total
  return from equity investments is 20.
• Given the above information, calculate the stock
  price, dividend yield, capital gains yield, and
  P/E ratio for the three cases

65
Illustration (contd)
Price P0 D1 / (r g) Dividend Yield (D1/P0) Capital Gains Yield (P1-P0)/P0 P/E Ratio P0/EPS
Low Growth Firm
Normal Growth Firm
Supernormal Growth Firm
66
Illustration (contd)
Price P0 D1 / (r g) Dividend Yield (D1/P0) Capital Gains Yield (P1-P0)/P0 P/E Ratio P0/EPS
Low Growth Firm 13.33 15 5 4.44
Normal Growth Firm 20.00 10 10 6.67
Supernormal Growth Firm 40.00 5 15 13.33
67
Inference

• As the expected growth in dividend, increases,
  other things remaining constant, the expected
  return depends more on capital gains yield and
  less on the dividend yield.
• As the expected growth rate in dividend
  increases, other things remaining constant, the
  P/E ratio increases.
• High dividend yield and low P/E ratio imply
  limited growth prospects.
• Low dividend yield and high P/E ratio imply
  considerable growth prospects.

68
Valuation of Common Stock

• Price Ratio Approach

69
Price Ratio Analysis

• Price-earnings ratio (P/E ratio)
• Current stock price divided by annual earnings
  per share (EPS).
• Earnings yield
• Inverse of the P/E ratio earnings divided by
  price (E/P).
• High-P/E stocks are often referred to as growth
  stocks, while low-P/E stocks are often referred
  to as value stocks.

70
Price Ratio Analysis

• Price-cash flow ratio (P/CF ratio)
• Current stock price divided by current cash flow
  per share.
• In this context, cash flow is usually taken to be
  net income plus depreciation.
• Most analysts agree that in examining a companys
  financial performance, cash flow can be more
  informative than net income.
• Earnings and cash flows that are far from each
  other may be a signal of poor quality earnings.

71
Price Ratio Analysis

• Price-sales ratio (P/S ratio)
• Current stock price divided by annual sales per
  share.
• A high P/S ratio suggests high sales growth,
  while a low P/S ratio suggests sluggish sales
  growth.
• Price-book ratio (P/B ratio)
• Market value of a companys common stock divided
  by its book (accounting) value of equity.
• A ratio bigger than 1.0 indicates that the firm
  is creating value for its stockholders.

72
Price Ratio Analysis
Intel Corp (INTC) - Earnings (P/E)
Analysis Current EPS 1.35 5-year average P/E
ratio 30.4 EPS growth rate 16.5
expected historical ? projected EPS stock
price P/E ratio 30.4 ?
(1.35?1.165) 47.81
73
Price Ratio Analysis
Intel Corp (INTC) - Cash Flow (P/CF)
Analysis Current CFPS 1.97 5-year average P/CF
ratio 21.6 CFPS growth rate 15.3
expected historical ? projected CFPS
stock price P/CF ratio 21.6 ?
(1.97?1.153) 49.06
74
Price Ratio Analysis
Intel Corp (INTC) - Sales (P/S) Analysis Current
SPS 4.56 5-year average P/S ratio 6.7 SPS
growth rate 13.3
expected historical ? projected SPS stock
price P/S ratio 6.7 ?
(4.56?1.133) 34.62
75
P/E Ratio Approach
76
Determinants of P/E Ratio
77
Determinants of P/E Ratio

• Factors that determine the P/E ratio are
• The dividend payout ratio, (1-b)
• The required rate or return, r
• Interest Rate
• Risk
• The expected growth rate, g ROE x b