Part 3: Stock Valuation

1
Part 3 Stock Valuation

• Organisation
• Common Stock Valuation Growing perpetuity
  formula
• Two-stage model
• Price-to-Earnings Ratio
• Free Cash Flow Approach

2
3.1 Concept of Stocks

• Firms raise money in stock market. If you
  purchase the shares, then you are one of the
  owners of the company.
• You are entitled to share the profit made by the
  company.
• You also have the voting right for major
  corporate decisions, such as electing the board
  of directors, and deciding whether to accept
  another firms offer of takeover.
• Firms pay their stockholders cash semi-annually
  in Australia. These payments are called
  dividends.

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3.2 Common Stock Valuation

• The fundamental theory of valuation The value
  today of any financial asset equals the present
  value of all of its expected future cash flows.
• The value of a firms stock is the discounted
  (expected) dividend cash flows.

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3.3 Stock Valuation The Zero Growth Case

• If all future dividends are the same, the
• present value of the dividend stream
• constitutes a perpetuity, which is equal
• to C/r or, in this case, D1/r.

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3.4 Example 1

• Question Cooper, Inc.s common stock currently
  pays a 1.00 dividend, which is expected to
  remain constant forever. If the required return
  on Cooper stock is 10, what should the stock
  sell for today?
• Answer P0 1/.10 10.
• Question
• Given no change in the variables, what will the
  stock be worth in one year?

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3.4 Example 1 (concluded)

• Answer One year from now, the value of the
  stock, P1, must be equal to the present value of
  all remaining future dividends. That is,
• P1 D2/r 1/.10 10.
• In the absence of any changes in expected
  dividend flows (and given a constant discount
  rate), there is no reason to expect capital gains
  from such a no-growth stock.

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3.5 Stocks Paying Dividend with Constant Growth
Rate

• In reality, investors generally expect the firm
  (and the dividends it pays) to grow over time. As
  long as the rate of change from one period to the
  next, g, is constant, we can apply the growing
  perpetuity model

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3.6 PV of a growing perpetuity

• PV of growing perpetuity next periods cash
  flow / (discount rate - growth rate).
• That is,

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3.7 Example 2

• Suppose the dividend next year is expected to be
  5 and afterwards the dividend is expected to
  grow by 6 per year forever. What should the
  stock price be? Assuming r 10.
• Answer 5 / (.10 - .06) 5 / .04 125.
• Note the dividend growth rate cannot be greater
  than the discount rate.

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3.8 Stock Price Sensitivity to g
Stock price
50
45
D1 1 Required return, r, 12
40
35
30
25
20
15
10
Dividend growth rate, g
5
0
8
2
4
6
10
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3.9 Stock Price Sensitivity to r
Stock price
100
90
80
D1 1 Dividend growth rate, g, 5
70
60
50
40
30
20
Required Return, r
10
6
8
10
14
12
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3.10 Stock Valuation - The Nonconstant Growth
Case

• For many growth firms, dividends are low but are
  expected to grow rapidly. As product markets
  mature, the dividend growth rate is then expected
  to slow to a steady state rate. How should
  stocks such as these be valued?
• Answer P0 PV of dividends in the nonconstant
  growth period(s) PV of dividends in the steady
  state period.

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3.11 Example 3

• Suppose a stock has just paid a 5 per share
  dividend. The dividend is projected to grow at 5
  per year indefinitely. If the required return is
  9, then what is the price today? (131.25)
• What will the price be in a year?
• P1 ? (137.8125)
• By what percentage does P1 exceed P0?
• P1 exceeds P0 by 5 -- the capital gains yield.

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3.12 Example 4

• Find the required return
• Suppose a stock has just paid a 5 per share
  dividend. The dividend is projected to grow at 5
  per year indefinitely.
• If the stock sells today for 65.625, what is
  the required return?

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3.12 Example 4 (Concluded)

• Solution
• P0 D1/(r - g) ?
• (r - g) D1/P0
• r D1/P0 g (Gordons Formula)
• 5.25/65.625 .05
• dividend yield ( .08 )
• capital gains yield ( .05 )
• .13 13

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3.13 Dividend Growth Rate

• Assume that the company reinvests (plows back)
  fraction b of its earnings, then the dividend
  growth rate is
• ROE (Return on Equity) Earnings/Book value of
  equity.

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3.14 Some useful definitions

• Market capitalization Price x Number of shares
• Book Value The value of the asset appears in the
  financial statement.
• ROE (return on equity) Earnings / Book value of
  equity.
• Market-to-book Market capitalization / Book
  value of equity

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3.15 In-class Exercise

• If the Rankine Company retains 40 of its
  earnings each year, and these earnings are
  reinvested to earn a 25 rate of return, what is
  the price of Rankines shares? Assuming r 15,
  and the latest dividend was 0.90 per share and
  was paid yesterday.
• Assume that the Rankines growth rate is expected
  to be 10 for only a further 3 years, and is then
  expected to fall to 6 per year afterwards. What
  is the price of Rankines shares?

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3.16 Example 5, two-stage model
Investment rate
40
Return on incremental investment
20
for terminal year and beyond
Cost of capital
10
Current
Terminal
Date
Year
Year
-1
0
1
2
3
Earnings
70


80


90


100


Payout
40


45


50


60


Retained
30


35


40


40


Equity
880


910


945


985


1,025


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3.16 Example 5 (concluded)
Current
Terminal
Date
Year
Year
0
1
2
3
Payout
40


45



50
Terminal value
3,300


PV factor
100
91
83
75
PV of payout/terminal value
40.0


40.9


41.3


2,479.3


Total value
2,601.6


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3.17 Price-Earnings Ratio

• P-E ratio reflects amount investors are willing
  to pay for each dollar of current earnings. If a
  stocks P/E 20, investors are paying 20 dollars
  for each dollar of stock current earnings.
• Using P-E Multiples approach, one estimates stock
  expected earnings per share (EPS) and times EPS
  by historical P-E ratio to arrive at stock value.

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3.18 Why P-E Ratios Differ

• Decompose stock price into two components

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3.19 P/E Ratio and Valuation

• P-E ratios are considered by some as indication
  of whether stocks are overvalued or undervalued.
  Comparison is made to historical or industry
  average ratios.
• If a firms P/E ratio is high, then it could be
  that the PVGO is high, or r is low, or both. It
  is not necessary that the stock is expensive so
  you should sell.

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3.20 Free Cash Flows

• Free Cash Flow (FCF) to shareholders - Net cash
  flow after paying for future investments by the
  firm. This approach is useful when a firm does
  not pay dividends to shareholders currently.
• When valuing a business, it is better to use FCF
  because FCF is more accurate measurement of firm
  financial position than either Div or EPS.

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3.21 Valuing a Business Using Free Cash Flows

• Value of a business is computed as discounted
  value of FCF out to a valuation horizon (H).
• Valuation horizon is sometimes called terminal
  value and is calculated using growing perpetuity
  formula.