Features of Common Stock Valuation of Securities: Stocks


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Valuation of Securities: Stocks
Econ 422: Investment, Capital & Finance University of Washington Eric Zivot Fall 2007 January 31, 2007
E. Zivot 2006 R.W. Parks/L.F. Davis 2004

Features of Preferred Stock

• Dividends

– Stated dividend must be paid before dividends can be paid to common stockholders.

– Dividends are not a liability of the firm, and preferred dividends can be deferred indefinitely.

– Most preferred dividends are cumulative – any missed preferred dividends have to be paid before common dividends can be paid.

• Preferred stock generally does not carry

voting rights.

E. Zivot 2006 R.W. Parks/L.F. Davis 2004

Features of Common Stock
• Voting rights (Cumulative vs. Straight) • Proxy voting • Classes of stock • Other rights
– Share proportionally in declared dividends – Share proportionally in remaining assets during
liquidation – Preemptive right – first shot at new stock issue
to maintain proportional E.Zivot2006 ownership if desired R.W. Parks/L.F. Davis 2004

The Stock Markets

• Dealers vs. Brokers

• New York Stock Exchange (NYSE)

– Largest stock market in the world

– Members

• Own seats on the exchange

• Commission brokers

• Specialists

• Floor brokers

• Floor traders

– Operations

– Floor activity

E. Zivot 2006 R.W. Parks/L.F. Davis 2004

1

NASDAQ

• Not a physical exchange – computer-based quotation system

• Multiple market makers

• Electronic Communications Networks

• Three levels of information

– Level 1 – median quotes, registered representatives

– Level 2 – view quotes, brokers & dealers

– Level 3 – view and update quotes, dealers only



Large

portion

of

technology E. Zivot2006 R.W. Parks/L.F. Davis 2004

stocks

Valuing Stock
• Valuing a firm’s equity involves the same ideas introduced for valuing a firm’s debt instruments
• To value a firm’s stock 1. Determine the expected cash flows 2. Calculate the present value of the cash flows
• Valuing stock, however, is more complicated than valuing bonds because the cash flows are not contractually specified or fixed.
E. Zivot 2006 R.W. Parks/L.F. Davis 2004

Stock Market Reporting

52 WEEKS

YLD VOL

NET

HI LO STOCK SYM DIV % PE 100s CLOSE CHG

25.72 18.12 Gap Inc GPS 0.18 0.8 18 39961 21.35 …

Gap has been as high as $25.72 in the last year.

Gap pays a dividend of 18 cents/share.
Given the current price, the dividend yield is .8%.

Gap ended trading at $21.35, which is unchanged from yesterday.

Gap has been as low as $18.12 in the last year.

Given the current
price, the PE ratio is
18 times earnings.
E. Zivot 2006 R.W. Parks/L.F. Davis 2004

3,996,100 shares traded hands in the last day’s trading.

Cash Flow
A stock’s cash flow consists of: • Stream of dividend payments received during
ownership of stock • The sale price for the stock upon deciding to sell
Note: • The dividend stream may continue indefinitely • The dividend stream may be finite • The dividend stream may change over time • There may be no dividend stream
E. Zivot 2006 R.W. Parks/L.F. Davis 2004
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Valuation of Stocks
Let’s calculate the rate of return for holding a stock for one
period (holding period return). Define:

P0 = today’s price of the stock P1 = next year’s price D1 = next year’s dividend

HPR = r = [P1 + D1 - P0]/P0 = [P1- P0]/P0 +

D1/P0

E. Zivot 2006 R.W. Parks/L.F. Davis 2004

Valuation of Stocks
r = [P1- P0]/P0 + D1/P0
Rewrite in terms of P0:
P0 = D1/(1+r) + P1/(1+r)
Today’s price equals the present value of next year’s dividend plus the present value of next year’s price.
E. Zivot 2006 R.W. Parks/L.F. Davis 2004

Example

• P0 = 100, P1 = 110, D1 = 5. Solve for r:

r = 110 − 100 + 5

100

100

= 0 .1 0 + 0 .0 5 = 0 .1 5

Given r, P1, and D1 = 5 now solve for P0
P = 5 + 110 =100 0 1.15 1.15
E. Zivot 2006 R.W. Parks/L.F. Davis 2004

Valuation of Stocks continued
P0 = D1/(1+r) + P1/(1+r) Similarly, we can write next year’s price as a function of the dividend in year 2 and the year 2 price of the stock:
P1 = D2/(1+r) + P2/(1+r) Substituting for P1:
P0 = D1/(1+r) + [D2/(1+r) + P2/(1+r)]/(1+r) P0 = D1/(1+r) + D2/(1+r)2 + P2/(1+r)2
E. Zivot 2006 R.W. Parks/L.F. Davis 2004
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Example
• r = 0.15, P0 = 100, P2 = 121, D1 = 5, D2 = 5.5
P = 5 + 5.5 + 121 =100
0 1.15 (1.15)2 (1.15)2
E. Zivot 2006 R.W. Parks/L.F. Davis 2004
Dividend Growth Models
• For a given discount rate r, stock prices will differ based on the firm dividends.
• The stock price is determined by how the firm dividends evolve.
• Typical assumptions are – No growth in dividends – Constant dividend growth
E. Zivot 2006 R.W. Parks/L.F. Davis 2004

Valuation of Stocks, continued
P0 = D1/(1+r) + D2/(1+r)2 + P2/(1+r)2
This equation is recursive, upon further substitution we can eventually arrive at the following expression:

P0 = D1/(1+r) + D2/(1+r)2 + … + DT/(1+r)T + …

P0 = Σ Dt/(1+r)t

for t = 1 to ∞

E. Zivot 2006 R.W. Parks/L.F. Davis 2004

Dividend Growth Models

• No growth in dividends: D1 = D2 = …=D

P0 = Σ D/(1+r)t

for t = 1 to ∞

Note the right hand side is a perpetuity, such that:

P0 = D/r

• Constant dividend growth: D1 = D; D2 = D(1+g); D3 = D(1+g)2; …
P0 = Σ D(1+g)t-1/(1+r)t for t = 1 to ∞ Note the right hand side is a growing perpetuity, such that:
P0 = D/(r-g) (for r > g)

E. Zivot 2006 R.W. Parks/L.F. Davis 2004

4

Numerical Examples
• D1 = 5, g = 0.10, r = 0.15
No growth: P = D1 = 5 = 33.33 0 r 0.15
Constant growth: P = D1 = 5 =100 0 (r − g) 0.05
E. Zivot 2006 R.W. Parks/L.F. Davis 2004
Numerical Example
• D1 = 5, r = 0.15, g0 = 0.10, g1 = 0.11
dP ≈ (r − g)−1dg P
= 0.01 = 0.01 = 0.2 (0.15 − 0.10) 0.05
= 20%
E. Zivot 2006 R.W. Parks/L.F. Davis 2004

Comparative Statics
• What happens to the stock price when the dividend growth rate changes?

P = D1 r−g

dP = −(r − g)−2 D ⋅ (−1)

dg

1

= (r − g)−1 P

⇒ dP ≈ (r − g)−1dg P

E. Zivot 2006 R.W. Parks/L.F. Davis 2004

Determining the Dividend Growth Rate
Q: What determines whether a firm will grow or issue increased dividends?
• A firm can either retain or payout earnings. • Dividends represent earnings that are paid out. • Retained earnings are those earnings not paid out
as dividends that the firm plows back into the business. • Investing retained earnings may provide growth opportunities for the firm.
E. Zivot 2006 R.W. Parks/L.F. Davis 2004
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Determining the Dividend Growth Rate
• Investing retained earnings will improve firm value (stock price) only if they are invested in projects with positive Net Present Value; i.e., the return to the retained earnings (return on equity) must exceed the market discount rate.
• Investing retained earnings in positive NPV projects, all else constant, will allow dividends to grow and the stock price to increase.
E. Zivot 2006 R.W. Parks/L.F. Davis 2004
Determining the Dividend Growth Rate
Growth in dividends can be derived from applying the return on equity to the percentage of earnings plowed back into operations:
Dividend growth = g
= return on equity * plowback ratio
= ROE * RR
E. Zivot 2006 R.W. Parks/L.F. Davis 2004

Determining the Dividend Growth Rate
If a firm elects to pay a lower dividend, and reinvest the funds, the stock price may increase because future dividends may be higher.
Payout Ratio - Fraction of earnings paid out as dividends
Plowback Ratio - Fraction of earnings retained by the firm. Also called the retention ratio (RR)
Note: Payout Ratio + Plowback Ratio = 1 => Payout Ratio = 1 - RR
E. Zivot 2006 R.W. Parks/L.F. Davis 2004
Example
A company forecasts to pay a $8.33 dividend next year, which represents 100% of its earnings. This will provide investors with a 15% expected return. Suppose, instead, the company decides to plow back 40% of the earnings at the firm’s current return on equity of 25%. What is the value of the stock before and after the plowback decision?
E. Zivot 2006 R.W. Parks/L.F. Davis 2004
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Stock price with no reinvestment of earnings:
D = EPS = $8.33 P = D = EPS = $8.33 = $55.56 0 r r 0.15
Where EPS = earnings per share P0 = $55.56 = no dividend growth stock price
E. Zivot 2006 R.W. Parks/L.F. Davis 2004
Stock price after investment of retained earnings:
g = ROE × RR = 0.25× 0.40 = 0.10 D = (1− RR) × EPS = 0.60×$8.33 = $5.00 P = D = $5.00 = $5.00 = $100 0 r − g 0.15 − 0.10 0.05
P0 = $100 = stock price with growing dividends
E. Zivot 2006 R.W. Parks/L.F. Davis 2004

Stock price with no reinvestment of earnings:
•With a fixed dividend forever, the stock price stays fixed at 55.56 (no capital gains) •The market rate of return on the stock is the dividend yield
r = D = $8.33 = 0.15 P0 $55.56
E. Zivot 2006 R.W. Parks/L.F. Davis 2004
If the company did not plowback some earnings, the stock price would remain at $55.56. With the plowback, the price rose to $100.00. The difference between these two numbers is called the Present Value of Growth Opportunities (PVGO)
PVGO = $100 − $55.56 = $44.44 = P − EPS
r ⇒ P = EPS + PVGO
r
E. Zivot 2006 R.W. Parks/L.F. Davis 2004
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Result: PVGO = 0 if ROE = r = market capitalization rate of stock
• EPS = $8.33, r = 0.15, ROE = 0.15
g = ROE × RR = 0.15 × 0.40 = 0.06 D = (1 − RR) × EPS = 0.60 × $8.33 = $5.00 P = D = $5.00 = $5.00 = $55.56 0 r − g 0.15 − 0.06 0.09 PVGO = $55.56 − $55.56 = 0
E. Zivot 2006 R.W. Parks/L.F. Davis 2004

NPVGO for Growth and Income Stocks

Stock

P0 EPS r PVGO= PVGO/P P0 EPS1/r
Income Stock (Dividend paying)

Exxon 42.29 2.13 .072 12.71 .30

Kellogg 29 1.42 .056 3.64

.13

Growth Stock (Small or no dividend)

Amazon 8.88 -.30 .24 10.13 1.14

Dell

23.66

.76

.22 20.20
E. Zivot 2006
R.W. Parks/L.F. Davis 2004

.85

Valuing Firms with No Dividends or Earnings • How do you value firms that do not issue
dividends? • How do you value firms with negative or
zero earnings (e.g., start-up companies, internet firms during recent market boom)? • A general formulation is:
P0 = EPS1/r + PVGO • If EPS1 = 0 then P0 = PVGO • Arguably, PVGOs were severely overstated
during tech boom years
E. Zivot 2006 R.W. Parks/L.F. Davis 2004
Comparing Different Stocks
• One way that investors and analysts compare different stocks is to look at Price/Earnings ratios or P/EPS: Recall: P0 = EPS1/r + PVGO Dividing through by EPS1 gives P0/ EPS1 = 1/r + PVGO/ EPS1
• The Price/Earnings ratio for different companies will differ based on their the ratio of growth opportunities to their ability to take advantage of the opportunities
E. Zivot 2006 R.W. Parks/L.F. Davis 2004
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Why Do Stock Prices Change?
From our valuation models: • Changes in dividends • Changes in dividend growth rates • Changes in PVGOs • Changes in relevant discount rate
E. Zivot 2006 R.W. Parks/L.F. Davis 2004

Why Do Stock Prices Change?
• From market equilibrium, demand for stock = supply of stock:
• Increases or decreases in demand (investor sentiment; expectations)
• Increases or decreases in supply (corporate finance: share buybacks, secondary offerings, stock splits, etc.)
E. Zivot 2006 R.W. Parks/L.F. Davis 2004

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Features of Common Stock Valuation of Securities: Stocks