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CHAPTER 5

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CHAPTER 5

Basic Stock Valuation

- Represents ownership.
- Ownership implies control.
- Stockholders elect directors.
- Directors hire management.
- Since managers are “agents” of shareholders, their goal should be: Maximize stock price.

- Classified stock has special provisions.
- Could classify existing stock as founders’ shares, with voting rights but dividend restrictions.
- New shares might be called “Class A” shares, with voting restrictions but full dividend rights.

- The dividends of tracking stock are tied to a particular division, rather than the company as a whole.
- Investors can separately value the divisions.
- Its easier to compensate division managers with the tracking stock.

- But tracking stock usually has no voting rights, and the financial disclosure for the division is not as regulated as for the company.

- A firm “goes public” through an IPO when the stock is first offered to the public.
- Prior to an IPO, shares are typically owned by the firm’s managers, key employees, and, in many situations, venture capital providers.

- A seasoned equity offering occurs when a company with public stock issues additional shares.
- After an IPO or SEO, the stock trades in the secondary market, such as the NYSE or Nasdaq.

- Dividend growth model
- Using the multiples of comparable firms
- Free cash flow method (covered in Chapter 11)

^

D1 D2 D3 D∞

P0 =

+

+…+

+

(1+rs)1 (1+rs)2 (1+rs)3 (1+rs)∞

What is a constant growth stock?

One whose dividends are expected to

grow forever at a constant rate, g.

^

D0(1+g)

D1

P0 =

=

rs - g

rs - g

D1 = D0(1+g)1

D2 = D0(1+g)2

Dt = D0(1+g)t

If g is constant and less than rs, then:

$

Dt = D0(1 + g)t

Dt

0.25

PV of Dt =

(1 + r)t

If g > r, P0 = ∞ !

Years (t)

^

D0(1+g)1 D0(1+g)2 D0(1+rs)∞

P0 =

+…+

+

(1+rs)1 (1+rs)2 (1+rs)∞

(1+g)t

^

If g > rs, then

> 1, and

P0 = ∞.

(1+rs)t

So g must be less than rs to use the constant growth model.

Use the SML to calculate rs:

rs= rRF + (RPM)bFirm

= 7% + (5%) (1.2)

= 13%.

- D0 = 2 and constant g = 6%
- D1 = D0(1+g) = 2(1.06) = 2.12
- D2 = D1(1+g) = 2.12(1.06) = 2.2472
- D3 = D2(1+g) = 2.2472(1.06) = 2.3820

0

1

2

3

4

g=6%

2.12

2.2472

2.3820

D0=2.00

1.8761

13%

1.7599

1.6508

^

D0(1+g)

D1

$2.12

$2.12

P0 =

=

= = $30.29.

rs - g

rs - g

0.13 - 0.06

0.07

Constant growth model:

D2

^

$2.2427

P1 =

=

= $32.10

rs - g

0.07

- D1 will have been paid, so expected dividends are D2, D3, D4 and so on.

D1

$2.12

Dividend yield = = = 7.0%.

P0

$30.29

^

P1 - P0

$32.10 - $30.29

CG Yield = =

P0

$30.29

= 6.0%.

- 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.

D1

^

^

D1

P0 =

to

rs

+ g.

=

rs - g

P0

^

Then, rs= $2.12/$30.29 + 0.06

= 0.07 + 0.06 = 13%.

0

1

2

3

rs=13%

2.00

2.00

2.00

PMT

$2.00

^

P0 = = = $15.38.

r

0.13

- Supernormal growth of 30% for 3 years, and then long-run constant g = 6%.
- Can no longer use constant growth model.
- However, growth becomes constant after 3 years.

0

1

2

3

4

rs=13%

g = 30%

g = 30%

g = 30%

g = 6%

D0 = 2.00 2.603.38 4.394 4.6576

2.3009

2.6470

3.0453

^

$4.6576

46.1135

P3 =

= $66.5371

0.13 – 0.06

^

54.1067 = P0

At t = 0:

D1

$2.60

Dividend yield = = = 4.8%.

P0

$54.11

CG Yield = 13.0% - 4.8% = 8.2%.

(More…)

- 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%.

$46.11

= 85.2%.

$54.11

- 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:

- If most of a stock’s value is due to long-term cash flows, why do so many managers focus on quarterly earnings?
- See next slide.

- Sometimes changes in quarterly earnings are a signal of future changes in cash flows. This would affect the current stock price.
- Sometimes managers have bonuses tied to quarterly earnings.

0

1

2

3

4

rs=13%

g = 0%

g = 0%

g = 0%

g = 6%

2.00 2.00 2.00 2.12

1.7699

1.5663

2.12

1.3861

P

30.2857

20.9895

3

0.07

25.7118

- Dividend Yield = D1 / P0
- Dividend Yield = $2.00 / $25.72
- Dividend Yield = 7.8%
- CGY = 13.0% - 7.8% = 5.2%.

- Now have constant growth, so:
- Capital gains yield = g = 6%
- Dividend yield = rs – g
- Dividend yield = 13% - 6% = 7%

^

D0(1+g)

D1

^

P0 =

=

rs - g

rs - g

$2.00(0.94)

$1.88

= = = $9.89.

0.13 - (-0.06)

0.19

Firm still has earnings and still pays

dividends, so P0 > 0:

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.

- Analysts often use the P/E multiple (the price per share divided by the earnings per share).
- 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.

- 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, Customers, Eyeballs, etc.
- Calculate the average entity ratio for a sample of comparable firms. For example,
- V/EBITDA
- V/Customers

- Find the entity value of the firm in question. For example,
- Multiply the firm’s sales by the V/Sales multiple.
- Multiply the firm’s # of customers by the V/Customers ratio

- 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.

- It is often hard to find comparable firms.
- The average ratio for the sample of comparable firms often has a wide range.
- For example, the average P/E ratio might be 20, but the range could be from 10 to 50. How do you know whether your firm should be compared to the low, average, or high performers?

D1

^

P0 =

rs - g

- rs = rRF + (RPM)bi could change.
- Inflation expectations
- Risk aversion
- Company risk

- g could change.

D1 = $2, rs = 10%, and g = 5%:

P0 = D1 / (rs-g) = $2 / (0.10 - 0.05) = $40.

What happens if rs or g change?

- Small changes in expected g and rs cause large changes in stock prices.
- As new information arrives, investors continually update their estimates of g and rs.
- If stock prices aren’t volatile, then this means there isn’t a good flow of information.

- 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…)

^

rs = D1/P0 + g = rs = rRF + (rM - rRF)b.

^

D1

P0

^

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 until:

D1/P0 + g = rs = rs.

^

- Securities are normally in equilibrium and are “fairly priced.” One cannot “beat the market” except through good luck or inside information.

(More…)

- 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.

- 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.

- 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.

- 100,000 or so trained analysts--MBAs, CFAs, and PhDs--work for firms like Fidelity, Merrill, Morgan, and Prudential.
- These analysts have similar access to data and megabucks to invest.
- Thus, news is reflected in P0 almost instantaneously.

- 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.

$5

Vps

= $50 =

^

rps

$5

^

rps

= 0.10 = 10.0%

=

$50