The Value of Common Stocks Oh, the ragman draws circles up and down the block. I’d ask him what the matter was, but I know he don’t talk. - Dylan.

The Value of Common Stocks

Oh, the ragman draws circles up and down the block. I’d ask him what the matter was, but I know he don’t talk. - Dylan

Stocks and stock markets

Primary Market: Market in which firm sells new shares to raise cash.

Secondary Market: Market in which investors trade existing shares among themselves.

Stock exchanges are secondary markets. They may either operate as auction markets or dealer markets.

The New York Stock Exchange is an auction market; the specialist keeps a record of orders to buy & sell stock.If (say) you wish to sell IBM stock, the specialist will identify the buyer who is prepared to pay the highest price.

NASDAQ is a dealer market. It consists of a network of dealers who quote prices at which they will buy or sell.

What determines a stock's true value?

Book Value records what a company has paid for its assets with a simple deduction for depreciation and no allowance for inflation.

Liquidation Value is what the company could realize by selling its assets and repaying debts. It does not measure the value of a going concern. It ignores intangible assets (e.g.., patents, brand name) and ignores that firms may be able to make profitable investments in the future.

True Value is market value, that is, the amount that investors are willing to pay for the firm. It depends on the earning power of

existing assets and the profitability of future investments.

The expected return on a stockExpected = Dividend + CapitalReturn Yield Gain

DIV P1 - P r = + P0 P0

eg Blue Skies stock price (P0 ) = $75. Investors expect nextyear a dividend (DIV1 ) of $3 & a price (P1 ) of $81.

3 81 - 75 r = + = .12 or 12% 75 75

Stock = Cash payoff to investorsPrice 1 + expected return

DIV1 + P1

P = 1 + r 3 + 81For Blue Skies: P0 = = $75 1.12

1 0

0

Stock price is equal to thediscounted stream of

dividendsStock = Cash payoff to investorsPrice 1 + expected return

DIV + P P = 1 + r

DIV + PSimilarly P = 1 + r

DIV DIV + PTherefore P = + 1 + r (1 + r)

We can also express P2 in terms of DIV3 & P3 etc. Thus

DIV DIV DIV3

P = + + + ...... 1 + r (1 + r)2 (1 + r)3

0

1 1

1

2 2

0

1 2 2

2

21

0

Valuing Common Stocks

Dividend Discount Model - Computation of today’s stock price which states that share value equals the present value of all expected future dividends.

PDiv

r

Div

r

Div P

rH H

H01

12

21 1 1

( ) ( )

...( )

H - Time horizon for your investment.

Valuing Common Stocks

Example

Current forecasts are for XYZ Company to pay dividends of $3, $3.24, and $3.50 over the next three years, respectively. At the end of three years you anticipate selling your stock at a market price of $94.48. What is the price of the stock given a 12% expected return?

PV

PV

300

1 12

324

1 12

350 94 48

1 12

00

1 2 3

.

( . )

.

( . )

. .

( . )

$75.

Valuing Common StocksAssuming No Growth

If we forecast no growth, and plan to hold out stock indefinitely, we will then value the stock as a PERPETUITY.

Perpetuity PDiv

ror

EPS

r 0

1 1

Assumes all earnings are paid to shareholders.

Constant-growth dividend discount model(the Gordon Growth model)

If dividends are expected to grow at a constant rate (g), the value of the stock is

DIV1

PV = (r – g)

Example:Blue Skies is expected to pay a $3 dividend next year (DIV1 = 3). Investors expect Blue Skies dividends to increase by 8% a year indefinitely (g = .08). The discount rate is 12% (r = .12).

DIV1 3PV = = = $75 (r – g) (.12 - .08)

Note: The formula works only if g is less than r

Estimating the capitalization rateIf dividends are expected to grow at a constant rate, g

DIV1

P0 = (r – g)

DIV1

r = + g P0

If a firm earns a constant return on book equity and plows back a constant proportion of earnings, then the dividend growth rate can be estimated as follows:

DIVIDEND = g = PLOWBACK x RETURNGROWTH RATE RATIO ON EQUITY

Also known as Sustainable Growth Rate – (i.e., steady rate at which a firm can grow): plowback ratio X return on equity

Valuing Common StocksEstimating the implied growth rate

Example

If a stock is selling for $100 in the stock market, what might the market be assuming about the growth in dividends?

$100$3.

.

.

00

12

09

g

g

Answer

The market is assuming the dividend will grow at 9% per year, indefinitely.

PVGO- Growth versus No GrowthSuppose Blue Skies earns $5 a share, which it pays outas dividends. DIV1 = $5 and g = 0. Then

DIV $5PV = = = $41.67 (r – g) (.12 - .0)

$41.67 is the value of Blue Skies' assets in place (i.e., assuming no growth).

Suppose Blue Skies reinvests 40% of profits at areturn of 12% (that is the same rate as investors require):

g = plowback ratio x return on equity = .4 x .12 = .048

.6 x $5PV = = $41.67 .12 - .048

NOTE: Firms that earn the required rate (r) on new investments, don't add value.

Recall Prior Estimated Price for Blue Skies = $75. If PV (assets in place) = $41.67,then $75 - $41.67 = $33.33 = PV(Growth Opportunities) = PVGO

1

Valuing Common Stocksanother PVGO example

Example

Our 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. Instead, we decide 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?

56.55$15.

33.80 P

No Growth With Growth

00.100$10.15.

00.5

10.40.25.

0

P

g

Valuing Common Stocks another PVGO example continued

Example - continuedIf 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 represents the net present value of a firm’s future investments. This is

called the Present Value of Growth Opportunities (PVGO).

44.44$56.5500.100 PVGO

r is not EPS/P unless PVGO=0

STOCK PRICE = PV (average earnings under a no-growth policy) plus PV (growth opportunities)

EPS1

P = + PVGO r

Thus EPS PVGO = r 1 - P P

If PVGO = 0, the earnings yield equals the capitalization rate.

PVGO IS POSITIVE ONLY IF THE FIRM CAN EARN MORETHAN THE COST OF CAPITAL ON INVESTMENTS.

0

1

0 0

( )

Estimated PVGOs

Stock Price EPS r PVGO

Income stocks:

AT&T $51.13 $3.76 .136 $23.48 46%

Conagra 32.88 2.16 .139 17.34 53

Growth stocks:Genzyme 39.00 2.09 .244 30.43 78

Microsoft 64.38 2.57 .165 48.80 76

Valuing a BusinessValuing a Business or Project

HH

HH

r

PV

r

FCF

r

FCF

r

FCFPV

)1()1(...

)1()1( 22

11

PV (free cash flows) PV (horizon value)

Valuing a BusinessExample

Given the cash flows for Concatenator Manufacturing Division, calculate the PV of near term cash flows, PV (horizon value), and the total value of the firm. r=10% and g= 6%

66613132020202020(%) growth .EPS

1.891.791.681.59.23-.20-1.39-1.15-.96-.80- FlowCash Free

1.891.781.681.593.042.693.462.882.402.00Investment

3.783.573.363.182.812.492.071.731.441.20Earnings

51.3173.2905.2847.2643.2374.2028.1740.1400.1200.10ValueAsset

10987654321

Year

Valuing a BusinessExample - continued


4.2206.10.

59.1

1.1

1 value)PV(horizon 6

6.3

1.1

23.

1.1

20.

1.1

39.1

1.1

15.1

1.1

96.

1.1

.80-PV(FCF) 65432

Valuing a BusinessExample - continued


$18.8

22.4-3.6

value)PV(horizonPV(FCF)s)PV(busines

Accounting Ratios

1. P0 = EPS x average P/EPS 2. P0 = Book value per share x average P/book value per

share

3. P0 = EBITDA x average P/EBITDA

Valuing the firm Summary1. Calculate the PV of expected future dividends.

2. Calculate the PV of expected free cash flow.

3. Calculate the PV of earnings under no growth policy (perpetuity) plus the PV of growth opportunities.

4. Use Ratios to estimate current or horizon values.

The Value of Common Stocks Oh, the ragman draws circles up and down the block. I’d ask him what the matter was, but I know he don’t talk. - Dylan.

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