fin 819: lecture 2'1 review of the valuation of common stocks how to apply the pv concept

FIN 819: lecture 2' 1

Review of the Valuation of Common Stocks

How to apply the PV concept


Today’s plan

Review what we have learned in the last lecture

Valuing stocks• Some terms about stocks

• Valuing stocks using dividends

• Valuing stocks using earnings

• Valuing stocks using free cash flows


Some terms about stocks

Book Value – The value of the stocks according to the balance sheet.

Liquidation Value - Net proceeds that would be realized by selling the firm’s assets and paying off its creditors.

Market Value Balance Sheet - Financial statement that uses market value of assets and liabilities.


Some terms about stocks

Secondary Market - market in which already issued securities are traded by investors.

Dividend - Periodic cash distribution from the firm to the shareholders.

P/E Ratio - Price per share divided by earnings per share.

Dividend yield – Dividends per share over the price of per share


Example

IBM has a trading price of $70 per share. Its annual earnings per share is $5. Its annual dividend per share is $3.5. What are the P/E and the dividend yield?

P/E=70/5=14 Dividend yield=3.5/70=1/20=0.05


Valuing Common Stocks using dividends (first approach)

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

H - Time horizon for your investment.

PDiv

r

Div

r

Div P

rH H

H01

12

21 1 1

( ) ( )

...( )


Example

George has bought one IBM share in the beginning of this year and decides to hold this share until next year. The expected dividend this year is $10 per share and the stock is expected to sell at $110 per share in the end of the year. If the cost of the capital is 10%, what is the current stock price?


Solution

P0=(110+10)/(1+0.1)=$109.1


Valuing common stocks using dividends

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?


Solution

00.75$

)12.1(

48.9450.3

)12.1(

24.3

)12.1(

00.3

0

3210

P

P


Valuing common stocks using dividends

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

r

EPSor

r

DivPperpetuityPV 11

0)(

Assumes all earnings are paid to shareholders.


Example

Suppose that a stock is going to pay a dividend of $3 every year forever. If the discount rate is 10%, what is the stock price for the following cases:• (a) you invest and hold it forever?

• (b) you invest and hold it for two years?

• (c) you invest and hold it for 20 years?


Solution

(a) P0=3/0.1=$30 (b)P0=PV (annuity) + PV( the stock price at

year 2) = 3/1.1 + 3/1.12+(3/0.1)/1.12

= 3/0.1=$30

(c) P0=PV (annuity of 20 years) + PV (the stock price at the year of 20) =$30


Valuing Common Stocks

Gordon Growth Model: A version of the dividend growth model in which dividends grow at a constant rate (Gordon Growth Model).

Stocks can be valued as a perpetuity with a growth rate, if you want to hold this stock forever, that is

gr

DivP

1

0


Example

Suppose that a stock is going to pay a dividend of $3 next year. Dividends grow at a growth rate of 3%. If the discount rate is 10%, what is the stock price for the following cases:• (a) you buy and hold it forever?

• (b) you buy and hold it for two years?

• (c) you buy and hold it for 20 years?


Solution (a) P0=3/(0.1-0.03)=$42.86 (b)P0=PV (annuity) + PV( the stock price at

year 2) = 3/1.1 + 3*1.03/1.12+(3*1.033/(0.1-

0.03))/1.12

= 3/(0.1-0.03)=$42.86 (c) P0=PV (annuity of 20 years) + PV (the stock price at the year of 20) =$42.86


Capitalization rate

Expected Return - The percentage yield that an investor forecasts from a specific investment over a set period of time. Sometimes called the market capitalization rate.

Expected Return

rDiv P P

P1 1 0

0


Example

If Fledgling Electronics is selling for $100 per share today and is expected to sell for $110 one year from now, what is the expected return if the dividend one year from now is forecasted to be $5.00?


Solution

According to the formula,

15.100

1001105Return Expected


Capitalization rate

The formula for the capitalization rate can be broken into two parts.

Capital. Rate = Dividend Yield + Capital Appreciation

Expected Return

rDiv

P

P P

P1

0

1 0

0


Using dividends models to derive the capitalization rate

Capitalization Rate can be estimated using the perpetuity formula, given minor algebraic manipulation.

gP

Divr

gr

DivP

0

1

10


Valuing Common Stocks

Example-

If a stock is selling for $100 in the stock market, the cost of capital is 12% and the next year dividend is $3, what might the market be assuming about the growth in dividends?

$100$3.

.

.

00

12

09

g

g


Some terms about dividend growth rates

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.


Deriving the dividend growth rate g

Growth can be derived from applying the return on equity to the percentage of earnings plowed back into operations.

g = return on equity X plowback ratio

SharePer Equity Book

EPS

Equityon Return

ROE

ROE


Example

Our company forecasts to pay a $5.00 dividend next year, which represents 100% of its earnings. This will provide investors with a 12% expected return. Instead, we decide to plow back 40% of the earnings at the firm’s current return on equity of 20%. What is the value of the stock before and after the plowback decision?


Solution

Without growth

With growth

75$08.012.0

6.0*5

08.02.0*4.0

0

P

g

67.41$12.0

50 P


Example (continued)

If the company did not plowback some earnings, the stock price would remain at $41.67. With the plowback, the price rose to $75.00.

The difference between these two numbers (75.00-41.67=33.33) is called the Present Value of Growth Opportunities (PVGO).


Valuing common stocks using earnings

We often use earnings to value stocks as

What is the relationship between this formula and the dividend growth formula?

PVGOr

EPSP 1

0


Example Firm A has a market capitalization rate of 15%. The

earnings are expected to be $8.33 per share next year. The plowback ratio is 0.4 and ROE is 25%. Every investment in year i is to yield a simple perpetuity starting in year (i+1) with each cash flow equal to total investment times ROE. All the investments have the same capitalization rate.• (a) Using the formula P=ESP1/r + PVGO to calculate the

stock price• (b) If ROE is increased, what will happen to the stock price?

Why?• (c) Use the dividend model to calculate the stock price?• (d) What have you found?• (e) Think about why you have this kind of result?


Simple Solution

(a)

g=10%, EPS1/r=8.33/0.15=$55.56

PVGO=NPV1/(r-g)=2.22/(0.15- 0.1)=$44.44, P=$100

(b) The price will be increased

(c) P=Div1/(r-g)=5/(0.15-0.1)=$100


Valuing common stocks using FCF (free cash flows)

The value of a business or stock is usually computed as the discounted value of FCF out to a valuation horizon (H).

The horizon value is sometimes called the terminal value .

HH

HH

r

PV

r

FCF

r

FCF

r

FCFPV

)1()1(...

)1()1( 22

11


FCF and PV

HH

HH

r

PV

r

FCF

r

FCF

r

FCFPV

)1()1(...

)1()1( 22

11

PV (free cash flows) PV (horizon value)


FCF and PV

Free Cash Flows (FCF) should be the theoretical basis for all PV calculations.

FCF is a more accurate measurement of PV than either Div or EPS.

The market price does not always reflect the PV of FCF.

When valuing a business for purchase, always use FCF.


FCF and PV

ExampleGiven 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


FCF and PV

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

Solution


FCF and PV

$18.8

22.4-3.6

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


How to estimate the horizon value?

It is very difficult to forecast or estimate the horizon value. There are several ideas that may be used to estimate the horizon value.• Competition

• Constant growth rate

• P/E ratio

• Dividend yield

• Book-to-market ratio

fin 819: lecture 2'1 review of the valuation of common stocks how to apply the pv concept

Documents

share slide

lecture valuing stocks

dividends valuing stocks

earnings valuing stocks

solution slide

current stock price

todays stock price

market price