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CHAPTER 9 Stocks and Their Valuation. Features of common stock Determining common stock values Preferred stock. Facts about common stock. Represents ownership Ownership implies control Stockholders elect directors Directors elect management. Corporate Organization. 1- 3.

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Chapter 9 stocks and their valuation

CHAPTER 9Stocks and Their Valuation

Features of common stock

Determining common stock values

Preferred stock


Facts about common stock
Facts about common stock

  • Represents ownership

  • Ownership implies control

  • Stockholders elect directors

  • Directors elect management



Intrinsic value and stock price
Intrinsic Value and Stock Price

  • corporate insiders, and analysts use a variety of approaches to estimate a stock’s intrinsic value (P0).

  • In equilibrium we assume that a stock’s price equals its intrinsic value.

    • Investors estimate intrinsic value to help determine which stocks are attractive to buy and/or sell.

    • Stocks with a price below (above) its intrinsic value are undervalued (overvalued).


Different approaches for estimating the intrinsic value of a common stock
Different approaches for estimating the intrinsic value of a common stock

  • Dividend growth model

  • Corporate value model


Dividend growth model
Dividend growth model common stock

  • Value of a stock is the present value of the future dividends expected to be generated by the stock.


Common stock valuation

Div 1 common stock

Common Stock Valuation

Div 2

Div 3

Div ∞

k%

k%

k%

k%


Bond valuation a comparison

Pmt 1 common stock

Bond Valuation: (a comparison)

Pmt 2

Pmt 3

Pmt 20

+

k%

k%

k%

k%


Constant growth stock
Constant growth stock common stock

  • A stock whose dividends are expected to grow forever at a constant rate, g.

    D1 = D0 (1+g)1

    D2 = D1 (1+g)1

    D3 = D2 (1+g)1


0 common stock

1

2

3

g = 6%

2.12A

2.247B

2.382C

D0 = 2.00

1.8761

rs = 13%

1.7599

1.6509

If D0 = $2 and g is a constant 6%, find the expected dividend stream for the next 3 years, and their PVs (assume rs = 13%.

Div ∞

rs%

A, D1= D0(1+g)1

= 2.00 (1+0.06)

= 2.12

B, D2= D1(1+g)1

= 2.12(1+0.06)

= 2.247

C, D3= D2(1+g)1

= 2.247 (1+0.06)1

= 2.382


Constant growth stock1
Constant growth stock common stock

  • A stock whose dividends are expected to grow forever at a constant rate, g.

    D1 = D0 (1+g)1

    D2 = D1 (1+g)1

    D3 = D2 (1+g)1

  • If g is constant, the dividend growth formula converges to:


What is the stock s intrinsic value
What is the stock’s intrinsic value? common stock

  • Using the constant growth model:

A , D0 (1+g)

= 2.0 (1+0.06)

= 2.12


What would the expected price today be if g 0

0 common stock

1

2

3

rs = 13%

...

2.00

2.00

2.00

What would the expected price today be, if g = 0?

  • The dividend stream would be a perpetuity.

*

* P0 = D

rs-g

If g = 0


Supernormal growth what if g 30 for 3 years before achieving long run growth of 6
Supernormal growth: common stockWhat if g = 30% for 3 years before achieving long-run growth of 6%?

  • Can no longer use just the constant growth model to find stock value.

  • However, the growth does become constant after 3 years.


Common stock valuation1

D1 common stock

Common Stock Valuation

g= 30%

g= 6%

D∞

D2

D3

D4

rs%

rs%

rs%

P3; Present value of

all future cash

flows to be

received beyond Yr 3

rs%

P3= D4

rs-g

= D3 (1+6%)

rs-g


Valuing common stock with nonconstant growthp example 1

0 common stock

1

2

3

4

rs = 13%

...

g = 30%

g = 30%

g = 30%

g = 6%

D0 = 2.00 2.600 3.380 4.394

4.658

2.301

2.647

3.045

4.658A

=

=

$66.54

46.114B

3

-

0.13

0.06

54.107 = P0

Valuing common stock with nonconstant growthp: (example 1)

rs=13%, n=1

rs=13%, n=2

A= D3 (1+g)

= 4.394(1+6%)

= 4658

rs=13%, n=3

$

rs=13%, n=3

P

^

B: FV=66.54, n=3, I/yr=13%, PV=?


Nonconstant growth example 2 what if g 0 for 3 years before long run growth of 6

0 common stock

1

2

3

4

rs = 13%

...

g = 0%

g = 0%

g = 0%

g = 6%

D0 = 2.00 2.00 2.00 2.00

2.12

1.77

1.57

1.39

2.12

$

P

=

=

$30.29

20.99

3

-

0.13

0.06

^

25.72 = P0

Nonconstant growth: (example 2)What if g = 0% for 3 years before long-run growth of 6%?

rs=13%, n=1

rs=13%, n=2

rs=13%, n=3

rs=13%, n=3


Super normal growth example 3 g 40 for 5 years before achieving l r growth of 7

D1 common stock

Super normal growth (example 3):G= 40% for 5 years before achieving L-r growth of 7%

G= 40%

G= 7%

D∞

D2

D3

D4

D5

D6

P5; Present value of

all future cash

flows to be

received beyond Yr 5

P5= D6

rs-g

= D5 (1+7%)

rs-g


What are the expected dividend yield, capital gains yield, and total return during the first year(assume D1 = 2.12, P1 = 32.10 & P0 = 30.29)?

  • Dividend yield

    = D1 / P0 = $2.12 / $30.29 = 7.0%

  • Capital gains yield

    = (P1 – P0) / P0

    = ($32.10 - $30.29) / $30.29 = 6.0%

  • Total return (rs)

    = Dividend Yield + Capital Gains Yield

    = 7.0% + 6.0% = 13.0%


Preferred stock
Preferred stock and total return during the first year(assume D1 = 2.12, P1 = 32.10 & P0 = 30.29)?

  • Hybrid security.

  • Like bonds, preferred stockholders receive a fixed dividend that must be paid before dividends are paid to common stockholders.

  • However, companies can omit preferred dividend payments without fear of pushing the firm into bankruptcy.


Preferred stock valuation
Preferred stock Valuation and total return during the first year(assume D1 = 2.12, P1 = 32.10 & P0 = 30.29)?

If a preferred stock pays an annual dividend of RM5 a share and market interest rate is 10%, what is the preferred stock’s current price?

Vp = D/rp

D= 5

rp=10% , Vp= RM5/ 10%

Vp = RM50


If preferred stock with an annual dividend of $5 sells for $50, what is the preferred stock’s expected return?

Vp = D / rp

$50 = $5 / rp

rp = $5 / $50

= 0.10 = 10%

^


What would be the intrinsic price for this stock one year from now
What would be the intrinsic price for this stock, one year from now?

D∞

D0

D1

D2

One year from now- to determine the intrinsic value(p1)

Today

If today: P0 = D1

rs - g

If one year: P1 = D2

from now rs - g


What is the expected market price of the stock one year from now p1
What is the expected market price of the stock, one year from now(p1)?

  • Assume D0 = 2, g= 6%, rs = 13%

  • P1 is the present value (as of year 1) of D2, D3, D4, etc.

  • Could also find expected P1 as:

*

*D2= D1 (1+g)

= 2.12 (1+0.06)

= 2.247

*D1= D0 (1+g)

= 2.00 (1+0.06)

= 2.12


Corporate value model
Corporate value model from now(p1)?

  • Also called the free cash flow method. Suggests the value of the entire firm equals the present value of the firm’s free cash flows.

  • Remember, free cash flow is the firm’s after-tax operating income less the net capital investment

    • FCF = NOPAT – Net capital investment


FCF= NOPAT – Net capital invest from now(p1)?

FCF = [EBIT(1-T) + Depreciation exp]

- [ capital exp + working capital]


Applying the corporate value model
Applying the corporate value model from now(p1)?

  • Find the market value (MV) of the firm, by finding the PV of the firm’s future FCFs.

  • Subtract MV of firm’s debt and preferred stock to get MV of common stock.

  • Divide MV of common stock by the number of shares outstanding to get intrinsic stock price (value).


0 from now(p1)?

1

2

3

4

r = 10%

...

g = 6%

-5 10 20

21.20

-4.545

8.264

15.026

21.20

398.197

530 = = TV3

0.10

-

0.06

416.942

Given the long-run beyond yr 3 is gFCF = 6%, and WACC of 10%, use the corporate value model to find the firm’s intrinsic value.

* FCF Y1= -5

Y2= 10

Y3= 20


If the firm has $40 million in debt and has 10 million shares of stock, what is the firm’s intrinsic value per share?

  • MV of equity = MV of firm – MV of debt

    = $416.94 - $40

    = $376.94 million

  • Value per share = MV of equity / # of shares

    = $376.94 / 10

    = $37.69


How is market equilibrium established
How is market equilibrium established? shares of stock, what is the firm’s intrinsic value per share?

  • If price is below intrinsic value …

    • The current price (P0) is “too low.

  • If price is above intrinsic value…

  • The current price (P0) is “too high”


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