stocks & valuation

7/31/2019 Stocks & Valuation

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9-1

CHAPTER 9Stocks and Their Valuation

Features of common stock Determining common stock valuesPreferred stock


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Facts about common stock Represents ownershipOwnership implies controlStockholders elect directorsDirectors elect management

Managements goal: Maximize thestock price


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Intrinsic Value and Stock PriceOutside investors, corporate insiders, andanalysts use a variety of approaches toestimate a stocks intrinsic value (P

0).

In equilibrium we assume that a stocks priceequals its intrinsic value.

Outsiders estimate intrinsic value to helpdetermine which stocks are attractive tobuy and/or sell.Stocks with a price below (above) itsintrinsic value are undervalued (overvalued ).


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Determinants of Intrinsic Value

and Stock Prices (Figure 1-1)


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Different approaches for estimating the

intrinsic value of a common stock Dividend growth modelCorporate value modelUsing the multiples of comparablefirms


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Dividend growth model Value of a stock is the present value of thefuture dividends expected to be generated by

the stock.

)r(1

D ...

)r(1

D

)r(1

D

)r(1

D P

s3

s

32

s

21

s

10

^


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Constant growth stock A stock whose dividends are expected togrow forever at a constant rate, g.

D1 = D 0 (1+g) 1 D2 = D 0 (1+g) 2Dt = D 0 (1+g) t

If g is constant, the dividend growth formulaconverges to:

g-rD

g-r

g)(1D P

s

1

s

00

^


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Future dividends and their

present valuest

0t )g1(DD

tt

t )r1(DPVD

t0PVDP

$

0.25

Years (t)0


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What happens if g > r s?If g > r s, the constant growth formulaleads to a negative stock price, whichdoes not make sense.The constant growth model can only beused if:

rs > gg is expected to be constant forever


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If r RF = 7%, r M = 12%, and b = 1.2,what is the required rate of return on

the firms stock? Use the SML to calculate the requiredrate of return (r s):

rs = r RF + (r M rRF)b= 7% + (12% - 7%)1.2= 13%


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9-11

If D0 = $2 and g is a constant 6%,find the expected dividend stream for

the next 3 years, and their PVs.

1.8761

1.7599

D0 = 2.00

1.6509

rs = 13%

g = 6%0 1

2.247

2

2.382

3

2.12


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What is the stocks intrinsic value? Using the constant growth model:

$30.29 0.07

$2.12

0.06-0.13$2.12 g-r D P s0

1


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What is the expected market price

of the stock, one year from now?D1 will have been paid out already. So,P1 is the present value (as of year 1) of

D2, D 3, D 4, etc.

Could also find expected P 1 as:$32.10

0.06-0.13$2.247

g-r

D P

s

2^

1

$32.10(1.06)PP 0^

1


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What are the expected dividend yield,capital gains yield, and total return

during the first year?Dividend yield

= D 1 / P 0 = $2.12 / $30.29 = 7.0%

Capital gains yield= (P 1 P0) / P 0 = ($32.10 - $30.29) / $30.29 = 6.0%

Total return (r s)= Dividend Yield + Capital Gains Yield= 7.0% + 6.0% = 13.0%


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What would the expected price

today be, if g = 0?The dividend stream would be aperpetuity.

2.00 2.002.00

0 1 2 3rs = 13% ...

$15.380.13

$2.00 r

PMT P^

0


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Supernormal growth:What if g = 30% for 3 years before

achieving long-run growth of 6%?

Can no longer use just the constant growthmodel to find stock value.However, the growth does becomeconstant after 3 years.


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Valuing common stock withnonconstant growth

rs = 13%

g = 30% g = 30% g = 30% g = 6%

$

P0.06

$66.5434.658

0.13

2.301

2.647

3.045

46.114

54.107 = P 0^

0 1 2 3 4

D0 = 2.00 2.600 3.380 4.394

...

4.658


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Find expected dividend and capital gainsyields during the first and fourth years.

Dividend yield (first year)= $2.60 / $54.11 = 4.81%

Capital gains yield (first year)= 13.00% - 4.81% = 8.19%

During nonconstant growth, dividend yieldand capital gains yield are not constant,and capital gains yield g.

After t = 3, the stock has constant growthand dividend yield = 7%, while capitalgains yield = 6%.


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

rs = 13%

g = 0% g = 0% g = 0% g = 6%

0.06

$

$30.29P32.12

0.13

1.77

1.57

1.39

20.99

25.72 = P 0^

0 1 2 3 4

D0 = 2.00 2.00 2.00 2.00

...

2.12


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Find expected dividend and capital gainsyields during the first and fourth years.

Dividend yield (first year)= $2.00 / $25.72 = 7.78%

Capital gains yield (first year)= 13.00% - 7.78% = 5.22%

After t = 3, the stock has constantgrowth and dividend yield = 7%,while capital gains yield = 6%.


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If the stock was expected to havenegative growth (g = -6%), would anyonebuy the stock, and what is its value?

The firm still has earnings and paysdividends, even though they may be

declining, they still have value.

$9.890.19

$1.88

(-0.06)-0.13(0.94)$2.00

g-r)g1(D

g-r

D P

s

0

s

1^

0


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Find expected annual dividend andcapital gains yields.

Capital gains yield= g = -6.00%

Dividend yield= 13.00% - (-6.00%) = 19.00%

Since the stock is experiencing constantgrowth, dividend yield and capital gainsyield are constant. Dividend yield issufficiently large (19%) to offset a negativecapital gains.


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Summary: Dividend Growth Model

D0 = $2.00 Assumption about g? Price

1. g = 6% constant $30.29

2. g = 0% constant $15.383. g = -6% constant $9.89

4. g s = a. 30% supernormal, 3 yrsgn = b. 6% constant $54.115. g = a. 0% for 3 years

b. 6% constant $25.72


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Corporate value model

Also called the free cash flow method.Suggests the value of the entire firmequals the present value of the firmsfree cash flows.Remember, free cash flow is the firms

after-tax operating income less the netcapital investment

FCF = NOPAT Net capital investment


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Applying the corporate value model

Find the market value (MV) of the firm,by finding the PV of the firms futureFCFs.Subtract MV of firms debt and preferredstock to get MV of common stock.

Divide MV of common stock by thenumber of shares outstanding to getintrinsic stock price (value).


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Issues regarding thecorporate value model

Often preferred to the dividend growthmodel, especially when considering number

of firms that dont pay dividends or whendividends are hard to forecast.Similar to dividend growth model, assumes atsome point free cash flow will grow at aconstant rate.Terminal value (TV N) represents value of firmat the point that growth becomes constant.


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Given the long-run g FCF = 6%, andWACC of 10%, use the corporate value

model to find the firms intrinsic value.

g = 6%

r = 10%

21.20

0 1 2 3 4

-5 10 20

...

416.942

-4.5458.264

15.026398.197

21.20530 = = TV 3 0.10 0.06-


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If the firm has $40 million in debt andhas 10 million shares of stock, what is

the firms 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


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Firm multiples method

Analysts often use the following multiplesto value stocks.

P / EP / CFP / Sales

EXAMPLE: Based on comparable firms,estimate the appropriate P/E. Multiply thisby expected earnings to back out anestimate of the stock price.


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What is market equilibrium?

In equilibrium, stock prices are stable andthere is no general tendency for people to

buy versus to sell.In equilibrium, two conditions hold:

The current market stock price equals itsintrinsic value (P 0 = P 0).Expected returns must equal required returns.

)br(rrr gPD

r RFMRFs0

1^

s -

^


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Market equilibrium

Expected returns are determined byestimating dividends and expectedcapital gains.Required returns are determined byestimating risk and applying the CAPM.


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How is market equilibriumestablished?

If price is below intrinsic value The current price (P 0) is too low andoffers a bargain.Buy orders will be greater than sellorders.P0 will be bid up until expected returnequals required return.


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How are the equilibriumvalues determined?

Are the equilibrium intrinsic value andexpected return estimated by

managers or are they determined bysomething else?Equilibrium levels are based on themarkets estimate of intrinsic value andthe markets required rate of return, whichare both dependent upon the attitudes of the marginal investor.


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Preferred stock

Hybrid security.Like bonds, preferred stockholdersreceive a fixed dividend that must bepaid before dividends are paid tocommon stockholders.

However, companies can omitpreferred dividend payments withoutfear of pushing the firm intobankruptcy.


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If preferred stock with an annualdividend of $5 sells for $50, what is the

preferred stocks expected return? Vp = D / r p $50 = $5 / r

p

rp = $5 / $50

= 0.10 = 10%

^

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