073_c5 equity valuation

8/2/2019 073_C5 Equity Valuation

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Equity Valuation

Course 5


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Valuation of Preferred Stock

Owner of preferred stock receives a promise to pay astated dividend, usually quarterly, forperpetuity

Dividends are typically fixed at the time of issue andmust be paid before common stockholders receive any

payment. Since payments are only made after the firm meets its

bond interest payments, there is more uncertainty ofreturns

Creditors have prior claim on earnings; interest ondebt must be paid before preferred stockholders canreceive anything.

Tax treatment of dividends paid to corporations (80%tax-exempt) offsets the risk premium.


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pk

Dividend=V

The value is simply the stated annual dividend divided bythe required rate of return on preferred stock (kp)


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pk

Dividend=V

The value is simply the stated annual dividend divided bythe required rate of return on preferred stock (kp)

Assume a preferred stock has a $100 par value and a dividend of$8 a year and a required rate of return of 9 percent

.09

$8=V 89.88$=


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Given a market price, you can derive its promised yield

At a market price of $85, this preferred stock yield would be

Price

Dividend

kp =

0941.$85.00$8kp ==


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Valuation of Preferred Stock - An Example

Suppose an investor is considering the purchase of a

preferred stock issue that is expected to pay $3.00 a

share in perpetuity. If the investor assigns a required rate

of return of 7.5 percent to the issue, whats the maximum

amount he/she should be willing to pay?


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Valuation of Preferred Stock -Solution

shareP /40$075.000.3$ ==


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Approaches to theValuation of Common Stock

Two approaches:

1. Discounted cash-flow valuation Present value of some measure of cash flow,

including dividends, operating cash flow, and freecash flow

2. Relative valuation technique

Value estimated based on its price relative tosignificant variables, such as earnings, cash flow,book value, or sales


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Valuation Approachesand Specific Techniques

Approaches to Equity Valuation

Discounted Cash FlowTechniques

Relative ValuationTechniques

Present Value of Dividends (DDM)

Present Value of Operating Cash Flow

Present Value of Free Cash Flow

Price/Earnings Ratio (PER)

Price/Cash flow ratio (P/CF)

Price/Book Value Ratio (P/BV)

Price/Sales Ratio (P/S)


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Which discount rate to use in the DiscountedCash Flow Valuation Approach

The measure of cash flow used: Dividends

Cost of equityas the discount rate

Operating cash flow (cash flow available to all capitalsuppliers (debt holders + shareholders)

Weighted Average Cost of Capital (WACC) as the

discount rate

Free cash flow to equity (cash flow available only to equityowners)

Cost of equityas the discount rate


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1. Discounted Cash-Flow ValuationTechniques

== +

=nt

tt

tj

k

CFV

1 )1(

Where:

Vj = value of stock j

n = life of the asset

CFt = cash flow in period t

k= the discount rate


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a. The Dividend Discount Model (DDM)

The value of a share of common stock is the presentvalue of all future dividends

=

+=

++++++++=

n

tt

t

j

k

D

k

D

k

D

k

D

k

DV

1

33

221

)1(

)1(...

)1()1()1(

Where:Vj = value of common stock j

Dt = dividend during time period t

k= required rate of return on stock j


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If the stock is not held for an infinite period, a sale at the endof year 2 would imply:

Selling price at the end of year two is the value of all

remaining dividend payments, which is simply anextension of the original equation

2

2

2

21

)1()1()1( k

SP

k

D

k

DV

j

j ++

++

+=


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Stocks with no dividends are expected to start paying

dividends at some point, say year three...

Where:

D1 = 0

D2 = 0

+++

++

++

+=

)1(...

)1()1()1( 33

2

21

k

D

k

D

k

D

k

DVj


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a. The Gordon growth model

The Gordon growth model assumes a constant growthrate for future dividends:

Where:

Vj = value of stock j

D0 = dividend payment in the current period

g = the constant growth rate of dividends

k= required rate of return on stock j

n = the number of periods, which we assume to be infinite

n

n

j

k

gD

k

gD

k

gDV

)1(

)1(...

)1(

)1(

)1(

)1( 02

2

00

+

+++

+

++

+

+=


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The Gordon growth model can be reduced to:

(Where D1 is the future period dividend)

To find the value V we must:

1. Estimate the required rate of return (k)

2. Estimate the dividend growth rate (g)

gk

DVj

= 1


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Example:

Stock ABC has a current dividend of 1$ per share. Youbelieve that, over the long run, this companys earningsand dividends will grow at 7 percent. If your required rateof return is 11 percent, how much would you be willing topay for the stock today?


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Solution

D1 = D0 (1 + g)

= 1$ x 1.07

= 1.07$

V = 1.07/ (0.11 0.07)

= 1.07 / 0.04

= 26.75$


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Assumptions of The Gordon growth model

Assumptions:

1. Dividends grow at a constant rate (g)

2. The constant growth rate will continue for an infinite period3. The required rate of return (k) is greater than the infinite

growth rate (g)


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Valuation with Temporary SupernormalGrowth Multistage DDM

Example:The Bourke company has a current dividend (D0) of 2 $ pershare and a 14 percent required rate of return for the stock (thecompanys cost of equity). The following are the expectedannual growth rates for dividends:

Year Dividend Growth Rate 1-3: 25% 4-6: 20%

7-9: 15% 10 on: 9%

What is the current value of the Bourke stock?


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Answer:

$355.94)14.1(

)09.14(.

)09.1()15.1()20.1()25.1(00.2

14.1

)15.1()20.1()25.1(00.2

14.1

)15.1()20.1()25.1(00.2

14.1

)15.1()20.1()25.1(00.2

14.1

)20.1()25.1(00.2

14.1

)20.1()25.1(00.2

14.1

)20.1()25.1(00.2

14.1

)25.1(00.2

14.1

)25.1(00.2

14.1

)25.1(00.2

9

333

9

333

8

233

7

33

6

33

5

23

4

3

3

3

2

2

=

+

++

++

++

++=iV


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The H Model

periodgrowthhightheofyearsinlifehalfH

rategrowthdividendtermlongnormalg

rategrowthdividendtermshortinitialg

where

grggHDgD

grggHD

grgDV

L

S

L

LSL

L

LS

L

L

++=

+

+=

:

,)()1()()1( 00000

H-models assume the growth rate starts out high, and then declineslinearly over the high-growth stage until it reaches the long-run averagegrowth rate.


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The H Model

Example: Bill's Hardware currently pays adividend of $1.00. The growth rate is 30%and is expected to decline over the next

10 years to a stable rate of 8% thereafter.The required return is 12%. Calculate thecurrent value of Bill's Hardware.

Answer:


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Answer:

Calculate a required return using


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Calculate a required return usingthe Gordon growth model and the

H-model

LLSL gggHgP

D

r +++

= )]()1[(00

gP

Dr +=

0

1

Example using the H-model:

Wettster, Inc. pays a current dividend of $1.33, which has

been growing at a rate of 12%. This growth rate is expectedto decline to 8% over the next five years and then remain at8% indefinitely. Calculate the implied required return forWettster's based on the current price of $26.00.


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Answer


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Define, calculate, and interpret the sustainablegrowth rate (g) of a company and explain the

calculations underlying assumptions The sustainable growth rate (SGR) is the rate at which earnings

(and dividends) can continue to grow indefinitely, assuming that thefirms debt-to-equity ratio is unchanged and it doesnt issue newequity.

SGR is a simple function of the earnings retention ratio and thereturn on equity:

g = b ROE

Example:Graham Inc., is growing earnings at an annual rate of 8%. Itcurrently pays out dividends equal to 25% of earnings. Graham'sROE is 21%. Calculate its SGR (g).


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Answer

Answer:g = (1 0.25) (21%) = 15.75%


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Demonstrate the use of the DuPont analysis of return onequity in conjunction with the sustainable growth rate

expression.

This has also been called the PRAT model, where P = profitmargin, R = retention rate, A = asset turnover, and T =financial leverage.

Example:Halo Construction has been successful in a mature industry.Over the last three years, Halo has averaged a profit margin of10%, a total asset turnover of 1.8, and a leverage ratio of1.25. Assuming Halo continues to distribute 40% of its

earnings as dividends, calculate its long-term SGR.

EquitysTotalAsset

sTotalAssetSales

SalesNetIncome

NetIncomeDividendsNetIncomeg

Equity

sTotalAsset

sTotalAsset

Sales

Sales

NetIncomeROE

Equity

NetIncomeROE

=

=

=


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Answer

g = 0.10 (1 0.4) 1.8 1.25 = 0.135 =13.5%


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b. Present Value of Operating Free CashFlows

=

=

+=

nt

t

t

j

tj

WACC

OCFV

1)1(

Where:

Vj= value of firm j

n = number of periods assumed to be infinite

OCFt= the firms operating free cash flow in period t

WACC = firm js weighted average cost of capital


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b. Present Value of Operating Free CashFlows

Similar to DDM, this model can be used to estimate aninfinite period:

OCFj

jgWACC

OCFV

= 1

Where:

OCF1=operating free cash flow in period 1

gOCF = long-term constant growth of operating free cash flow


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b. Present Value of Operating Free Cash Flows

Assuming several different rates of growth for OCF,these estimates can be divided into stages as with thesupernormal dividend growth model

Estimate the rate of growth and the duration of growth

for each period


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Weighted Average Cost Of Capital -WACC

The WACC equation is the cost of each capital component multipliedby its proportional weight and then summing:

Where:

Re = cost of equityRd = cost of debtE = market value of the firm's equityD = market value of the firm's debtV = E + DE/V = percentage of financing that is equityD/V = percentage of financing that is debtTc = corporate tax rate


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WACC exercise

Suppose that B2B, Inc. has a capital structureof 34 percent equity, 14 percent preferredstock, and 52 percent debt.

The before-tax cost of equity is 15.3 percent,

the before-tax cost of preferred stock is 10.5percent and the before-tax cost of debt is 8.6percent.

What is B2B's WACC if the firm faces anaverage tax rate of 30%?


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WACC exercise answer:

WACC = Wd * Kd(1-t) + Wp * Kp + We * Ke= 0.52 * 8.6%(1 - 0.30) + 0.14 * 10.5% + 0.34 *

15.3%= 3.130% + 1.47% + 5.202%

= 9.802%


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c. Present Value of Free Cash Flows toEquity

Free cash flows to equity are derived after operatingcash flows have been adjusted for debt payments (interestand principal)

The discount rate used is the firms cost of equity(k)

rather than WACC


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c. Present Value of Free Cash Flows toEquity

Where:

Vj = Value of the stock of firmj

n = number of periods assumed to be infinite

FCFEt = the firms free cash flow in period t

Kj=the cost of equity

= +

=n

tt

j

tj

k

FCFEV

1 )1(


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2. Relative Valuation Techniques

Value can be determined by comparing to similar stocksbased on relative ratios

Relevant variables include earnings, cash flow, bookvalue, and sales

The most popular relative valuation technique is based onprice to earnings


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a. Earnings Multiplier Model (PER model)

This values the stock based on expected annual earnings

The price earnings (P/E) ratio, or Earnings Multiplierequals:

PER = P0/EPS1(leading PER)


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The infinite-period dividend discount model indicates thevariables that should determine the value of the P/E ratio

Dividing both sides by expected earnings during the next 12months (EPS1)

gk

DP =

10

gk

b

gk

EPSD

EPS

P

=

=

1/11

1

0


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Thus, the P/E ratio is determined by

1. Expected dividend payout ratio

2. Required rate of return on the stock (k)

3. Expected growth rate of dividends (g)

gk

b

gk

EPSD

EPS

P

==

1/ 11

1

0


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As an example, assume:

Dividend payout = 50%

Required return = 12%

Expected growth = 8%

P/E = ?


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12.5.50/.04

.08-.12

.50P/E

=

=

=


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Example 2

Retention rate = 70%

Required return = 12%

Expected growth = 8%

P/E = ?


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Answer

7.5

.30/.04

.08-.12.30P/E

==

=


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A small change in either or both korgwillhave a large impact on the multiplier

gk

ED

E

Pi

= 11

1

/


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A small change in either or both korgwillhave a large impact on the PER

D/E = .50; k=.13; g=.08

gk

ED

E

Pi

= 11

1

/


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D/E = .50; k=.13; g=.08

P/E = .50/(.13-/.08) = .50/.05 = 10

gkED

EPi

= 11

1

/


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D/E = .50; k=.13; g=.08 P/E = 10

gk

ED

E

Pi

= 11

1

/


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D/E = .50; k=.13; g=.08 P/E = 10

D/E = .50; k=.12; g=.09

gk

ED

E

Pi

= 11

1

/


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D/E = .50; k=.13; g=.08 P/E = 10

D/E = .50; k=.12; g=.09

P/E = .50/(.12-/.09) = .50/.03 = 16.7

gk

ED

E

Pi

= 11

1

/


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D/E = .50; k=.13; g=.08 P/E = 10

D/E = .50; k=.12; g=.09 P/E = 16.7

gkED

EPi

= 11

1

/


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D/E = .50; k=.13; g=.08 P/E = 10

D/E = .50; k=.12; g=.09 P/E = 16.7

D/E = .50; k=.11; g=.09

gk

ED

E

Pi

= 11

1

/


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D/E = .50; k=.13; g=.08 P/E = 10

D/E = .50; k=.12; g=.09 P/E = 16.7

D/E = .50; k=.11; g=.09

P/E = .50/(.11-/.09) = .50/.02 = 25

gk

ED

E

Pi

= 11

1

/


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D/E = .50; k=.13; g=.08 P/E = 10

D/E = .50; k=.12; g=.09 P/E = 16.7

D/E = .50; k=.11; g=.09 P/E = 25

gk

ED

E

Pi

= 11

1

/


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Example: Earnings Multiplier Model

Given current earnings (EPS0) of $2.00, 50% dividendpayout ratio, 12% required return and a growth rate of9%, what is the estimated current value of the stock?


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Solution:

EPS1 = EPS0 (1 + g) = 2 x 1.09 = $2.18

P/E = 0.5/0.03 =16.7$

Then we have:P/2.18 = 16.7

P = 2.18 x 16.7 = 36.41$

Compare this estimated value to market price to decide ifyou should invest in it.


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b. The Price-Cash Flow Ratio

Companies can manipulate earnings

Cash-flow is less prone to manipulation

Cash-flow is important for fundamental valuation and incredit analysis

1

/+

=t

ti

CF

PCFP

Where:

P/CFj = the price/cash flow ratio for firm j

Pt = the price of the stock in period t

CFt+1

= expected cash low per share for firm j


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c. The Price-Book Value Ratio

Where:

P/BVj = the price/book value for firmj

Pt = the end of year stock price for firmj

BVt+1 = the estimated end of year book value per share for

firmj

1

/+

=t

tj

BV

PBVP


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d. The Price-Sales Ratio

Where:

1+=

t

t

SP

SP

tjSjP

jS

P

t

t

j

j

Yearduringfirmforsharepersalesannualfirmforpricestockyearofend

firmforratiosalestoprice

1 ==

=

+


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Taxes and International

Investments

C l l h i f diff i l


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Calculate the impact of different national taxes onthe return of an international investment

Example:

Suppose a U.S. investor buys 100 shares of SAP Systems (SAP)listed in Germany on the XETRA, quoted at EUR 14.5 per share(including commissions) for a total trade cost of EUR1,450. Theexchange rate is one EUR = USD 0.90. The U.S. currency cost isUSD 1,305 for the entire trade, including commissions charged bythe U.S. broker.

Three months later a one-euro dividend is paid for each shareowned. Dividends are subject to a 15% withholding tax in Germany,and 28% tax on short-term capital gains and dividends in the U.S. Atthis point, the investor decides to sell the 100 shares of SAP nowworth EUR 16. The current exchange rate is now one EUR = USD0.95. Calculate the impact of taxes on the total return.


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Answer


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Stock Dividends and Stock Splits

Stock Dividends and Stock


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Stock Dividends and StockSplits

Stock dividend: payment of additionalshares of stock to commonstockholders.

Example: Citizens Bancorporation ofMaryland announces a 5% stockdividend to all shareholders of record.

For each 100 shares held, shareholdersreceive another 5 shares.

Does the shareholders wealth

increase?



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Stock Split: the firm increases thenumber of shares outstanding andreduces the price of each share.

Example: Joule, Inc. announces a 3-for-2stock split. For each 100 shares held,shareholders receive another 50 shares.

Does this increase shareholder wealth? Are a stock dividend and a stock split the

same?



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Stock Splits and Stock Dividends areeconomically the same: the number ofshares outstanding increases and the

price of each share drops. The value ofthe firm does not change.

Example: A 3-for-2 stock split is the

same as a 50% stock dividend. Foreach 100 shares held, shareholdersreceive another 50 shares.



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Effects on Shareholder Wealth:



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Effects on Shareholder Wealth: thesewill cut the company pie into morepieces but will not create wealth. A

100% stock dividend (or a 2-for-1stock split) gives shareholders 2 half-sized pieces for each full-sized piece

they previously owned.



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Effects on Shareholder Wealth: thesewill cut the company pie into morepieces but will not create wealth. A

100% stock dividend (or a 2-for-1 stocksplit) gives shareholders 2 half-sizedpieces for each full-sized piece theypreviously owned.

For example, this would double thenumber of shares, but would cause a$60 stock price to fall to $30.



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Why bother? Proponents argue that these are used to

reduce high stock prices to a more

popular trading range (generally $15 to$70 per share).

Opponents argue that most stocks are

purchased by institutional investors whohave millions of dollars to invest and areindifferent to price levels. Plus, stocksplits and stock dividends are

expensive!

Stock Dividend Example


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Stock Dividend Example

shares outstanding: 1,000,000

net income = $6,000,000;

P/E = 10 25% stock dividend.

An investor has 120 shares. Doesthe value of the investors shareschange?


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Before the 25% stock dividend:

EPS = 6,000,000/1,000,000 = $6

P/E = P/6 = 10, so P = $60 per share. Value = $60 x 120 shares = $7,200

After the 25% stock dividend: # shares = 1,000,000 x 1.25 = 1,250,000.

EPS = 6,000,000/1,250,000 = $4.80

P/E = P/4.80 = 10, so P = $48 per share. Investor now has 120 x 1.25 = 150 shares.

Value = $48 x 150 = $7,200

St k Di id d


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Stock DividendsIn-class Problem

shares outstanding: 250,000

net income = $750,000;stock price = $84

50% stock dividend.

What is the new stock price?


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Hint:

stock price

P/E = net income

# shares( )



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EPS = 750,000 / 250,000 = $3

P/E = 84 / 3 = 28.

Afterthe 50% stock dividend: # shares = 250,000 x 1.50 = 375,000.

EPS = 750,000 / 375,000 = $2 P/E = P / 2 = 28, so P = $56 per share.

(a 50% stock dividend is equivalent to a3-for-2 stock split)

073_c5 equity valuation

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