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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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Valuation of Preferred Stock
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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Valuation of Preferred Stock
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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Valuation of Preferred Stock
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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a. The Dividend Discount Model (DDM)
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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a. The Dividend Discount Model (DDM)
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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a. The Dividend Discount Model (DDM)
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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a. Earnings Multiplier Model (PER model)
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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a. Earnings Multiplier Model (PER model)
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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a. Earnings Multiplier Model (PER model)
As an example, assume:
Dividend payout = 50%
Required return = 12%
Expected growth = 8%
P/E = ?
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a. Earnings Multiplier Model (PER model)
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. Earnings Multiplier Model (PER model)
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. Earnings Multiplier Model (PER model)
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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a. Earnings Multiplier Model (PER model)
A small change in either or both korgwillhave a large impact on the multiplier
D/E = .50; k=.13; g=.08
P/E = .50/(.13-/.08) = .50/.05 = 10
gkED
EPi
= 11
1
/
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a. Earnings Multiplier Model (PER model)
A small change in either or both korgwillhave a large impact on the multiplier
D/E = .50; k=.13; g=.08 P/E = 10
gk
ED
E
Pi
= 11
1
/
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a. Earnings Multiplier Model (PER model)
A small change in either or both korgwillhave a large impact on the multiplier
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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a. Earnings Multiplier Model (PER model)
A small change in either or both korgwillhave a large impact on the multiplier
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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a. Earnings Multiplier Model (PER model)
A small change in either or both korgwillhave a large impact on the multiplier
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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a. Earnings Multiplier Model (PER model)
A small change in either or both korgwillhave a large impact on the multiplier
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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a. Earnings Multiplier Model (PER model)
A small change in either or both korgwillhave a large impact on the multiplier
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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a. Earnings Multiplier Model (PER model)
A small change in either or both korgwillhave a large impact on the multiplier
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?
Stock Dividends and Stock
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Stock Dividends and StockSplits
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?
Stock Dividends and Stock
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Stock Dividends and StockSplits
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.
Stock Dividends and Stock
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Stock Dividends and StockSplits
Effects on Shareholder Wealth:
Stock Dividends and Stock
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Stock Dividends and StockSplits
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.
Stock Dividends and Stock
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Stock Dividends and StockSplits
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.
Stock Dividends and Stock
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Stock Dividends and StockSplits
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( )
Before the 50% stock dividend:
8/2/2019 073_C5 Equity Valuation
77/77
Before the 50% stock dividend:
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)