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8/11/2019 Valuation of Financial Assets
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Theory of Valuation
The value of an asset is the present valueof its expected cash flows
You expect an asset to provide a streamof cash flows while you own it
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Theory of Valuation
To convert this stream of returns to avalue for the security, you must discountthis stream at your required rate of return
This requires estimates of:
The stream of expected cash flows, and
The required rate of return on the investment
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Stream of Expected Cash Flows
Form of cash flows
Earnings
Cash flows
Dividends
Interest payments
Capital gains (increases in value)
Time pattern and growth rate of cash flows
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Uncertainty of Returns
Internal characteristics of assets
Business risk (BR)
Financial risk (FR) Liquidity risk (LR)
Exchange rate risk (ERR)
Country risk (CR)
Market determined factors
Systematic risk (beta) or
Multiple APT factors
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Investment Decision Process: AComparison of Estimated Values and
Market PricesIf Estimated Value > Market Price, Buy
If Estimated Value < Market Price, Dont Buy
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Valuation of Alternative Investments
Valuation of Bonds is relatively easybecause the size and time pattern of cashflows from the bond over its life are known
1. Interest payments usually every six monthsequal to one-half the coupon rate times theface value of the bond
2. Payment of principal on the bonds maturitydate
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Valuation of Bonds
Example: in 2000, a $10,000 bond due in2015 with 10% coupon
Discount these payments at the investors
required rate of return (if the risk-free rateis 9% and the investor requires a riskpremium of 1%, then the required rate of
return would be 10%)
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Valuation of Bonds
Present value of the interest payments is anannuity for thirty periods at one-half therequired rate of return:
$500 x 15.3725 = $7,686
The present value of the principal is similarlydiscounted:
$10,000 x .2314 = $2,314
Total value of bond at 10 percent = $10,000
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Valuation of Bonds
The $10,000 valuation is the amount that aninvestor should be willing to pay for thisbond, assuming that the required rate of
return on a bond of this risk class is 10percent
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Valuation of Bonds
If the market price of the bond is above thisvalue, the investor should not buy itbecause the promised yield to maturity will
be less than the investors required rate ofreturn
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Valuation of Bonds
Alternatively, assuming an investor requiresa 12 percent return on this bond, its valuewould be: $500 x 13.7648 = $6,882
$10,000 x .1741 = 1,741
Total value of bond at 12 percent = $8,623
Higher rates of return lower the value !
Compare the computed value to the marketprice of the bond to determine whetheryou should buy it.
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Valuation of Preferred Stock
Owner of preferred stock receives apromise to pay a stated dividend, usuallyquarterly, for perpetuity
Since payments are only made after thefirm meets its bond interest payments,there is more uncertainty of returns
Tax treatment of dividends paid tocorporations (80% tax-exempt) offsets therisk premium
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Valuation of Preferred Stock
pk
DividendV
The value is simply the stated annualdividend divided by the required rate ofreturn on preferred stock (kp)
Assume a preferred stock has a $100 par valueand a dividend of $8 a year and a required rate ofreturn of 9 percent
.09
$8V 89.88$
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Approaches to theValuation of Common Stock
Two approaches have developed
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 to
significant variables, such as earnings, cash flow,book value, or sales
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Approaches to theValuation of Common Stock
These two approaches have some factors incommon
Investors required rate of return
Estimated growth rate of the variable used
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Discounted Cash-FlowValuation Techniques
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 that is equal to the investorsrequired rate of return for asset j, which is determinedby the uncertainty (risk) of the stocks cash flows
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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 (PE)
Price/Cash flow ratio (P/CF)
Price/Book Value Ratio (P/BV)
Price/Sales Ratio (P/S)
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The Dividend Discount Model(DDM)
The value of a share of common stock is thepresent value of all future dividends
n
t
t
t
j
k
D
kD
kD
kD
kDV
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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The Dividend Discount Model(DDM)
If the stock is not held for an infinite period,a sale at the end of year 2 would imply:
Selling price at the end of year two is the
value of all remaining dividend payments,which is simply an extension of the originalequation
2
2
221
)1()1()1( k
SP
k
D
k
DV
j
j
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The Dividend Discount Model(DDM)
Stocks with no dividends are expected tostart paying dividends at some point, sayyear 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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The Dividend Discount Model(DDM)
Infinite period model assumes a constantgrowth rate for estimating futuredividends
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
jkgD
kgD
kgDV
)1()1(...
)1()1(
)1()1( 0
2
2
00
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The Dividend Discount Model(DDM)
Infinite period model assumes a constantgrowth rate for estimating futuredividends
This can be reduced to:
1. Estimate the required rate of return (k)
2. Estimate the dividend growth rate (g)
n
n
jkgD
kgD
kgDV
)1()1(...
)1()1(
)1()1( 0
2
2
00
gk
DVj
1
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Infinite Period DDMand Growth Companies
Assumptions of DDM:
1. Dividends grow at a constant rate
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
The infinite period DDM assumes constant growth for an infinite period,
but abnormally high growth usually cannot be maintained indefinitelyCombine the models to evaluate the years of supernormal growth and
then use DDM to compute the remaining years at a sustainable rate
For example:With a 14 percent required rate of return and dividend growth of:
Dividend
Year Growth Rate
1-3: 25%4-6: 20%
7-9: 15%
10 on: 9%
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Valuation with Temporary SupernormalGrowth
The value equation becomes
9
333
9
333
8
233
7
33
6
33
5
23
4
3
3
3
2
2
)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
iV
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Computation of Value for Stock of Company withTemporary Supernormal Growth
Discount Present Growth
Year Dividend Factor Value Rate
1 2.50$ 0.8772 2.193$ 25%
2 3.13 0.7695 2.408$ 25%
3 3.91 0.6750 2.639$ 25%
4 4.69 0.5921 2.777$ 20%
5 5.63 0.5194 2.924$ 20%
6 6.76 0.4556 3.080$ 20%
7 7.77 0.3996 3.105$ 15%
8 8.94 0.3506 3.134$ 15%
9 10.28 0.3075 3.161$ 15%
10 11.21 9%
224.20$a
0.3075b
68.943$94.365$
aValue of dividend stream for year 10 and all future dividends, that is
$11.21/(0.14 - 0.09) = $224.20bThe discount factor is the ninth-year factor because the valuation of the
remaining stream is made at the end of Year 9 to reflect the dividend in
Year 10 and all future dividends.
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Present Value ofFree Cash Flows to Equity
Free cash flows to equity are derived after operating
cash flows have been adjusted for debt payments(interest and principle)
The discount rate used is the firms cost of equity (k)
rather than WACC
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Present Value ofFree Cash Flows to Equity
Where:
Vsj= Value of the stock of firm j
n= number of periods assumed to beinfinite
FCFt= the firms free cash flow in period t
nt
t
t
j
tsj
k
FCFV
1 )1(
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Relative Valuation Techniques
Value can be determined by comparing tosimilar stocks based on relative ratios
Relevant variables include earnings, cashflow, book value, and sales
The most popular relative valuationtechnique is based on price to earnings
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Earnings Multiplier Model
This values the stock based on expectedannual earnings
The price earnings (P/E) ratio, or
Earnings Multiplier
EarningsMonth-TwelveExpected
PriceMarketCurrent
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Earnings Multiplier Model
The infinite-period dividend discountmodel indicates the variables thatshould determine the value of the P/E
ratio
Dividing both sides by expected earnings
during the next 12 months (E1)
gkDPi
1
gk
ED
E
Pi
11
1
/
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Earnings Multiplier 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)
gkED
EPi
11
1
/
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Earnings Multiplier Model
As an example, assume: Dividend payout = 50%
Required return = 12%
Expected growth = 8%
D/E = .50; k= .12; g=.08
12.5
.50/.04
.08-.12
.50P/E
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Earnings Multiplier Model
A small change in either or both kor gwillhave 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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Earnings Multiplier Model
Given current earnings of $2.00 and growthof 9%
You would expect E1to be $2.18
D/E = .50; k=.12; g=.09 P/E = 16.7
V= 16.7 x $2.18 = $36.41
Compare this estimated value to marketprice to decide if you should invest in it
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Estimating the Inputs: The Required Rate of Returnand the Expected Growth Rate of Dividends
Valuation procedure is the same forsecurities around the world, but the
required rate of return (k) and expectedgrowth rate of dividends (g) differ amongcountries
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Required Rate of Return (k)
The investors required rate of return must
be estimated regardless of theapproach selected or technique applied
This will be used as the discount rate andalso affects relative-valuation
This is not used for present value of free
cash flow which uses the required rate ofreturn on equity (K)
It is also not used in present value ofoperating cash flow which uses WACC
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Required Rate of Return (k)
Three factors influence an investors
required rate of return:
The economys real risk-free rate (RRFR)
The expected rate of inflation (I)
A risk premium (RP)
Th E R l Ri k F
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The Economys Real Risk-FreeRate
Minimum rate an investor should require
Depends on the real growth rate of theeconomy
(Capital invested should grow as fast as theeconomy)
Rate is affected for short periods by
tightness or ease of credit markets
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The Expected Rate of Inflation
Investors are interested in real rates ofreturn that will allow them to increase theirrate of consumption
The investors required nominal risk-freerate of return (NRFR) should be increasedto reflect any expected inflation:
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The Risk Premium
Causes differences in required rates ofreturn on alternative investments
Explains the difference in expected returnsamong securities
Changes over time, both in yield spreadand ratios of yields
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Time-Series Plot of Corporate Bond YieldSpreads (Baa-Aaa): Monthly 1973 - 1997
-
0.50
1.00
1.50
2.00
2.50
3.00
1966 1970 1974 1978 1982 1986 1990 1994 1998
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Time-Series Plot of the Ratio Corporate BondYield Spreads (Baa/Aaa): Monthly 1966 - 1997
1.000
1.050
1.100
1.150
1.200
1.250
1.300
1966
1968
1970
1972
1974
1976
1978
1980
1982
1984
1986
1988
1990
1992
1994
1996
1998
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Risk Components
Business risk
Financial risk
Liquidity risk Exchange rate risk
Country risk
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Expected Growth Rate of Dividends
Determined by
the growth of earnings
the proportion of earnings paid in dividends
In the short run, dividends can grow at adifferent rate than earnings due to changes inthe payout ratio
Earnings growth is also affected bycompounding of earnings retention
g = (Retention Rate)x(Return on Equity)
= RRxROE
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Breakdown of ROE
EquityCommon
AssetsTotal
AssetsTotal
Sales
Sales
IncomeNet
ROE
Profit Total Asset Financial
Margin Turnover Leverage= xx