Valuation of Financial Assets

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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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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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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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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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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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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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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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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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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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

Valuation of Financial Assets

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