Principles of valuation

PRINCIPLES OF VALUATION

ARINDOM MUKHERJEE

VALUE ITS DEFINITION

• A SINGLE ITEM OF OWNERSHIP HAVING EXCHANGE VALUE

• IN GENERAL, THE VALUE OF AN ASSET IS THE PRICE THAT A WILLING AND ABLE BUYER PAYS TO A WILLING AND ABLE SELLER

• NOTE THAT IF EITHER THE BUYER OR SELLER IS NOT BOTH WILLING AND ABLE, THEN AN OFFER DOES NOT ESTABLISH THE VALUE OF THE ASSET

KINDS OF “VALUE”

• THERE ARE SEVERAL TYPES OF VALUE, OF WHICH WE ARE CONCERNED WITH FOUR:– BOOK VALUE : (ECONOMICS, ACCOUNTING & FINANCE / STOCK

EXCHANGE) THE VALUE OF A SHARE IN A COMPANY CALCULATED BY DIVIDING THE DIFFERENCE BETWEEN THE TOTAL OF ITS ASSETS AND ITS LIABILITIES BY THE NUMBER OF ORDINARY SHARES ISSUED (TOTAL ASSETS LESS TOTAL LIABILITIES)

– TANGIBLE BOOK VALUE : BOOK VALUE MINUS INTANGIBLE ASSETS (GOODWILL, PATENTS, ETC)

– MARKET VALUE : THE PRICE OF AN ASSET AS DETERMINED IN A COMPETITIVE MARKETPLACE

– INTRINSIC VALUE : THE PRESENT VALUE OF THE EXPECTED FUTURE CASH FLOWS DISCOUNTED AT THE DECISION MAKER’S REQUIRED RATE OF RETURN

FACTORS DETERMINING INTRINSIC VALUE OF AN ASSET

• THERE ARE TWO PRIMARY DETERMINANTS OF THE INTRINSIC VALUE OF AN ASSET TO AN ENTITY:– THE SIZE AND TIMING OF THE EXPECTED FUTURE

CASH FLOWS.– THE ENTITY’S REQUIRED RATE OF RETURN

(DETERMINED BY FACTORS SUCH AS RISK/RETURN PREFERENCES, RETURNS ON COMPETING INVESTMENTS,, ETC.).

• NOTE THAT THE INTRINSIC VALUE OF AN ASSET CAN BE, AND OFTEN IS, DIFFERENT FOR EACH ENTITY (THAT’S WHAT MAKES MARKETS WORK).

MYTHS OF VALUATION

VALUATION IS OBJECTIVE A WELL RESEARCHED VALUATION IS TIMELESS A GOOD VALUATION ESTIMATES ACCURATELY. MORE QUANTITATIVE A MODEL BETTER

VALUATION THE MARKET IS GENERALLY WRONG VALUE IS WHAT MATTERS NOT THE PROCESS

OF VALUATION

FIRM VALUATION IN MERGERS AND ACQUISITIONS

BALANCE SHEET VALUATION MODELS : BOOK VALUE, LIQUIDATION VALUE, REPLACEMENT COSTPRICE EARNING RATIO MODELECONOMIC PROFIT MODELGORDON GROWTH MODELDIVIDEND DISCOUNT MODELS SPREADSHEET ANALYSIS : DISCOUNTED CASH

FLOW MODELS FOR EQUITY & FIRM VALUATIONCOMPARATIVE COMPANIES MODEL OPTION PRICING MODEL

SEARCH FOR VALUE DRIVERS

• EARN A HIGHER RETURN ON EXISTING INVESTED CAPITAL

1. INCREASE CUSTOMER DELIGHT THROUGH: PRODUCT INNOVATIONS , DISTRIBUTION/DELIVERY CUSTOMER SERVICES2. INCREASE CONTRIBUTION FROM EXISTING

PRODUCT OFFERINGS

SEARCH FOR VALUE DRIVERS(CONTD)

3.OPTIMISE PRODUCT MIX4.INCREASE PRODUCTIVITY5.INCREASE CAPACITY UTILISATION6.OPTIMISE FIXED OVERHEADS7.BENCHMARKING ITS VALUE DRIVERS

W.R.T ITS COMPETITORS

SEARCH FOR VALUE DRIVERS(CONTD)

• INCREASE THE RETURN ON NEW CAPITAL INVESTMENT.

• INCREASE ITS GROWTH RATE BUT ONLY AS LONG AS THE RETURN ON NEW CAPITAL EXCEEDS WACC.

• REDUCE ITS COST OF CAPITAL.

LIVE EXAMPLES OF VALUE DRIVERS

FIRM VALUATION IN M&A : BALANCE SHEET VALUATION MODEL

EQUITY VALUATION FROM BALANCE SHEET• BOOK VALUE: THE NET WORTH OF A COMPANY AS

SHOWN ON THE BALANCE SHEET.

• TANGIBLE BOOK VALUE : BOOK VALUE MINUS INTANGIBLE ASSETS (GOODWILL, PATENTS, ETC)

• LIQUIDATION VALUE: THE VALUE THAT WOULD BE DERIVED IF THE FIRM’S ASSETS WERE LIQUIDATED.

• REPLACEMENT COST: THE REPLACEMENT COST OF ITS ASSETS LESS ITS LIABILITIES.

PRICE-EARNINGS RATIO MODEL FOR VALUATION

• THE EARNINGS MODEL SEPARATES EARNINGS (EPS) INTO TWO COMPONENTS:– CURRENT EARNINGS, WHICH ARE ASSUMED TO BE

CONSTANT WITH 100% PAYOUT.– GROWTH OF EARNINGS WHICH DERIVES FROM

FUTURE INVESTMENTS.• IF THE CURRENT EARNINGS ARE A PERPETUITY

WITH 100% PAYOUT, THEN THEY ARE WORTH:

k

EPSVCE

1

WHERE VCE IS THE VALUE OF EQUITY & k=WEIGHTED AVERAGE COST OF CAPITAL

PRICE-EARNINGS RATIO MODEL FOR VALUATION(CONTD)

• ASSUMING PROFITABLE GROWTH VCE ,THEREFORE, REPRESENTS THE MINIMUM VALUE

• IF THE COMPANY GROWS BEYOND THEIR CURRENT EPS BY REINVESTING A PORTION OF THEIR EARNINGS, THEN THE VALUE OF THESE GROWTH OPPORTUNITIES IS THE PRESENT VALUE OF THE ADDITIONAL EARNINGS IN FUTURE YEARS.

• THE GROWTH IN EARNINGS WILL BE EQUAL TO THE ROE TIMES THE RETENTION RATIO (1 – PAYOUT RATIO):

• WHERE b = RETENTION RATIO AND r = ROE (RETURN ON EQUITY).

brg


• IF THE COMPANY CAN MAINTAIN THIS GROWTH RATE FOREVER, THEN THE PRESENT VALUE OF THEIR GROWTH OPPORTUNITIES IS:

• WHICH, SINCE NPV IS GROWING AT A CONSTANT RATE CAN BE REWRITTEN AS:

1 1tt

t

k

NPVPVGO

gkkr

RE

gk

REkr

RE

gk

NPVPVGO

11111

Where RE1=retained earnings ,r=ROE, g=growth in earning & k=WACC


• THE VALUE OF THE COMPANY TODAY MUST BE THE SUM OF THE VALUE OF THE COMPANY IF IT DOESN’T GROW AND THE VALUE OF THE FUTURE GROWTH:

• WHERE RE1 IS THE RETAINED EARNINGS IN PERIOD 1, r IS THE RETURN ON EQUITY, k IS THE REQUIRED RETURN, AND g IS THE GROWTH RATE

gkkr

RE

k

EPS

gk

NPV

k

EPSVCS

11

111

ECCONOMIC PROFIT MODEL

• THE ECONOMIC PROFIT MODEL: THE VALUE OF A COMPANY EQUALS THE AMOUNT OF CAPITAL INVESTED PLUS A PREMIUM EQUAL TO THE PRESENT VALUE OF THE VALUE CREATED EACH YEAR GOING FORWARD.

P r ( )E c o n o m i c o f i t I n v e s t e d C a p i t a l x R O I C W A C C

w h e r e R O I C = R e t u r n o n I n v e s t e d C a p i t a l

W A C C = W e i g h t e d A v e r a g e C o s t o f C a p i t a l

P r ( )E c o n o m i c o f i t N O P L A T I n v e s t e d C a p i t a l x W A C C

w h e r e N O P L A T = N e t O p e r a t in g P r o f it L e s s A d j u s t e d T a x e s

V a lu e = I n v e s t e d C a p i t a l+ P r e s e n t V a lu e o f P r o j e c t e d E c o n o m ic P r o f i t

COMMON STOCK VALUATION

• AS WITH ANY OTHER SECURITY, THE FIRST STEP IN VALUING COMMON STOCKS IS TO DETERMINE THE EXPECTED FUTURE CASH FLOWS AND DETERMINE THE SUM OF THEIR FUTURE PRESENT VALUES . TO PUT IT MATHEMATICALLY :

• FOR A STOCK, THERE ARE TWO CASH FLOWS:– FUTURE DIVIDEND PAYMENTS– THE FUTURE SELLING PRICE

1 1tt

tCS

k

CFV

ESTABLISHMENT OF DIVIDEND DISCOUNT MODEL

WHERE:

Div t : Dividend received at the end of year t

Pt : Value of share at the end of year t

DIVIDEND DISCOUNT MODEL (DDM) FOR STOCK VALUATION

• THE DDM MODEL OF VALUATION PERMITS USE OF MULTIPLE DIVIDEND GROWTH RATE OVER TIME HORIZON

• THE DIVIDEND GROWTH RATE CAN BE ESTIMATED IN THREE WAYS:– USE THE HISTORICAL GROWTH RATE AND ASSUME IT WILL CONTINUE– THE GROWTH IN EARNINGS WILL BE EQUAL TO THE ROE TIMES

THE RETENTION RATIO (1 – PAYOUT RATIO):

WHERE b = RETENTION RATIO and r = ROE (RETURN ON EQUITY).– GENERATE FORECAST WITH WHATEVER METHOD SEEMS APPROPRIATE

• THE REQUIRED RATE OF RETURN IS OFTEN ESTIMATED BY USING THE CAPITAL ASSET PRICING MODEL(CAPM) : ki = krf + bi(km – krf) OR SOME OTHER ASSET PRICING MODEL.

brg

DIVIDEND DISCOUNT MODEL FOR VALUATION OF A FIRM

• STEP 1 : ESTIMATE FUTURE DIVIDEND PAYMENT:- CONSTANT THROUGH OUTGROWS AT A CONSTANT RATE g THROUGH OUTGROWS AT DIFFERENTIAL RATES IN 2 OR MULTIPLE

STAGES , SETTLING DOWN TO A CONSTANT RATE• STEP2 : ESTIMATE REQUIRED RATE OF RETURN kcs

THROUGH CAPM OR ALLIED PROCEDURE• STEP3 : CALCULATE THE PRESENT VALUE OF THE

FIRM STOCK Vcs AND THEN THE FIRMVALUE ITSELF

GORDON MODEL FOR STOCK VALUATION

• AT CONSTANT GROWTH RATE g THE GORDON MODEL VALUES THE STOCK AT :

• NOTE IF DIVIDEND IS CONSTANT THROUGH OUT i.e g=0,

• Vcs =D1/kcs

• THIS MODEL GIVES US THE PRESENT VALUE OF AN INFINITE STREAM OF DIVIDENDS THAT ARE GROWING AT A CONSTANT RATE.

V

D g

k g

D

k gCS

CS CS

0 11

DETERMINATION OF STOCK VALUE IN NTH YEAR THROUGH GORDON MODEL

• WE CAN USE THE DDM TO CALCULATE THE PRICE THAT A STOCK SHOULD SELL FOR IN NTH YEARS AS FOLLOWS:

• FOR EXAMPLE, TO VALUE A STOCK AT YEAR 2, WE SIMPLY USE THE DIVIDEND FOR YEAR 3 (D3). REMEMBER , THE VALUE AT PERIOD 2 IS SIMPLY THE PRESENT VALUE OF D3, D4, D5, …, D∞

V

D g

k g

D

k gNN

CS

N

CS

1

1

GORDON MODEL : AN EXAMPLE

• FIND THE STOCK VALUE WHEN THE CURRENT YEAR DIVIDEND IS Rs 1.85 per share,THE GROWTH RATE OF 8% & DESIRED RATE OF RETURN IS 15%

• THE VALUE OF THE STOCK WILL BE :

VCS

185 1 08

15 08

2 00

015 082857

. .

. .

.

. ..

WHAT IF GROWTH ISN’T CONSTANT?

• THE GORDON GROWTH MODEL ASSUMES THAT DIVIDENDS WILL GROW AT A CONSTANT RATE FOREVER, BUT WHAT IF THEY DON’T?

• IF WE ASSUME THAT GROWTH RATE OF DIVIDEND PAYMENT WILL EVENTUALLY BE CONSTANT, THEN WE CAN MODIFY GORDON GROWTH MODEL TO DIVIDEND DISCOUNT MODEL(DDM)

• WE CAN DETERMINE THE VALUE OF THE STOCK AT SOME FUTURE PERIOD WHEN GROWTH IS CONSTANT. IF WE CALCULATE THE PRESENT VALUE OF THAT PRICE AND THE PRESENT VALUE OF THE DIVIDENDS WITH ALTERNATE GROWTH PATTERN UP TO THAT POINT, WE WILL HAVE THE PRESENT VALUE OF ALL OF THE FUTURE CASH FLOWS ALLOWING DIFFERENTIAL DIVIDEND GROWTH.

WHAT IF GROWTH ISN’T CONSTANT? (AN EXAMPLE)

• LET’S TAKE OUR PREVIOUS EXAMPLE, BUT ASSUME THAT THE DIVIDEND WILL GROW AT A RATE OF 15% PER YEAR FOR THE FIRST THREE YEARS BEFORE SETTLING DOWN TO A CONSTANT 8% PER YEAR.

• WHAT’S THE VALUE OF THE STOCK NOW?

0 1 2 3 4

2.1275 2.4466 2.8136 3.0387 …

g = 15% g = 8%

WHAT IF GROWTH ISN’T CONSTANT? (AN EXAMPLE CONTD.)

• FIRST, NOTE THAT WE CAN CALCULATE THE VALUE OF THE STOCK AT THE END OF PERIOD 3 USING D4 OF GORDON MODEL:-

• NOW, FIND THE PRESENT VALUES OF THE FUTURE SELLING PRICE AND D1, D2, AND D3:

• SO, THE VALUE OF THE STOCK IS $34.09 AND WE DIDN’T EVEN HAVE TO ASSUME A CONSTANT GROWTH RATE. NOTE ALSO THAT THE VALUE IS HIGHER THAN THE ORIGINAL VALUE BECAUSE THE AVERAGE GROWTH RATE IS HIGHER.

41.4308.15.

0387.33

V

09.3415.1

41.438136.2

15.1

4466.2

15.1

1275.2320

V

TWO-STAGE DDM VALUATION MODEL

• THE PREVIOUS EXAMPLE SHOWED STEP BY STEP WAY TO VALUE A STOCK WITH TWO (OR MORE) GROWTH RATES.

• WE CAN ALSO USE THE FOLLOWING TWO-STAGE GROWTH MODEL WHICH IS NOT AS INTIMIDATING AS IT LOOKS:– THE FIRST TERM IS SIMPLY THE PRESENT VALUE OF THE

FIRST N DIVIDENDS (THOSE BEFORE THE CONSTANT GROWTH PERIOD)

– THE SECOND TERM IS THE PRESENT VALUE OF THE FUTURE STOCK PRICE.

nCS

CS

n

n

CSCSCS

k

gkggD

k

g

gk

gDV

1

11

1

11

1 2

210

1

1

10

GRAPHICAL REPRESENTATION OF DIVIDEND GROWTH MODEL

source:

STEPS IN VALUATION OF DISCONTED CASH FLOW MODEL

ANALYZE HISTORICAL PERFORMANCE. IDENTIFY VALUE DRIVERS OF THE CO. & ITS BUSINESSESFORECAST FREECASH FLOWS TO EQUITY & TARGET

FIRM CONSIDERING BENEFITS OF SYNERGY & ESTIMATING GROWTH PROSPECT.ESTIMATE THE WEIGHTED AVERAGE COST OF CAPITALCALCULATE EQUITY AND FIRM VALUECARRY OUT A SENSITIVITY ANALYSIS INTERPRET THE RESULTS FOR DECISION

COST OF CAPITAL MEASUREMENT

• STEPS INVOLVED IN CALCULATION OF COST OF CAPITAL– CALCULATE COST OF EQUITY CAPITAL FROM CAPM– CALCULATE COST OF PREFERENCE CAPITAL FROM

BALANCE SHEET– CALCULATE COST OF DEBT FROM BALANCE SHEET DATA– FORMULATE APPLICABLE DEBT EQUITY RATIO– FINAL RESULT IS WEIGHTED COST OF CAPITAL

• WACC=KD(1-T)*B/V+KP*P/V+KE*S/V

• WHERE WACC= WEIGHTED AVERAGE COST OF CAPITAL, KD= COST OF DEBT, KP= COST OF PREFERENCE CAPITAL, KE= COST OF EQUITY

,V=B+P+S VALUE OF ENTERPRISE

DETERMINATION OF COST OF CAPITAL

• CAPITAL ASSET PRICING MODEL(CAPM)• ARBITRAGE PRICING MODEL(APM)• AVERAGE BOND YIELD MODEL• ESTIMATE COST OF EQUITY USING MULTIPLES• SURVEY GENERAL EQUITY MARKET UNCERTAINTY• CONSIDER ESTIMATES FOR OTHER COMPANIES IN

SAME INDUSTRY• USE JUDGMENT TO ARRIVE AT AN ESTIMATE

CAPITAL ASSET PRICING MODEL

• COST OF EQUITY IS DETERMINED FROM CAPM AS PER FOLLOWING FORMULA :

KS = RF + [RM - RF] J • RISK-FREE RATE (RF) : RELATES TO RETURNS ON LONG TERM

GOVERNMENT BONDS• MARKET PRICE OF RISK (RM) : IT IS ESTIMATED BY REGRESSING

STOCK INDEX(BSE100 /S&P500) WITH GOVT. BOND RATE• BETA (J ) : MEASURES HOW RETURNS ON THE FIRM'S

COMMON STOCK VARIED WITH RETURNS ON THE STOCK INDEX. HIGH BETA STOCKS EXHIBIT HIGHER VOLATILITY THAN LOW BETA STOCKS IN RESPONSE TO CHANGES IN MARKET RETURNS

MAJOR ASSUMPTIONS OF CAPM

ALL INVESTORS:• AIM TO MAXIMIZE ECONOMIC UTILITIES. • ARE RATIONAL AND RISK-AVERSE. • ARE BROADLY DIVERSIFIED ACROSS A RANGE OF INVESTMENTS. • ARE PRICE TAKERS, I.E., THEY CANNOT INFLUENCE PRICES. • CAN LEND AND BORROW UNLIMITED AMOUNTS UNDER THE RISK

FREE RATE OF INTEREST. • TRADE WITHOUT TRANSACTION OR TAXATION COSTS. • DEAL WITH SECURITIES THAT ARE ALL HIGHLY DIVISIBLE INTO

SMALL PARCELS. • ASSUME ALL INFORMATION IS AVAILABLE AT THE SAME TIME TO

ALL INVESTORS.

34FGS

0.1

10

1000

1925 1933 1941 1949 1957 1965 1973 1981 1989 1997

S&PSmall CapCorp BondsLong BondT Bill

THE VALUE OF AN INVESTMENT OF $1 IN 1926

Source: Ibbotson Associates

Inde

x

Year End

1

613

203

6.15

4.34

1.58

Real returns

CAPITAL ASSET PRICING MODEL

The Security Market Line, seen here in a graph, describes a relation between the beta and the asset's expected rate of return.

CAPM ESTIMATES THE COST OF FIRM EQUITY AS PER THE FOLLOWING FORMULA :-

1. TOTAL RISK = DIVERSIFIABLE RISK + MARKET RISK2. MARKET RISK IS MEASURED BY BETA, THE SENSITIVITY TO MARKET CHANGES.

http://en.wikipedia.org/wiki/File:SecMktLine.png

STANDARD DEVIATION AS A MEASURE OF VOLATILITY

• VOLATILITY IN STOCK RETURNS CAN BE MEASURED THROUGH STANDARD DEVIATION

THE AVERAGE & STANDARD DEVIATION OF ONE-YEAR S&P 500 RETURNS DURING 1926-94 PERIOD IS 12.45 & 22.28% RESPECTIVELY. IF S&P RETURNS ARE NORMALLY DISTRIBUTED, THIS MEANS THAT ABOUT 2/3 OF THE TIME WE SHOULD OBSERVE AN ANNUAL RETURN WITHIN THE RANGE -9.93 AND 34.73.

ESTIMATING BETA

• THE STANDARD PROCEDURE FOR ESTIMATING BETAS IS TO REGRESS STOCK RETURNS (RJ) AGAINST MKT RETURNS (RM) :

RJ = A + B RM

– WHERE A IS THE INTERCEPT AND B IS THE SLOPE OF THE REGRESSION.

• THE SLOPE OF THE REGRESSION CORRESPONDS TO THE BETA OF THE STOCK, AND MEASURES THE RISKINESS OF THE STOCK.

• THIS BETA HAS THREE PROBLEMS:– IT HAS HIGH STANDARD ERROR– IT REFLECTS FIRM’S PAST & NOT CURRENT BUSINESS MIX– IT REFLECTS FIRM’S PAST & NOT CURRENT LEVERAGE

SIGNIFICANCE OF BETA VALUE

THE SLOPE OF THE REGRESSION LINE DRAWN BY PLOTTING COMPANY RETURN &MARKET RETURN IS CALLED THE BETA OF THAT STOCK.

THE STEEPER THE SLOPE, THE MORE SYSTEMATIC RISK, THE SHALLOWER THE SLOPE, LESS EXPOSED THE COMPANY IS TO THE MARKET VARIATION .

FOR INSTANCE, CONSIDER A COMPANY WITH A BETA OF 1.5. IF THE MARKET RETURN IS 20 PERCENTAGE POINTS OVER THE T-BILL RATE IN ONE YEAR, THEN WE EXPECT THE STOCK RETURN TO BE 30 PERCENTAGE POINTS OVER T-BILLS IN THAT YEAR.

BETAS TEND TO BE RELATED TO INDUSTRY. HIGH-TECHNOLOGY, FOR INSTANCE, IS A HIGH-BETA INDUSTRY. THE FOOD INDUSTRY IS A LOW BETA INDUSTRY

DETERMINANTS OF BETAS

Beta of Firm (Unlevered Beta)

Beta of Equity (Levered Beta)

Nature of product or service offered by company:Other things remaining equal, the more discretionary the product or service, the higher the beta.

Operating Leverage (Fixed Costs as percent of total costs):Other things remaining equal the greater the proportion of the costs that are fixed, the higher the beta of the company.

Financial Leverage:Other things remaining equal, the greater the proportion of capital that a firm raises from debt,the higher its equity beta will be

Implications1. Cyclical companies should have higher betas than non-cyclical companies.2. Luxury goods firms should have higher betas than basic goods.3. High priced goods/service firms should have higher betas than low prices goods/services firms.4. Growth firms should have higher betas.

Implications1. Firms with high infrastructure needs and rigid cost structures should have higher betas than firms with flexible cost structures.2. Smaller firms should have higher betas than larger firms.3. Young firms should have higher betas than more mature firms.

ImplciationsHighly levered firms should have highe betas than firms with less debt.Equity Beta (Levered beta) = Unlev Beta (1 + (1- t) (Debt/Equity Ratio))

THE SOLUTION: BOTTOM-UP BETAS

Step 1: Find the business or businesses that your firm operates in.

Step 2: Find publicly traded firms in each of these businesses and obtain their regression betas. Compute the simple average across these regression betas to arrive at an average beta for these publicly traded firms. Unlever this average beta using the average debt to equity ratio across the publicly traded firms in the sample.Unlevered beta for business = Average beta across publicly traded firms/ (1 + (1- t) (Average D/E ratio across firms))

If you can, adjust this beta for differencesbetween your firm and the comparablefirms on operating leverage and product characteristics.

Step 3: Estimate how much value your firm derives from each of the different businesses it is in.

While revenues or operating income are often used as weights, it is better to try to estimate the value of each business.

Step 4: Compute a weighted average of the unlevered betas of the different businesses (from step 2) using the weights from step 3.Bottom-up Unlevered beta for your firm = Weighted average of the unlevered betas of the individual business

Step 5: Compute a levered beta (equity beta) for your firm, using the market debt to equity ratio for your firm. Levered bottom-up beta = Unlevered beta (1+ (1-t) (Debt/Equity))

If you expect the business mix of your firm to change over time, you can change the weights on a year-to-year basis.

If you expect your debt to equity ratio to change over time, the levered beta will change over time.

Possible Refinements

ARBITRAGE PRICING MODEL

RPK IS THE RISK PREMIUM OF THE FACTOR, RF IS THE RISK-FREE RATE,

WHERE :

ECONOMIC FACTORS GENERALLY USED IN APM ESTIMATES:INFLATION RATE;INDUSTRIAL PRODUCTION INDEX; CHANGES IN DEFAULT PREMIUM IN CORPORATE BONDS; YIELD CURVE. SHORT TERM INTEREST RATES; THE DIFFERENCE IN LONG AND SHORT-TERM INTEREST RATES; OIL PRICES GOLD OR OTHER PRECIOUS METAL PRICES CURRENCY EXCHANGE RATES SOURCE: WIKIPAEDIA

http://en.wikipedia.org/wiki/Risk_premium

http://en.wikipedia.org/wiki/Risk-free_rate

http://en.wikipedia.org/wiki/Inflation

http://en.wikipedia.org/wiki/Yield_curve

http://en.wikipedia.org/wiki/Exchange_rate

AVERAGE BOND YIELD MODEL

• COST OF EQUITY = AVERAGE YIELD TO MATURITY OF BONDS FOR THE INDUSTRY WITH SAME RATING AS THE FIRM'S DEBT PLUS HISTORICAL AVERAGE OF FIRM'S EQUITY RISK PREMIUM OVER ITS BOND YIELD

• FOR THE INDUSTRY, ANALYZE HISTORICAL YIELD ON EQUITY AS COMPARED WITH AVERAGE YIELD TO MATURITY ON BONDS FOR THE INDUSTRY

COMPUTATION OF COST OF DEBT

COST OF DEBT IS CALCULATED ON AN AFTER-TAX BASIS BECAUSE INTEREST PAYMENTS ARE TAX DEDUCTIBLEAFTER-TAX COST OF DEBT = KB(1 - T )BEFORE-TAX COST OF DEBT, KB

CAN BE OBTAINED FROM A WEIGHTED AVERAGE OF THE YIELDS

TO MATURITY OF ALL THE FIRM'S OUTSTANDING PUBLICLY HELD

BONDS

CAN BE OBTAINED FROM PUBLISHED PROMISED YIELDS TO

MATURITY BASED ON BOND RATING CATEGORY

COMPUTATION OF WEIGHTED AVERAGE COST OF CAPITAL(WACC)

• K = KB(1-T)(B/V)+KS(S/V) WHERE:

• KB = COST OF DEBTKS = COST OF EQUITYT = TAX RATEB = VALUE OF DEBTS = VALUE OF EQUITY

V = TOTAL VALUE OF FIRM = B + S• OR• K = KU(1-TL) WHERE:

• KU = COST OF CAPITAL OF AN UNLEVERED FIRM

• L = B/V

LIMITATIONS IN USE OF DISCOUNTED CASH FLOW VALUATION

• A TROUBLED FIRM• CYCLICAL FIRMS• FIRMS WITH UNDER UTILISED ASSETS• FIRMS WITH PATENTS OR PRODUCT

OPTIONS• FIRMS IN THE PROCESS OF

RESTRUCTURING

FIRM VALUATION IN M&A : SPREADSHEET APPROACH TO VALUATION

• STEP1 : DETAILED FINANCIAL ANALYSIS IS PERFORMED BASED ON HISTORICAL DATA FOR 7 TO 10 YEARS FOR EACH ELEMENT OF BALANCE SHEET, INCOME STATEMENT, AND CASH FLOW STATEMENT TO DISCOVER UNDERLYING VALUE DRIVERS & FINANCIAL PATTERNS OF THE FIRM

• STEP2 : ADDITIONAL ANALYSIS OF BUSINESS ECONOMICS OF INDUSTRY IN WHICH THE FIRM OPERATES, ITS COMPETITIVE POSITION AND ASSESSMENTS OF INDUSTRY VALUE DRIVERS FINANCIAL PATTERNS, STRATEGIES, AND ACTIONS OF COMPETITORS

• STEP3: BASED ON STEPS1&2 AS ABOVE IDENTIFY VALUE DRIVERS, POTENTIAL FOR SYNERGY & PROJECT RELEVANT CASH FLOWS TAKING INTO CONSIDERATION SYNERGY & VALUE DRIVERS


• STEP4: AN ACQUISITION IS FUNDAMENTALLY A CAPITAL BUDGETING PROBLEM. NPV OF ACQUISITION IS OBTAINED FROM SUM OF FREE CASH FLOWS DISCOUNTED AT APPLICABLE COST OF CAPITAL.

capital ofcost

periodin outlays investment

ratetax

periodin flowscash tax -before

1 periodin flowscash free

:ere wh)1(1

k =

tI

T =

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FCFNPV

t

t

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SOURCES OF SYNERGY

Synergy is created when two firms are combined and can be either financial or operating

Operating Synergy accrues to the combined firm as Financial Synergy

Higher returns on new investments

More newInvestments

Cost Savings in current operations

Tax BenefitsAdded Debt Capacity Diversification?

Higher ROC

Higher Growth Rate

Higher Reinvestment

Higher Growth RateHigher Margin

Higher Base-year EBIT

Strategic Advantages Economies of Scale

Longer GrowthPeriod

More sustainableexcess returns

Lower taxes on earnings due to - higher depreciaiton- operating loss carryforwards

Higher debt raito and lower cost of capital

May reducecost of equity for private or closely heldfirm

THE PATHS TO VALUE CREATION• USING THE DCF FRAMEWORK, THERE ARE FOUR BASIC WAYS IN WHICH

THE VALUE OF A FIRM CAN BE ENHANCED:– INCREASE CASH FLOWS FROM EXISTING ASSETS

• INCREASE AFTER-TAX EARNINGS FROM ASSETS IN PLACE• REDUCE REINVESTMENT NEEDS

– INCREASE GROWTH RATE OF NET CASH FLOWS• INCREASE THE RATE OF REINVESTMENT IN THE FIRM• IMPROVE THE ROC ON THOSE REINVESTMENTS

– EXTEND LENGTH OF THE HIGH GROWTH PERIOD– REDUCE THE COST OF CAPITAL

• REDUCING THE DEBT EQUITY RATIO• REDUCING THE OPERATING & FINANCIAL LEVERAGE • CHANGING THE FINANCING COMPOSITION

WAYS OF INCREASING CASH FLOWS FROM ASSETS IN PLACE

Revenues

* Operating Margin

= EBIT

- Tax Rate * EBIT

= EBIT (1-t)

+ Depreciation- Capital Expenditures- Chg in Working Capital= FCFF

Divest assets thathave negative EBIT

More efficient operations and cost cuttting: Higher Margins

Reduce tax rate- moving income to lower tax locales- transfer pricing- risk management

Live off past over- investment

Better inventory management and tighter credit policies

VALUE ENHANCEMENT THROUGH GROWTH

Reinvestment Rate

* Return on Capital

= Expected Growth Rate

Reinvest more inprojects

Do acquisitions

Increase operatingmargins

Increase capital turnover ratio

BUILDING COMPETITIVE ADVANTAGES: INCREASE THE GROWTH PERIOD

Increase length of growth period

Build on existing competitive advantages

Find new competitive advantages

Brand name

Legal Protection

Switching Costs

Cost advantages

REDUCING COST OF CAPITAL

Cost of Equity (E/(D+E) + Pre-tax Cost of Debt (D./(D+E)) = Cost of Capital

Change financing mix

Make product or service less discretionary to customers

Reduce operating leverage

Match debt to assets, reducing default risk

Changing product characteristics

More effective advertising

Outsourcing Flexible wage contracts &cost structure

Swaps Derivatives Hybrids

CLAIM OF SYNERGY IN M&A : A STUDY BY MCKINSEY & KPMG

• MCKINSEY EXAMINED 58 ACQUISITIONS DURING 1972-83 TO DETERMINE

WETHER THE RETURN ON THE AMOUNT INVESTED IN THE ACQUISITIONS EXCEEDED THE COST OF CAPITAL?

WETHER THE ACQUISITIONS HELP THE PARENT COMPANIES OUTPERFORM THE COMPETITION?

• THEY FOUND THAT 28 OF THE 58 PROGRAMS FAILED BOTH TESTS, AND 6 FAILED AT LEAST ONE TEST

• KPMG IN A MORE RECENT STUDY OF GLOBAL ACQUISITIONS CONCLUDED THAT MOST MERGERS (>80%) FAIL .THE MERGED COMPANIES DO WORSE THAN THEIR PEER GROUP. THE DIVESTITURE RATE OF ACQUISITIONS IS AROUND 50%.

FACTORS CRITICAL FOR DETERMININGFREE CASH FLOW TO THE FIRM

• GROWTH RATE (G) IN REVENUE• NET OPERATING INCOME MARGIN (M)• ACTUAL TAX RATE (T)• INVESTMENT (IT) NECESSARY TO MAINTAIN GROWTH

MOMENTUM• PERIODS OF SUPERNORMAL GROWTH (N)• MARGINAL WEIGHTED COST OF CAPITAL (K)• VALUE DRIVERS FOR NET OPERATING INCOME MARGIN

(M) AND INVESTMENT (I) EXPRESSED AS A PERCENTAGE OF SALES


• ADVANTAGES OF SPREADSHEET APPROACH– PROVIDE GREAT FLEXIBILITY IN PROJECTIONS– HELPS TO UNDERSTAND UNDERLYING GROWTH PATTERNS

& ITS VALUE DRIVERS – INCORPORATES DESIRED DETAIL OF INDIVIDUAL ITEMS OF

BALANCE SHEET OR INCOME STATEMENT ACCOUNTS– FLEXIBILITY AND JUDGMENT IN MAKING PROJECTIONS

• DISADVANTAGES OF SPREADSHEET APPROACH– NUMBERS USED IN PROJECTIONS MAY CREATE ILLUSION– MAY BLUR LINK OF BUSINESS LOGIC & PROJECTION– MAY BECOME HIGHLY COMPLEX– DETAILS MAY OBSCURE IMPORTANT DRIVING FACTORS

•

Cashflow to FirmEBIT (1-t)- (Cap Ex - Depr)- Change in WC= FCFF

Expected GrowthReinvestment Rate* Return on Capital

FCFF1 FCFF2 FCFF3 FCFF4 FCFF5

Forever

Firm is in stable growth:Grows at constant rateforever

Terminal Value= FCFF n+1/(r-gn)

FCFFn.........

Cost of Equity Cost of Debt(Riskfree Rate+ Default Spread) (1-t)

WeightsBased on Market Value

Discount at WACC= Cost of Equity (Equity/(Debt + Equity)) + Cost of Debt (Debt/(Debt+ Equity))

Value of Operating Assets+ Cash & Non-op Assets= Value of Firm- Value of Debt= Value of Equity

Riskfree Rate :- No default risk- No reinvestment risk- In same currency andin same terms (real or nominal as cash flows

+Beta- Measures market risk X

Risk Premium- Premium for averagerisk investment

Type of Business

Operating Leverage

FinancialLeverage

Base EquityPremium

Country RiskPremium

DISCOUNTED CASHFLOW VALUATION

SOURCE :ASWATHDAMODARAN

Forever

Terminal Value= 1881/(.0961-.06)=52,148

Cost of Equity12.90%

Cost of Debt6.5%+1.5%=8.0%Tax rate = 0% -> 35%

WeightsDebt= 1.2% -> 15%

Value of Op Assets $ 14,910+ Cash $ 26= Value of Firm $14,936- Value of Debt $ 349= Value of Equity $14,587- Equity Options $ 2,892Value per share $ 34.32

Riskfree Rate :T. Bond rate = 6.5%

+Beta1.60 -> 1.00 X

Risk Premium4%

Internet/Retail

Operating Leverage

Current D/E: 1.21%

Base EquityPremium

Country RiskPremium

CurrentRevenue$ 1,117

CurrentMargin:-36.71%

Reinvestment:Cap ex includes acquisitionsWorking capital is 3% of revenues

Sales TurnoverRatio: 3.00

CompetitiveAdvantages

Revenue Growth:42%

Expected Margin: -> 10.00%

Stable Growth

StableRevenueGrowth: 6%

StableOperatingMargin: 10.00%

Stable ROC=20%Reinvest 30% of EBIT(1-t)

EBIT-410m

NOL:500 m

$41,346 10.00% 35.00%$2,688 $ 807 $1,881

Term. Year

2 431 5 6 8 9 107

Cost of Equity 12.90% 12.90% 12.90% 12.90% 12.90% 12.42% 12.30% 12.10% 11.70% 10.50%Cost of Debt 8.00% 8.00% 8.00% 8.00% 8.00% 7.80% 7.75% 7.67% 7.50% 7.00%AT cost of debt 8.00% 8.00% 8.00% 6.71% 5.20% 5.07% 5.04% 4.98% 4.88% 4.55%Cost of Capital 12.84% 12.84% 12.84% 12.83% 12.81% 12.13% 11.96% 11.69% 11.15% 9.61%

Revenues $2,793 5,585 9,774 14,661 19,059 23,862 28,729 33,211 36,798 39,006 EBIT -$373 -$94 $407 $1,038 $1,628 $2,212 $2,768 $3,261 $3,646 $3,883EBIT (1-t) -$373 -$94 $407 $871 $1,058 $1,438 $1,799 $2,119 $2,370 $2,524 - Reinvestment $559 $931 $1,396 $1,629 $1,466 $1,601 $1,623 $1,494 $1,196 $736FCFF -$931 -$1,024 -$989 -$758 -$408 -$163 $177 $625 $1,174 $1,788

Amazon.comJanuary 2000Stock Price = $ 84

SOURCE : ASWATHDAMODARAN

RELATIVE VALUE MODELS• STOCKS CAN BE VALUED RELATIVE TO ONE ANOTHER.• A STOCK MAY BE UNDERVALUED BECAUSE OF LOWER P/E

RATIO DESPITE HIGHER EARNINGS GROWTH RATE.• THESE MODELS ARE POPULAR, BUT HAVE PROBLEMS:

– COMPANIES ARE RARELY PERFECTLY COMPARABLE.– “CORRECT” PRICE MULTIPLE IS ELUSIVE– INDETERMINATE RELATIONSHIP BETWEEN EARNINGS

GROWTH AND PRICE MULTIPLES– A COMPANY’S (OR INDUSTRY’S) HISTORICAL MULTIPLES

MAY NOT BE RELEVANT TODAY DUE TO CHANGES IN EARNINGS GROWTH OVER TIME.

THE P/E APPROACH

• AS A RULE OF THUMB, OR SIMPLIFIED MODEL, ANALYSTS OFTEN ASSUME THAT A STOCK IS WORTH SOME “JUSTIFIED” P/E RATIO TIMES THE FIRM’S EXPECTED EARNINGS.

• THIS JUSTIFIED P/E MAY BE BASED ON THE INDUSTRY AVERAGE P/E, THE COMPANY’S OWN HISTORICAL P/E, OR SOME OTHER P/E THAT THE ANALYST FEELS IS JUSTIFIED.

• TO CALCULATE THE VALUE OF THE STOCK, WE MERELY MULTIPLY ITS NEXT YEARS’ EARNINGS BY THIS JUSTIFIED P/E:

1EPSEPVCS

THE P/S APPROACH

• IN SOME CASES, COMPANIES AREN’T CURRENTLY EARNING ANY MONEY AND THIS MAKES THE P/E APPROACH IMPOSSIBLE TO USE (BECAUSE THERE ARE NO EARNINGS).

• IN THESE CASES, ANALYSTS OFTEN ESTIMATE THE VALUE OF THE STOCK AS SOME MULTIPLE OF SALES (PRICE/SALES RATIO).

• THE JUSTIFIED P/S RATIO MAY BE BASED ON HISTORICAL P/S FOR THE COMPANY, P/S FOR THE INDUSTRY, OR SOME OTHER ESTIMATE:

1SalesSPVCS

DETAILED PROCEDURE ADOPTED RELATIVE VALUE MODEL

• SELECT GROUP OF COMPANIES COMPARABLE WITH RESPECT TO SIZE, PRODUCTS, RECENT TRENDS & FUTURE PROSPECTS.

• IDENTIFY THE MOST REPRESENTATIVE KEY RATIOS FOR THE BUSINESS OF THE TARGET FIRMFROM AMONGST PRICE/EARNING, PRICE/BOOK VALUE , PRICE/SALES , PRICE/CASH FLOW , PRICE/DIVIDEND & MARKET VALUE/REPLACEMENT VALUE RATIOS.

• COMPUTE THE KEY RATIOS FOR EACH SELECT GROUP OF COMPANIES • KEY RATIOS ARE AVERAGED FOR GROUP• AVERAGE RATIOS ARE APPLIED TO ABSOLUTE DATA FOR TARGET

COMPANY• INDICATED MARKET VALUES OBTAINED FROM EACH RATIO• VALUATION JUDGMENTS ARE MADE

FIRM VALUATION IN M&A COMPARABLE COMPANIES MODEL

• ADVANTAGES– COMMON SENSE APPROACH– MARKETPLACE TRANSACTIONS ARE USED– WIDELY USED IN LEGAL CASES, FAIRNESS EVALUATION, AND

OPINIONS– USED TO VALUE A COMPANY NOT PUBLICLY TRADED

• LIMITATIONS– MAY BE DIFFICULT TO FIND COMPANIES THAT ARE ACTUALLY

COMPARABLE BY KEY CRITERIA– RATIOS MAY DIFFER WIDELY FOR COMPARABLE COMPANIES– DIFFERENT RATIOS MAY GIVE WIDELY DIFFERENT RESULTS

UNDERLYING THEME OF OPTION PRICING MODEL: SEARCHING FOR AN ELUSIVE PREMIUM

• TRADITIONAL DISCOUNTED CASH FLOW MODELS UNDER ESTIMATE THE VALUE OF INVESTMENTS, WHERE THERE ARE OPTIONS EMBEDDED IN THE INVESTMENTS TO:-– DELAY OR DEFER– FLEXIBILITY– EXPANSION– ABANDONMENT

• PUT ANOTHER WAY, OPTION VALUE ADVOCATES BELIEVE THAT THERE SHOULD BE A PREMIUM ON DISCOUNTED CASHF LOW VALUE ESTIMATES.

DETERMINANTS OF OPTION VALUE

• VARIABLES RELATING TO UNDERLYING ASSET– VALUE OF UNDERLYING ASSET– VARIANCE IN THAT VALUE– EXPECTED DIVIDENDS ON THE ASSET

• VARIABLES RELATING TO OPTION– STRIKE PRICE OF OPTIONS– LIFE OF THE OPTION

• LEVEL OF INTEREST RATES; AS RATES INCREASE, THE RIGHT TO BUY (SELL) AT A FIXED PRICE IN THE FUTURE BECOMES MORE (LESS) VALUABLE.

OPTION PRICING MODEL : THE BLACK SCHOLES MODEL

VALUE OF CALL = S N (d1) - K e-rt N(d2)WHERE,

– d2 = d1 - √t

• THE REPLICATING PORTFOLIO IS EMBEDDED IN THE BLACK-SCHOLES MODEL. TO REPLICATE THIS CALL, YOU WOULD NEED TO– BUY N(d1) SHARES OF STOCK; N(d1) IS CALLED THE OPTION DELTA– BORROW K e-rt N(d2)

d1 = ln

S

K+ (r +

2

2) t

t

OPTION PRICING MODEL : VALUING PRODUCT PATENT OF AVONEX

• BIOGEN, A BIO-TECHNOLOGY FIRM, HAS A PATENT ON AVONEX, A DRUG TO TREAT MULTIPLE SCLEROSIS, FOR THE NEXT 17 YEARS, AND IT PLANS TO PRODUCE AND SELL THE DRUG BY ITSELF. THE KEY INPUTS ON THE DRUG ARE AS FOLLOWS:

PV OF CASH FLOWS FROM INTRODUCING THE DRUG NOW = S = $ 3.422 BILLION PV OF COST OF DEVELOPING DRUG FOR COMMERCIAL USE = K = $ 2.875 BILLIONPATENT LIFE = T = 17 YEARS RISKLESS RATE = R = 6.7% (17-YEAR T.BOND RATE)VARIANCE IN EXPECTED PRESENT VALUES =S2 = 0.224 (INDUSTRY AVERAGE FIRM

VARIANCE FOR BIO-TECH FIRMS)EXPECTED COST OF DELAY = y = 1/17 = 5.89%d1 = 1.1362 N(d1) = 0.8720d2 = -0.8512 N(d2) = 0.2076

CALL VALUE= 3,422 exp(-0.0589)(17) (0.8720) - 2,875 (exp(-0.067)(17) (0.2076) = $ 907 million

SENSITIVITY ANALYSIS– PURPOSE

• CHECK IMPACT OF A RANGE OF ALTERNATIVE POSSIBILITIES• PROVIDE FRAMEWORK FOR PLANNING AND CONTROL

– SENSITIVITY ANALYSIS OF MODEL VARIABLES:• DECREASE IN REVENUES GROWTH RATE (G) LOWERS VALUATION• INCREASE IN INVESTMENT REQUIREMENT PERCENTAGE (I) LOWERS VALUATION• OPERATING PROFIT MARGIN (M) IS A POWERFUL VALUE DRIVER — WHEN M IS

INCREASED, VALUATION INCREASES• VALUATION IS VERY SENSITIVE TO THE COST OF CAPITAL (K) USED IN ANALYSIS

— WHEN COST OF CAPITAL IS INCREASED, VALUATION FALLS• SENSITIVITY TO N AND T PREDICTABLE IN DIRECTION AND MAGNITUDE

– WHEN PERIOD OF SUPERNORMAL GROWTH IS REDUCED, VALUATION IS REDUCED

– WHEN TAX RATE IS REDUCED, VALUATION IS INCREASED– IN MANY PRACTICAL CASES, SECOND TERM IN VALUATION MODEL REPRESENTS A

HIGHER PROPORTION OF VALUATION THAN FIRST TERM — MUST BE CAREFUL AS TO ASSUMPTIONS ABOUT FACTORS AFFECTING EXIT OR TERMINAL VALUE

MERGER PREMIUM IN SHARE SWAP OR SHARE PLUS CASH DEAL

• IN SHARE SWAP DEAL THE PREMIUM PAID IS REFLECTED THROUGH % OF OWNERSHIP EACH PARTY WILL CONTROL IN THE MERGED ENTITY. HIGHER PREMIUM PAID MEANS :

GREATER THE PERCENTAGE OWNERSHIP OF THE NEW FIRM BY THE SHAREHOLDERS OF THE ACQUIRED FIRM

GREATER THE VALUE PER SHARE DILUTION FOR ACQUIRER SHAREHOLDERS

GREATER THE EPS DILUTION FOR ACQUIRER SHAREHOLDERS• PRESENCE OF MERGER ECONOMIES FROM SYNERGIES, COST

SAVINGS, ETC. CAN RECOVER ACQUIRER PREMIUMS PAID, COULD EVEN MAKE MERGERS ACCRETIVE

SUMMARY OF VALUATION ANALYSIS

• ALL VALUATION METHODS HAVE STRENGTHS AND WEAKNESSES

• EMPLOY MULTIPLE METHODS OF VALUATION IN TAKEOVER ANALYSIS

• VALUATION SHOULD BE GUIDED BY A BUSINESS ECONOMICS OUTLOOK FOR THE FIRMS

• ULTIMATELY JUDGMENTS ARE REQUIRED FOR VALUATIONS

EXTRA SLIDES

FORMULAE FOR FREE CASH FLOW

• FREE CASH FLOW=GROSS CASH OPERATING INCOME-INCEASE IN NET FIXED ASSET-(INCREASE IN CURRENT ASSET-NON INTEREST BEARING DEBT)

• GROSS CASH OPERATING INCOME IS EQUAL TO: • 1.EBIDAT*(1-T)+T*D• 2.(EBIT+D)*(1-T) +T*D• 3.EBIT*(1-T)+D• 4. (EBT+INTEREST)*(1-T)+D• 5.PAT+D+INTEREST*(1-T)

SOME USEFUL FORMULAE IN VALUATION

• gt =ROE(1-pay out ratio)• ROE=ROC+D/E*{ROC-i(1-t)}• ROC=EBIT(1-t)/(BV of debt+BV ofequity)• g=(1-payout ratio)*[ROC+D/E*{ROC-i(1-t)}]• WACC=kd(1-T)*B/V+kp*P/V+ke*S/V where

WACC=weighted average cost of capital, kd= cost of debt, kp= cost of preference capital, ke=

cost of equity ,V=B+P+S value of enterprise

SOME USEFUL FORMULAE IN VALUATION

• P = D / R WHERE P= PRICE, D=CONST DPS & R=RATE OF RETURN• P = D1 / (R-G) WHERE P= PRICE, D1=NEXT YR DPS & R=RATE OF

RETURN• Z + Z2 + Z3 + . . . + ZN = [ZN+1 - Z]/[Z - 1] • Z + Z2 + Z3 + . . . + ZN + . . . = [ - Z]/[Z - 1] (FOR 0 <= Z < 1)• PV = FV / (1 + R)Y OR R = (FV / PV)1 / Y - 1 WHERE R= CAGR

(COMPOUND ANNUAL GROWTH RATE), FV=VALUE AT YTH YEAR, PV=PRESNT VALUE

• P=C(1 + R)-1 + C(1 + R)-2 + . . . + C(1 + R)-Y + B(1 + R)-Y WHERE P = PURCHASE PRICE ,C = ANNUAL COUPON PAYMENT (IN RUPEES, NOT A PERCENT) , Y = NUMBER OF YEARS TO MATURITY, B = PAR VALUE, & R=YIELD TO MATURITY

DEGREE OF CORRELATION BETWEEN TWO VARIABLES

EFFICIENT FRONTIERS OF PORTFOLIO INVESTMENT

EFFICIENT FRONTIERS OF PORTFOLIO INVESTMENT

8 10 12 14 16 18 20 22 24 26 2802468

101214161820

Y-Values

Y-Values

OPTION PRICING MODEL : INPUTS FOR PATENT VALUATION

Input Estimation Process

1. Value of the Underlying Asset Present Value of Cash Inflows from taking projectnow

This will be noisy, but that adds value.

2. Variance in value of underlying asset Variance in cash flows of similar assets or firms Variance in present value from capital budgeting

simulation.

3. Exercise Price on Option Option is exercised when investment is made. Cost of making investment on the project ; assumed

to be constant in present value dollars.

4. Expiration of the Option Life of the patent

5. Dividend Yield Cost of delay Each year of delay translates into one less year of

value-creating cashflows

Annual cost of delay = 1

n

PRICE-EARNINGS RATIO MODEL FOR VALUATION

0

1

11

/

P PVGO

E k Ek

where PVGO = Present Value of Growth Opportunity

0 1

1

(1 )P E b

E k ROExb

Implying P/E ratio

0

1

1P b

E k ROExb

where ROE = Return On Equity

80FGS

Beta and Market Risk

beta

Expected

return

Expectedmarketreturn

10%10%- +

-10%+10%

stock

-10%

1. Total risk = diversifiable risk + market risk2. Market risk is measured by beta, the sensitivity to market changes.

81FGS

Markowitz Portfolio Theory

Bristol-Myers Squibb

McDonald’s

Standard Deviation

Expected Return (%)

45% McDonald’s

Expected Returns and Standard Deviations vary given different weighted combinations of the stocks.

82FGS

Markowitz Portfolio TheoryPrice changes vs. Normal distribution

Microsoft - Daily % change 1986-1997

0

100

200

300

400

500

600

-10% -8% -6% -4% -2% 0% 2% 4% 6% 8% 10%

# of

Day

s (f

requ

ency

)

Daily % Change

• Dividend Signaling------------------------------------------------------------ A theory that suggests company announcements of an increase in dividend payouts acts as an indicator of the firm possessing strong future prospects. The rationale behind dividend signaling models stems from game theory. A manager that has good investment opportunities is more likely to "signal", than one who doesn't, because it is in their best interest to do so.

Investopedia Says:------------------------------------------------------------Over the years the concept that dividend signaling can predict positive future performance has been a hotly contested subject. Many studies have been done to see if the markets reaction to a "signal" is significant enough to support this theory. For the most part the tests have shown that dividend signaling does occur when companies either increase or decrease the amount of dividends they will be paying out.

The theory of dividend signaling is also a key concept used by proponents of inefficient markets.

©2001 Prentice Hall Takeovers, Restructuring, and Corporate Governance,

3/e Weston - 84

• Cost of equity– Capital Asset Pricing Model (CAPM)

ks = Rf + [RM - Rf] j• Risk-free rate (Rf)

– Related to returns on U.S. government bonds– Rates on relatively long-term bonds should be used since discount

factor is used in valuation involving long periods

• Market price of risk (RM - Rf)– For many years, estimated to be in range of 6.5 to 7.5%– For new economic paradigm since mid 1990s, estimated to be in the

range 4% to 5%

• Beta (j )– Measures how returns on the firm's common stock vary with returns on

the market as a whole– High beta stocks exhibit higher volatility than low beta stocks in

response to changes in market returns


3/e Weston - 85

– Dividend growth model• Cost of equity based on the constant-growth

dividend valuation model

• Required return on equity is expected dividend yield (D1/S0) plus expected growth rate of dividends in perpetuity (g)

SD

k gk

D

Sgo

ss

o

1 1


3/e Weston - 86

– Estimating the cost of equity capital• Use information generated by financial markets• Estimate cost of equity using multiple methods• Consider general equity market uncertainty• Consider estimates for other companies in same

industry• Use judgment to arrive at an estimate


3/e Weston - 87

– Methodology focuses on current market opportunity costs, not book or historical costs

– May use book or market values to provide guidelines

– Use judgment to estimate target financial proportions


3/e Weston - 88

• Merger premiums– It is wrong to conclude that number of shares

paid in a stock-for-stock deal is unimportant just because it is a paper-for-paper deal

– Premium paid decides the percentage of combined ownership each party to the merger will control

FIRM VALUATION IN MERGERS AND ACQUISITIONS-2

• DIVIDEND DISCOUNT MODELS

31 20 2 3 . . . . . . .

1 ( 1 ) ( 1 )

DD DV

k k k

W h e r e V o = v a l u e o f t h e f i r m

D i = d i v i d e n d i n y e a r I

k = d i s c o u n t r a t e


• THE CONSTANT GROWTH DDM2

0 00 2

( 1 ) ( 1 ). . . . . .

1 ( 1 )

D g D gV

k k

A n d th is e q u a t io n c a n b e s im p lif ie d to :

0 10

(1 )D g DV

k g k g

w h e re g = g ro w th ra te o f d iv id e n d s .


• CASH FLOW VALUATION MODELS- THE ENTITY DCF MODEL : THE ENTITY DCF MODEL VALUES THE VALUE OF A COMPANY AS

THE VALUE OF A COMPANY’S OPERATIONS LESS THE VALUE OF DEBT AND OTHER INVESTOR CLAIMS, SUCH AS PREFERRED STOCK, THAT ARE SUPERIOR TO COMMON EQUITY

. VALUE OF OPERATIONS: THE VALUE OF OPERATIONS EQUALS THE DISCOUNTED VALUE OF EXPECTED FUTURE FREE CASH FLOW.

. VALUE OF DEBT

. VALUE OF EQUITY

Net Operating Profit - Adjusted TaxesContinuing Value =

WACC

STEPS IN VALUATION

• ANALYZING HISTORICAL PERFORMANCE

NOPLATReturn on Investment Capital =

Invested Capital

FCF = Gross Cash Flow – Gross Investments

Economic Profit = NOPLAT – (Invested Capital x WACC)

STEPS IN VALUATION-2

• FORECAST PERFORMANCE - EVALUATE THE COMPANY’S STRATEGIC POSITION, COMPANY’S

COMPETITIVE ADVANTAGES AND DISADVANTAGES IN THE INDUSTRY. THIS WILL HELP TO UNDERSTAND THE GROWTH POTENTIAL AND ABILITY TO EARN RETURNS OVER WACC.

- DEVELOP PERFORMANCE SCENARIOS FOR THE COMPANY AND THE INDUSTRY AND CRITICAL EVENTS THAT ARE LIKELY TO IMPACT THE PERFORMANCE.

- FORECAST INCOME STATEMENT AND BALANCE SHEET LINE ITEMS BASED ON THE SCENARIOS.

- CHECK THE FORECAST FOR REASONABLENESS.

STEPS IN VALUATION-3• ESTIMATING THE COST OF CAPITAL

- DEVELOP TARGET MARKET VALUE WEIGHTS- ESTIMATE THE COST OF NON-EQUITY FINANCING - ESTIMATE THE COST OF EQUITY FINANCING

( 1 - )b c p s

B P SW A C C k T k k

V V V

w h e r e

k b = t h e p r e t a x m a r k e t e x p e c t e d y i e l d t o m a t u r i t y o n n o n - c a l l a b l e , n o n c o n v e r t i b l e d e b t

T c = t h e m a r g i n a l t a x e r a t e f o r t h e e n t i t y b e i n g v a l u e d

B = t h e m a r k e t v a l u e o f i n t e r e s t - b e a r i n g d e b t

k p = t h e a f t e r - t a x c o s t o f c a p i t a l f o r p r e f e r r e d s t o c k

P = m a r k e t v a l u e o f t h e p r e f e r r e d s t o c k

k s = t h e m a r k e t d e t e r m i n e d o p p o r t u n i t y c o s t o f e q u i t y c a p i t a l

S = t h e m a r k e t v a l u e o f e q u i t y

STEPS IN VALUATION-4• ESTIMATING THE COST OF EQUITY FINANCING - CAPM

. DETERMINING THE RISK-FREE RATE (10-YEAR BOND RATE)

. DETERMINING THE MARKET RISK PREMIUM 5 TO 6 PERCENT RATE IS USED FOR THE US COMPANIES

. ESTIMATING THE BETA

( )s f m fk r E r r

w h e r e r f = t h e r i s k - f r e e r a t e o f r e t u r n

E ( r m ) = t h e e x p e c t e d r a t e o f r e t u r n o n t h e o v e r a l l m a r k e t p o r t f o l i o

E ( r m ) - r f = m a r k e t r i s k p r e m i u m

В = t h e s y s t e m a t i c r i s k o f e q u i t y

STEPS IN VALUATION-5• THE ARBITRAGE PRICING MODEL (APM)

1 1 2 2( ) ( ) . . . .s f f fk r E F r E F r

w h e r e E ( F k ) = t h e e x p e c t e d r a t e o f r e t u r n o n a p o r t f o l i o t h a t m i m i c s t h e k t h f a c t o r a n d i s

i n d e p e n d e n t o f a l l o t h e r s .

B e t a k = t h e s e n t i v i t y o f t h e s t o c k r e t u r n t o t h e k t h f a c t o r .

STEPS IN VALUATION-6• ESTIMATING THE CONTINUING VALUE- SELECTING AN APPROPRIATE TECHNIQUE. LONG EXPLICIT FORECAST APPROACH . GROWING FREE CASH FLOW PERPETUITY FORMULA. ECONOMIC PROFIT TECHNIQUE

T+1 T+1Economic Profit (NOPLAT )( / )( )CV = +

( )

g ROIC ROIC WACC

WACC WACC WACC g

where

Economic Profit T+1 = the normalized economic profit in the first year after the explicit

forecast period.

NOPLAT T+1 = the normalized NOPLAT in the first year after the explicit forecast period.

g = the expected growth rate of return in NOPLAT in perpetuity

ROIC = the expected rate of return on net new investment.

WACC = weighted average cost of capital

STEPS IN VALUATION-7

• CALCULATING AND INTERPRETING RESULTS - CALCULATING AND TESTING THE RESULTS- INTERPRETING THE RESULTS WITHIN THE

DECISION CONTEXT

FIRM VALUATION : DIVIDEND PAYOUT MODEL

103FGS

USING CAPM TO ESTIMATE EXPECTED RETURNS

• EXPECTED RETURN DEPENDS ON:– RISK-FREE INTEREST RATE– EXPECTED MARKET RISK PREMIUM– BETA

• EXAMPLE:– EXP. RETURN ON EXXON STOCK = 4.8% + (.61 X 9%) = 10.3%

• COMPARE PROJECT RETURN AND OPPORTUNITY COST OF CAPITAL– SECURITY MARKET LINE PROVIDES A STANDARD FOR PROJECT

ACCEPTANCE. IF PROJECT IRR ABOVE SML => ACCEPT THE PROJECT

104FGS

Standard deviation of rates of return (1926-1998)

(in %) Standard deviationT bills 3.2 Government bonds 9.2 Common stocks 20.3

105FGS

Rates of Return 1926-1997

Source: Ibbotson Associates

-60

-40

-20

0

20

40

60

26 30 35 40 45 50 55 60 65 70 75 80 85 90 95

Common Stocks

Long T-Bonds

T-Bills

Year

Perc

enta

ge R

etur

n

106FGS

Average rates of return (1926-1998)

(in %) Average return Av. Risk premiumT bills 3.80 - Government bonds 5.70 1.90 Corporate bonds 6.10 2.30 Common stocks 13.20 9.40

107FGS

Markowitz Portfolio Theory

• Combining stocks into portfolios can reduce standard deviation below the level obtained from a simple weighted average calculation.

• Correlation coefficients make this possible.• The various weighted combinations of stocks

that create this standard deviations constitute the set of efficient portfolios.

The Normal Distributiond N(d) d N(d) d N(d)

-3.00 0.0013 -1.00 0.1587 1.05 0.8531 -2.95 0.0016 -0.95 0.1711 1.10 0.8643 -2.90 0.0019 -0.90 0.1841 1.15 0.8749 -2.85 0.0022 -0.85 0.1977 1.20 0.8849 -2.80 0.0026 -0.80 0.2119 1.25 0.8944 -2.75 0.0030 -0.75 0.2266 1.30 0.9032 -2.70 0.0035 -0.70 0.2420 1.35 0.9115 -2.65 0.0040 -0.65 0.2578 1.40 0.9192 -2.60 0.0047 -0.60 0.2743 1.45 0.9265 -2.55 0.0054 -0.55 0.2912 1.50 0.9332 -2.50 0.0062 -0.50 0.3085 1.55 0.9394 -2.45 0.0071 -0.45 0.3264 1.60 0.9452 -2.40 0.0082 -0.40 0.3446 1.65 0.9505 -2.35 0.0094 -0.35 0.3632 1.70 0.9554 -2.30 0.0107 -0.30 0.3821 1.75 0.9599 -2.25 0.0122 -0.25 0.4013 1.80 0.9641 -2.20 0.0139 -0.20 0.4207 1.85 0.9678 -2.15 0.0158 -0.15 0.4404 1.90 0.9713 -2.10 0.0179 -0.10 0.4602 1.95 0.9744 -2.05 0.0202 -0.05 0.4801 2.00 0.9772 -2.00 0.0228 0.00 0.5000 2.05 0.9798 -1.95 0.0256 0.05 0.5199 2.10 0.9821 -1.90 0.0287 0.10 0.5398 2.15 0.9842 -1.85 0.0322 0.15 0.5596 2.20 0.9861 -1.80 0.0359 0.20 0.5793 2.25 0.9878 -1.75 0.0401 0.25 0.5987 2.30 0.9893 -1.70 0.0446 0.30 0.6179 2.35 0.9906 -1.65 0.0495 0.35 0.6368 2.40 0.9918 -1.60 0.0548 0.40 0.6554 2.45 0.9929 -1.55 0.0606 0.45 0.6736 2.50 0.9938 -1.50 0.0668 0.50 0.6915 2.55 0.9946 -1.45 0.0735 0.55 0.7088 2.60 0.9953 -1.40 0.0808 0.60 0.7257 2.65 0.9960 -1.35 0.0885 0.65 0.7422 2.70 0.9965 -1.30 0.0968 0.70 0.7580 2.75 0.9970 -1.25 0.1056 0.75 0.7734 2.80 0.9974 -1.20 0.1151 0.80 0.7881 2.85 0.9978 -1.15 0.1251 0.85 0.8023 2.90 0.9981 -1.10 0.1357 0.90 0.8159 2.95 0.9984 -1.05 0.1469 0.95 0.8289 3.00 0.9987 -1.00 0.1587 1.00 0.8413

d1

N(d1)

VALUATION , PORTFOLIO MANAGEMENT & INVESTMENT PHILOSOPHY

• FUNDAMENTAL ANALYST• FRANCHISE BUYER• CHARTISTS• INFORMATION TRADERS• MARKET TIMERS • EFFICIENT MARKETERS

BEST & THE WORST DECADE OF S&P 500 STOCK PERFORMANCE IN U.S.A

Courtesy : Ibbotson Associates

http://www.ibbotson.com/

ESTIMATION OF EQUITY RISK PREMIUM PERIOD : 1926-1995

Investment

geom. mean

arith.mean std high ret. low ret.

S&P total return 10.30 12.45 22.28 42.56 -29.73

U.S. Small Stock TR 12.28 17.28 35.94 73.46 -36.74

U.S. LT Govt TR 4.91 5.21 8.00 15.23 -8.41

U.S. LT Corp. TR 5.49 5.73 7.16 13.76 -8.90

U.S. 30 day T-Bills 3.70 3.70 .96 1.35 -0.06

Summary Statistics of U.S. Investments from 1926 through March, 1995. Source:Ibbotson Associates

M&A DRIVERS: A SURVEY RESULT

3 HARD KEYS TO SUCCESSFUL M&A

KEY AREAS TARGETED FOR SYNERGY

3 SOFT KEYS FOR SUCCESSFUL MERGERS

VALUATION OF FIRMS IN MERGERS AND ACQUISITIONS

OKAN BAYRAK

Definitions• A merger is a combination of two or more

corporations in which only one corporation survives and the merged corporations go out of business.

• Statutory merger is a merger where the acquiring company assumes the assets and the liabilities of the merged companies

• A subsidiary merger is a merger of two companies where the target company becomes a subsidiary or part of a subsidiary of the parent company

Types of Mergers

• Horizontal Mergers- between competing companies

• Vertical Mergers- Between buyer-seller relation-ship companies

• Conglomerate Mergers- Neither competitors nor buyer-seller relationship

History of Mergers and Acquisitions Activity in United States

• The First Wave 1897-1904 - After 1883 depression- Horizontal mergers- Create monopolies

• The Second Wave 1916-1929- Oligopolies- The Clayton Act of 1914

• The Third Wave 1965-1969 - Conglomerate Mergers- Booming Economy

• The Fourth Wave 1981-1989 - Hostile Takeovers- Mega-mergers

• Mergers of 1990’s - Strategic mega-mergers

Motives and Determinants of Mergers

• Synergy Effect

- Operating Synergy- Financial Synergy• Diversification • Economic Motives - Horizontal Integration - Vertical Integration - Tax Motives

NAV= Vab –(Va+Vb) – P – E

Where Vab = combined value of the 2 firms

Vb = market value of the shares of firm B.

Va = A’s measure of its own value

P = premium paid for B

E = expenses of the operation

HP-COMPAQ MERGER CASE The HP/Compaq merger. By The Numbers:

HIGH-END

High-end Unix Servers: Worldwide (2000)

Factory

Revenues ($m) Market Share

Hewlett-Packard 512 11.4%

Compaq 134 3.0%

Closest Rival: Sun Microsystems with factory revenues of $2.1 billion and a 47.1% market share

High-end Unix servers: US (2000)

Factory



Compaq 66 3.3%

Closest Rival: Sun Microsystems with factory revenues of $1.2 billion and a 60.1% market share

MID-RANGE

Mid-range Unix servers: Worldwide (2000)

Factory


Hewlett-Packard 3,673 30.3%

Compaq 488 4.0%

Closest Rival: Sun Microsystems with $2.8 billion in factory revenue and a 23.5% market share

Mid-range Unix servers: US (2000)

Factory



Compaq 296 5.4%

Market Leader: Sun Microsystems with revenues of $1.7 billion and a 30.5% market share)

PERSONAL COMPUTERS

PC Shipments: Worldwide (in thousands of units)

Hewlett- Packard Compaq

Units (q2/01) 2,065 3,590

Share (q2/01) 6.9% 12.1%

Units (q2/00) 2,260 4.011

Share(q2/00) 7.4% 13.2%

Growth -8.6% -10.5%

PC Shipments: US(in thousands of units)


Units (q2/01) 991 1,332

Share (q2/01) 9.4% 12.7%

Units (q2/00) 1,221 2,293

Share(q2/00) 10.7% 20.1%

Growth -18.8% --21.3%

Market leader: Dell Computer Corp. with a 24% market share and a 9.8% growth in the same period.

LAPTOPS/NOTEBOOKS SMART HANDHELDS

Worldwide shipments of portable computers (thousands of units)


Units(q4/00) 318 817

Share(q4/00) 4.5% 11.6%

Units(q4/99) 139 739

Shipments (in 000s)

Share 2000 Rank

Hewlett-Packard 254 3.8% 4

Compaq 129 1.9% 9 Market Leader: Palm with a 52.9% market share and 3.53 million units.

HP-COMPAQ MERGER CASE-2

• Arguments About The Merger- Supporters. HP-COMPAQ will become the leader in most of the sub-sectors . Ability to offer better solutions to customer’s demands . New strategic position will make it possible to increase R&D

efforts and customer research . Decrease in costs and increase in profitability. Financial strength to provide chances to invest in new profitable

areas


• Arguments About The Merger- Opponents. Acquiring market share will not mean the leadership . No new significant technology capabilities added to HP . Large stocks will increase the riskiness of the company (Credit

rating of the HP is lowered after the merger announcement) . Diminishing economies of scale sector which both companies

have already a great scale.


• Valuation Process- Relative Historical Stock Price Performance

Historical Exchange Ratios

Period ending August 31,

2001

Average Exchange Ratio Implied Premium (%)

August 31 2001 0.532 18.9

10-Day Average 0.544 16.3

20-Day Average 0.568 11.3

30 Day Average 0.573 10.3

3 Months Average 0.557 13.7





• Comparable Public Market Valuation Analysis

Firm Values As a Multiple of Revenue EBITDA and LTM EBIT

Firm Values as a Multiple of

Companies LTM Revenue LTM EBITDA LTM EBIT

Compaq 0.5 X 5.7 X 9.8 X

HP 1.0 X 12.4 X 19.8 X

Selected Group 0.2-2.1 X 5.3-18.2 X 8.9-19.9 X

Closing Stock Prices As a Multiple of EPS

Closing Stock Price as a Multiple of

Companies 2001 EPS 2002 EPS 2003 EPS

Compaq 34.3 X 18.4 X 14.0 X

HP 35.7 X 19.2 X 12.5 X

Selected Group 18.5-57.3 X 10.7-27.1 X 9.3-19.5 X

HP-COMPAQ MERGER CASE-6• Similar Transactions Premium Analysis

• Salomon Smith Barney's analysis resulted in a range of premiums of: - (8)% to 46% over exchange ratios implied by average prices for the 10 trading days prior to

announcement, with a median premium of 23%.- (7)% to 58% over exchange ratios implied by average prices for the 20 trading days prior to announcement, with a median premium of 23%. - (12)% to (29) over exchange ratios implied by average prices for the 1 trading days prior to announcement with a median premium of 15%.

Based on its analysis, Salomon Smith Barney determined a range of implied exchange ratios of 0.585x to 0.680x by applying the range of premiums for other transactions to the closing prices of Compaq and HP on August 31, 2001 and the average historical exchange ratio for Compaq and HP for the 10-day period ending on August 31, 2001, as appropriate.

HP-COMPAQ MERGER CASE-7• Contribution Analysis

Percentage Contribution Analysis Percentage

Contribution

Period Compaq HP

Revenues LTM 46.0 54.0 2001 Estimated 44.0 56.0 2002 Estimated 44.0 56.0 2003 Estimated 44.0 56.0 LTM 45.7 54.3 2001 Estimated 38.1 61.9 2002 Estimated 36.9 63.1 2003 Estimated 32.7 67.3 Net Income 2001 Estimated 32.3 67.7 Next Four Fiscal Q 31.6 68.4 2002 Estimated 32.7 67.3 2003 Estimated 29.2 70.8 At Market Equity Value 31.7 68.3


• Pro Forma Earnings Per Share Impact to Compaq

Accretion/Dilution Analysis

Accretion/Dilution

EPS

2002

EPS

2003

Compaq stand-alone 0.67 0.88

HP stand-alone 1.21 1.86

Combined entity pro-forma, excluding proj. synergies 0.74 1.09

Combined entity pro-forma, including proj. synergies 1.05 1.51

Accretion/(Dilution) to Compaq, excluding proj. synergies 11% 24%

Accretion/(Dilution) to Compaq, including proj. synergies 57% 71%

MYTHS OF VALUATION

• VALUATION IS OBJECTIVE• A WELL RESEARCHED VALUATION IS TIMELESS• A GOOD VALUATION ESTIMATES ACCURATELY. • MORE QUANTITATIVE A MODEL BETTER

VALUATION• THE MARKET IS GENERALLY WRONG• VALUE IS WHAT MATTERS NOT THE PROCESS

OF VALUATION

APPROACHES TO VALUATION

• SINGLE PERIOD CAPITALISATION• MULTIPLE PERIOD DISCOUNTED CASHFLOW• RELATIVE (COMPARABLE COMPANY)

VALUATION• ADJUSTED BOOK VALUE• LIQUIDATION VALUE• REPLACEMENT COST• OPTION PRICING MODEL

VALUATION OF COMMON STOCK WITH CONSTANT DIVIDEND GROWTH

• ASSUMPTION 1 : HOLDING PERIOD IS INDEFINITE (THIS DISPENSES THE NEED FOR FORECASTING A FUTURE SELLING PRICE).

• ASSUMPTION 2 : THE DIVIDEND PAYMENT GROWS AT A CONSTANT RATE

• THE SECOND ASSUMPTION PREDICTS EACH & EVERY FUTURE DIVIDEND, SO LONG AS THE MOST RECENT DIVIDEND & THE GROWTH RATE ARE KNOWN

Two-Stage DDM Valuation Model (cont.)

• The two-stage growth model is not a complex as it seems:– The first term is simply the present value of the first N dividends (those before

the constant growth period)– The second term is the present value of the future stock price.

– So, the model is just a mathematical formulation of the methodology that was presented earlier. It is nothing more than an equation to calculate the present value of a set of cash flows that are expected to follow a particular growth pattern in the future.

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Three-Stage DDM Valuation Model

• One improvement that we can make to the two-stage DDM is to allow the growth rate to change slowly rather than instantaneously.

• The three-stage DDM is given by:

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Common Stock Valuation: An Example

• Assume that you are considering the purchase of a stock which will pay dividends of $2 (D1) next year, and $2.16 (D2) the following year. After receiving the second dividend, you plan on selling the stock for $33.33. What is the intrinsic value of this stock if your required return is 15%?

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Some Notes About Common Stock

• In valuing the common stock, we have made two assumptions:– We know the dividends that will be paid in the future.– We know how much you will be able to sell the stock

for in the future.• Both of these assumptions are unrealistic,

especially knowledge of the future selling price.• Furthermore, suppose that you intend on holding

on to the stock for twenty years, the calculations would be very tedious!

The DDM Example (cont.)

• In the earlier example, how did we know that the stock would be selling for $33.33 in two years?

• Note that the period 3 dividend must be 8% larger than the period 2 dividend, so:

• Remember, the value at period 2 is simply the present value of D3, D4, D5, …, D∞

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The Dividend Discount Model (DDM)• For a COMMON stock, there are two cash flows:

– Future dividend payments– The future selling price

• If we make the following assumptions, we can derive a simple model for common stock valuation:– Your holding period is infinite (i.e., you will never sell the stock so you don’t have to worry about forecasting a future selling price).– The dividends will grow at a constant rate forever.

• Note that the second assumption allows us to predict every future dividend, as long as we know the most recent dividend and the growth rate.

• With these assumptions, we can derive a model that is variously known as the Dividend Discount Model, the Constant Growth Model, or the Gordon Model:

• This model gives us the present value of an infinite stream of dividends that are growing at a constant rate.

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Estimating the DDM Inputs

• The DDM requires us to estimate the dividend growth rate and the required rate of return.

• The dividend growth rate can be estimated in three ways:– Use the historical growth rate and assume it will continue– Use the equation: g = br– Generate your own forecast with whatever method seems appropriate

• The required return is often estimated by using the CAPM: ki = krf + i(km – krf) or some other asset pricing model.

The DDM: An Example

• Recall our previous example in which the dividends were growing at 8% per year, and your required return was 15%.

• The value of the stock must be (D0 = 1.85):

• Note that this is exactly the same value that we got earlier, but we didn’t have to use an assumed future selling price.

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The DDM Extended

• There is no reason that we can’t use the DDM at any point in time.

• For example, we might want to calculate the price that a stock should sell for in two years.

• To do this, we can simply generalize the DDM:

• For example, to value a stock at year 2, we simply use the dividend for year 3 (D3).

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The DDM Example (cont.)

• In the earlier example, how did we know that the stock would be selling for $33.33 in two years?

• Note that the period 3 dividend must be 8% larger than the period 2 dividend, so:

• Remember, the value at period 2 is simply the present value of D3, D4, D5, …, D∞

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What if Growth Isn’t Constant?• The DDM assumes that dividends will grow at a constant rate

forever, but what if they don’t?• If we assume that growth will eventually be constant, then we

can modify the DDM.• Recall that the intrinsic value of the stock is the present value

of its future cash flows. Further, we can use the DDM to determine the value of the stock at some future period when growth is constant. If we calculate the present value of that price and the present value of the dividends up to that point, we will have the present value of all of the future cash flows.

What if Growth Isn’t Constant? (cont.)

• Let’s take our previous example, but assume that the dividend will grow at a rate of 15% per year for the next three years before settling down to a constant 8% per year. What’s the value of the stock now? (Recall that D0 = 1.85)

0 1 2 3 4

2.1275 2.4466 2.8136 3.0387 …

g = 15% g = 8%

What if Growth Isn’t Constant? (cont.)

• First, note that we can calculate the value of the stock at the end of period 3 (using D4):

• Now, find the present values of the future selling price and D1, D2, and D3:

• So, the value of the stock is $34.09 and we didn’t even have to assume a constant growth rate. Note also that the value is higher than the original value because the average growth rate is higher.

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Two-Stage DDM Valuation Model

• The previous example showed one way to value a stock with two (or more) growth rates. Typically, such a company can be expected to have a period of supra-normal growth followed by a slower growth rate that we can expect to last for a long time.

• In these cases we can use the two-stage DDM:

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Two-Stage DDM Valuation Model (cont.)

• The two-stage growth model is not a complex as it seems:– The first term is simply the present value of the first N dividends (those before

the constant growth period)– The second term is the present value of the future stock price.

– So, the model is just a mathematical formulation of the methodology that was presented earlier. It is nothing more than an equation to calculate the present value of a set of cash flows that are expected to follow a particular growth pattern in the future.

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Three-Stage DDM Valuation Model

• One improvement that we can make to the two-stage DDM is to allow the growth rate to change slowly rather than instantaneously.

• The three-stage DDM is given by:

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Other Valuation Methods

• Some companies do not pay dividends, or the dividends are unpredictable.

• In these cases we have several other possible valuation models:– Earnings Model– Free Cash Flow Model– P/E approach– Price to Sales (P/S)


3/e Weston - 149

FIRM VALUATION IN M&A FORMULA APPROACH

• No real distinction between spreadsheet approach and formula approach– Both use discounted cash flow analysis– Spreadsheet approach expressed in form of

financial statements over period of time– Formula approach summarizes same data in

compact form– Formula approach helps focus on underlying

drivers of valuation


3/e Weston - 150

• Development of compact valuation formulas– Valuation necessarily requires forecasts– Usually assumes systematic relations between

time periods, variables• Key variables and relationships

– Revenues (Rt)• Basic driver of a firm's value• Market value to revenue multiples usually calculated

for comparing values of firm in same industry• Main approach to valuing Internet stocks


3/e Weston - 151

– Growth rate (g)• Defined as rate of change in revenues• Growth rate will mirror various combinations of cash

flow patterns that reflect ebb and flow of strategic and competitive factors

– Net operating income margin (m) after deducting operating costs from revenues including:

• Cost of goods sold• Selling, general, and administrative expenses• Depreciation expenses

– Actual tax rate (T)


3/e Weston - 152

– Investment (It)• Investment as a ratio of revenues• Defined as the change in total capital over the

previous period • Change in total capital

– Investment in working capital, gross or net– Investment in fixed assets, gross or net

– Number of periods of supernormal growth (n)• Defined by firm's competitive advantage• Supernormal growth period will end when

competition erodes the firm's competitive advantage


3/e Weston - 153

– Marginal weighted cost of capital (k)• Cost of equity• After-tax cost of debt• Weighted average of the two based on target

financing proportions

– Value drivers for net operating income margin (m) and investment (I) are expressed as a percentage of sales — could be obtained through a linear regression relationship with revenues


3/e Weston - 154

• Sensitivity analysis– Purpose

• Check impact of a range of alternative possibilities• Provide framework for planning and control

– Sensitivity analysis of model variables:• Decrease in revenues growth rate (g) lowers valuation• Increase in investment requirement percentage (I)

lowers valuation• Operating profit margin (m) is a powerful value driver

— when m is increased, valuation increases


3/e Weston - 155

• Valuation is very sensitive to the cost of capital (k) used in analysis — when cost of capital is increased, valuation falls

• Sensitivity to n and T predictable in direction and magnitude

– When period of supernormal growth is reduced, valuation is reduced

– When tax rate is reduced, valuation is increased

– In many practical cases, second term in valuation model represents a higher proportion of valuation than first term — must be careful as to assumptions about factors affecting exit or terminal value


3/e Weston - 156

• Limitations of the formula approach– Less flexibility in reflecting forecasts for

individual years– Calculations use financial statement data not

directly shown in the formulas

The Free Cash Flow Model

• Free cash flow is the cash flow that’s left over after making all required investments in operating assets:

• Where NOPAT is net operating profit after tax• Note that the total value of the firm equals

the value of its debt plus preferred plus common:

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The Free Cash Flow Model (cont.)

• We can find the total value of the firm’s operations (not including non-operating assets), by calculating the present value of its future free cash flows:

• Now, add in the value of its non-operating assets to get the total value of the firm:

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The Free Cash Flow Model (cont.)

• Now, to calculate the value of its equity, we subtract the value of the firm’s debt and the value of its preferred stock:

• Since this is the total value of its equity, we divide by the number of shares outstanding to get the per share value of the stock.

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Principles of valuation

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