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Equity ValuationDated:16th Sep 2012.

Important Terms The Nature of Equity Securities Preferred Share Valuation Valuation of Equities Constant Growth Model Multistage Growth Model H - Model Using Multiples to Value Shares Retained Earnings Valuation.

Common share Constant growth DDM Dividend discount model Equity securities Enterprise Value to EBIT ratio Enterprise Value to EBITDA

ratio Price-to-Book Value ratio H- Ratio Retained Earnings. Du-Pont Model.

Preferred share Price-earnings ratio Price-to-cash-flow ratio Price-to-sales ratio Relative valuation Sustainable growth rate

Equity Valuation

Equities represent ownership claims onbusinesses.

Despite having residual claims to earnings aftertax and to assets upon dissolution equities offerthe prospect for participation in the growth andprofitability of the business.

Equity securities can be valued based onapproaches using the present value of expectedfuture dividend stream.

Equity Securities

Include preferred (Disputed) and common shares.

Represent ownership claims on the underlying entity.

Usually have no specified maturity date, and since theunderlying entity has a life separate and apart fromit’s owners, equities are treated as investments withinfinite life.

Equities may pay dividends from after-tax earnings atthe discretion of the board of directors.

Have some preference over the common share class Usually have the following characteristics:

A fixed annual dividend (not legally enforceable by shareholders if not declared)

Have prior claim to dividends and assets upon dissolution/liquidation over and above the common shares

Non-voting – except if dividends are in arrears (Cumulative). No maturity date Often have a cumulative feature (dividends in arrears must be paid

before common shareholders can receive dividends) Often called a ‘fixed income’ investment because the regular annual

dividend is fixed (set) at the time the shares are originally issued.

Equity Valuation

Premium.Risk * R f eK

Valuation of equities can follow a discounted cash flow approach.

The discount rate used reflects current levelof interest rates (based on the risk-free rate)plus a risk premium.

This relationship is expressed as:

The risk-free rate is

equal to the real rate of

return plus expected

inflation (Fisher

Equation)

The risk premium is

based on an estimate of

the risk associated with

the security.

[ 7-1]

Risk of Equity

Security M

Required

Return (%)

RF

Risk

Required

return on

Equity

Security (M) Risk

Premium

Real Return

Expected Inflation Rate

Equity Valuation

Pps is the market price (or present value)Dp is the annual dividend amountkp is the required rate of return investors demand (or discount rate)

p

p

psk

DP

Preferred shares can be viewed as perpetuities because of the nature of thedividend stream they offer.

A perpetuity is an infinite series of equal and periodic cash flows.

Determine the market price of a $100 par value preferred share that

pays dividend based on a 7 percent dividend rate when investors require a return of 10 percent on the investment.

What happens to the market price if interest rates rise and investors now require a 12 percent rate of return on the investment?

00.70$10.0

00.7$

10.0

100$07.

p

p

psk

DP[ 7-2]

33.58$12.0

00.7$

12.0

100$07.

p

p

psk

DP[ 7-2]

What happens to the market price if interest rates fall and investors

now require a 7 percent rate of return on the investment?

Like bonds, when the required return is equal to the preferred

dividend rate, the preferred will be priced to equal its par value.

00.100$07.0

00.7$

07.0

100$07.

p

p

psk

DP[ 7-2]

The preferred share valuation equation can be modified to solve for

the investor’s required rate of return.

Remember, for market traded preferred shares, the stock price will be observable (known) and so too will the annual dividend, so this type of calculation is very common.

ps

p

pP

Dk [ 7-3]

Assuming the previous 7%, $100 par value preferred share is currently trading for $57.25, what is the implied market-demanded required return?

You knew that the share was trading for less than its par value, so even

before trying to solve for the answer, you should have known that

investors were requiring a higher rate of return than 7%.

%22.1225.57$

00.7$

25.57$

100$07.

ps

p

pP

Dk[ 7-3]

So How do we value a Preference Share which is set to retireafter a given period of time??

Kp = { Dividend + [Redemption Value – Net Proceeds]Number of Preference share issue }

[Redemption Value + Net Proceeds]2

Where,Net Proceeds = Market Price of Preference Share * (1-Floatation Cost)

Equity Valuation

All discount valuation models estimate the current economic value of anysecurity as the sum of the discounted (present) value of all promised future cashflows.

The current value is therefore a function of the timing, magnitude and riskiness of all future cash flows:

n

ii

i

n

n

k

FlowCash

k

FlowCash

k

FlowCash

k

FlowCashV

1

2

2

1

10

)1(

)1(

...)1()1(

In the case of common stock the cash flows of a going-concern business are expected to go on in perpetuity (forever).

The purchaser exchanges the price she/he paid for the investment at time O with a possible series of future cash flows.

Risk is factored into the equation through k (investor’s required return)

1

2

2

1

10

)1(

)1(

...)1()1(

ii

i

k

FlowCash

k

FlowCash

k

FlowCash

k

FlowCashV

Remember, the amount and timing of future dividends (if that is the cash flow you are using) is highly uncertain for most businesses because dividends are not fixed obligation of the firm, but rather are declared at the discretion of the board of directors, when, and if the firm is profitable, and doesn’t have other uses for the cash.

1

2

2

1

10

)1(

)1(

...)1()1(

ii

i

k

FlowCash

k

FlowCash

k

FlowCash

k

FlowCashV

The DDM says the intrinsic value or inherent economic worth of the stock is equal to the sum of the present value of all future dividends to be received.

n

e

n

ee k

D

k

D

k

DP

)1(...

)1()1( 2

2

1

10

[ 7-4]

Security analysts that use the DDM model are called FUNDAMENTALANALYSTS because they base the estimate of inherent worth on theeconomic fundamentals of the stock.

Once they have estimated the inherent worth, they compare theirestimate with the actual stock price in the market to determine whetherthe stock is UNDER, OVER, or FAIRLY valued.

12

2

1

10

)1()1(...

)1()1( tt

e

t

eee k

D

k

D

k

D

k

DP

When the firm’s dividends are growing at a slow, constant rate, and

reasonably can be expected to do so for the foreseeable future, we use the constant growth dividend discount model.

Which can be simplified by multiplying D0 by a factor of (1+g)/(1+kc)

every period to get:

)1(

)1(...

)1(

)1(

)1(

)1( 0

2

2

0

1

1

0

0

eee k

gD

k

gD

k

gDP

[ 7-6]

gk

D

gk

gDP

ee

10

0

)1(

The Constant Growth DDM can be reorganized to solve for the investor’s required return

This formula can be decomposed into two components, demonstrating thatequity investors receive two forms of prospective income from theirinvestment, dividends and capital gains.

YieldGain Capital Yield DividendCurrent

0

1

g

P

Dkc

gP

Dke

0

1[ 7-8]

Assuming the firm has no profitable growth opportunities g should be equal to 0, and D1=EPS1 Or RoE = Ke resulting in 100% Payout.

The Constant Growth DDM reduces to:

Therefore, the share price of any constant growth common stock is made up of two components:▪ The no-growth components or ROE = Ke and▪ The present value of growth opportunities

This can be expressed as:

ek

EPSP 1

0

Decomposing the constant-growth DDM into its twocomponents gives us an analytical tool to examine thetwo sources of current value of the firm.

iesopportunitgrowthofvaluepresentcomponentgrowthno

PVGOk

EPSP

c

10

[ 7-10]

The formula assumes that the growth rate will remain the same inperiod 1 through infinity.▪ This is a very long period of time

▪ Because of compounding over time, small changes in g will have dramaticeffects on the estimated stock value today.

▪ If g is assumed to be greater than kc a non-sense answer would result. Inpractice this could never happen because no company can continue togrow at compound rates of return to infinity at a rate that exceeds thelong-term rate of growth in the economy.

gk

DP

c 1

0[ 7-7]

The formula predicts stock price increases if:▪ D1 is increased

▪ g is increased

▪ Ke is decreased

Conversely, the formula predicts stock price increases if:▪ D1 is decreased

▪ g is decreased

▪ Ke is increased

gk

DP

e 1

0

Sustainable growth can be estimated using the following equation:

Where: b = the firm’s earnings retention ratio

= (1 – firm’s dividend payout ratio)

and

ROE = firm’s return on common equity

= net profit/common equity

ROEbg [ 7-11]

Clearly, the value of the firm will rise if the firm retains and

reinvests its profits at a rate of return (ROE) greater than kc

Under such conditions, g increases more than kc

Decomposing ROE using the DuPont system allows managers to see how they can increase the value of the firm:

▪ increase the profit margin on sales

▪ Increase the turnover rate on sales

▪ Leverage the firm using less equity and more debt (although use of more debt implies higher risk and the benefits may be offset by a higher kc)

ROEbg [ 7-11]

Ratio Leverage RatioTurnover Margin Profit Net

Equity

Assets Total

Assets Total

Sales

Sales

incomeNet ROE

[ 7-12]

Firms with earnings that are growing rapidly (more rapid than the general rate of economic expansion) require another approach.

Remember, no firm’s growth in earnings can exceed the general rate of economic expansion forever…at some point, earnings growth will fall.

... 54321 gggggg

Time

Earnings

g1= 50%

g2= 30%

g3= g4= gα=4%

2

2

2

2

1

1

2

3210

2

210

1

100

)1()1()1(

)1(

)1)(1)(1(

)1(

)1)(1(

)1(

)1(

eee

e

e

ee

k

P

k

D

k

D

k

gk

gggD

k

ggD

k

gDP

Predict each dividend during the high growth years.

Predict the first dividend during the constant growth years.

Discount the individual dividends to the present and sum together with theprice at time t when the constant growth model is used.

The following is the formula you would use for two years of high earningsgrowth followed by a constant growth in years three through infinity.

Forecast Assumptions: Investor’s required return = k = 10.9% Most recent dividend per share = D0 = $0.25 Growth rate in first year = g1 =14.8% Growth rate in second year= g2 = 10% Growth rate in years three through infinity = g3-α = 5%

08.5$)109.1(

62.5$

)109.1(

32.0$

)109.1(

29.0$

)109.1(

05.109.

)05.1)(1.1)(148.1(25.0$

)109.1(

)1.1)(148.1(25.0$

)109.1(

)148.1(25.0$

)1()1()1(

22

221

2

2

210

ccc k

P

k

D

k

DP

Time

Dividend / Price

Calculation

Dividend

/Price

Present

Value

Factor

Present

Value

1 $0.25 X (1+.148) = $0.29 0.901713 $0.26

2 $0.287 X (1+.1) = $0.32 0.813087 $0.26

2 P(2) = D(3)/ (.109 - .05) = $5.62 0.813087 $4.57

Intrinsic Value Estimate = $5.08

The Model predictions are highly sensitive to changes in g and kc

Not helpful in valuing non-dividend paying firms.

gk

DP

c 1

0[ 7-7]

Use of the Model is best suited to:

Firms that pay dividends based on a stable dividendpayout history that are likely to maintain that practiceinto the future.

Are growing at a steady and sustainable rate.

This model works for large corporations in matureindustries such as banks and utility companies.

H-Model developed by Fuller & Hsia (1984). It is also an extension of Two-Stage Model. In this model, growth begins at a High rate and declines

linearly throughout Supernormal growth period until itreaches a normal rate at the end.

Where, r = required rate of return on equity. H=Half-Life in years of high-growth period. Gs = Initial Short Term dividend growth rate. GL = Normal Long-Term dividend growth rate afterYear 2H.

)(

))((

)(

)1( 000

L

Ls

L

L

Gr

GGHD

Gr

GDV

Siemens A.G(Frankfurt :SIE) has current dividend of Є1.00.Dividend Growth rate is 29.28%, declining linearly over a 16 yearperiod to a final and Perpetual growth rate of 7.26%. Rf is 5.34%and Beta of Company against DAX is 1.37.

Using CAPM to find out Required rate of return i.e 12.63%.

Use H – Model to value Per share estimate:

)0726.01263.0(

)0726.028.29.0)(8(00.1

77.52

)0726.01263.0(

)07261(00.1 .0

V

Equity Valuation

Relative valuation approaches estimate thevalue of common shares by comparing marketprices of similar companies, relative to somevariable such as: Earnings EBITDA Cash flow Book value Sales

The challenge is finding the right comparable!!

Also known as the price-earnings multiple.

The ratio tells you how many times projected annual earnings (per

share) the share is currently trading

If you buy a company that is trading 10 times projected earnings, it

will take 10 years of those earnings to recover your investment.

If you buy a company trading 100 times projected earnings, it will

take 100 years of those earnings to simply recover your investment

(not including any time value of money or return on your

investment).

1

01

10

E

PEPS

ratio P/E JustifiedEPS Estimated

P

[ 7-13]

Given the constant growth DDM

Divide both sides by expected earnings per share.

Notice that D1/EPS1 is the expected dividend payout ratio at time 1.

The following equation indicates: The higher the expected payout ratio, the higher the P/E The higher the expected growth rate, g, the higher the P/E The higher the required rate of return, Ke the lower the P/E

gk

DP

e 1

0

gk

EPS

D

E

P

EPS

P

e 1

1

1

0

P/Es are uninformative when companies have negative (or very small)earnings

The volatility in earnings creates great volatility in P/Es throughout the business cycle.

Given the foregoing problems, analysts normally use smoothed orNormalized estimates of earnings for the forecast year, as well as using avariety of different approaches to develop a range of potential values forthe stock.

P/E Ratios in the Paper and Forest Products Sector

Company Price 2006

EPS

Forecast

EPS

P/E P/E

Forecast

TSX

Symbol

Abitibi 2.72 -0.30 0.12 nm 22.67 A

Canfor 11.13 -0.27 0.47 nm 23.68 CFP

Cascades 11.54 0.71 0.60 16.25 19.23 CAS

Canfor Pulp 11.56 1.38 1.20 8.38 9.63 CFX.UN

Catalyst 3.22 -0.07 0.03 nm nm CTL

Fraser Papers 7.01 -1.35 -0.41 nm nm FPS

International 6.6 0.26 0.53 25.38 12.45 IFPA

Mercer 9.69 -0.07 0.14 nm 54.35 MERC

Norbord 8.41 0.74 0.40 10.24 18.95 NBD

PRT 11.2 0.69 0.70 16.23 16.00 PRT.UN

SFK Pulp 4.14 0.64 0.82 6.47 5.05 SFK.UN

Tembec 1.43 -2.00 -1.11 nm nm TBC

TimberWest Forest14.07 0.01 -0.27 nm nm TWF.UN

West Fraser Timber37.45 0.94 2.35 39.84 15.94 WFT

Note: nm = not meaningful

Source: RBC Dominion Securities Inc., September 2006.

Large

number

of firms

with

negative

earnings

Price-to-Book Value (P/BV) ratio Price-to-sales (P/S) ratio Price-to-cash-flow (P/CF) ratio Enterprise Value to EBIT ratio Enterprise Value to EBITDA ratio

Shareper ValueBook

Shareper PriceMarket / ratioBVP

Multiply justifiable P/BV ratio times the firm’s book value per share to get anestimate of intrinsic value.

Advantages Book values provide a relatively stable, intuitive measure of value relative to

market values. Eliminates problems associated with P/E multiples because book values are rarely

negative and are not volatile.

Disadvantages Book values may be sensitive to accounting standards. Book values may be uninformative for companies with few fixed assets.

Multiply justifiable P/S ratio times the firm’s sales per share to get an estimate of intrinsic value

Advantages

Sales are relatively insensitive to accounting decisions and are never negative

Sales are not as volatile as earnings

Sales provide useful information about corporate decisions such as product pricing

Disadvantages

Sales do not provide information about expenses and profit margins which are key determinants of corporate performance.

Cash Flow is estimated as Net Income + Depreciation andAmortization + Deferred Taxes.

Multiply justifiable P/CF ratio times the firm’s cash flow per shareto get an estimate of intrinsic value.

Advantages

Reduces accounting concerns regarding earnings measurement

Multiply justifiable ratio times the firm’s forecast EBIT or EBITDA per share to get an estimate of intrinsic value.

Use Market Value of both Debt and Equity reflecting the fact that EBIT or EBITDA represents income available to satisfy the claims of both debt and equity holders.

Advantages

Using EBIT and EBITDA instead of net income eliminates volatility caused by EPS

Sales Volume 1 million units

Unit price $10 $10 million

Variable costs 5.0

Fixed cash costs 1.7

EBITDA 3.3

Depreciation 0.8

EBIT 2.5

Interest 0.5

EBT 2.0

Income Tax @ 50 percent 1.0

Net Income 1.0

Dividends 0.5

Book value of equity 5.0

Book value of debt 5.0

3.3

EV

EBITDA

CashMVEquityDebtMVratioEBITDA

2.5

EV

EBIT

CashMVEquityDebtMVratioEBIT

Use of comparative multiples is a popularapproach to valuing stock

Despite apparent simplicity of generating theratios, consideration of the accounting,volatility and other issues affecting theusefulness of these approaches.

Can we use Relative Valuation Techniquesin DCF to find out the Cost of Equity &Subsequently Price per share???

Retained Earnings / Reserves & Surplus / Internal Equity. Is it the same as Cost of Equity?? Kre = Ke

Can also be determined through Bond –Yield plus Risk Premium Approach.

Cost of Retained Earning < Cost of External Equity.

Ke1 = Kre

(1-f)