Security Analysis &

Portfolio Management “Equity Valuation"

ByB.Pani M.Com,LLB,FCA,FICWA,ACS,DISA,MBA

9731397829 bpani2001@yahoo.co.in

Features of Equity

• No defined life• No defined income• Fixed income securities have defined life and

cash flow. Therefore, they are easier to analyse than equity.

Technique of valuation• Balance sheet techniqueBook ValueLiquidation ValueReplacement cost• Discounted cash flow techniqueDividend discount modelFree cash flow model• Relative valuation techniquePrice Earning RatioPrice Book Value RatioPrice Sales Ratio

Book Value

• The book value per share is equal to net worth of the company divided by no of shares. Net worth of a company is equal to paid up equity capital plus reserves and surplus

Liquidation value

• The liquidation value per share is equal to value realised from the firm by liquidating all the assets of the firm minus amount to be paid to all creditors and preference shareholders divided by no of share.

• Limitation1.Difficult to estimate value to be realised.2. It does not reflect earning capacity

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Dividend Discount Model

• Cash Flows for Stockholders:• If you buy a share of stock, you can receive

cash in two ways– The company pays dividends– You sell your shares, either to another investor in

the market or back to the company

• As with bonds, the price of the stock is the present value of these expected cash

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One-Period Example

• Suppose you are thinking of purchasing the stock of Moore Oil, Inc. and you expect it to pay a $2 dividend in one year and you believe that you can sell the stock for $14 at that time. If you require a return of 20% on investments of this risk, what is the maximum you would be willing to pay?

• Compute the PV of the expected cash flows• Price = (14 + 2) / (1.2) = $13.33

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Two-Period Example

• Now what if you decide to hold the stock for two years? In addition to the dividend in one year, you expect a dividend of $2.10 in two years and a stock price of $14.70 at the end of year 2. Now how much would you be willing to pay?

• PV = 2 / (1.2) + (2.10 + 14.70) / (1.2)2 = 13.33

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Three-Period Example

• Finally, what if you decide to hold the stock for three years? In addition to the dividends at the end of years 1 and 2, you expect to receive a dividend of $2.205 at the end of year 3 and the stock price is expected to be $15.435. Now how much would you be willing to pay?

• PV = 2 / 1.2 + 2.10 / (1.2)2 + (2.205 + 15.435) / (1.2)3 = 13.33

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Developing The Model : Dividend Discount Model :

• You could continue to push back the year in which you will sell the stock.

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221

233

221

22

221

2210

332

221

110

)1()1()1()1(

)1(

)1/()(

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)1(

)1/()(

)1/()(

)1/()(

)1/()(P

R

P

R

D

R

D

R

D

R

RPD

R

D

R

D

R

P

R

D

R

D

R

RPDDP

RPDP

RPDP

RPD

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Dividend Discount model… contd..

• Likewise if one finds P3 in terms of D4 and P4 and P4 in terms of D5 and P5 the process will continue and you would find that the current price of the stock is really just the present value of all expected future dividends

• So, how can we estimate all future dividend payments?– in principle there can be infinite number of dividends and impossible to forecast so many dividends.

• -----There are some special cases when we can get around this problem.

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Special Cases • Constant dividend i.e zero growth rate of dividend

– The firm will pay a constant dividend forever– This is like preferred stock– The price is computed using the perpetuity formula

• Constant dividend growth– The firm will increase the dividend by a constant percent every

period• Supernormal growth initially and then normal growth till

perpetuity– Dividend growth is not consistent initially, but settles down to

constant growth eventually

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Special cases… contd..• 1)Zero Growth• If constant dividends are expected at regular intervals

forever, then this is a perpetuity and the present value of expected future dividends can be found using the perpetuity formula– P0 = D / R

• Suppose stock is expected to pay a $0.50 dividend every quarter and the required return is 2.5% per quarter. What is the price?

– P0 = .50 / (.1 / 4) = $20• Point to note : if dividends are paid annually or semiannually,

then the discount rate must be for corresponding periods.

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Special cases … contd..• 2) Constant Dividend Growth Model… dividend grows

at a constant rate :• Dividends are expected to grow at a constant percent per

period.P0 = D1 /(1+R) + D2 /(1+R)2 + D3 /(1+R)3 + …

Or, P0 = D0(1+g)/(1+R) + D0(1+g)2/(1+R)2 +

D0(1+g)3/(1+R)3 + …

• With a little algebra and some series work, this reduces to: (g is the growth rate in dividends; the subscripts denote the period in which the dividend is paid).

g-R

D

g-R

g)1(DP 10

0

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Special cases … contd..

• This Model can actually be used to get the stock price at any point in time, not just the current price. In general the price at time ‘t’ is given by,

gR

gDP tt

)1(*

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Special cases … contd..• DGM – Example 1• Suppose Big D, Inc. just paid a dividend of $.50. It is expected

to increase its dividend by 2% per year. If the market requires a return of 15% on assets of this risk, how much should the stock be selling for?

• P0 = .50(1+.02) / (.15 - .02) = $3.92

• The biggest mistake that people make with the DGM is using the wrong dividend. Be sure to emphasize that we are finding a present value, so the dividend needed is the one that will be paid NEXT period, not the one that has already been paid.

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DGM – Example 2

• Suppose TB Pirates, Inc. is expected to pay a $2 dividend in one year. If the dividend is expected to grow at 5% per year and the required return is 20%, what is the price?

– P0 = 2 / (.2 - .05) = $13.33

– Why isn’t the $2 in the numerator multiplied by (1.05) in this example?

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DGM – Example 2

0

50

100

150

200

250

0 0.05 0.1 0.15 0.2

Growth Rate

Sto

ck P

rice

D1 = $2; R = 20%

Stock Price Sensitivity to Dividend Growth, gAs the growth rate approaches the required return, the stock price increases dramatically.

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DGM … Example 8.3.

• Gordon Growth Company is expected to pay a dividend of $4 next period and dividends are expected to grow at 6% per year. The required return is 16%.

• What is the current price?

P0 = 4 / (.16 - .06) = $40

Note that we already have the dividend expected next year, so we don’t multiply the dividend by 1+g

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DGM … Example 8.3..contd

• What is the price expected to be in year 4?

P4 = D4(1 + g) / (R – g) = D5 / (R – g)P4 = 4(1+.06)4 / (.16 - .06) = 50.50 – (We know the dividend in one year is expected to be $4 and it will grow at 6%

per year for four more years. So, D5 = 4(1.06)(1.06)(1.06)(1.06) = 4(1.06)4

• What is the implied return given the change in price during the four year period?

50.50 = 40(1+return)4; return = 6%• The price grows at the same rate as the dividends• the formula is completely general. The dividend in the numerator is

always for one period later than the price we are computing. This is because we are computing a Present Value, so we have to start with a future cash flow.

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Stock Valuation… contd..• 3)Super normal Growth initially and then normal growth :

Non constant Growth : This model is considered for companies which are at an early stage of their life cycle and growing very fast ( growth rate g> r, so that the constant growth model cannot be applied directly, then they settle down into a mature, more stable rate of growth)

• Example :Suppose a firm is expected to increase dividends by 20% in year one and by 15% in year two. After that dividends will increase at a rate of 5% per year indefinitely. If the last dividend was $1 and the required return is 20%, what is the price of the stock?

• Remember that we have to find the PV of all expected future dividends.

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Stock Valuation… contd..• Compute the dividends until growth levels off

D1 = 1(1.2) = $1.20D2 = 1.20(1.15) = $1.38D3 = 1.38(1.05) = $1.449

• Find the expected future priceP2 = D3 / (R – g) = 1.449 / (.2 - .05) = 9.66(P2 is the value, at year 2, of all expected dividends year 3 on.)

• Find the present value of the expected future cash flowsP0 = 1.20 / (1.2) + (1.38 + 9.66) / (1.2)2 = 8.67

• (The final step is exactly the same as the 2-period example at the beginning. We can look at it as if we buy the stock today and receive the $1.20 dividend in 1 year, receive the $1.38 dividend in 2 years and then immediately sell it for $9.66.)

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Determining the constant growth rate

• What determines ‘g’?• If we define a firm’s dividend payout rate as the fraction of

its earnings the firm pays every year as dividends, then the firm’s dividend per share is given by

• Thus the firm can increase its dividends in three ways :– By increasing its earnings (to shareholders)– By increasing its dividend payout rate– By decreasing its shares outstanding

tt

t RatePayoutDividendxrsshareholdetoEarnings

DivgoutstandinShares

)(

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Determining the constant growth rate

• A firm can do two things with its earnings– It can pay them out to investors as cash– It can retain and reinvest them– If all earnings( payable to shareholders) is distributed and nothing retained

then the firm’s equity does not grow and so the current level of earnings generated by the firm remains constant.

• If all increases in future earnings to shareholders) result from new investment made out of retained earnings( which is basically new investment made by shareholders) then rate of change in earnings to shareholders = retained earnings x Returns earned on such investment =retention ratio x ROE ( b =retention ratio = part of earnings to shareholders that is not distributed = 1-dividend payout ratio)

• That is g = b x ROE

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No Dividend Firm• If the dividend discount model is correct why aren't no

dividend stocks selling at zero?– The firm can pay dividends now or it can choose to invest in positive

NPV projects that will guarantee even higher dividends in the future (or Capital appreciation).

– Rational shareholders should believe that they will either receive dividends at some point or they will receive something just as good ( capital appreciation).

– Empirical evidence suggests that firms with very high growth rates are likely to pay lower dividends, a result consistent with the above argument.

– Example : Mcdonald’s Corporation started in the 1950s and grew rapidly for many years. It paid its first dividend in 1975,though it was a billion dollar company ( in both sales and market value of stockholder’s equity) by that time.

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PE Multiplier Model• If a firm is not paying dividends or has a very erratic growth rate, the DDM

may not be suitable. An alternative approach is the PE multiplier approach.

• PE = Price per share/ EPS

P= PE x EPS

• PE used will be PE of ‘comparable firms’ from the same industry and knowing EPS of the firm concerned, one can find the Price .

• The weakness of the PE approach to valuation is that by using an industry average, firm specific factors that might contribute to a long term PE ratio above or below the average are ignored. A skilled analyst should adjust the PE ratio up or down to reflect uniqueness of the firm when estimating its stock price.

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Practice Problem 1 – Part I

• What is the value of a stock that is expected to pay a constant dividend of $2 per year if the required return is 15%?

• What if the company starts increasing dividends by 3% per year, beginning with the next dividend? The required return stays at 15%.

• Soln :• Zero growth – 2 / .15 = 13.33• Constant growth: 2(1.03) / (.15 - .03) = $17.17

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Practice Problem 1 – Part 2

• A company’s dividend is expected to grow @20% for the next five years. After that, the growth rate is expected to be 4% forever. If the required return is 10%, what is the value of the stock. The dividend just paid was $2.

• Soln : D1=2*1.2=2.4• D2=2.88• D3=3.46• D4=4.15• D5=4.98• D6=4.98*1.04= 5.18• P5=D6/(0.1-0.04) = 5.18/0.06 =86.26• P0= 2.4/1.1 + 2.88/(1.12)+

3.46/(1.13)+4.15/(1.14)+(4.98+86.26)/(1.15)= 66.64

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Components of The Required return ‘r’:

• Using the DGM to Find R : Start with the DGM:

• D1 / P0 is the dividend yield and g is the capital gains yield

gP

D g

P

g)1(D R

Rfor solve and rearrange

g-R

D

g - R

g)1(DP

0

1

0

0

100

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Components of The Required return ‘r’: Example:

• Example• Suppose a firm’s stock is selling for $10.50. They just

paid a $1 dividend and dividends are expected to grow at 5% per year. What is the required return?

R = [1(1.05)/10.50] + .05 = 15%• What is the dividend yield?

1(1.05) / 10.50 = 10%• What is the capital gains yield?

g =5%

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Practice problem 2

• Great Pumpkin farms just paid a dividend of $3.50 on its stock. The growth rate in dividends is expected to be a constant 5% per year indefinitely. Investors require a 16% return on the stock for the first 3 years, a 14% return on the stock for the next 3 years and an 11% return thereafter. What should be the current share price?

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Practice Problem 3

• Metallica Bearings Inc. is a young start up company. No dividends will be paid on the stock over the next nine years because the firm needs to plough back its earnings to fuel growth. The company will pay a $10 per share dividend in year 10 and will increase the dividend by 6% per year thereafter. If the required return on the stock is 13%, what is the current share price?

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Practice problem 4

• Spears Inc. has an odd dividend policy. The company has just paid a dividend of $7 per share and announced that it will increase the dividend by $4 per share for each of the next four years, and then never pay another dividend. If you require an 11% return on the company’s stock, how much will you pay for a share today? What do you think should be price of the share four years after?

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Practice Problem 5• Consider four different stocks, all of which have a required

rate of return of 18% and a most recent dividend of $4.50 per share. Stocks W, X and Y are expected to maintain constant growth rates in dividends for the foreseeable future of 10%, 0% and -5% per year respectively. Stock Z is a growth stock that will increase its dividend by 20% for the next two years and then maintain a constant 12% growth rate thereafter. What is the dividend yield for each of these four stocks ?What is the expected capital gains yield ? Discuss the relationship among the various returns that you find for each of these stocks ?

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Practice problem 6

• Storico Co. just paid a dividend of $2.75 per share. The company will increase its dividend by 20% next year and will then reduce its dividend growth rate by 5% points per year until it reaches the industry average of 5% dividend growth, after which the company will keep a constant growth rate forever. If the required rate on Storico stock is 13%, what will a share sell for today?

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Features of common & Preferred stock

• Principal types of stock: – Common : Normal equity which has no priority for

dividends or in payment in case of bankruptcy.– Preferred : Stocks with dividend priority over

common stocks, normally with a fixed dividend rate, mostly without voting rights.

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Features of common stock… contd..

a) Discretionary Dividend Payments : • While common stockholders can potentially receive unlimited

dividend payments if the firm is highly profitable, they have no special or guaranteed dividend rights. Rather, the payment and size of dividends are determined by the board of directors of the issuing firm (who are elected by the share holders).

• Further, unlike interest payments on debt, a corporation does not default if it misses a dividend payment to common stockholders. Thus, common stockholders have no legal recourse if dividends are not received, even if a company is highly profitable and chooses to use these profits to reinvest for achieving firm growth.

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Features of common stock… contd..

• b) Residual Claim :

Common stockholders have the lowest priority claim on a corporation's assets. In the event of bankruptcy, they have a residual claim i.e only after all senior claims are paid (i.e. payments owed to creditors such as the firm's employees, bond holders, the government (taxes), and preferred stockholders) are common stockholders entitled to what assets of the firm are left. The residual claim feature associated with common stock makes it riskier than bonds as an investable asset.

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Features of common stock… contd..

• C) Limited Liability: • One of the most important characteristics of common stock is its limited

liability feature.

• Legally, limited liability implies that the issuing stockholder losses are limited to the amount of their original investment in the firm. That is, the common stockholders' personal wealth held outside their ownership claims in the firm are unaffected by bankruptcy of the corporation - even if the losses of the firm exceed its total common stock ownership claims.

• In contrast, sole proprietorship or partnership stock interests mean the stockholders may be liable for the firm's debts out of their total private wealth .This is the case of "unlimited" liability.

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Features of common stock… contd..

• D) Voting rights :

• A fundamental privilege assigned to common stock is voting rights. While common stockholders do not exercise control over the firm's daily activities (these activities are overseen by managers hired to act in the best interests of the firm's common stockholders and bond holders), they do exercise control over the firm's activities indirectly through the election of the board of directors.

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Preferred Stock • It is a hybrid security that has characteristics of both a bond

and a common stock. Preferred stock is senior to common stock but junior to bonds.

• payment of dividends & reimbursement during termination of the company : a preference shareholder gets preference over the ordinary shareholder and receives his dues first.

• preference shareholders assume lower risk ---- reasonable to think that in the long run they should normally expect to earn less than ordinary shareholders.

• rate of dividend for the preference shares may be :– Fixed rate OR– a minimum fixed dividend on the share with an additional variable

component depending on the extent of profit made during the year.

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Preference Stock – Types

• Participating and non participating : Participating– a minimum fixed dividend component plus a variable component depending on the profit made. Non Participating – fixed dividend irrespective of the profits made.

• Cumulative vs Non cumulative : In case of the cumulative pref. shares ,if the dividend is not paid in a particular year due to say insufficient profit ,it is cumulatively made good in the following year or years. Thus the preference shareholders are provided additional assurance. For the non cumulative ones there is no such assurance and are thus riskier.

• Redeemable vs irredeemable : The former may be repurchased by the company at a future date while the latter may be permanent like the ordinary shares.

• Convertible preference shares: The preference share may be convertible to ordinary shares in the future on terms and conditions specified in advance.

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Equity Markets

• Primary market : – Market of IPOs, – First time issue by companies, subscribed by

investors– Facilitated by an Investment bank

• Secondary market :– Already outstanding shares change hands.

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Equity markets… contd..• Secondary market operations :• Transactions in exchanges : (US system)• Exchanges have members, who obtain license (against payment of a fee)

to buy and sell securities at the exchange.

• Some of these members are registered as commission brokers whose primary responsibility is to match buyers and sellers and charge a fee in return. A part of the responsibility of the commission brokers is sometimes delegated to another sub class called floor brokers.

• A second category of members are assigned the post of ‘market makers’ or ‘specialists’ , so named because each of them act as an assigned dealer for a small set of securities, often only one security for a single specialist.

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Equity markets… contd..• Secondary market operations… .• Specialists are called market makers because they

are obliged to ‘make a market’, or maintain fair amount of liquidity for the securities assigned to them, by standing ready to buy( and put into their inventory) or sell ( from their inventory) whenever there is a temporary disparity between the flow of buy or sell orders.

• For buying a share, the specialists quote a ‘bid price’ and for selling a share a specialists quote an ‘ask price’. The difference between a bid and ask price takes care of the profit of the specialist.

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FUNCTIONING OF THE EQUITY MARKETS ..contd.

• Trading process in a stock exchange … contd…

• When an individual want to transact on an exchange, they contact their broker. The broker then sends the order to its representative at the exchange (who is a commission broker) or a floor broker to conduct the trade with the appropriate specialist or market maker in the stock. The process is as follows:

Investor

Order

Shares

Cash

Order

Shares

Cash

Order

Shares

Cash

Broker Commission or Floor Broker

Market Maker

FUNCTIONING OF THE EQUITY MARKETS ..contd.

• The Indian system : – In India the system of market maker is not there.

Instead ,the buy sell orders are routed through member brokers via their terminals connected vide Vsat, to an automated system ( BOLT BSE’s online trading system for BSE and NEAT –National exchange for Automated Trading for NSE) and automatic machine driven matching takes place, for fulfilling the orders, based on price, time , size, criteria.

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Assignment 2 • Minicase –• Stock valuation at Ragan Inc. pg 262, RWJ .• Note the following in connection with the case:• Try and answer qs. 1,2,3 and 5.– EPS– earnings per share,– DPS- Dividends per share– Retention ratio = b= proportion of EPS that is reinvested

in the business ( not distributed as dividend)– Dividend payout ratio = 1-b= DPS/EPS– g=growth rate = ROE x b