Ch 30 DividendandValuation

7/31/2019 Ch 30 DividendandValuation

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Tata McGraw-Hill Publishing Company Limited, Financial Management 30 - 1

Chapter 30

Dividend And Valuation


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DIVIDEND AND VALUATION

Irrelevance of Dividends

Relevance of Dividends

Solved Problems


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Irrelevance of Dividends

Dividend

Dividend refers to the corporate net profits distributed

among shareholders.The crux of the argument supporting the irrelevance of

dividends to valuation is that the dividend policy of a firm is

a part of its financing decision. As a part of the financing

decision, the dividend policy of the firm is a residualdecision and dividends are a passive residual.

Residual Dividend

Residual dividend policy pays out only excess cash.


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Dividends are irrelevant, or are a passive residual, isbased on the assumption that the investors are

indifferent between dividends and capital gains. So

long as the firm is able to earn more than the equity-

capitalisation rate (ke), the investors would be content

with the firm retaining the earnings. In contrast, if the

return is less than the ke, investors would prefer to

receive the earnings (i.e. dividends).


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Modigliani and Miller (MM)Hypothesis

The most comprehensive argument in support of theirrelevance of dividends is provided by the MMhypothesis. Modigliani and Miller maintain thatdividend policy has no effect on the share price ofthe firm and is, therefore, of no consequence.Dividend Irrelevance

Dividend irrelevance implies that the value of a firmis unaffected by the distribution of dividends and is

determined solely by the earning power and risk ofits assets.


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Assumptions

The MM hypothesis of irrelevance of dividends is based on the

following critical assumptions:

1) Perfect capital markets in which all investors are rational.There are no taxes. Alternatively, there are no differences in tax

rates applicable to capital gains and dividends.

2) A firm has a given investment policy which does not change.

There is a perfect certainty by every investor as to future

investments and profits of the firm.

Crux of the Argument

The crux of the MM position on the irrelevance of dividend is the arbitrage

argument. The arbitrage process involves a switching and balancing

operation. In other words, arbitrage refers to entering simultaneously intotwo transactions which exactly balance or completely offset each other. The

two transactions here are the acts of paying out dividends and raising

external fundseither through the sale of new shares or raising additional

loansto finance investment programmes.


7/29 Tata McGraw-Hill Publishing Company Limited, Financial Management 30 - 7

Proof: MM provide the proof in support of their argument in the followingmanner.

Step 1: The market price of a share in the beginning of the period is equalto the present value of dividends paid at the end of the period plus the

market price of share at the end of the period. Symbolically,

1periodofendtheatshareaofpriceMarketP

1periodofendtheatreceivedbetoDividendDcapitalequityofCostk

shareaofpricemarketPrevailingwhereP

(1)PDk1

1P

1

1

e

0

11

e

0

Step 2: Assuming no external financing, the total capitalised value of the

firm would be simply the number of shares (n) times the price of eachshare (P0). Thus,

)2(1

nP1

nD

ek1

1

0nP


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Step 3: If the firms internal sources of financing its investmentopportunities fall short of the funds required, and n is the number ofnew shares issued at the end of year 1 at price of P1, Eq. 2 can be writtenas:

)3(nPPnnnDk1

1nP

111

e

0

where n = Number of shares outstanding at the beginning of the period

n = Change in the number of shares outstanding during the

period/Additional shares issued

Equation 3 implies that the total value of the firm is the capitalised value

of the dividends to be received during the period plus the value of the

number of shares outstanding at the end of the period, considering new

shares, less the value of the new shares. Thus, in effect, Eq. 3 is

equivalent to Eq. 2.


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Step 4: If the firm were to finance all investment proposals, thetotal amount raised through new shares issued would be given inEq. 4.

nP1 = I (E nD1)or nP1 = I E + nD1 (4)

where nP1 = Amount obtained from the sale of new shares of

finance capital budget.

I = Total amount/requirement of capital budget

E = Earnings of the firm during the period

nD1 = Total dividends paid

(E nD1) = Retained earnings

According to Equation 4, whatever investment needs (I) are not

financed by retained earnings, must be financed through the sale

of additional equity shares.


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Step 5: If we substitute Eq. 4 into Eq. 3 we derive Eq. 5.

(6)

ek1

EI1Pnn

0nP

havethenWecancels.1nDTherefore,.1nDnegativeand1nDpositiveaisThere

ek1

1nDEI

1Pnn

1nD

0nP

havewe5eq.Solving

5)1

nDEI1Pnn

1nD

ek1

1

0nP (

Step 6: Conclusion Since dividends (D) are not found in Eq. 6, Modiglianiand Miller conclude that dividends do not count and that dividend policyhas no effect on the share price.


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Example 1

A company belongs to a risk class for which the approximatecapitalisation rate is 10 per cent. It currently has outstanding 25,000

shares selling at Rs 100 each. The firm is contemplating the

declaration of a dividend of Rs 5 per share at the end of the current

financial year. It expects to have a net income of Rs 2,50,000 andhas a proposal for making new investments of Rs 5,00,000. Show

that under the MM assumptions, the payment of dividend does not

affect the value of the firm.

Solution


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25,00,000Rs1.10

27,50,000Rs2,50,000

5,00,000Rs105Rs21

75,0001

25,000)ek(1

EI1

Pnn

0nP

firm,theofValue(iv)

Shares21

75,000105Rs

3,75,000Rsn

issued,betosharesadditionalofNumber(iii)

3,75,000Rs1,25,000Rs-2,50,000Rs-5,00,000Rs1

nDEI1

nP

shares,newofissuethefromraisedbetorequiredAmount(ii)1P105

1P5Rs110

1P5Rs

1.101100Rs

1P

1D

ek11

0P

1,yearofendtheatshareperPrice(i)

:PaidAreDividendsWhenFirm,theofPrice(a)


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25,00,000Rs1.1

27,50,000Rs

2,50,000Rs5,00,000Rs110Rs11

25,0001

25,000firmtheofValue(iv)

shares11

25,000

110Rs

2,50,000Rsissued,betosharesadditionalofNumber(iii)

2,50,000Rs2,50,000Rs-5,00,000Rs1nshares,newofissuetheformraisedbetorequiredAmount(ii)

1P110or/1.101P100Rs1,yeartheofendtheatshareperPrice(i)

PaidNotAreDividendsWhenFirmtheofValue(b)


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The validity of the MM Approach is open to question on two

counts:

1) Imperfection of capital market, and

2) Resolution of uncertainty.

Market Imperfection Modigliani and Miller assume that capitalmarkets are perfect. This implies that there are no taxes;

flotation costs do not exist and there is absence of

transaction costs. These assumptions are untenable in actual

situations.


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Resolution of Uncertainty

(i) near vs distant dividend; (ii) informational content of dividends; (iii)

preference for current income; and (iv) sale of stock at uncertain

price/underpricing.

Near Vs Distant Dividend One aspect of the uncertainty situation is the

payment of dividend now or at a later date. The argument that near dividend

implies resolution of uncertainty is referred to as the bird-in-hand

argument. Bird-in-hand argument is the belief that current dividend

payments reduce uncertainty and result in higher value of shares of a firm.

Informational Content of Dividends Another aspect of uncertainty, very

closely related to the first (i.e. resolution of uncertainty or the bird-in-hand

argument) is the informational content of dividend argument. Informational

content is the information provided by dividend of a firm with respect to

future earnings which causes owners to bid up or down the price of shares.

Preference for Current Income The third aspect of the uncertainty question

relating to dividends is based on the desire of investors for current income

to meet consumption requirements.

Underpricing implIes sale of shares at price lower than the current market.


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Walters model supports the doctrine that dividends are relevant. Theinvestment policy of a firm cannot be separated from its dividends policyand both are, according to Walter, interlinked. The choice of an appropriatedividend policy affects the value of an enterprise.

Assumptions

1. All financing is done through retained earnings: external sources offunds like debt or new equity capital are not used.

2. With additional investments undertaken, the firms business risk doesnot change. It implies that rand kare constant.

3. There is no change in the key variables, namely, beginning earnings pershare, E, and divi-dends per share, D. The values of D and E may bechanged in the model to determine results, but, any given value of EandDare assumed to remain constant in determining a given value.

4. The firm has perpetual (or very long) life.

Relevance of Dividends


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D)/E-(ErateRetentionb

sinvestmentfirmsonreturnofrateExpectedrwhere

rbekD

P

havewe,retentionsearningsreflectToearningsofrategrowthExpectedg

capitalequityofCostek

dividendInitialD

sharesequityofPricePwhere

gekDP

)8(

)7(


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investmentfirmstheonreturnofrateTher

shareperEarningsE

shareperDividendD

shareaofpricemarketprevailingThewherePe

k

DEek

rD

P

P

DEek

rD

ek

havewe,

ofvaluethengsubstituti

,DEek

rPsinceand

P

P

P

Dek

have,WePPg

(9)gP

Dek

ekdetermingforequationanderivewe7,equationtheFrom

)10(


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Equation 10 shows that the value of a share is the present value of all

dividends plus the present value of all capital gains. Walters model with

reference to the effect of dividend/retention policy on the market value of

shares under different assumptions of r (return on investments) is illustrated in

Example 2.

Example 2

The following information is available in respect of a firm:

Capitalisation rate (ke) = 0.10

Earnings per share (E) = Rs 10

Assumed rate of return on investments (r): (i) 15, (ii) 8, and (iii) 10.

Show the effect of dividend policy on the market price of shares, using Walters

model.

Solution(1) When r is 0.15, that is, r > ke: The effect of different D/P ratios depicted in

Table 1.

(2) When r = 0.08 and 0.10, that is, r < ke and r = ke respectively: The effect of

different D/P ratios on the value of shares is shown in Table 2.


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Table 1 : Dividend Policy and Value of Shares (Walters Model)

100Rs0.10

10100.10

0.1510

p

10)Rsshareper(Dividend100ratio(e)D/P

112.50Rs0.10

7.5100.10

0.157.5

P

7.5)Rsshareper(Dividend75ratio(d)D/P

125Rs0.10

5100.10

0.155

P

5)Rsshareper(Dividend50ratio(c)D/P

137.50Rs0.10

2.5100.10

0.152.5

P

2.5)Rsshareper(Dividend25ratio(b)D/P

Rs1500.10

0100.10

0.150

P

zero)shareper(Dividend0ratio(a)D/P


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Table 2: Dividend Policy and Value of Shares (Walters Model)

(A) r = 0.8 (r < ke) (B) r = 0.10 (r = ke)

100Rs0.10

10100.10

0.1010

p100Rs0.10

10100.10

0.0810

p

100ratioD/P(e)

100Rs0.10

7.5100.10

0.10

7.5p95Rs

0.10

7.5100.10

0.08

7.5p

75RatioD/P(d)

100Rs0.10

5100.10

0.105

p90Rs0.10

5100.10

0.085

p

50ratioD/P(c)

100Rs0.10

2.5100.10

0.102.5

p85Rs0.10

2.5100.10

0.082.5

p

25RatioD/P(b)

100Rs0.10

0100.100.100

p80Rs0.10

0100.100.080

p

ZeroratioD/P(a)

G d M d l


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Gordons Model

Another theory which contends that dividends are relevant is Gordons model. Thismodel, which opines that dividend policy of a firm affects its value, is based on thefollowing assumptions:

1. The firm is an all-equity firm. No external financing is used and investment

programmes are financed exclusively by retained earnings.2. r and ke are constant.

3. The firm has perpetual life.

4. The retention ratio, once decided upon, is constant. Thus, the growth rate, (g = br)is also constant.

5. ke > br.

Dividend Capitalisation Model

According to Gordon, the market value of a share is equal to the present value of futurestreams of dividends. A simplified version of Gordons model can be symbolicallyexpressed as

firm.equity-allanofinvestmentonreturnofraterateGrowthgbr

capitalofrate/costtionCapitalisak

dividendsasddistributeearningsofpercentagei.e.ratio,D/Pb1

retained.earningsofpercentageorratioRetentionb

shareperEarningsE

shareaofPricewhereP

brk

b1Ep

e

e

)11(


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Example 3

The following information is available in respect of the rate of return on investment

(r), the capitalisation rate (ke) and earnings per share (E) of Hypothetical Ltd.

r = 12 per centE = Rs 20

Determine the value of its shares, assuming the following:

D/P ratio (1 b) Retention ratio (b) ke (%)

(a)

(b)

(c)

(d)

(e)

(f)

(g)

10

20

30

40

50

60

70

90

80

70

60

50

40

30

20

19

18

17

16

15

14

Solution

The value of shares of Hypothetical Ltd for different D/P and retention ratios is

depicted in Table 3.


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Table 3: Dividend Policy and Value of Shares of Hypothetical Ltd (Gordons Model)

134.62Rs0.036-0.14

0.3-120RsP

0.0360.12x0.3br30ratioRetention70ratio(g)D/P

117.65Rs0.048-0.15

0.4-120RsP

0.0480.12x0.4br40ratioRetention60ratio(f)D/P

100Rs0.072-0.17

0.5-120RsP

0.0600.12x0.5br50ratioRetention50ratio(e)D/P

81.63Rs0.072-0.17

0.6-120RsP

0.720.12x0.6br60ratioRetention40ratio(d)D/P

62.50Rs0.084-0.18

0.7-120RsP

0.0840.12x0.7br70ratioRetention30ratio(c)D/P

42.55Rs0.096-0.19

0.8-120RsP

0.0960.120.8br80ratioRetention20ratio(b)D/P

21.74Rs0.1080.20

0.9-120RsP

0.1080.12x0.9br(g)90ratioRetention10ratio(a)D/P


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SOLVED PROBLEMS


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SOLVED PROBLEM 1

(a) X company earns Rs 5 per share, is capitalised at a rate of 10 per cent and has a

rate of return on investment of 18 per cent.

According to Walters model, what should be the price per share at 25 per cent

dividend payout ratio? Is this the optimum payout ratio according to Walter?

(b) Omega company has a cost of equity capital of 10 per cent, the current market

value of the firm (V) is Rs 20,00,000 (@ Rs 20 per share). Assume values for I (new

investment), Y (earnings) and D (dividends) at the end of the year as I = Rs

6,80,000, Y = Rs 1,50,000 and D = Re 1 per share. Show that under the MM

assumptions, the payment of dividend does not affect the value of the firm.

80Rs0.10

1.25Rs-5.0Rs0.10

0.181.25Rs

ek

DE

ek

rD

P)a(

Solution

This is not the optimum dividend payout ratio because Walter suggests a zero

per cent dividend payout ratio in situations where r > ke to maximise the value

of the firm. At this ratio, the value of the share would be maximum, that is, Rs

90.


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6,30,000Rs1,00,000)Rs1,50,000(Rs6,80,000Rs)1nD-(YI:financingnewforrequired(ii)Amount

1P21Rs1

P20Rs

1P21Rs

1.10

1Re1P

20Rs

1D

1P

ek1

10P:yeartheofendtheatsharetheofprice(i)Market

:s)assumption(MMpaidaredividendswhenfirm,theof(b)Value

10.1

1Re

20,00,0001.10

1,00,000Rs1,50,000Rs6,80,000Rs21Rs30,0001,00,0001,00,000Rs

nD1]-YI-1

n)(n1

[nDek1

1:firmtheof(iv)Value

shares30,00021Rs

6,30,000Rs:issuedbetosharesofr(iii)Numbe


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5,30,000Rs1,50,000Rs-6,80,000Rs)1

nD-(Y-I:financingnewforrequired(ii)Amount1P22Rs,1.10

Zero1P

20Rs:yeartheofendtheatsharetheofprice(i)Market

:paidnotaredividendswhenfirmtheof(c)Value

firmtheofvaluetheaffectnotdoesdividend

paid,notaredividendswhenandpaidaredividendswhensituationsthebothin20,00,000,RsisfirmtheofvaluetheSince

20,00,000Rs1.10

1,50,000Rs6,80,000Rs-22Rs22

5,30,0001,00,000

]YI-1

Dn)P[(nek1

1:firmtheof(iv)Value

shares22Rs

5,30,000RsissuedbetosharesnewofNumber(iii)


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Tata McGraw-Hill Publishing Company Limited Financial Management 30 - 29

SOLVED PROBLEM 2

From the following information supplied to you, determine the theoretical marketvalue of equity shares of a company as per Walters model:

Earnings of the company Rs 5,00,000

Dividends paid 3,00,000Number of shares outstanding 1,00,000

Price earning ratio 8

Rate of return on investment 0.15

Are you satisfied with the current dividend policy of the firm? If not, what should be

the optimal dividend payout ratio in this case?

zero.beshouldcase,theoffactsthegivenratio,payoutdividendoptimalThepolicy.dividendcurrentthewithsatisfiednotareweNo,

43.20Rs0.125

3Rs5Rs0.125

0.153Rs

ek

DEek

rD

P

Solution

Working Notes

(i) ke is the reciprocal of P/E ratio = 1/8 = 12.5 per cent

(ii) E = Total earnings Number of shares outstanding

(iii) D = Total dividends Number of shares outstanding

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Ch 30 DividendandValuation