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Dividend And ValuationDividend And Valuation

DIVIDEND AND VALUATION

Irrelevance of Dividends

Relevance of Dividends

Solved Problems

Irrelevance of DividendsIrrelevance 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 residual decision and dividends are a passive residual.

Residual Dividend

Residual dividend policy pays out only excess cash.

Dividends are irrelevant, or are a passive

residual, is based 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).

Modigliani and Miller (MM) Modigliani and Miller (MM) HypothesisHypothesis

The most comprehensive argument in support of the irrelevance of dividends is provided by the MM hypothesis. Modigliani and Miller maintain that dividend policy has no effect on the share price of the firm and is, therefore, of no consequence.

Dividend Irrelevance

Dividend irrelevance implies that the value of a firm is unaffected by the distribution of dividends and is determined solely by the earning power and risk of its assets.

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 into two transactions which exactly balance or completely offset each other. The two transactions here are the acts of paying out dividends and raising external funds–either through the sale of new shares or raising additional loans–to finance investment programmes.

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

Step 1:  The market price of a share in the beginning of the period is equal to 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,

1 period of end the at share a of price Market P

1 period of end the at received be to Dividend D

capitalequity of Cost k

share a of price market Prevailing whereP

(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 each share (P0). Thus,

)2(1nP1nDek1

10nP

Step 3: If the firm’s internal sources of financing its investment opportunities fall short of the funds required, and Δn is the number of new shares issued at the end of year 1 at price of P1, Eq. 2 can be written as:

)3(nPPnnnDk1

1nP 111

e

0

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

Δn = 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.

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

ΔnP1 = I – (E – nD1)

or ΔnP1 = I – E + nD1 (4)

where ΔnP1 = 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.

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

(6)

ek1

EI1PΔnn

0nP

have then Wecancels. 1nD Therefore, .1nD negative and1nD positive a is There

ek1

1nDEI1PΔnn1nD

0nP

have we5 eq. Solving

5)1nDEI1PΔnn1nD

ek1

1

0nP

(

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

Example 1  

A company belongs to a risk class for which the approximate

capitalisation 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 and

has 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

25,00,000Rs1.10

27,50,000 Rs2,50,000

5,00,000 Rs105 Rs21

75,0001

25,000)ek(1

EI1

PΔnn

0nP

firm, the of Value(iv)

Shares21

75,000105 Rs

3,75,000 RsΔn

issued, be to shares additional of Number (iii)3,75,000 Rs1,25,000 Rs-2,50,000 Rs-5,00,000 Rs

1nDEI

1ΔnP

shares,new of issue the from raised be to required Amount(ii)1

P1051

P5Rs1101

P5 Rs1.10

1 100 Rs

1P

1D

ek11

0P

1, yearof end the at share per Price (i)

:Paid AreDividends WhenFirm, the of Price (a)

25,00,000Rs1.1

27,50,000Rs

2,50,000Rs5,00,000Rs110Rs11

25,0001

25,000firm the of Value(iv)

shares11

25,000110 Rs

2,50,000 Rsissued, be to shares additional of Number (iii)

2,50,000Rs2,50,000 Rs-5,00,000 Rs1 ΔΔnshares,new of issue the form raised be to required Amount(ii)1P 110 or /1.101P 100 Rs 1, yearthe of end the at share per Price (i)

PaidNot AreDividends WhenFirm the of Value (b)

Walter’s model supports the doctrine that dividends are relevant. The investment policy of a firm cannot be separated from its dividends policy and both are, according to Walter, interlinked. The choice of an appropriate dividend policy affects the value of an enterprise.

Assumptions  

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

2. With additional investments undertaken, the firm’s business risk does not change. It implies that r and k are constant.

3. There is no change in the key variables, namely, beginning earnings per share, E, and dividends per share, D. The values of D and E may be changed in the model to determine results, but, any given value of E and D are assumed to remain constant in determining a given value.

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

Relevance of Dividends Relevance of Dividends

Valuation as per Walter model

D +r /ke (E-D)P = ------------------------

ke

where P = The prevailing market price of the share

D = Dividend per share

E= Earnings per share

r= the rate of return on the firm’s investment

The value of a share is the present value of all dividends plus the present value of all capital gains. Walter’s 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 Walter’s 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.

Table 1 : Dividend Policy and Value of Shares (Walter’s Model)

100Rs

0.10

10100.100.15

10p

10) Rs share per (Dividend 100 ratio (e)D/P

112.50 Rs 0.10

7.5100.100.15

7.5 P

7.5) Rs share per (Dividend 75 ratio (d)D/P

125 Rs 0.10

5100.100.15

5 P

5) Rs share per (Dividend 50 ratio (c)D/P

137.50 Rs 0.10

2.5100.100.15

2.5 P

2.5) Rs share per (Dividend 25 ratio (b)D/P

Rs150 0.10

0100.100.15

0P

zero) share per (Dividend 0 ratio (a)D/P

Table 2: Dividend Policy and Value of Shares (Walter’s Model)

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

100Rs

0.10

10100.10

0.1010

p100Rs0.10

10100.10

0.0810

p

100ratio D/P(e)

100Rs0.10

7.5100.10

0.107.5

p95Rs0.10

7.5100.10

0.087.5

p

75 Ratio D/P(d)

100Rs0.10

5100.10

0.105

p90Rs0.10

5100.10

0.085

p

50 ratio D/P (c)

100Rs0.10

2.5100.10

0.102.5

p85Rs0.10

2.5100.10

0.082.5

p

25Ratio D/P (b)

100Rs0.10

0100.10

0.100

p80Rs0.10

0100.10

0.080

p

Zeroratio D/P (a)

Gordon’s Model

Another theory which contends that dividends are relevant is Gordon’s model. This model, which opines that dividend policy of a firm affects its value, is based on the following 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 future streams of dividends. A simplified version of Gordon’s model can be symbolically expressed as

firm.equity -all an of investment on return of rate rate Growth g br

capital of rate/cost tionCapitalisa k

dividends as ddistribute earnings of percentage i.e. ratio, D/P b 1

retained. earnings of percentage or ratio Retention b

share per Earnings E

share a of Price whereP

brk

b1Ep

e

e

)11(

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 cent E = 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)

10203040506070

90807060504030

20191817161514

Solution  

The value of shares of Hypothetical Ltd for different D/P and retention ratios is depicted in Table 3.

Table 3: Dividend Policy and Value of Shares of Hypothetical Ltd (Gordon’s Model)

134.62 Rs

0.036-0.14

0.3-120 Rs P

0.036 0.12 x 0.3 br 30 ratio Retention 70 ratio (g)D/P

117.65 Rs 0.048-0.15

0.4-120 Rs P

0.048 0.12 x 0.4 br 40 ratio Retention 60 ratio (f)D/P

100 Rs 0.072-0.17

0.5-120 Rs P

0.060 0.12 x 0.5 br 50 ratio Retention 50 ratio (e)D/P

81.63 Rs 0.072-0.17

0.6-120 Rs P

0.72 0.12 x 0.6 br 60 ratio Retention 40 ratio (d)D/P

62.50 Rs 0.084-0.18

0.7-120 Rs P

0.084 0.12 x 0.7 br 70 ratio Retention 30 ratio (c)D/P

42.55 Rs 0.096-0.19

0.8-120 Rs P

0.096 0.12 0.8 br 80 ratio Retention 20 ratio (b)D/P

21.74 Rs 0.1080.20

0.9-120 Rs P

0.108 0.12 x 0.9 br(g) 90 ratio Retention 10 ratio (a)D/P

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SOLVED PROBLEMSSOLVED PROBLEMS

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 Walter’s 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.

80Rs

0.10

1.25 Rs-5.0 Rs0.10

0.181.25Rs

ek

DEek

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.

6,30,000 Rs 1,00,000) Rs 1,50,000 (Rs 6,80,000 Rs )1

nD -(Y I :financingnew for required (ii)Amount

1P 21 Rs 1

P 20 Rs

1P21Rs

1.10

1Re1

P 20 Rs

1D

1P

ek1

1

0P : yearthe of end the at share the of price (i)Market

:s)assumption (MM paid are dividends whenfirm, the of (b)Value

10.1

1Re

20,00,0001.10

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

nD1] - Y I - 1

ΔΔn) (n 1

[nDek1

1 :firm the of (iv)Value

shares 30,000 21Rs

6,30,000 Rs :issued be to shares of r(iii)Numbe

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

nD -(Y - I :financingnew for required (ii)Amount

1

P 22 Rs ,1.10

Zero1

P 20 Rs : yearthe of end the at share the of price (i)Market

:paid not are dividends whenfirm the of (c)Value

firm the of value theaffect not does dividend

paid,not are dividends when and paid are dividends when situations the both in 20,00,000, Rs is firm the of value the Since

20,00,000 Rs 1.10

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

5,30,0001,00,000

] Y I - 1Dn)P [(n ek1

1 :firm the of (iv)Value

shares22 Rs

5,30,000Rs issued be to shares new ofNumber (iii)

SOLVED PROBLEM 2

From the following information supplied to you, determine the theoretical market value of equity shares of a company as per Walter’s model:

Earnings of the company Rs 5,00,000

Dividends paid 3,00,000

Number 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. be should case, the of facts the given ratio, payout dividend optimal The policy. dividend current the withsatisfied not are weNo,

43.20 Rs 0.125

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

Determinants of Dividend PolicyDeterminants of Dividend Policy

• Dividend Payout ratio ( Constant DPS, Dividend Payout ratio ( Constant DPS, Constant D/P ratio, Stable rupee dividend Constant D/P ratio, Stable rupee dividend plus extra dividend)plus extra dividend)

• Stability of dividendsStability of dividends• Legal, contractual and internal constraintsLegal, contractual and internal constraints• Owner’s considerationsOwner’s considerations• Capital market considerationsCapital market considerations• InflationInflation