Dividend Policy

DIVIDEND POLICY

BY, SRIDEVI VALLATH MBA HOSPITALITY MANAGEMENT (2ND SEMESTER)

DIVIDEND - ?

• The part of earning that is distributed is called DIVIDEND. The optimum dividend policy would be one that maximizes the value of the firm.

• The ratio of retained to distributed earnings is referred to as DIVIDEND DECISION or POLICY.

SCHOOLS OF THOUGHT ON DIVIDEND POLICY

RELEVANCE OF DIVIDEND

IRRELEVANCE OF DIVIDEND

WALTER’S MODEL

GORDON’S MODEL

MILLER AND MODIGLIANI

THEORY

HOME-MADE DIVIDEND

RELEVANCE OF DIVIDEND :

The Walter’s and the Gordon’s Models support the view that:

the dividend policy is material to the value of the firm, and is dependent upon the kind of investment

opportunities that are available to the firm, in comparison with the expectations of shareholders.

WALTER’S MODEL

Walter’s Model links the value of the firm to the earning level, dividend level, reinvestment rate and the shareholder’s expectations.

P˳ = D + k(E – D)/r r rwhere P˳ = current price D = dividend E = earnings r = expected returns by shareholders k = reinvestment rate of the firm

Walter’s Model considers the value of the firm to be the sum of two components :

o An infinite stream of dividend, D

o An infinite stream of retained earning, E – D reinvested at a constant rate k, which are generated each year for an infinite length of time.

DERIVATION. . . .

• Present value of constant dividend ‘n’ perpetuity

= D + D + D + D + . . . 1 + r (1 + r)² (1 + r)³ (1 + r)⁴

= D r

Present value of first retained earnings reinvested at ‘k’

= (E – D)k + (E – D)k² + (E – D)k³ + . . . (1 + r)² (1 + r)³ (1 + r)⁴ = (E – D)k r(1 + r)

Present value of second retained earnings reinvested at ‘k‘

= (E – D)k + (E – D)k² + (E – D)k³ + . . . (1 + r)³ (1 + r)⁴ (1 + r)⁵ = (E – D)k r(1 + r)²

Present value of third retained earnings reinvested at ‘k’

= (E – D)k + (E – D)k² + (E – D)k³ + . . . (1 + r)⁴ (1 + r)⁵ (1 + r)⁶

= (E – D)k r(1 + r)³ When all the retained earnings are added for an infinite

period, they would add up to k(E – D)/r r

Thus, the equation

P˳ = D + k(E – D)/r r r

can alternatively be viewed as returns to shareholders, consisting of the sum of (i) dividend yield and (ii) the capital appreciation in price.

r = D + ΔP P˳ P˳

Capital appreciation is provided by the retained earnings as amount retained with the ratio of reinvestment rate and shareholders’ expectations.

ΔP = k (E – D) r

and the value of the firm is

P˳ = D + k (E – D) r r

ASSUMPTIONS AND LIMITATIONS :

• Funding of new projects is done solely from earnings and issuing fresh equity or raising debt to fund the growth is not considered. Based on this assumption alone the conclusions made will be unaffected even if some amount of external funding, either through equity or through borrowing, is used to fund the growth.

• Growth opportunities do not alter the risk profile of the firm as a whole, and therefore the market capitalization remains constant. This assumption too holds as most of the firms engage in diversification projects in fields that are related. However, such conclusions may not hold true from a long-term view point, as the risk profile may change over longer periods and may not hold true if the firm undertakes a diversification plan that is unrelated.

• The firm is a going concern and the pricing model assumes perpetual earnings. This assumption seems reasonable, the effects of distant cash flows on the price of shares in the valuation model are minimal, as they are discounted.

• Lastly, there is an implied assumption that the reinvestment rate ‘k’ remains constant. Normally, all available projects do not have the same rate of return. However, as long as the assumptions of comparative values of reinvestment rate and market capitalization rate hold good, the conclusions made about the impact on prices would remain valid.

IMPACT OF DIVIDEND POLICY ON PRICE – WALTER’S MODEL

GROWING FIRM DECLINING FIRM NORMAL FIRMREINVESTMENT RATE

(k>r) REINVESTMENT RATE

(k<r) REINVESTMENT RATE

(k = r)

Current Dividend Payout 50%

E = Rs.20 E = Rs.20 E = Rs.20

D = Rs.10 D = Rs.10 D = Rs.10

k = 20% k = 12% k = 16%

r = 16% r = 16% r = 16%

P˳ = D + k (E – D) r r

= 10 + 0.20 (20 – 10) 0.16 0.16 = 140.63

P˳ = D + k (E – D) r r

= 10 + 0.12 (20 – 10) 0.16 0.16 = 109.37

P˳ = D + k (E – D) r r

= 10 + 0.16 (20 – 10) 0.16 0.16 = 125.00

Current Market Price, P˳

Increased dividend payout to 75%, i.e. Rs.15 per share

P˳ = 15 + 0.20 (20 – 15) 0.16 0.16 = 132.81

P˳ = 15 + 0.12 (20 – 15) 0.16 0.16 = 117.19

P˳ = 15 + 0.16 (20 – 15) 0.16 0.16 = 125.00

P˳ = 5 + 0.20 (20 – 5) 0.16 0.16 = 148.48

P˳ = 5 + 0.12 (20 – 5) 0.16 0.16 = 101.62

P˳ = 5 + 0.16 (20 – 5) 0.16 0.16 = 125.00

Decreased dividend payout to 25% i.e. Rs.5 per share

Impact of the dividend policy on the price

If dividend payout increases, the price DECREASES.

If dividend payout decreases, the price INCREASES.

Price remains the SAME irrespective of the dividend payout.

CONCLUSIONS OF THE WALTER’S MODEL :

The following are the observations made :-

For a growing firm, the market value will INCREASE if dividend payout ratio is decreased and DECREASE if dividend payout is increased. A 0% payout would maximize the share price of the firm.

For a declining firm, the market value will DECREASE if dividend payout ratio is increased and INCREASE if dividend payout ratio is decreased. A 100% payout ratio will maximize the value of the firm.

For a normal firm, investors are indifferent to the dividend policy because retained earnings will yield the same return as distributed earnings.

Therefore, the share price for a firm remains constant, and the dividend policy becomes irrelevant.

GORDON’S MODEL

The value of the firm, as per the constant growth dividend capitalization model, is the discounted value of the dividend in perpetuity. Dividend is not constant, because the portion of earnings that is retained is reinvested in the growth of the firm and hence, results in the growth of dividend period after period.

If earnings and dividend for the next period are E₁ and D₁ respectively, and the growth in dividend each year is ‘g’, then the value of the firm is

P˳ = D₁ r – g

TO INCORPORATE DIVIDEND POLICY. . .

• If the earnings level for the next period is E₁ and if ‘b’ is the retention ratio, the amount of dividend is E₁(1 – b). The growth in absolute terms will be E₁ X b X k. The relative growth, ‘g’ will be b X k. Therefore, the value of the firm

P˳ = E₁ X (1 – b) r – bk Therefore, the dividend policy as reflected in the retention

rate of ‘b’ is one of the important determinants of the valuation of the firm.

ASSUMPTIONS :

The Gordon's Model lies in the relationship between dividend and growth and the balancing of the two. An increase in dividend would lead to an increase in price as the value of the numerator increases. Further increase in dividend, lesser the amount that is retained and hence, a lesser growth ‘g’ is expected. A reduction in the growth would push the price of the share downwards. There would be two forces operating on the value of the firm.

IMPACT OF DIVIDEND POLICY ON PRICE (GORDON’S MODEL)

GROWING FIRM DECLINING FIRM NORMAL FIRM REINVESTMENT RATE

(k > r)

REINVESTMENT RATE

(k < r)

REINVESTMENT RATE

(k = r)

Current dividend payout 50%

E₁ = Rs.20D₁ = Rs.10k = 20%r = 16%

E₁ = Rs.20D₁ = Rs.10k = 12%r = 16%

E₁ = Rs.20D₁ = Rs.10k = 16%r = 16%

Current Market Price P˳

P˳= E₁ x(1 – b) = 10

r – bk 0.16 – 0.10 = Rs.166.36

P˳= E₁ x(1 – b) = 10

r – bk 0.16 – 0.06 = Rs.100.00

P˳= E₁ x(1 – b) = 10

r – bk 0.16 – 0.08 = Rs.125.00

P˳ = 15 = Rs.136.36 0.16 – 0.05

P˳ = 15 = Rs.115.38 0.16 – 0.03

P˳ = 15 = Rs.125.00 0.16 – 0.04

Increased dividend payout to 75% i.e., Rs.15 per share

Decreased dividend payout to 25% i.e., Rs.5 per share

P˳ = 5 = Rs.500.00 0.16 – 0.15

P˳ = 5 = Rs.71.43 0.16 – 0.09

P˳ = 5 = Rs.125.00 0.16 – 0.12

Expected Price

Impact of the dividend policy on the price

If dividend payout INCREASES, the price DECREASES.

If dividend payout DECREASES, the price INCREASES.

Price remains the SAME irrespective of dividend payout.

CONCLUSIONS OF THE GORDON’S MODEL :

The following can be observed from the table :

the value of the firm must RISE with increasing retention, if the firm’s reinvestment rate exceeds shareholders’ expectations(and vice versa)

the value of the firm must FALL with increasing retention, if the reinvestment rate is lower than the expectations of the shareholders(and vice versa)

the value of the firm remain the SAME if the reinvestment rate equals shareholders’ expectations.

• When k = r i.e., when the firm matches investors’ expectations, the price of the share becomes independent of the dividend policy. The value of the firm under such circumstances purely becomes a function of the earning power of the assets, E₁ and the shareholders’ expectations, r

When k = r, P˳ = E₁ x (1 – b) = E₁ r – bk r

This is for a NORMAL firm.

• When the firm is unable to match the expectations of the shareholders (k < r), retention is not favorable, because investors can generate more than the firm can. The optimum dividend policy will then be a 100% payout, i.e., b = 0. Again, the value of the firm would be the same.

When k < r, then optimum value would be at b = 0

P˳ = E₁ x (1 – b) = E₁ r – bk r

This is for a DECLINING firm.

• When a firm can exceed the expectations of investors, the optimum payout dividend would be 0% i.e., b = 100. This makes the price indeterminable. Therefore, an additional assumption can be made because the growth rate of dividend ‘g’ cannot exceed the market capitalization rate ‘r’.

• Therefore, it would then be (b x k < r) or (b < r/k). It is difficult to imagine a situation where the firm can offer a growth, of about 20% in dividend and the investors seem pleased with a return less than 20%. If a firm can offer 20% growth, the investors must immediately revise their expectations to beyond 20%, and therefore, ‘r’ would be greater than b x k.

This is for a GROWING firm.

WALTER’S MODEL vs. GORDON’S MODEL

• The difference in Walter’s Model and Gordon’s Model relates to dividend growth. Walter’s Model keeps the dividend amount constant in each period while Gordon’s Model assumes growing dividend in each period. This can be illustrated through an example :-

QUESTION: With earnings and dividend at Rs.20 and Rs.10 respectively, a reinvestment rate of 20% and shareholders’ expectations at 16%, find the value of the firm as per (i)Walter’s Model and

(ii)Gordon’s Model

• The value of the firm as per Walter’s Model is P˳ = D + k (E – D) r r = 10 + 0.20 (20 – 10) = Rs.140.63 0.16 0.16

• The value of the firm as per Gordon’s Model is P˳ = E₁ x (1 – b) = 20(1 – 0.5) = Rs.166.67 r – bk 0.16 – 0.5 x 0.20

EXAMPLE :

QUESTION :

Assume that a firm has current earnings of Rs.10 per share. It can use these earnings in projects that provide a return of 15%. The expected return to shareholders is 20%. What is the value of the firm under (a) Walter’s Model (b) Gordon’s Model, if it retains (i) 40% (ii) 50% (iii) 60% of the earnings?

(a) As per Walter’s Model, the market price of the share is

with 40% payout P˳ = D + k (E – D) = 4 + 0.15 (10 – 4) = Rs.40.50 r 0.20 r 0.20 with 50% payout P˳ = D + k (E – D) = 5 + 0.15 (10 – 5) = Rs.43.75 r 0.20 r 0.20

with 60% payout P˳ = D + k (E – D) = 6 + 0.15 (10 – 6) = Rs.45.00 r 0.20 r 0.20

As per the Gordon’s Model the market price of the share is

with 40% payout P˳ = E₁ x (1 – b) = 10(1 – 0.6) = Rs.36.36 r – bk 0.20 – 0.6 x 0.15



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