dividend decision & valuation of firm

Dividend Decision & Valuation of Firm

Dept. of Business and Financial StudiesUniversity of Kashmir


Learning Goals:Dividend decision: what it is all about?

Dividend decision & valuation of firm:Walters modelGordon’s modelLinters modelGraham & Dods modelM-M Hypothesis


DividendDecision

Amt. distributed among

shareholders

Amount of earnings to be

retained

Impact on Internal source of finance

Increases current wealth

Information value


High payout:• Less retained earnings…..slower growth

perhaps lower MPLow payout:• More RE…. Higher growth….higher capital

gain….perhaps higher MP.

Payout Ratio

Low High


Q: Does div. decision influence Value of a shares

Dividend Models:Walter’s Model

• Gordon’s Model Relevant• Linter’s Model• Graham & Dodd’s Model• M-M Hypothesis………Irrelevant

Walters Model

Contention:

C1: Div. Decision influences Value of a share……..Optimum P/O Ratio

E1: Relationship between IRR & K Used in determining optimum Decision

E2: Classifies companies into:

Growing, Normal, & Declining

Walters Model

• Less fin. Resources

• Req. more funds

• Difficult to obtain funds

• Suff. Investment opportunities

r > k

• Sufficient resource

• Req. less funds

•Access to funds

•Less feasible Investments opp.

R=k

• Little res.Req

• Little access

• Revamping

R<k

Growth Matured Declining

Walters Model

Assumptions:A1: Only retained earnings used to Finance

investments.

A2: IRR & K remains constant

A3: All earnings are either distributed or reinvested internally immediately

A4: EPS & Dividends never change

A5: Firm has infinite life

Walters Model

Growth Firm………..r > k

C: Optimum payout ratio is zero

E: Able to reinvest at a rate… higher than k

ResultAt zero payout ratio, weighted benefit of RE will be more than the dividends

Walters Model

Normal Firm………..r = k

C: No optimum payout ratio

E: Able to invest at a rate……=k

Result: At any payout ratio, weighted benefit of RE is

equal to that of dividends.

Walters Model

Declining Firm………r < k

C: Optimum payout ratio is 100%

E: No investment opp. or can earn

Less than the rate expected by...

Walters Model

D + (r/k) ( E – D ) P = -------------------------- k

Where: P = Market price of share D = Dividend per share r = IRR k = cost of capital E = EPS

D + (r/k) ( E – D ) P = -------------------------- k

Where: P = Market price of share D = Dividend per share r = IRR k = cost of capital E = EPS

P = Present value of stream of dividends & Capital gain

P = Present value of stream of dividends & Capital gain

Valuation of Shares

Walters Model

Example: The following estimates about three companies viz., A, B, & C are given:

A B C R …………15% 10% 8% K………….10% 10% 10% EPS………Rs 10 Rs 10 Rs 10

Walters ModelPayout Ratio = zero Payout Ratio = zero

Div = 00+(.15/.10) (10-0) .10 = Rs 150

Div = 00+(.10/.10)(10-0) .10 = Rs 100

Div = 00+(.08/.10) (10-0) .10 = Rs 80

Payout ratio = 40%

Div = 44+(.15/.10) (10- 4) .10 = Rs 130

Div = 44+(.10/.10)(10- 4) .10 = Rs 100

Div = 44+(.08/.10) (10- 4) .10 = Rs

Payout ratio = 100% Div =10

10+(.15/.10)(10-10) .10 = Rs 100

Div =100+(.10/.10)(10-10) .10 = Rs 100

Div =100+(.08/.10)(10-10) .10 = Rs 100

Payout Ratio = zero Payout Ratio = zero Div = 0

0+(.15/.10) (10-0) .10 = Rs 150

Div = 00+(.10/.10)(10-0) .10 = Rs 100


0+(.15/.10) (10-0) .10 = Rs 150

Div = 00+(.08/.10) (10-0) .10 = Rs 80

Div = 00+(.10/.10)(10-0) .10 = Rs 100


0+(.15/.10) (10-0) .10 = Rs 150

Div = 44+(.08/.10) (10- 4) .10 = Rs

Div = 00+(.08/.10) (10-0) .10 = Rs 80

Div = 00+(.10/.10)(10-0) .10 = Rs 100


0+(.15/.10) (10-0) .10 = Rs 150

Payout ratio = 40%

Div = 44+(.08/.10) (10- 4) .10 = Rs

Div = 00+(.08/.10) (10-0) .10 = Rs 80

Div = 00+(.10/.10)(10-0) .10 = Rs 100


0+(.15/.10) (10-0) .10 = Rs 150

Div = 44+(.10/.10)(10- 4) .10 = Rs 100

Payout ratio = 40%

Div = 44+(.08/.10) (10- 4) .10 = Rs

Div = 00+(.08/.10) (10-0) .10 = Rs 80

Div = 00+(.10/.10)(10-0) .10 = Rs 100


0+(.15/.10) (10-0) .10 = Rs 150

Div = 44+(.15/.10) (10- 4) .10 = Rs 130

Div = 44+(.10/.10)(10- 4) .10 = Rs 100

Payout ratio = 40%

Div = 44+(.08/.10) (10- 4) .10 = Rs

Div = 00+(.08/.10) (10-0) .10 = Rs 80

Div = 00+(.10/.10)(10-0) .10 = Rs 100


0+(.15/.10) (10-0) .10 = Rs 150

Payout ratio = 100%

Div = 44+(.15/.10) (10- 4) .10 = Rs 130

Div = 44+(.10/.10)(10- 4) .10 = Rs 100

Payout ratio = 40%

Div = 44+(.08/.10) (10- 4) .10 = Rs

Div = 00+(.08/.10) (10-0) .10 = Rs 80

Div = 00+(.10/.10)(10-0) .10 = Rs 100


0+(.15/.10) (10-0) .10 = Rs 150

Div =1010+(.15/.10)(10-10) .10 = Rs 100

Payout ratio = 100%

Div = 44+(.15/.10) (10- 4) .10 = Rs 130

Div = 44+(.10/.10)(10- 4) .10 = Rs 100

Payout ratio = 40%

Div = 44+(.08/.10) (10- 4) .10 = Rs

Div = 00+(.08/.10) (10-0) .10 = Rs 80

Div = 00+(.10/.10)(10-0) .10 = Rs 100


0+(.15/.10) (10-0) .10 = Rs 150

Div =100+(.10/.10)(10-10) .10 = Rs 100

Div =1010+(.15/.10)(10-10) .10 = Rs 100

Payout ratio = 100%

Div = 44+(.15/.10) (10- 4) .10 = Rs 130

Div = 44+(.10/.10)(10- 4) .10 = Rs 100

Payout ratio = 40%

Div = 44+(.08/.10) (10- 4) .10 = Rs

Div = 00+(.08/.10) (10-0) .10 = Rs 80

Div = 00+(.10/.10)(10-0) .10 = Rs 100


0+(.15/.10) (10-0) .10 = Rs 150

Div =1010+(.08/.10)(10-10) .10 = Rs 100

Div =1010+(.10/.10)(10-10) .10 = Rs 100

Div =1010+(.15/.10)(10-10) .10 = Rs 100

Payout ratio = 100%

Div = 44+(.15/.10) (10- 4) .10 = Rs 130

Div = 44+(.10/.10)(10- 4) .10 = Rs 100

Payout ratio = 40%

Div = 44+(.08/.10) (10- 4) .10 = Rs

Div = 00+(.08/.10) (10-0) .10 = Rs 80

Div = 00+(.10/.10)(10-0) .10 = Rs 100


0+(.15/.10) (10-0) .10 = Rs 150

Gordon’s Model

Contention:

C1: Div. Decision Influences Value of Firm ………… Optimum P/O Ratio

Determination:D1: Used IRR & K in determining optimum Pay out Ratio

D2: Classifies companies into Growth, Normal, & Declining.

Gordon’s Model

Prepositions of Gordon

r > k Zeror < k 100%r = k….Irrelevant

Gordon’s Model

AssumptionsA1: Firm is all equity

A2: Uses RE to finance investments.


A4: Retention ratio once decided remains constant

A5: No corporate taxes

A6: Firm derives its earnings perpetually

AssumptionsA1: Firm is all equity

A2: Uses RE to finance investments.


A4: Retention ratio once decided remains constant

A5: No corporate taxes

A6: Firm derives its earnings perpetually

Gordon’s Model

C2: If risk is considered then, P/ratio would influence Value even when r = k

Assumptions:

A1: Rational investors are risk averse

A2: Prefer nearer Div. than distant Div.

A3: Expect risk premium when retained

Gordon’s Model

Effects of Retention:

E1: Retention means postponement of current Div. in promise of more future

div…………….. RiskE2: More the risk, more the k…..

based on Bird-In-The-Hand argument

Gordon’s Model

Bird-in-the-Hand Argument• One Bird in a hand is better than 2 birds in a

bush• Shareholders Prefer Nearer Div. Over Distant

Dividends

Krishman:Two identical stocks, one paying more dividend will have more MP.. vice versa

Gordon’s ModelRelationship between p/ratio & k

DR(k)

RR(b)

Conclusion•More the retention, more risk, more the k…less MP•Less the retention, less risk, less the k… more MP

K

Gordon’s Model: Valuation of shares

D1 D2 Dn P = ------ +------ …..+----- (1+k) (1+k) (1+k)

Where: P = Market price of share D = Dividend per share r = IRR k = cost of capital E = EPS b = Retention ratio

D1 D2 Dn P = ------ +------ …..+----- (1+k) (1+k) (1+k)

Where: P = Market price of share D = Dividend per share r = IRR k = cost of capital E = EPS b = Retention ratio

P = present value of stream of dividends P = present value of stream of dividends

E1 ( 1 – b ) = --------------------

k - br

Gordon’s Model: Valuation of shares

20 (1- 0.2) .11 – (0.2 x 0.08) = Rs 1,000

20 (1- 0.2) .11 – (0.2 x 0.11) = Rs 100

20 (1- 0.2) .11 – (0.2 x 0.12) = Rs 186

Payout Ratio = 80%

20 (1- 0.6) .11 – (0.6 x 0.12) = Rs 210

20 (1- 0.6) .11 – (0.6 x 0.11) = Rs 100

Payout Ratio = 40%

20 (1- 0.6) .11 – (0.6 x 0.08) = Rs 129

r= 8, k= .11 20 (1- 0.9) .11 – (0.9 x 0.08) = Rs 52.63

r =.11, k=.11 20(1- 0.9) .11 – (0.9 x 0.1I) = Rs 181

Payout Ratio = 10% Payout Ratio = 10% r =.12, k = .11

20 (1- 0.9) .11 – (0.9 x 0.12) = Rs 1,000

M-M Hypothesis

Contention: P/ratio does not influence Value of a Firm

Arguments:A1: Value…….. earning capacity & earnings …….investment decisions.

A2: When company Retains, investor

enjoys C/gain = amount of RE. When company pays investor enjoy Div. in

value = amount of C/gain

M-M Hypothesis

A3: Benefit of Div. is offset by external financing

A4: Shareholders are indifferent to Dividend Decision……..able to Construct Own Div. Policy

M-M Hypothesis

Assumptions:A1: Perfect capital market

• Easy to buy & sell• No buyer/seller large enough to influence MP• Access to information• No transaction costs• Securities are divisible

A2: Rational investors

M-M Hypothesis

A3: No risk of uncertainty (dropped)

A4: No corporate taxes…(no diff.)

A5: k & r is identical for all the shares

A6: IRR = k

M-M Hypothesis

Conclusion:

C1: When r=k, then weighted benefit of RE will be equal to weighted benefit of Div…V constant

C2: When r is same, no shift will take place from low yielding companies to high yielding companies.

M-M Hypothesis

Valuation of shares: P1 = Po ( 1 + k ) – D1

Where:P1 = market price per share at time 1Po = market price per share at time 0K = dr or cost of capital= rD1 = dividend per share at time 1

M-M Hypothesis

Example: ABC Comp. currently has outstanding 1,00,000 shares, selling at Rs 100 each. It is thinking to pay a div. of Rs 5 Ps at t1. K is 10%. What will be the price of the share if:

A div. is not paid.A div. is paid @ Rs 5 per share.How many new shares are to be sold, if

the company requires Rs 20 lakhs & the net profit is Rs 10 lakhs?

M-M Hypothesis

P1 = Po ( 1 + k ) – D1

Po = Rs 100 K = 0.10 D1 = 0.0

P1 = 100(1 + 0.10) –0……= 110

P1 = 100(1 + 0.10) –5……= 105

M-M Hypothesis

No of shares: ∆np1 = I – ( E – D1 )

Where:∆np1 = change in MP of share = 105I = amount to be invested = 20 lacs E = earnings ……………... = 10 lacs D1 = Div. at t = 1………….. = 5 lacs∆n105 = 20,00,000 – ( 10,00,000 -5,00,000)∆n105 = 20,00,000 – 5,00,000∆n = 15,00,000 105 = 14,285

Traditional ApproachAdvocated by Gram & Dodd

Arguments:A1: Div. Dec. is a relevant………Influences value A2: Stock market places considerable Weight age on Div. than RE

Weight assigned to DIV is 3 times the weight assigned to RE

P = m( D + E/3 )

Traditional Approach

Criticism: Based on subjective judgment rather than on empirical evidence

Explanation

E1: Hypothesis Based on empirical evidence…..cite results of cross section regression analysis

E2: DIV. coefficient is much higher than RE.


Analysis: Conclusions reached by Gram & Dodd are not justified

R1: Omits risk……….., thus Distorts results

R2: Measurement of earnings Is subject to error… Transmitted to

RE.......Coefficient is biased

dividend decision & valuation of firm

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