Fundamentals of Firm Valuation based on Dividend Declaration Policy

1. Dividend and Firm
ValuationValuation
Dr. A N Shankar
Associate Prof. in Commerce
Sikkim University
Gangtok, Sikkim, India
anshankar9@gmail.com

2. Theories on Relationship between Dividend and Firm Value
Basic
Relevance
Gordon
WalterBasic
Theories
Walter
Irrelevance
Miller and
Modigliani

3. Relevance of Dividend for Firm Valuation Theories
Shareholders prefer current dividends and there is direct relationship
between dividend policy and market value of the firm depending upon its
growth stage.
WALTER’s MODEL
• Arguments:
– The relationship between r the (IRR) of the firms and k the cost of
capital of the firm . Firm would have optimum dividend policy
based on the relationship between r and k. , if r exceeds the k the
firm would retain the dividends (r>k not pay out) else it would pay
out.
– As long as there is a possibility to generate more wealth the firm
will not declare dividends (r>k). Such firms are called growth
firms.⸫ the dividend payout ratio =0%. OR,
– When r<k the shareholders may be given opportunity to maximise
their wealth from other avenues. ⸫ the dividend payout ratio
=100%. OR,
– Where r=k, managers will be indifferent and (Normal Firms) there
is no optimum dividend policy.

4. • Assumptions underlying Walter’s Model
– All financing is resorted to the retained earnings.
– There is no additional risk thus the r and k remain constant for
the new peoject.
– During the decision period the E= EPS and the D= Dividend Per
Share do not change for calculating firm value.
– Firm has perpetual life.
• Model :
P= Price of Equity shares, D= initial Dividend, ke=Cost of Equity capital,
g= expected growth rate of earnings.
– To capture earnings retentions we have :
– r= expected rate of returns of the firm or (IRR) , b = , retention rate
– ,

5. • Cost of Equity =
• Now: growth rate = change in Market Price of Equity ;
⸫ by substitution of value of g in ke equation we get :
Also, Change in Firm value measured in terms of change in Market value of shares
⸫ On substitution of value of ΔP we get for cost of equity⸫ On substitution of value of ΔP we get for cost of equity
And Firm value

6. From the following information show the effect of dividend policy of the firm on its Market price
of shares: Capitalisation rate, ke = 0.10 or 10%. Earnings Per Share = Rs 10.
Assume r = i) 15% , ii) 8%, and iii) 10%.
and D/P ratios i) 0% ii)25%, iii) 50%, iv)75%, v)100%
Solution (Proof)
EPS =E r ke
D/P ratio
=(1-b)
D= EPS
×(1-b)
E-D (E-D)
10 0.15 0.1 0 0 10 1.5 15 15 150
10 0.15 0.1 0.25 2.5 7.5 1.5 11.25 13.75 137.5
10 0.15 0.1 0.5 5 5 1.5 7.5 12.5 125
10 0.15 0.1 0.75 7.5 2.5 1.5 3.75 11.25 112.5
10 0.15 0.1 1 10 0 1.5 0 10 100
10 0.08 0.1 0 0 10 0.8 8 8 8010 0.08 0.1 0 0 10 0.8 8 8 80
10 0.08 0.1 0.25 2.5 7.5 0.8 6 8.5 85
10 0.08 0.1 0.5 5 5 0.8 4 9 90
10 0.08 0.1 0.75 7.5 2.5 0.8 2 9.5 95
10 0.08 0.1 1 10 0 0.8 0 10 100
10 0.1 0.1 0 0 10 1 10 10 100
10 0.1 0.1 0.25 5 5 1 5 10 100
10 0.1 0.1 0.5 7.5 2.5 1 2.5 10 100
10 0.1 0.1 0.75 10 0 1 0 10 100
10 0.1 0.1 1 0 10 1 10 10 100
It is observed that for r=ke the market price of share remains constant, r>ke the
Market Price of share increases with dividend retention ratio, and r<ke, Market Price
of share declines with increase in Dividend retention ratio.

7. EPS =E r ke
D/P ratio
=(1-b)
D=
EPS×(1-b)
E-D (E-D)
25 0.18 0.1 0 0 25 1.8 45 45 450
25 0.18 0.1 0.25 6.25 18.75 1.8 33.75 40 400
25 0.18 0.1 0.5 12.5 12.5 1.8 22.5 35 350
25 0.18 0.1 0.75 18.75 6.25 1.8 11.25 30 300
25 0.18 0.1 1 25 0 1.8 0 25 250
25 0.09 0.1 0 0 25 0.9 22.5 22.5 225
From the following information show the effect of dividend policy of the firm on its Market price
of shares
Capitalisation rate, ke = 0.10 or 10%. Earnings Per Share = Rs 25.
Assume r = i) 18% , ii) 9%, and iii) 10%.
and D/P ratios i) 0% ii)25%, iii) 50%, iv)75%, v)100%
Solution (Proof)
25 0.09 0.1 0 0 25 0.9 22.5 22.5 225
25 0.09 0.1 0.25 6.25 18.75 0.9 16.875 23.125 231.25
25 0.09 0.1 0.5 12.5 12.5 0.9 11.25 23.75 237.5
25 0.09 0.1 0.75 18.75 6.25 0.9 5.625 24.375 243.75
25 0.09 0.1 1 25 0 0.9 0 25 250
25 0.1 0.1 0 0 25 1 25 25 250
25 0.1 0.1 0.25 12.5 12.5 1 12.5 25 250
25 0.1 0.1 0.5 18.75 6.25 1 6.25 25 250
25 0.1 0.1 0.75 25 0 1 0 25 250
25 0.1 0.1 1 0 25 1 25 25 250
It is observed that for r=ke the market price of share remains constant, r>ke the
Market Price of share increases with dividend retention ratio, and r<ke, Market Price
of share declines with increase in Dividend retention ratio.

8. Gordon’s Dividend Capitalisation Model
• Assumptions:
• All equity Funded firm
• r and ke are constant
• The firm has perpetual life
• Retention ratio (D/P ratio)is constant. ⸫ growth rate, g=br is
constant.
• ke > br
Arguments
• Investors are risk averse. bird in a hand argument.• Investors are risk averse. bird in a hand argument.
• They penalise for uncertainty (charge premium for risk bearing)
• P= Price of a share, E= Earnings per share, b= percentage of
EPS retained,
⸫ (1-b) = Dividend Payout ratio,
ke= Capitalization rate or cost of capital.
br=g= Growth rate of the all equity firm

9. Solution
Given
EPS
Given
D/P ratio
=(1-b)
Given
ke
Given
r
b =(1-D/P
ratio)
br = g
ke- br
E × (1-b)
20 0.1 0.2 0.12 0.9 0.108 0.092 2 21.74
20 0.2 0.19 0.12 0.8 0.096 0.094 4 42.55
Example: Gordon’s Dividend Capitalisation Model.
From the following information about Hypo Ltd. r =0.12, EPS= Rs 20. Determine
the value of shares for
D/P ratio
=(1-b)
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
ke 0.2 0.19 0.18 0.17 0.16 0.15 0.14 0.13 0.12 0.11
20 0.2 0.19 0.12 0.8 0.096 0.094 4 42.55
20 0.3 0.18 0.12 0.7 0.084 0.096 6 62.5
20 0.4 0.17 0.12 0.6 0.072 0.098 8 81.63
20 0.5 0.16 0.12 0.5 0.06 0.1 10 100
20 0.6 0.15 0.12 0.4 0.048 0.102 12 117.65
20 0.7 0.14 0.12 0.3 0.036 0.104 14 134.62
20 0.8 0.13 0.12 0.2 0.024 0.106 16 150.94
20 0.9 0.12 0.12 0.1 0.012 0.108 18 166.67
20 1 0.11 0.12 0 0 0.11 20 181.82
It is observed that for given r and EPS with change in ke and D/P ratio the market
price of share changes. D/P ratio and Market price are positively related with
increasing ke the converse holds true.

10. Example: Gordon’s Dividend Capitalisation Model.
From the following information about Hypo Ltd. r =0.2, EPS= Rs 15. Determine
the value of shares for:
D/P ratio
=(1-b)
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
ke 0.2 0.19 0.18 0.17 0.16 0.15 0.14 0.13 0.12 0.11
Given
EPS
Given
D/P ratio
=(1-b)
Given
ke
Given
r
b =(1-D/P
ratio)
br = g
ke- br
E × (1-b)
15 0.1 0.2 0.2 0.9 0.18 0.02 1.5 75
15 0.2 0.19 0.2 0.8 0.16 0.03 3 100
15 0.3 0.18 0.2 0.7 0.14 0.04 4.5 112.5
Solution
15 0.3 0.18 0.2 0.7 0.14 0.04 4.5 112.5
15 0.4 0.17 0.2 0.6 0.12 0.05 6 120
15 0.5 0.16 0.2 0.5 0.1 0.06 7.5 125
15 0.6 0.15 0.2 0.4 0.08 0.07 9 128.57
15 0.7 0.14 0.2 0.3 0.06 0.08 10.5 131.25
15 0.8 0.13 0.2 0.2 0.04 0.09 12 133.33
15 0.9 0.12 0.2 0.1 0.02 0.1 13.5 135
15 1 0.11 0.2 0 0 0.11 15 136.36
It is observed that for given r and EPS with change in ke and D/P ratio the market
price of share changes. D/P ratio and Market price are positively related with
increasing ke

11. Miller M H and Modigliani F Dividend Irrelevance Theory
Value of a firm is indifferent to the distribution of profits. Firms value is purely a function
of the power of its assets and the underlying risk.
Assumptions
1. Perfect capital Markets
2. No taxes and Transaction Costs
3. Firms investment policy does noit change during the dividend decision period.
4. Investors are able to forecast the returns. (it was later dropped)
Argument :
Crux lies in arbitrage: The process of switching from one asset to another to
balance the risk and returns, is known as arbitrage. In this case the act of
dividend distribution is offset by issue of new stocks. This compensates the firm
with funds desired for investment.
Investment Avenue
Use Retained
Earnings
Arbitrage
Distribute retained Earnings and
Issue new Stock for amount
distributed.

12. Tenets
Investors are indifferent to the Dividend Payout : The amount dividend is declared the market
price of shares will decline, such a decline will be equal to sum of present value of
dividend received and the market value of shares.
Firms’ cost of capital won't affect the leverage and capital structure.
Proof :
Equation 1. Market Price of the shares in the beginning of the period equals the sum of PV
of Dividends and Market Price of shares.
P0 = Prevailing Market Price of Share
D1= Dividend received at the end of period 1,
P1= Market Price of share at the end of period , and ke= Cost of Equity Capital1 e
Equation 2. Assuming 100% Equity firm the capitalized value of the firm will be number of
shares (n) times the market price of shares :
Equation 3. If firm needs to resort to additional funds from external sources then Δn will be
the number of new shares issued at price P1 .
Total value of the firm is the sum of capitalized value of dividends due to be received at the
end of period 1, and difference between number of shares outstanding at the end of the
period 1 (including fresh issue) and value of new shares issued,

13. Equation 4. If the total of investment to be funded with new issue of shares:
ΔnP1 = Amounts collected from fresh proceeds
I = Funds for total Investment, ΔnD1 = Total Dividends Paid,
(E- nD1) = Retained Earnings.
5. On substitution of Equation 4 to Equation 3 we get
Equation 4 Equation 3
We get Equation 5
On solving we get
Since dividends are absent in Equation 6
we get that dividend dividends are irrelevant for determining firm value.

14. MM Co. Shares Trades @ Rs 200 with 20 Lakh shares outstanding . It has current income
of Rs 4 Crores with Rs20/- as EPS. Its earnings are earmarked for Investment. The Co.
announces dividends of Rs10/share, leaving Rs 2 Crores for capital investment. The
company resolves to issue another Rs2 Crores by fresh issue of shares. Find the following :
a) The issue price of new shares.
b) Number of Shares to be issued.
c) Value of the firm after the issue of new shares.
d) Value of Firm before and After New Issue.
Solution
If dividends are announced @ Rs 10/Share, before Fresh Issue ,If dividends are announced @ Rs 10/Share, before Fresh Issue ,
the Ex Dividend Price = 200-10=190.
The value of New Shares would be Rs 2 Crores = (Rs 10× 20,00,000 Shares)
Number of New Shares = =1,05,263.3
Total number of shares after Fresh Issue = 20,00,000 + 1,05,263 =21,05,263.
Total value of the MM Corp after Fresh Issue = 21,05,263.33 × Rs 190 = Rs 39,99,99,970
Approximately Rs 40 Crores .
So payment of Dividends is irrelevant for firm value

15. Example
Given : Existing shares 2,000, Current Price per share Rs500,
Expected returns 20% (ke). Retained Earnings Rs 6,00,000,
Investment needed Rs 10,00,000. Find the Market value of the firm,
for following dividend payment scenario per share in Rs: i) No
Dividend, ii) Rs 50, ii) Rs 75, iii)Rs100, iv) Rs125 v)Rs150 and
vi)Rs200.In case on no dividend is declared the projected price of
share would be
SolutionSolution

16. Given : Current Price of share Rs 500, r=20%, and 2000 Shares are outstanding
Proof of MM Dividend policy Irrelevance for Firm value
Dividend
Particulars
No
Dividend
50 75 100 125 150 200
Projected Price ={( Current Price (
1+r)) -Dividend Per Share}
600 550 525 500 475 450 400
Investment required in Rs 1,000,000 1,000,000 1,000,000 1,000,000 1,000,000 1,000,000 1,000,000
Earnings Available in Rs 600,000 600,000 600,000 600,000 600,000 600,000 600,000
Dividend (Amount of Dividend × No
Existing Shares) in Rs
- 100,000 150,000 200,000 250,000 300,000 400,000
Post Dividend Retained Earnings
(Retained Earnings - Dividend
Payment) ion Rs
600,000 500,000 450,000 400,000 350,000 300,000 200,000
Additional Funds Needed ( Total
Capital needed -Amount of Dividend
announced) in Rs
400,000 500,000 550,000 600,000 650,000 700,000 800,000
No. of New Shares to be Issued (
Capital needed ÷ Ex Dividend Price)
666.67 909.09 1,047.62 1,200 1,368.42 1,555.56 2,000
Total Shares in The Firm ( 2000
+New Issue) Units
2,666.67 2,909.09 3,047.62 3,200.00 3,368.42 3,555.56 4,000
Market value of Firm (Total Shares
× Ex Dividend Price) in Rs
1,600,000 1,600,000 1,600,000 1,600,000 1,600,000 1,600,000 1,600,000

17. Given : Current Price of share Rs 300, r=0.15%, and 1000 Shares are outstanding , Investment required Rs 10 Lakhs
Proof of MM Dividend policy Irrelevance for Firm value ( Retained Earnings Rs 3 Lakhs)
Dividend
Particulars
No
Dividend
20 30 40 50 75 90
Projected Price ={( Current Price (
1+r)) -Dividend Per Share}
345 325 315 305 295 270 255
Investment required in Rs 1,000,000 1,000,000 1,000,000 1,000,000 1,000,000 1,000,000 1,000,000
Earnings Available in Rs 300,000 300,000 300,000 300,000 300,000 300,000 300,000
Dividend (Amount of Dividend × No
Existing Shares) in Rs
0 20,000 30,000 40,000 50,000 75,000 90,000
Post Dividend Retained EarningsPost Dividend Retained Earnings
(Retained Earnings - Dividend Payment)
ion Rs
300,000 280,000 270,000 260,000 250,000 225,000 210,000
Additional Funds Needed ( Total Capital
needed -Amount of Dividend
announced) in Rs
700,000 720,000 730,000 740,000 750,000 775,000 790,000
No. of New Shares to be Issued ( Capital
needed ÷ Ex Dividend Price)
2028.99 2215.38 2317.46 2426.23 2542.37 2870.37 3098.04
Total Shares in The Firm ( 2000 +New
Issue) Units
3,028.99 3,215.38 3,317.46 3,426.23 3,542.37 3,870.37 4,098.04
Market value of Firm (Total Shares ×
Ex Dividend Price) in Rs
1,045,000 1,045,000 1,045,000 1,045,000 1,045,000 1,045,000 1,045,000

18. Alternative Forms of Dividend
• Capitalizing Reserves into shares, it changes the
form not the wealth of shareholders. Its Re-
organization of Shareholders Funds
• Impact on Book value of shares and Reserve and
Surplus. For Shareholders it’s a foresight of
incoming cash. Transaction cost is Zero
Bonus Shares
• Splitting the number of shares by increasing the
holding per share holder proportionately.
• Transaction cost is Zero, Wealth of shareholdersStock Splits • Transaction cost is Zero, Wealth of shareholders
in not affected.
Stock Splits
• The firm buys its own shares at a prescribed rate
from the willing shareholders. This enhances
control over the firm, and reflects firm’s wealth.
• The Process is subject to regulations.
Share Buy Back

19. References
Miller, M.H. and Modigliani, F. (1961) Dividend Policy, Growth, and the Valuation of Shares. The Journal of
Business, 34, 411-433.
Walter, J.E. (1963) Dividend Policy Its Influence on the Value of the Enterprise. The Journal of Finance, 18(2)
280-291.
Gordon, M. J. (1962). The Savings, Investment, and Valuation of a Corporation. Review of Economics and
Statistics, 44(1), 37-51.
Gordon M J(1963) Optimum Investment and Financing Policy, Journal of Finance, 18(3), 264-272
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