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DIVIDEND DECISIONS
Solution 1:

Solution 2:

After Doing Analysis of above table it seems Y ltd is more stable in distribution of dividend, compared
to X ltd that is why avg price of Y ltd (Rs.25.40) is higher than avg price of X ltd (Rs.24.00).

Advice to X Ltd:

• Pay Constant Dividend.

• More Payout Ratio.

Walter’s Model:
Theoretical Market Value of Equity Share (P0) = D + {R/Ke (E-D)} => D + {R/Ke (E-D)}
Ke Ke Ke
D – Dividend per share
E – Earnings per share
R – Return on Investment
Ke – Cost of Equity

If R>Ke – 0% Dividend Payout is the optimum payout Ratio

If R<Ke – 100% Dividend Payout is the optimum payout Ratio
If R=Ke – ANY Dividend Payout Ratio will give the same P0.

P0 = PV of all Future Cash Flows => PV of Dividend + PV of Retained Earnings

Solution 3:

Walter Model

(P0) = D + {R/Ke (E-D)}

Ke
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P0 = (6*30%) + 0.20/0.10 (6-1.80)

0.10

P0 = 1.80 + 2(4.20)
0.10

P0 = Rs.102

This is not the Optimum dividend payout ratio as R (20%) > Ke (10%) optimal dividend payout shall be
0%, as per Walter Model.
Hence at Optimum Dividend P/o Ratio P0 = 0 + {0.20/0.10 (6 - 0)} = Rs.120.
0.10

Note: At optimum dividend policy P0 shall be the highest under Walter Model.

Solution 4:

Walter Model

(P0) = D + {R/Ke (E-D)}

Ke

E = 5,00,000/1,00,000 = Rs.5
D = (5*60%) = Rs.3
Ke = 12%
R = 15%

P0 = 3 + {0.15/0.12 (5-3)}
0.12

P0 = Rs.45.83

Optimum Dividend Payout ratio in this case shall be 0% as R (15%) > Ke(12%), hence P0 at that P/o
Ratio is = 0 + {0.15/0.12 (5 - 0)} = Rs.52.083
0.12

Solution 5:

Walter Model
(P0) = D + {R/Ke (E-D)}
Ke
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EPS = Rs.10
Ke = 10%

Return on Dividend Payout Ratio

Investment Dividend 50% Dividend 75% Dividend 100%
(ie.D=Rs.5.00) (ie.D=Rs.7.50) (ie.D=Rs.10.00)
5 + 0.15/0.10 (10 – 5) 7.50 + 0.15/0.10 (10 - 7.50) 10 + 0.15/0.10 (10 – 10)
0.10 0.10 0.10

R = 15%

P0 = Rs.125 P0 = Rs.112.50 P0 = Rs.100

5 + 0.10/0.10 (10 – 5) 7.50 + 0.10/0.10 (10 – 7.50) 10 + 0.10/0.10 (10 – 10)

0.10 0.10 0.10

R = 10%

P0 = Rs.100 P0 = Rs.100 P0 = Rs.100

5 + 0.05/0.10 (10 – 5) 7.50 + 0.05/0.10 (10 – 7.5) 10 + 0.05/0.10 (10 – 10)

0.10 0.10 0.10

R = 5%

P0 = Rs.75 P0 = Rs.87.50 P0 = Rs.100

Solution 6:

Walter Model

(P0) = D + {R/Ke (E-D)}

Ke

42 = D + 0.20/0.16 (6 – D)
0.16

42 = D + 1.25 (6 – D)
0.16

6.72 = D + 7.50 – 1.25D

0.25D = 0.78
D = Rs.3.12

Working Notes:
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#1: Computation of EPS

Particulars Amount (Rs.)
Net Profits (PAT) 30,00,000
(-) Preference Dividend (12,00,000)
EAESH 18,00,000
No. of Shares 3,00,000
EPS 6

Dividend Payout Ratio = DPS/EPS

Dividend Payout Ratio = 3.12/6*100 = 52%

Solution 7:

Walter Model
(P0) = D + {R/Ke (E-D)}
Ke

ROI = Total Earnings/ Total Investment

ROI = 4,00,000/40,00,000 = 10%

Price Earnings (P/E) Ratio = MPS/EPS

Ke (Earnings Approach) = EPS/MPS = 1…
P/E
Ke = 1/12.50 = 0.08*100 = 8%

Total No. of shares (FV as Rs.100) = 40,000

EPS = Earnings/ No. of shares

EPS = 4,00,000/40,000 = Rs.10

DPS = Total Dividend/No. of Shares

DPS = 3,20,000/40,000 = Rs.8

P0 = 8 + 0.10/0.08 (10-8)
0.08

P0 = Rs.131.25

Optimum Dividend Payout Ratio is 0% as R (10%) > Ke (8%). Hence the company is not having Optimum
payout Ratio.

Optimal P0, under 0% dividend payout ratio shall be

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P0 = 0 + 0.10/0.08 (10-0)
0.08

P0 = 12.50 / 0.08
P0 = Rs.156.25

Solution 8:

EPS = 2,00,000/20,000 = Rs.10

DPS = 1,50,000/20,000 = Rs.7.50

ROI = 2,00,000/20,00,000 = 0.10*100 = 10%

Ke = 1/12.50 = 8%

Part (i)
No, the company is not following optimum dividend payout ratio.
As ROI (10%) > Ke (8%), Optimum dividend P/O should be 0%.
However the company is having D/P ratio of 75%.

Part (ii)
Dividend Policy will have no effect on the value of the shares when ROI = Ke
Hence if ROI is 10% = Ke should be 10%

Ke (0.10) = 1/P/E
P/e = 1/0.10 = 10 times

Part (iii)
If P/E Ratio is 8 instead of 12.50 Times then in that case
Ke = 1/8 = 0.1250*100 = 12.50%

Hence ROI (10%) < Ke (12.50%), Hence optimum dividend Payout ratio is 100% in this case.
Yes my decision will change if P/E is 8 instead of 12.50 Times.

Gordon Model (Dividend Discount Model):

TMP (P0) = D/Ke

(Without Growth)

TMP (P0) = D1/Ke-g

(With Growth)
This formula is derived from Ke = D1/P0 + g => Ke – g = D1/P0

TMP = PV of all future dividends only.

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Solution 10:

Gordon’s Model

TMP (P0) = D1/Ke-g

(With Growth)

Ke (Given) = 12%
ROI (Given) = 15%

PAT = (PBT) 2.50 Cr (-) (Tax @ 40%) 1.00 Cr = 1.50 Cr

EPS = PAT/No. of shares = 1.50 Cr/0.50 Cr = Rs.3

DPS = Dividend Paid/ No. of shares

Dividend Payout Ratio = 1 – Retention Ratio = 1 – 0.40 = 0.60*100 = 60%

DPS = (1.50*0.60) / 0.50 = 0.90/0.50 = Rs.1.80

G = Retention Ratio (b) * Return on Investment (r)

G = 0.40 * 0.15
G = 0.06 * 100 = 6%

D1 = D0 + g = 1.80 + 6% = 1.908

P0 = 1.908 / (0.12 – 0.06)

P0 = 31.80

Solution 11:

Particulars Payout @ 50% Payout @ 80% Payout @ 20%

Retention Ratio (1 – P/O) 50% 20% 80%
Ke 10% 10% 10%
No. of shares 50,00,000 50,00,000 50,00,000
EPS (Total Earnings 1.50 1.50 1.50
(500L*15% = 75L)/(No of
shares 50L)
D0 (EPS * Payout Ratio) 0.75 1.20 0.30
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G (Retention (b) * ROI (r) 7.5% 3% 12%

D1 (D0 * (1 + G)) 0.806 1.236 0.336
P0 = D1/(Ke-g) 0.806/(0.10-0.075) 1.236/(0.10-0.03) 0.336/(0.10-0.12)
P0 32.25 17.65 Not Valid
(coz G is Higher than Ke)

Growth rate in this case is hidden, so if the profits are retained then generally there shall be growth
in the business

Alternatively, Do shall also be considered as D1, due to lack of information.

Solution 12:

Gordon’s Model

TMP (P0) = D1/Ke-g

(With Growth)

Before Budget:

P0 = 2.10/(0.10-0.05) = Rs.42

After Budget:
If DDT is imposed then, Shareholder Expected return shall be after tax since earlier he used to get
10% from company and pay 3% (ie. 30% of the 10% received) from his own pocket. So effectively his
return was only 7%.
Ke = 10% - (10%*30%) = 7% (after Tax)

P0 = (1.80 + 5%)/(0.07-0.05) = Rs.94.50

Solution 13:

Gordon’s Model

TMP (P0) = D1 / (Ke - g)

(With Growth

Do – Rs.2
Ke – 15.50%
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CMP if growth rate is 5%

P0 = (2 * 1.05) / (0.155 – 0.05)
P0 = Rs.20

Part (i): If growth rate rises to 8%

P0 = (2 * 1.08) / (0.155 – 0.08)
P0 = Rs.28.80

Part (ii): If growth rate falls to 3%

P0 = (2 * 1.03) / (0.155 – 0.03)
P0 = Rs.16.48

Solution 14:

Part (i):
Gordon’s Model

(P0) = D1/Ke-g
(With Growth

Ke = D1/P0 + g

Ke = {(3.36/146)} + 0.075

Ke = 9.80%

Part (ii):

Ke = 5.376 (# 2) + 0.06 (#1)

146
Ke = 9.68%

# Working Notes

# 1: Calculation of Growth Rate:

G = Retention Ratio (b) * Return on Investment (r)
G = 0.60 * 10% = 6%

# 2: Calculation of DPS:
Dividend Payout Ratio = 40%
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DPS = EPS (# 3) * Payout Ratio

DPS = 13.44*40

DPS = Rs. 5.376

# 3: Calculation of EPS of Part (i)

G = br
7.50% = b * 10%
Retention Ratio (b) = 75%
Hence Payout Ratio = 25%

EPS = DPS/Payout Ratio

EPS = 3.36/25%
EPS = Rs.13.44

Note:
• Calculation of EPS is very different
• Calculation of new dividend is unique
• In this question growth rate is hidden in part (ii) which was calculated through Retention ratio
and return on book equity.

Solution 15:

Gordon’s Model

TMP (P0) = D1/Ke-g

(With Growth

Year EPS DPS PVF @ 15% PV of DPS

2015 12.00 4.80 0.870 4.176
(9.60*125%) (3.84*125%)
2016 15.00 6.00 0.756 4.536
(12.00*125%) (4.80*125%)
2017 16.50 8.25 0.658 5.429
(15*110%) (50%^^ of 16.50)
14.141

^^ Payout Ratio changed to 50%

After 2017, the perpetuity value assuming 10% constant annual growth is:
D4 = 8.25 * 110% = 9.075
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Therefore P3 (after 3 years) from the end of 2017

P3 = D4 / ke - g
9.075/0.15 – 0.10 = Rs.181.50

This must be discounted back to the Present Value, using the 3 year Discount Factor @ 15%.

Particulars Rs.
PV of P0 (181.50 * 0.658) 119.43

(+) PV of Dividends 2015 to 2017 14.14

Expected Market price per share 133.57
PE Ratio (Current Year is 2015) (133.57/12) 11.13 times

Traditional or Graham & Dodd Model

P = m [D + E/3]

P = Market Price
M = multiplier
D = DPS
E = EPS

From the Formula we can say that this approach gives more weight to DPS when compared to EPS,
Since EPS is divided by 3 and DPS is divided by 1.

Solution 16:

P = m [D + E/3]

58.33 = 7 (5 + E/3)
58.33 = 35 + 2.31E
2.31E = 23.33
E = Rs.10

Solution 17:

P = m [D + E/3]
P = 9 (0.40E + E/3)
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P = 9 (0.40E + 0.33E)
P = 6.57E
ie. MP is 6.60 times of E
P/E Ratio = MPS/EPS, Hence 6.60 is my P/E Ratio

Lintner’s Model:

D1 = D0 + {(EPS*Target Payout) – D0} * Af

EPS = Shall be the future EPS1 and not EPS0

Af = Adjustment Factor

Solution 18:

D1 = D0 + {(EPS*Target Payout) – D0} * Af

D1 = 9.80 + {(20*60%) – 9.80} * 45%

D1 = 9.80 + 0.99

D1 = Rs.10.79

Solution 19:

D1 = D0 + {(EPS*Target Payout) – D0} * Af

D1 = 1.20 + {(3*60%) – 1.20} * 0.70

D1 = 1.20 + 0.42

D1 = Rs.1.62

Modigliani & Miller’s Approach:

MM approach - Dividend Irrelevancy Approach

Formula No.1: P1 = P0 (1+Ke)
This formula can be understood with the help of following
If the investor invests Rs.100 and expects 10% return. Then he would Require Rs.110 P1.
Hence P1 = 100 (1 + 10%) = Rs.110
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Formula No.2: P1 = P0 (1+Ke) – D1

When company makes the payment of Dividend Eg. Rs.5. Earlier investor was expecting Rs.110
Now he will Expect P1 Rs.105 (110 – 5)

P0 = P1 + D1
1 + Ke

Solution 20:

∆n = Investment – (Earnings - Dividend)

MV1 = n1 * P1
Situations P1 = P0 (1 + Ke) – D1 P1

Mv1 =
P1 =100 (1 + 0.12) – ∆n = 10,00,000 – (5,00,000 – 1,00,000)
a) If dividend (10,000+5,882) *
10 102
paid 102
P1 = 102 ∆n =5,882.35
Mv1 = 16,19,964
Mv1 =
b) If ∆n = 10,00,000 – (5,00,000 – 0)
P1 =100 (1 + 0.12) – 0 (10,000+4,464.28)
dividend 112
P1 = 112 * 112
not paid ∆n =4,464.28
Mv1 = 16,19,964

Solution 21:

∆n = Investment – (Earnings - Dividend)

Situations P1 = P0 (1 + Ke) – D1 P1

∆n = 3,20,00,000 – (1,60,00,000 – 51,20,000)

P1 =120 (1 + 0.096) – 6.40
a) If dividend paid 125.12
P1 = 125.12
∆n =1,68,798
∆n = 3,20,00,000 – (1,60,00,000 – 0)
P1 =120 (1 + 0.096) – 0
b) If dividend not paid 131.52
P1 = 131.52
∆n =1,21,654.50

Solution 22:

# Working Notes

# 1: Calculation of Price of shares:

P1 = P0 (1 + Ke) – D1
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(a) When Dividend is not paid

P1 = 100 (1 + 0.10)
P1 = Rs.110

(b) When Dividend is paid

P1 = 100 (1 + 0.10) – 5
P1 = Rs.105

#2: Calculation of Additional No. of shares

∆n = Investment – (Earnings - Dividend)
P1

a) When dividend is not paid

∆n = 10,00,000 – (5,00,000 – 0)
110
∆n = 4,545 shares

b) When dividend is paid

∆n = 10,00,000 – (5,00,000 – 2,50,000)
105
∆n = 7,142 shares

#3: Market Value of shares

Mv1 = n1 * P1

a) When dividend is not paid

Mv1 = (50,000 + 4,545) * 110
Mv1 = 59,99,950 => 60,00,000

b) When dividend is paid

Mv1 = (50,000 + 7,142) * 105
Mv1 = 59,99,910 => 60,00,000