dividend decision sol

7/29/2019 Dividend Decision Sol

1/25

DIVIDEND DECISION

Q1 a. Market price per share of the company at the end of the year (i.e P1)

i. When dividend not paid

P0 =

150 =

P1 = 150( 1.12) - 0

P1 = 168

ii. When Dividend paid

P0 =

150 =

P1 = 150( 1.12) - 8

P1 = 160

b. New shares to be issued by the company (i.e m)


m =

=

= 1,19,047.619047 shares

ii. When dividend paid

m =

=

= 1,75,000 shares

c. Value of Firm (i.e nP0)


nP0 =

=

= Rs 1500 lakh


nP0 =

=

= Rs 1500 lakh

Thus market value of the Firm is same (Rs 1500 lakh) whether dividend is paid or not

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Q2 a. Market price per share of the company at the end of the year (i.e P1)

I When dividend not paid

P0 =

125 =

P1 = 125( 1.08) - 0P1 = 135

ii When Dividend paid

P0 =

125 =

P1 = 125( 1.08) - 6

P1 = 129

b. New shares to be issued by the company (i.e m)


m =

=

= 2962.962962 shares


m =

=

= 4961.240310 shares

c. Value of Firm (i.e nP0

)


nP0 =

=

= Rs 50 lakh


nP0 =

=

= Rs 50 lakh

Thus market value of the Firm is same (Rs 50 lakh) whether dividend is paid or not

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Q3 a. Market price of share according to MM approach


P0 =

15 =

P1 = 15( 1.14) - 1.35

P1 = 15.75

ii. When Dividend paid

P0 =

15 =

P1 = 15( 1.14) - 0

P1 = 17.10

b. Expected return after tax

i. If dividend paid

Dividend Received = Rs 1.35

Dividend after ordinary tax = 1.35 ( 10.3 )

= 0.945

Capital gains = 15.7515

= 0.75

Capital gains after tax = 0.75( 10.26)

= 0.555

Total Income after Tax = 0.945 + 0.555

= 1.5

Investment = Rs 15

Rate of Return = x 100

= 10%

ii. If dividend paid

Capital gains = 17.1015

= 2.1

Capital gains after tax = 2.1( 10.26)

= 1.554

Investment = Rs 15

Rate of Return = x 100

= 10.36%

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Q4If r = 20% ( i.e r > ke)

1. DP ratio 10% i.e b = 90 %

P0=

=

= Rs 180

2. DP ratio 40% i.e b = 60 %

P0=

=

= Rs 160

3. DP ratio 80% i.e b = 20 %

P0=

=

= Rs 120

4. DP ratio 100% i.e b = 0 %

P0=

=

= Rs 100

If r = 10% ( i.e r = ke)

1. DP ratio 10% i.e b = 90 %

P0=

=

= Rs 100

2. DP ratio 40% i.e b = 60 %

P0=

=

= Rs 100

3. DP ratio 80% i.e b = 20 %

P0=

=

= Rs 100

4. DP ratio 100% i.e b = 0 %

P0=

=

= Rs 100

If r = 8% ( i.e r < ke)

1. DP ratio 10% i.e b = 90 %

P0=

=

= Rs 84

2. DP ratio 40% i.e b = 60 %

P0=

=

= Rs 88

3. DP ratio 80% i.e b = 20 %

P0=

=

= Rs 96

4. DP ratio 100% i.e b = 0 %

P0=

=

= Rs 100

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Q5 E= Rs 6, kE= 10%, r= 20% , DP = 30%

P0 =

=

= Rs 102

According to Walter model, if r > KE, optimum DP ratio is 0% i.e Retention ratio should be 100%.

In given question DP is 30%, so it is not optimum ratio

Q6 Earnings of company = Rs 10,00,000

No. of shares = 2,00,000

EPS = Rs 5

DP ratio = 60%

Dividend per share = Rs 3 per share

i. Market value per share as per Walters model

P0 =

=

= Rs 34.26

ii. According to Walter model, if r > KE, optimum DP ratio is 0% i.e Retention ratio should

be 100%. If DP ratio is 0% then MP will be

P0 =

=

= Rs 52.083

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Q7 Statement of EPS

Earnings 30,00,000

Less Preference dividend

12 % of 100 lakhs 12,00,000

Earnings for equity share holders 18,00,000

No. of shares 3,00,000

EPS Rs 6 per share

r = 20%

KE =

PE =

KE =

= x 100 = 14.285714%

Dividend per share if MP is Rs 42 per share

P0 =

42 =

42 x 0.14285714 = d +

6 = d + 8.4 - d

68.4 = d ( 1 - )

- 2.4 = - d ( 0.40)

d =

d = 6

DP ratio = x 100

= 100 %

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Q8 Earnings Rs 2,00,000

No. of shares 20,000

EPS Rs 10 per share

Total dividend Rs 1,50,000

Dividend per share Rs 7.5 Current DP ratio 75%

KE =

= = 0.08 or 8%

r = x 100

= x 100

= 10%

If DP ratio is 75%, then according to Walter model MP of share is

P0 =

=

= Rs 132.81

According to Walter model if r > KE , then optimal dividend policy would be to pay Zero dividend.

Thus DP ratio 75% is not an optimum dividend policy. If no dividend is paid MP will be

P0 =

=

= Rs 156.25

So, MP can be increased by adopting a Zero dividend policy

ii. Companys Dividend policy will have no effect on the market value of share if r = K E,

i.e KE= 10%, And since PE =

So, PE at which dividend policy has no effect on market value of firm is = 10 times

iii. IF PE is 8 instead of 12.5, then which is the inverse of PE ratio would be 12.5 (i.e ) and in

such a situation KE> r and Market price as per Walter model would be

P0 =

=

= Rs 76

Since r < KE , optimum DP ratio will be 100%

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Q9 Market price of share

Walter model P0 =

=

= Rs 55

Gordon Model P0 =

=

= Rs 60

Q10 MP per share according to Gordon Model

Book value per share = Rs 137.80Return on Equity = 15%

Thus earnings = 15% x 137.80

= Rs 20.67

DP Ratio = 1 - 0.6

= 0.4 or 40%

P0 =

=

= Rs 91.87

MP per share according to Walter Model

P0 =

=

= Rs 103.35

MP per share according to perpetual growth model

P0 =

=

= Rs 91.89

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9/25

Q11 a. MP of share = Rs 40

EPS = Rs 12 per share

DP ratio = 45%

b = 10.45 = 0.55

r = 14%

P0 =

40 =

= + 0.077

= 0.212 or 21.2%

b. Dividend distributed during the year = 10 Lakh x 10 x 0.20

= Rs 20 lakh

Dividend per share =

= Rs 20 per share

Value of share = P0 =

=

= Rs 156.923

Q12 According to Linter model

Current Year dividend = ( 1 - A) x Last Year Dividend + EPS X DP ratio x A

a. Last year Dividend = Rs 9.8

Adjustment 45%Pay out ratio 60%

EPS Rs 20

Current year dividend = ( 10.45) 9.8 + 20 x 0.6 x 0.45

= Rs 10.79

b. If Adjustment is 20%

Current year dividend = ( 10.2) 9.8 + 20 x 0.6 x 0.2

= Rs 10.24



Last year Dividend = Rs 1.2

Adjustment 0.7

Pay out ratio 0.6

EPS Rs 3

Current Year dividend = ( 10.7) 1.20 + 3 x 0.6 x 0.7

= Rs 1.86

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10/25



Last year Dividend = Rs 5

Adjustment 0.5

Pay out ratio 70%

EPS Rs 10

Current Year dividend = ( 10.5) 5 + 10 x 0.7 x 0.5

= Rs 6

If incremental dividend to be maintained is 70%


= Rs 6.4

If incremental dividend is 30%


= Rs 5.6

Q15 a. According to residual approach, current years profits or earnings can be used for

financing capital expenditure and after financing capital expenditure, balance is

distributed as dividend

Current year profit = x 20

= Rs 600,00,000

So, capital expenditure of Rs 600,00,000 can be incurred without raising additional equity

b. i. Equity FundsESC 300,00,000

Reserves 1500,00,000

1800,00,000

Debt

12% debt 1000,00,000

15% debt 200,00,000

1200,00,000

Debt equity ratio = 12 : 18

= 2 : 3

Capital expenditure = 550 lakh

Raised from equity

reserves = 550 lakh x

= Rs 330 lakh

Raised from debt = Rs 220 lakh

Dividend distribution = Rs 600 lakhRs 330 lakh

= Rs 270 lakh

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ii. Dividend distribution without bothering about capital structure

Rs 600 lakh550 lakh

= Rs 50 lakh

c. If capital expenditure is Rs 800 lakh

i. Dividend distribution without affecting capital structure

Debt equity ratio = 2: 3

Capital Expenditure financed by equity reserves

800 lakh x = Rs 480 lakh

Dividend distribution = 600 lakh480 lakh

= 120 lakh

Dividend per share = = Rs 4 per share

ii. Dividend distribution without bothering about capital structure

Since capital expenditure of Rs 800 lakh is more than available profit of

Rs 600 lakh, so nil dividend

Q16 i. Statement of Dividend per share and external financing under residual approach

Particulars 1 2 3 4

Profit after tax 40 45 50 35

Capital expenditure 10 50 20 50

Profit for distribution 30 - 30 -

Dividend per share

(no of shares 8 crore) 3.75 - 3.75 -External financing - 5 - 15

ii Statement of Dividend per share and external financing if Debt equity ratio

of 7:3 is to be maintained

Particulars 1 2 3 4



Capital Expenditure from equity 10 x = 3 50 x = 15 20 x = 6 50 x = 15

PAT for distribution 37 30 44 20

Dividend per share = 4.625 = 3.75 = 5.5 = 2.5

External financing 103 = 7 5015 = 35 206 = 14 5015 = 35

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iii. Statement of Dividend per share and external financing required

if Dividend Pay-out ratio is 40%

Particulars 1 2 3 4



Profit for dividend (40%) 16 18 20 14

Dividend per share = 2 = 2.25 = 5.5 =2.5

Profit for capital exp. 24 27 30 21

External financing - 23 - 29

iv. Statement of Dividend per share and external financing if DP ratio

is 30% and minimum dividend per share to be Rs 1.5 per share

Particulars 1 2 3 4Profit after tax 40 45 50 35


Total dividend, if div per share

is Rs 1.5 per share 12 12 12 12

Total dividend if

DP ratio is 30% 12 13.5 15 10.5

Dividend payable 12 13.5 15 12

Dividend per share 1.5 1.6875 1.875 1.5

Profit for cap exp. 28 31.5 35 23

External financing - 18.5 - 27

v. I II III IV

Div per share 3.75 16.375 8.5 6.5625

Total Dividend 60 cr 131 cr 68 cr 52.5 cr

External financing 20 cr 91 cr 52 cr 45.5 cr

In case II both shareholders and Financial institutions will be happy

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Q17 Statement of Current market Price

A B

Market value of share after 1 year 640 600

Less Current market price p q

Capital gains 640p 600q

Less tax on capital gains @ 10% 640.10p 600.10q

Capital gains after tax (640p)(640.10p) (600q)(60q)

= Rs 5760.90p = Rs 5400.90q

Dividend receivable - Rs 40

Less tax on dividend 15% - Rs 6

Dividend income after tax - 406 = Rs 34

Return on investment in shares Rs 5760.90p 5400.90q + 34

Return on investment 16% 16%

Current MP 0.16 = 0.16 =

p = 543.40 p = 541.51

Q18 Statement of cash flow if dividend distributed Now

Earnings per share Rs 200

Dividend Pay out Rs 60

No. of share outstanding 2 crore

Total dividend pay-out ( 60 x 2crore) 12000 lakh

Less Dividend distribution tax x 12,000 1655.17 lakh

Amount received by investors Rs 10344.83 Lakh

Amount invested in Bank Rs 10344.83 lakh

Interest on Bank deposits 9%

Personal Income tax at 25% on 9% interest 2.25%

Effective interest rate on deposits 6.75%

Post maturity value of deposits

10344.83 x (1.0675)3 Rs 12,584.49 lakh

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Statement of cash flow if dividend distributed 3 years later

Earnings per share rs 200

Dividend pay-out (200 x 0.3) Rs 60

No of shares outstanding 2 crore

Total amount payable for dividend pay-out Rs 12000 lakh

Amount invested in Bank by MPL Rs 12000 lakh

Interest on Bank deposits 11%

Corporate tax rate on Interest 34% of 11% 3.74%

Effective Interest rate 7.265

Maturity value of deposits 12000 lakh (1 + 0.0726)3 14,808 lakh

Less dividend distribution tax 14,808 lakh x 2042.48 lakh

Amount available for investors 12,765.52 lakh

It is better for company to retain the dividend payout and invest the same in Bank and

distribute after 3 years, as it yields higher return to investors

Q19 d0 = Rs 2

g = 5%

KE = 10( 10.3) = 7%

Current Market price P0 =

Before budget announcement = = Rs 42

After Budget announcement = = rs 94.50

Q20 If the company invests Rs 1000 in Market

Pre tax rate of return on investment = 8%

Corporate tax rate = 36.75%

Effective rate of return on investment = 8(1-0.3675)

= 5.06%

Matured value of deposit = 1000(1.0506)5

= Rs 1279.93

Dividend payable = Rs 1279.93

Less dividend distribution tax 12.5% = Rs 142.21 1279.93 x

Amount available to shareholders = Rs 1137.72

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15/25

If dividend is distributed Now

Dividend to be distributed Rs 1000

Dividend distribution tax 1000 x Rs111.11

Amount available to shareholders Rs 888.89

Amount invested in bank for 5 years Rs 888.89

Rate of Interest 8%

Income tax rate for shareholders 30

Effective ROI 8 ( 10.3)

5.6%

Amount in the hands of investors 888.89(1.056)5

Rs 1167.26

Company should distribute dividend today and shareholder should invest in bank, as it will

increase yield of shareholders

Q21 i. Statement of Post tax return of A

Amount invested Rs 100

Dividend paid by co. Rs 15

Tax on dividend 30% Rs 4.5

Dividend income after tax Rs 10.50

Return after tax x 100 10.50%

ii. Statement of Post tax return on share of B


Appreciation in value of share 15% p.a ( assumed compounded)MP of share after 2 years 100(1.15)

2Rs 132.25

Capital gain 32.25

Tax on capital gain 30% x 32.25 Rs 9.675

Capital gain after tax Rs 22.575

Return after tax x 100 22.575 5 for 2 years i.e 11.2875% p.a

iii. Statement of Post tax return of A (if tax on dividend is 10%)


Dividend paid by co. Rs 15

Tax on dividend 10% Rs 1.5

Dividend income after tax Rs 13.50

Return after tax x 100 13.50%

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Statement of Post tax return on share of B (if tax on capital gains 15%)


Appreciation in value of share 15% p.a ( assumed compounded)

MP of share after 2 years 100(1.15)2

Rs 132.25

Capital gain 32.25

Tax on capital gain 15% x 32.25 Rs 4.8375

Capital gain after tax Rs 27.4125

Return after tax x 100 27.4125 % for 2 years i.e 13.706% p.a

Q22 Current market price of share is present value of all future dividends. Co is paying Rs 13 per

share indefinitely

Current market price =

= Rs 144.44

Q23 Current market price of share is present value of all futuredividends.

Co is planning to pay ( 5 x 1.2) Rs 6 per share indefinitely


= Rs 30

Q24 Current market price of share is present value of all future dividends.

If life expectancy of MD is 20 years, then company will pay dividend of Rs 30 per share

indefinitely from year 21

Current market price = x 0.149

= Rs 44.70

Market Price of share if company pays a dividend of Rs 5 per share indefinitely


= Rs 50 per share

Thus if MDs dividend policy is adopted Value of share is reduced by Rs 5.30 per share

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17/25

Q25 a. Current market price of share is present value of all future dividends.

P0 =

= = Rs 30

B i. Earning Price Model

P0 =

= = Rs 32.786

If Current market price per share is Rs 35 , share is overvalued

ii According to PE model

PE =

= = 9.524 times

Current market price = PE x EPS

= 9.524 x 2.25

= Rs 21.429

Q26 a. Growth rate of dividends

d5 = d1( 1 + g)4

14.03 = 10.7 ( 1 + g )4

( 1 + g) =

g = 1.07001

= 0.07 or 7%

b. Cost of Equity on old shares

KE = + g

= + 0.07

= 19%

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18/25

c. Cost of equity of new shares

KE = + g

= + 0.07

= 19.38 %

Q27 d0 = Rs 2

g = 5%

Ke = 15.5%

a. MP If g is 5%

P0 =

= = Rs 20

b. MP if g is 8%

P0 =

= = Rs 28.8

c. MP if g is 3%

P0 =

= = Rs 16.48

Q28 Growth rate12 year = 12%

34 year = 10%

From 5thyear = 8%

d0 = Rs 1.50 r = 16%

Current Market price or intrinsic value of share is Present value of all future dividends

Current market price = Present value of d1to d4 + Present value of P4

= 1.68 x 0.862 + 1.88 x 0.743 + x 0.552

+ 2.068 x 0.640 + 2.274 x 0.552= 5.42 + 16.94

= 22.36

(PTO)

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19/25

Price at the end of 1st, 2nd, 3rd, 4th, 5thyear

Year 1 P0 =

22.36 =

P1 = 24.257

Year 2 P1 =

24.257 =

P2 = 26.25812

Year 3 P2 =

26.25812 =

P3 = 28.3914

Year 4 P3 =

28.3914 =

P4 = 30.66

Year 5 P4 =

30.66 =

P5 = 33.10

Q29 d0 = 3.50

g = 6%

r = 15%

Intrinsic value of share P0 =

= = Rs 41.222

If Current market price is Rs 50, g is

P0 =

50 =

7.5 - 50g = 3.5 + 3.5g

53.5 g = 4

g = = 0.0748 or 7.48%

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Q30 Growth rate

12 years 10% d0 = Rs 5

35 years 12% r = 17.5%

67 12.50%

Above 7 11%

Current market price is present value of all future outflows

Year Dividend / outflow factor Present value / Price

1 5.50 0.851 4.681

2 6.05 0.724 4.380

3 6.776 0.616 4.174

4 7.589 0.525 3.984

5 8.5 0.446 3.791

6 9.5625 0.380 3.634

7 10.758 0.323 3.475

7 = 183.714 0.323 59.340

Current market price 87.459

Q31 earnings - 2.4 lacs

Shares - 1 lac

KE - 12%

i. MP if all earnings are distributed as dividend

PE =

= = 8.333 times

PE =

8.333 =

Price = 8.333 x 2.4 = Rs 20

ii. If dividend payout is 50 % and earnings and dividends likely to grow by 8%

CMP =

= Rs 32.40

iii. Earnings and dividends grow at 10% for 2 years and at 4 % thereafter

Year Dividend factor Present value

1 2.4 x 1.1 = 2.64 0.893 2.358

2 2.904 0.797 2.314

2 = 37.752 0.797 30.088

Market price 34.76

or

CMP =

= Rs 20

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21/25

Q32 E0 = 2 Growth rate of EPS DP ratio

14 years 20% ------ 25%

58 years 12% ------ 40%

Above 8 years 6% ------ 50%

At the end of 8thyears PE ratio is 8.5 times, EPS in denominator is of 9thyear

i. Statement of annual EPS and DPSYear EPS DPS

1 2.4 0.6

2 2.88 0.72

3 3.456 0.864

4 4.1472 1.0368

5 4.645 1.858

6 5.2024 2.081

7 5.827 2.331

8 6.526 2.6104

9 6.918 3.459

Current market price is PV of all future dividendsPE (of 8

thyr using 9

thyr EPS) = 8.5

Price at the end of 8 thyr = PE (8thyr) x EPS (9thyr)

= 8.5 x 6.918

= Rs 58.803

Current Market Price = Present value of d1 - d8 + Present value of MP at the

End of 8thyear

= 0.6 x 0.877 + 0.72 x 0.769 + 58.803 x 0.351

0.864 x 0.675 + 1.0368 x 0.592

1.858 x 0.519 + 2.081 x 0.456

2.331 x 0.4 + 2.6104 x 0.351

= 6.039 + 20.640= Rs 26.68

b. Expected rate of Return, when stock price is Rs 30

Rate of return will be that rate at which present value of cash outflow (dividend) is equal

to cash inflow (MP) i.e rate at which PV of all dividend is $ 30

Present value of all cash outflows at 14% = 26.68

Present value of cash outflow at 10% = 0.6 x 0.909 + 0.72 x 0.826 +

0.864 x 0.753 + 1.0368 x 0.683 + 1.858

x 0.620 + 2.081 x 0.564 + 2.331 x 0.513

2.6104 x 0.467 + 58.803 x 0.467= Rs 34.70

Expected rate of return is

= 14 - x 4

= 12.344%

14%------------26.68

? ------------- 30

10%------------34.70

For diff of IRR of 4%, change in price is

8.02, for diff in rate of 3.32 Change in

price is 14 - x 4

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22/25

Q33 PE ratio = 7.5

Retained earnings Rs 3 (37.5%)

Total earnings = Rs 8 per share Div per sh = 83 = 5

i. MP = PE x EPS

= 7.5 x 8

= Rs 60

KE = + g

= + 0.12

= 21.33%

ii. P0 =

=

= Rs 67.80

iii. P0 =

=

= Rs 191.67

Q34 Statement of profit after Tax

Operating Profit 25,00,000

Less Interest on secured loan 3,75,000 ( 25 lac x 0.15)

Interest on unsecured loan 1,25,000 (10,00,000 x 0.125)

Profit before tax 20,00,000

Tax 10,00,000

Profit after tax 10,00,000

Number of equity shares 2,50,000

EPS 4

PE ratio (given) 12.5

Value of share 4 x 12.5 Rs 50

Q35 EPS0 = Rs 5 Growth rate Past 4 years 4%

DPS0 = Rs 2 Future 2%

Current PE = 7 times = 14%

i. Current MP P0 =

= = Rs 17

Estimated PE ratio = = 3.4 times

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ii. Current PE ratio = 7 times

Current EPS = 5

Actual price in the market = 7 x 5 = Rs 35

P0 =

35 =

35 (0.14 - g) = 2 ( 1 + g)

4.9 - 35g = 2 + 2g

37 g = 2.9

g = 0.0784 or 7.84%

Q36 d1 Rs 2 per share

g 7%

RF 9%

r 13% 1.5 , likely to increase to 1.75

KE = RF+ ( RM - RF)

= 9 + 1.5 (139)

= 15%

P0 =

= = Rs 26.75

If increased to 1.75

KE = RF+ ( RM - RF)

= 9 + 1.75 (139)

= 16%

P0 =

= = Rs 23.778

Q37 RF = 10% d (2002) = d7 = Rs3

RM- RF= 5% d (1996) = d1 = Rs 2.115

= 1.6

Growth rate d7 = d1( 1 + g )6

3 = 2.115 ( 1 + g)6

g = - 1

= 0.06 or 6%

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Cost of Equity = RF+ ( RM - RF)

= 10 + 1.6 (5 )

= 18%

P0 =

= = Rs 26.5

Q38 i. d1 = Rs 7

DP ratio = (10.3)

= 0.7

EPS = = Rs 10

ii. g = b.r

0.06 = 0.3 x r

r = = 0.2 or 20%

iii. Value of share Value of share without + Growth

(along with growth = growth opportunities opportunities

Opportunities)

= + Vg

= + Vg

175 = 100 + Vg

Vg = 175 - 100

= Rs 75

Q39 KE = 15%

P0 = Rs 80 ( after growth)

Value of growth opportunities = Rs 20

Value of share without growth = Rs 80Rs 20 = Rs 60

Value of share Value of share without + Growth

(along with growth = growth opportunities opportunities

Opportunities)

= + Vg

80 = + 20

60 =

EPS = 60 x 0.15

= Rs 9

Earning Price Ratio = = = 0.1125

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dividend decision sol

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