Shares & Dividends — Exercise 3

Find the market value of:

(i) 350, ₹ 100 shares at a premium of ₹ 8.

(ii) 240, ₹ 50 shares at a discount of ₹ 5.

Answer

(i) Given,

Face Value = ₹ 100

Premium = ₹ 8

Market Value per share = Face Value + Premium = ₹ 100 + ₹ 8 = ₹ 108.

∴ Total market value of 350 shares = 350 × ₹ 108 = ₹ 37,800.

Hence, the market value is ₹ 37,800.

(ii) Given,

Face Value = ₹ 50

Discount = ₹ 5

Market Value per share = Face Value - Discount = ₹ 50 - ₹ 5 = ₹ 45

∴ Total market value of 240 shares = 240 × 45 = ₹ 10,800.

Hence, the market value is ₹ 10,800.

Find the annual income from 450, ₹ 25 shares, paying 12% dividend.

Answer

Given,

Number of shares = 450

Face Value of 1 share = ₹ 25

Rate of dividend = 12%

By formula,

Annual income = No. of shares × Rate of div. × N.V. of 1 share

= $450 \times \dfrac{12}{100} \times 25$

= 450 × 3

= ₹ 1,350.

Hence, the annual income from the shares equal to ₹ 1,350.

Mr. Gupta invested ₹33000 in buying ₹100 shares of a company at 10% premium. The dividend declared by the company is 12%.

Find:

(i) the number of shares purchased by him.

(ii) his annual dividend.

Answer

(i) Money invested = ₹33000

N.V. of share = ₹100

M.V. = N.V + Premium

= ₹100 + $\dfrac{10}{100}$ × 100

= ₹100 + ₹10

= ₹110.

Number of shares = $\dfrac{\text{Money invested}}{\text{M.V}} = \dfrac{33000}{110} = 300$

Hence, no. of shares purchased = 300.

(ii) By formula,

Annual dividend = Number of shares × Rate of dividend × N.V.

= 300 × $\dfrac{12}{100}$ ×100

= ₹3600.

Hence, annual dividend = ₹3600.

A man invests ₹ 22,500 in ₹ 50 shares available at 10% discount. If the dividend paid by the company is 12%, calculate :

(i) the number of shares purchased;

(ii) the annual dividend received;

(iii) the rate of return he gets on his investment.

Answer

Given,

Investment = ₹ 22,500

Face Value = ₹ 50

Discount Rate = 10%

Discount = $\dfrac{10}{100} \times 50$ = ₹ 5

Market Value = Face Value - Discount = ₹ 50 - ₹ 5 = ₹ 45

Rate of dividend = 12%

(i) By formula,

Number of shares = $\dfrac{\text{Investment}}{\text{Market value of each share}}$

= $\dfrac{22,500}{45}$

= 500.

Hence, the number of shares purchased is 500.

(ii) By formula,

Annual dividend = No. of shares × Rate of div. × N.V. of 1 share

= $500 × \dfrac{12}{100} \times 50$

= ₹ 3,000.

Hence, the annual dividend received is ₹ 3,000.

(iii) By formula,

Rate of return = $\dfrac{\text{Income}}{\text{Investment}} \times 100$

= $\dfrac{3000}{22500} \times 100$

= 13.33%.

Hence, the rate of return is 13.33%.

Find the market price of 12%, ₹ 25 shares of a company which pays a dividend of ₹ 1,875 on an investment of ₹ 20,000.

Answer

Given,

Face Value = ₹ 25

Rate of dividend = 12%

Annual dividend = ₹ 1,875

Investment = ₹ 20,000

By formula,

Income from each share = Rate of div. × N.V. of 1 share

= $\dfrac{12}{100} \times 25$

= ₹ 3.

$\text{Number of shares bought} = \dfrac{\text{Total annual income}}{\text{Annual income from 1 share} }\\[1em] = \dfrac{1875}{3} \\[1em] = 625. \\[1em] \text {Market price per share} = \dfrac{\text{Investment}}{\text{Number of shares}} \\[1em] =\dfrac{20000}{625} \\[1em] = ₹ 32.$

Hence, the market price per share is ₹ 32.

Mr. Ram Gopal invested ₹ 8,000 in 7%, ₹ 100 shares at ₹ 80. After a year, he sold these shares at ₹ 75 each and invested the proceeds (including his dividend) in 18%, ₹ 25 shares at ₹ 41. Find :

(i) his dividend for the first year;

(ii) his annual income in the second year;

(iii) the percentage increase in his return on his original investment.

Answer

Given,

For initial investment,

Investment = ₹ 8,000

Face Value = ₹ 100

Market Value = ₹ 80

Dividend Rate = 7%

(i) By formula,

Number of shares = $\dfrac{ \text{Investment}}{ \text{Market value of each share}} = \dfrac{8000}{80}$ = 100

By formula,

Dividend for the first year = No. of shares × Rate of div. × N.V. of 1 share

$= 100 \times \dfrac{7}{100} \times 100$

= ₹ 700

Hence, dividend for the first year is ₹ 700.

(ii) Given,

Selling Price of each share = ₹ 75

Total sale value = Number of shares × Selling Price of each share = 100 × 75 = ₹ 7,500

Total proceeds = Total sale value + Dividend from first year

= ₹ 7,500 + ₹ 700 = ₹ 8,200.

He invested the proceeds in 18%, ₹ 25 shares at ₹ 41.

In second Investment :

Face Value = ₹ 25

Market Value = ₹ 41

Dividend Rate = 18%

By formula,

Number of shares = $\dfrac{\text{Investment}}{\text{Market value of each share}} = \dfrac{8200}{41}$ = 200.

By formula,

Annual income = No. of shares × Rate of div. × N.V. of 1 share

= $200 \times \dfrac{18}{100} \times 25$

= ₹ 900.

Hence, Mr. Ram's annual income in the second year equals to ₹ 900.

(iii) Original annual income = ₹ 700

New annual income = ₹ 900

Increase in income = ₹ 900 - ₹ 700 = ₹ 200

Percentage increase = $\dfrac{\text{Increase in income}}{ \text{Initial investment}} \times 100$

= $\dfrac{200}{8000} \times 100$

= 2.5%

Hence, the percentage increase in return on original investment equals to 2.5%.

Amit Kumar invests ₹ 36,000 in buying ₹ 100 shares at ₹ 20 premium. The dividend is 15% per annum. Find :

(i) the number of shares he buys;

(ii) his yearly dividend;

(iii) the percentage return on his investment.

Give your answer correct to the nearest whole number.

Answer

Given,

Investment = ₹ 36,000

Face Value = ₹ 100

Premium = ₹ 20

Market Value = Face value + Premium = ₹ 100 + ₹ 20 = ₹ 120

Dividend Rate = 15%

(i) By formula,

Number of shares = $\dfrac{\text{Investment}}{\text{Market value of each share}} = \dfrac{36000}{120}$ = 300

Hence, Amit buys 300 shares.

(ii) By formula,

Annual dividend = No. of shares × Rate of div. × N.V. of 1 share

= $300 \times \dfrac{15}{100} \times 100$

= ₹ 4,500.

Hence, Amit's yearly dividend is ₹ 4,500.

(iii) By formula,

Percentage return = $\dfrac{\text{Income}}{\text{Investment}} \times 100$

= $\dfrac{4500}{36000} \times 100$

= 12.5% ≈ 13%.

Hence, the percentage return on investment equals to 13%.

Ajay owns 560 shares of a company. The face value of each share is ₹ 25. The company declares a dividend of 9%. Calculate :

(i) The dividend that Ajay will get;

(ii) The rate of interest on his investment, if Ajay had paid ₹ 30 for each share.

Answer

Given,

Number of shares = 560

Face Value = ₹ 25

Dividend Rate = 9%

(i) By formula,

Annual dividend = No. of shares × Rate of div. × N.V. of 1 share

= $560 \times \dfrac{9}{100} \times 25$

= ₹ 1,260.

Hence, the dividend that Ajay receives equals to ₹ 1,260.

(ii) Given,

Market value = ₹ 30

By formula,

Investment = Number of shares × Market value

= 560 × 30 = ₹ 16,800.

By formula,

Percentage return = $\dfrac{\text{Income}}{\text{Investment}} \times 100$

= $\dfrac{1260}{16800} \times 100$

= 7.5%.

Hence, the rate of interest (return) is 7.5%.

Mohan Lal invested ₹ 29,040 in 15%, ₹ 100 shares of a company quoted at a premium of 20%. Calculate :

(i) the number of shares bought by Mohan Lal;

(ii) his annual income from shares;

(iii) the percentage return on his investment.

Answer

Given,

Investment = ₹ 29,040

Face Value = ₹ 100

Premium Rate = 20%

Premium = $\dfrac{20}{100} \times 100$ = ₹ 20

Market Value = Face Value + Premium = ₹ 100 + ₹ 20 = ₹ 120

Dividend Rate = 15%

(i) By formula,

Number of shares = $\dfrac{\text{Investment}}{\text{Market value of each share}} = \dfrac{29040}{120}$ = 242.

Hence, Mohan Lal bought 242 shares.

(ii) By formula,

Annual income = Number of shares × Rate of dividend × N.V. of 1 share

= $242 \times \dfrac{15}{100} \times 100$

= ₹ 3,630.

Hence, the annual income from shares is ₹ 3,630.

(iii) By formula,

$\text{Percentage return} = \dfrac{\text{Income}}{\text{Investment}} \times 100$

Hence, the percentage return on investment equals to 12.5%.

A man invests ₹ 8,800 on buying shares of face value ₹ 100 each at a premium of 10%. If he earns ₹ 1,200 at the end of the year as dividend, find :

(i) the number of shares he has in the company,

(ii) the dividend percentage per share.

Answer

Given,

Investment = ₹ 8,800

Face Value = ₹ 100

Premium rate = 10%

Premium = $\dfrac{10}{100} \times 100$ = ₹ 10

Market Value = Face Value + Premium = ₹ 100 + ₹ 10 = ₹ 110

Dividend = ₹ 1,200

(i) Number of shares = $\dfrac{\text{Investment}}{\text{Market value of each share}} = \dfrac{8800}{110}$ = 80

Hence, the number of shares the man has in the company equals to 80.

(ii) By formula

Dividend per share = $\dfrac{\text{Total dividend}}{\text{Number of shares}} = \dfrac{1200}{80}$ = ₹ 15.

Dividend percentage per share = $\dfrac{15}{100} \times 100$ = 15%.

Hence, the dividend percentage per share is 15%.

A man invests a sum of money in ₹ 100 shares, paying 10% dividend and quoted at 20% premium. If his annual dividend from these shares is ₹ 560, calculate :

(i) his total investment,

(ii) the rate of return on his investment.

Answer

Given,

Rate of Dividend = 10%

Annual dividend = ₹ 560

Face Value = ₹ 100

Premium Rate = 20%

Premium = $\dfrac{20}{100} \times 100$ = ₹ 20

Market Value = Face Value + Premium = ₹ 120

(i) By formula,

$\text{Annual income from one share} = \dfrac{\text{Rate of Dividend}}{100} \times \text{Face Value of one share} \\[1em] = \dfrac{10}{100} \times 100 = ₹10 \\[1em] \text{Number of shares} = \dfrac{\text{ Annual income}}{\text{ Annual income from 1 share}} \\[1em] =\dfrac{560}{10} \\[1em] = 56.$

By formula,

Investment = Number of shares × Market value of each share

= 56 × 120

= ₹ 6,720.

Hence, his total investment is ₹ 6,720.

(ii) By formula,

$\text{Percentage return} = \dfrac{\text{Income}}{\text{Investment}} \times 100$

Hence, the rate of return on his investment is $8\dfrac{1}{3}$.

A man invests a sum of money in ₹ 25 shares, paying 12% dividend and quoted at ₹ 36. If his annual income from these shares is ₹ 720, calculate :

(i) his total investment,

(ii) the number of shares bought by him,

(iii) the percentage return on his investment.

Answer

Given,

Face Value = ₹ 25

Market Value = ₹ 36

Rate of Dividend = 12%

Annual Income = ₹ 720

(i) Let the man bought x shares.

By formula,

Annual Income = No. of shares × Rate of div. × N.V. of 1 share

$\Rightarrow 720 = x \times \dfrac{12}{100} \times 25 \\[1em] \Rightarrow 720 = 3x \\[1em] \Rightarrow x = \dfrac{720}{3} \\[1em] \Rightarrow x = 240.$

∴ No. of shares bought = 240

By formula,

Investment = Number of shares × Market value of each share

= 240 × 36

= ₹ 8,640.

Hence, the total investment equals to ₹ 8,640.

(ii) From part (i), we get :

No. of shares bought = 240

Hence, the number of shares bought equals to 240.

(iii) By formula,

$\text{Percentage return} = \dfrac{\text{Income}}{\text{Investment}} \times 100$

Hence, the percentage return on his investment is $8\dfrac{1}{3}$.

A man buys 250, ten-rupee shares each at ₹12.50. If the rate of dividend is 7%, find the :

(i) dividend he receives annually.

(ii) percentage return on his investment.

Answer

(i) Nominal Value of 1 share = ₹10

Market Value of 1 share = ₹12.50

Number of shares purchased = 250

Nominal Value of 250 shares = 250 x 10 = ₹2500

Rate of dividend = 7%

∴ Dividend received = 7% of 2500

= $\dfrac{7}{100} \times 2500$

= ₹175.

Hence, annual dividend = ₹175.

(ii) Amount Invested = No. of shares x Market Value

= 250 x 12.50

= ₹3125

$\text{Return percentage } = \dfrac{\text{Dividend received}}{\text{Investment}} \times 100 \\[1em] = \dfrac{175}{3125} \times 100 \\[1em] = \dfrac{17500}{3125} \\[1em] = 5.6$

Hence, return percentage = 5.6%.

Divide ₹ 35,400 into two parts such that if one part is invested in 9%, ₹ 100 shares at 4% discount, and the other in 12%, ₹ 50 shares at 8% premium, the annual incomes are equal.

Answer

Given,

Total Investment = ₹ 35,400

Let the investments be ₹ x and ₹ 35,400 - x.

For the first investment,

Face Value = ₹ 100

Discount Rate = 4%

Discount = 4% of 100 = $\dfrac{4}{100} \times 100 = ₹ 4$

Market Value = Face Value - Discount = ₹ 96

Dividend Rate = 9%

By formula,

Number of shares = $\dfrac{\text{Investment}}{\text{Market value of each share}} = \dfrac{x}{96}$

$\text{Income from first part} = \text{No. of shares × Rate of div. × N.V. of 1 share}\\[1em] = \dfrac{x}{96} \times \dfrac{9}{100} \times {100}\\[1em]= \dfrac{9x}{96} \\[1em] = \dfrac{3x}{32}.$

For the second investment,

Face Value = ₹ 50

Premium Rate = 8%

Premium = 8% of 50 = $\dfrac{8}{100} \times 50$ = ₹ 4

Market Value = Face Value + Premium = ₹ 54

Dividend Rate = 12%

By formula,

Number of shares = $\dfrac{\text{Investment}}{\text{Market value of each share}} = \dfrac{35400 - x}{54}$

$\text{Income from second part} =\text{ No. of shares × Rate of div. × N.V. of 1 share}\\[1em] =\dfrac{35400 - x}{54} \times \dfrac{12}{100} \times 50\\[1em] = \dfrac{35400 - x}{54} \times 6 \\[1em] = \dfrac{35400 - x}{9}.$

Given,

Income from the both the investments are equal.

$\therefore \dfrac{3x}{32} = \dfrac{35400 - x}{9} \\[1em] \Rightarrow 9 \times 3x = 32(35400 - x) \\[1em] \Rightarrow 27x = 1132800 - 32x \\[1em] \Rightarrow 27x + 32x = 1132800 \\[1em] \Rightarrow 59x = 1132800 \\[1em] \Rightarrow x = \dfrac{1132800}{59} \\[1em] \Rightarrow x = ₹ 19,200.$

First part = x = ₹ 19,200

Second part = ₹ (35,400 - x) = ₹ 35,400 - ₹ 19,200 = ₹ 16,200

Hence, first part = ₹ 19,200 and second part = ₹ 16,200.

Divide ₹ 50,760 into two parts such that if one part is invested in 8%, ₹ 100 shares at 8% discount and the other in 9%, ₹ 100 shares at 8% premium, the annual incomes from both the investments are equal.

Answer

Given,

Total Investment = ₹ 50,760

Let the first part invested in 8%, ₹ 100 shares at 8% discount be ₹ x.

Second part = ₹ 50,760 − ₹ x

For the first investment :

Face Value = ₹ 100

Discount Rate = 8%

Discount = 8% of 100 = $\dfrac{8}{100} \times 100$ = ₹ 8

Market Value = Face Value - Discount = ₹ 92

Dividend Rate = 8%

By formula,

Number of shares = $\dfrac{\text{Investment}}{\text{Market value of each share}} = \dfrac{x}{92}$

By formula,

$\text{Income from first part} =\text{ No. of shares × Rate of div. × N.V. of 1 share}\\[1em] = \dfrac{x}{92} \times \dfrac{8}{100} \times {100}\\[1em] = \dfrac{8x}{92}.$

For the second investment :

Face Value = ₹ 100

Premium Rate = 8%

Premium = 8% of 100 = $\dfrac{8}{100} \times 100$ = ₹ 8

Market Value = Face Value + Premium = ₹ 108

Dividend Rate = 9%

Number of shares = $\dfrac{\text{Investment}}{\text{Market value of each share}} = \dfrac{50760 - x}{108}$

By formula,

$\text{Income from second part} = \text{No. of shares × Rate of div. × N.V. of 1 share}\\[1em] = \dfrac{50760 - x}{108} \times \dfrac{9}{100} \times {100} \\[1em] = \dfrac{50760 - x}{108} \times 9$

Given,

Income from the both the investments are equal.

$\therefore \dfrac{8x}{92} = \dfrac{50760 - x}{108} \times 9 \\[1em] \Rightarrow 8 \times 108x = 9 \times 92(50760 - x) \\[1em] \Rightarrow 864x = 828(50760 - x) \\[1em] \Rightarrow 864x = 42029280 - 828x \\[1em] \Rightarrow 864x + 828x = 42029280 \\[1em] \Rightarrow 1692x = 42029280 \\[1em] \Rightarrow x = \dfrac{42029280}{1692} = ₹24,840.$

First part = x = ₹ 24,840

Second part = ₹ (50,760 − x) = ₹ 25,920

Hence, first part = ₹ 24,840 and second part = ₹ 25,920.

Which is the better investment:

(10%, ₹ 100 shares at ₹ 120) or (8%, ₹ 100 shares at ₹ 72)?

Answer

Since,

Profit% on M.V. = Dividend% on N.V.

In first case,

P% on ₹ 120 = 10% on ₹ 100

$\Rightarrow \dfrac{P}{100} \times 120 = \dfrac{10}{100} \times 100 \\[1em] \Rightarrow 120P = 1000 \\[1em] \Rightarrow P = \dfrac{1000}{120} = 8.33$

In second case,

P% on ₹ 72 = 8% on ₹ 100

$\Rightarrow \dfrac{P}{100} \times 72 = \dfrac{8}{100} \times 100 \\[1em] \Rightarrow 72P = 800 \\[1em] \Rightarrow P = \dfrac{800}{72} = 11.11$

Hence, 8% ₹ 100 shares at ₹ 72 is the better investment.

Which is the better investment:

(12%, ₹ 20 shares at ₹ 16) or (15%, ₹ 20 shares at ₹ 24)?

Answer

Since,

Profit% on M.V. = Dividend% on N.V.

In first case,

P% on ₹ 16 = 12% on ₹ 20

$\Rightarrow \dfrac{P}{100} \times 16 = \dfrac{12}{100} \times 20 \\[1em] \Rightarrow P \times 16 = 240 \\[1em] \Rightarrow P = \dfrac{240}{16} = 15$

In second case,

P% on ₹ 24 = 15% on ₹ 20

$\Rightarrow \dfrac{P}{100} \times 24 = \dfrac{15}{100} \times 20 \\[1em] \Rightarrow P \times 24 = 15 \times 20 \\[1em] \Rightarrow P = \dfrac{300}{24} = 12.5$

Hence, 12% ₹ 20 shares at ₹ 16 is the better investment.

Ashish bought 4,500, ₹ 10 shares paying 12% per annum. He sold them when the price rose to ₹ 23 and invested proceeds in ₹ 25 shares paying 10% per annum at ₹ 18. Find the change in his annual income.

Answer

Given,

Initial Investment,

Number of shares = 4,500

Face Value = ₹ 10

Dividend Rate = 12%

By formula,

Initial Annual Income = No. of shares × Rate of div. × N.V. of 1 share

= $4500 \times \dfrac{12}{100} \times 10$

= ₹ 5,400.

Given,

Ashish sold the shares when the price rose to ₹ 23.

Selling Price per share = ₹ 23

Sale Amount = No.of Shares × S.P.

= 4500 × ₹ 23

= ₹ 1,03,500

For the new Investment :

Face Value = ₹ 25

Market Value = ₹ 18

Dividend Rate = 10%

By formula,

$\text{Number of shares} = \dfrac{\text{Investment}}{\text{ Market value of each share}} \\[1em] = \dfrac{103500}{18} \\[1em] = 5750. \\[1em] \text{New Annual Income} = \text{No. of shares} \times \text{Rate of div.} \times \text{N.V. of 1 share}\\[1em] = 5750 \times \dfrac{10}{100} \times 25 \\[1em] = ₹ 14,375.$

Change in Income = New Annual Income - Initial Annual Income

= ₹ 14,375 - ₹ 5,400 = ₹ 8,975.

Hence, Ashish's annual income increased by ₹ 8,975.

Amit owns 1500, ₹ 25 shares of a company which declares a dividend of 14%. He sells the shares at ₹ 40 each and invests the proceeds in 8%, ₹ 100 shares at ₹ 80. What is the change in his annual dividend income ?

Answer

Given,

Initially,

Number of shares = 1500

Face Value = ₹ 25

Dividend Rate = 14%

Initial Annual Income = No. of shares × Rate of div. × N.V. of 1 share

$= 1500 \times \dfrac{14}{100} \times 25$

= 750 × 7

= ₹ 5,250.

Selling price per share = ₹ 40

By formula,

Sale Amount = No. of Shares × Selling price per share = 1500 × 40 = ₹ 60,000.

For new Investment,

Face Value = ₹ 100

Dividend Rate = 8%

Market Value = ₹ 80

By formula,

$\text{Number of shares} = \dfrac{\text{ Investment }}{\text{ Market value of each share}} \\[1em] = \dfrac{60000}{80} \\[1em] = 750. \\[1em] \text{New Annual Income} = \text{No. of shares} \times \text{Rate of div.} \times \text{N.V. of 1 share}\\[1em] = 750 \times \dfrac{8}{100} \times 100\\[1em] = ₹ 6,000.$

Change in Income = New Annual Income - Initial Annual Income = 6,000 - 5,250 = ₹ 750.

Hence, Amit's annual dividend income increases by ₹ 750.

Vimal sold a certain number of ₹ 20 shares paying 8% dividend at ₹ 18 and invested the proceeds in ₹ 10 shares paying 12% dividend at 50% premium (i.e. ₹ 15). If his annual income decreases by ₹ 120, find the number of shares sold by Vimal.

Answer

Let the number of shares Vimal sold be x.

For initial shares,

N.V. = ₹ 20

Rate of dividend = 8%

By formula,

Annual income (from first investment) = No. of shares × Rate of div. × N.V. of 1 share

$= x \times \dfrac{8}{100} \times 20 = \dfrac{8x}{5}$

S.P. of each share = ₹ 18.

Amount obtained on selling shares = S.P × No. of shares = ₹ 18x.

The proceeds he invested in ₹ 10 shares at ₹ 15, paying 12% dividend.

N.V. = ₹ 10

M.V. = ₹ 15

No. of shares bought by man = $\dfrac{\text{Amount invested}}{\text{M.V. of each share}} = \dfrac{18x}{15} = \dfrac{6x}{5}.$

By formula,

Annual income (from second investment) = No. of shares × Rate of div. × N.V. of 1 share

$= \dfrac{6x}{5} \times \dfrac{12}{100} \times 10$

$= \dfrac{720x}{500} = \dfrac{36x}{25}$.

Given, decrease in income = ₹ 120

$\therefore \dfrac{8x}{5} - \dfrac{36x}{25} = 120 \\[1em] \Rightarrow \dfrac{40x - 36x}{25} = 120 \\[1em] \Rightarrow \dfrac{4x}{25} = 120 \\[1em] \Rightarrow x = \dfrac{120 \times 25}{4} \\[1em] \Rightarrow x = 750.$

Hence, Vimal sold 750 shares.

₹100 shares of a company giving 10% dividend are selling at ₹150. Mr. Saha invests ₹ 18,000 to buy these shares. He sells 80% of his shares after one year. Find :

(i) the number of shares he purchased.

(ii) the number of shares he sold.

(iii) his annual income from the remaining 20% shares he still holds.

Answer

(i) Given,

Total investment = ₹ 18,000

Market value = ₹ 150

N.V = ₹ 100

By formula,

⇒ Total investment = Number of shares × Market value of one share

⇒ 18000 = Number of shares × 150

⇒ Number of shares = $\dfrac{18000}{150}$

⇒ Number of shares = 120.

Hence, the number of shares Mr.Saha purchased = 120.

(ii) Number of shares sold by Mr Saha = 80% of 120

= $\dfrac{80}{100} \times 120$

= 0.8 × 120

= 96.

Hence, the number of shares Mr.Saha sold = 96.

(iii) Number of shares remaining = Total no. of shares - No. of shares sold = 120 - 96 = 24.

By formula,

Annual income = Number of shares × Rate of dividend × N.V. of 1 share

= 24 × $\dfrac{10}{100} \times 100$

= ₹ 240.

Hence, annual income from remaining shares = ₹ 240.

Deepak invested in ₹ 25 shares of a company paying 12% dividend. If he received 10% on his investment, at what price did he buy each share?

Answer

Given,

Face Value = ₹ 25

Dividend Rate = 12%

Return percentage = 10%

Let M.V. be ₹ x.

By formula,

Rate of dividend × N.V. = Profit (return) % × M.V.

$\therefore \dfrac{12}{100} \times 25 = \dfrac{10}{100} \times x \\[1em] \Rightarrow 12 \times 25 = 10x \\[1em] \Rightarrow x = \dfrac{300}{10}\\[1em] \Rightarrow x =₹\ 30.$

Hence, Deepak bought each share at ₹ 30.

At what price should a 10%, ₹ 25 share be quoted when money is worth 8%?

Answer

Given,

Face Value = ₹ 25

Dividend Rate = 10%

Return percentage = 8%

Let M.V. be ₹ x.

By formula,

Rate of dividend × N.V. = Profit (return) % × M.V.

$\therefore \dfrac{10}{100} \times 25 = \dfrac{8}{100} \times x \\[1em] \Rightarrow x = \dfrac{250}{8}\\[1em] \Rightarrow x = ₹ 31.25.$

Hence, the share should be quoted at ₹ 31.25.

How much should a man invest in ₹ 25 shares selling at ₹ 36 to obtain annual income of ₹ 1,500, if dividend declared is 12% ?

Answer

Given,

Face Value = ₹ 25

Market Value = ₹ 36

Dividend Rate = 12%

Required annual income = ₹ 1,500

Let no. of shares sold be ₹ x.

By formula,

Annual income = No. of shares × Rate of div. × N.V. of 1 share

$\Rightarrow 1500 = x \times \dfrac{12}{100} \times 25 \\[1em] \Rightarrow x = \dfrac{1500 \times 100}{25 \times 12} \\[1em] \Rightarrow x = 500.$

By formula,

Investment = No. of shares × Market value of each share

= 500 × 36

= ₹ 18,000.

Hence, the man should invest ₹ 18,000.

How much should a man invest in ₹ 50 shares selling at ₹ 60 to obtain an income of ₹ 450, if the rate of dividend declared is 10% ? Also, find his yield percent, to the nearest whole number.

Answer

Given,

Face Value = ₹ 50

Market Value = ₹ 60

Dividend Rate = 10%

Required Annual Income = ₹ 450

Let no. of shares sold be x.

By formula,

Annual income = No. of shares × Rate of div. × N.V. of 1 share

$\Rightarrow 450 = x \times \dfrac{10}{100} \times 50 \\[1em] \Rightarrow 450 = 5x \\[1em] \Rightarrow x = \dfrac{450}{5} = 90.$

Investment = No. of shares × Market value of each share

= 90 × 60 = ₹ 5,400.

By formula,

Yield % = $\dfrac{\text{Income}}{\text{Investment}} \times 100$

= $\dfrac{450}{5400} \times 100$ = 8.33% ≈ 8%.

Hence, the man should invest ₹ 5,400 and the yield percent is 8%.

By investing ₹ 11,440 in a company paying 10% dividend, an annual income of ₹ 520 is received. What is the market value of each ₹ 50 share?

Answer

Given,

Investment = ₹ 11,440

Annual Income = ₹ 520

Face Value = ₹ 50

Dividend Rate = 10%

Let market value of each share be ₹ x.

$\text{No. of share} = \dfrac{\text{Investment}}{\text{Market value of each share}} = \dfrac{11440}{x}$

By formula,

Annual dividend = No. of shares × Rate of div. × N.V. of 1 share

$\therefore 520 = \dfrac{11440}{x} \times \dfrac{10}{100} \times 50\\[1em] \Rightarrow x = \dfrac{11440 \times 5}{520} \\[1em] \Rightarrow x = ₹ 110$

Hence, the market value of each share is ₹ 110.

A man invests ₹ 4,500 in shares of a company which is paying 7.5% dividend. If ₹ 100 shares are available at a discount of 10%, find :

(i) number of shares he purchases;

(ii) his annual income.

Answer

Given,

Investment = ₹ 4,500

Face Value = ₹ 100

Discount Rate = 10%

Discount = $\dfrac{10}{100} \times 100 = ₹\ 10$

Market Value = Face Value - Discount = ₹ 90.

Dividend Rate = 7.5%

(i) By formula,

Number of shares = $\dfrac{\text{Investment}}{\text{Market value of each share}} = \dfrac{4500}{90} = 50$

Hence, the number of shares purchased equals to 50.

(ii) By formula,

Annual dividend = No. of shares × Rate of div. × N.V. of 1 share

$\therefore \text{Annual dividend} = 50 \times \dfrac{7.5}{100} \times 100$

= 50 × 7.5

= ₹ 375

Hence, his annual income is ₹ 375.

Sachin invests ₹ 8,500 in 10%, ₹ 100 shares at ₹ 170. He sells the shares when the price of each share rises by ₹ 30. He invests the proceeds in 12%, ₹100 shares at ₹ 125. Find :

(i) the sale proceeds;

(ii) the number of ₹ 125 shares he buys;

(iii) the change in his annual income.

Answer

(i) Given,

Initially,

Investment = ₹ 8,500

Dividend rate = 10%

Face value = ₹ 100

Market value = ₹ 170

By formula,

$\text{No. of shares} = \dfrac{\text{Investment}}{\text{Market value of each share}} = \dfrac{8500}{170} = 50$

Given, shares are sold when price rises to ₹ 30,

Selling price = 170 + 30 = ₹ 200

By formula,

Sale proceeds = No. of shares × Sale Price

= 50 × 200

= ₹ 10,000.

Hence, sale proceeds = ₹ 10,000.

(ii) Given, the proceeds are invested in 12%, ₹ 100 shares at ₹ 125.

Investment = ₹ 10,000

Face value = ₹ 100

Market value = ₹ 125

Dividend rate = 12%

By formula,

No. of shares = $\dfrac{\text{ Investment }}{\text{ Market value of each share}} = \dfrac{10000}{125} = 80$

Hence, Sachin buys 80, ₹ 125 shares.

(iii) Annual income = No. of shares × Rate of div. × N.V. of 1 share

In first case,

Annual income = 50 × $\dfrac{10}{100} \times 100$ = ₹ 500.

In second case,

Annual income = 80 × $\dfrac{12}{100} \times 100$ = ₹ 960.

Change in income = 960 - 500 = ₹ 460.

Hence, the change in his annual income is ₹ 460.

A company with 500 shares of nominal value ₹ 120 declares an annual dividend of 15%. Calculate :

(i) the total amount of dividend paid by the company;

(ii) annual income of Mr. Sharma who holds 80 shares of the company;

If the return percent of Mr. Sharma from his shares is 10%, find the market value of each share.

Answer

Given,

Total number of shares = 500

Nominal Value (Face Value) = ₹ 120

Dividend Rate = 15%

(i) By formula,

Total dividend = Total number of shares × Rate of div. × N.V. of 1 share

∴ Total dividend = $500 \times \dfrac{15}{100} \times 120$ = ₹ 9,000.

Hence, the total amount of dividend paid by the company is ₹ 9,000.

(ii) Given,

Mr. Sharma holds 80 shares.

By formula,

Annual dividend = No. of shares × Rate of div. × N.V. of 1 share

∴ Annual dividend = $80 \times \dfrac{15}{100} \times 120$ = ₹ 1,440

Hence, Mr. Sharma's annual income is ₹ 1,440.

Given,

The return percent of Mr. Sharma from his shares is 10%

Let the market value of shares be ₹ x.

By formula,

Rate of dividend × N.V. = Profit (return) % × M.V

$\therefore \dfrac{15}{100} \times 120 = \dfrac{10}{100} \times x \\[1em] \Rightarrow 15 \times 120 = 10x \\[1em] \Rightarrow x = \dfrac{1800}{10}\\[1em] \Rightarrow x = ₹\ 180.$

Hence, the market value of each share is ₹ 180.

A man bought ₹200 shares of a company at 25% premium. If he received a return of 5% on his investment. Find the :

(i) market value

(ii) dividend percent declared

(iii) number of shares purchased, if annual dividend is ₹1,000.

Answer

For one share:

Face value = ₹200

Premium = 25% of Face value

= $\dfrac{25}{100} \times 200$

= ₹50

(i) By formula,

M.V. = Face value + Premium

= ₹200 + ₹50

= ₹250.

Hence, market Value = ₹ 250.

(ii) Given,

Return = 5%

Return on 1 share = $\dfrac{5}{100} \times 250$

= ₹ 12.50

By formula,

Dividend earned = No. of shares × rate of dividend × F.V. of 1 share

Let rate of dividend be r%.

Substituting values we get :

⇒ 12.50 = 1 × $\dfrac{r}{100}$ × 200

⇒ r = $\dfrac{12.50}{200} \times 100$

⇒ r = 6.25%

Hence, dividend percent = 6.25%.

(iii) By formula,

Annual dividend = Number of shares × Dividend% × Face value of 1 share

⇒ 1000 = Number of shares × $\dfrac{6.25}{100}$ × 200

⇒ 1000 = Number of shares × 12.5

⇒ Number of shares = $\dfrac{1000}{12.5}$ = 80.

Hence, number of shares purchased = 80.

Ms. Kaur invested ₹ 8,000 in buying ₹100 shares of a company paying 6% dividend at ₹ 80. After a year, she sold these shares at ₹75 each and invested the proceeds including the dividend received during the first year in buying ₹ 20 shares, paying 15% dividend at ₹ 27 each. Find the :

(i) dividend received by her during the first year.

(ii) number of shares purchased by her using the total proceeds.

Answer

(i) Given,

For initial investment,

Investment = ₹ 8,000

Face Value = ₹ 100

Market Value = ₹ 80

Dividend Rate = 6%

By formula,

Number of shares = $\dfrac{\text{Investment}}{\text{Market value of each share}} = \dfrac{8000}{80}$ = 100

By formula,

Dividend for the first year = No. of shares × Rate of div. × N.V. of 1 share

= 100 × $\dfrac{6}{100}$ × 100

= ₹ 600

Hence, dividend for first year = ₹ 600.

(ii) Given,

Number of shares sold = 100

Selling price per share = ₹ 75

Proceeds from sale = Number of shares × selling price

= 100 × 75

= ₹ 7,500

Total proceeds = Proceeds from sale + Dividend received = 7500 + 600 = ₹ 8,100

Total investment = ₹ 8,100

Market value per share = ₹ 27

Number of new shares = $\dfrac{\text{Investment}}{\text{Market value of each share}} = \dfrac{8100}{27}$ = 300

Hence, number of shares purchased by Ms. Kaur = 300.