Shares & Dividends — Exercise 3(B)

The number of ₹ 25 shares, paying 24% dividend, with total dividend ₹ 1,350 is :

1. 125

2. 27

3. 225

4. 200

Answer

Given,

Dividend = ₹ 1350

N.V. of share = ₹ 25

Rate of dividend = 24%

Let no. of shares be n.

By formula,

Dividend = No. of shares × Rate of dividend × N.V. of share

Substituting values we get :

$\Rightarrow 1350 = n \times 24$

Hence, Option 3 is the correct option.

₹ 600 shares of a company are available at a discount of 20%. If the company pays a dividend of 20%, the rate of return is :

1. 16%

2. 25%

3. 10%

4. 12.5%

Answer

Given,

N.V. of share = ₹ 600

Discount = 20%

M.V. = N.V. - Discount

= ₹ 600 - 20%

= ₹ 600 - $\dfrac{20}{100} \times 600$

= ₹ 600 - ₹ 120 = ₹ 480.

Dividend = 20%

Let rate of return be r%.

We know that,

Interest on M.V. = Dividend on N.V.

r% of ₹ 480 = 20% of ₹ 600

$\Rightarrow \dfrac{r}{100} \times 480 = \dfrac{20}{100} \times 600 \\[1em] \Rightarrow 4.8r = 120 \\[1em] \Rightarrow r = \dfrac{120}{4.8} \\[1em] \Rightarrow r = 25$

Hence, Option 2 is the correct option.

100 shares at par value of ₹ 120 each, give 10% half-yearly dividend. The annual dividend from these shares is :

1. ₹ 7200

2. ₹ 2400

3. ₹ 1200

4. ₹ 10800

Answer

Given,

Dividend % = 10% half-yearly or 20% yearly.

N.V. = ₹ 120

No. of shares = 100

By formula,

Dividend = No. of shares × Rate of dividend × N.V. of share

Substituting values we get :

$\text{Dividend} = 100 \times 20$

Hence, Option 2 is the correct option.

Amit invested a certain amount of money in ₹ 100 shares, paying a 7.5% dividend. The rate of return on his investment is 10%. The money invested by Amit to purchase 10 shares is :

1. ₹ 250

2. ₹ 750

3. ₹ 900

4. ₹ 1,100

Answer

Let ₹ P be the price per share.

Amit brought 10 shares, so total investment = ₹ 10P

Dividend = 7.5%

Dividend per share = $\dfrac{7.5}{100} \times 100$ = ₹ 7.5

Total dividend = ₹ 7.5 × 10 = ₹ 75.

Rate of return = 10%

By formula,

Rate of return × Investment = Dividend

$\Rightarrow 10$

Total investment = 10P = 10 × ₹75 = ₹750.

Hence, Option 2 is the correct option.

200 ₹ 20 shares, each available at a discount of 20%, give 10% dividend. The rate of return is :

1. 12.5%

2. 15%

3. 16%

4. 25%

Answer

Given,

Dividend = 10%

N.V. = ₹ 20

Discount = 20%

M.V. = N.V. - Discount

= ₹ 20 - 20%

= ₹ 20 - $\dfrac{20}{100} \times 20$

= ₹ 20 - ₹ 4 = ₹ 16.

Dividend = 10%

Let rate of return/interest be r%.

We know that,

Interest on M.V. = Dividend on N.V.

r% of 16 = 10% of 20

$\Rightarrow \dfrac{r}{100} \times 16 = \dfrac{10}{100} \times 20 \\[1em] \Rightarrow r = \dfrac{10 \times 20}{16} \\[1em] \Rightarrow r = \dfrac{200}{16} \\[1em] \Rightarrow r = 12.5$

Hence, Option 1 is the correct option.

By purchasing ₹ 25 gas shares for ₹ 40 each, a man gets 4 percent profit on his investment. What rate percent is the company paying ? What is his dividend if he buys 60 shares?

Answer

Profit = 4% = $\dfrac{4}{100} \times 40 = 1.6$

Let company be paying x% dividend.

As,

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

⇒ 1.6 = 1 × $\dfrac{x}{100}$ × 25

⇒ x = $\dfrac{160}{25}$ = 6.4%.

For 60 shares dividend = 60 $\times \dfrac{6.4}{100} \times 25$ = ₹ 96.

Hence, rate paid by company = 6.4% and dividend = ₹ 96.

Hundred rupee shares of a company are available in the market at a premium of ₹ 20. Find the rate of dividend given by the company when a man's return on his investment is 15 percent.

Answer

We know that,

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

Market value = ₹ 100 + ₹ 20 = ₹ 120.

Let rate of dividend be x%

$\Rightarrow \dfrac{x}{100} \times 100 = \dfrac{15}{100} \times 120 \\[1em] \Rightarrow x = 18$

Hence, rate of dividend = 18%.

₹ 50 shares of a company are quoted at a discount of 10%. Find the rate of dividend given by the company, the return on the investment on these shares being 20 percent.

Answer

We know that,

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

Market value = ₹ 50 - ₹ $\dfrac{10}{100} \times 50$ = ₹ 50 - ₹ 5 = ₹ 45.

Let rate of dividend be x%

$\Rightarrow \dfrac{x}{100} \times 50 = \dfrac{20}{100} \times 45 \\[1em] \Rightarrow x = \dfrac{20 \times 45}{50} \\[1em] \Rightarrow x = 18$

Hence, rate of dividend = 18%.

How much should a man invest in ₹ 100 shares selling at ₹ 110 to obtain an annual income of ₹ 1,680, if the dividend declared is 12% ?

Answer

Let man invest ₹ x

∴ No. of shares = $\dfrac{x}{110}$

We know that,

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

$\Rightarrow 1680 = \dfrac{x}{110} \times \dfrac{12}{100} \times 100 \\[1em] \Rightarrow x = \dfrac{1680 \times 110}{12} \\[1em] \Rightarrow x = 15,400$

Hence, investment = ₹ 15,400.

A company declares a dividend of 11.2% to all its share-holders. If its ₹ 60 share is available in the market at a premium of 25%, how much should Rakesh invest, in buying the shares of this company, in order to have an annual income of ₹ 1,680?

Answer

Let man invest ₹ x

Market value = ₹ 60 + $\dfrac{25}{100} \times 60$ = ₹ 60 + ₹ 15 = ₹ 75

∴ No. of shares = $\dfrac{x}{75}$

We know that,

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

$\Rightarrow 1680 = \dfrac{x}{75} \times \dfrac{11.2}{100} \times 60 \\[1em] \Rightarrow x = \dfrac{1680 \times 100 \times 75}{11.2 \times 60} \\[1em] \Rightarrow x = 18,750$

Hence, investment = ₹ 18,750.

A man buys 400, twenty-rupee shares at a premium of ₹ 4 each and receives a dividend of 12%. Find :

(i) the amount invested by him

(ii) his total income from the shares

(iii) percentage return on his money.

Answer

(i) Market value = ₹ 20 + ₹ 4 = ₹ 24.

Amount invested = 400 × ₹ 24 = ₹ 9,600

Hence, amount invested = ₹ 9,600.

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

= 400 × $\dfrac{12}{100} \times 20$

= ₹ 960.

Hence, annual income = ₹ 960.

(iii) Percentage return = $\dfrac{\text{Income}}{\text{Investment}} \times 100 = \dfrac{960}{9600} \times 100$ = 10%.

Hence, percentage return = 10%.

A company with 10,000 shares of ₹ 100 each, declares an annual dividend of 5%.

(i) What is the total amount of dividend paid by the company ?

(ii) What should be the annual income of a man who has 72 shares in the company ?

(iii) If he received only 4% of his investment, find the price he paid for each share.

Answer

(i) Dividend = No. of shares × Rate of div. × N.V. of 1 share

= 10,000 × $\dfrac{5}{100} \times 100$

= ₹ 50,000.

Hence, total dividend = ₹ 50,000.

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

= 72 × $\dfrac{5}{100} \times 100$

= ₹ 360.

Hence, annual income of man = ₹ 360.

(iii) Let investment be ₹ x.

Given return % = 4%.

$\therefore 4 = \dfrac{360}{x} \times 100 \\[1em] \Rightarrow x = \dfrac{36000}{4} = 9,000.$

Price paid for each share = $\dfrac{\text{Investment}}{\text{No. of shares}} = \dfrac{9000}{72} = 125.$

Hence, price of each share = ₹ 125.

A lady holds 1800, ₹ 100 shares of a company that pays 15% dividend annually. Calculate her annual dividend. If she had bought these shares at 40% premium, what is the return she gets as percent on her investment?

Give your answer to nearest integer.

Answer

Market value = ₹ 100 + ₹ $\dfrac{40}{100} \times 100$ = ₹ 100 + ₹ 40 = ₹ 140.

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

= 1800 × $\dfrac{15}{100} \times 100$

= ₹ 27,000.

Investment = No. of shares × M.V. = 1800 × ₹ 140 = ₹ 2,52,000.

Return % = $\dfrac{\text{Dividend}}{\text{Investment}} \times 100 = \dfrac{27000}{252000} \times 100 =$ 10.71% ≈ 11%.

Hence, annual dividend = ₹ 27,000 and return % = 11%.

Mr. Sharma has 60 shares of N.V. ₹ 100 and sells them when they are at a premium of 60%. He invests the proceeds in shares of nominal value ₹ 50, quoted at 4% discount, and paying 18% dividend annually. Calculate :

(i) the sale proceeds

(ii) the number of shares he buys; and

(iii) his annual dividend from the shares.

Answer

(i) Market value of initial shares = ₹ 100 + $\dfrac{60}{100} \times 100$ = ₹ 100 + ₹ 60 = ₹ 160.

Sale proceeds = 60 × ₹ 160 = ₹ 9,600.

Hence, sale proceeds = ₹ 9,600.

(ii) M.V. of second shares = ₹ 50 - $\dfrac{4}{100} \times 50$ = ₹ 50 - ₹ 2 = ₹ 48.

No. of shares = $\dfrac{9600}{48}$ = 200.

Hence, no. of shares = 200.

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

= 200 × $\dfrac{18}{100} \times 50$

= ₹ 1,800.

Hence, annual dividend = ₹ 1,800.

A company with 10,000 shares of nominal value ₹ 100 declares an annual dividend of 8% to the share-holders.

(i) Calculate the total amount of dividend paid by the company.

(ii) Ramesh had bought 90 shares of the company at ₹ 150 per share. Calculate dividend he receives and percentage return on his investment.

Answer

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

= 10,000 × $\dfrac{8}{100} \times 100$

= ₹ 80,000.

Hence, annual dividend paid by company = ₹ 80,000.

(ii) Investment = 90 × ₹ 150 = ₹ 12,500

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

= 90 × $\dfrac{8}{100} \times 100$

= ₹ 720.

Return% = $\dfrac{\text{Annual dividend}}{\text{Investment}} \times 100 = \dfrac{720}{12500} \times 100 = 5\dfrac{1}{3}$%

Hence, dividend received by Ramesh = ₹ 720 and return % = $5\dfrac{1}{3}$%.

Which is better investment : 16% of ₹ 100 shares at 80 or 20% ₹ 100 shares at 120?

Answer

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

In first case :

P% on ₹ 80 = 16% on ₹ 100

$\Rightarrow \dfrac{P}{100} \times 80 = \dfrac{16}{100} \times 100 \\[1em] \Rightarrow P = \dfrac{16}{80} \times 100 = 20$

In second case :

P% on ₹ 120 = 20% on ₹ 100

$\Rightarrow \dfrac{P}{100} \times 120 = \dfrac{20}{100} \times 100 \\[1em] \Rightarrow P = \dfrac{20}{120} \times 100 = 16\dfrac{4}{6}$

Hence, 16% of ₹ 100 shares at 80 is the better investment.

A man has a choice to invest in hundred-rupee shares of two firms at ₹ 120 or at ₹ 132. The first firm pays a dividend of 5% per annum and the second firm pays a dividend of 6% per annum. Find :

(i) which company is giving a better return.

(ii) if a man invests ₹26,400 with each firm, how much will be the difference between the annual returns from the two firms ?

Answer

(i) First company's dividend = 5% and second company's = 6%.

∴ Second company is giving a better return.

(ii) No. of shares of first company = $\dfrac{26400}{120} = 220$

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

= 220 × $\dfrac{5}{100} \times 100$

= ₹ 1,100.

No. of shares of second company = $\dfrac{26400}{132} = 200$

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

= 200 × $\dfrac{6}{100} \times 100$

= ₹ 1,200.

Difference between annual returns = ₹ 1200 - ₹ 1100 = ₹ 100.

Hence, difference between annual returns of two firms = ₹ 100.

A man bought 360, ten-rupee shares of a company, paying 12 percent per annum. He sold shares when their price rose to ₹ 21 per share and invested the proceeds in five-rupee shares paying 4.5 percent per annum at ₹ 3.50 per share. Find annual change in his income.

Answer

In first case :

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

= 360 × $\dfrac{12}{100} \times 10$

= ₹ 432

S.P. of shares = 360 × ₹ 21 = ₹ 7,560

M.V. of second shares = ₹ 3.50

No. of shares purchased = $\dfrac{\text{Investment}}{\text{M.V. of share}} = \dfrac{7560}{3.5}$ = 2160.

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

= 2160 × $\dfrac{4.5}{100} \times 5$

= ₹ 486.

Change in income = ₹ 486 - ₹ 432 = ₹ 54.

Hence, the change in income = ₹ 54 (increase).

Two brothers A and B invest ₹ 16,000 each in buying shares of two companies. A buys 3% hundred rupee shares at 80 and B buys ten-rupee shares at par. If they both receive equal dividend at the end of the year, find the rate percent of the dividend received by B.

Answer

For A,

M.V. of shares = 80

Investment = ₹ 16,000

No. of shares = $\dfrac{16000}{80}$ = 200.

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

= 200 × $\dfrac{3}{100} \times 100$

= ₹ 600.

For B,

M.V. of shares = 10

Investment = ₹ 16,000

No. of shares = $\dfrac{16000}{10}$ = 1600.

Let rate of dividend be x%

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

$\Rightarrow 600 = 1600 \times \dfrac{x}{100} \times 10 \\[1em] \Rightarrow x = \dfrac{600 \times 100}{1600 \times 10} \\[1em] \Rightarrow x = \dfrac{60000}{16000} = 3.75$

Hence, the rate percent of the dividend received by B = 3.75%.