Shares & Dividends — Exercise 3(A)

The money required to buy 50, ₹ 20 shares at 10% premium is :

1. ₹ 800

2. ₹ 1,100

3. ₹ 500

4. ₹ 900

Answer

Given,

N.V. of share = ₹ 20

M.V. of share = N.V. + Premium = ₹ 20 + $\dfrac{10}{100} \times 20$ = ₹ 20 + ₹ 2 = ₹ 22.

By formula,

Money required to buy shares = No. of shares × M.V. of each share

= 50 × ₹ 22

= ₹ 1,100.

Hence, Option 2 is the correct option.

The money required to buy 50, ₹ 20 shares at ₹ 10 discount is :

1. ₹ 900

2. ₹ 1,100

3. ₹ 500

4. ₹ 800

Answer

Given,

N.V. of share = ₹ 20

M.V. of share = N.V. - Discount = ₹ 20 - ₹ 10 = ₹ 10.

By formula,

Money required to buy shares = No. of shares × M.V. of each share

= 50 × ₹ 10

= ₹ 500.

Hence, Option 3 is the correct option.

The money required to buy 50, ₹ 20 shares quoted at ₹ 22 is :

1. ₹ 1,100

2. ₹ 2,100

3. ₹ 1,540

4. ₹ 1,440

Answer

Given,

M.V. of share = ₹ 22

By formula,

Money required to buy shares = No. of shares × M.V. of each share

= 50 × ₹ 22

= ₹ 1100.

Hence, Option 1 is the correct option.

₹ 200 shares are available at a discount of 20%. The market price of 50 shares is :

1. ₹ 11,000

2. ₹ 8,000

3. ₹ 19,000

4. ₹ 14,000

Answer

Given,

N.V. of each share = ₹ 200

Discount % = 20%

M.V. of each share = N.V. - Discount = ₹ 200 - $\dfrac{20}{100} \times 200$ = ₹ 200 - ₹ 40 = ₹ 160.

Market price of 50 shares = 50 × Market price of each share

= 50 × ₹ 160

= ₹ 8000.

Hence, Option 2 is the correct option.

500, ₹ 50 shares at par earn a dividend of ₹ 1250 in one year. The rate of dividend is :

1. 10%

2. 7.5%

3. 12.5%

4. 5%

Answer

Given,

N.V. = ₹ 50

No. of shares = 500

Dividend = ₹ 1250

By formula,

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

Let rate of dividend be x%.

Substituting values we get :

$\Rightarrow 1250 = 500 \times x$

Rate of dividend = 5%.

Hence, Option 4 is the correct option.

A man invested in a company paying 12% dividend on its share. If the percentage return on his investment is 10%, then the shares are :

1. at par

2. below par

3. above par

4. cannot be determined

Answer

Given,

Dividend rate = 12% of face value.

So, if face value = ₹100, dividend = ₹12.

Return = 10%

By formula,

Return % = $\dfrac{\text{Dividend on one share}}{\text{Investment on one share}} \times 100$

Investment on one share equals to the market value of the share.

Substituting values we get :

⇒ 10 = $\dfrac{12}{\text{Market value}}$ × 100

⇒ Market value = $\dfrac{12}{10}$ × 100

⇒ Market value = ₹ 120.

Since market value > face value, the shares are said to be above par.

Hence, Option 3 is the correct option.

How much money will be required to buy 400, ₹ 12.50 shares at a premium of ₹ 1?

Answer

No. of shares to be bought = 400.

₹ 12.50 shares at a premium of ₹ 1 means; nominal value of the share is ₹ 12.50 and its market value = ₹ 12.50 + ₹ 1 = ₹ 13.50

∴ Money required to buy 400 shares = 400 × ₹ 13.50 = ₹ 5,400.

Hence, money required to buy 400 shares = ₹ 5,400.

How much money will be required to buy 250, ₹ 15 shares at a discount of ₹ 1.50 ?

Answer

No. of shares to be bought = 250.

₹ 15 shares at a discount of ₹ 1.50 means; nominal value of the share is ₹ 15 and its market value = ₹ 15 - ₹ 1.50 = ₹ 13.50

∴ Money required to buy 250 shares = 250 × ₹ 13.50 = ₹ 3,375.

Hence, money required to buy 250 shares = ₹ 3,375.

Find the annual income derived from 125, ₹ 120 shares paying 5% dividend.

Answer

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

= $125 × \dfrac{5}{100} \times 120$

= ₹ 750.

Hence, annual income = ₹ 750.

A man invests ₹ 3,072 in a company paying 5% per annum, when its ₹ 10 share can be bought for ₹ 16 each. Find :

(i) his annual income

(ii) his percentage income on his investment.

Answer

(i) Man invests ₹ 3,072 and M.V. of each share = ₹ 16

No. of shares bought = $\dfrac{3072}{16}$ = 192.

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

= $192 × \dfrac{5}{100} \times 10$

= ₹ 96.

His total annual income = ₹ 96.

(ii) Percentage income = $\dfrac{96}{3072} \times 100 = \dfrac{9600}{3072}$ = 3.125%.

Hence, percentage income = 3.125%.

A man invests ₹ 7,770 in a company paying 5 percent dividend when a share of nominal value of ₹ 100 sells at a premium of ₹ 5. Find :

(i) the number of shares bought;

(ii) annual income;

(iii) percentage income.

Answer

Total money invested = ₹ 7,770

Market value = ₹ 100 + ₹ 5 = ₹ 105

(i) No. of shares bought = $\dfrac{7770}{105}$ = 74.

Hence, no. of shares bought = 74.

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

= $74 × \dfrac{5}{100} \times 100$

= ₹ 370.

His total annual income = ₹ 370.

(iii) Percentage income = $\dfrac{370}{7770} \times 100 = \dfrac{37000}{7770}$ = 4.76%.

Hence, percentage income = 4.76%.

A man buys ₹ 50 shares of a company, paying 12 percent dividend, at a premium of ₹ 10. Find :

(i) the market value of 320 shares;

(ii) his annual income;

(iii) his profit percent.

Answer

(i) Market value of 1 share = ₹ 50 + ₹ 10 = ₹ 60.

∴ Market value of 320 shares = 320 × ₹ 60 = ₹ 19,200.

Hence, market value of 320 shares = ₹ 19,200.

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

= $320 × \dfrac{12}{100} \times 50$

= ₹ 1,920.

His total annual income = ₹ 1,920.

(iii) Profit % = $\dfrac{1920}{19200} \times 100 = \dfrac{192000}{1920}$ = 10%.

Hence, profit % = 10%.

A man invests ₹ 8,800 in buying shares of a company of face value of rupees hundred 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 percent per share.

Answer

(i) F.V. = ₹ 100

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

Market value = ₹ 100 + ₹ 10 = ₹ 110.

Investment = ₹ 8,800

No. of shares = $\dfrac{8800}{110}$ = 80.

Hence, the no. of shares = 80.

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

Let dividend percent = x%,

1200 = $80 × \dfrac{x}{100} \times 100$

1200 = 80x

x = $\dfrac{1200}{80} = 15$%.

Hence, dividend percent per share = 15%.

A man invests ₹ 3,360 in buying shares of nominal value ₹ 24 and selling at 12% premium. The dividend on the shares is 15% per annum. Calculate:

(i) the number of shares he buys;

(ii) the dividend he receives annually.

Answer

(i) F.V. = ₹ 24

Premium = 12% = $\dfrac{12}{100} \times 24$ = ₹ 2.88.

Market value = ₹ 24 + ₹ 2.88 = ₹ 26.88

Investment = ₹ 3,360

No. of shares = $\dfrac{3,360}{26.88}$ = 125.

Hence, the no. of shares = 125.

(ii) By formula,

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

= $125 × \dfrac{15}{100} \times 24$

= ₹ 450.

Hence, dividend received annually = ₹ 450.

By investing ₹ 7,500 in a company paying 10 percent dividend, an annual income of ₹ 500 is received. What price is paid for each of ₹ 100 share ?

Answer

Let x be price paid for each share.

No. of shares = $\dfrac{7500}{x}$

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

$\Rightarrow 500 = \dfrac{7500}{x} × \dfrac{10}{100} \times 100 \\[1em] \Rightarrow x = \dfrac{75000}{500} = 150.$

Hence, price paid for ₹ 100 share = ₹ 150.