Chapter 3 - Shares and Dividends Exercise Ex. 3(B)

Question 1

A man buys 75, Rs100 shares paying 9 percent dividend. He buys shares at such a price that he gets 12percent of his money. At what price did he buy the shares ?

Solution 1

Nominal value of 1share= Rs100

Nominal value of 75 shares= 100  75= Rs7,500

Dividend% = 9%

Let market price of 1 share= Rsy

Then market price of 75 shares= Rs75y

Profit% on investment= 12%

Question 2

By purchasing Rs25 gas shares for Rs40 each, a man gets 4percent profit on his investment. What rate percent is the company paying? What is his dividend if he buys 60 shares?

Solution 2

Nominal value of 1 share= Rs25

Market value of 1 share= Rs40

Profit% on investment= 4%

Then profit on 1 share = 4% of Rs40= Rs1.60

 Ans.

No. of shares purchased= 60

Then dividend on 60 shares= 60  Rs1.60= Rs96.

Question 3

Hundred rupee shares of a company are available in the market at a premium of Rs20. Find the rate of dividend given by the company, when a man's return on his investment is 15%.

Solution 3

Nominal value of 1 share= Rs100

Market value of 1 share= Rs100+ Rs20= Rs120

Profit% on investment of 1 share=15%

Then profit= 15% of Rs120= Rs18

Question 4

Rs 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.

Solution 4

Nominal value of 1 share= Rs50

Market value of 1 share= Rs50 - 10% of Rs50

= Rs50 - Rs5= Rs45

Profit % on investment= 20%

Then profit on 1 share= 20% of Rs45= Rs9

 

Question 5

A company declares 8 percent dividend to the share holders. If a man receives Rs2,840 as his dividend, find the nominal value of his shares.

Solution 5

Dividend% = 8%

Dividend = Rs2,840

Let nominal value of shares= Rsy

Question 6

How much should a man invest in Rs100 shares selling at Rs110 to obtain an annual income of Rs1,680, if the dividend declared is 12%?

Solution 6

Nominal value of 1 share= Rs100

Market value of 1 share= Rs110

Let no. of shares purchased= n

Then nominal value of n shares= Rs(100n)

Dividend%= 12%

Dividend= Rs1,680

Then market value of 140 shares= 140  110= Rs15,400.

Question 7

A company declares a dividend of 11.2% to all its share-holders. If its Rs60 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 Rs1,680?

Solution 7

Nominal value of 1 share= Rs60

Market value of 1 share= Rs60+ 25% of Rs60

= Rs60+ Rs15= Rs75

Let no. of shares purchased= n

Then nominal value of n shares= Rs(60n)

Dividend%= 11.2%

Dividend= Rs1,680

Then market value of 250 shares= 250  75= Rs18,750.

Question 8

A man buys 400, twenty-rupee shares at a premium of Rs4 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.

Solution 8

Nominal value of 1 share= Rs20

Market value of 1 share= Rs20+Rs4= Rs24

No. of shares purchased= 400

Nominal value of 400 shares= 400 x 20= Rs8,000

(i)Market value of 400 shares= 400 x 24= Rs9,600

(ii)Dividend%= 12%

Dividend = 12% of Rs8,000

 

(iii)

Question 9

A man buys 400, twenty-rupee shares at a discount of 20% and receives a return of 12% on his money. Calculate:

(i)the amount invested by him.

(ii)the rate of dividend paid by the company.

Solution 9

Nominal value of 1 share= Rs20

Market value of 1 share= Rs20 - 20% of Rs20

= Rs20 - Rs4 = Rs16

No. of shares purchased= 400

Nominal value of 400 shares= 400 x 20= Rs8,000

(i)Market value of 400 shares= 400 x 16= Rs6,400 

(ii)Return%= 12%

Income= 12% of Rs6,400

Question 10

A company, with 10,000 shares of Rs100 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.

Solution 10

Nominal value of 1 share= Rs100

Nominal value of 10,000shares =10,000 x Rs100= Rs10,00,000

(i)Dividend%= 5%

Dividend = 5% of Rs10,00,000

 

(ii)Nominal value of 72 shares= Rs100 x 72= Rs7,200

Dividend= 5% of Rs7,200

(iii)Let market value of 1 share= Rs y

Then market value of 10,000 shares= Rs(10,000y)

Return%= 4%

Question 11

A lady holds 1800, Rs100 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 the nearest integer.

Solution 11

Nominal value of 1 share= Rs100

Market value of 1 share= Rs100+40% of Rs100

= Rs100+Rs40= Rs140

No. of shares purchased= 1800

Nominal value of 1800 shares= 1800 x 100= Rs1,80,000

Market value of 1800 shares= 1800 x 140 = Rs2,52,000

(i)Dividend%= 15%

Dividend = 15% of Rs1,80,000

 

(ii)

Question 12

A man invests Rs11,200 in a company paying 6 percent per annum when its Rs 100 shares can be bought for Rs140. Find:

(i)his annual dividend

(ii)his percentage return on his investment.

Solution 12

Nominal value of 1 share= Rs100

Market value of 1 share= Rs140

Total investment= Rs11,200

Then nominal value of 80 shares= 80 x 100= Rs8,000

(i)Dividend%= 6%

Dividend= 6% of Rs8,000

(ii)

Question 13

Mr. Sharma has 60 shares of nominal value Rs100 and sells them when they are at a premium of 60%. He invests the proceeds in shares of nominal value Rs50, 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.

Solution 13

1^st case

Nominal value of 1 share= Rs100

Nominal value of 60 shares= Rs100 x 60= Rs6,000

Market value of 1 share= Rs100+ 60% of Rs100

= Rs100+ Rs60= Rs160

Market value of 60 shares= Rs160 x 60= Rs9,600 Ans.

(ii)Nominal value of 1 share= Rs50

Market value of 1 share= Rs50 - 4% of Rs50

= Rs50 - Rs2= Rs48

 Ans.

(iii)Nominal value of 200 shares=Rs50 x 200= Rs10,000

Dividend%= 18%

Dividend= 18% of Rs10,000

Question 14

A company with 10,000 shares of nominal value Rs100 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 Rs150 per share. Calculate the dividend he receives and the percentage of return on his investment.

Solution 14

(i)

Nominal value of 1 share= Rs100

Nominal value of 10,000 shares= Rs100 x 10,000= Rs10,00,000

Dividend%= 8%

Dividend = 8% of Rs10,00,000

(ii)

Market value of 90 shares= Rs150 x 90= Rs13,500

Nominal value of 90 shares= Rs100 x 90= Rs9,000

Dividend = 8% of Rs9,000

(iii)

Question 15

Which is the better investment :

16% Rs.100 shares at 80 or 20% Rs.100 shares at 120?

Solution 15

1^st case

16%Rs.100 shares at 80 means;

Market value of 1 share= Rs80

Nominal value of 1 share= Rs100

Dividend= 16%

Income on Rs80= 16% of Rs100= Rs16

Income on Rs1

2^nd case

20% Rs.100 shares at 120 means;

Market value of 1 share= Rs120

Nominal value of 1 share= Rs100

Dividend= 20%

Income on Rs120= 20% of Rs100= Rs20

Income on Rs1

Then 16% Rs.100 shares at 80 is better investment.

Question 16

A man has a choice to invest in hundred-rupee shares of two firms at Rs120 or at Rs132. 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 Rs26,400 with each firm, how much will be the difference between the annual returns from the two firms.

Solution 16

(i)

1^st firm

Market value of 1 share= Rs120

Nominal value of 1 share= Rs100

Dividend= 5%

Income on Rs120= 5% of Rs100= Rs5

Income on Rs1

2^nd firm

Market value of 1 share= Rs132

Nominal value of 1 share= Rs100

Dividend= 6%

Income on Rs132= 6% of Rs100= Rs6

Income on Rs1

Then investment in second company is giving better return Ans.

(ii)

Income on investment of Rs26,400 in first firm

Income on investment of Rs26,400 in second firm

Question 17

A man bought 360, ten-rupee shares of a company, paying 12% per annum. He sold the shares when their price rose to Rs21 per share and invested the proceeds in five-rupee shares paying 4.5 percent per annum at Rs3.50 per share. Find the annual change in his income.

Solution 17

1^st case

Nominal value of 1 share= Rs10

Nominal value of 360 shares= Rs10 x 360= Rs3,600

Market value of 1 share= Rs21

Market value of 360 shares= Rs21 x 360= Rs7,560

Dividend%= 12%

Dividend= 12% of Rs3,600

2^nd case

Nominal value of 1 share= Rs5

Market value of 1 share= Rs3.50

Nominal value of 2160 shares=Rs5 x 2160= Rs10,800

Dividend%= 4.5%

Dividend= 4.5% of Rs10,800

Annual change in income= Rs486 - Rs432

= Rs54 increase.

Question 18

A man sold 400 (Rs20) shares of a company, paying 5% at Rs18 and invested the proceeds in (Rs10) shares of another company paying 7% at Rs12. How many (Rs10) shares did he buy and what was the change in his income?

Solution 18

1^st case

Nominal value of 1 share= Rs20

Nominal value of 400 shares= Rs20 x 400= Rs8,000

Market value of 1 share= Rs18

Market value of 400 shares= Rs18 x 400= Rs7,200

Dividend%= 5%

Dividend= 5% of Rs8,000

2^nd case

Nominal value of 1 share= Rs10

Market value of 1 share= Rs12

 Ans.

Nominal value of 600 shares=Rs10 x 600= Rs6,000

Dividend%= 7%

Dividend= 7% of Rs6,000

Annual change in income= Rs420 - Rs400

= Rs20 increase.

Question 19

Two brothers A and B invest Rs16,000 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 per cent of the dividend received by B.

Solution 19

For A

Total investment= Rs16,000

Nominal value of 1 share= Rs100

Market value of 1 share= Rs80

Nominal value of 200 shares= Rs100 x 200= Rs20,000

Dividend%= 3%

Dividend = 3% of Rs20,000

For B

Total investment= Rs16,000

Nominal value of 1 share= Rs10

Market value of 1 share= Rs10

Nominal value of 1600shares= 10 x 1600= Rs16,000

Dividend received by B= Dividend received by A

= Rs600

Question 20

A man invests Rs20,020 in buying shares of nominal value Rs26 at 10% premium. The dividend on the shares is 15% per annum. Calculate : (i)the number of shares he buys.

(ii)the dividend he receives annually.

(iii)the rate of interest he gets on his money.

Solution 20

Total investment= Rs20,020

Nominal value of 1 share= Rs26

Market value of 1 share= Rs26+ 10% of Rs26

= Rs26+ Rs2.60= Rs28.60

 

Nominal value of 700 shares= Rs26 x 700= Rs18,200

Dividend%= 15%

Dividend= 15% of Rs18,200