Exercise : Chapter 3 Shares and Dividends Exercise 3B MCQ Questions and Answers
1. A man buys 75, ₹ 100 shares of a company which pays 9 percent dividend. He buys shares at such a price that he gets 12 percent of his money. At what price did he buy the shares ?
Solution :
Nominal value of 1 share = ₹ 100
Nominal value of 75 shares = 100 x 75 = ₹ 7500
Dividend % = 9%
∴ Dividend = 9% of ₹ 7500
= 9/100 x 7500 = ₹ 675
Let market price of 1 share = ₹ 1 y
Then market price of 75 shares = ₹ 75 y
Profit % on investment = 12%
12% of 75y = ₹ 657
⇒ 12/100 x 75y = ₹ 657
⇒ y = ₹ 75
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2. 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?
Solution :
Nominal value of 1 share = ₹ 25
Market value of 1 share = ₹ 40
Profit% on investment = 4%
Then profit on 1 share = 4% of ₹ 40= ₹ 1.60
∴ Dividend% = 1/}25 } × 100% = 6.4%
No. of shares purchased= 60
Then dividend on 60 shares = 60 × ₹ 1.60 = ₹ 96
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3. 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%.
Solution :
Nominal value of 1 share = ₹ 100
Market value of 1 share = ₹ 100 + ₹ 20 = ₹ 120
Profit% on investment of 1 share =15%
Then profit= 15% of ₹ 120 = ₹ 18
∴ Dividend% = 18/100 × 100% = 18%
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4. ₹ 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 :
Nominal value of 1 share = ₹ 50
Market value of 1 share = ₹ 50 – 10% of ₹ 50
= ₹ 50 – ₹ 5 = ₹ 45
Profit % on investment = 20%
Then profit on 1 share = 20% of ₹ 45 = ₹ 9
∴ Dividend% = 9/50 × 100% = 18%
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5. A company declares 8 percent dividend to the share holders. If a man receives ₹ 2,840 as his dividend, find the nominal value of his shares.
Solution :
Dividend% = 8%
Dividend = ₹ 2,840
Let nominal value of shares = ₹ y
then 8% of y = ₹ 2,840
⇒ 8/100 × y = ₹ 2,840
⇒ y = ₹ 35000
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6. 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%?
Solution :
Nominal value of 1 share = ₹ 100
Market value of 1 share = ₹ 110
Let no. of shares purchased = n
Then nominal value of n shares = ₹ (100n)
Dividend% = 12%
Dividend = ₹ 1,680
∴ 12% of 100n = ₹ 1,680
⇒ 12/100 x 100n = ₹ 1,680
⇒ n = (1,680 x 100)/(12 x 100) = 140
Then market value of 140 shares= 140 × 110 = ₹ 15,400
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7. 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?
Solution :
Nominal value of 1 share = ₹ 60
Market value of 1 share = ₹ 60+ 25% of ₹ 60
= ₹ 60 + ₹ 15 = ₹ 75
Let no. of shares purchased = n
Then nominal value of n shares = ₹ (60n)
Dividend% = 11.2%
Dividend = ₹ 1,680
∴ 11.2% of 60n = ₹ 1,680
⇒ 11.2/100 x 60n = ₹ 1,680
⇒ n = (1,680 x 100)/(11.2 x 60) = 250
Then market value of 250 shares = 250 × 75 = ₹ 18,750
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8.
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.
Solution :
Nominal value of 1 share = ₹ 20
Market value of 1 share = ₹ 20 + ₹ 4 = ₹ 24
No. of shares purchased = 400
Nominal value of 400 shares = 400 × 20 = ₹ 8,000
(i) Market value of 400 shares = 400 × 24 = ₹ 9,600
(ii) Dividend % = 12%
Dividend = 12% of ₹ 8000
= 12/100 x ₹ 8000 = ₹ 960
(iii)
∴ Percentage return = (income/investment) x 100 %
= 960/9600 x 100 % = 10 %
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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 :
Nominal value of 1 share = ₹ 20
Market value of 1 share = ₹ 20 – 20% of ₹ 20
= ₹ 20 – ₹ 4 = ₹ 16
No. of shares purchased = 400
Nominal value of 400 shares = 400 x 20 = ₹ 8,000
(i) Market value of 400 shares = 400 x 16 = ₹ 6,400
(ii) Return%= 12%
Income = 12% of ₹ 6,400
= 12/100 x 6400 = ₹ 768
Dividend % = (Income/Nominal value) x 100%
= 768/8000 x 100% = 9.6%
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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.
Solution :
Nominal value of 1 share = ₹ 100
Nominal value of 10,000 shares = 10,000 x ₹ 100 = ₹ 10,00,000
(i) Dividend% = 5%
Dividend = 5% of ₹ 10,00,000
= 5/100 × 10,00,000 = ₹ 50,000
(ii) Nominal value of 72 shares= ₹ 100 x 72 = ₹ 7,200
Dividend = 5% of ₹ 7,200
= 5/100 × 7,200 = ₹ 360
(iii) Let market value of 1 share = ₹ y
Then market value of 10,000 shares = ₹ (10,000y)
Return% = 4%
then 4% of ₹ 10,000y = ₹ 50,000
⇒ 4/100 × 10,000y = ₹ 50,000
⇒ y = ₹ 125
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11. 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 the nearest integer.
Solution :
Nominal value of 1 share = ₹ 100
Market value of 1 share = ₹ 100 + 40% of ₹ 100
= ₹ 100 + ₹ 40 = ₹ 140
No. of shares purchased = 1800
Nominal value of 1800 shares = 1800 × 100 = ₹ 1,80,000
Market value of 1800 shares= 1800 × 140 = ₹ 2,52,000
(i)Dividend% = 15%
Dividend = 15% of ₹ 1,80,000
= 15/100 x 180000 = ₹ 27,000
(ii)
∴ Return % = (Income/Nominal value) x 100%
= (27000/252000) x 100% = 10.7 % = 11%
Question 12.
A man invests ₹ 11,200 in a company paying 6 percent per annum when its ₹ 100 shares can be bought for ₹ 140. Find:
(i) his annual dividend
(ii) his percentage return on his investment.
Solution:
Nominal value of 1 share = ₹ 100
Market value of 1 share = ₹ 140
Total investment = ₹ 11,200
No of shares purchased = 11/ 140 } = 80 shares
Then nominal value of 80 shares= 80 × 100= ₹ 8,000
(i) Dividend% = 6%
Dividend = 6% of ₹ 8,000
= 6/100 x 8000 = ₹ 480
(ii) Return % = (Income/Nominal value) x 100%
= 480/11200 x 100 %
= 4.29 %
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12.
Mr. Sharma has 60 shares of nominal value ₹ 100 and decides to sell 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.
Solution :
1st case
Nominal value of 1 share = ₹ 100
Nominal value of 60 shares = ₹ 100 × 60= ₹ 6,000
Market value of 1 share = ₹ 100 + 60% of ₹ 100
= ₹ 100+ ₹ 60 = ₹ 160
Market value of 60 shares = ₹ 160 × 60 = ₹ 9,600 Ans.
(ii) Nominal value of 1 share = ₹ 50
Market value of 1 share= ₹ 50 – 4% of ₹ 50
= ₹ 50 – ₹ 2 = ₹ 48
No of shares purchased = 9/ 48 } = 200 shares
(iii) Nominal value of 200 shares = ₹ 50 × 200 = ₹ 10,000
Dividend% = 18%
Dividend = 18% of ₹ 10,000
= 18/100 × 10,000 = ₹ 1800
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13.
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 the dividend he receives and the percentage of return on his investment.
Solution :
(i) Nominal value of 1 share = ₹ 100
Nominal value of 10,000 shares = ₹ 100 × 10,000 = ₹ 10,00,000
Dividend% = 8%
Dividend = 8% of ₹ 10,00,000
= 8/100 × 10,00,000 = ₹ 80,000
(ii) Market value of 90 shares = ₹ 150 × 90 = ₹ 13,500
Nominal value of 90 shares = ₹ 100 × 90 = ₹ 9,000
Dividend = 8% of ₹ 9,000
= 8/100 × 9,000 = ₹ 720
(iii)
Return % = (Income/Nominal value) x 100%
= 720/13500 x 100 %
= 5 1/3 %
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14.
Which is the better investment :
16% ₹ 100 shares at 80 or 20% ₹ 100 shares at 120?
Solution :
1st case
16% of ₹ 100 shares at 80 means;
Market value of 1 share = ₹ 80
Nominal value of 1 share = ₹ 100
Dividend = 16%
Income on ₹ 80= 16% of ₹ 100 = ₹ 16
Income on ₹ 1 = 16/80 = ₹ 0.20
2nd case
20% of ₹ 100 shares at 120 means;
Market value of 1 share = ₹ 120
Nominal value of 1 share = ₹ 100
Dividend = 20%
Income on ₹ 120 = 20% of ₹ 100= ₹ 20
Income on ₹ 1 = 20/120 = ₹ 0.17
Then 16% ₹ 100 shares at 80 is better investment.
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15.
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.
Solution :
(i) 1st firm
Market value of 1 share = ₹ 120
Nominal value of 1 share = ₹ 100
Dividend = 5%
Income on ₹ 120 = 5% of ₹ 100 = ₹ 5
Income on ₹ 1 = 5/120 = ₹ 0.041
2nd firm
Market value of 1 share = ₹ 132
Nominal value of 1 share = ₹ 100
Dividend = 6%
Income on ₹ 132 = 6% of ₹ 100 = ₹ 6
Income on ₹ 1 = 6/132 = ₹ 0.045
Then investment in second company is giving better return.
(ii) Income on investment of ₹ 26,400 in fi₹ t firm
= 5/120 × 26,400 = ₹ 1,100
Income on investment of ₹ 26,400 in second firm
= 6/132 × 26,400 = ₹ 1,200
∴ Difference between both returns = ₹ 1,200 – ₹ 1,100 = ₹ 100
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16. A man bought 360, ten-rupee shares of a company, paying 12% per annum. He sold the 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 the annual change in his income.
Solution :
1st case
Nominal value of 1 share = ₹ 10
Nominal value of 360 shares = ₹ 10 × 360 = ₹ 3,600
Market value of 1 share = ₹ 21
Market value of 360 shares = ₹ 21 × 360 = ₹ 7,560
Dividend% = 12%
Dividend = 12% of ₹ 3,600
= 12/100 × 3,600 = ₹ 432
2nd case
Nominal value of 1 share= ₹ 5
Market value of 1 share= ₹ 3.50
∴ No of shares purchased = 7/ 3.50 } = 2,160 shares
Nominal value of 2160 shares=₹ 5 × 2160= ₹ 10,800
Dividend%= 4.5%
Dividend= 4.5% of ₹ 10,800
= 4/{32 } × 10,800 = ₹ 486
Annual change in income = ₹ 486 – ₹ 432
= ₹ 54 increase
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17. A man sold 400 (₹ 20) shares of a company, paying 5% at ₹ 18 and invested the proceeds in (₹ 10) shares of another company paying 7% at ₹ 12. How many (₹ 10) shares did he buy and what was the change in his income?
Solution :
1st case
Nominal value of 1 share = ₹ 20
Nominal value of 400 shares = ₹ 20 x 400= ₹ 8,000
Market value of 1 share = ₹ 18
Market value of 400 shares = ₹ 18 x 400= ₹ 7,200
Dividend% = 5%
Dividend = 5% of ₹ 8,000
= 5/100 × 8,000 = ₹ 400
2nd case
Nominal value of 1 share = ₹ 10
Market value of 1 share = ₹ 12
∴ No of shares purchased = 7/ 12 } = 600 shares
Nominal value of 600 shares = ₹ 10 x 600 = ₹ 6,000
Dividend% = 7%
Dividend = 7% of ₹ 6,000
= 7/100 × 6,000 = ₹ 420
Annual change in income = ₹ 420 – ₹ 400
= ₹ 20 increase
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18. 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 per cent of the dividend received by B.
Solution :
For A
Total investment = ₹ 16,000
Nominal value of 1 share = ₹ 100
Market value of 1 share = ₹ 80
∴ No of shares purchased = 16/ 80 } = 200 shares
Nominal value of 200 shares = ₹ 100 × 200 = ₹ 20,000
Dividend% = 3%
Dividend = 3% of ₹ 20,000
= 3/100 × 20,000 = ₹ 600
For B
Total investment= ₹ 16,000
Nominal value of 1 share= ₹ 10
Market value of 1 share= ₹ 10
∴ No of shares purchased = 16/ 10 } = 1600 shares
Nominal value of 1600shares= 10 × 1600= ₹ 16,000
Dividend received by B = Dividend received by A = ₹ 600
Dividend % = (Dividend/Nominal value) x 100%
= 600/16000 x 100%
= 3.75 %
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19.
A man invests ₹ 20,020 in buying shares of nominal value ₹ 26 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 :
Total investment = ₹ 20,020
Nominal value of 1 share = ₹ 26
Market value of 1 share = ₹ 26+ 10% of ₹ 26
= ₹ 26+ ₹ 2.60 = ₹ 28.60
∴ No of shares purchased = 20/ 28.60 } = 700 shares
Nominal value of 700 shares= ₹ 26 x 700 = ₹ 18,200
Dividend% = 15%
Dividend = 15% of ₹ 18,200
= 15/100 × 18,200 = ₹ 2,730
∴ Income % = (Income/Investment) x 100%
= (2730/20020) x 100%
= 150/11 % = 13 7/11 %
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