Q: A man bought ₹200 shares of a company at 25% premium. If he received a return of 5% on his investment. Find the: (a) market value (b) dividend percent declared (c) number of shares purchased, if annual dividend is ₹1000.

(a) Market Value MV = 200 + 25% of 200 = 200 + 50 = ₹250 . [1 Mark] (b) Return = 5% of MV = 0.05 × 250 = ₹12.50 per share. Dividend % = (Dividend / NV) × 100% = (12.50 / 200) × 100% = 6.25% (or 6¼%). [1 Mark] (c) Number of shares = Total Annual Dividend / Dividend per share = 1000 / 12.50 = 80 shares . [1 Mark]

Question 1

The dividend received on 50 shares of face value ₹100, quoted at an 8% premium, when the company declares a 12% dividend is:

Accepted Answer

Correct Option: (a) ₹600 Rule Dividend is ALWAYS calculated on Face Value (FV), independent of market premium. Annual Dividend = No. of shares × FV × d% = 50 × 100 × 0.12 = ₹600 .

Question 2

A man invests ₹9,600 in ₹100 shares at a discount of 20%. If the company pays an annual dividend of 8%, find the:
(a) number of shares purchased.
(b) annual dividend received.
(c) rate of return on his investment.

Accepted Answer

Part (a) Face Value = ₹100, Market Value = 100 − 20 = ₹80.
Number of shares = Investment / MV = 9,600 / 80 = 120 shares. [1 Mark]

Part (b) Annual Dividend = 120 × 100 × (8 / 100) = ₹960. [1 Mark]

Part (c) Rate of Return = (Annual Income / Investment) × 100 = (960 / 9,600) × 100 = 10%. [1 Mark]

Question 3

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:

Accepted Answer

Let Nominal Value NV = 100. Dividend = ₹12. Return = (Dividend / MV) × 100% = 10% ⇒ MV = ₹120. Since Market Value > Nominal Value (120 > 100), the shares are above par (at premium). [1 Mark]

Question 4

A man bought ₹200 shares of a company at 25% premium. If he received a return of 5% on his investment. Find the:
(a) market value
(b) dividend percent declared
(c) number of shares purchased, if annual dividend is ₹1000.

Accepted Answer

(a) Market Value MV = 200 + 25% of 200 = 200 + 50 = ₹250. [1 Mark]
(b) Return = 5% of MV = 0.05 × 250 = ₹12.50 per share.
Dividend % = (Dividend / NV) × 100% = (12.50 / 200) × 100% = 6.25% (or 6¼%). [1 Mark]
(c) Number of shares = Total Annual Dividend / Dividend per share = 1000 / 12.50 = 80 shares. [1 Mark]

Question 5

The sum invested to purchase 15 shares of a company of nominal value ₹75 available at a discount of 20% is:

Accepted Answer

Correct Option: (d) ₹900 Nominal Value (NV) = ₹75. Discount = 20% of 75 = ₹15. Market Value (MV) per share = 75 − 15 = ₹60. Sum invested = 15 × 60 = ₹900 . [1 Mark]

Question 6

Mr. Gupta invested ₹33,000 in buying ₹100 shares of a company at 10% premium. The dividend declared by the company is 12%. Find: (a) the number of shares purchased by him. (b) his annual dividend.

Accepted Answer

NV = ₹100, Premium = 10% ⇒ MV = 100 + 10 = ₹110. Dividend rate = 12%.
(a) Number of shares: 33000 / 110 = 300 shares. [1.5 Marks]
(b) Annual dividend: 300 × (12% of 100) = 300 × 12 = ₹3,600. [1.5 Marks]

Question 7

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.

Accepted Answer

Nominal Value (NV) per share $= ₹120$, Dividend rate $= 15\%$.
(i) Total NV of 500 shares $= 500 \times 120 = ₹60,000$.
Total dividend paid $= 15\% \text{ of } 60,000 = \frac{15}{100} \times 60000 = \mathbf{₹9,000}$. [1 Mark]
(ii) Dividend on 1 share $= 15\% \text{ of } 120 = ₹18$.
Annual income of Mr. Sharma (holding 80 shares) $= 80 \times 18 = \mathbf{₹1,440}$. [1 Mark]
(iii) Return percent on investment $= 10\%$.
Let MV be the market value of each share.
$\text{Return on 1 share} = 10\% \text{ of MV} = \text{Dividend on 1 share} = ₹18$.
$\frac{10}{100} \times \text{MV} = 18 \implies \mathbf{\text{MV} = ₹180}$. [1 Mark]

Question 8

A man invests ₹ 4500 in shares of a company which is paying $7.5\%$ dividend. If ₹ 100 shares are available at a discount of $10\%$, find: Number of shares he purchases. His annual income.

Accepted Answer

Step 1 Find Market Value ($MV$) of each share:
Nominal Value ($NV$) = ₹ 100.
Discount = $10\%$ of ₹ 100 = ₹ 10.
$\therefore MV = 100 - 10 = \text{₹ } 90$. [1 Mark]
Step 2 (i) Number of shares purchased:
$\text{Number of shares} = \frac{\text{Total Investment}}{MV \text{ per share}} = \frac{4500}{90} = \mathbf{50\text{ shares}}$. [1 Mark]
Step 3 (ii) Annual income from shares:
$\text{Annual Income} = \text{Number of shares} \times \text{Dividend \%} \times NV$
$\text{Annual Income} = 50 \times \frac{7.5}{100} \times 100 = 50 \times 7.5 = \mathbf{\text{₹ } 375}$. [1 Mark]

Question 9

Sachin invests ₹ 8500 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: the sale proceeds. the number of ₹ 125 shares he buys. the change in his annual income.

Accepted Answer

Step 1 Initial Investment Analysis:
Investment = ₹ 8500, $NV_1 = \text{₹ } 100, MV_1 = \text{₹ } 170, D_1 = 10\%$.
$\text{Number of shares } n_1 = \frac{8500}{170} = 50\text{ shares}$.
$\text{Initial Annual Income } I_1 = 50 \times 10\% \times 100 = \text{₹ } 500$. [1 Mark]
Step 2 (i) Determine sale proceeds:
Price rises by ₹ 30 $\implies \text{New Selling Price} = 170 + 30 = \text{₹ } 200$.
$\mathbf{\text{Sale Proceeds} = 50 \times 200 = \text{₹ } 10,000}$. [1 Mark]
Step 3 (ii) Second investment in ₹ 125 shares:
Proceeds available = ₹ 10,000, $NV_2 = \text{₹ } 100, MV_2 = \text{₹ } 125, D_2 = 12\%$.
$\mathbf{\text{Number of new shares bought } n_2 = \frac{10000}{125} = 80\text{ shares}}$. [1 Mark]
Step 4 (iii) Change in annual income:
$\text{New Annual Income } I_2 = 80 \times 12\% \times 100 = \text{₹ } 960$.
$\text{Change in Annual Income} = I_2 - I_1 = 960 - 500 = \mathbf{\text{₹ } 460\text{ increase}}$. [1 Mark]

Question 10

A company declares $9\%$ dividend on its shares of ₹ 100 available at ₹ 120. It means a person will receive annual dividend which is $9\%$ of:

Accepted Answer

Solution Dividend declared by a company is always calculated as a percentage of the nominal value (face value) of each share, regardless of market value fluctuations.
Correct Answer: (b) face value [1 Mark]

Question 11

Prasoon invests ₹ 7500 in a company paying $6\%$ dividend annually. ₹ 100 shares of this company are available at ₹ 150. Find the number of shares he purchased. Find his annual income. After one year, he sold $50\%$ of his original shares at ₹ 175 each. Find his gain on the shares he sold.

Accepted Answer

Step 1 (a) Number of shares purchased:
$n = \frac{\text{Investment}}{MV} = \frac{7500}{150} = \mathbf{50\text{ shares}}$. [1 Mark]
Step 2 (b) Annual income:
$\text{Income} = n \times \text{Dividend \%} \times NV = 50 \times \frac{6}{100} \times 100 = \mathbf{\text{₹ } 300}$. [1 Mark]
Step 3 (c) Gain on selling $50\%$ shares ($25$ shares) at ₹ 175:
Gain per share $= 175 - 150 = \text{₹ } 25$.
$\mathbf{\text{Total Gain} = 25 \times 25 = \text{₹ } 625}$. [1 Mark]

Question 12

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. Give your answer correct to the nearest whole number.

Accepted Answer

Step 1 Nominal value $NV = ₹50$.
Discount $= 10\% \text{ of } 50 = ₹5$.
Market Value per share $MV = 50 - 5 = ₹45$.
(i) Number of shares purchased:
$$n = \frac{\text{Total Investment}}{MV} = \frac{22,500}{45} = \mathbf{500\text{ shares}}$$ [1 Mark]
(ii) Annual dividend received:
$$\text{Dividend per share} = 12\% \text{ of } 50 = \frac{12}{100} \times 50 = ₹6$$ $$\text{Total Annual Dividend} = 500 \times 6 = \mathbf{₹3,000}$$ [1 Mark]
(iii) Rate of return on investment:
$$\text{Rate of return} = \frac{\text{Annual Dividend}}{\text{Total Investment}} \times 100 = \frac{3000}{22500} \times 100 = \frac{40}{3}\% = 13.33\% \approx \mathbf{13\%}$$ [1 Mark]
Answers: (i) 500 shares, (ii) ₹3,000, (iii) $13\%$.

Question 13

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.

Accepted Answer

Step 1 $NV = ₹50$, $MV = ₹60$, Dividend Rate $= 10\%$.
Dividend per share $= \frac{10}{100} \times 50 = ₹5$.
Number of shares $= \frac{\text{Total Income}}{\text{Dividend per share}} = \frac{450}{5} = 90\text{ shares}$. [1 Mark]
Step 2: Total Investment
$$\text{Investment} = 90 \times 60 = \mathbf{₹5,400}$$ [1 Mark]
Step 3: Yield Percent
$$\text{Yield \%} = \frac{\text{Annual Income}}{\text{Investment}} \times 100 = \frac{450}{5400} \times 100 = \frac{25}{3}\% = 8.33\% \approx \mathbf{8\%}$$ [1 Mark]
Answers: Total Investment $= ₹5,400$; Yield percent $\approx 8\%$.

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