Rohit invested $₹ 9600$ on $₹ 100$ shares at $₹ 20$ premium paying $8 %$ dividend. Rohit sold the shares when the price rise to $₹ 160$ . He invested the proceeds (excluding dividend) in $10 %$ , $₹ 50$ shares at $₹ 40$ . Find
(i) the original number of shares.
(ii) the sale proceeds.
(iii) the new number of shares.
(iv) the change in the two dividends.

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Solution

Step 1: Given Data
Investment on shares sold, $I_{1} = ₹ 9600$
Face value of shares sold, $F_{1} = ₹ 100$
Premium on shares sold, $P_{1} = ₹ 20$
Selling price of one share, $S P_{1} = ₹ 160$
Dividend % on shares sold, $d_{1} = 8 %$
Face value of shares bought, $F_{2} = ₹ 50$
Market value of shares bought, $M_{2} = ₹ 40$
Dividend % on shares bought, $d_{2} = 10 %$
Step 2: Calculate the number of shares Rohit sold
(i) If the shares are sold at a premium value then the market value becomes greater than the face value because
$M a r k e t v a l u e = F a c e v a l u e + P r e m i u m v a l u e$
$M_{1} = F_{1} + P_{1} = 100 + 20 = ₹ 120$
∴ $N u m b e r o f s h a r e s = \frac{I n v e s t m e n t}{M a r k e t v a l u e}$
$N_{1} = \frac{I_{1}}{M_{1}} = \frac{9600}{120} = 80 shares$
Step 3: Calculate the sale proceed of Rohit
(ii) $S a l e p r o c e e d s = N u m b e r o f s h a r e s \times S e l l i n g P r i c e o f o n e s h a r e$
$= N_{1} \times S P_{1} = 80 \times 160 = ₹ 12800$
Step 4: Calculate the number of shares Rohit bought
(iii) Let us assume the number of shares bought be $N_{2}$
$N u m b e r o f s h a r e s = \frac{I n v e s t m e n t}{M a r k e t v a l u e}$
$N_{2} = \frac{S a l e p r o c e e d s}{M_{2}} = \frac{12800}{40} = 320 shares$
Step 5: Calculate the number of shares Rohit bought
(iv) Let us assume the annual dividend of shares sold be $A_{1}$
$A n n u a l d i v i d e n d = N u m b e r o f s h a r e s \times F a c e v a l u e \times \frac{R a t e o f d i v i d e n d}{100}$
$A_{1} = N_{1} \times F_{1} \times \frac{d_{1}}{100} = 80 \times 100 \times \frac{8}{100} = ₹ 640$
Let us assume the annual dividend of shares bought be $A_{2}$
$A n n u a l d i v i d e n d = N u m b e r o f s h a r e s \times F a c e v a l u e \times \frac{R a t e o f d i v i d e n d}{100}$
$A_{2} = N_{2} \times F_{2} \times \frac{d_{2}}{100} = 320 \times 50 \times \frac{10}{100} = ₹ 1600$
∴ $C h a n g e i n h i s a n n u a l d i v i d e n d = A_{2} - A_{1}$
$= 1600 - 640 = ₹ 960$
Hence,
(i) Original number of Rohit's shares is $80$ .
(ii) Sale proceeds of Rohit is $₹ 12800$ .
(iii) New number of Rohit's shares is $320$ .
(iv) Change in the two dividends $₹ 960$ .

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