Amit and Richa invest $₹ 12000$ each in buying shares of two companies. Amit buys $15 %$ , $₹ 100$ shares at a discount of $₹ 20$ , while Richa buys $₹ 25$ shares at a premium of $20 %$ . If both receive equal dividends at the end of the year, then find the rate percent of the dividend declared by Richa's company.

Open in App

Solution

Step 1: Given Data
Investment done individually by both, $I = ₹ 12000$
Face value of Amit's shares, $F_{1} = ₹ 100$
Discount on Amit's shares, $D = ₹ 20$
Rate of dividend on Amit's shares, $D_{1} = 15 %$
Face value of Richa's share, $F_{2} = ₹ 25$
Premium% on Richa's share, $P = 20 %$
Amit's annual dividend = Richa's annual dividend
Step 2: Calculate the dividend for one share of Amit's company
$D i v i d e n d = \frac{R a t e o f d i v i d e n d}{100} \times F a c e v a l u e$
$I_{1} = \frac{D_{1}}{100} \times F_{1} = \frac{15}{100} \times 100 = ₹ 15$
Step 3: Calculate the dividend for one share of Richa's company
Let us assume that the rate of dividend on Richa's shares, $D_{2} = r %$
$D i v i d e n d = \frac{R a t e o f d i v i d e n d}{100} \times F a c e v a l u e$
$I_{2} = \frac{D_{2}}{100} \times F_{2} = \frac{r}{100} \times 25 = ₹ \frac{r}{4}$
Step 4: Calculate the annual dividend of Amit's company
As Amit bought the shares at a discount,
∴ $M a r k e t v a l u e = F a c e v a l u e - D i s c o u n t = 100 - 20 = ₹ 80$
$N o o f s h a r e s = \frac{I n v e s t m e n t}{M a r k e t v a l u e} = \frac{12000}{8} = 150 shares$
∴ $T o t a l a n n u a l d i v i d e n d = N u m b e r o f s h a r e s \times D i v i d e n d f r o m o n e s h a r e$
$A_{1} = 150 \times 15 [∵ i n c o m e c a l c u l a t e d i n s t e p 2] A_{1} = ₹ 2250$
Step 5: Calculate the annual dividend of Richa's company
As Richa bought the shares at a premium,
∴ $M a r k e t v a l u e = F a c e v a l u e + P r e m i u m % o f F a c e v a l u e = 25 + \frac{20}{100} \times 25 = 25 + 5 = ₹ 30$
$N o o f s h a r e s = \frac{I n v e s t m e n t}{M a r k e t v a l u e} = \frac{12000}{30} = 400 shares$
∴ $T o t a l a n n u a l d i v i d e n d = N u m b e r o f s h a r e s \times D i v i d e n d f r o m o n e s h a r e$
$A_{2} = 400 \times \frac{r}{4} [∵ i n c o m e c a l c u l a t e d i n s t e p 3] A_{2} = ₹ 100 r$
Step 6: Calculate the rate of the dividend of Richa's shares
Given, Amit's annual dividend = Richa's annual dividend
∴ $A_{1} = A_{2}$
$2250 = 100 r r = \frac{2250}{100} r = 22.5 %$
Hence, The rate percent of the dividend declared by Richa's company is $22.5 %$ .

Suggest Corrections

Similar questions

Sachin and Dhoni invest Rs. 36,000 each in buying shares of two companies. Sachin buys 15% Rs. 40 shares at a discount of 20%, while Dhoni buy Rs. 75 share at a premium of 20%. If both receive equal dividend at the end of the year, find the rate percent of dividend declared by Dhoni company.

Q. Two brothers

A

and

B

invest

R s .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 percent of the dividend received by

B

Mihir and Sameer both invested $₹ 90000$ each in buying shares of two companies. Mihir invested in buying $₹ 150$ shares of 'ABC Solutions' available at a $20 %$ premium and paying a dividend of $18 %$ . Sameer invested in buying $₹ 225$ shares of 'Mphasis Ltd.' available at a $20 %$ discount and paying a dividend of $16 %$ . Whose investment is better?