Question

A man has some shares of rs 100 par value paying 5% dividend. He sells half of these at a discount of 10% and invests proceeds in 6% rs 50 shares at a premium of rs 10. This transaction decreases his annual income from dividend by rs 50. Calculate
No. Of shares before the transaction
The no. Of shares he hold
His initial annual income from shares

Answer 1

Given nominal price of the share = 100.

Given that he has some shares. Let the nominal value of shares he has be x.

Given that he sells half of these shares = x/2.

Given rate of dividend = 5%.

So, Dividend on each share = 5% of 100

= > (5/100) * 100

= > 5.

But we want x/2 shares, So x/2 * 5 = 5x/2

Now,

Given that he sells at a discount of 10%.

So, selling price = 90.

So, the selling price of x/2 shares = 90 * (x/2) = 45x.

Now,

Given that he invests proceeds in 6% of rs.50.

So, Dividend on each share = 6% of 50 = (6/100) * 50 = 6/2 = 3.

Now,

Given that nominal value of each share = 50 at a premium of rs.10.

Then the Market value = 60.

Hence,

The number of shares = 45x/60 = 3x/4.

Then total dividend = 3 * (3x/4)

= > 9x/4.

Now,

Given that his annual income decreases by rs.50

= > (5x/2) - (9x/4) = 50

= > 10x - 9x = 200

= > x = 200.

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(i)

Number of shares before the transaction = 200.

(ii)

The number of shares he hold = x/2 = 200/2 = 100.

(iii)

His annual income from shares = 5 * 200 = 1000.

Hope this helps!