Quants 20 - Stocks & Shares

Key Points to Remember:

To start a big business or an industry, a large amount of money is needed. It is beyond the capacity of one or two persons to arrange such a huge amount. However, some persons associate together to form a company. They, then draft a proposal, issue a prospectus in the name of the company, explaining the plan of the project and invite the public to invest money in this project. Thus, they pool up the funds from the public, by assigning them shares of the company. 

Stock Capital - The total amount of money needed to run the company.

Shares or Stocks - The whole capital is divided into small units.

For each investment, the company issues a share certificate, showing the value of each share and the number of shares held by a person.

The person who subscribes in shares or stocks is called a share holder or a stock holder.

Dividend - The annual profit distributed among share holders. Dividend is paid annually as per share or as a percentage.

Face Value - The value of share or stock printed on the share - certificate is called Face value or Nominal value or Par value.

Market Value - The stocks of different companies are sold and bought in the open market through brokers at stock-exchanges. 

A share is said to be:

(i) At Premium or Above Par - if it's market value is more than it's face value.

(ii) At Par - if it's market value is same as the face value.

(iii) At Discount or Below Par - if it's market value is less than it's face value.

Examples, 

If a Rs. 100 stock is quoted at a premium of 16, then market value of the stock is 100 + 16 = 116.

If a Rs. 100 stock is quoted at a discount of 7, then market value of the stock is 100 - 7 = 93.

Brokerage - The Broker's charge.

When Stock is purchased, brokerage is added to the cost price.

When Stock is sold, brokerage is subtracted from the selling price.

The face value of the share always remains the same.

The market value of the share changes from time to time. 

Dividend is always paid on the face value of the share.

Number of shares held by a person = (Total Investment / Investment in 1 share) = (Total Income / Income from 1 share) = (Total Face Value / Face Value of 1 share)

Thus, by a Rs. 100, 9% stock at 120, we mean that,

Face Value of Stock - Rs. 100

Market Value of Stock - Rs. 120

Annual Dividend on 1 Share - 9% of Face Value = Rs. 9

An Investment of Rs. 120 gives an annual income of Rs. 9

Rate of Interest per annum = Annual Income from an investment of Rs. 100 = (9/120) * 100 = 7.5%

Practice Questions:

Question 1:
Find the cost of:
(i) Rs. 7200, 8% stock at 90.
(ii) Rs. 4500, 8.5% stock at 4 Premium.
(iii) Rs. 6400, 10% stock at 15 Discount.

(i) Cost of Rs. 100 stock = Rs. 90
Cost of Rs. 7200 stock = (90/100) * 7200 = Rs. 6480.

(ii) Cost of Rs. 100 stock = Rs. 100 + 4 = 104
Cost of Rs. 4500 stock = (104/100) * 4500 = Rs. 4680.

(iii) Cost of Rs. 100 stock = Rs. 100 - 15 = 85
Cost of Rs. 6400 stock = (85/100) * 6400 = Rs. 5440.


Question 2:
Find the cash required to purchase, Rs. 3200, 7.5% stock at 107 (Brokerage 1/2%).
Cash required to purchase Rs. 100 stock = Rs. 107 + 1/2 = Rs. 215/2
Cash required to purchase Rs. 3200 stock = Rs. 215/2 * 1/100 * 3200 = Rs. 3440.


Question 3:
Find the cash realized by selling Rs. 2400, 9.5% stock at 4 discount (Brokerage 1/4%).
By selling Rs. 100 stock, cash realized = Rs. (100 - 4) - 1/4 = 96 - 1/4 = 383/4
By selling Rs. 2400 stock, cash realized = Rs. (383/4) * (1/100) * 2400 = Rs. 2298.


Question 4:
Find the annual income derived from Rs. 2500, 8% stock at 106.
Income from Rs. 100 stock = Rs. 8
Income from Rs. 2500 stock = Rs. (8/100) * 2500 = Rs. 200.


Question 5:
Find the annual income derived by investing Rs. 6800 in 10% stock at 136.
By investing Rs. 136, income obtained = Rs. 10
By investing Rs. 6800, income obtained = Rs. 10/136 * 6800 = Rs. 500.


Time to Think:

The cost price of a Rs. 100 stock at 4 discount, when brokerage is 1/4% is: