Quantitative Aptitude - SPLessons

Stock and Share

Chapter 30

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Stock and Share

shape Introduction

Stock and Share chapter deals with the topics like stock capital, shares or stock, dividend, face value, market value, and brokerage.


shape Methods

To start a big business or an industry, a large amount of money is required. This may be beyond the capacity of one or two individuals. Hence, a number of individuals join hands to form a company called Joint Stock Company.


1. Stock capital: Stock capital is defined as the total amount of money needed to run the company.


2. Shares or stock: The whole capital of the company is divided into equal units. Each unit is called a share or a stock.

    (i) For each investment, the company issues a shares held by a person.

    (ii) The person who describes in shares or stock is called a share holder or stock holder.


3. Dividend: The annual profit distributed among share holders is called dividend. Dividend is paid annually as per share or as a percentage.


4. Face value: Face value of a share is the value printed on the share certificate. It is also called nominal value or par value. The face value of a share always remains the same.


5. Market value: The stocks of different companies are sold and bought in the open market through a broker/brokers at stock – exchangers. For a share:

    (a) If the market value is more than its face value, then the stock is at premium or above par.

    (b) If the market value is the same as its face value, then the stock is traded at par.

    (c) If its market value is less than its face value, then the stock is traded at discount or below par.


Example: Assume that the face value of a company \(x\) is Rs. 10 and it is now traded at a premium of Rs. 2. Then its market value now is (Rs. 10 + Rs. 2) = Rs. 12.

Similarly, if the company \(x\) having face value of Rs. 10 is now traded at a discount of Rs. 2, it means the market value of \(x\) now is (Rs. 10 – Rs. 2) is Rs. 8.


6. Brokerage: As it is known that, stocks of different companies can be traded (bought or sold) in the market through brokers at stock exchanges. The brokers charge is called brokerage.

    (i) Brokerage is added to the cost price when the stock is purchased.

    (ii) Brokerage is subtracted from the selling price when the stock is sold.


Remember:

    (i) Face value of a share always remain same.

    (ii) The market value of a share changes from time to time.

    (iii) Dividend is always paid on the face value of a share.

    (iv) Number of shares held by a person. is equal to ratio of total investment (or income or face value) and investment in 1 share.

    \(Number \ of \ shares \ held \ by \ a \ person\) = \(\frac{Total \ investment}{Investment \ in \ 1 \ share}\) = \(\frac{Total \ income}{Income \ from \ 1 \ share}\) = \(\frac{Total \ face \ value}{face \ value \ of \ 1 \ share}\)


Rs.100, 10% stock at 120 means:

    a) The face value of stock = Rs.100

    b) Dividend= 10% of the Face Value = Rs.10

    c) Market Value = Rs.120.


Example 1:
Find the cash required to buy Rs.3200, 7.5% stock at 107.

Solution:

    Face Value = Rs.3200 => 32 shares must be purchased [Assume Face Value = Rs.100]

    Market Price of 32 shares = 3200 x 107 = Rs.3424


Example 2:
In order to obtain an income of Rs.650 from 10% stock at Rs.96, what amount must one invest?

Solution:

    Face Value = Rs.100

    Dividend = 10% of Rs.100 = Rs.10

    Thus, for gaining Rs.650, investment = 96 x (650 / 10) = Rs.6240.


Example 3:
Which is better investment: 11% stock at 143 or 9.75% stock at 117?

Solution:

    Let the investment be Rs. \(X\). Then,


    Income on \(1^{st}\) stock = \(X\) x \(\frac{11}{143}\) = \(\frac{x}{13}\)


    Income on \(2^{nd}\) stock = \(X\) x \(\frac{9.75}{117}\) = \(\frac{X}{12}\)


    Thus, income on \(2^{nd}\) stock > Income on \(1^{st}\) stock. Hence, \(2^{nd}\) stock is a better investment.


Example 1:
Juno invests a part of Rs.12000 in 12% stock at Rs.120 and the remainder in 15% stock at Rs.125. If her total dividend per annum is Rs.1360, how much does she invest in 12% stock at Rs.120?

Solution:

    Let the investment in the 1st stock be X. Then, investment in 2nd stock = 12000 – X.


    Income on \(1^{st}\) stock = \(\frac{12}{120}\) x \(X\) = \(\frac{X}{10}\).


    Income on \(2^{nd}\) stock = \(\frac{15}{125}\) x (12000 – \(X\)) = \(3\frac{(12000 – X)}{25}\)


    => \(\frac{X}{10}\) + \(3\frac{(12000 – X)}{25}\) = Rs.1360.


    => \(5X\) + 72000 – \(6X\) = 1360 x 50.


    => \(X\) = Rs.4000.


Example 2:
Rs.9800 are invested partly in 9% stock at 75 and 10% stock at 80 to have equal amount of incomes. Find the investment in 9% stock.

Solution:

    Let the investment in the \(1^{st}\) stock be X. Then, investment in \(2^{nd}\) stock = 9800 – \(X\).


    Income on \(1^{st}\) stock = \(\frac{9}{75}\) x \(X\) = \(\frac{3X}{25}\) & on \(2^{nd}\) stock = \(\frac{10}{80}\) x (9800 – \(X\)) = \(\frac{(9800 – X)}{8}\).

shape Samples

1. Find the cost of 86 shares of Rs. 100 each at \(\frac{}{}\)

Solution:

    Given that,

    86 shares of RS. 100 each

    Now, cost of 1 share = Rs. [(10 – \(\frac{3}{4}\))] + \(\frac{1}{4}\) = Rs.\(\frac{19}{2}\)

    Cost of 86 shares = Rs.\(\frac{19}{2} * 86\) = Rs. 817


2. Which is better investment from

    (i) 7\(\frac{1}{2}\)% stock at 105 (or)

    (ii) 6\(\frac{1}{2}\)% stock at 94 ?



Solution:

    Let the investment in each case be Rs. (105 * 94)

    Case 1: 7\(\frac{1}{2}\)% stock at 105

    On investing Rs. 105, income = Rs. \(\frac{15}{2}\).

    On investing Rs. (105 * 94), income = Rs. (\(\frac{15}{2} * \frac{1}{105} * 105 * 94\)) = Rs. 705.

    Case 2: 6\(\frac{1}{2}\)% stock at 94

    On investing Rs. 94, income = Rs. \(\frac{13}{2}\).

    On investing Rs. (105 * 94), income = Rs. (\(\frac{13}{2} * \frac{1}{94} * 105 * 94\)) = Rs. 682.50.

    So, the income from 7\(\frac{1}{2}\)% stock at 105 is more.

    Therefore, the investment in 7\(\frac{1}{2}\)% stock at 105 is better.


3. Find the cost of: Rs. 6400, 10% stock at 15 discount?

Solution:

    Cost of Rs. 100 stock = Rs. (100 – 15) = Rs. 85

    Cost of Rs. 6400 stock = Rs.(\(\frac{85}{100} * 6400\)) = Rs. 5440


4. Find the income derived from 88 shares of Rs. 25 each at 5 premium, brokerage being \(\frac{1}{4}\) per share and the rate of dividend being 7\(\frac{1}{2}\)% per annum. Also, find the rate of interest on the investment?

Solution:

    Cost of 1 share = Rs. (25 + 5 + \(\frac{1}{4}\)) = Rs. \(\frac{121}{4}\)

    cost of 88 shares = Rs. (\(\frac{121}{4} * 88\)) = Rs. 2662.

    Therefore,

    Investment made = Rs. 2662.

    Face value of 88 shares = Rs. (88 * 25) = Rs. 2200.

    Dividend on Rs. 100 = \(\frac{15}{2}\).

    Dividend on Rs. 2200 = Rs.(\(\frac{15}{2} * \frac{1}{100} * 2200\)) = Rs. 165.

    Therefore, Income derived = Rs. 165.

    Rate of interest on investment = (\(\frac{165}{2662} * 100\)) = 6.2%.


5. A person sells Rs. 5000, 12% stock at 156 and invests the proceeds partly in 8% stock at 90 and 90% stock at 108. The person thereby increases income by Rs. 70. How much of the proceeds were invested in each stock?

Solution:

    Selling price of Rs. 5000 stock = Rs. (\(\frac{156}{100} * 5000\)) = Rs. 7800

    Income from this stock = Rs. (\(\frac{12}{100} * 5000\)) = Rs. 600

    Let the investment in 8% stock be \(x\) and that in 9% stock = (7800 – \(x\)).

    Therefore, (\(x\) x \(\frac{8}{90}\)) + (7800 – \(x\)) x \(\frac{9}{108}\) = (600 + 70)

    ⇒ \(\frac{4x}{45} + \frac{7800 – x}{12}\) = 670

    ⇒ 16\(x\) + 117000 – 15\(x\) = 670 * 180

    ⇒ \(x\) = 3600.

    Therefore,

    Money invested in 8% stock at 90 = Rs. 3600.

    Money invested in 9% at 108 = Rs.(7800 – 3600) = Rs. 4200