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 company), explaining the plan of the project
and invite the public to invest money in this project. They, thus, pool up the
funds from the public, by assigning them shares of the company.
IMPORTANT FACTS AND FORMULAE
1. Stock-capital: The
total amount needed to run the company is called the stock-capital
2. Shares or stock: The whole capital is divided into small units, called shares or
stock.
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 subscribers 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: The
value of a share or stock printed on the share-certificate is called its Face
Value or Nominal Value or Par Value.
5. Market Value: The
stocks of different companies are sold and bought in the open market through
brokers at stock-exchanges. A share (or stock) is said to be:
(i)
At premium or Above par, if its market value is more than
its face value.
(ii)
At par, if its market value is the same as its face value.
(iii)
At discount or Below par, if its market value is less than
its face value.
Thus, if a Rs.100 stock is quoted at a premium of 16,
then market value of the stock = Rs. (100+16) = Rs. 116.
Likewise, I f a Rs. 100 stock is quoted at a discount
of 7, then market value of the stock = Rs. (100-7) = Rs. 93.
6. Brokerage:
The broker’s charge is called brokerage.
(i)
When stock is
purchased, brokerage is added to the cost price.
(ii)
When stock is
sold, brokerage is subtracted from the selling price.
Remember:
(i)
The face value of
a share always remains the same.
(ii)
The market value of
a share changes form time to time.
(iii)
Dividend is
always paid on the face value of a share.
(iv)
Number of shares
held by a person
= Total Investment_ = _Total Income _
= _Total Face Value
Investment in 1 share Income from 1 share
face Value of 1 share
Thus, by a Rs. 100,
9% stock at 120, we mean that:
(i)
Face Value
(N>V) of stock = Rs. 100.
(ii)
Market Value
(M>V) of stock = Rs. 120.
(iii)
Annual dividend
on 1 share = 9% of face value = 9% of Rs. 100 = Rs. 9.
(iv)
An investment of
Rs. 120 gives an annual income of Rs. 9.
(v)
Rate of interest
p.a = Annual income from an investment of Rs. 100.
= (9/120 * 100) % = 7 (1/2) %.
SOLVED EXAMPLES
Ex. 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.
Sol. (i) Cost of Rs. 100 stock = Rs. 90
Cost of Rs. 7200 stock = Rs. (90/100 *
7200 ) = Rs. 6480.
(ii)
Cost of Rs. 100 stock = Rs. (100+4)
Cost of Rs. 4500 stock = Rs. (104/100 *
4500 ) = Rs. 4680
(iii) Cost of Rs. 100 stock =
Rs. (100-15)
Cost of Rs. 6400 stock = Rs. (85/100 * 6400
) = Rs. 5440.
Ex. 2. Find the cash required to purchase Rs. 3200,
7(1/2) % stock at 107 (brokerage
(1/2) %)
Sol. Cash required to purchase Rs. 100 stock = Rs
(107+(1/2)) = Rs. (215/2).
Cash required to purchase Rs. 100 stock = Rs
[(215/2)*(1/100)*3200] = Rs. 3440.
Ex. 3. Find the cash realised by selling Rs. 2440, 9.5% stock at 4 discount (brokerage
(1/4) %)
Sol. By
selling Rs. 100 stock , cash realised = Rs. [(100-4)-(1/4)] = Rs. (383/4).
By selling Rs. 2400 stock, cash realised = Rs.
[(383/4)*(1/100)*2400] = Rs 2298.
Ex. 4. Find the annual income derived from Rs. 2500,
8% stock at 106.
Sol. Income
from Rs. 100 stock = Rs. 8.
Income from Rs. 2500 = Rs. [(8/1000*2500) =Rs. 200.
Ex. 5. Find the annual income derived by investing Rs.
6800 in 10% stock at 136.
Sol. By
investing Rs. 136, income obtained = Rs. 10.
By
investing Rs. 6800, income obtained = Rs. [(10/136)*6800] = Rs. 500.
Ex. 6. Which is better investment? 7(1/2) % stock at
105 or 6(1/2) % at 94.
Sol. Let the
investment in each case be Rs. (105*94).
Case I :
7(1/2) 5 stock at 105:
On
investing Rs. 105, income = Rs. (15/2).
On investing Rs. (105*94), income = Rs.
[(15/2)*(1/105)*105*94] = Rs 705.
Case
II : 6(1/2) % stock at 94:
On
investing Rs. 94, income = Rs. (13/2).
On investing Rs. (105*94), income = Rs. [(13/2)*(1/94)*105*94] = Rs. 682.5.
Clearly, the income from 7(1/2) % stock at
105 is more.
Hence, the investment in 7(1/2) % stock at
105 is better.
Ex. 7. Find the cost of 96 shares of Rs. 10 each at
(3/4) discount, brokerage being
(1/4) per share.
Sol. Cost of
1 share = Rs. [(10-(3/4)) + (1/4)] = Rs. (19/2).
Cost of 96 shares = Rs. [(19/2)*96] = Rs. 912.
Ex. 8. Find the income derived from 88 shares of Rs.
25 each at 5 premium, brokerage being (1/4) per share and the rate of dividend
being 7(1/2) % per annum. Also, find the rate of interest on the investment.
Sol. Cost of
1 share = Rs. [25+5+1/4)] = Rs. (121/4).
Cost of 88 shares = Rs.[(121/4)*88] = Rs. 2662.
\ Investment made = Rs. 2662.
Face
value of 88 shares = Rs. (88*25) = Rs. 2200.
Dividend
on Rs. 100 = (15/2).
Dividend
on Rs. 2200 = Rs. [(15/20*(1/100)*2200] = Rs. 165.
\ Income derived = Rs. 165.
Rate of
interest on investment = [(165/2662)*100] = 6.2 %.
Ex. 9. A man buys Rs. 25 shares in company which pays 9 % dividend. The money
invested is such that it gives 10 % on investment. At what price did he buy the
shares?
Sol. Suppose
he buys each share for Rs. x.
Then, [25*(9/100)] = [x*(10/100)] or x = Rs. 22.50.
Cost of
each share = Rs. 22.50.
Ex. 10. A man sells Rs.5000, 12 % stock at 156 and
uinvests the proceeds parity in 8 % stock at 90 and 9 % stock at 108. He hereby
increases his income by Rs. 70. How much of the proceeds were invested in each
stock?
Sol. S.P of
Rs. 5000 stock = Rs. [(156/100)*5000] = Rs. 7800.
Income from this stock = Rs. [(12/100)*5000] = Rs.
600.
Let
investment in * % stock be x and that in 9 % stock = (7800-x).
\ [x*(8/90)] + (7800-x) *
(9/108) = (600+7)
ó (4x/45) +
[(7800-x)/12] = 670 ó 16x + 117000-15x = (670*180) ó x = 3600.
\ Money invested in 8 % stock at 90 = Rs. 3600.
Money
invested in 9 % at 108 = Rs. (7800-3600) = Rs. 4200.
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