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Stocks and Shares – Questions and Concepts for CAT

Friday, September 25th, 2020

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Whenever someone starts a new business, some money is needed to start the business. This initial investment is called the CAPITAL. In large companies & enterprises, it is very much possible that there could be more than one person investing the money. These could be either partners or shareholders. Both mean the same thing except for the liability they have for the business. It is easier for a shareholder to quit the business, by selling his SHARES in the stock exchange, whereas a partner cannot leave just like that.

So, what is a Share? In simple terms, it is a certificate issued by the business or the company which signifies that the holder of this certificate is entitled to a specific part/ share of profits in the business.

Some Basic Terms

When the business is new, then all shareholders will typically share profits in proportion to the investment that they have made in the business – or in proportion to the number of shares that they hold. The shares issued by the business are sold for usually Rs. 10 or Rs. 100 at the time of the first issue. The amount of money invested during the first-time purchase of that particular share is called THE FACE VALUE of that share. After a certain amount of time, when the trading of the shares starts, the value of these shares that an investor might give may be different from the face value of that particular share. To quote an instance, a share of TCS with face value of Rs 1 was quoted at Rs. 900 in the year 2001. While buying or selling shares in the stock exchange, you use an intermediary between the seller and the buyer – the broker. His charges – brokerage – are typically a percentage of the Purchase / Sale price – i.e., the market value and not the face value, but in questions you will always calculate the brokerage on the face value.

The earnings are distributed by the company/ business to the owners of the company through way of dividend. It is always declared as a percentage of the face value of that particular share.

Sometimes, companies require money at somewhat later stage. If the company is making profits, then the market value of the share is higher than the face value of the shares. Then it is said to issue at a premium. Example, TCS is issuing shares, the face value of the shares being INR 10 at INR 200. Therefore, the premium in this case is INR 190. Similarly, if that particular share is issued at a price which is less than the face value of that share, it is said to be issued at a discount.

 

Recapitulation of the concepts – I

1. Stock Capital: The total amount of money needed to run a company is called its stock capital.
2. Shares or Stock: The whole capital of the company is divided into equal units. Each unit is called a share or a stock.
3. Shareholder or Stockholder: Each individual who purchases one or more shares is called a shareholder (stockholder) of the company. The company issues share certificates to each of its shareholders indicating the number of shares allocated and the value of each share.
4. Dividend: The annual profit distributed among shareholders is called dividend. It is paid annually as per share or as a percentage. Dividend is always paid on the face value of a share.
5. 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. The face value of a stock always remains the same.

 

Recapitulation of the concepts – II

1. Market Value: The stock of different companies is sold and bought in the open market through brokers at stock-exchanges. A share or stock is said to be:At premium or Above par, if its market value is more than its face value.
   At par, if its market value is the same as its face value.
   At discount or Below par, if its market value is less than its face value.

Thus, if a Rs. 100 stock is quoted at premium of 16,
then market value of the stock = Rs. (100 + 16) = Rs. 116.

Likewise, if a Rs. 100 stock is quoted at a discount of 7,
then market value of the stock = Rs. (100 -7) = 93.

The market value (trading price) of a share can vary time to time.

Let’s consider an 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

2. 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:

The face value of a share always remains the same.

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

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

Number of shares held by a person

=	Total Investment	=	Total Income	=	Total Face Value
	Investment in 1 share		Income from 1 share		Face of 1 share

 

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

Face Value of stock = Rs. 100.

Market Value (M.V) of stock = Rs. 120.

Annual dividend on 1 share = 9% of face value = 9% of Rs. 100 = Rs. 9.

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

Rate of interest p.a   =   Annual income from an investment of Rs. 100

Investment/Cash required = Stock × Market Price/100Stock purchased/sold = Investment × 100/Market Price
In shares and stock questions, there could be two – three methods to find answer to a particular question. It is advised to remember all the following formulas.
Important Formulas of Stocks and Shares

Income/Dividend = Stock × Rate/100

Stock purchased/sold = Income × 100/Rate%

Investment/Cash required = Income ×Market Price/Rate%

Income/Dividend = Investment × Rate/Market Price

 

Tip #1: Interpret the question correctly

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.

Question: 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

Question: 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.

 

Question: 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 × 11 / 143 = X / 13

Income on 2^nd stock = X × 9.75 / 117 = X / 12

Thus, income on 2^nd stock > Income on 1^st stock. Hence, 2^nd stock is a better investment.

 

Tip #2: If investment is not mentioned, choose the investment in the relevant stock as x

 

Question: 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 1^st stock be X. Then, investment in 2^nd stock = 12000 – X.

Income on 1^st stock = 12 / 120 x X = X / 10.

Income on 2^nd stock = 15 / 125 x (12000 – X) = 3(12000 – X) / 25

=>    X / 10 + 3 (12000 – X) / 25 = Rs.1360.

=>    5x + 72000 – 6x = 1360 x 50.

=>    x = Rs.4000.  

Question: 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 = 9/75 x X = 3X/25 & on 2^nd stock = 10/80 x (9800 – X) = (9800 – X)/8.

=>    3X / 25 = (9800 – X) / 8

=>    24x = 9800 x 25 – 25x

=>    49x = 9800 x 25

=>    x = Rs.5000.

 

Questions for practice:

Ques 1: Ram invests a part of Rs. 12,000 in 12% stock at Rs. 120 and the remainder in 15% stock at Rs. 125. If his total dividend per annum is Rs. 1360, how much does he invest in 12% stock at Rs. 120?

A. Rs. 4000 B. Rs. 4500 C. Rs. 5500 D. Rs. 6000

Answer: Option A

Explanation

Let investment in 12% stock be Rs. x.

Then, investment in 15% stock = Rs. (12000 – x).

∴ 12/120 x x + 15/125 × (12000 – x) = 1360.

⇒ x/10 + 3/25 (12000 – x) = 1360.

⇒ 5x + 72000 -6x = 1360 × 50

⇒ x = 4000

 

Ques 2: The market value of a 10.5% stock, in which an income of Rs. 756 is derived by investing Rs. 9000, brokerage being %, is:

A. Rs. 108.25 B. Rs. 112.20 C. Rs. 124.75 D. Rs. 125.25 Answer: Option C   Explanation: For an income of Rs. 756, investment = Rs. 9000. ∴For an Rs. 100 stock, investment = Rs. 125.

Ques 3: A man sells Rs.5000, 12 % stock at 156 and invests 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?

A. 4000	B. 4200
C. 4002	D. 4020

Answer: Option B

 Explanation:

S.P of Rs. 5000 stock = Rs.(156/100*5000) =  Rs. 7800.

Income from this stock = Rs.(12100*5000) = Rs. 600.

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

Therefore,

(x*⁸/₉₀) + (7800−x) * ⁹/₁₀₈ = [600+70]

^4x/₄₅ + ^{(7800−x)}/₁₂ = 670 ⇔ x = 3600

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

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

 

Ques 4: Find the annual dividend received by Ram from 1200 preferred shares and 3000 common shares both of par value Rs. 50 each if the dividend paid on preferred shares is 10% and semi-annual dividend of 3½ % is declared on common shares.
A. Rs. 18500	B. Rs. 16500
C. Rs. 14500	D. Rs. 19500

Answer: Option B

Explanation:

Total number of preferred shares = 1200

Face value = Rs.50

dividend paid on preferred shares is 10%

Dividend per share = 50×10/100 = Rs.5

Total Dividend = 1200 × 5 = 6000

Total number of common shares = 3000

Face value = Rs.50

Semi-annual dividend of 3½ % is declared on common shares.

semi-annual dividend per share = 50×7/2×100 = Rs.74
Total semi-annual dividend = 74×3000 = Rs.5250
annual dividend = Rs.5250 × 2 = Rs.10500

Total dividend on all shares(preferred and common) = 6000 + 10500 = Rs.16500

Ques 5: A company has issued 500 preferred shares and 400 common shares both of par value Rs. 100 each. The dividend on a preferred share and a common share is 8% and 12%, respectively. The company had a total profit of 150000 rupees out of which some amount was kept in reverse fund and the remaining disturbed as dividend. Find the amount kept in reserve fund.

A. Rs.141200
B. Rs.160000

C. Rs.7200
D. Rs.182200
 

 Answer: Option A

Explanation:

Face value of each preferred share = 100

Dividend per preferred share = 100×⁸/₁₀₀
Total dividend in all preferred shares = 500×100×⁸/₁₀₀=Rs.4000
Face value of each common share = 100

Dividend per common share = 100×¹²/₁₀₀
Total dividend in all common shares = 400×100×¹²/₁₀₀ = Rs.4800
Total dividend = Rs.4000 + Rs.4800 = Rs.8800

amount kept in reserve fund = Rs.150000 – Rs.8800 = Rs.141200

Ques 6: Ram buys 100 shares of par value Rs. 5 each, of a company, which pays an annual dividend of 12% at such a price that he gets 10% on his investment. Find the market value of a share.
A. Rs.6	B. Rs.12
C. Rs.4	D. Rs.8

Answer: Option A

Explanation:

Face value of each share = Rs.5

Total dividend received by Ram = 100×5×¹²/₁₀₀ = Rs.60
Let market value of 100 shares = Rs. x

x×¹⁰/₁₀₀ = 60
x = 600

i.e. Market value of 100 shares = Rs.600

Hence, Market value of each share = Rs.6

Ques 7: 12500 shares, of par value Rs. 20 each, are purchased from Shyam by Ram at a price of Rs. 25 each. If Ram further sells the shares at a premium of Rs. 11 each, find his gain in the transaction.
A. Rs. 75000	B. Rs. 70000
C. Rs. 85000	D. Rs. 65000

Answer: Option A

Explanation:

Face value of each share = Rs.20

Market value of each share = Rs.25

Number of shares = 12500

Amount required to purchase the shares = 12500 × 25 = 312500

Ram further sells the shares at a premium of Rs. 11 each

ie, Ram further sells the shares at Rs.(20+11) = Rs.31 per share

total amount he gets by selling all the shares = 12500 × 31 = 387500

His gain = 387500 – 312500 = Rs.75000

 

Ques 8: A man invested Rs. 5050 in 5% stock at 99 and sold it when the price rose to Rs. 101. He invested the sale proceeds in 8% stock at 88. Find the change in man’s income if the Brokerage is Rs. 2.
A. 0	B. Rs.160
C. Rs.180	D. Rs.190

Answer: Option D

Explanation:

Purchase price of the first stock = Rs.99 + Rs.2 = Rs.101

Number of stocks purchased in this case = 5050/101 = 50

Since the face value is not given, it can be taken as Rs.100. So, dividend per share = Rs.5

Income = 50 × 5 = Rs.250

Sale Price of the stock = 101-2 = 99

Amount received by selling the stock = 50 × 99 = 4950

Then he invests this Rs.4950 in 8% stock at 88

Purchase price of this stock = 88+2 = 90

Number of stocks purchased in this case = 4950/90 = 55

Since the face value is not given, it can be taken as Rs.100. So, dividend per share = Rs.8

Income = 55 × 8 = Rs.440

Change in income = 440-250 = Rs.190

 

Ques 9: A man invested Rs. 26000 in 5% stock at 104. He sold the stock when the price rose to Rs. 120 and invested the sale proceeds in 6% stock. By doing this his income increased by Rs. 2500. At what price did he purchase the second stock?
A. Rs. 125	B. Rs. 48
C. Rs. 24	D. None of these

Answer: Option B

Explanation:

Assuming that face value of the first stock = Rs.100 as it is not given in the question

Since it is a 5% stock, we can take the dividend per stock = Rs.5

Market Value of the first stock = Rs.104

Investment on the first stock = Rs.26000

Number of stocks purchases = 26000/104 = 250

His total income from all these stocks = Rs.250 × 5 = Rs.1250

He sells each of this stock at Rs.120

ie, amount he earns = Rs.120 × 250 = Rs.30000

He invest this Rs.30000 in 6% stock (here also face value is not given and hence take it as Rs.100)

His new income = Rs.(1250 + 2500) = Rs.3750

ie, By Rs.30000 of investment , he earns an income of Rs.3750

To get an income of Rs.6, investment needed = 30000×63750=Rs.48To get an income of Rs.6, investment needed = 30000×63750=Rs.48

This is the market value of the second stock

 

Ques 10: Ram and Shyam are business partners. Ram invests Rs 35,000 for a period of 8 months and Shyam invests Rs 42,000 for a period of 10 months. Out of a total profit of Rs 31,570 what is Ram’s share?

A. Rs 12,420
B. Rs 18,040
C. Rs 18,942
D. Rs 12,628

Answer: Option A

Explanation: 
For a given business profit is directly dependent upon the capital invested and the time of investment.

=> Ratio of shares of Ram and Shya, becomes: (35,000*8)/(42,000*10) = 2/3
=>% of profit belonging to Akash: 2/(3+2)*(31,570)
=>Rs 12,768

You can also see: Shortcuts for CAT – Descartes’ Rule of Signs

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