Stock and Shares

PAGE 1 — BASIC CONCEPTS

Stock and Shares is an important topic in commercial mathematics. Questions are generally based on the value of shares, market price, face value, dividend, rate of return, brokerage and number of shares.

1. IMPORTANT TERMS

Term	Meaning
Share	A unit representing a portion of ownership in a company.
Face Value (FV)	The nominal value assigned to one share.
Market Value (MV)	The current price at which a share is bought or sold in the market.
Dividend	The amount distributed to shareholders, usually stated as a percentage of face value.
Brokerage	A charge paid to a broker for buying or selling shares.
Investment	The money spent to purchase shares, including applicable charges when specified.

2. FACE VALUE AND MARKET VALUE

Face value and market value are different quantities.

Face Value = Nominal Value of Share

Market Value = Actual Buying/Selling Price of Share

Example: A share has a face value of ₹100 and is currently quoted at ₹125.

Face Value = ₹100
Market Value = ₹125

3. SHARES AT PAR, PREMIUM & DISCOUNT

Condition	Meaning	Market Value
At par	Market value equals face value	MV = FV
At premium	Market value is greater than face value	MV > FV
At discount	Market value is less than face value	MV < FV

Premium = Market Value − Face Value

Discount = Face Value − Market Value

Example: A ₹100 share is quoted at ₹120.

Premium = 120 − 100 = ₹20
Therefore, the share is at ₹20 premium.

4. NUMBER OF SHARES

Number of Shares = Total Investment ÷ Market Value per Share

Example: How many ₹50 shares can be purchased for ₹5,000 when the market value is ₹40 per share?

Number = 5000 ÷ 40
= 125 shares

TIP: In share problems, first identify whether the percentage is based on Face Value or Market Value. Dividend percentages are normally calculated on face value.

PAGE 2 — DIVIDEND & INCOME

5. DIVIDEND

Dividend is generally expressed as a percentage of the face value of a share, not its market value.

Dividend per Share = FV × Dividend Rate ÷ 100

Total Dividend = Number of Shares × FV × Dividend Rate ÷ 100

Example: A company declares 8% dividend on ₹100 shares. Find the dividend received from 500 shares.

Dividend per share = 100 × 8/100 = ₹8
Total dividend = 500 × 8
= ₹4,000

6. ANNUAL INCOME FROM SHARES

Annual Income = Number of Shares × Dividend per Share

Example: A person owns 800 shares of face value ₹50 each. The dividend rate is 12%.

Dividend/share = 50 × 12/100 = ₹6
Annual income = 800 × 6
= ₹4,800

7. RATE OF RETURN / YIELD

The dividend is based on face value, while the investor's return is generally measured against the amount actually invested.

Yield % = (Annual Income ÷ Investment) × 100

If brokerage is ignored:

Yield % = (Dividend Rate × Face Value ÷ Market Value) × 100

Example: A ₹100 share is available at ₹125 and pays 10% dividend. Find the yield.

Dividend = ₹10
Yield = (10/125) × 100
= 8%

8. FINDING MARKET VALUE FROM YIELD

Market Value = (Dividend per Share × 100) ÷ Yield %

Example: A ₹100 share pays 12% dividend. If the yield is 8%, find its market value.

Dividend/share = ₹12
Market Value = 12 × 100 ÷ 8
= ₹150

9. FINDING NUMBER OF SHARES FROM INCOME

Number of Shares = Required Annual Income ÷ Dividend per Share

Example: A ₹50 share pays 10% dividend. How many shares are required to earn ₹2,500 annually?

Dividend/share = 50 × 10/100 = ₹5
Number = 2500 ÷ 5
= 500 shares

Exam Rule: Dividend percentage → calculate on Face Value. Yield → compare dividend income with Market Value/Investment.

PAGE 3 — ADVANCED FORMULAS

10. INVESTMENT IN SHARES

Investment = Number of Shares × Market Value per Share

Example: Find the investment required to buy 300 shares at ₹160 each.

Investment = 300 × 160
= ₹48,000

11. SHARES PURCHASED AT PREMIUM

If a share of face value ₹100 is quoted at a premium of ₹20:

Market Value = Face Value + Premium

Example: Find the cost of 250 shares of face value ₹100 quoted at 15% premium.

Premium = 15% of 100 = ₹15
Market value = 100 + 15 = ₹115
Investment = 250 × 115
= ₹28,750

12. SHARES PURCHASED AT DISCOUNT

Market Value = Face Value − Discount

Example: A ₹100 share is quoted at 8% discount. Find the market value.

Discount = 8% of ₹100 = ₹8
Market value = 100 − 8
= ₹92

13. BROKERAGE

Brokerage is generally calculated as a percentage of the transaction value. The exact treatment depends on whether the question concerns purchase or sale.

Brokerage = Transaction Value × Brokerage Rate ÷ 100

Example: A person buys shares worth ₹40,000 through a broker charging 1% brokerage.

Brokerage = 40,000 × 1/100
= ₹400
Total amount paid = 40,000 + 400
= ₹40,400

14. PURCHASE PRICE INCLUDING BROKERAGE

Total Purchase Cost = Share Value + Brokerage

Total Purchase Cost = Number of Shares × MV × (1 + Brokerage Rate/100)

15. SALE PRICE AFTER BROKERAGE

Net Sale Proceeds = Sale Value − Brokerage

Example: Shares worth ₹60,000 are sold at 0.5% brokerage.

Brokerage = 60,000 × 0.5/100
= ₹300
Net proceeds = 60,000 − 300
= ₹59,700

16. COMPARING TWO INVESTMENTS

If two shares have different face values, market values and dividend rates, compare their annual income or yield separately.

Yield = Annual Dividend ÷ Market Investment × 100

Example:
Share A: FV ₹100, dividend 10%, MV ₹125.
Share B: FV ₹100, dividend 8%, MV ₹80.

Yield of A = 10/125 × 100 = 8%
Yield of B = 8/80 × 100 = 10%

Remember: A higher dividend percentage does not automatically mean a higher yield. Market price must also be considered.

PAGE 4 — QUICK FORMULA SHEET

Concept	Formula
Premium	MV − FV
Discount	FV − MV
Market value at premium	FV + Premium
Market value at discount	FV − Discount
Dividend/share	FV × Dividend % ÷ 100
Total dividend	No. of shares × Dividend/share
Investment	No. of shares × MV
Yield	Annual income ÷ Investment × 100
Market value from yield	Dividend/share × 100 ÷ Yield %
Brokerage	Transaction value × Brokerage % ÷ 100
Purchase cost	Share value + Brokerage
Net sale proceeds	Sale value − Brokerage

17. SOLVED MIXED EXAMPLES

Example 1: A ₹100 share is quoted at ₹140 and pays 12% dividend. Find the annual income from 200 shares.

Dividend/share = 100 × 12/100 = ₹12
Income = 200 × 12
= ₹2,400

Example 2: A ₹50 share is quoted at ₹75 and pays 10% dividend. Find the yield.

Dividend/share = 50 × 10/100 = ₹5
Yield = 5/75 × 100
= 6⅔%

Example 3: How much must be invested in ₹100 shares quoted at ₹125 to receive ₹5,000 annually at 8% dividend?

Dividend/share = ₹8
Required shares = 5000 ÷ 8 = 625
Investment = 625 × 125
= ₹78,125

Example 4: A person buys 400 shares at ₹90 each and pays 1% brokerage. Find the total amount paid.

Share value = 400 × 90 = ₹36,000
Brokerage = 1% of 36,000 = ₹360
Total = 36,000 + 360
= ₹36,360

18. PRACTICE QUESTIONS