ICSE Class 10
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๐Ÿ“– Summaries โ€บ Mathematics

Shares and Dividend

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Chapter in a nutshell: A company raises capital by issuing shares of a fixed face (nominal) value, bought/sold at the market value. The company pays a dividend (a % of the face value) on each share. You compute investment, number of shares, annual income (dividend) and the percentage return (yield).

1. Key Ideas & Terms

  • Face/Nominal Value (FV/NV): the printed value of a share (dividends are always a % of this).
  • Market Value (MV): the price at which a share is bought/sold in the market.
  • At par: MV = FV; at premium (above par): MV > FV; at discount (below par): MV < FV.
  • Dividend: profit shared by the company, declared as r % of the face value per share.
  • Yield / rate of return: the income as a percentage of the money actually invested.

2. Formulas (quick reference)

  • Number of shares $=\dfrac{\text{total investment}}{\text{MV of one share}}=\dfrac{\text{total face value}}{\text{FV of one share}}$
  • Investment $=\text{number of shares}\times \text{MV}$
  • Dividend (annual income) $=\dfrac{r}{100}\times\text{FV}\times\text{number of shares}=\dfrac{r}{100}\times\text{total face value}$
  • Income per share $=\dfrac{r}{100}\times\text{FV}$
  • Return % (yield) $=\dfrac{\text{annual income}}{\text{investment}}\times100$
  • MV at premium $=\text{FV}+\text{premium}$; at discount $=\text{FV}-\text{discount}$.

3. Prerequisite (earlier-class) Idea

  • Percentage: $x\%\text{ of }A=\dfrac{x}{100}\times A$ โ€” used for both dividend and yield.

4. Worked Example (one, for the method)

Q. A man buys shares of FV โ‚น100 at โ‚น125; the company pays a 15% dividend. He invests โ‚น25000. Find his income and yield. Solution: Number of shares = 25000 รท 125 = 200. Income = 15% ร— 100 ร— 200 = โ‚น3000. Yield = (3000/25000)ร—100 = 12%.

5. Common Mistakes to Avoid

  • Taking the dividend on the market value โ€” it is always on the face value.
  • Computing yield on the face value โ€” yield is on the money invested (MV).
  • Confusing premium (MV above FV) with discount (MV below FV).
  • Mixing number of shares found from MV (for investment) vs FV (for face value).

6. Likely Exam Questions (with crisp answers)

  1. On what value is the dividend calculated? โ†’ The face (nominal) value.
  2. On what value is the yield/return calculated? โ†’ The money invested (market value).
  3. Define a share at premium. โ†’ A share whose market value is above its face value.
  4. Number of shares = ? โ†’ Total investment รท market value of one share.
  5. Annual income = ? โ†’ (dividend% ร— FV) ร— number of shares.
  6. Yield % = ? โ†’ (annual income รท investment) ร— 100.
  7. FV โ‚น100, 12% dividend โ€” income per share? โ†’ โ‚น12.
  8. A โ‚น50 share at โ‚น60 is at par, premium or discount? โ†’ Premium (by โ‚น10).
  9. If MV = FV, the share is said to be at? โ†’ Par.
  10. Investment = ? โ†’ Number of shares ร— market value.

Formulas โ€” Current & Prerequisite

Current

  • Number of shares $= \dfrac{\text{Total investment}}{\text{Market Value (MV) of 1 share}} = \dfrac{\text{Total face value}}{\text{Nominal Value (NV)}}$.
  • Annual income (dividend) $= \text{No. of shares}\times \text{NV}\times \dfrac{\text{rate of dividend}}{100}$.
  • Total investment $= \text{No. of shares}\times MV$.
  • Return (yield) % $= \dfrac{\text{Annual income}}{\text{Investment}}\times100$.
  • Premium: $MV = NV + \text{premium}$; Discount: $MV = NV - \text{discount}$; at par: $MV = NV$.

Prerequisite

  • Percentage and ratio (income vs investment); profit/loss on sale of shares.