Shares and dividends

A share is a unit of ownership in a company. Every share carries a Face Value (FV), also called Nominal Value — the fixed amount printed on the certificate (commonly ₹10 or ₹100) — which never changes regardless of how the company performs. The Market Value (MV) is the price at which the share is actually bought or sold on a given day, and it moves with investor demand.

• If $MV > FV$, the share trades at a premium, and premium $= MV - FV$.
• If $MV < FV$, the share trades at a discount, and discount $= FV - MV$.
• If $MV = FV$, the share is at par.

A company shares part of its profit with shareholders as dividend, stated as a percentage of face value called the Rate of Dividend. This is the single most important rule in the whole chapter: dividend is computed on face value, never on market value, because face value is the fixed "ownership unit" the company's dividend policy is pegged to.

where: $N$ is the number of shares held, $r$ is the rate of dividend written as a fraction (9% is used as $\frac{9}{100}$), and $FV$ is the face value of one share. The investment, by contrast, is the real cash the buyer handed over, and that is governed entirely by the market price:

Combining the two gives the return — the percentage yield the investor is actually earning on money spent, as opposed to the rate the company declared:

Because income sits on face value and investment sits on market value, the return percentage and the dividend rate percentage are two genuinely different numbers, and the gap between them is entirely explained by whether the share was bought at a premium or a discount.

Show that when a share of face value $FV$ and dividend rate $r$ is bought at market value $MV$, the investor's true percentage return works out to the compact form $\text{Return} = r \times \dfrac{FV}{MV} \times 100$, which lets you compare two completely different share deals in a single glance without recomputing income and investment from scratch each time.

Step 1. Take one share as the unit of comparison, since the number of shares $N$ cancels out of a ratio of income to investment — it does not matter whether you hold 1 share or 10,000, the percentage return is identical.

Step 2. Write income and investment for one share. Income per share $= r \times FV$ (dividend on the fixed face value), and investment per share $= MV$ (the actual price paid).

Step 3. Substitute into the return formula. $\text{Return} = \dfrac{\text{Income}}{\text{Investment}} \times 100 = \dfrac{r \times FV}{MV} \times 100 = r \times \dfrac{FV}{MV} \times 100$.

Step 4. Read what the ratio $FV/MV$ is doing. If the share is at a premium ($MV > FV$), then $FV/MV < 1$, so the return is pulled below the dividend rate $r$. If the share is at a discount ($MV < FV$), then $FV/MV > 1$, so the return is pushed above $r$. At par, $FV = MV$ and the return exactly equals the dividend rate — the one case where the two percentages agree. Check against Worked example: with $r = 9\%$, $FV = 10$, $MV = 12$, this gives $9 \times \frac{10}{12} = 7.5\%$ — matching the direct calculation below.

Mr. Sharma bought 200 shares, each of face value ₹10, at a premium of ₹2. The company pays a dividend of 9% per annum. Find (a) his total investment, (b) his annual income, and (c) his rate of return.

Step 1. Find the market value: $MV = FV + \text{Premium} = 10 + 2 = ₹12$.

Step 2. Find the total investment: $\text{Investment} = 200 \times 12 = ₹2{,}400$.

Step 3. Find the annual income: $\text{Income} = 200 \times \frac{9}{100} \times 10 = 200 \times 0.9 = ₹180$.

Step 4. Find the rate of return: $\text{Return} = \frac{180}{2400} \times 100 = 7.5\%$. So Mr. Sharma invested ₹2,400, earns ₹180 a year, and his true rate of return is 7.5%, lower than the 9% dividend rate because he paid a premium above face value.

Competitive stretch

Mrs. Iyer, meanwhile, invested ₹9,000 in a different company's shares — face value ₹100, available at a discount of ₹10, dividend 12%. Which investment gives the better return, Mr. Sharma's or Mrs. Iyer's?

Step 1. Find Mrs. Iyer's market value: $MV = 100 - 10 = ₹90$.

Step 2. Find her number of shares: $\text{Number of shares} = \frac{9000}{90} = 100$.

Step 3. Find her income and return: $\text{Income} = 100 \times \frac{12}{100} \times 100 = ₹1{,}200$, so $\text{Return} = \frac{1200}{9000} \times 100 = 13.33\%$.

Step 4. Compare. Mr. Sharma's return is 7.5% (bought at a premium); Mrs. Iyer's is 13.33% (bought at a discount). Mrs. Iyer's investment gives the better return, even though her company's stated dividend rate (12%) is only slightly higher than Mr. Sharma's (9%) — the discount she bought at, versus the premium he paid, is what really drives the gap.

• Calculating dividend income using market value instead of face value — dividend is always on face value.
• Calculating investment or number of shares using face value instead of market value — money is actually spent at market value.
• Mixing up premium and discount: premium means $MV > FV$ (costs more), discount means $MV < FV$ (costs less).
• Treating "rate of dividend" and "rate of return" as the same percentage — they agree only when the share is bought exactly at par.

Ask the tutor: if a problem gives you several numbers and you're not sure which formula to reach for, ask the AI tutor to help you label each given quantity as face-value-based or market-value-based before you calculate.