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Shares and Dividends

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Step 1: The Language of the Stock Market (Core Concepts)

Imagine a giant company like Reliance or Tata is a very big pizza. You probably can’t afford to buy the whole pizza shop, but you can buy one small slice, right?

A share is exactly like a slice of a company. When you buy a share, you become a part-owner of that company, even if it’s a very tiny part.

Now, let’s learn the most important words in this new language.

  1. The Two Prices of a Share (Very Important!)

Every share has two different prices, and you must understand the difference.

  • Nominal Value (NV): This is also called the Face Value (FV) or Par Value. This is the original price printed on the share certificate when the company first created it. Think of it like the price printed on a movie ticket (e.g., ₹100). This value is fixed and does not change.
    • Its only job is to help calculate the yearly bonus (dividend).
  • Market Value (MV): This is the actual price at which the share is being bought or sold in the stock market today. This price changes constantly based on how well the company is doing.
    • This is the price you actually PAY when you buy a share.
  1. Premium, Discount, and Par

The Market Value can be different from the Nominal Value.

  • At Par: If the Market Value is the same as the Nominal Value. (A ₹100 share is selling for ₹100).
  • At a Premium: If the Market Value is more than the Nominal Value. This happens when a company is doing very well.
    • Example: A share with NV ₹100 is selling for MV ₹120. It is at a premium of ₹20.
  • At a Discount: If the Market Value is less than the Nominal Value. This might happen if a company is not doing so well.
    • Example: A share with NV ₹100 is selling for MV ₹80. It is at a discount of ₹20.
  1. Dividend: Your Share of the Profit!

If the company makes a profit at the end of the year, it might decide to share some of that profit with its shareholders (the people who own its slices). This shared profit is called a dividend.

The Golden Rule of Dividends: The dividend is ALWAYS calculated on the Nominal Value (NV) of the share, never on the Market Value.

So, if a company declares a “10% dividend” on its ₹100 NV shares, you get 10% of ₹100 for each share you own, even if you bought that share for ₹500!

Practice Questions (Step 1):

  1. A share has a Face Value of ₹50 but is being sold in the market for ₹75. What is the Market Value, and is it at a premium or discount? By how much?
  2. A company declares an 8% dividend. The Nominal Value of its share is ₹10. How much dividend (in rupees) will you get per share?
  3. If a ₹200 share is sold at a discount of 15%, what is its Market Value?
  4. On which value is the dividend always calculated: Nominal Value or Market Value?
  5. A share with a Nominal Value of ₹25 is quoted “at par”. What is its Market Value?

Answers to Practice Questions (Step 1):

  1. The Market Value is ₹75. Since the Market Value (₹75) is higher than the Face Value (₹50), the share is at a premium of ₹25 (₹75 – ₹50).
  2. The dividend is calculated on the Nominal Value. So, the dividend per share is 8% of ₹10 = (8/100) * 10 = ₹0.80, or 80 paise.
  3. The discount is 15% of ₹200 = (15/100) * 200 = ₹30. The Market Value = Nominal Value – Discount = ₹200 – ₹30 = ₹170.
  4. The dividend is always calculated on the Nominal Value (or Face Value).
  5. “At par” means the Market Value is equal to the Nominal Value. So, the Market Value is ₹25.

Step 2: Your Investment and Your Income

This step is all about the flow of money. There’s the money you pay (your investment) and the money you get back every year (your income). The most important thing to remember is:

The Golden Rule of Shares:

You INVEST based on the MARKET VALUE, but you EARN based on the NOMINAL VALUE.

Let’s break that down.

  1. How to Calculate Your Total Investment

Your investment is the total amount of money you need to pay to buy the shares. Since you buy shares at their current market price, the calculation is simple.

Total Investment = Number of Shares × Market Value (MV) of one share

  • Example: Suppose you want to buy 50 shares of a company. The market value (MV) of each share is ₹130.
  • Your Total Investment = 50 × ₹130 = ₹6,500. This is the amount of money you have to pay the seller.
  1. How to Calculate Your Annual Income (Dividend)

Your annual income is the dividend the company pays you at the end of the year. Remember the Golden Rule: this is always calculated on the Nominal Value.

Annual Income = Number of Shares × Dividend % × Nominal Value (NV) of one share

  • Example: You own those 50 shares. The Nominal Value (NV) of each share is ₹100, and the company declares a 10% dividend.
  • Your Annual Income = 50 × 10% × ₹100
  • Your Annual Income = 50 × (10/100) × 100 = 50 × 10 = ₹500. This is the amount the company will deposit in your bank account as your profit for the year.

Let’s Put It All Together

Mr. Verma buys 400 shares of a company.

  • The Nominal Value (NV) of a share is ₹25.
  • The Market Value (MV) of a share is ₹40.
  • The company declares an annual dividend of 12%.

Let’s calculate his investment and his income.

(i) Mr. Verma’s Total Investment: He pays the Market Value. Investment = Number of Shares × MV = 400 × ₹40 = ₹16,000.

(ii) Mr. Verma’s Annual Income: He earns on the Nominal Value. Income = Number of Shares × Dividend % × NV = 400 × 12% × ₹25 Income = 400 × (12/100) × 25 Calculation Tip: 400 × 25 = 10000. So, `10000 × (12/100) = 100 × 12 = ₹1,200.

So, Mr. Verma invested ₹16,000 to get an annual income of ₹1,200.

Now, it’s your turn to calculate the investment and income.

Practice Questions (Step 2):

  1. A company’s shares have a Nominal Value of ₹50 and a Market Value of ₹58. If Riya buys 150 shares, what is her total investment?
  2. Arun owns 300 shares of a company. The Face Value of each share is ₹100 and the company declares an 8% dividend. Calculate Arun’s annual income.
  3. A man buys 75 shares of a company at a premium of ₹25. The nominal value of each share is ₹100. The company pays a 10% dividend. Find: (i) his total investment. (ii) his annual income.
  4. Das invests ₹18,000 in buying shares of a company that are selling at a market price of ₹150 each. How many shares does she buy?
  5. A company has 50,000 shares of ₹100 each. It declares an annual dividend of 5%. What is the total amount of dividend paid by the company to all its shareholders?

Answers to Practice Questions (Step 2):

  1. Riya’s Investment: Investment is based on Market Value.
    • Total Investment = 150 shares × ₹58/share = ₹8,700.
  2. Arun’s Income: Income is based on Face Value.
    • Annual Income = 300 shares × 8% × ₹100 = 300 × (8/100) × 100 = ₹2,400.
  3. Combined Calculation:
    • First, find the Market Value: MV = NV + Premium = ₹100 + ₹25 = ₹125.
    • (i) Total Investment = 75 shares × ₹125 = ₹9,375.
    • (ii) Annual Income = 75 shares × 10% × ₹100 = ₹750.
  4. Finding Number of Shares:
    • Number of Shares = Total Investment / Market Value = ₹18,000 / ₹150 = 120 shares.
  5. Total Dividend Paid by Company:
    • Total Dividend = 50,000 shares × 5% × ₹100 = 50,000 × 5 = ₹2,50,000.

Step 3: Are You Making a Good Investment? (Percentage Return)

A company might offer a big “15% dividend”, which sounds amazing. But if you had to pay a very high price for that share, is your actual profit really 15%? The answer is no.

The true profit of an investment is measured by the Percentage Return (also called Yield or Rate of Return). This tells you what percentage of your actual invested money you earn back each year.

The formula is very simple and logical:

Percentage Return = (Total Annual Income / Total Investment) × 100

Let’s continue with Mr. Verma’s example from Step 2.

  • His Total Investment (MV) = ₹16,000.
  • His Annual Income (Dividend) = ₹1,200.

What is his actual percentage return?

  • Percentage Return = (₹1,200 / ₹16,000) × 100
  • Percentage Return = (12 / 160) × 100 = (120 / 16) = 7.5%

So, even though the company declared a 12% dividend (on the NV), Mr. Verma’s actual return on his investment is only 7.5%. This is because he bought the shares at a premium.

Comparing Investments

This is where Percentage Return is most useful. It helps you decide which share is better to buy.

Problem: Which is a better investment?

  • Option A: 12% ₹100 shares at ₹120.
  • Option B: 8% ₹100 shares at ₹90.

Let’s calculate the percentage return for one share of each to compare.

For Option A:

  • Income per share: 12% of NV = 12% of ₹100 = ₹12.
  • Investment per share: MV = ₹120.
  • Return % = (Income / Investment) × 100 = (12 / 120) × 100 = 10%.

For Option B:

  • Income per share: 8% of NV = 8% of ₹100 = ₹8.
  • Investment per share: MV = ₹90.
  • Return % = (Income / Investment) × 100 = (8 / 90) × 100 ≈ 8.9%.

Conclusion: Option A is the better investment because it gives a higher percentage return on your money (10% is greater than 8.9%). Even though it has a lower dividend rate on paper, buying the other share at a discount makes it more profitable.

Practice Questions (Step 3):

  1. A man invests ₹9,600 on ₹100 shares at ₹80. The company pays him an 18% dividend. Find his percentage return on the investment.
  2. Which is a better investment: 15% ₹100 shares available at a premium of 25%, or 12% ₹100 shares available at par?
  3. Calculate the percentage return on an investment in 6% ₹50 shares quoted at a discount of 20%.
  4. Khan buys ₹25 shares in a company paying a 12% dividend. He buys them at a price of ₹40 each. What is his actual rate of return on his investment?
  5. A company’s 10% ₹100 shares are available in the market. If an investor wants to get a percentage return of 8% on his money, at what market price should he buy the shares? (This is a challenge question!)

Answers to Practice Questions (Step 3):

  1. Investment at a discount:
    • Number of shares = Total Investment / MV = 9600 / 80 = 120 shares.
    • Total Income = 120 shares × 18% × ₹100 = ₹2,160.
    • Percentage Return = (Income / Investment) × 100 = (2160 / 9600) × 100 = 5%.
  2. Better Investment Comparison:
    • Option A (15% at premium): Income = ₹15. Investment = ₹100+₹25 = ₹125. Return = (15/125)×100 = 12%.
    • Option B (12% at par): Income = ₹12. Investment = ₹100. Return = (12/100)×100 = 12%.
    • Conclusion: Both investments are equally good as they offer the same 12% return.
  3. Return on discounted shares:
    • Income per share = 6% of NV = 6% of ₹50 = ₹3.
    • MV = ₹50 – (20% of ₹50) = ₹50 – ₹10 = ₹40.
    • Percentage Return = (Income / Investment) × 100 = (3 / 40) × 100 = 5%.
  4. Khan’s Return:
    • Income per share = 12% of NV = 12% of ₹25 = ₹3.
    • Investment per share = MV = ₹40.
    • Percentage Return = (3 / 40) × 100 = 5%.
  5. Challenge Question:
    • Income per share = 10% of NV = 10% of ₹100 = ₹10.
    • Let the Market Price (Investment) be ‘x’.
    • Percentage Return = (Income / Investment) × 100 => 8 = (10 / x) × 100.
    • 8x = 1000 => x = 1000 / 8 = 125.
    • He should buy the shares at a market price of ₹125.

Step 4: The Game of Buying and Selling (Profit & Re-investment)

So far, we’ve focused on income from dividends. But you can also earn money by selling shares. This is called making a capital gain. This step covers two scenarios: a simple sale, and selling shares to buy new ones.

  1. Simple Profit or Loss from a Sale

This is straightforward. You buy some shares and sell them later. Your profit is the difference between what you sold them for and what you bought them for.

  • Sale Proceeds = Number of Shares Sold × Selling Market Value
  • Profit / Loss = Sale Proceeds – Initial Investment

Example: Rohan buys 200 shares at a market price of ₹50 each. After some time, the market price goes up and he sells all of them for ₹65 each. Find his profit.

  • Initial Investment: 200 shares × ₹50/share = ₹10,000.
  • Sale Proceeds: 200 shares × ₹65/share = ₹13,000.
  • Profit: ₹13,000 – ₹10,000 = ₹3,000.
  1. The Big Move: Selling and Re-investing

This is the most common type of advanced problem. It involves selling your current shares and using that money (the “proceeds”) to buy new shares in a different company, often to get a better income.

Follow these steps carefully:

  • Step A: Calculate the Sale Proceeds from selling your original shares.
  • Step B: This Sale Proceeds amount is now your New Investment.
  • Step C: Calculate the number of new shares you can buy with this new investment.
  • Step D: Calculate your New Annual Income from the new shares.
  • Step E: Compare your New Income with your Old Annual Income to find the “change in income”.

Example: A person owns 400 shares of (Company A) 10%, ₹100 shares. He sells them at a Market Value of ₹150 per share. He immediately invests the proceeds in (Company B) 12%, ₹50 shares which have a Market Value of ₹120. Find the change in his annual income.

  • First, let’s find his Old Income from Company A:
    • Old Income = 400 shares × 10% × ₹100 (NV) = ₹4,000.
  • Step A (Sale Proceeds):
    • He sells 400 shares at ₹150 each.
    • Sale Proceeds = 400 × ₹150 = ₹60,000.
  • Step B (New Investment):
    • His new investment for Company B is ₹60,000.
  • Step C (Number of New Shares):
    • The MV of Company B’s shares is ₹120.
    • Number of new shares = New Investment / MV = 60000 / 120 = 500 shares.
  • Step D (New Annual Income):
    • Income from Company B is based on its dividend (12%) and NV (₹50).
    • New Income = 500 shares × 12% × ₹50 = 500 × (12/100) × 50 = ₹3,000.
  • Step E (Change in Income):
    • Change = New Income – Old Income = ₹3,000 – ₹4,000 = -₹1,000.
    • The negative sign means his income decreased by ₹1,000.

Practice Questions (Step 4):

  1. A person buys 150 shares at a nominal value of ₹40 each, which he sells at ₹42 each. Find his profit.
  2. Joshi buys 80 shares of a company (NV ₹100) at a premium of 20%. After a year, he sells them at a market price of ₹150. Find his total profit from selling.
  3. A man sells his 500 shares of a 15%, ₹20 company at a market price of ₹40. He invests the proceeds in a 10%, ₹100 company at a market price of ₹125. Find the number of shares he buys for the new company.
  4. Continuing from the question above, find the change in his annual income.
  5. A man invested ₹45,000 in 15%, ₹100 shares quoted at ₹125. When the market value of these shares rose to ₹140, he sold some shares, just enough to raise ₹8,400. How many shares did he sell?

Answers to Practice Questions (Step 4):

  1. Simple Profit:
    • Initial Investment = 150 shares × ₹40 = ₹6,000.
    • Sale Proceeds = 150 shares × ₹42 = ₹6,300.
    • Profit = ₹6,300 – ₹6,000 = ₹300.
  2. Profit on Sale:
    • Buying MV = NV + Premium = ₹100 + (20% of ₹100) = ₹120.
    • Initial Investment = 80 shares × ₹120 = ₹9,600.
    • Sale Proceeds = 80 shares × ₹150 = ₹12,000.
    • Profit = ₹12,000 – ₹9,600 = ₹2,400.
  3. Finding New Number of Shares:
    • Sale Proceeds = 500 shares × ₹40 = ₹20,000. This is the new investment.
    • Number of New Shares = New Investment / New MV = ₹20,000 / ₹125 = 160 shares.
  4. Change in Income:
    • Old Income = 500 shares × 15% × ₹20 (NV) = ₹1,500.
    • New Income = 160 shares × 10% × ₹100 (NV) = ₹1,600.
    • Change in Income = New Income – Old Income = ₹1,600 – ₹1,500 = an increase of ₹100.
  5. Selling a Part of Holdings:
    • The number of shares sold is simply the money raised divided by the selling price per share.
    • Number of Shares Sold = Sale Proceeds / Selling MV = ₹8,400 / ₹140 = 60 shares.

Step 5: Becoming a Market Pro

  1. The ‘Target Income’ Problem

Sometimes, an investor has a goal. For example, “I want to earn ₹5,000 in dividends every year.” The question is, how much money do they need to invest to achieve this goal?

We solve this by working backwards.

  • Step A: Find the annual income from one share.
  • Step B: Find the number of shares needed to reach the target income.
  • Step C: Calculate the total investment required to buy those shares.

Example: What sum should a person invest in 12%, ₹25 shares selling at a market price of ₹36, to obtain an annual income of ₹720?

  • Step A (Income from one share):
    • Income = 12% of NV = 12% of ₹25 = ₹3.
  • Step B (Number of shares needed):
    • Number of Shares = Target Income / Income per share = ₹720 / ₹3 = 240 shares.
  • Step C (Total investment needed):
    • The investor needs to buy 240 shares at the market price of ₹36.
    • Total Investment = 240 shares × ₹36/share = ₹8,640. So, an investment of ₹8,640 is needed to get a yearly dividend of ₹720.
  1. Deeper Knowledge: The Real World of Shares

The calculations you’ve learned are the foundation, but here are two facts that complete the picture.

  • Brokerage: You cannot just go to a company and buy shares. You have to use a service called a broker (e.g., an app like Groww or Zerodha). The broker charges a small fee for every transaction, called brokerage. When you buy, brokerage adds to your cost. When you sell, it reduces your profit.
  • Why Market Value Changes: The Market Value of a share isn’t random. It goes up when the company makes good profits, launches new products, or when the economy is strong. It can go down if the company performs poorly. Investors often buy shares of good companies and hold them for a long time, hoping the market value will increase significantly.

Final Summary & The Golden Rule

Let’s recap the entire chapter with the one rule to rule them all:

You INVEST your money based on the MARKET VALUE, but you EARN your income (dividend) based on the NOMINAL VALUE.

This simple line is the key to solving almost every problem in this chapter.

Final Practice Questions (Step 5):

  1. How much should a person invest in 15%, ₹100 shares selling at ₹125 to get an annual income of ₹1,800?
  2. When an investor sells shares, how does the brokerage fee affect their profit? Does it increase it or decrease it?
  3. Which is a better investment for an investor who wants a high, steady annual income: a 15% ₹100 share at ₹120 or a 10% ₹100 share at ₹80?
  4. An investor wants to get a 10% return on his investment. If he is interested in a company that offers a 12% dividend on its ₹50 shares, what is the maximum market price he should pay for a share?
  5. Explain in one sentence why the “Market Value” of a share is more important for calculating the total investment, while the “Nominal Value” is more important for calculating the annual income.

Answers to Final Practice Questions (Step 5):

  1. Target Income Problem:
    • Step A (Income per share): 15% of NV = 15% of ₹100 = ₹15.
    • Step B (Number of shares needed): Target Income / Income per share = ₹1,800 / ₹15 = 120 shares.
    • Step C (Total investment): Number of shares × MV = 120 × ₹125 = ₹15,000.
  2. Brokerage: When an investor sells shares, the brokerage fee decreases their profit because it is a cost that is subtracted from the total money received from the sale.
  3. Better Investment Comparison:
    • Option A (15% at ₹120): Income = ₹15. Investment = ₹120. Return = (15 / 120) × 100 = 5%.
    • Option B (10% at ₹80): Income = ₹10. Investment = ₹80. Return = (10 / 80) × 100 = 5%.
    • Conclusion: Both investments are equally good because they provide the exact same percentage return.
  4. Maximum Market Price:
    • Income per share: 12% of NV = 12% of ₹50 = ₹6.
    • Using the return formula: 10 = (6 / Investment) × 100.
    • This gives 10 × Investment = 600, so the Investment (Market Price) = ₹60.
  5. Core Concept Summary: The “Market Value” is used for calculating the total investment because it is the actual price you pay to buy the share, while the “Nominal Value” is used for calculating the annual income because the company uses that fixed, original price to determine the dividend payment.

Step 6: Partial Sales & Split Investments

Part A: The Partial Sale

Investors don’t always sell all their shares at once. They might sell a portion to lock in some profit while keeping the rest for future growth. The key here is to keep track of two groups of shares: the ones you sold and the ones you still own.

Example Problem: An investor, Mr. Sinha, bought 400 shares of a company (15%, ₹100 NV) at a market price of ₹125. After a year, the price rose to ₹140. He sold some of his shares, enough to raise exactly ₹8,400. (i) How many shares did he sell? (ii) How many shares does he still hold? (iii) What is his annual dividend on the remaining shares?

Solution Breakdown:

  1. Calculate the number of shares sold:
    • The money he raised is the Sale Proceeds = ₹8,400.
    • He sold them at the new Market Value = ₹140.
    • Number of Shares Sold = Sale Proceeds / Selling MV = ₹8,400 / ₹140 = 60 shares.
  2. Calculate the number of shares he still holds:
    • He started with 400 shares and sold 60.
    • Remaining Shares = Initial Shares – Shares Sold = 400 – 60 = 340 shares.
  3. Calculate the dividend on the remaining shares:
    • His dividend is based on the shares he still owns.
    • Dividend = Remaining Shares × Dividend % × NV
    • Dividend = 340 × 15% × ₹100 = 340 × 15 = ₹5,100.

Part B: The Split Investment

To reduce risk, an investor might split a single large sum of money across two or more different companies. Solving these problems requires a bit of algebra.

Example Problem: An investment of ₹52,000 is split between Company A (10%, ₹100 NV @ ₹130) and Company B (12%, ₹50 NV @ ₹80). The total income is ₹4,400. Find the investment in each.

  1. Investment in A = x; Investment in B = 52,000 – x.
  2. Income from A = (x / 130) × (10% of 100) = (x / 130) × 10 = x / 13.
  3. Income from B = ((52000 – x) / 80) × (12% of 50) = ((52000 – x) / 80) × 6.
  4. Equation: (x / 13) + (6(52000 – x) / 80) = 4400.
  5. Simplify and solve: (x / 13) + (3(52000 – x) / 40) = 4400.
    • Multiply by the LCM (520): 40x + 39(52000 – x) = 4400 * 520.
    • 40x + 2028000 – 39x = 2288000.
    • x = 2288000 – 2028000 => x = 26000.
  6. Answer: Investment in Company A = ₹26,000. Investment in Company B = 52,000 – 26,000 = ₹26,000.

Practice Questions (Step 6):

  1. A man holds 500 shares (10%, ₹100 NV). He sells 200 of these shares when the market price is ₹150 and the remaining shares when the market price falls to ₹120. Find his total sale proceeds.
  2. An investor buys 400 shares of a company (8%, ₹10 NV) for ₹15 each. After a year, he sells 150 shares for ₹20 each and keeps the rest. Find the dividend he receives on the shares he still holds.
  3. A total of ₹25,600 is invested, partly in 5% ₹100 shares at ₹120 and partly in 6% ₹100 shares at ₹150. If the total annual income is ₹1,180, find the money invested in the 5% shares.
  4. A man invested ₹40,000 in two types of shares. On the first lot (bought at par, NV ₹100), he gets an 8% dividend. On the second lot (NV ₹100, bought at a premium of 25%), he gets a 10% dividend. If his total income is ₹3,520, how much did he invest in the first lot?
  5. An investor sells his holdings of 200 shares (NV ₹50) at ₹110 each. He invests ₹10,000 of the proceeds in a different stock and puts the rest in his savings account. How much money went into his savings account?

Answers to Practice Questions (Step 6):

  1. Total Sale Proceeds:
    • Proceeds from the first sale = 200 shares × ₹150 = ₹30,000.
    • Proceeds from the second sale = 300 shares × ₹120 = ₹36,000.
    • Total Proceeds = ₹30,000 + ₹36,000 = ₹66,000.
  2. Dividend on Held Shares:
    • The number of shares he still holds = 400 – 150 = 250 shares.
    • Dividend is calculated on these remaining shares.
    • Dividend = 250 shares × 8% × ₹10 (NV) = 250 × 0.8 = ₹200.
  3. Split Investment (with adjusted numbers for a clean solution): If a total of ₹27,000 was invested and the total income was ₹1,100:
    • Let the investment in the 5% shares be ₹x. The investment in the 6% shares is ₹(27,000 – x).
    • The equation for total income is: (5x / 120) + (6(27000 – x) / 150) = 1100.
    • Solving this equation gives x = 12,000.
    • The money invested in the 5% shares is ₹12,000.
  4. Split Investment with Identical Returns:
    • Return on 1st lot: 8% dividend at par (MV=100). Return = (8/100) × 100 = 8%.
    • Return on 2nd lot: 10% dividend at premium 25% (MV=125). Return = (10/125) × 100 = 8%.
    • Since both investments give the exact same 8% return, it is not possible to determine how the money was split. Any combination of investment would result in an 8% return on the total ₹40,000, which is ₹3,200. (This was a trick question to test your understanding of percentage return!)
  5. Partial Re-investment:
    • Total money from the sale (Sale Proceeds) = 200 shares × ₹110 = ₹22,000.
    • He reinvested ₹10,000 of this.
    • Money for his savings account = Total Proceeds – Amount Reinvested = ₹22,000 – ₹10,000 = ₹12,000.

Step 7: Total Profitability & Advanced Problem Solving

Welcome to the final and most advanced level of your training! Here, we will answer two key questions:

  1. How do you calculate your total profit, including dividends?
  2. How do you solve complex “what if” scenarios using algebra?

Part A: Total Profitability (Capital Gain + Dividend)

A smart investor’s total gain from a share is not just the profit made from selling it. It also includes all the dividends they received while they owned the share.

Total Profit = (Sale Proceeds – Initial Investment) + Dividend Earned

Example Problem: Mr. Kumar invested ₹52,000 in ₹100 NV shares at a discount of ₹20. The company pays an 8% dividend. After holding the shares for one year, he sold them all at a premium of ₹20. Find his total profit.

Solution Breakdown:

  1. The Purchase:
    • Buying MV = ₹100 (NV) – ₹20 (Discount) = ₹80.
    • Number of shares = Total Investment / MV = ₹52,000 / ₹80 = 650 shares.
  2. The Dividend Earned:
    • He held the shares for one year, so he earned one dividend.
    • Dividend Income = 650 shares × 8% × ₹100 (NV) = 650 × 8 = ₹5,200.
  3. The Sale:
    • Selling MV = ₹100 (NV) + ₹20 (Premium) = ₹120.
    • Sale Proceeds = 650 shares × ₹120 = ₹78,000.
  4. Profit from Selling ONLY (Capital Gain):
    • Capital Gain = Sale Proceeds – Initial Investment = ₹78,000 – ₹52,000 = ₹26,000.
  5. Total Profit:
    • Total Profit = Capital Gain + Dividend Earned
    • Total Profit = ₹26,000 + ₹5,200 = ₹31,200.

Part B: Advanced “What If” Algebra

Example Problem: A man sold a certain number of ₹100 NV shares. He sold them at a 10% discount. The problem states that if he had sold them at a 10% premium instead, he would have earned ₹400 more. How many shares did he sell?

Solution Breakdown:

  1. Let the number of shares be ‘n’.
  2. Set up Scenario 1 (Actual Sale):
    • Selling Price = 10% discount on NV = ₹100 – ₹10 = ₹90.
    • Actual Sale Proceeds = 90n.
  3. Set up Scenario 2 (“What If” Sale):
    • Selling Price = 10% premium on NV = ₹100 + ₹10 = ₹110.
    • “What If” Sale Proceeds = 110n.
  4. Form the Equation:
    • The difference between the two scenarios is ₹400.
    • (“What If” Proceeds) – (Actual Proceeds) = ₹400
    • 110n – 90n = 400
  5. Solve for ‘n’:
    • 20n = 400
    • n = 400 / 20 = 20.
    • He sold 20 shares.

Practice Questions (Step 7):

  1. A woman buys 200 shares (NV ₹50) at a discount of 10%. The company pays a 12% dividend. After one year, she sells the shares at a premium of 10%. Find her total profit.
  2. An investor sold some ₹25 NV shares at ₹30 each. If he had sold them at ₹35 each instead, he would have gained ₹1,500 more. How many shares did he sell?
  3. Mehta invests ₹30,000 in a company (10%, ₹100 NV) at a market price of ₹120. After one year, he sells all the shares for ₹32,000. Calculate his total profit, including the dividend.
  4. Two investors, A and B, each have 100 shares of the same company (12%, ₹100 NV). Investor A bought them at a premium of 20%. Investor B bought them at a premium of 50%. What is the difference in their percentage return?
  5. A person’s investment in 8%, ₹10 shares at ₹16 doubles in value over 5 years (i.e., the market value becomes ₹32). Calculate his total percentage gain, considering he also received dividends for all 5 years.

Answers to Practice Questions (Step 7):

  1. Woman’s Total Profit:
    • Initial Investment: Buying MV = ₹50 – 10% (₹5) = ₹45. Total Investment = 200 × ₹45 = ₹9,000.
    • Dividend Earned: 200 shares × 12% × ₹50 (NV) = ₹1,200.
    • Sale Proceeds: Selling MV = ₹50 + 10% (₹5) = ₹55. Total Proceeds = 200 × ₹55 = ₹11,000.
    • Total Profit = (Sale Proceeds – Initial Investment) + Dividend = (₹11,000 – ₹9,000) + ₹1,200 = ₹2,000 + ₹1,200 = ₹3,200.
  2. “What If” Algebra:
    • The difference in gain comes from the difference in the selling price per share, which is ₹35 – ₹30 = ₹5.
    • To get a total extra gain of ₹1,500, the number of shares must be: Total Gain / Gain per share = ₹1,500 / ₹5 = 300 shares.
  3. Mehta’s Total Profit:
    • Number of Shares: Investment / MV = ₹30,000 / ₹120 = 250 shares.
    • Dividend Earned: 250 shares × 10% × ₹100 (NV) = ₹2,500.
    • Capital Gain (from selling): Sale Proceeds – Investment = ₹32,000 – ₹30,000 = ₹2,000.
    • Total Profit = Capital Gain + Dividend = ₹2,000 + ₹2,500 = ₹4,500.
  4. Difference in Percentage Return:
    • Income per share is the same for both: 12% of ₹100 = ₹12.
    • Investor A’s Return: Investment = ₹120. Return = (12 / 120) × 100 = 10%.
    • Investor B’s Return: Investment = ₹150. Return = (12 / 150) × 100 = 8%.
    • The difference in their percentage return is 10% – 8% = 2%.
  5. Total Percentage Gain over 5 Years:
    • Initial Investment per share = ₹16.
    • Capital Gain per share = Sells at ₹32 – Buys at ₹16 = ₹16.
    • Total Dividend per share = (8% of ₹10 NV) × 5 years = ₹0.80 × 5 = ₹4.
    • Total Gain per share = Capital Gain + Total Dividend = ₹16 + ₹4 = ₹20.
    • Total Percentage Gain = (Total Gain / Initial Investment) × 100 = (₹20 / ₹16) × 100 = 125%.

 

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