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Commercial Mathematics - Shares and Dividends

Grade 10ICSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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Nominal Value (NV) and Face Value (FV): This is the fixed value of a share determined by the company at the time of issue. It is the value printed on the share certificate. Visual: Imagine a physical certificate where the value 'Rs 100' is permanently embossed; this value never changes even if the trading price fluctuates.

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Market Value (MV): This is the current price at which a share is bought or sold in the stock market. It changes constantly based on demand and supply. Visual: Think of a digital stock ticker or a line graph showing a price line moving up and down daily relative to a fixed horizontal baseline (the NV).

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Shares at Par, Premium, and Discount: These terms describe the relationship between MV and NV. If MV=NVMV = NV, the share is 'at par'. If MV>NVMV > NV, it is 'at premium' (above par). If MV<NVMV < NV, it is 'at discount' (below par). Visual: Picture a balancing scale where the MV can be higher, lower, or equal to the NV weight.

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Dividend: This represents the portion of the company's profit distributed to shareholders. It is always expressed as a percentage of the Nominal Value (NVNV), regardless of the Market Value at which the share was bought. Visual: Imagine a company 'pie' where a slice is cut out and distributed to you based on the original size of your 'plate' (NV).

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Number of Shares: The total quantity of shares held by an investor. It is calculated by dividing the total investment by the Market Value of one share. Visual: If you have a stack of money (Total Investment) and each share costs a certain amount (MV), the number of shares is how many units you can 'buy' from that stack.

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Yield or Return Percentage: This is the actual percentage profit an investor earns on their real investment. Since shares are often bought at MV but dividends are paid on NV, the yield tells the investor the true efficiency of their capital. Visual: A comparison bar chart showing the 'stated' dividend rate versus the 'actual' return rate based on the money spent.

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Brokerage: A small fee or commission charged by a stockbroker for buying or selling shares. When buying, brokerage is added to the MV (MV+BrokerageMV + \text{Brokerage}). When selling, brokerage is subtracted from the MV (MV−BrokerageMV - \text{Brokerage}). Visual: A small 'transaction tax' deducted from your pocket during every trade.

📐Formulae

Investment=n×MV\text{Investment} = n \times MV

n=InvestmentMVn = \frac{\text{Investment}}{MV}

Annual Income (Total Dividend)=n×r100×NV\text{Annual Income (Total Dividend)} = n \times \frac{r}{100} \times NV

Dividend on one share=r100×NV\text{Dividend on one share} = \frac{r}{100} \times NV

\text{Yield (Return %)} = \frac{\text{Total Income}}{\text{Investment}} \times 100

\text{Yield (Return %)} = \frac{\text{Dividend on one share}}{MV} \times 100

r%×NV=Yield %×MVr \% \times NV = \text{Yield } \% \times MV

💡Examples

Problem 1:

A man invests Rs. 9,600 in shares of a company paying 12% dividend. If the face value of each share is Rs. 100 and they are bought at a premium of Rs. 20, find: (i) the number of shares bought, and (ii) his annual income.

Solution:

Given: Investment = Rs. 9,600; Dividend rate (rr) = 12%; NVNV = Rs. 100; Premium = Rs. 20.

Step 1: Calculate Market Value (MVMV) MV=NV+Premium=100+20=Rs. 120MV = NV + \text{Premium} = 100 + 20 = \text{Rs. 120}

Step 2: Find the number of shares (nn) n=InvestmentMV=9600120=80 sharesn = \frac{\text{Investment}}{MV} = \frac{9600}{120} = 80 \text{ shares}

Step 3: Calculate Annual Income Annual Income=n×r100×NV\text{Annual Income} = n \times \frac{r}{100} \times NV Annual Income=80×12100×100=80×12=Rs. 960\text{Annual Income} = 80 \times \frac{12}{100} \times 100 = 80 \times 12 = \text{Rs. 960}

Explanation:

First, we determine the actual purchase price per share (MV) by adding the premium to the face value. Then, we divide the total investment by this MV to find how many shares were acquired. Finally, we calculate the dividend income based on the Nominal Value (not the Market Value).

Problem 2:

Which is a better investment: 10% Rs. 100 shares at Rs. 120 or 15% Rs. 100 shares at Rs. 150?

Solution:

We compare the Yield (Return %) of both investments.

Case 1: NVNV = Rs. 100, rr = 10%, MVMV = Rs. 120 Yield1=r×NVMV=10×100120=10012=8.33%\text{Yield}_1 = \frac{r \times NV}{MV} = \frac{10 \times 100}{120} = \frac{100}{12} = 8.33 \%

Case 2: NVNV = Rs. 100, rr = 15%, MVMV = Rs. 150 Yield2=15×100150=1500150=10%\text{Yield}_2 = \frac{15 \times 100}{150} = \frac{1500}{150} = 10 \%

Since 10%>8.33%10 \% > 8.33 \%, the second investment is better.

Explanation:

To compare two different share opportunities, we calculate the percentage of return (Yield) on the actual money spent (MV). The investment with the higher Yield is the better choice.