Rajesh invest ₹6500 in share, which pay 8% dividend when a share of ₹100 costs ₹120 . what is the annual income of Rajesh from shares
Answers
Answer:
Dividend, Rate of Dividend
The part of the annual profit of a company distributed among its shareholders is called dividend. The dividend is always reckoned on the face value of a share irrespective of its MV.
The rate of dividend is expressed as a percentage of the NV of a share per annum.
Meaning of the statement “r% Rs 100 at Rs M”
The statement r% Rs 100 shares at Rs M means the following:
The NV of a share is Rs 100.
The MV of a share is Rs M.
The dividend on a share is r% of NV, i.e., Rs r per annum.
An investment of Rs M gives an annual income of Rs r.
Rate of return per annum = Annual income from an investment of Rs 100
Look at the statement given below:
9% Rs 100 shares at Rs 120 means
Face value (NV) of 1 share = Rs 100.
Market value (MV) of 1 share = Rs 120.
The dividend on a share is 9% of its face value = 9% of Rs 100 = Rs 9
An investment of Rs 120 gives an annual income of Rs 9.
Rate of return per annum = Annual income from an investment of Rs 100
share}
3. Income (return or profit) = (No. of shares)
\times (rate of dividend)
\times (NV) =(No. of shares)
\times (Dividend on 1 share)
4. Return % = Income (profit) %
NOTE: The face value of a share remains the same. The market value of a share changes from time to time.
Examples
Example 1: Calculate the money required to buy: (i) 350, Rs 20 shares at a premium of Rs 7. (ii) 275, Rs 60 shares at a discount of Rs 10. (iii) 50, Rs 75 shares quoted at Rs 71.50.
Solution: (i) No. of shares = 350
NV = Rs 20
MV = Rs (20+7) = Rs 27
Therefore, money required to buy 350 shares = Rs (350
\times 27)= Rs 9450
(ii) No. of shares = 275
NV= Rs 60
MV= Rs (60-10) = Rs 50
Therefore, money required to buy 275 shares = Rs (275
\times 50) =Rs 13750
(iii) No. of shares = 50
NV= Rs 75
MV= Rs 71.50
Therefore, money required to buy 50 shares= Rs (50
\times 71.50) = Rs 3575
Example 2: A man invests in shares for which we have the condition “7% Rs 100 shares at Rs 120”. What is the annual income of a person holding 150 such shares? Also, find his annual profit percentage.
Solution: Given,
Rate of dividend=7%
Nominal value (NV) = Rs 100
Market value (MV) = Rs 120
No. of shares= 150
Therefore, Income =No. of shares
\times rate of dividend
\times NV=
Rs \
First we need to find the sum invested to find the profit percentage.
Investment=No. of shares
\times MV=
Rs \: (150 \times 120)=Rs \: 18000
Therefore, Required profit percentage
Example 3: Which is a better investment: 16% at 80 or 20% at 120?
Solution: 16% at 80 means MV of 1 share is Rs 80, NV of 1 share is Rs100 and dividend paid is 16%.
Similarly, 20% at 120 means MV of 1 share is Rs 120, NV of 1 share is Rs 100 and dividend paid is 20%.
Case 1:
Income on Rs 80=16% of Rs 100=Rs 16
Therefore, income on
Re \:
Case 2:
Income on Rs 120=20% of Rs 100= Rs 20
Therefore, income on
Therefore, the first investment is better.
Example 4: A company declares semiannual dividend of 6%. A man has 500 shares of NV Rs 25 each. Find his annual income.
Solution: Total NV of shares= Rs(25
\times 500)= Rs 12500
Semiannual dividend = 6% of Rs 12500=
Therefore, his annual income= Rs (750
\times 2)=Rs 1500
Example 5: Divide Rs 29184 into two parts such that if one part is invested in 12%, Rs 100 shares at 4% discount and the other in 15%, Rs 100 shares at 8% premium, the annual incomes are equal.
Solution: Let the investment in 12%, Rs 100 shares at 4% discount be
Rs \: x .
Then, investment in 15%, Rs 100 shares at 8% premium be
Rs \: (29184-x) .
MV of Rs 100 shares at 4% discount= Rs (100-4% of 100) = Rs 96
Annual income on 1 share of Rs 96=Rs (12% of 100) = Rs 12
Annual income on
MV of Rs 100 shares at 8% premium= Rs (100+8% of 100) = Rs 108
Annual income on 1 share of Rs 108=Rs (15% of 100) = Rs 15
Annual income on
\therefore
\
So,
x=15360
So, the first part is Rs 15360.
Second part= Rs (29184-15360) = Rs 13824
Example 6: Mukul invests Rs 9000 in a company paying a dividend of 6% per annum when a share of NV Rs 100 stands at Rs 150. What is his annual income? If he sells 505 of his shares when the price rises to Rs 200, what is his gain in this transaction?
Solution: No. of shares bought by Mukul=
\
His annual income on 1 share=6% of NV=6% of Rs 100= Rs 6
His total annual income=60
\times Rs 6= Rs 360
Since, 50% of shares= 50% of 60 =30
Money received on selling these shares =30
\times Rs 200=Rs 6000
Also, cost of these shares=30
\times Rs 150=Rs 4500
Therefore, Mukul’s gain= Rs (6000-4500) = Rs 1500
Example 7: A man wants to buy 62 shares available at Rs 132(NV being Rs 100).
How much will he have to invest?
If the dividend is 7.5%, what will be his annual income?
If he wants to increase his annual income by Rs 150, how many extra shares should he buy?
Solution: 1. He will have to invest= 62
\times Rs 132= Rs 8184
2. Dividend on 1 share= 7.5% of Rs 100=Rs 7.50
Therefore, his annual income = 62
\times Rs 7.50= Rs 465
3. The man wants to increase his income by Rs 150 and income on 1 share= Rs 7.50
Therefore, no. of extra shares he must buy= $latex\dfrac{150}{7.50} = 20 $