We will discuss here about the calculation of income, return and number of shares.
Computation of income and return
If the number of shares held by a shareholder = n, rate of dividend = r% per annum and face value = F then
Annual income = \(\frac{nrF}{100}\)
Annual return = \(\frac{annual income}{investment in shares}\) × 100%
Calculation of number of shares
To find the number of shares held by a person, we sue the following.
Number of share held = \(\frac{investment}{investment for the share (i.e., FV or MV as the case may be)}\)
Or \(\frac{ annual income}{ income from one share}\)
Or, \(\frac{ total face value}{ face value of one share}\).
Solved example on computation of income, return and number of shares:
1. Michael buys $ 100 shares at $ 20 premium in a company paying 15% divided. Find the MV of 200 shares, his annual income and his percentage income.Market value of one share = $ 100 + $ 20 = $ 120
Therefore, the market value of 200 shares = 200 × $ 120 = $ 24,000
Annual income = Number of shares × Rate of dividend × nominal value or face value of 1 share
= \(\frac{200 × 15}{100 × 100}\)
= $ 3000
$ 3000 is the income obtained on investing $ 24000
Therefore, the percentage income = \(\frac{3000}{24000}\) × 100 % = 12.5 %
2. A man invests in shares for which we have the condition “7% of $ 100 shares at $ 120”. What is the annual income of a person holding 150 such shares? Also, find his annual profit percentage.
Solution:
“7% of $ 100 shares at $ 120” means that
The annual income from 1 share of NV $ 100 is $ 7, invest for 1 share being $ 120.
Therefore, the annual income from 150 shares = \(\frac{nrF}{100}\) = \(\frac{150 × 7 × $ 100}{100}\)
= $ 7 × 150 = $ 1050.
His investment for 150 shares = 150 × $ 120 = $ 18000
Therefore, the required profit percentage (return) = \(\frac{$ 1050}{$ 18000}\) × 100% = 5\(\frac{5}{6}\)%
3. Alexander bought some shares of $ 10 at par value which yields 10% divided per annum. At the end of one year he received $ 2000 as dividend. How many shares did he buy?
Solution:
Let the number of shares be n. Then
Annual income or dividend = \(\frac{nrF}{100}\)
⟹ $ 2000 = \(\frac{n × 10 × $ 10}{100}\)
⟹ n = \(\frac{2000 × 100}{10 × 10}\) = 2000
Therefore, the required number of shares = 2000
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