# Calculation of Income, Return and Number of Shares

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.

Solution:

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

Shares and Dividends