Question

A dividend of $ 9\% $ was declared on a share of $ {\rm{FV}} $ $ {\rm{Rs }}100 $ at a certain price. If the rate of return is $ 7.5\% $ , calculate $ {\rm{MV}} $ of the share. How many shares would a person get on investing $ {\rm{Rs }}8400 $ ?

Answer 1

Hint: The market value is equivalent to the product of fact value and dividend which is divided by the rate of return. The share invested is ratio of obtained dividend to rate of return.

Complete step-by-step answer:
Given:
The dividend percent $ d\% $ on share is $ 9\% $ .
Face value $ \left( {FV} \right) $ at a certain share is $ {\rm{Rs }}100 $ .
Rate of return $ \left( {r\% } \right) $ for the share is $ 7.5\% $ .
We know the formula to find the market value is,
 $ {\rm{FV}} \times d\% = {\rm{MV}} \times r\% $
Here, \[{\rm{MV}}\]is the market value.
Now, om substituting the face value for certain share, dividend percentage on share and rate of return from the share in the above equation, we get,
 $ \begin{array}{l}
100 \times 9 = {\rm{MV}} \times 7.5\\
{\rm{MV}} = \dfrac{{100 \times 9}}{{7.5}}\\
{\rm{MV}} = {\rm{Rs }}120
\end{array} $
Thus, the market value is $ {\rm{Rs}}{\rm{. }}120 $ .
Now, we have to find the dividend, the formula to find the dividend is,
 $ {\rm{dividend}} = r - {\rm{MV}} $
On putting the values of return rate and the value of market value in the above equation we obtain,
 $ \begin{array}{c}
{\rm{dividend}} = {\rm{750}} - {\rm{120}}\\
 = {\rm{630}}
\end{array} $
Hence, the dividend is equal to $ {\rm{Rs }}630 $ .
Since, we know the formula to find the total sum invested is,
 $ {\rm{sum invested}} = \dfrac{{{\rm{dividend}}}}{{{\rm{rate of return}}}} \times 100 $
Substituting the values of dividend and rate of return then,
 $ \begin{array}{c}
{\rm{sum invested}} = \dfrac{{630}}{{7.5}} \times 100\\
{\rm{sum invested}} = {\rm{Rs }}8,400
\end{array} $
The number of shares is calculated as:
 $ {\rm{dividend}} = d \times n $
Here, $ n $ is the number of shares.
On putting the values in the above equation we will get the number of shares,
 $ \begin{array}{c}
{\rm{630}} = \left( 9 \right) \times n\\
n = \dfrac{{630}}{9}\\
n = 70
\end{array} $
Therefore, the number of shares would a person get on investing $ {\rm{Rs }}8400 $ is $ 70 $ .

Note: Here, in this problem do not take dividend percentage instead of dividend. Shares invested is the same as the sum of money invested by the person only in this question. Generally, every time shares invested will not be equal to the sum of money invested.