Question

A dividend of 9% was declared on INR 100 share selling at certain price. If the rate of return is 7.5%.
Calculate:
A.The market value of the share.
B.The amount to be invited to obtain an annual dividend of INR 630.

Answer 1

Hint- We will find the market value of the share using the dividend percentage and the rate of return. Also the amount to be invited is also found using the rate of return and given INR

Complete step-by-step answer:
It is given that, a dividend of 9% was declared on INR 100 share selling at certain price.
Now the market value of the share is the sum of invested price and the amount of return after one year.
a)
Here a dividend of 9% was declared on INR 100 shares selling at a certain price means nothing but the Face value (FV) of 1 share = Rs.100.
Also the Market value (MV) of 1 share is not given.
The dividend on a share is 9% of its face value
That is nothing but 9% of Rs.100 which is denoted as d%.
And rate of return is denoted by r%.
The total profit per year is distributed as dividend on face value.
Hence it is written as
d% × FV = r% × MV
On substituting the values we know we get,
\[9\% \times 100 = 7.5\% \times MV\]
Now we use the formula of percentage to solve the equation,
\[\dfrac{9}{{100}} \times 100 = \dfrac{{7.5}}{{100}} \times MV\]
Let us solve the above equation further to find the market value.
\[MV = \dfrac{{9 \times 100}}{{7.5}} = 120\]
Thus the Market value of the share is Rs.120. \[\]
b) \[\]
The amount to be invited to obtain an annual dividend of INR 630 is found using the following formula\[\dfrac{{630}}{{r\% }}\].
On substituting the values we know we get
\[\dfrac{{630}}{{7.5\% }}\]
Using the formula of percentage,
\[ = 630 \times \dfrac{{100}}{{7.5}}\]
\[ = 8400\]
 Thus we have found the amount to be invited to obtain an annual dividend of INR 630 as Rs.8400.

Note: We know that, the percentage of x is denoted by x% and defined by,
\[x\% = \dfrac{x}{{100}}\]
The original value of a share printed in the certificate of the share is called its face value or nominal value.
 The total dividend amount = MV ×r %
So, \[MV = \dfrac{{dividend}}{{r\% }}\].