Q.A ₹100 share pays a dividend of 10%, which is about to be declared, and is quoted at ₹95 ex-dividend. Find its cum-dividend price.

The cum-dividend price is the ex-dividend price plus the forthcoming dividend, with the dividend reckoned on the face value.

The ₹95 ex-dividend price excludes the ₹10 dividend, so adding it back gives the price that includes the right to that dividend.

Given: face value $FV = ₹100$, dividend rate $r = 10\%$, ex-dividend price $= ₹95$.

Step 1 — Dividend about to be paid (on face value):

Step 2 — Cum-dividend price (ex-dividend price plus the dividend, §7):

Cross-check by reversing the conversion. Removing the dividend from the cum-dividend price should return the ex-dividend price: $105 - 10 = ₹95$, exactly the quoted ex-dividend price — confirming the conversion.

Students sometimes subtract the dividend when moving from ex-dividend to cum-dividend, getting ₹85. The cum-dividend price is the higher of the two (it carries the extra right to the dividend), so the dividend must be added when going ex → cum.