Does a company have to pay accumulated dividends before they call their preferred stock stock?

1.  Your question pertains to cumulative dividend due on the  Cumulative Redeemable Preference Shares.

2.   Preference shares do not participate in a company?s profits in the same way as equity shares do in that their rate of dividend is fixed.

3.   If the company makes no profit or inadequate profit, dividend to equity shareholders being discretionary, can be skipped, but the preference shareholder?s dividends are due and are accumulated till such time as the company can declare a dividend, when the preference shareholders? accumulated arrears of dividend have to be paid first, before any distribution can be made to equity shareholder.

http://www.sharemarketbasics.com/Terms/Cumulative-Redeemable-Preference-Shares.php

4.  Therefore, if, at the time of redemption, some dividend is due to the preference share holders,the cumulative dividend will be paid later when a dividend is declared on the equity.