Government Employes Insurance Co.'s board has approved an offer to exchange a new issue of 20-year subordinated debentures for up to 5 million common equivalent shares.

Geico said the exchange would be for its outstanding common stock and its convertible preferred stock.

Meanwhile, Geico Corp., parent company of Government Employes Insurance Corp., declared a dividend of 8 cents a share on the common stock payable March 30 to shareholders of record March 9. The last dividend paid by Geico Corp.'s main subsidiary was 5 cents a share. Geico Corp. also declared a dividend of 18.4 cents a share on cumulative convertible preferred stock payable April 1 to shareholders of record March 9.

Geico also said that it agreed on Monday to purchase 572,900 shares of its convertible preferred stock from an institutional investor at $18 a share.

Geico said that under its proposed offer, holders of outstanding common and convertible preferred stock will be able to exchange their shares for the new debentures at the rate of $10 principal amount of debentures for each share of common stock and $20 principal amount of debentures for each share of convertible preferred.

Geico said the formal offer of exchange will be mailed March 1.

Geico said it would be obligated to accept tenders for up to $50 million principal amount of the debentures on a pro-rata basis for all shares tendered before the initial expiration date of the offer.