This is a very common misconception. He did not burn his ships. He scuttled them. Why you might ask? For several reasons, first he had already sent a ship back to Spain under the command of Francisco de Montejo who was charged with presenting the Emperor Charles V with a petition by the 'city of Veracruz' that asked that the emperor authorize Cortes to conquer on the mainland.

Why was that necessary? When Cortes left Cuba the governor of Cuba had only authorized him to trade and explore not conquer. To get around that Cortes and his men 'founded' the city of Veracruz (on paper no buildings) and then as the city of Veracruz provisionally authorized Cortes to conquer and requested that the emperor support that authorization. In the Spanish political hierarchy, cities could opperate as autonomous political actors. Consequently, a petition from the 'city' of Veracruz carried much greater weight than a petition from Cortes especially when it was going up against the interests and political clout of a regional governor.

Why scuttle the remaining ships? Cortes knew that he did not have that many men and by this time he knew of the Aztec Empire and knew that he was vastly outnumbered (although even at this point he was planning to use alliances to change that disparity). So by skuttling the ships he was able to press all the sailors into service as footmen. Had he not scuttled the ships they would have stayed with the ships on the coast or worse gone back to Cuba where the governor was upset with him.

As to the cost of the 'navy's ships' there was no royal navy in the Western Atlantic. And the royal navy that existed back in the Mediterranian was almost exclusively a coast guard that used galleys. All the ships used by conquistadors and explorers were privately owned and operated. Cortes and his company had hired the ships they used. After scuttling them those sailors, pilots, etc. became partners in the conquest venture and were eligible for the spoils of that expedition, which they previously would not have been as simple contract hires for transportation.

Some good resources would be Restall's Seven Myths of the Spanish Conquest and a new book about to come out Schwaller and Nader's The First Letter from New Spain