Just charge your normal rate then, you already lost some money to begin with. If you accept the previous rate, you won't be happy working with him and probably

Just charge your normal rate then, you already lost some money to begin with. If you accept the previous rate, you won't be happy working with him and probably lose better potential clients that would be will to pay you your normal rate. If you own the IP, you do have the upper hand. In case your clients owns it, he would spend more money/time migrating to another developer, just negotiate with him and explain that you underestimated. If he doesn't like it, his loss.