I think asking for theories is great and can play a big role in interpersonal relationships contrary to what the comment from Catija might imply - What I do feel however is that your question is poorly phrased around it. Rather than wanting some theoretical frameworks to base your interpersonal solution around it sounds as if you're simply playing on the stock market hoping to make the most out of a bad situation.
With that foray done, let's move on to the meatier bits.
I once read in a book that people overvalue favors given and devalue favors received over time as represented in a the study
Flynn, F. J. (2003), 'What have you done for me lately? Temporal adjustments to favour evaluations'. I have not read much other on the subject and it seems quite hard to get a hold of this study, which means I haven't read it in its entirety, but I can add some anecdotal evidence to the point. People will often devalue favors they have received as time passes. If we are to look at this from the perspective of your friend you have done him a favor and he is not at all likely to consider the value of your favor as high as you do.
Now, if we are to discuss how you might get the most out of your situation you might look to some very common salesmen tactics; In this case the Door-in-the-face technique might be of relevance to you.
Since your friend is very likely to devalue the amount of money he owes you one thing you could to is to ask for more than you are likely to receive, very much like bartering. As he (if he) tells you that it's too much then you say something akin to "well, I could settle for at least 400 grokensons" which is much more likely to be accepted following your initial outrageous offer. You could also make use of Cognitive Dissonance. In short, attempt to make your friend say that he wanted to pay this money and make it seem as if it was his idea in some way as people want to stay consistent with their actions and previous opinions.
These are basic suggestions and following up on the study as well as continuing on Wikipedia from the links I provided will lead you to more argumentative techniques.
My only advice following this is to ask yourself what kind of friend you want to be. I would personally not want to be friends with a person employing these techniques on me. Rather than optimizing your monetary net gain you should seriously consider if this is someone you want to be friends with, and if the answer is yes just ask for a sum you will be satisfied with which you feel adequately covers some of the expenses. If he refuses to pay what you feel is a reasonable sum then you should have become quite aware that this is not someone you should be friends with and that this is a person you should keep out of your life.