Upon sale of an LLC, how would I express the values of intangible assets the LLC has generated (e.g. certain access rights, processes and procedures, IP, and customer relationships)? These are assets the LLC has generated after its formation so they don't show up as initial contributions. Also, the assets are not physical assets so they don't show up as fixed assets on the LLC's balance sheets.
What concerns me is that from what I understand, most exits of LLC take the form of an asset sale so where an LLC's value is primarily in intangible assets how does one get paid for that value?
Regardless of whether the exit of an LLC is the sale of its assets or the sale of the ownership of the LLC itself, you still need to value intangible assets.
Putting a value on intangible assets is very much an art rather than a science. It is basically a lot of speculation and a gamble that you are getting a good price.
Probably the best method for putting a value on such assets is to look at comparables -- what have other people paid for similar things. The problem is that it can be very difficult to find comparables as intangible assets tend to be unique and hard to compare precisely against other intangible assets.
If you are selling, you want to get the highest price possible. Come up with a rational explanation for the price that you want. The buyer will come up with a rational explanation for a lower price, and then you start negotiating.