80% sounds like a great offer to me, particularly for a starting point. I wouldn't expect they will accept that offer but it won't turn them off completely. I would suggest a nice round number like $240,000 for the actual offer with 3% closing costs from the seller. Assuming it is still under the construction loan from the time it was built you would expect them to be wanting to get it off their books ASAP.
Don't expect a cash offer to entice anyone any more than a well qualified pre-approval letter would. Unless you were buying it sans realtor, the price paid is still the same and the bottom line for the seller is the same.
Don't run an inspection until you have an accepted offer on the property because there are still more negotiations to be made if there are any problems with the home that could potentially lower the price as well after concessions are asked for.
Just my
Sorry, obviously seller is the bank, which is likely the one who issued the construction loan. Could be significantly lower than the price asking, but it may be very near the price they are asking which could make negotiations tougher. You'll have to see if the bank is even offering concessions for issues or if they are willing to negotiate closing costs too.
Best of luck with the upcoming home purchase.