This is one of those things i've never got a good answer to, I think because there are so many variables.  Let's say you have a fully depreciated tractor and are buying a new tractor.  Which scenario is best?

A. Buy the new tractor outright and sell your old tractor yourself.  Everyone "knows" you can sell it for more than the dealer offers in trade.  That's the theory we'll work off of anyway.  You get full depreciation on the new one but when you sell the old one you are paying taxes on the gain between what your selling price and your depreciated value is. (I'm sure the IRS has a form for it) For discussion let's just call it recapturing the gain.  That's assuming you don't just stick the cash under the mattress and don't tell Uncle Sam.

B. Trade the old tractor on a new one. You are done messing with it.  You don't get as much depreciation and you don't get as much trade in as you could have sold it for.  But there's no paper gain to deal with.  No advertising, dealing with buyers, worrying about the check being good, etc.

Part of the decision is numbers, and in real life you could put hard numbers to.  But it will take answering questions like this:
     Is the dealer selling price the same for cash or finance?
     Is the dealer selling price the same with or without trade?
     Is the trade in value different than what you can sell it for?
     What will it cost when recapturing the depreciation?
     How is that affected by my tax situation?
     Can I really get away with putting the cash under my mattress?

Can we put all these numbers in a spreadsheet to come up with an answer?

Of course these numbers vary a lot with the actual machinery.  The answer for replacing your 2007 Case MX275 with a new AFS Connect™ Magnum™ 340 is going to be a lot different than replacing the 1975 IH 1066 Farmall with a 1992 CaseIH 7120 Magnum.  And if you made a truck load of money this year it's different than the year you barely scraped by. Your tax bracket has to figure in somehow.

And what value do the intangibles have?  If I trade it in I'm done.  I don't have to mess around selling it, dealing with people or looking up IRS forms.  I know for many the not dealing with people or forms has a value beyond numbers.

I've done both over the years and still can't decide which is better.

Any opinions or maybe even facts?

Edit: Typos fixed, I hope