What underwriting looks at
Age and hours or mileage. Most funders set a limit, and an asset that will exceed it before the term ends is the usual reason for a decline.
Whether the term outlasts the asset. A funder will not write five years against a machine with three years of life left, which is often what caps the term rather than your credit.
Evidence of value: a dealer invoice, an independent valuation, an inspection report, or auction results for comparable units.
Buying private or at auction
Both are financeable, but the process is slower. Expect the funder to want an inspection and to pay the seller directly rather than reimbursing you.
Title and lien position matter enormously. A UCC search on the seller before you commit is worth the hour — buying an asset with somebody else's lien attached is a genuinely bad week.
Auction timelines rarely match funding timelines. Arrange the facility before the sale, not after you have won a lot.
When used is the right call
For long-lived, slow-moving assets, used equipment is usually excellent value and the depreciation has already been taken by somebody else.
For fast-dating assets it is a false economy, because the remaining useful life is short and the term will be short with it.
Compare total cost of ownership rather than purchase price. A cheaper machine with higher maintenance and a shorter financing term is often the more expensive one.