Can we sell donated equipment and use the proceeds?

Summary:

The feelings of the donor as well as federal regulations must be considered when determining the use of a donation.

In general, the question of what is done with the donation is of concern
to the donor. The authorities view the donation as support for your
mission and are not likely to be interested in how you go about
achieving it. The tax code, though, distinguishes between gifts that directly support your mission (food to a food bank, for example), and gifts that aren't (items for sale at a charity auction).

Further, as John H. Taylor has said, a "donor" can't convert trash to a
tax-deduction by "giving" it to a worthy recipient who connives in the
transaction and then simply discards the unwanted stuff.

On Apr 13, 2002, Stephan Leimberg wrote to GIFTPLAN (a service of CharityChannel.COM):
It is very important to determine if the donated tangible
personal property will be used in a manner consistent with the charity's
charitable purpose. For example, a donation of a valuable book collection
to a library which will display the collection in its archives and make the
book available for reading by scholars and researchers falls into this
category. (I'd get a letter from the charity agreeing to that).

On the other hand, a gift of the same books - even to the same library - will
be "unrelated" if the donor and/or charity intends that the book be
sold - even if the proceeds will be used to purchase new books.

A donor of related use gifts can deduct the full fair market value - up to
30% of Adjusted Gross Income.

But for "unrelated gifts" the donor may deduct ONLY the lesser of (a) the
fair market value or (b) adjusted basis, up to 50% of adjusted gross income.

Check out IRC Sec. 170(e)(1)B.