The IRS rules for market value determination are defined in their publication 526, "Determining the Value of Charitable Donations". Similarly, yet separately, rules for the qualification and resale of donated property are set forth in publication 561 (see appendix for publications and links). In many cases the market value as determined by the IRS suggested methods allow for a tax credit that approaches that of a market sale. The rules for resale (following material improvements being completed) allow for resale by the charity at a price unrelated to the market value used for donation. This price may be below market as the charity simply wants to liquidate the asset quickly and is not bound by the tax basis established earlier.
This works for donors when the tax benefit, both federal and state taxes included, approaches the selling price less the broker's fees and assumed price negotiations that would be expected in a market sale. It works for brokers since AFF pays the broker directly and returns a central agency listing to them to market the asset. Most importantly, there is the personal gratification of having accomplished all this while making a needed donation to a worthy charitable organization.