Inauguration medals are issued and sold to commemorate US Presidents' assumption of office. Usually tens of thousands of medals are produced, so there are plenty to go around. Typical prices range from $20 to $500, depending on condition and date of issue. They are usually made of bronze, although some come in silver and gold.
The US Mint still sells some of these medals which are re-strikes of prior presidents. If you find a John Adams medal packaged in a polyethylene bag with a plastic display stand, it was not produced when President Adams was alive. It is a re-strike worth $20 or so. If you find an Adams medal paper-packed in the bottom of your great great great grandma's trunk in the attic, it may be an original and worth $500 or more. If in doubt, consult a knowledgeable collector or coin dealer, or send it to an authentication service: PCGS, NGC, ICG, or ANACS (find these on the Internet. Do not use other services).
Medals issued in precious metal are worth their weight in the metal, plus a few US dollars for collector premium. If you have a medal for sale, anticipate at least a 100 percent mark-up between what your item would sell for at retail versus what a dealer will pay to add it to their inventory.
Watch out also for imitations. Red's medal is probably an unofficial copy, since the true Eisenhower medal is dated 1953, while Red's is dated 1955. Imitations are worth very little.