What company is it?
Usually companies do this stuff because they want to retire a bunch of shares (or debt or...) all at once rather than messing around with open market purchases. The most common structure I have seen is a modified dutch auction wheere they offer to buy $X of shares at a price between Y and Z per share. You can submit with a specific min price or just take what everyone else gets. The lowest price that gets them $X of shares is the price everyone gets.
So should you tender? If you were looking to sell anyway and you likethe price offered, its worth considering. I have owned two stocks which have done tender offers and passed on both. In both cases it turned out to be a good choice (the stock rose above the tender price range), but nothing is guaranteed.
Heh, "tender offer." Sounds like something you make to a lady of negotiable affection our for her evening constitutional.
"To be a man means that you are brave, loyal and true. When you are in the wrong, you own up and take your punishment. You don't take advantage of women. As a husband, you support and protect your wife and children. You are gracious in victory and a good sport in defeat. Your word is your bond. Your handshake is as good as your word... When the ship goes down, you put the women and children into the lifeboats and wave good-bye with a smile." C Murray