What does 'face value' mean?

The derivation of "face value" in this sense most likely has to do with the phrase as used in talking about currency: the value of a coin or bill is directly apparent from the numbers printed on it. So it means taking the meaning of someone's speech or actions directly. (w/o looking for hidden meanings as the other answerers have said)

What does it mean to take an offer at face value?

to accept something as it appears to be rather than studying it more closely: I took the offer at face value. I didn't think they might be trying to trick me. Want to learn more? Improve your vocabulary with English Vocabulary in Use from Cambridge. Learn the words you need to communicate with confidence.

Should you take something at face value?

If you take something at face value, you accept it and believe it without thinking about it very much, even though it might be untrue . Statements from the groups involved should not necessarily be taken at face value. Collins COBUILD Advanced Learner’s Dictionary. Copyright © HarperCollins Publishers

What is a bond's face value?

A bond's face value is the amount the issuer provides to the bondholder, once maturity is reached. A bond may either have an additional interest rate, or the profit may be based solely on the increase from a below-par original issue price and the face value at maturity.