To some people, valuation is seen as a science.  This means once we
input the neededdata into soe elegantly developed formula, then we
should get a firm price as a result.  To others however, valuation is
seen as an art- meaning there is more to valuation than a mere
mechanical operation.  A co- worker asks you what you think?  Outline
your thoughts in a paragraph or two. Specifically state the reasons
for your argument.

I am a valuation guy myself.  I am on the side of it being art.  

Most of my valuation experience comes from figuing out what something
is worth to anothers and to ourselves.  The firm price comes when it
transaction settles.  I consider the art of valuaiton being the
process to getting to the firm number not the number itself.  When I
create my numbers I imagine myself as the other person trying to
figure out the value of it is to themselves, e.g., "how bad do they
want to sell", "does this fit into my plan", "how riskness is this to
me", "what is my cost of captial", etc.

Then I do the same to our company, e.g. "how bad do we want to get rid
of this", "how risky are those revenues", etc.  I share my view of
with others and we talk about how the numbers were derived. If you
think about it this is what art is.  Art is not the object itself but
the skill, background, experience of someone who created that object
that allows it to be discussed, admirred, rejected with others.