I am trying to refute the notion that if a company's bonds are trading
at less than face value, then that company must be in financial
trouble. Can bonds trade at less than face value but the company that
issued them be in good financial shape?

Hi!!

what I can give you is an theoretical example in which the actual bond
value is less than the face value (this could happen if the coupon
rate is lower than the required rate of return).

By the way I think that a company can issue debt at less than the face
value to finance some new invests if the result of this could result
in a rate similar than they must pay to an investing bank, with the
intend to keep the indepence (no bankers in the directory board) .

Rhubarb1 --

Bond prices are largely determined by interest rates and the types of
bond involved.  The following is a good article explaining how price
vs. par has little to do with the company's financial condition:
"Sensitivity of Bond Prices to Parallel Shifts in the Yield Curve"
http://www.mathworks.com/access/helpdesk/help/toolbox/finance/samples4.html

I might suggest a Google search strategy of:
"bond prices" + "yield curve"

And Livioflores, who's an excellent financial resource, may come up
with more concise ways to explain it.  (But don't let him start
talking about Modigliani-Miller!)

Best regards,

Omnivorous-GA

Depending on the context of your argument, here's a very easy answer:
The U.S. Treasury sell brand new bonds at a discount to face value.
U.S. Treasury debt is used as a proxy for risk-free debt... it's the
safest thing on the market. Ergo, trading at a discount doesn't mean a
company is in trouble. QED.

The longer answer is that some bonds are referred to as Zero-Coupon
Bonds; they pay no coupon, so all of the interest must be 'earned' by
the holder through price appreciation. The company sells the bond at
$80... at maturity, the company buys it back at $100.

Other bonds (those that do pay coupons) trade at a discount when their
coupon rate is less than market yields. In order to entice buyers to
purchase these below-market coupon rates, sellers in the secondary
market must discount the price. This is known as trading at a
discount. Again, the 'missing' interest is made up for in price
appreciation (because all healthy bonds trade a par the day before
maturity)