As you may have noticed, I have recently gotten into investing and I
need some guidance.  Can you please explain how each of the following
factors affect the valuation of a firm?s bonds assuming that all other
factors remain constant?:

1) An increase in the general level of interest rates;
2) An increase in foreign competition; and
3) An increase in the firm?s balance sheet 

General answers are fine, as I know this is a very broad question.

Thank you.

1.  The valuation will fall - assuming the risk premium of the bond
stays constant the underlying yield [of the economy] increasing will
push the yield of the bond down (and price is inverse of yield to
maturity and inverted to simple yield).

2.  Foreign competition, again assuming all other things are equal,
will increase the risk the firm will go bust so will increase the risk
premium of the debt.  An increased risk premium is another way of
saying the price will fall on response to increased risk.

3.  Not sure what you mean by this.  If you mean a general growth of
the firm (knocking on to more assets on their balance sheet and more
'money' in the capital/reserve account) then there are more assets
should the firm go bust, the chance of getting repaid as a debt holder
increases, so the risk premium of the bond falls (and the 'price'
increases).  If, however, the balance sheet has grown as a result of
the firm undertaking riskier business practices and the growth is a
result of it 'getting lucky' the risk on the balance sheet may mean,
in event of liquidation, assets are harder to get rid of or
autocorrelated to the health of the firm (general conditions which
made it go illiquid in the first place), in this case the risk premium
of the bond will increase and the valuation decrease.  The change in
risk premium (valuation) is subjective on whether the expansion of the
balance sheet is percieved as 'healthy' or 'unhealthy' by the market.