If given the screen below as an example, how would you analyze the risk of a bond? I am not sure what to look for to know if this is a good investment.
What risk factors should be considered when looking at a bond for investment?
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There are six principal risks that you assume when investing in bonds, see this Investopedia article.
Generally, longer term bonds are riskier than shorter term bonds. The suggested bond matures in 2042, so 30 years from the present -- a very long term. If you hold this bond to maturity for the next 30 years (and the issuer does not default), you will receive interest at the coupon rate of 6%. Since you would be paying a premium to buy this bond, your effective return would be 4.986% per year (or, if the issuer decides to redeem the bonds early by paying back the par value of the bond, the worst-case return would be 3.554% per year).
If you wish to sell this bond prior to 2042, the price you will receive for it will most likely vary.
On this particular investment, I would be most concerned about the effects of rising interest rates (which will diminish the value of this bond issue) and inflation (even in the current environment with inflation relatively tame, the interest payments net of taxes barely preserve the purchasing power of your investment).
Currently, S&P rates this bond A+, but if the rating is downgraded, the value of this bond will most likely decline because investors will regard it as a riskier issue. You should research the general conditions of the issuer. Independent of a rating agency's credit grade, the market may view that the issuer's financial situation may be deteriorating, which raises the risk of a default (and drives down the price of the bond).
A default by the issuer can mean anything from a delayed interest payment to a complete loss of principal. If the issuer goes bankrupt and its assets are dissolved to pay off creditors, secured creditors will be paid first, then bondholders, then unsecured creditors. Anything that is left over goes to the shareholders. So, in an extreme case, you could lose your entire investment if the issuer goes under and there are insufficient assets to satisfy the bondholders. Bonds by the same issuer are sometimes also sold in tier: In the event of a default, holders of senior notes will get paid off before holders of subordinated debt.
Concerning the price you pay for a bond, you will typically pay more attention to the yield to maturity (the actual annual return of your investment) rather than the price. Buying a bond at a discount doesn't necessarily mean you are getting a deal -- rather, as @duffbeer703 points out, it could signal that the market views the bond as riskier than it was when it was originally issued. Bonds will typically also trade at a discount after interest rates have risen -- after all, if an investor can get a similar bond that pays more interest, why would he pay full price for one with a lower coupon rate?
Lastly, keep in mind that if you pay a premium, you may put yourself at greater risk in the event the issuer calls the bond (i.e. repays it before the maturity date). You will be paid back the par value, not the price you actually paid for the bond, and you wind up losing the difference. The yield to worst figure will tell you the lowest annual rate of return you can expect if you buy the bond at the indicated price, and it is called at the worst possible time (However, this still assumes the issuer does not default).
In the short-term, you can assess the market's feeling about a bond by looking at the price. If a bond is trading over 100, it's low-risk enough that buyers are sacrificing yield by paying over face value.
In the longer term, you need to think about default and rate risk. (See: Are long-term bonds risky assets? for more detail.)
Default risk for your example bonds is pretty low. The bonds are explicitly backed by Puerto Rico sales tax revenue, and as a U.S. Territory, it is implicitly backed by the U.S. government as well. Interest rate risk is the thing to worry about. The Fed is keeping rates at the current low levels through 2013, and they have nowhere to go but up.
How important interest rate risk is depends on you. If your intention is to hold the bond to maturity, you'll continue to get tax-free coupon payments until the bond is paid off. I know a few people who continuously maintain ladders of 10-year treasuries, and don't care about the market value of the bonds.