What are the theories that expplain the choice of discount rates?

Answer 1

Capital Asset Pricing Model (CAPM) and Arbitrage Pricing Theory (APT):

http://en.wikipedia.org/wiki/Capital_Asset_Pricing_Model
http://en.wikipedia.org/wiki/Arbitrage_pricing_theory
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Answer 2

Discount rate for investment for companies is basically the the return on Investment.
If you are looking at the discount rate fixed by the Federal Reserve, it usually is the base interest rate. This can be reached by plotting capital/labor on the x axis and ROI of different firms on the y axis. This gives a second order curve whic has to be curve fitted to get its quadratic equation. You differentiate this curve and you will get the equation of the line. The Y intercept of this line will give the base interest rate which is the discount rate.
Another way is through the IS and LM curve. You plot the Interest rate for which investment = savings which is the IS curve which is upward slopping. Then you plot the Moneysupply - spculative income. Plot this on the x axis and interest rate for it on the y axis whic is the LM curve which is downward slopping. Plott this IS andLM curve on a graph and their intersection gives the base interest rate or discount rate.

Answer 3

The Wikipedia artical on monetary policy includes a history. This should be a good starting point.