How much is faith worth?

The Civilization 5 expansion Gods and Kings added a new faith mechanic. I noticed you can now use faith points instead of gold to buy units, but I did not see a conversion rate between prayers and gold.

How much is a point of faith worth when trying to immediately purchase units or buildings?

Solution 1:

Faith is used as currency to buy specific items governed by the Follower Bonuses of the majority religion within that city. These include:

• Cathedrals (Building, grants 3 Culture/turn, 1 Faith/turn, 1 Happiness, 1 Artist specialist slot; 200 Faith)
• Monasteries (Building, grants 2 Faith/turn and 2 Culture/turn, effects are boosted for each nearby improved Wine and Incense; 150 Faith)
• Mosques (Building, grants 3 Faith/turn, 2 Culture/turn, and 1 Happiness; 200 Faith)
• Pagodas (Building, grants 2 Faith/turn, 2 Culture/turn, and 2 Happiness; 200 Faith)
• Holy Warriors (Any Pre-Industrial Era ground unit; 2 Faith:1 Hammer ratio)
• Missionaries and Inquisitors (no Follower Bonus required; 200 Faith)

Note that any given Religion can have, at most, two of these options unless it was founded by the Byzantium Empire, as their UA grants them a fifth Religion trait (Founder or Follower or Enhancer). Faith prices also increase in post-Industrial eras (though I don't have accurate numbers on by how much yet).

(Source: In-game Civolopedia)

Solution 2:

First of all there is a special trait you have to chose when you found your religion (unless already taken) that allows you to buy pre industrial units with faith.

Unlike when buying with gold, the cost increases with each buy of the same unit.

One more thing to note is you can also buy great persons, once you unloked certain policies. For instance, rationalism allows you to buy great scientists. Price starts at 1000 faith and increases with 500 for each buy.