When it comes to FX long-term projections, I do believe that you already heard of the PPP (Purchasing Power Parity) model. A popular one was introduced in The Economist in 1986 (September 6) by Pam Woodall and is called the Big Mac Index (or Big Mac PPP). Basically, the BMI index measures the Purchasing Power Parity between nations using the price of a Big Mac as the benchmark. The Big Mac PPP between two countries is obtained by dividing the price of a Big Mac in one country by the price of a Big Mac in another country (both in local currencies).
The Big Mac Index for 2015 has not been published yet and the latest index was published on July 24 last year.
In July 2014, the average price of a Big Mac in the US was $4.80. In Norway, the hamburger costed 48 NOK at that time, which obviously gives you an implied exchange rate of 10 NOK for 1 USD. The actual rate chosen on that day by The Economist was 6.19NOK / 1USD. Therefore, the implied FX rate was approximately 61.6% higher than the actual FX rate, bringing the Big Mac price to $7.76 in Norway.
The chart below (on the right) represents which currency is overvalued (blue) or undervalued (red) against the select base currency, in this case the US Dollar. As you can see, Switzerland and Norway were the two expensive countries with the NOK and CHF overvalued by 61.6% and 42.4% against the Dollar, while Ukrainian Hryvnia UAH was undervalued the most by 66.1%.
More elaborate models take into account economic indicators depending on the major activities of the country (export-driven nation, developed or EM economy, …).
Even though we agree that there is no explicit answer regarding which model delivers the correct fair value of a currency (the Art of predicting), I believe that it is interesting to visit the work that has been done by some brilliant academicians and major institutions (Banks, Investment Managers).