A Big Mac in China costs 11 yuan, or $1.45, an undervaluation of 58%. However, local inputs such as low rents and wages tend to be lower in poorer countries and less easily arbitraged across borders, so PPP is a better guide to misalignments between countries at a similar stage of development. Most rich-world currencies are overvalued against the dollar, including the euro (by 22%) and the Swiss franc (by 53%). The yen is an exception, but although it is undervalued by 33% in Big Mac terms, broader PPP measures would suggest that it is close to fair value.
Although it is unlikely that anyone would travel to China to arbitrage hamburgers (good luck finding a buyer willing to pay US prices for the re-imported Big Mac once you get it back to the US) the index has been shown in some studies to have modest predictive power for future currency exchange rates.
I own the IShares Japan ETF (NYSEARCA:EWJ) primarily because their markets performed so poorly for so long that I think the current rally can continue for many years on the back of mean reversion alone. But the possibility that the returns could be even higher due to a positive currency move while I own the fund is another attractive consideration.
Disclosure: Author is long IShares MSCI Japan Index (EWJ) at time of publication.