Burger King Holdings, which recently rolled out its biggest menu overhaul in history, has decided to go public less than two years after being taken private in a $3.3 billion deal by 3G Capital.

Whether the new Burger King IPO will give investors indigestion remains to be seen.

Under the terms of the deal, Justice Holdings, a special-purpose acquisition company co-founded by the investor William Ackman, will pay $1.4 billion in cash to 3G for 29% of Burger King, which Wendy's (WEN) recently dethroned as the second-largest burger chain. 3G, an investment firm backed by Brazilian billionaires, will own 71% of the new company, according to Bloomberg. How many crumbs -- or french-fry remnants -- will be left for the rest of the shareholders remains to be seen.

The bigger question, though, is what sane person would buy Burger King shares.

The Miami burger chain, which has about 12,512 restaurants, has struggled for years against better-run rivals, including McDonald's (MCD). In 2011, it posted net income of $107 million on revenue of $2.34 billion, according to a filing with the Securities and Exchange Commission. Sales at restaurants open for at least 13 months fell 0.5%, and Burger King reported "aggregate outstanding indebtedness of $2.62 billion."

More than 50% of Burger King restaurants are in three states -- Florida, North Carolina and Indiana --  for reasons that are not immediately clear. If the company ever hopes to compete against McDonald's or other rivals like Subway, it will have to address that geographical disparity. Moreover, the chain has had at least seven consecutive quarters of negative comparable sales in the U.S. and Canada. That's another problem that will not be easy to fix.

Earlier this week, Burger King announced more than a dozen new menu items, such as fruit smoothies, snack wraps, salads and fancy coffee drinks. The company apparently decided that if it can't beat McDonald's, it will turn itself into McDonald's. On a positive note, Burger King has ditched the creepy "king" commercials.

Burger King has been in the midst of a turnaround for years that has proved elusive. This is one stock that investors should avoid.

Jonathan Berr is long McDonald's.