Despite a few green shoots in the economy and a rocketing stock market, many large companies are still struggling to avoid bankruptcy.

A new report by Audit Integrity identifies some high-profile names "that have the highest probability of declaring bankruptcy among publicly traded firms."

Which companies appear the worst off? We took the list and removed any company with a market cap under $3 billion. We then ranked the remaining names by a simple measure of the market's perceived bankruptcy risk - Market Cap (MC) divided by Enterprise Value (EV). The less MC vs. EV, the less residual shareholders' value (above what debt holders can claim) the market is pricing-in for the company. Thus a lower MC/EV means the market thinks the company is more likely to go bankrupt.