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As part of $3.29 billion in federal payroll loans and grants to Southwest, the company may not lay off workers through Sept. 30 due to the coronavirus pandemic.
"We've got $14 billion in cash, you can do the quick math in your head," Kelly told FOX Business' "Mornings With Maria." "Things have to improve here quickly or we run out of money, and if they don't improve after Sept. 30, we would have to radically restructure not just Southwest Airlines but the whole industry."
Travel demand is down around 90 percent as a result of COVID-19, Kelly said, but things have begun to improve in May. Southwest and American Airlines will begin offering international travel again in June as restrictions ease around the world and in the U.S.
"I haven't seen anything like this in my career, obviously," Kelly told Maria Bartiromo. "We came into the crisis with very low debt to total capital, we're investment-grade credit rating, and we had a lot of cash. We boosted our cash reserve up to almost $14 billion. Normally, we'd have $3 billion in the bank, so you get an idea of the magnitude of the war chest we're trying to build just to get us through this crisis."
Kelly hopes June will be even more positive, especially for business to Mexico and the Caribbean.
"Within the domestic U.S., as long as fares are low, I think consumers want to travel, and they want to travel to these resort-type destinations," he said.
Kelly predicted business travel will be "very weak" for years.
U.S. airlines are spending more than $10 billion per month during COVID-19, even though most flights are averaging only a dozen customers and 50 percent of the active U.S. fleet has been grounded, industry trade group Airlines for America told Reuters.
A number of major carriers including Southwest, American, Delta, JetBlue, United, Frontier Airlines and Spirit have rolled out new safety measures amid COVID-19, such as required masks for passengers and staff, for that reason.
The U.S. Treasury has given airlines $25 billion in cash grants to keep workers employed during the outbreak.