After the board of directors of Spirit Airlines rejected a takeover proposal from JetBlue, the company decided to stick with its plan to merge with Frontier Airlines.

A tender offer is when a company offers to buy all of the outstanding stock of a company. The total purchase price was slightly less than it was originally offered to.

The price of Spirit's stock was $19.18 per share on Monday, a 13 percent increase from its closing price on Friday. The merger with Frontier will be voted on by shareholders on June 10.

If Spirit cooperated and shared the same information as it did with Frontier, it would be willing to pay $33 a share, the price it initially offered last month.

Within 10 business days, the board of Spirit will share its position with shareholders on the proposal. The airline encouraged shareholders to not take action until the review is complete.

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The proxy statement was filed by the airline to oppose the Frontier merger. The cash-and-stock proposal from Frontier was worth less than the all-cash offer from JetBlue. Frontier's share price has fallen since it announced its merger with Spirit.

Two weeks ago, the chairman of the company said that his company stood by its plan to merge with Frontier. He said that it reflected the best interests of long-term shareholders, and that the regulators were unlikely to approve the deal.

The two low-fare airlines announced a plan to combine in February. Last month, JetBlue made an offer for Spirit. Both deals would come under scrutiny by the U.S. government.

The administration was particularly concerned with protecting JetBlue, as they were concerned about an antitrust lawsuit against them by the Justice Department. It has been argued that a Spirit acquisition would allow it to quickly achieve a long-sought expansion and compete more effectively with large airlines. The board of the airline unanimously rejected the offer from the airline because regulators would not approve the deal if the alliance remained in place.

It is unlikely that the D.O.J. or a court will be persuaded that the D.O.J. should be allowed to form an anticompetitive alliance with a legacy carrier and then also undertake an acquisition that would eliminate the largest U.L carrier.

The airline said it would pre-emptively sell certain airports to address regulatory concerns. Frontier has not offered to pay a fee if the merger falls through over antitrust concerns. If a deal failed, the airline would pay $200 million.

JetBlue offers more value, a significant premium in cash, more certainty, and more benefits for all stakeholders, according to a letter from the company's chief executive.

Concerns have been raised about the proposed merger between Spirit and Frontier. In March, Elizabeth Warren, Democrat of Massachusetts, and other progressive lawmakers warned that the merger could hurt customer service and raise ticket prices. The Justice Department sent the two airlines second requests for information about their merger last month, meaning that the deal is on hold until the companies answer the agency's long list of questions.

On 104 nonstop routes, Frontier and Spirit overlap twice as much as they do with each other.

Two budget carriers with strengths on opposite coasts would be combined in a merger. The four big US airlines have a combined 66 percent share of the domestic market. A combined Frontier and Spirit would control more than 8 percent of the market.

The management of Spirit was blinded to the benefits of its offer by their relationship with Frontier. The same year it bought Frontier, the private equity firm that invests in budget airlines, owned a controlling interest in Spirit.

Bill Franke, a co-founder of Indigo, is the chairman of Frontier. Several members of the board have ties to Indigo.

"Ask yourself a simple question: Why won't the Spirit board engage with us in a constructive way?" Mr. Hayes wrote in the letter.