On December 30, 2013:

• Company Y trades at $10 per share
• Enterprise Value / EBITDA multiple of 5.0x
• Leverage ratio of 0.6x (Net debt/EBITDA)
• 2013 EBITDA = $2.0 billion
• Assume no cash on company Y's balance sheet

On December 31, 2013:

• Company Y undergoes an LBO and is recapitalized
• The company's new leverage ratio becomes 5.0x
• Financial sponsor exit is planned for Year 5. Assume that the EV/ EBITDA multiple at exit year is the same as the current multiple.
• Required rate of return is 25%
• Exit year EBITDA projected to be $3.0 billion
• The company's year-end leverage ratio is 1.6x

What is the initial equity necessary to achieve the rate of return required by the financial sponsors?