Anticipated ROE in Leveraged Buyout Valuation

In a Leveraged Buyout (LBO) scenario, a private equity firm utilizes a significant amount of debt to acquire a target company. When performing a valuation of the target, it's essential to understand how the debt influences the company's free cash flow and overall returns.

Consider the following hypothetical: A private equity firm is evaluating a potential LBO of a company. The firm's analysis suggests that upon acquisition, the company will generate annual free cash flows of $10 million, and the firm intends to finance the deal with $50 million in debt and $30 million in equity. The firm anticipates selling the company in 5 years at a projected exit multiple of 7 times EBITDA.

Given these assumptions, what is the anticipated return on equity (ROE) if the company achieves an EBITDA of $20 million at the time of sale?