In a leveraged buyout, investors borrow huge sums of money to buy companies, hoping to pay off the debt by using the company's earnings and to profit richly by the later resale of the companies or their divisions.
Option Elimination -
(A) by using the company's earnings and to profit - We need the plural "companies' ." Moreover, hoping "to pay" parallels "to profit."
Pay + with is commonly used when specifying a payment method, as in this question. E.g., I paid for the groceries with my credit card.
Pay + by is less common but used when we would like to specify the time. E.g., Please pay the bill by Friday.
(B) by using the companies' earnings and by profiting - same as explained above. We need "pay + with" as we discuss the payment method. Moreover, hoping "to pay" parallels "to profit."
(C) using the companies' earnings and profiting - same as B.
(D) with the company's earnings, profiting - with is ok. But we need plural "companies' ." Moreover, hoping "to pay" parallels "to profit."
(E) with the companies' earnings and to profit - perfect.