Expected Exit Value Calculation in LBO

In a leveraged buyout (LBO), a private equity firm acquires a company using a significant amount of debt to finance the purchase. This approach aims to enhance returns for investors through leverage, but it also increases financial risk. Consider a scenario where a private equity firm is evaluating the potential acquisition of Company X, which has a stable cash flow but requires substantial capital expenditures to maintain its competitive position. The firm is analyzing Company's X projected cash flows, the cost of debt, and exit strategy options over a typical 5-year holding period.

At the end of 5 years, the private equity firm's investment committee estimates Company X will be sold for a multiple of 8 times its projected earnings before interest, taxes, depreciation, and amortization (EBITDA) at that time. Assuming Company X’s EBITDA at the time of sale is projected to be $20 million, what is the expected exit value of Company X for the private equity firm?