Final answer:
An annual free cash flow of approximately $24.521 million would justify the purchase price of Kenneth Cole Productions at an acquisition price of $14.84 per share, given a weighted average cost of capital of 10.9% and no assumed growth.
Step-by-step explanation:
To determine the level of annual free cash flow that would justify the acquisition price for Kenneth Cole Productions, we can use the valuation formula for a perpetuity since no future growth is assumed. The acquisition price per share is $14.84 and there are 18.1 million shares outstanding. Considering the company had $43.6 million in cash and no debt, the total acquisition value would be the acquisition price per share multiplied by the number of shares, less the cash available.
The total acquisition cost is therefore $14.84 multiplied by 18.1 million, which equals $268.564 million. Subtracting the cash, $268.564 million - $43.6 million gives us $224.964 million. To find the annual free cash flow that would justify this price given a weighted average cost of capital (WACC) of 10.9%, we apply the perpetuity formula:
Acquisition Value = Annual Free Cash Flow / WACC
Therefore, Annual Free Cash Flow = Acquisition Value * WACC.
Annual Free Cash Flow = $224.964 million * 10.9% which equals approximately $24.521 million.
This means that an annual free cash flow of around $24.521 million would be needed to justify the acquisition price of Kenneth Cole Productions assuming a WACC of 10.9% and no future growth.