(Fast Growth Start-Up Company; valuation involving perpetuity growth model assumptions.) Fast Growth Start-Up Company (FGSUC) has a new successful internet business model.

It earned $100 million of after-tax free cash flows this year. The company proposes to go public and the company's internal financial staff suggests to the board of directors that a valuation of $2.5 billion seems reasonable for the company. The investment banking firm's analyst and the financial staff at the company agree that the growth rate in free cash flows will be 25 percent per year for several years before the growth rate drops back to one more closely resembling the growth rate in the economy as a whole, which all assume to be 4 percent per year. Assume that the after-tax discount rate suitable for such a new venture is 15 percent per year.

How many years of growth in after-tax free cash flow of 25 percent per year will the FGSUC need to earn to justify a market valuation of $2.5 billion? Do not attempt to work this problem without using a spreadsheet program.