(Fast Growth Start-Up Company; valuation involving perpetuity growth model assumptions.) Fast Growth Start-Up Company (FGSUC) has a new successful Internet business. It expects to earn $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% 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% per year. Assume that the after-tax discount rate suitable for such a new venture is 15% per year.
How many years of growth in after-tax free cash flow of 25% per year will 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.