Consider the Hart Company.In the year that just ended, Hart’s free cash flow was negative $10 million due to a significant capital expenditure.  Hart expects to realize free cash flow of negative $5 million in one year, $0 (zero) in two years, and positive $5 million in three years.  After three years, free cash flow is expected to grow at a constant rate forever.
 
Hart received an offer for the company from a private equity firm.  Hart is tempted to take the offer but wants to understand how the offer price was determined.  Hart’s two items of interest are (a) the appropriate rate of return for the business and (b) the growth rate in free cash flow.
 
(a) Firms in the same industry as Hart deliver an average return of 20% to their shareholders, and have a typical capital structure of 25% debt and 75% equity.  Assume that Hart is an all-equity firm, and that the risk-free rate is 4% and the market risk premium is 5%.  Also assume that the debt betas are zero.  Determine the return that would be required for the shareholders in The Hart Company.
 
(b) For this part of the problem, ignore the answer to part (a) and assume that the required return is 16%.  If Hart was just offered $50 million for the business, determine the constant growth rate in free cash flow after three years that would justify this offer price.