is a small firm that sells antique furnishings. In the most recent year, the firm generated $ $4$ million in after$-$tax operating income on revenues of $$40$ million; the firm reported book value of equity of $ $8$ million and book value of debt of $ $4$ million at the beginning of the year. During the year, the firm invested $$2$ million in a new warehouse for furniture $($its only cap ex$)$ and reported depreciation of $$1$ million in its income statement. The firm$$s only working capital item is its inventory, which increased by $ $200,000$ during the course of the year. The cost of capital for the firm is expected to be $12\%$ for the next $3$ years and $10\%$ thereafter. You have been asked to appraise the value of the company

a$.$ Assuming that the firm maintains its existing return on capital and reinvestment rate for the next $3$ years, estimate the expected free cash flow to the firm each year for the next $3$ years.

b$.$ Estimate the value of the firm at the end of year $3,$ assuming that the return on capital stays at the current level but the growth rate drops to $3\%.$

c$.$ Assuming that Past Perfect Inc. has $5$ million shares outstanding, estimate the value of equity per share. $($You can assume that the book value of debt $=$ market value of debt, and that the debt remained unchanged over the most recent year$).$ You can also assume no cash holdings.