Here is an example of the most common use of the growing perpetuity model $($called a pro forma$).$ Your firm just finished the year, in which it had cash earnings of $$100$ million. Excluding this amount, you want to determine the value of the firm. You forecast your firm to have a quick growth phase for $3$ years, in which it grows at a rate of $20\%$ per annum $($ending year $1$ with $$120$ up to ending year $3$ with $$172\mathrm{.}8).$ Your firm$$s growth then slows down to $10\%$ per annum for the next $3$ years $($ending year $4$ with $$190\mathrm{.}1,$ etc.$).$ Finally, beginning in year $7,$ you expect it to settle into its long$-$term growth rate of $5\%$ per annum. You also expect your cost of capital to be $10\%$ in your $20\%$ growth phase, $9\%$ in your $10\%$ growth phase, and $8\%$ in your $5\%$ growth phase. Excluding the $$100$ million, what do you think your firm is worth today?