You are asked to value a small start$-$up company that is expected to generate a $($negative$)$ cash flow of $-$ $$10$ million next year, and $-$ $$5$ million in the following year $($year $2),$ before the firm turns profitable in year $3.$ Its first positive cash flow $($in year $3)$ is equal to $$2$ million, and cash flows are expected to grow at a rate of $20\%$ per year for $7$ years $($until year $10).$ After year $10,$ the growth rate drops to $5\%$ indefinitely. Determine the value the start$-$up company if the relevant

discount rate is equal to $8\%.$