Nature's Friend Co$.$ is a young eco$-$friendly paper, personal care, and cleaning product company that newly listed on the TSX Venture Exchange. Because the company is growing at a significantly high rate, management would like to reinvest all profits generated over the next $7$ years back into operations, as such, no dividend will be paid over this period. The company however expects to pay dividends after that, starting with a $$1\mathrm{.}50$ dividend at the end of year $8.$ The company also expects to be able to keep the dividends growing at the pace of the earnings, at $25\%$ for the $5$ years after the first dividend $($years $9$ to $13),$ lowering slightly to $20\%$ for the following $2$ years, and then stabilizing at a sustainable growth rate of

$5\%$ thereafter. Because of the high risk of the young companies like Nature's Friend, investors required a rate of return of $20\%$ on their investment.

How much would you be willing to pay for Nature's Friend Co$.\text{'}$s shares?

Please provide a written calculation answer. Thank you