Lady Antebella is trying to use a spreadsheet model to value the stock of Renaissance Limited. The model has projections for the next four years based on the following assumptions.

Sales will be $$250$ million in Year $1,$

Sales will grow at $15\%$ in Year $2$ and Year $3$ and $10\%$ in Year $4.$

Operating profits $($EBIT$)$ will be $12\%$ of sales in each year.

Interest expense will be $$10$ million per year.

Income tax rate is $21\%.$

Earnings retention ratio would stay at $0\mathrm{.}35.$

The per$-$share dividend growth rate will be constant from Year $4$ forward and this final growth rate will be $200$ basis points less than the growth rate from Year $3$ to Year $4.$

The company has $10$ million shares outstanding.

Antebella uses the CAPM to estimate the cost of equity.

She uses the annual yield of $2\mathrm{.}5\%$ on the $10-$year Treasury bond as the risk$-$free return. She estimates the expected US equity risk premium to be $6\mathrm{.}5\%.$ The estimated Beta of Renaissance is $1\mathrm{.}75.$

$($a$)$ Estimate the value of the stock at the end of Year $4$ based on the above assumptions.

$($b$)$ Estimate the current value of the stock using the above assumptions.

$($c$)$ Lady Antebella is wondering how a change in the projected sales growth rate would affect the estimated value. Estimate the current value of the stock if the sales growth rate in Year $3$ is $10\%$ instead of $15\%.$