Firm $X$ is about to be offered publicly, and the investment banking firm that is facilitating the offering is working to determine an appropriate offering price. There is a publicly traded company $\mathrm{Y}$ that is quite similar to $\mathrm{X}$. The 1-year value of $\mathrm{Y}$ (the total value of all shares of stock) is expected to be $\$ 500$ million with a volatility of $20 %$, and that of $X$ is expected to be $\$ 100$ million with a volatility of $30 %$. The coefficient of correlation between $X$ and $Y$ is $ho=0.8$. The interest rate is $10 %$, and the growth rate of $Y$ 's price is expected to be $20 %$. That is, currently $P_{Y} G=\bar{Y}$, where $G$ is the expected total return equal to 1 plus the expected growth rate. What is the appropriate price for firm $X$, and what is the discount rate that is equivalent to this price?