You are an associate at Bank IB$.$ You are assisting in the initial public offering $($IPO$)$ of PayPal. Your task is to determine the price that IB should sell PayPal$$s shares at using the dividend discount model. PayPal$$s IPO will occur at t$=0,$ at which time PayPal will have no liabilities. Initially, at t$=0,1,$ and $2,$ PayPal is in a high growth phase and does not pay dividends. In three years, at t$=3,$ PayPal will pay a $$50$ per share dividend. Then in four years, at t$=4,$ PayPay will pay a dividend of $$75$ per share. PayPal will enter a steady growth phase in year $5($t$=5).$ In this steady growth phase PayPalwill pay a dividend of $$100$ per share at t$=5$ and thereafter dividends will grow at a steady rate of $9\%$ per year, forever; for example, the dividend in year $6,$ at t$=6,$ would be $$100(1+9\%)=$$$109.$PayPal$$s discount rate is $21\%.$

$1.$ What is the PV today at t$=0$ of the dividends paid in PayPal's growth phase from t$=0$ up to and including t$=4?$

$2.$What is the PV at t$=4$ of the dividends paid during PayPal's steady growth phase; i$.$e$.,$ what is the terminal value?

$3.$ What is the PV at t$=0$ of the dividends paid during PayPal's steady growth phase?

$4.$ At what price should PayPal$$s stock be sold for at t$=0?$