Using Gordon's Constant Growth Model

FV = D1/(COE - g)

1) Show that the P/E ratio - like its sister the P/B ratio - is a function of ROE, g and COE and,

2) Show that your new model cannot yield an equity value (i.e., fair value = 0) if the firm retains 100% of its net income. After all, it is derived from the "dividend" discount model.