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.

3) You know that firms should retain profits and invest them if ROE > COE, distribute profits if ROE = COE and liquidate if ROE < COE. Hope you remember that!

Now,

Calculate the P/E ratio using the model you derived above under 3 scenarios:

1) ROE = 11%, COE = 10%

2) ROE = 10%, COE = 10%

3) ROE = 9%, COE =10%

Use payout ratios of 25%, 50% and 75% in each scenario to calculate the sustainable g.

To present the above results, prepare a matrix that looks as follows:

3 rows representing the 3 scenarios.

3 columns representing the 3 payout ratios in each scenario.

So, it's a 3 x 3 matrix

Are the 9 figures in the matrix consistent with what you learned about EVA? In other words, does the retention of profit boost the P/E ratio of firms that generate EVA and hurts the P/E ratio of firms that generate negative EVA?