# Intuition behind calculating equity return when P/E ratio changes

In book "A Random Walk Down Wall Street" I came across the calculation of long-term equity return which was

long-run equity return = Initial dividend yield + growth rate

Where the growth rate, as the author explained subsequently, being

growth of earnings and dividend

This kind of made sense to me since I suppose (return = rate of growth in stock price + dividend yield) and if assuming P/E ratio being constant, the rate of growth in stock price is just the rate of growth in EPS. However, the author explained in an example later how to adjust for change in P/E ratio, which is basically adding the rate of change in P/E into the equation. So the new equation, according to the author, is

rate of return = initial dividend yield + growth rate + rate of change in P/E

I was trying to work out the math but I got (return = initial dividend yield + growth rate + rate of change in P/E * (future EPS / current EPS)). Feel like I'm getting something wrong somewhere. Can anyone please explain the math behind it please? Thx.