In the CFAI text, it shows HPR with two formulas:

r = Dividend Yield + Price Appreciation, [(Div + Price_{1})/Price_{0}] - 1

Then it restates that it could be thought of as

E® = required return + convergence of price to value, such that E® = r + [(V_{0}-P_{0})/P_{0}], where V_{0} is the intrinsic value

I understand the first formula, but the second formula is tripping me up as we’re adding the required return on top of the original HPR formula…

Could you provide the chapter section number please? Or page.

As I understand the second formula, the holding period return of an investment can be described by the required return we demand on that investment and the deviation of the price at purchase vs intrinsic value. If intrinsic value is lower than price at purchase, then you will eventually bear a negative return on your investment (price correction downward), so added to your required return will give you the HPR. The reverse case also apply.

The thing is that the required return is a function of current price.