NPV and APV

For npv calculation, we minus tax allowable depreciation (TAD) and calculate tax. after that we add the TAD.

However for apv, we simply add the TAD and calculate the tax rate (i know there are two methods to calculate but i prefer this method)

May i know why for npv we deduct and add while for apv, we simply add the TAD ??

Is it like a formula that we must memorize or is there a reason behind it

I know that those ways are the method for npv and apv but i cant seem to find out the reason behind it.