Custom proration for a level with a subscription delay until a specified date (like "Y1-08-01"). Requires Paid Memberships Pro and Subscription Delays Add On.

pmprosd_prorate_delay.php

// Custom proration for levels with a subcription delay until a specified date (like "Y1-08-01").
// Prorates initial payment based on days until end of subscription delay for level 1
function my_pmprosd_prorate_delay( $level )
{

  // change this to the ID of the membership level to prorate
  if( $level->id == 1 ){

    // change this to the day of year the subscription delay ends, in MM-DD format
    $subscription_day = "08-01";

    $now = new DateTime();

    // don't prorate if today is when the delay ends
    if( $now->format("Y-m-d") == ( $now->format('Y') . "-" . $subscription_day ) ){
      return $level;
    }
    $end_year = intval( $now->format('Y') );
    if( $now->format('m-d') >= $subscription_day ){
      $end_year += 1;
    }
    $subscription_start = new DateTime( strval( $end_year ) . "-" . $subscription_day );
    $interval_seconds = $subscription_start->getTimeStamp() - time();
    // how much should we prorate them?
    $proration_amount = $interval_seconds / (24 * 60 * 60 * 365);
    // don't prorate if we're charging more than the base cost or it's going to lead to a negative/zero initial payment
    if( $proration_amount > 1 || $proration_amount <= 0 )
        return $level;
    $level->initial_payment = $level->initial_payment*( $proration_amount );
  }

  return $level;
}

add_filter('pmpro_checkout_level', 'my_pmprosd_prorate_delay');