PHP - How to calculate one month or one year later

I'd like to calculate next billing date of Recurly plan in PHP. There are 2 types of billing cycle: yearly | monthly. I tried to use DateTime and DateInterval classes, but didn't get expected results.

<?php
$referenceTime = new \DateTime('2016-01-31');
$oneMonthLater = $referenceTime->modify('+1 month');
var_dump($oneMonthLater);
// public 'date' => string '2016-03-02 00:00:00.000000'

Adding one month to the 31st of Januray gives me the second of March and not the 29th (or 28th) of February as I would expect.

The same for the 31st of August:

<?php
$referenceTime = new \DateTime('2016-08-31');
$oneMonthLater = $referenceTime->modify('+1 month');
var_dump($oneMonthLater);
// public 'date' => string '2016-10-01 00:00:00.000000'

If yearly, I expect Feb 29, 2016 + 1 year => Feb 28, 2017

Thanks.

function get_next_billing_date($now, $type, $format = 'Y-m-d')
{
    $date = new DateTime($now);

    $y = $date->format("Y");
    $m = $date->format("m");
    $d = $date->format("d");

    if ($type == 'year') {
        $y++;
        if ($m == 2 && $d == 29) {
            $d = 28;
        }
    } else if ($type == 'month') {
        if ($m == 12) {
            $y++;
            $m = 1;
        } else {
            $m++;
        }

        $first_date = sprintf("%04d-%02d-01", $y, $m);
        $last_day_of_next_month = date('t', strtotime($first_date));

        if ($d > $last_day_of_next_month) {
            $d = $last_day_of_next_month;
        }
    } else {
        // not supported
        return false;
    }

    $date->setDate($y, $m, $d);

    return $date->format($format);
}