Woocommerce Onepage checkout does not show shipping costs

I have a Woocommerce One Page Checkout website with currently one product. Everything is working so far but for some reason I don’t see the shippingcosts displayed.

The price calculcation is correct and when I go to the paymentportal the shippingcosts are added to the total price but the shipping costs are not displayed.

To give some insight in my search for the solution:
Rendering all the data happens in /woocommerce/templates/checkout/review-order.php

There is called:

<?php wc_cart_totals_shipping_html(); ?>

This function can be found in /woocommcerce/includes/wc-cart-functions.php

There the code being executed is:

/**
 * Get shipping methods
 *
 * @access public
 * @return void
 */
function wc_custom_cart_totals_shipping_html() {

    $packages = WC()->shipping->get_packages();
    foreach ( $packages as $i => $package ) {
        $chosen_method = isset( WC()->session->chosen_shipping_methods[ $i ] ) ? WC()->session->chosen_shipping_methods[ $i ] : '';

        wc_get_template( 'cart/cart-shipping.php', array( 'package' => $package, 'available_methods' => $package['rates'], 'show_package_details' => ( sizeof( $packages ) > 1 ), 'index' => $i, 'chosen_method' => $chosen_method ) );
    }
}

The problem is that $packages = WC()->shipping->get_packages();
returns an empty array.

The function get_packages in /woocommerce/includes/class-wc-shipping.php is as follows:

/**
     * Get packages
     * @return array
     */
    public  function get_packages() {
        return $this->packages;
    }

So property $this->packages is not set. This property is set in function calculate_shipping in the same file /woocommerce/includes/class-wc-shipping.php

I tried calling that function right before $packages = WC()->shipping->get_packages(); but that did not work.

Is there someone who can help me out? Please note that I don’t have much experience in programming in WordPress.

Kind regards,

Pim