In magento sometimes we are requiered to apply our own discount on the cart total section. 
To do so we can work upon the event sales_quote_collect_totals_after.

Lets see how we can do it:

1. Create a module with namespace as Custom and module as Discount.

2. Then Create a file config.xml in etc folder in our module.

3. Afterwards create a file Observer.php in Model folder.

Now, in our config.xml file at the path Custom/Discount/etc/config.xml write the below code in it :

<?xml version="1.0"?>
<config>
 <modules>
  <Custom_Discount>
   <version>0.1.1</version>
  </Custom_Discount>
 </modules>
 <frontend>
  <events>
    <sales_quote_collect_totals_after>
      <observers>
        <discount>
          <class>custom_discount/observer</class>
          <method>setDiscount</method>
        </discount>
      </observers>
    </sales_quote_collect_totals_after> 
  </events>
   </frontend> 

</config>

In the above code we have defined our module with the version 0.1.1 and 
then in global we have called our Observer at the event sales_quote_collect_totals_after

Now in our Observer at the path Custom/Discount/Model/Observer.php write the below code:

<?php
class Custom_Discount_Model_Observer{

 
  public function setDiscount($observer) {
   

      $quote = $observer->getEvent()->getQuote();
      $quoteid = $quote->getId();
     
$discountAmount = 10; //custom discount value that we want to apply
     
      if ($quoteid) {
       
          $total = $quote->getBaseSubtotal();
          $quote->setSubtotal(0);
          $quote->setBaseSubtotal(0);

          $quote->setSubtotalWithDiscount(0);
          $quote->setBaseSubtotalWithDiscount(0);

          $quote->setGrandTotal(0);
          $quote->setBaseGrandTotal(0);


          $canAddItems = $quote->isVirtual() ? ('billing') : ('shipping');
          foreach ($quote->getAllAddresses() as $address) {

            $address->setSubtotal(0);
            $address->setBaseSubtotal(0);

            $address->setGrandTotal(0);
            $address->setBaseGrandTotal(0);

            $address->collectTotals();

            $quote->setSubtotal((float) $quote->getSubtotal() + $address->getSubtotal());
            $quote->setBaseSubtotal((float) $quote->getBaseSubtotal() + $address->getBaseSubtotal());

            $quote->setSubtotalWithDiscount(
                (float) $quote->getSubtotalWithDiscount() + $address->getSubtotalWithDiscount()
            );
            $quote->setBaseSubtotalWithDiscount(
                (float) $quote->getBaseSubtotalWithDiscount() + $address->getBaseSubtotalWithDiscount()
            );

            $quote->setGrandTotal((float) $quote->getGrandTotal() + $address->getGrandTotal());
            $quote->setBaseGrandTotal((float) $quote->getBaseGrandTotal() + $address->getBaseGrandTotal());

            $quote->save();

            $quote->setGrandTotal($quote->getBaseSubtotal() - ($quote->getBaseSubtotal() * ($discountAmount/100)))
                ->setBaseGrandTotal($quote->getBaseSubtotal() - ($quote->getBaseSubtotal() * ($discountAmount/100)))
                ->setSubtotalWithDiscount($quote->getBaseSubtotal() - ($quote->getBaseSubtotal() * ($discountAmount/100)))
                ->setBaseSubtotalWithDiscount($quote->getBaseSubtotal() - ($quote->getBaseSubtotal() * ($discountAmount/100)))
                ->save();

            if ($address->getAddressType() == $canAddItems) {
              //echo $address->setDiscountAmount; exit;
              $address->setSubtotalWithDiscount((float) $address->getSubtotalWithDiscount() - ($quote->getBaseSubtotal() * ($discountAmount/100)));
              $address->setGrandTotal((float) $address->getGrandTotal() - ($quote->getBaseSubtotal() * ($discountAmount/100)));
              $address->setBaseSubtotalWithDiscount((float) $address->getBaseSubtotalWithDiscount() - ($quote->getBaseSubtotal() * ($discountAmount/100)));
              $address->setBaseGrandTotal((float) $address->getBaseGrandTotal() - ($quote->getBaseSubtotal() * ($discountAmount/100)));
            
              if ($address->getDiscountDescription()) {
                $address->setDiscountAmount(-($address->getDiscountAmount() - ($quote->getBaseSubtotal() * ($discountAmount/100))));
                $address->setDiscountDescription($address->getDiscountDescription() . ','. $discountAmount. '%');
                $address->setBaseDiscountAmount(-($address->getBaseDiscountAmount() - ($quote->getBaseSubtotal() * ($discountAmount/100))));
              } else {
                $address->setDiscountAmount(-(($quote->getBaseSubtotal() * ($discountAmount/100))));
                $address->setDiscountDescription($discountAmount. '%');
                $address->setBaseDiscountAmount(-(($quote->getBaseSubtotal() * ($discountAmount/100))));
              }
             
              $address->save();

            }//end: if

          } //end: foreach
          //echo $quote->getGrandTotal();

          foreach ($quote->getAllItems() as $item) {
            //We apply discount amount based on the ratio between the GrandTotal and the RowTotal
            $rat = $item->getPriceInclTax() / $total;
            $ratdisc = $discountAmount * $rat;
            $item->setDiscountAmount(($item->getDiscountAmount() + $ratdisc) * $item->getQty());
            $item->setBaseDiscountAmount(($item->getBaseDiscountAmount() + $ratdisc) * $item->getQty())->save();
          }

      }
   
  }

}

In the above code we are loading the product first and then with $discountAmount variable we have setup the discount percentage, which is then used to calculate the percentage value from the subtotal.
In this way we can change any the value of $discountAmount and apply our own discount percentage.