如何强制客户退出Magento

Is there any ways to force a customer to log out? The use case is that after changing the customer's group in backend, i would need to force him to log out and log back in to see the new prices for his new group. I'm not trying to log the current user out so can't use Mage::getSingleton('customer/session')->logout()

I looked into sessions but there seems to be no way to init a session from a customer's ID

What i tried was setting customer id directly but it doesn't work

$session = Mage::getModel('customer/session')->loginById(1234)->logout();

You can use Mage::getSingleton('customer/session')->logout() or redirect the customer to the below url

/customer/account/logout/

How to force magento to logout