To my knowledge expiry date is not available. The same holds true for many other European TLDs. Your best bet is to base your calculation on the reg date but it's not necessarily accurate.
I know that with .be when you transfer to another registrar, this will reset the birthday to the actual transfer date instead of just adding one year (as for .com for example). Perhaps .de operates in a similar fashion.
Other indirect means could include checking the website or DNS.
Check the .de registry for more information:
www.denic.de