Is it OK for a DNS A record to resolve to another URL rather than an IP address?

My company use a domain registrar who also offer a web forwarding service.

We have a large number of different domain names purchased over the years and are using this web forwarding service to allow us to forward on requests to old domain names to a suitable location on our main website, as follows:

• User browses to www.an-old-domain.example
• www.an-old-domain.example resolves via DNS to the IP of our registrar's forwarding server.
• The web forwarding server has been set up to serve an HTTP 302 redirect from www.an-old-domain.example to www.our-corporate-website.example/some-page
• The user is redirected to www.our-corporate-website.example/some-page which in turn resolves via DNS to the IP of our web server

We're having a few problems with the reliability of this redirection service and I was wondering whether it would be OK to create a DNS A record for www.an-old-domain.example to resolve to www.our-corporate-website.example/some-page, which in turn resolves to the IP address of our web server.

I've always thought that DNS A records should resolve to an IP address rather than a URL, thereby creating a chain of DNS entries. A colleague tells me they that this approach is fine however, but I'm suspicious that it's a bit of a hack.