Building a website from scratch is a great cost benefit for responsive web design. It is less complex to implement a responsive web design on a new site than an old one.
But more often, we are dealing with an existing, complex website. One that likely has a heavily modified theme. This means we can’t replace theme. We are basically married to it going forward. For the cost of replacing theme and all the work that went into it is substantial.
In this case, the cost of creating a new responsive design website vs implementing it into our existing site needs to be measured.
In considering cost associated with a new site (assuming you want very similar functionality that is probably not available in any stock theme), we are not only rebuilding existing functionality, we are also implementing a responsive design. I believe the cost associated with rebuilding existing functionality will be higher than the responsive design cost.
Depending on the theme that will be chosen, existing functionality will be difficult to port over to the new theme. This difficulty greatly increases if you go with a completely new framework. In that regard, I don’t think a new framework adds much additional time except in learning how to use the new framework.
In considering implementing a responsive web design into an existing site, all current functionality will be saved. This is not a cost we’ll need to deal with.
Because the responsive web design is a different architecture than that of the current theme, this is where our cost will be focused. An analogy is retrofitting an old English building with modern wiring. It can be a lot of work but it really depends on how the building was built.
The more fixed widths and non specific height of elements, the more difficult it will be to implement a responsive web design. But that is the starting point.
Some areas of the site won’t be fixed with just a 100% width and height specification on elements. These areas will require new thinking and design.
In summary, the more complex and large your site, the lower cost will be when implementing a responsive web design vs scrapping the site and starting over.