Capabilities in a sentence or two
Definitions of EA are diverse. Capability definitions are even much more so and usually useless in practice. Here is one you can use.
A capability is a feature of your enterprise (such as it can produce screws, it can recruit by itself...). It is something you may aim to achieve at first. When realised, a capability is described by an EA view illustrating a few components in interaction delivering the feature.
An enterprise capability is concrete in that it is implemented by specific resources (human and technological).
In many cases it is thought to be a business function, which it can be but not always. It can be implemented by a few interacting business functions.
How to make Finance part of EA
A reason for which finance is often left out of the EA effort is that the EA effort is typically focused on IT alone. Well, the People dimension, the organisation is often left out too.
There can be an unlimited number of views in an EA. Hence financial views can be created when requested. Every enterprise function and flow, described by the EA, could be associated then with a cost of execution of the resources (technology) associated with them.
Financial flows could be specifically documented. Flows can show how value added may be converted to profit. Check the GODS one page business architecture where you would see a (financial) Revenue Flow, core to any business architecture.
What EA has in store for the business
Business users would understand the EA and its benefits had you delivered the architecture to them rather than the big "talk" - most EA efforts do today - about business models, operating models, strategy... which are, strictly speaking, not the "business" of EA but rather the business of the business people. Few EA developments deliver the integrated blueprint of the enterprise they are supposed to.
To improve the operation of the part of the business they are concerned with, the business users need from EA the architecture of their part in the context of the whole enterprise. That is, they need to see the structure of the part, its components, its processes, the information, the implementation technology and so on. And all these would be integrated to all the other parts of the enterprise of concern to other stakeholders.
For that, EAs should indeed employ a proper framework such as GODS for a generic one page business architecture and FFLV for integration of the enterprise process, technology and people tiers components.
All the above concepts are integral and natural parts of the FFLV-GODS framework you can find more about from these ebooks
An Enterprise Architecture Development Framework, 4th http://tinyurl.com/kwhrwgg
The Enterprise Architecture matters blog http://tinyurl.com/mvb6ztb