It can be part of a designer's job to talk about the benefits, and on that note here's a report that might help with your client/designer dealings.
It's the result a Finnish study carried out between September 2011 and September 2012 by a research team from Aalto University. The aim was to develop a model and a set of metrics for measuring design's return on investment.
I looked at it from a brand identity viewpoint, and on a basic level, qualitative metrics such as user satisfaction, desirability, and aesthetics were appropriate and could be measured with customer surveys. Then there were quantitative metrics like the number of new customers, mentions and "fans" in social media, and the number of website visits or registrations.
If a client is to get a full report you'll need to track those metrics before and after (there are companies who specialise in conducting surveys). The more time spent on the "before" section, the easier it'll be to measure the impact of "after." Granted, not all clients will have the time or the budget to do this properly, but it's worth talking about during an initial designer/client chat.
Design ROI framework (from the report).
There's a lot to take in (143 pages), and it won't give all the answers, but as mentioned on the Moving Brands blog, it's an interesting first step in trying to make sense of the concept.
View the full report here.