Throughout my advertising career I constantly had to justify advertising budgets. The comment (attributed to John Wanamaker) that Half the money I spend on advertising is wasted; the trouble is I don't know which half was often banded about. This drew me into all sorts of statistical gymnastics, using econometric modelling and digging into the intricacies of multiple linear regression analysis. But, there are so many variables that affect price and market share that I found it impossible to provide a precise ROI on advertising, or any other activity that builds brands.
The valuation methodologies of companies like Interbrand, Millward Brown's BrandZ and BrandFinance are fascinating (I partnered with BrandFinance in Hong Kong a few years ago). However, their valuations vary considerably, which opens them up to criticism. And I have questions, such as how to distinguish the affect of a strong brand from monopoly control (e.g. Chinese SOEs).
But, just because something cannot be measured easily does not mean it does not exist.
IPO and M&A activity show how the perceptions people have of a product, service or corporation can price a company at several times its tangible assets. We have also all seen what happens to the market cap of a company when perceptions dramatically shift against it. This can happen due to a reputation destroying scandal or, as markets and trends change, a gradual failure to make sure the brand stays relevant and up-to-date.