If the directors can't put a value on the work, you need to work with them in order to do so. If they don't know the value of a project, they'll never be able to figure out if it should be funded or not. If you can help them at this stage, your value to them will go up, and your opinion will be respected more than that of a "mere technician". You don't want to be the guy who wrote the switching algorithm. You want to be "the guy who saved the firm six million dollars." The latter looks much better on a consultant's resume. Also, the directors can pass your analysis along to their managers to show how well they manage their affairs.

Charging by value isn't simply about setting prices. It's about figuring out how to include items that might not cost you much money but provides extreme value to your customer. As an example, I worked for an organization where I bundled a specific type of graph into their software. Time for me to build: a few hours. Value to the customer: saved thousands of man-hours per year. That's a BIG savings that I could charge a lot for.

The key aspect of value pricing is that you will charge different amounts to different people for the exact same work. Why? The value a given piece of software will create will depend upon who is using it. Want to sell me a system to manage huge amounts of data? I wouldn't even pay a penny for it. Want to sell it to Google? They might spend a hundred million without a second thought.

I think that Sean Wes has a good worksheet for interviewing clients: http://seanwes.com/value-based-pricing/

As a shameless plug, I also wrote a book on how to price software http://TapRun.com/pricing