They don't cut to the meat of the question: the intangible benefits - though they at least try to walk through an example. The formulas are just to get ROI as a nice percentage - if "using build tools" was a stock, how much return would I get on my investment?
Which already shows that the question itself is flawed: An automated build is mainly an instrument to improve quality; improving productivity is usually a secondary concern.
However, this doesn't help when talking to the guys sitting on the money.
Metrics I woud use to analyse effect of a build tool:
- Turnaround time from checkin to final media
- Number of builds (for testing, for release, ..)
- Number of build requested (with faster builds, you can expect an increase in demand)
- Number of errors introduced during manual build (assuming you track those)
- Number of developers able to publish a release
- Estimated resources (time, licences, build server, ..) for implementation and maintenance
- Analysis of low-probability, high risk scenarios
Often, an automated build tool pays for itself just by removing a bottleneck: every developer can publish the software, not just John the Builder.
The last point is important (but hardest to give numbers for), as the total cost of bugs doesn't have a normal distribution, but is highly "pareto": a single bug can give you some nasty press, or make key customers switch to competition.
The core argument for maintaining an automated build is that publishing bugs are mostly avoidable.