When we want to make a time-saving investment we often have to create a formal business justification. When I say “time-saving investment” I’m thinking about addressing tech debt, buying and implementing a tool, refactoring a system component, and so on. Those assessing priorities will ask what the benefit is. That relies on estimation—we can take a past project and ask “if we did this again, with the investment, what might we gain?”—but even then it’s good to produce some numbers.
As far as I can see there two, and possibly three, kinds of benefits to consider and add up.
The first kind is the cost of people. If we look at that past project we might estimate it would have finished a week (five working days) earlier. If it consisted of four people costed at £250 a day, then the benefit is 5 x 4 x £250 = £5,000 saved for a project just like that.
The second kind is the revenue being realised earlier. If that past project is estimated at generating £1,000 of revenue per day, then the earlier project completion means we’d have started generating that revenue seven days earlier. (Seven days, in our fictional example, because it generates revenue on weekends, too.) That’s another 7 x £1,000 = £7,000 of financial benefit.
If the team on our past project was hired to delivery that, and only that, then that’s the end of the story. The team leaves and they’re seen no more.
But if our team is an internal team, and they immediately move onto the next project, then there is a third benefit.
The third benefit is also of revenue being realised earlier, but this time from that next project, because now it starts earlier and (presumably) finishes earlier. Once again we start realising that revenue sooner. If that next project is estimated to generate £800 a day then we see a further 7 x £800 = £5,600 benefit.
So, depending on the nature of the team whose time we have saved, our time-saving investment is estimated to create the sum of these benefits: £12,000, or maybe £17,600. That is by comparing the as-is and to-be picture from one past project. There may be others to consider, too.
In these situations I’ve found people usually consider the people-cost benefit but forget about the other kinds. This isn’t the case for those who think about cost of delay, though.
I don’t think I’m double-counting or over-counting anything here, but I’d welcome comments.
niksilver.com 
Another interesting post Nik +1
There is also possibly a friction / ergonomics point of view. Often we’re saddled with cumbersome tech that bleeds away our time and focus, and gets in the way of realizing the system designs we want. Removing these obstacles removes those “oh, wait, what about ?” and “how will we work around ?” type anxieties and annoyances.
Yes, that kind of thing is also real, and definitely possible to quantify, too. And it reminds me of the similar (and too frequent) question about buying suitably spec’d (ie more expensive) laptops for engineers. It’s all about removing the daily friction or “hygeine”.