Disclaimer: I have not been through this myself, but I have been following the literature quite closely.

- How does it work in a business who 'sells it's time'?

This is a really good question. In simplest form, we know that as the supply of a scarce and desirable resource goes down, so the price goes up. So if you're going to reduce the supply of your resource (the time of your agents) by 20%, the price should go up accordingly. Now, if you also capture the savings that pertain to the reduction then you might be able to modify that to 17-19%, offset by the increase in savings. But for the purposes of your partners, it's much better to increase prices by 20% and revert the efficiency savings directly to gross profit.

- Impact on shareholders/profit share which is split equally between all partners

I am pretty sure that partners would be excluded from the arrangement. They aren't usually contracted employees of the business. Consequently, I would see no reason for any impact on profit share except so far as profits are affected by the change (hopefully positively!).

- How much admin time is involved in the move

Assuming you run it as a trial for a period, not much would need to be involved as it can be implemented by a letter of variation for a temporary period. There would need to be consultation with the employees and assurances about how it will work (a simple three-day weekend, or will the "day off" vary depending on role, team, project or the needs of the business?) and how it will affect their pay (hopefully not at all, but if you have bonuses etc you'll need to think about whether these will need any changes) and holiday.

- Is targeting 25% more productivity over days without negatively impacting wellbeing achievable. Some offices already work long hours (through choice) our model allows teams to decline work if there is a negative impact on wellbeing - will this get worse

This sounds like you're planning on a "compressed week" approach in which the same number of worked hours are compressed into four days, given the apparent expectation of a negative impact on wellbeing, which is unlikely to achieve a 25% increase in productivity. Most employers trialling the 4-day week have just reduced the total weekly hours by 20% and work it over four days without reducing pay. This is unlikely to have a negative impact on wellbeing - quite the opposite! Evidence so far is that there is very little change in total performance and output in a change from a 5-day week to a 4-day week. Where output does go down, the losses are compensated for by lower turnover and better retention.

But the fact is that it doesn't work for everyone.

The single biggest factor in determining whether it works or not is whether the decision to change is led from the very top. If the partners believe in it and want the change to work, the odds are that it will. If they are sceptical and feel pressured into it by HR or other shareholders, the odds are that it will struggle.

None of my clients have gone down the four day work route so I, sadly, can't help with the practical implementation. I am sure you are considering the rationale for considering the change, the purpose and how it aligns with the business and it's culture.

I personally have a lot of professional services experience and I find many quite risk averse and a little nervous about being ahead of the curve when it comes to innovation and flexible working. That might be unkind and unfair, I often find them fixed on billing by time andless able despite a lot of talking about it to shift to value billing which would probably help when you are working less time for the same level of pay.

I know there's been research on it, forgive me if you are all over it - www.4dayweek.co.uk/research - and it doesn't suit everyone. It can be done without impacting well being because it's not about cramming five days of work into four- but it does require a lot of commitment to iron out the practical implications and needs a 'learn and iterate as we go' mentality. If the partners don't back it and really believe it's a good thing worth investing in, then you might have your answer as to whether it will truly work in your business.

Good luck whatever you choose. It's fascinating and I'm curious to know what impact it will have on the workplace of the future. I'm especially curious when you see government putting pressure on councils to cancel 4-day week pilots...interesting times.