As with most companies, my employer isn't really interested in anything unless it saves them money.
truse of most...or as G2 says below
It all depends on the size of company and what they deem to be 'costly'.
Whilst the cost of the 'equipment' in terms of a portacabin is low, I agree that the cost of installation could be high. You would then need to be sure that it is maintained properly and believe me that this is another problem all together.
In my opinion, as a Company Director, you need to get someone senior on your side. The benefits as mentioned by Tony are very good and worth promoting in any company.
But in my opinion I would also look at what is likely to be a lower cost addition of a shower in existing toilet facilities. Or adjacent to existing toilet facilities. Perhaps the 'cyclists' and 'runners' amongst you are or have experience at building these sort of things. Or you have a friendly family member who could help out. This way the company is only providing the space and hardware.
If I was to look at this as a project, the first thing I would do is look at the logistics of installing internally. Then arrange a meeting of all the 'healthy' types in the company to work out how you could find 'lower' costs ways of implementing it. Do this planning correctly and if your company has the budget, you might find yourself in a good position to get this done and as a by product be watched for future promotion!
But be warned, if you showcase this and it fails you will also be watched for future redundancy
Perhaps try not to focus on cyclists (your management team may think little of them) and focus on those who run at lunchtime, do Yoga in the board room (more and more popular these days) or need to freshen up for that important presentation (which will make money).
£20k for 5 years worth of return is little to ask for all of this.
Unfortunately with square footage costs being so expensive, your company is more likely to place "people" in the space where a shower could go as people generally create revenue and showers don't (arguably).
Perhaps focus on the bigger picture and involve your colleges with some form of poll. But be warned, fighting this through if it is neither wanted nor needed will result in a failure that you most likely don't need to be associated with.
Be sure it's not just you who wants it.