There will still be a portion around in the first half of 2023, but substantially smaller already than the run rate that we have seen in 2022, can think roughly half of that run rate. And then as we have now a full visibility into the completion of the program, there’s essentially only one line of business left with some data center migrations and then the final asset retirement, but that is absolutely certain now to happen on time. The second half year will be completely free of these cloud delivery harmonization related expenses. And therefore, in terms of the progression on the cloud margin front, you have seen that we had a decent progress already in 2022, more than two percentage points against this headwind is actually already a very good progress.
I would not have entirely expected this to be quite honest, to be the case already this year, for the first half year. I’m also confident that, despite the remaining headwinds from the program, you will already see some further acceleration in the cloud margin in the first half year. And then obviously, a more pronounced one in the second half year. I would not be surprised, if we had an exit rate ultimately at the end of the year in the neighborhood of what we always soft guided for, for 2023, even a few years ago without the S/4HANA private cloud search of around about 75% plus and minus. And again, the plus and minus is really the success in sales of S/4 in the private cloud deployment option in the first half year. Because especially as you start the build of those landscapes, of course, you have a small ramp.
Yet, you have already a relatively high level of cost and set of cost for those landscapes. So that’s the remaining uncertainty here. But certainly, the exit rate will be significantly ahead of where we are currently. And then for 2025, it’s basically unchanged from what I said at our Capital Markets Day, assuming that RISE with SAP and S/4 private cloud remain as successful as they are today, and we have more and more customers of the likes of BMW moving their entire landscape in massive contracts to the cloud with us. There is going to be an increasing headwind against the continued progress in the public cloud that we expect now where, I would say, that all of our main assets will end up come 2025 above the 80% mark. But then again, with the dampening impact of the private cloud, we could end up a couple of percentage points below the 80% mark.
But if that was the case, then we would actually have, at the same time, a massive search in cloud gross profit, which would be actually more than an offsetting help to guide us towards our profit ambition for 2025. So, that’s a nice problem to have. And rest assured that we will stay focused as we have been in the last two years of pulling all of the available levers in order to further improve our performance. To a certain extent, the development of prepaid expenses that you saw in the free cash flow side and that we discussed are also a means to set us up for more efficient consumption of cloud infrastructure entitlements that will further help with the margin.
