Just say no.
I know it isn't the question you asked, but in my opinion this is an absurd use of resources. You are taking more than half the capacity of your home electric service and sending it to the other side of the house (125' - another building?) in order to produce (based on looking up some tankless water heaters based on 113A) ~ 5 GPM of hot water output. Actually, I see 3 possible scenarios:
- Most of the time you don't need much, but once in a while (2 showers plus kitchen sink all going full blast at one time) you need that much output.
- You rarely need that much output but want to have it in case you need it.
- You actually need huge amounts of hot water at a rate of 5 GPM for large amounts of time.
In the first 2 cases, an appropriately sized tank heater, which typically uses a single 30A or 40A circuit, will do just fine. Yes, there is significant recovery time, but if the stored water can get you through the peaks then you're fine. Maybe 50 gallons isn't enough, so go for 80 gallons. You will save a lot on wire, you cut down your peak demand, which is becoming a real concern for electric utilities (and that peak demand might someday cost you quite a bit extra $ every month) and it just makes a lot more sense.
The main exception is the last case. If you truly have a need for that much water - literally hundreds of gallons per hour on a regular basis, then tankless may actually make sense. Short of a commercial laundry or similar operation, I'm not sure why you would actually need that much hot water. And if you really did, I would seriously consider natural gas, if available in your area, as being more cost-effective at those usage levels. The raw energy cost of natural gas vs. electric varies by location and current (pun intended) rates, but overall they are comparable and natural gas doesn't come with a peak demand surcharge.
Based on comments, there is already natural gas in the building. If you're going to go for tankless, I would definitely go for gas rather than electric.
Also based on comments, OP is considering a tank + tankless setup. Be careful. That doesn't always work the way you want it to work. Not dangerous, but not necessarily as effective as you might think.
One more concern is your total electric capacity. 200A is enough (more than enough) for a typical house, even with all electric appliances, until you add either electric tankless water heating or Level 2 electric vehicle charging. You may be just fine. But consider that 200A - 113A leaves you with just 87A for everything else. The correct thing to do is a load calculation to figure out how much capacity you actually have available. You may find that 113A is OK. You may find that you can squeeze out 80A and add a reasonable-but-not-quite-as-big tankless heater, or you may find that you can only spare 50A and that you're better off adding another tank or going with gas.
Rethink this. Running essentially a full service entrance cable from one end of the house to the other for hot water just doesn't seem to make sense.