Do you want to split expenses of the new apartment, or split your income/assets equally too (as for instance with a marriage where no sort of "yours, mine, and ours" are split out)?
I'm going to assume you have beliefs similar to me in my answer, in that you desire to split expenses of the new place but don't suddenly want to split all of your assets and income 50/50 too. So here's how I'd approach this.
I am somewhat unsure of what you mean by "living expenses" for your flat. Does this mean the cost of ownership per month - what it takes to not get rid of the place - and no portion of this is interest/mortgage?
To make the calculations a little simpler, I'll assume that all the money you pay out as expenses is just gone - none of it remains as equity or is dis-proportionally accumulating value in some other such way.
So, you move in with your girlfriend. The cost for her place - the place itself, taxes, utilities, whatever - is 7892 per month. So since you are both getting equal use of the place, you would split this into 3946 per month for each of you.
What about your place?
Well, I don't see how that really matters at all, anymore than if you owned a company or stocks and bonds. If you rent it out for less per month than it costs you, I don't see why your girlfriend should take any part of the loss. Conversely if you make more money per month than it costs you, that is your investment profit - the payment you get for owning the apartment and dealing with renting it out.
Now if your girlfriend is going to partner with you in handling renting out the apartment you own and you want to look at this as an investment partnership, then you should pay all expenses out of the income first and then you can split the profit if you really want.
One question to ask would be, what if you just sold your apartment completely? Would you give your girlfriend have the money from the sale? If not then I don't see why you would split the investment profit from holding on to the place.
While this is what I recommend and would feel comfortable with personally and if the situation was reversed (and it was my girlfriend that owned a place and was moving in with me), ultimately this is about your personal values, beliefs, and relationship. You are very wise to seek something that both of you will find fair, and so you should discuss a proposed arrangement with your girlfriend and see if you are on the same page.
If you are both fine with the agreement and feel OK with it, then great - none of us have to like or agree with it, because we aren't a part of your relationship. Psychologically and financially this situation seems the most reasonable to me, but YMMV.
By The Numbers
After some more thought and from comments, I realize that it's probably best to explore a few possibilities numerically. So I'll run a few sets of numbers which may help pick which one is right for your relationship.
- Share Her Place's Expenses, Your Investment Is Yours
This is approximately the same as paying her "rent" for getting to live with her. You pay her for sharing her place, splitting the expense: 3946 paid to you. She pays the other 3946 for her place. Financially it's like being room-mates. You can do whatever you want with your place - rent or sell, hold on to it for security, etc.
This deal makes your girlfriend financially better off by 3946. The financial advantage to you is wholly dependent on what you do with your place.
This option would give you each the most financial independence, which is why I like it - but you might be keen on being more interdependent.
Which leads us to the next option.
- Share Her Place's Expenses, Rent Your Apartment, Share Profits
Here you behave as before in splitting her expenses, but you include renting out your place as part of the deal. Let's say you get 10k a month for it. You pay the expenses on that place from the rent, then you have 2108 left as 'profit'. You split the profits monthly 1054 to each of you.
There's a bit of problem here, though - what happens when the place is vacant? Do you share the full expense of the rent, so she'd actually be paying you each month while it sits open? What about repairs, taxes (costs and credits), etc?
I would recommend instead what you do, if you go this way, to account for the apartment as an investment and don't pay out ANY of the profits right away. All rents stay in their own account, and you pay expenses from that same account. For you both it's like it doesn't exist, accept it is a nice earning asset. When you decide it has accumulated more than enough to pay for itself and has enough money to cover vacancy, repairs, etc, then when you pull out money for the duration you are together you just pay it out to both of you equally. You might also pull this "equity" out and spend it on something for both of you, like a nice vacation, etc - something you both enjoy, so you are still sharing the profits.
I don't object to this, and it could be a nice arrangement. I would only note that this makes you have a personal relationship, you live together as roommates, and now you are co-landlords/business partners. That's a lot of types of relationships, and I can tell you from personal experience each type has it's own stresses - and this sort of stress can stack (or if you don't handle it well, multiply). So just make sure you are both clear what sort of responsibility you are really both signing up for up front, and what you'd do if you part.
- Pool all apartment expenses and income (50/50 partnership)
Combine your apartment expenses, which would equal 14753, so that's 7376 cost to each of you a month. If you rent your place then whatever money you get you split, and whatever costs come up (repairs, cleaning, etc) you would also split. So if you get an average of 10000 a month for the apartment you each are paying living expenses of 2376 total.
But notice that this isn't exactly equal, either. You will pay 5516 less per month than you are now, and she will pay 4485 less than she was before.
There's nothing morally wrong with this or anything - it's a 100% partnership across the board. Yet advantage is still not equal - you actually will see a larger benefit to your budget than she will. But if you seek equal benefit, you will have to pay 515 a month more than she does.
This sort of thing is basically the model marriage uses, a pure 50/50 partnership, or "communal property". And note that one of you will either be paying more than the other, will be benefiting more than the other - no matter what you do! It's impossible to balance both costs and benefits, because your income and expenses are not the same going in.
If you go this way you'll need to choose what is most important - splitting the expenses/income equally, or benefiting financially equally.
So I say again, ultimately you have to choose based upon your individual and shared values, and also on just what sort of relationship and layers of commitment you want to have together. You could start slow with option 1, then progress to sharing more - that's what I'd recommend, because I like the idea of developing things one layer at a time rather than jumping in head-first (like I have personally done in the past, haha!). Once bitten twice shy, I might just be more risk-averse or careful than you desire to be, but that's a personal choice.
I personally believe the relationship can be far more valuable than any investment, but at the same time I'll take $1 over a relationship that has turned sour any day of the week. This is why I suggest the more gradual, careful approach - to let your love bloom and grow deeper one layer at a time, without the complexities of fully shared finances or investment partnership. Relationships are hard enough, so this is why I favor trying to protect them aggressively from unnecessary complexity. Some favor the "sink or swim" model of seeking out trials and challenges, while I favor the "relationship as tender, growing sapling" model.
I hope seeing these options laid out more is helpful to you, and good luck to you, your relationship, and - lastly - to your investments!