How to buy into a mortgage?

[RuffledKestrel]

So there is lots of guides on how to buy someone out of a mortgage (ex partner etc) but I am looking for advice on how to fairly let a partner buy into an existing mortgage/home.

So for example, Y bought the house for £250k 8 years ago and has been paying the mortgage one their own since. £200k left to pay on the mortgage currently.
Z moved in 3 years ago and as agreed, paid half of all other bills except the mortgage (Y did not want anyone else to have a claim on the house).
Y and Z are both now happy to have Z legally have a share in the house and also pay towards the mortgage.
What is a fair way of working out a lump sum Z should pay for a 50% share?

I think you would need to get a conveyancer involved when person Z is added to the property deeds and the mortgage. If Z doesn't want to pay a lump sum up front, the conveyancer could possibly look to arrange the property ownership as tenants in common (where the owners own specific shares of the property rather than 50/50) so Y's larger share of the property is protected. I am assuming they would help you work it out but I'm not sure!

Z is fine with and able to pay a sizable lump sum. It just the working out how much it would be for a 50% share that we are stuck with.

What is the current value of the house? That's what's relevant, not how much Y paid for it 8 years ago. That doesn't matter at all.

Work out the value of Y's equity and divide by 2. Z pays that amount to Y, then they pay the mortgage equally.

Exactly this. So if the house is worth £350k with £150k on the mortgage, the incoming partner pays £100k to house owner then the mortgage is paid 50/50 from then on and the house is owned equally.

It’s based on current property values. Not what was paid in the past

If the house is worth £500k now, with £200k left on the mortgage, there is £300k of equity. Z needs to pay Y £150k and then they each pay 50% of the mortgage going forward.

I'd also argue that Z should pay legal fees and stamp duty as Y had to pay these before.

It should be based on the current valuation, not the purchase price. Z has benefitted from living rent free so far and would have to pay current price if they bought anywhere else.

Get the house valued.

Say it is worth £500k.

Let's say the mortgage outstanding is £200k, there is £300k equity in the house.

The new partner would need to pay £150k to the original owner (50% of the equity), plus pay 50% of the mortgage in future. They would then have equal financial stakes in the property.

You have to question if this is the best thing for both parties. What will the original owner do with the £150k? They have less of an asset than they used to. Is there a better use of the ££?

Work out the value of Y's equity and divide by 2. Z pays that amount to Y, then they pay the mortgage equally.

Or 'Z' pays off that amount of mortgage, from then on split costs 50:50.