Donnie,
IMO, who lived in the house and who didn't is irrelevant for attributing an increase in value during that period to that party. Both were co-owners all the time and should benefit from the total increase in price caused by the market.
If there's a significant portion of a higher selling prise caused by additions or improvements it should be attributed to the party who paid those changes.
Also, I wouldn't make it too complicated by trying to split it into too many components, just use the original down-payments and mortgage to establish the ownership ratio.
I suggest four simple steps:
1. Establish (and agree upon) the amount of ownership of each party.
2. Establish and agree upon the price you would reasonably get if you sold the property to a third party. (The fact that in practice you are that third party is irrelevant here.)
3. From that price "pay" each party the costs they made to substantially improve the house.
4. Split the rest according to the ratio established under #1.
The total amount your sister would get that way (#3 + #4) is what you'll have to pay her.
Your figures:
(1) Each owns exactly half.
(2) It would be sold for $140,000.
(3) You paid $15,000 for a substantial improvement (or perhaps, as Joe suggested, worth slightly less), your sister paid $0.
So, $15,000 of the $140,000 goes to you, $0 to your sister, leaving $125,000 to be split according to the ratio in #1.
(4) Your sister would receive $62,500.
Of course, there may be some additional costs, like the costs of transferring the house to you, which you may have to split. And it's VERY important to establish the ratio of ownership, based on initial downpayments and mortgages (and or, even more important: legal documents).
Part (or all) of your payment to your sister could be evened out with a formal transfer to you of her share of the mortgage, if that's applicable.
Also, remember this: value of real estate will most probably still (moderately?) rise in the near future. You are getting a good deal anyway, achieving the whole property: be kind to your sister. If you value a good and lasting relationship, that is.
Or if you just love her.
Cees