I wanted to refinance and then apply for a loan to purchase a new multi-unit.

I am stuck on how to apply the existing credit, without it being recorded as another deposit.

Its a basement apartment in a 1958 built triplex. natural light is limited. walls are light gray and trim is white. floor is concrete and a darker grey.

Most banks are pretty tight when it comes to forced appreciation even though it's natural for a property that's been renovated to command better rents.Even some portfolio lenders require a 12 month seasoning to use the appraised value. 

One word of caution: value-add and forced appreciation really only apply to property 5-units+ that are valued based on the income approach. 3 unit deals generally don't benefit from this.That said, I'm sure the value of the property will indeed increase due to your improvements.

Natural appreciation should be the butter, not the bread of your profits. 

Being analytical in nature I have to fight against the analysis paralysis when looking at non-performing loans because its easy to find things wrong with them,  but that's why they will sell at a discount. 

In order to open a business account I applied  for an EIN number under the category of partnership.

There is not enough building damage for the property to be razed, so it needs to be fixed.  50% depreciation can apply if the building has not had major updates the last 20 years. 

20 year 5/5 ARM 20% down minus repair allowance of $10,500 (applied towards down payment), seller paid $3000 closing costs also.