If it's a good deal, just factor this in and adjust the repair costs if needed after the inspection.

The gain on your residence is a function of what you originally paid for the property + capital improvements = your adjusted basis in the property (how much you owe on the property doesn't factor into the equation).  

for the AC, one easy option is to put adjustable vents in the units and move the thermostat out of one of the units and make it set to some permanent temperature (e.g. 72 degrees) which you can control.

Adjust your cash offer to an amount that takes into consideration that fear of the unknown, and drop the 14 days to 0 (or maybe 3) - or pay a substantial enough non-refundable DD fee.

if I use $20k immediately and use $50k a year from now, will my payment adjust to reflect the new balance? 

Half the time we end up adjusting an advertised CAP rate once we go in and do our own assessment of how much capital is really required to stabilize a property.  

You take recently sold comps of similar properties in the same area and adjust for any differences in size, amenities and condition.

Appreciate your comments without you having to take us down that rabbit hole.So depreciation reduces your adjusted basis. 

...You really don't want to purchase your first home when the money is, inflation adjusted, about as free as it could possibly get?

Question, if I do have a bump in the interest rate, am I to assume that bump would apply across the entire term of the loan and not be adjusted just for the final month (based on the above example)?