A 9% cap = $577,777 (mathematically divide the NOI by .1 for 10% or .09 for 9%, etc). 

She was trapped by debt once, understands through Dave Ramsey that getting out from under it is as much about psychology as it is about mathematics.

Constructing the additional unit will mathematically generate more income in the long run, but I am concerned the smaller bedrooms could be a negative when marketing as luxury. 

This is where you determine if it is SF or MF as the vehicle that will get you to the strategy to achieve your goals.Both SF and MF have pluses and minuses, you have to make sure that is part of your strategy to take you to your goal.The reality is that when you own real estate you own a business, that business has processes, procedures and structure.Part of that are systems wrapped around those tactics so that your are not dealing with the actual property if you are truly running it like a business it wont matter because owning real estate is a purely mathematical equation based on the numbers not on emotions.Just my opinion for what its worth.

I'm looking for a financial/mathematical approach to making these decisions.

Aside from all the logistical and mathematical issues with supply/demand cycle of all this, there is now a new component, PROFIT. 

because we've (hopefully) made money in RE, but making money in this field is really little more than mathematics, hard work, and some external luck.

I had similar feelings and I tie it to the bachelors degree in applied mathematics. 

Their mathematical models have to be redesigned.

I generally have a good grasp of mathematics, I enjoy it, what I am doing wrong in the above has me confused though, for a 12% note I am calculating a yearly return of around 8.5%, which just doesn't make sense.