From what I've read, you should stay away from complex math. You might be falling into analysis paralysis, which happens to many people. The calculators on bigger pockets are very straightforward and useful tools that can help you determine if you're buying right or not. If you need to use a complex calculator to make the calculation, you shouldn't buy it. Just my two cents. Good Luck!
The only reason I ask is because I’m a math major and I’m going to be working on getting my PhD in mathematical finance and going into the hedge fund private equity world I was just wondering if you could apply this advanced math to things like on a value add deal where you want to buy an apartment and raise rents but you don’t want to many vacancies so you need to calculate the sweet spot to maximize profit. I was just wondering about types of situations like that where I see this kind of math being useful.
Not really necessary, real estate is fairly simple. If you're trying to predict the future with math you're going to have a bad time.
As for the vacancy vs price, you have a pretty small range and most people will want a round number. $742 might be the most profitable on paper but you can't really charge that, tenants may stray away from that, or a large number of other unknowns. If you have a ton of units you can do tests etc but the rental demand changes from month to month in almost every market.
Here is an example of where I though it would be helpful say have 50 office units that rent for 2200 a month and for every 25 dollar increase in rent you gain 1 vacancy. What should you increase rent to to maximize profit? You can easily calculate that number using calculus.
@Storm S. I realize this is 3 years later, but aren't there too many independent variables at play for something so rudimentary to be accurate?