Impact of Leverage on Cash-on-Cash Returns

[J Scott]

In the spirit of truly understanding some important concepts behind investing decisions many of us are making, I wouldn't to start this thread...

Basically, I was surprised at the information I'm about to provide (I did this analysis in another thread a couple days ago and got some unexpected results), and figured a couple of you may be surprised as well.  At least for me, it will impact some decisions I make down the road...

Assume a rental property that generates 2% of its cost in monthly rent and that operates at a 50% expense ratio (actually, expenses + rent loss + capex).  Further, assume the property is leveraged somewhere between 0% (all-cash, no leverage) and 100% (fully leveraged at all-in acquisition cost).

The following graph plots two curves -- one representing a typical conventional loan amortization/rate and the other representing a typical portfolio loan amortization/rate -- with leverage amount indicated on the X-axis and it's resulting cash-on-cash return indicated on the Y-axis:

What I see in this graph:

• Below 60% leverage, CoC is basically flat, without much opportunity for leverage to impact CoC, regardless of type of loan
• Between 60-80% leverage, amortization/rate of the loan will determine whether you can start to increase your CoC or not
• Above 80%, any positive leverage will greatly increase your CoC, but the amortization/rate will play a HUGE role in the extent of the increase

The key takeaway for me is that, for lower amounts of leverage, conventional versus portfolio loans make no difference -- and, in fact, leverage doesn't make much of a difference at all. For medium amounts of leverage (60-80%), there is a big difference in CoC based on type of loan chosen. And for larger amounts of leverage, both loan choices are good, but conventional terms/rates are very beneficial.

There are some obvious implications here (for me, at least) in terms of:

• Whether I would even want to leverage at lower percentages, given the paperwork, DTI hit and loan costs
• What types of loans I would pursue based on the amount of leverage available
• The value of using the small amount of conventional loans available to their best advantage

Anyway, thought the results were interesting, and thought I would post them...enjoy!

[J Scott]

Originally posted by @Dawn Anastasi:

Originally posted by @Nancy Larcom:

I teach math part-time at a local high school, and after a recent discussion with my students about if/how the math (and specifically graphing concepts) we teach is useful, I'd really like to use your graph in a lesson if that would be ok?

I would really like to know how to use the calculus I learned in every day life.  I've been waiting 20 years for some way to use it and never have. Anyone?  Anyone?  :)

I actually used it yesterday.  Was driving with someone on a toll road, and he was speeding.  I was explaining to him that, if the cops wanted to catch him speeding, all they'd need to do was check the amount of time it took him to get from one toll booth to another, and then divide by the distance.  This would give his average speed for the duration of the trip.

His defense was that knowing the "average" speed wouldn't prove that he was speeding at any one specific point during the trip.  But, as I explained, one of the most important theorems from Calculus is "The Mean Value Theorem," which -- as applied to this situation -- says that if his average speed of the trip is X, then there MUST be at least one point in the trip where his speed was X.  

In other words, based on Calculus, if his average speed is above the speed limit, there was at least one point where he was speeding.