Buy vs. Rent App
a simulation-based advanced calculator
Giovanni Fossati
What is it and why we want it
The Buy vs. Rent question confuses countless people daily.
We seek help online, being almost invariably mislead by over-simplistic tools.
The plethora of calculators found on the web in the majority of cases do not properly handle several important aspects of the cost/benefit analysis of buying vs. renting.
For instance:
- tax-related items, namely the tax benefits of the mortgage interest deduction, also considering the fact that applying it means itemizing deductions, hence losing the standard deduction.
- the benefits of re-investing money potentially saved by renting instead of buying,
- the benefit of the return of investment of the capital not put into a down-payment.
This calculator implements a more comprehensive and realistic picture, including these and other ingredients, and yields a statistical assessment of the buy vs. rent question by means of simulations.
A Simulations-based Approach
Given a set of input parameters, 250 simulations are performed, with stochastic “predictions” of time variation of:
- property appreciation,
- return of investment of the “unused cash” when renting,
- inflation,
- rent increase (over inflation).
For the first three, values are drawn from Normal distributions with means and standard deviations given among the application inputs. The additional rent increase rate is drawn from an exponential distribution.
For each simulation a “trade-off” amount (i.e. the difference between buying and renting) for each year, for the duration of the mortgage loan.
Application Results
The simulations results are summarized in three plots showing:
- the trends of the ‘tradeoff’ amount,
- the fraction of simulations favoring buying over renting, over time,
- the distribution of tradeoff amounts over time, highligthing the distributions at 1/2, 3/4 and at the end of the loan period.
An example is shown in the final slide. The plot is made on-the-fly by _slidify, with the full code which is hidden with echo=FALSE.
Example of Summary Plot
