Buying vs Renting
Analysis based on a 5 year simulation
Baseline
The following values will form the baseline for the simulation. The coloured variables are the
independent* variables we'll be adjusting in this analysis.
*These are treated as independent for the purpose of studying
their effects. In reality, there will be ecomomic dependencies between them.
| Deposit | £30,000 |
| Initial property value | £200,000 |
| Property value yearly increase | 2.5% |
| Mortgage interest rate | 5% |
| Mortgage term | 25 years |
| Initial monthly rent price | £1200 |
| Rent price yearly increase | 3% |
| Savings interest rate | 5% |
Method
| Buy | Rent |
|
The initial loan is the initial property value minus the deposit. |
£30,000 is immediately payed into the savings account. |
The result of the rent scenario is subtracted from that of the buy scenario to compute what
we'll call the delta (the dependent variable).
delta = (buy equity) - (rent equity)
A positive value indicates that the buyer is better off and a negative value indicates that the
renter is better off.
For the baseline as outlined above, the delta is £56,008 meaning you'd be £56k better off*
if you chose to buy rather than rent. The monthly mortgage payment is £993.80.
*Costs associated with property purchase (e.g. stamp duty,
solicitor fees, mortgage product fees, maintenance fees or mortgage early repayment fees)
are not considered.
Sensitivity Analysis
One at a time
What happens to the delta when we change each of the input variables in turn? All the other inputs stay at their baseline value.
If we take the first order derivative (slope) of each of these traces:We can see that the simulation's result (delta) is most sensitive to:
- Property value yearly increase: each 1% pt increase results in the buyer being £5k-£17k better off
- Mortgage interest rate: each 1% pt increase results in the buyer being £8k-£10k worse off
- Initial monthly rent price: each £100 increase results in the buyer being £7k better off.
Two at a time
The previous anaysis changed just one variable at a time. The contour plots below show the
effect on the delta when we change two variables.
A positive delta (better to buy) is blue and a negative delta
(better to rent) is red.
We'd normally expect the mortgage and savings interest rates to be linked (perhaps as an offset from the Bank of England's base rate). Here's how the mortgage interest rate and savings interest rate affect the simulation:
We can see that high interest rates (whether mortgage or savings) are bad for buying and good for renting.For a buyer, we know that high mortgage interest rates are bad and that high property value growth is good. Let's see what the interplay between the two is and where the breakeven point is (i.e. where the delta is £0).
So far, we've assumed that the prospective buyer can borrow enough money for a property valued at £200,000 which is roughly equivalent to a monthly rent of £1,200. What are the results if the budget is reduced or stretched? The grey dotted line shows an approximate expected relationship between property values and rent prices.
We can see that increasing or decreasing the budget results in a linear change to the delta. I.e. doubling the budget doubles the delta.
Three at a time
Let's see how the delta is affected when we sweep through a range of values for the 3 most powerful variables:
- Property value yearly increase
- Mortgage interest rate
- Initial monthly rent price
Like with the 2D contour plots, a positive delta (better to buy) is blue
and a negative delta (better to rent) is red.
Surfaces are drawn at
+£300k,
+£200k,
+£100k,
£0,
-£100k,
-£200k,
-£300k.
Click and drag to orbit the 3D volume plot.
View the simulation source code, Jupyter notebooks and data on GitHub.
This is a personal project and does not constitute financial advice.