How the Rich get Richer

I’m currently in the process of trying to buy a house in London as a first time buyer and it is not a fun activity. One of the key anxieties is that what you may be able to afford today you may not be able to afford in a few months due to rising prices. It struck me that those who had been able to buy a couple of years ago would have benefited significantly from this rise in prices. Of course the key blocker to many people being able to buy earlier than they do is access to a deposit. Therefore, those with access to a deposit earlier (e.g. those with some sort of family assistance) would be much better off. It’s what economists refer to as the ‘Time Value of Money’.

What I wanted to do was see if I could model how this advantage would play out over time. Here’s the model I went with. Imagine a house costs £300,000 with house prices rising 5% per annum and an interest rate of 3%. We have three buyers, all with the same income which allows them £2700 a month to spend on rent/mortgage and savings. Say rent is £1200 a month. This means that each can save half of the 10% deposit required for a house a year. So they are all in the same situation other than one key difference. Buyer1 starts out with no money, Buyer2 has £15,000 (i.e. half a deposit) and Buyer3 has £30,000 (i.e. the full deposit).

The amount of equity that a buyer will accumulate each month is going to be the amount they save plus, if they have bought, the amount of house appreciation and the amount of capital they pay off on their mortgage.

Here’s what happens over a three year period.

Month	House Price	Buyer1 Equity	Buyer2 Equity	Buyer3 Equity
Buyer3 buys with mortgage repayment 1280
1	300000	1500	16500	32025
2	301222	3000	18000	35273
3	302449	4500	19500	38528
4	303681	6000	21000	41790
5	304918	7500	22500	45059
6	306161	9000	24000	48333
7	307408	10500	25500	51615
8	308660	12000	27000	54903
9	309918	13500	28500	58198
10	311181	15000	30000	61499
11	312448	16500	31500	64807
Buyer2 buys with mortgage repayment 1338
12	313721	18000	33494	68122
13	315000	19500	36767	71444
14	316283	21000	40048	74772
15	317571	22500	43336	78107
16	318865	24000	46630	81449
17	320164	25500	49931	84798
18	321469	27000	53239	88153
19	322778	28500	56554	91516
20	324093	30000	59876	94885
21	325414	31500	63205	98262
22	326740	33000	66541	101645
Buyer1 buys with mortgage repayment 1400
23	328071	34961	69884	105036
24	329407	38261	73234	108433
25	330750	41569	76591	111837
26	332097	44883	79955	115249
27	333450	48204	83326	118667
28	334809	51533	86705	122093
29	336173	54869	90090	125526
30	337542	58212	93483	128966
31	338917	61563	96883	132413
32	340298	64920	100291	135868
33	341685	68285	103705	139330
34	343077	71658	107127	142799
35	344474	75037	110557	146275
36	345878	78424	113993	149759

Whilst I was aware that Buyer3 would be better off, it’s the amount that they are better off by that’s striking. They started with £30,000 more but by the end of three years they are over £70,000 better off. Note also that even though all three have bought a house Buyer3 still does better on a monthly basis due to the fact their mortgage payments are £1280 and not £1400 as they are for Buyer1.

The above analysis is performed with house price rises of 5% which is perhaps a little conservative for the market that can be seen in London. If I perform the above analysis with house price rises of 8% I get the following situation after three years.

Month	House Price	Buyer1 Equity	Buyer2 Equity	Buyer3 Equity
Buyer3 buys with mortgage repayment 1280 in month 1
Buyer2 buys with mortgage repayment 1382 in month 13
Buyer1 buys with mortgage repayment 1493 in month 25
36	375497	84647	132261	179378

In other words they are nearly £100,000 better off at the end of the three years.

Now, of course, house prices can go down as well as up. Prices dipped in London back in 2008 and they crashed back in 1989. However, even with this in mind the only situation where Buyer3 is worse off is house prices going down between Buyer3 buying and Buyer1 buying. If they fall after Buyer1 buys, Buyer1 still has the greatest amount of debt and thus the highest chance of being in negative equity.

Supposing, that house prices do fall immediately after Buyer3 buys and stagnate thereafter. We can see below the effect that this will have on the situation.

Percentage Decrease	House Price	Buyer1 Equity	Buyer2 Equity	Buyer3 Equity
1%	297000	62689	83322	100881
2%	294000	62796	83492	97881
3%	291000	62902	83663	94881
4%	288000	63008	83833	91881
5%	285000	63696	84601	88881
10%	270000	64876	86116	73881
15%	255000	66121	87695	58881

It takes a drop of over 3% to eat into Buyer3s’ advantage. Even a 10% drop has only cost them about a third of their original advantage. By 15% Buyer3 has lost all of their advantage and is worse off than Buyer1. It’s also worth noting that Buyer1 will have lower mortgage payments than Buyer3 so will be gaining month on month (and thus reversing the situation outlined above).

Overall though. The ability to buy early tends to confer massive advantages.

Any thoughts or suggestions are more than welcome.